[{"data":1,"prerenderedAt":30241},["ShallowReactive",2],{"series-posts-Motor Control":3,"series-data-Motor Control":30010,"series-authors":30054,"post-count":22333},[4,185,400,603,758,7357,7576,7846,8523,9556,9865,10108,10368,10579,10725,10975,11236,15993,16104,16289,16760,17030,17202,17310,17488,17645,17789,18164,18359,18469,18713,18969,19153,19310,19441,19603,19760,19874,19954,20120,20272,20364,20458,20561,20722,20823,20940,21014,21127,21180,21327,21407,21506,21717,21752,22636,22862,23110,23165,26778,26853,26898,28466,28608,28857,29494,29610,29719,29785,29865],{"id":5,"title":6,"author":7,"body":8,"date":172,"description":173,"draft":174,"edited_at":172,"extension":175,"featured_image":176,"meta":177,"navigation":178,"path":179,"pinned":174,"seo":180,"series":181,"seriesOrder":181,"sitemap":182,"stem":183,"tags":181,"__hash__":184},"blog\u002Fblog\u002F小兒發展（二）.md","小兒發展（二）","hibiki12141132",{"type":9,"value":10,"toc":168},"minimark",[11,15,34,37,40,71,73,76,104,106,109,123,125,128,142,144,147,155,157,160],[12,13,14],"p",{},"那正常的寶寶下肢的生理變化也會按照一個叫鐘擺現象的過程發展",[16,17,18,22,25,28,31],"ol",{},[19,20,21],"li",{},"新生兒——中度的膝內翻（O型腿）",[19,23,24],{},"六個月——輕度的O型腿",[19,26,27],{},"一歲半——直的",[19,29,30],{},"三歲半——輕度的膝外翻（X型腿）",[19,32,33],{},"五到七歲——直的",[35,36],"hr",{},[12,38,39],{},"而步態的發展會按照以下時期發展",[16,41,42,45,56,59,62,65,68],{},[19,43,44],{},"反射踏步（靠反射）",[19,46,47,48,55],{},"抑制或靜止期（不過這裡有實驗提到，是因為脂肪比肌肉重，導致反射出不來，並不是因為高階抑制低制—— ",[49,50,54],"a",{"href":51,"rel":52},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002Fmotor-learning?series=%E5%B0%8F%E5%85%92%E7%89%A9%E6%B2%BB",[53],"nofollow","倒數第二段","）",[19,57,58],{},"過渡期",[19,60,61],{},"刻意跨步",[19,63,64],{},"獨立行走",[19,66,67],{},"Heell-toe步態",[19,69,70],{},"整合或直立行走成熟期",[35,72],{},[12,74,75],{},"接著來看不同系統的發展進程，從出生至九個月",[77,78,79,86,92,98],"ul",{},[19,80,81,82,85],{},"神經系統——在九個月的時候感覺系統已經成熟（視覺，本體覺，前庭覺）",[83,84],"br",{},"\n尤其是視覺發展遠大於粗大動作",[19,87,88,89,91],{},"身體機能——寶寶的脂肪站比高，在六個月時體重就已經是剛出生兩倍，一歲時還來到了三倍",[83,90],{},"\n那關節部份——剛出生的寶寶：Hip會呈flexion contracture, ER>IR；膝內翻；假如承重時，會呈現旋前足",[19,93,94,95,97],{},"抗重力肌力——Hip flexor(訓練方法是supine kicking)；Hip extensor(訓練方法是prone, 爬行, 跪姿)",[83,96],{},"\nHip abduction(訓練方法是扶物側行)",[19,99,100,101,103],{},"功能性步態——那在扶著的情況下寶寶的腳會呈現弓形腿(bowed legs)，拆開來看是",[83,102],{},"\n步寬外展；外轉(O型腿)；髖屈曲；足跟外翻",[35,105],{},[12,107,108],{},"時間來到了九個月到第十五個月之間的發展進程",[16,110,111,114,117],{},[19,112,113],{},"神經系統——開始能在視覺刺激或引導情況下行走，且開始具備有CPG的能力(反射抑或身體機能成熟以達成)",[19,115,116],{},"力學因素——重心較高(在下胸椎層級)，BOS左右積大前後面積小，直立姿勢下肌力尚有不足",[19,118,119,120,122],{},"功能性步態——雖然能獨自行走，但還是會呈現弓形腿(bowed legs)，拆開來看是",[83,121],{},"\n步頻增加；步寬大；髖和膝關節屈曲角度增加；全足著地；擺盪期有垂足",[35,124],{},[12,126,127],{},"接下來時間來到了十八個月到二十四個月的發展進程",[16,129,130,136],{},[19,131,132,133,135],{},"力學因素——重心下降(由於腿快速生長)，BOS減少",[83,134],{},"\nROM的話O型腿消失，但有旋前足出現",[19,137,138,139,141],{},"功能性步態——擺盪期學會用慣性甩出腳，支撐腳也開始會伸直承重；",[83,140],{},"\n足跟著地還不穩定；Initical contact有knee屈曲(在足跟著地發展後出現)",[35,143],{},[12,145,146],{},"時間繼續來到了三歲到三歲半的發展進程",[16,148,149,152],{},[19,150,151],{},"力學因素——ROM的話膝外翻(X型腿)，且有旋前足出現",[19,153,154],{},"功能性步態——足跟著地穩定，且出現Knee flexion",[35,156],{},[12,158,159],{},"最後時間來到了六歲到七歲的發展進程",[16,161,162,165],{},[19,163,164],{},"力學因素——已經能直立行走，並且不在有旋前足",[19,166,167],{},"功能性步態——與成人一樣",{"title":169,"searchDepth":170,"depth":170,"links":171},"",2,[],"2026-04-12","步態~步態發展",false,"md","\u002Fimages\u002Fuploads\u002F1775979234822-139196433_p0_master1200.webp",{},true,"\u002Fblog\u002F小兒發展（二）",{"title":6,"description":173},null,{"loc":179},"blog\u002F小兒發展（二）","ScVwjiCjwCAhdOVX_aORN11S38Xd5Fb_3-0haIKlezk",{"id":186,"title":187,"author":7,"body":188,"date":391,"description":392,"draft":174,"edited_at":391,"extension":175,"featured_image":393,"meta":394,"navigation":178,"path":395,"pinned":174,"seo":396,"series":181,"seriesOrder":181,"sitemap":397,"stem":398,"tags":181,"__hash__":399},"blog\u002Fblog\u002FGait-analysis小兒（一）.md","Gait analysis小兒（一）",{"type":9,"value":189,"toc":389},[190,193,196,213,216,227,230,247,277,283,286,303,312,323,338,344,372,375],[12,191,192],{},"我也不知道這一課要怎麼說開篇語，還是乖乖按著老師的講對寫好了",[12,194,195],{},"那下肢雙關節肌肉有以下",[16,197,198,201,204,207,210],{},[19,199,200],{},"腰大肌——Hip Flexion, Trunk Flexion",[19,202,203],{},"腿後肌——Hip Extension, Knee Flexion",[19,205,206],{},"股直肌——Hip Flexion, Knee Extension",[19,208,209],{},"腓腸肌——Knee Flexion, PF",[19,211,212],{},"縫匠肌——Hip Flexion, Hip ER",[12,214,215],{},"那單關節的肌肉有",[16,217,218,221,224],{},[19,219,220],{},"臀大肌——Hip Extension, Hip ER",[19,222,223],{},"脛前肌——DF, inversion",[19,225,226],{},"腓骨長肌——PF, eversion",[12,228,229],{},"那以下動作的抗重力與無抗重力的擺位姿勢為",[16,231,232,235,238,241,244],{},[19,233,234],{},"Hip Extension——Prone 抗重力, side-lying 無抗重力",[19,236,237],{},"Hip Flexion——Sitting 抗重力, side-lying 無抗重力",[19,239,240],{},"Hip Abduction——Side-lying 抗重力, supine 無抗重力",[19,242,243],{},"Knee Extension——Sitting 抗重力, side-lying 無抗重力",[19,245,246],{},"PF——Standing 抗重力, prone 無抗重力",[12,248,249,250,252,253,260,261,266,268,269,271,272,276],{},"接下來講一個異常步態——Crouch gait",[83,251],{},"\n為甚麼他會呈現屈曲狀態，主要是因為",[254,255,259],"span",{"className":256},[257,258],"underline","red-3","雙關節肌肉張力過強","，而",[254,262,265],{"className":263},[257,264],"green-3","單關節肌肉力量不足",[83,267],{},"\n不是單純的肌肉太緊，也是一種肌力失衡的表現",[83,270],{},"\n其中，在",[254,273,275],{"className":274},[257],"腿固定時(stand)，屈曲大腿的肌肉作用，會讓骨盤前傾","(像是髂腰肌)",[12,278,279,280,282],{},"接著來講步態的參數",[83,281],{},"\nStep length(步距,左右之間距離),Stride length(步幅,左右左的左左之間距離),Speed(速度),Cadence(步頻)",[12,284,285],{},"這邊提到一個中風後會出現的代償步態",[77,287,288,291,294,297,300],{},[19,289,290],{},"步速下降",[19,292,293],{},"步距縮短或不對稱",[19,295,296],{},"步寬變大(BOS增加)",[19,298,299],{},"雙腳站立期變長",[19,301,302],{},"依賴手部支撐",[12,304,305,306,308,309,311],{},"接著講Gait cycle，分別為站立期以及擺盪期",[83,307],{},"\n而站立期要去做承重以及單腳支撐的任務，擺盪期則要做肢體向前的任務",[83,310],{},"\n完成這三個任務又分成了這八個動作",[16,313,314,317,320],{},[19,315,316],{},"承重——Initial contact和Loading Response",[19,318,319],{},"單腳支撐——Mid-stance, Terminal Stance和Pre-swing",[19,321,322],{},"肢體向前——Pre-swing, Initial swing, Mid-swing和Terminal Swing",[12,324,325,326,330,331,333,334],{},"而Pre-swing雖然腳尖還沒離地，但",[254,327,329],{"className":328},[257,264],"重心其實已經轉移去另一隻腳","了",[83,332],{},"\n其中 ",[254,335,337],{"className":336},[257],"Initial contact和Pre-swing為雙腳承重期",[12,339,340,341,343],{},"我們現在攤開來看站立期和擺盪期下肢各關節變化",[83,342],{},"\n首先是站立期",[16,345,346,354,357,363,369],{},[19,347,348,349,353],{},"在雙腳承重期，",[254,350,352],{"className":351},[257,264],"足部會放平","，準備Push Off",[19,355,356],{},"Hip的話，在Initical Contact的Flexion到Terminal Stance的Hyperextension",[19,358,359,360,362],{},"Knee的話，會從Flexion姿勢，到Mid-stance的Extension，再變回Pre-swing的Flexion",[83,361],{},"\n(Flexion>Extension>Flexion)",[19,364,365,366,368],{},"Ankle的話，在Initical Contact的Neutral姿勢，Loading Response的PF，",[83,367],{},"\nMid-stance的DF，最後是Terminal Stance\u002FPre-swing的PF（Neutral>PF>DF>PF）",[19,370,371],{},"Pelvis的話，基本保持水平，但在Terminal stance會略微前傾",[12,373,374],{},"然後是擺盪期",[16,376,377,380,383,386],{},[19,378,379],{},"Knee的話，在Initical swing時會呈現Flexion，在Terminal swing會Full-extension",[19,381,382],{},"Hip的話，從Initical swing的Hyperextension，在Terminal swing會變成Flexion",[19,384,385],{},"Ankle的話，保持DF狀態，使腳尖不會碰到地板",[19,387,388],{},"Pelvis的話，會Rotation",{"title":169,"searchDepth":170,"depth":170,"links":390},[],"2026-04-11","肌肉~步態各分期關節姿勢","\u002Fimages\u002Fuploads\u002F1775885400167-37100769_p0.png",{},"\u002Fblog\u002FGait-analysis小兒（一）",{"title":187,"description":392},{"loc":395},"blog\u002FGait-analysis小兒（一）","IPE1YCLIHjaGM3K3t637opIC_UJyveODI_bALybZ_94",{"id":401,"title":402,"author":7,"body":403,"date":391,"description":595,"draft":174,"edited_at":391,"extension":175,"featured_image":596,"meta":597,"navigation":178,"path":598,"pinned":174,"seo":599,"series":181,"seriesOrder":181,"sitemap":600,"stem":601,"tags":181,"__hash__":602},"blog\u002Fblog\u002FGait-analysis小兒（二）.md","Gait analysis小兒（二）",{"type":9,"value":404,"toc":593},[405,408,524,527,564,576,582],[12,406,407],{},"現在我們將八個步態分期拆開了細看",[16,409,410,434,448,466,476,499,518,521],{},[19,411,412,413,417,421,422,426,430,431,433],{},"Initical Contact——用",[254,414,416],{"className":415},[257],"股四頭肌和脛前肌做",[254,418,420],{"className":419},[257,258],"離心收縮","，這時",[254,423,425],{"className":424},[257],"腿後肌做",[254,427,429],{"className":428},[257,264],"向心收縮","協同加速穩定",[83,432],{},"\n（減速與準備承重）",[19,435,436,437,441,444,445,447],{},"Loading Response——",[254,438,440],{"className":439},[257],"肌內側肌與脛前肌做",[254,442,420],{"className":443},[257,258],"，而臀大肌以及腿後肌輔助Hip加速，將重心向前移動",[83,446],{},"\n（避震）",[19,449,450,451,260,455,459,462,463,465],{},"Mid-stance——膝蓋後方有關節囊結構的緣故，肌四頭肌幾乎",[254,452,454],{"className":453},[264],"不需用力",[254,456,458],{"className":457},[257],"比目魚肌此時做",[254,460,420],{"className":461},[257,258],"控制脛骨速度",[83,464],{},"\n（省力）",[19,467,468,469,473,475],{},"Terminal stance——",[254,470,472],{"className":471},[257,264],"腓腸肌與比目魚肌做向心收縮",[83,474],{},"\n（產生推進力）",[19,477,478,479,483,486,487,489,490,494],{},"Pre-swing——假如是慢速走路，會利用",[254,480,482],{"className":481},[257],"縫匠肌(Sartorius)和肌薄肌(Graillis)做",[254,484,429],{"className":485},[257,264],"，",[83,488],{},"\n快速行走則靠",[254,491,493],{"className":492},[257],"肌直肌做",[254,495,498],{"className":496},[257,497],"yellow-3","等長收縮",[19,500,501,502,506,509,511,512,515],{},"Initial swing——在慢速走路中，",[254,503,505],{"className":504},[257],"股薄肌與縫匠肌會進行",[254,507,429],{"className":508},[257,264],[83,510],{},"\n而快速走路中，",[254,513,493],{"className":514},[257],[254,516,498],{"className":517},[257,497],[19,519,520],{},"Mid swing——靠慣性推進，基本沒有肌肉參與",[19,522,523],{},"Terminal swing——腿後肌做等長收縮，限制Knee extension速度",[12,525,526],{},"接著來講小腿後肌群無力的話會有甚麼問題",[77,528,529,539],{},[19,530,531,532,486,536,538],{},"Mid-stannce——比目魚肌無力的話，會讓",[254,533,535],{"className":534},[258,257],"Ankle做DF",[83,537],{},"\n那由於代償原因，Knee會做flexion來讓腳踩在地面，結果變成股四頭肌必須要加入收縮才能穩定站立",[19,540,541,542,546,548,549,553,554,558,559],{},"Terminal stance和Pre-swing——腓腸肌力量不足的話，",[254,543,545],{"className":544},[257,258],"沒辦法產生足夠的推進力",[83,547],{},"\n只好讓",[254,550,552],{"className":551},[258,257],"髖屈肌收縮","提起整段下肢，確保",[254,555,557],{"className":556},[264],"腳尖離地","，導致",[254,560,563],{"className":561},[562],"bg-red-3","步距變短",[12,565,566,567,569,570,572,573,575],{},"最後講小孩的步態發展過程",[83,568],{},"\n在18個月就會出現交互雙手擺動以及腳跟著地（Heel strike）的形態",[83,571],{},"\n2歲的小孩懂得矢狀面(Sagittal-plane)關節旋轉",[83,574],{},"\n7歲的小孩步態已經能達到成人標準了",[12,577,578,579,581],{},"CP的小孩在五歲時——有54%不需要輔具獨立行走，16%需要輔具行走，30%無法行走",[83,580],{},"\n那CP小孩預測能力方面也分成了三個時段",[16,583,584,587,590],{},[19,585,586],{},"9~18個月——頭部控制能力",[19,588,589],{},"24個月——不需要支撐能獨自坐穩",[19,591,592],{},"30個月——做爬行",{"title":169,"searchDepth":170,"depth":170,"links":594},[],"八分期肌肉拆解，腿後肌力不足的問題以及小兒步態發展過程","\u002Fimages\u002Fuploads\u002F1775898442489-136249570_p0_master1200.webp",{},"\u002Fblog\u002Fgait-analysis",{"title":402,"description":595},{"loc":598},"blog\u002FGait-analysis小兒（二）","b8ag1j-41EkcDyPxusedc-OHiManHuzgidmXxtyxgcc",{"id":604,"title":605,"author":7,"body":606,"date":391,"description":750,"draft":174,"edited_at":172,"extension":175,"featured_image":751,"meta":752,"navigation":178,"path":753,"pinned":174,"seo":754,"series":181,"seriesOrder":181,"sitemap":755,"stem":756,"tags":181,"__hash__":757},"blog\u002Fblog\u002F小兒發展（一）.md","小兒發展（一）",{"type":9,"value":607,"toc":748},[608,611,626,632,635,661,670,672,675,692,694,697],[12,609,610],{},"（PS：別問我為甚麼寫完步態動作寫習跟CP才回頭來寫這個，我真忘了你信嗎）",[12,612,613,614,616,617,619,620,622,623,625],{},"那先來講發展遲緩的定義，它不單指運動層面上，還包括了",[83,615],{},"\n知覺，語言，心理，社會，情緒等層面",[83,618],{},"\n而這個動作遲緩有標準的",[83,621],{},"\n發展過程成未達到正常小孩的90%，或者在評估測驗分數上落後兩個標準差，即屬發展遲緩",[83,624],{},"\n根據WHO的數據，發生率為6~8%",[12,627,628,629,631],{},"那高危族群有以下",[83,630],{},"\n視障兒童，聽障兒童，心理行為障礙兒童，生理狀況障礙兒童，家庭問題兒童",[12,633,634],{},"接下來講寶寶的正常發育過程，先從視角說起，如下",[16,636,637,640,643,646,649,652,655,658],{},[19,638,639],{},"剛出生數天——眨眼反射",[19,641,642],{},"六周——注射物體",[19,644,645],{},"二到三個月——對明亮的東西感興趣",[19,647,648],{},"四個月——協調眼球轉動",[19,650,651],{},"一歲——影像認知發展完成，能看清輪廓",[19,653,654],{},"三歲——能分辨紅黃藍綠",[19,656,657],{},"五到六歲——可以分辨大多數顏色",[19,659,660],{},"八歲以前——有遠視現象（我問了Gemini也看不太懂就是了）",[12,662,663,664,666,667,669],{},"那關於視覺發展異常的問題包括了",[83,665],{},"\n視覺注視不良，視線不隨物體移動，對熟悉的臉孔或物體缺乏反應 手眼協調異常",[83,668],{},"\n眼睛外觀異常，因視覺問題的代償性頭部姿勢異常，只能看近物，怕光",[35,671],{},[12,673,674],{},"接著是聽覺發展，如下",[16,676,677,680,683,686,689],{},[19,678,679],{},"四個月——追尋聲音或說話來源",[19,681,682],{},"七到八個月——被叫名字有反應",[19,684,685],{},"十個月——仿說（無意義內容）",[19,687,688],{},"一到一歲半——初步聽懂簡單的話",[19,690,691],{},"兩歲以後——鸚鵡式學說話",[35,693],{},[12,695,696],{},"接下來是粗大動作的發展，如下",[16,698,699,702,705,708,711,714,717,720,723,731,739,742,745],{},[19,700,701],{},"兩個月——不穩定的抬頭控制",[19,703,704],{},"四個月——抬頭控制適當",[19,706,707],{},"五個月——翻身（先學會Prone to supine, 接著是supine to prone）",[19,709,710],{},"七個月——坐起來",[19,712,713],{},"八個月——爬行",[19,715,716],{},"九個月——需要支撐的站起來",[19,718,719],{},"十個月——僅需要極小輔助的從坐到站",[19,721,722],{},"一歲——獨立行走",[19,724,725,726,730],{},"兩歲——跑，",[254,727,729],{"className":728},[264],"上樓梯","，踢球，投球，蹲下來",[19,732,733,734,738],{},"三歲——",[254,735,737],{"className":736},[258],"下樓梯","，雙腳跳，騎三輪車",[19,740,741],{},"四歲——單腳跳",[19,743,744],{},"五歲——走直線",[19,746,747],{},"六歲——騎腳踏車",{"title":169,"searchDepth":170,"depth":170,"links":749},[],"定義~粗大動作發展","\u002Fimages\u002Fuploads\u002F1775957410970-EebbBUPUcAYSTE9.webp",{},"\u002Fblog",{"title":605,"description":750},{"loc":753},"blog\u002F小兒發展（一）","4ejiPQ8a9xnXVIFdzih8PoJrok3muVwRlBhhByq5HeI",{"id":759,"title":760,"author":761,"body":762,"date":391,"description":169,"draft":174,"edited_at":172,"extension":175,"featured_image":181,"meta":7352,"navigation":178,"path":753,"pinned":174,"seo":7353,"series":181,"seriesOrder":181,"sitemap":7354,"stem":7355,"tags":181,"__hash__":7356},"blog\u002Fblog\u002F資料前處理與迴歸分析.md","資料前處理與迴歸分析","chinono",{"type":9,"value":763,"toc":7331},[764,769,777,780,785,791,809,815,821,1123,1129,1135,1149,1152,1155,1175,1179,1182,1185,1191,1202,1238,1241,1244,1586,1679,1683,1686,1835,1841,1896,1900,1906,2118,2552,2647,2651,2654,2775,2778,2936,3332,3359,3362,3367,3370,3574,4196,4203,4207,4217,4222,4252,4257,4261,4266,4269,4296,4303,4307,4314,4317,4537,4936,4963,4967,5014,5021,5212,5215,5374,5377,5384,5665,5965,5968,6306,6977,6988,6993,7184,7231,7234,7327],[765,766,768],"h2",{"id":767},"資料前處理為什麼清理資料這麼重要","資料前處理：為什麼清理資料這麼重要？",[12,770,771,772,776],{},"在我們訓練任何機器學習模型之前，必須先面對現實中亂七八糟的原始數據。",[773,774,775],"strong",{},"資料前處理 (Data preprocessing)"," 就是把這些數據變成好看的報告的過程。想像一下，你在煮飯前總得先洗菜、切菜吧？如果食材又髒又沒切過，是做不出好菜的。",[12,778,779],{},"原始數據通常會有一堆問題，像是異常值 (outliers)、缺失值 (missing values)、無意義的組合，還有亂七八糟的單位。前處理就是要把這些混亂，變成模型真正能看得懂、學得會的東西。",[781,782,784],"h3",{"id":783},"資料前處理的-7-個步驟","資料前處理的 7 個步驟",[12,786,787,790],{},[773,788,789],{},"1. 取得資料集 (Acquire the dataset)。"," 從各個來源收集資料，然後把它們整合成適當的格式。資料集的結構會根據你的領域而有所不同（比如商業資料跟醫療資料就長得不一樣）。",[12,792,793,796,797,800,801,804,805,808],{},[773,794,795],{},"2. 匯入關鍵函式庫 (Import crucial libraries)。"," 在 Python 裡，有三個函式庫是前處理的鐵三角：",[773,798,799],{},"NumPy","（科學運算）、",[773,802,803],{},"Pandas","（資料操作與分析）和 ",[773,806,807],{},"Matplotlib","（2D 繪圖跟視覺化）。",[12,810,811,814],{},[773,812,813],{},"3. 匯入資料集 (Import the dataset)。"," 把資料載入你的工作環境。記得確認你的工作目錄 (working directory) 設定正確，程式才找得到檔案喔。",[12,816,817,820],{},[773,818,819],{},"4. 處理缺失值 (Handle missing values)。"," 這點超級重要！如果你無視缺失資料，模型就會得出錯誤的結論。常見的做法包含用該欄位的平均數或中位數來填補，或是乾脆把缺漏的那一整列刪掉。",[822,823,827,831],"details",{"className":824},[825,826],"info-box","info-box-info",[828,829,830],"summary",{},"欄位？列？都是什麼？",[832,833,836,839,865,868,871,944,951,1112],"div",{"className":834},[835],"info-box-content",[12,837,838],{},"為了更容易理解，我們可以把資料想像成一個 Excel 表格。在資料科學中，表格的兩個維度分別代表：",[77,840,841,855],{},[19,842,843,846,847,850,851,854],{},[773,844,845],{},"欄位 (Column \u002F 垂直方向)："," 代表一個特定的 ",[773,848,849],{},"「特徵 (Feature)」"," 或 ",[773,852,853],{},"「變數」","。例如：每個人的「年齡」、「身高」或「收入」。",[19,856,857,860,861,864],{},[773,858,859],{},"列 (Row \u002F 水平方向)："," 代表 ",[773,862,863],{},"「一筆完整的資料 (Observation \u002F Record)」","。例如：某位特定使用者的所有基本資料。",[781,866,867],{"id":867},"實際範例解析",[12,869,870],{},"假設我們有一個如下的客戶資料表：",[872,873,874,897],"table",{},[875,876,877],"thead",{},[878,879,880,887,892],"tr",{},[881,882,884],"th",{"align":883},"left",[773,885,886],{},"姓名",[881,888,889],{"align":883},[773,890,891],{},"年齡 (欄位)",[881,893,894],{"align":883},[773,895,896],{},"收入 (欄位)",[898,899,900,916,931],"tbody",{},[878,901,902,910,913],{},[903,904,905,906,909],"td",{"align":883},"小明 (",[773,907,908],{},"這是一列 Row",")",[903,911,912],{"align":883},"25",[903,914,915],{"align":883},"50,000",[878,917,918,923,928],{},[903,919,920,921,909],{"align":883},"小華 (",[773,922,908],{},[903,924,925],{"align":883},[773,926,927],{},"(缺失值)",[903,929,930],{"align":883},"60,000",[878,932,933,938,941],{},[903,934,935,936,909],{"align":883},"小美 (",[773,937,908],{},[903,939,940],{"align":883},"27",[903,942,943],{"align":883},"55,000",[12,945,946,947,950],{},"當我們提到",[773,948,949],{},"用該欄位的平均數或中位數填補","，它的執行動作如下：",[16,952,953,956,963,1109],{},[19,954,955],{},"系統發現「小華」的「年齡」空缺了。",[19,957,958,959,962],{},"系統會去尋找「年齡」",[773,960,961],{},"這個欄位 (Column)"," 裡其他已知的數值（也就是小明的 25 歲和小美的 27 歲）。",[19,964,965,966,1108],{},"計算這個欄位的平均數：",[967,968,972],"mjx-container",{"className":969,"jax":971},[970],"MathJax","SVG",[973,974,983,1023],"svg",{"style":975,"xmlns":976,"width":977,"height":978,"role":979,"focusable":980,"viewBox":981,"xmlnsXLink":982},"vertical-align: -0.566ex;","http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","16.593ex","2.262ex","img","false","0 -750 7334 1000","http:\u002F\u002Fwww.w3.org\u002F1999\u002Fxlink",[984,985,986,991,995,999,1003,1007,1011,1015,1019],"defs",{},[987,988],"path",{"id":989,"d":990},"MJX-1-TEX-N-28","M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z",[987,992],{"id":993,"d":994},"MJX-1-TEX-N-32","M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z",[987,996],{"id":997,"d":998},"MJX-1-TEX-N-35","M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z",[987,1000],{"id":1001,"d":1002},"MJX-1-TEX-N-2B","M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z",[987,1004],{"id":1005,"d":1006},"MJX-1-TEX-N-37","M55 458Q56 460 72 567L88 674Q88 676 108 676H128V672Q128 662 143 655T195 646T364 644H485V605L417 512Q408 500 387 472T360 435T339 403T319 367T305 330T292 284T284 230T278 162T275 80Q275 66 275 52T274 28V19Q270 2 255 -10T221 -22Q210 -22 200 -19T179 0T168 40Q168 198 265 368Q285 400 349 489L395 552H302Q128 552 119 546Q113 543 108 522T98 479L95 458V455H55V458Z",[987,1008],{"id":1009,"d":1010},"MJX-1-TEX-N-29","M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z",[987,1012],{"id":1013,"d":1014},"MJX-1-TEX-N-2F","M423 750Q432 750 438 744T444 730Q444 725 271 248T92 -240Q85 -250 75 -250Q68 -250 62 -245T56 -231Q56 -221 230 257T407 740Q411 750 423 750Z",[987,1016],{"id":1017,"d":1018},"MJX-1-TEX-N-3D","M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z",[987,1020],{"id":1021,"d":1022},"MJX-1-TEX-N-36","M42 313Q42 476 123 571T303 666Q372 666 402 630T432 550Q432 525 418 510T379 495Q356 495 341 509T326 548Q326 592 373 601Q351 623 311 626Q240 626 194 566Q147 500 147 364L148 360Q153 366 156 373Q197 433 263 433H267Q313 433 348 414Q372 400 396 374T435 317Q456 268 456 210V192Q456 169 451 149Q440 90 387 34T253 -22Q225 -22 199 -14T143 16T92 75T56 172T42 313ZM257 397Q227 397 205 380T171 335T154 278T148 216Q148 133 160 97T198 39Q222 21 251 21Q302 21 329 59Q342 77 347 104T352 209Q352 289 347 316T329 361Q302 397 257 397Z",[1024,1025,1029],"g",{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},"currentColor","0","scale(1,-1)",[1024,1030,1032,1040,1053,1060,1069,1076,1087,1092,1099],{"dataMmlNode":1031},"math",[1024,1033,1035],{"dataMmlNode":1034},"mo",[1036,1037],"use",{"dataC":1038,"xLinkHref":1039},"28","#MJX-1-TEX-N-28",[1024,1041,1044,1048],{"dataMmlNode":1042,"transform":1043},"mn","translate(389,0)",[1036,1045],{"dataC":1046,"xLinkHref":1047},"32","#MJX-1-TEX-N-32",[1036,1049],{"dataC":1050,"xLinkHref":1051,"transform":1052},"35","#MJX-1-TEX-N-35","translate(500,0)",[1024,1054,1056],{"dataMmlNode":1034,"transform":1055},"translate(1611.2,0)",[1036,1057],{"dataC":1058,"xLinkHref":1059},"2B","#MJX-1-TEX-N-2B",[1024,1061,1063,1065],{"dataMmlNode":1042,"transform":1062},"translate(2611.4,0)",[1036,1064],{"dataC":1046,"xLinkHref":1047},[1036,1066],{"dataC":1067,"xLinkHref":1068,"transform":1052},"37","#MJX-1-TEX-N-37",[1024,1070,1072],{"dataMmlNode":1034,"transform":1071},"translate(3611.4,0)",[1036,1073],{"dataC":1074,"xLinkHref":1075},"29","#MJX-1-TEX-N-29",[1024,1077,1081],{"dataMmlNode":1078,"dataMjxTexclass":1079,"transform":1080},"TeXAtom","ORD","translate(4000.4,0)",[1024,1082,1083],{"dataMmlNode":1034},[1036,1084],{"dataC":1085,"xLinkHref":1086},"2F","#MJX-1-TEX-N-2F",[1024,1088,1090],{"dataMmlNode":1042,"transform":1089},"translate(4500.4,0)",[1036,1091],{"dataC":1046,"xLinkHref":1047},[1024,1093,1095],{"dataMmlNode":1034,"transform":1094},"translate(5278.2,0)",[1036,1096],{"dataC":1097,"xLinkHref":1098},"3D","#MJX-1-TEX-N-3D",[1024,1100,1102,1104],{"dataMmlNode":1042,"transform":1101},"translate(6334,0)",[1036,1103],{"dataC":1046,"xLinkHref":1047},[1036,1105],{"dataC":1106,"xLinkHref":1107,"transform":1052},"36","#MJX-1-TEX-N-36","。",[19,1110,1111],{},"最後把 26 填入小華年齡的缺失值中。",[12,1113,1114,1115,1118,1119,1122],{},"而後半段提到的",[773,1116,1117],{},"把缺漏的那一整列刪掉","，則是另一種暴力的做法：只要發現小華有一項資料沒填（年齡缺失），就把「小華」",[773,1120,1121],{},"這一整筆資料（Row）"," 直接從表格中剔除，連帶他完好的收入資料也不採納了。",[12,1124,1125,1128],{},[773,1126,1127],{},"5. 類別資料編碼 (Encode categorical data)。"," 機器學習模型是靠數學運作的——它們只懂數字，不懂「紅色」或「男生」這種標籤文字。編碼的方法有虛擬變數 (dummy variables)、標籤編碼 (label encoding，把類別變成整數) 以及獨熱編碼 (one-hot encoding，為每個類別建立二元欄位)。",[12,1130,1131,1134],{},[773,1132,1133],{},"6. 特徵縮放 (Feature scaling)。"," 當你的特徵範圍差超多的時候（例如年齡 0–100 歲 vs 薪水 0–1,000,000 元），有些演算法會被搞混。特徵縮放就是把變數標準化到同一個範圍裡。最常用的兩個方法是 Min-Max 縮放和標準化 (Standardization \u002F z-score)。",[12,1136,1137,1140,1141,1144,1145,1148],{},[773,1138,1139],{},"7. 切割資料集 (Split the dataset)。"," 把資料分成",[773,1142,1143],{},"訓練集 (training set)","（給模型學習用）和",[773,1146,1147],{},"測試集 (test set)","（用來驗證模型好壞）。最常見的切法是跟著八二法則走：80\u002F20，或者 70\u002F30、60\u002F40 也很常見。",[781,1150,1151],{"id":1151},"其他的前處理技巧",[12,1153,1154],{},"除了這 7 個核心步驟，你可能還會遇到：",[77,1156,1157,1163,1169],{},[19,1158,1159,1162],{},[773,1160,1161],{},"資料整合 (Data Integration)"," — 把來自不同來源系統的資料，合併成單一的資料集。",[19,1164,1165,1168],{},[773,1166,1167],{},"資料轉換 (Data Transformation)"," — 把資料從一種格式轉成另一種格式（e.g.: source system format → destination format）。",[19,1170,1171,1174],{},[773,1172,1173],{},"資料離散化 (Data Discretization)"," — 把連續數值變成離散的區間（比如把確切的年齡，變成「18–25 歲」、「26–35 歲」這種年齡層）。",[765,1176,1178],{"id":1177},"第二部分迴歸分析-預測連續數值","第二部分：迴歸分析 — 預測連續數值",[12,1180,1181],{},"現在資料乾淨了，我們來看看怎麼做預測。先從一個經典的例子開始。",[781,1183,1184],{"id":1184},"房價問題",[12,1186,1187,1188],{},"想像一下，我們有一份包含 47 間房子的資料集，裡面有居住面積（平方英尺）跟價格（千元馬幣）。問題很簡單：",[773,1189,1190],{},"給定一間房子的面積，我們能預測它的價格嗎？",[12,1192,1193,1194,1197,1198,1201],{},"這是一個",[773,1195,1196],{},"監督式學習 (supervised learning)"," 的問題。我們有「輸入-輸出」的配對資料，並想找出它們之間的關聯規則。因為輸出（價格）是一個連續的數值，所以這具體來說叫作",[773,1199,1200],{},"迴歸 (regression)"," 問題。",[822,1203,1205,1208],{"className":1204},[825,826],[828,1206,1207],{},"補充說明：連續的數值？迴歸？都是什麼？",[832,1209,1211,1217,1223,1229,1232],{"className":1210},[835],[12,1212,1213,1216],{},[773,1214,1215],{},"連續的數值是可以無限細分、有大小之分的數字","。它們通常是「測量」出來的，而不是一個一個「數」出來的。它包含了所有的小數和分數。比如，房價可以是 50 萬馬幣，也可以是 50.5 萬馬幣，甚至是 50.512 萬馬幣。只要儀器或計算夠精確，數字可以無限切分下去。生活中的面積、身高、體重、溫度、時間，都是連續數值。",[12,1218,1219,1222],{},[773,1220,1221],{},"相對的概念是「離散數值」(Discrete Value)："," 這是只能跳躍式出現、通常是整數的數字。例如：「這間房子有幾間臥室？」答案只能是 1 間、2 間或 3 間，不可能有 2.38 間臥室。",[12,1224,1225,1226,1108],{},"在機器學習的領域裡，",[773,1227,1228],{},"只要你的目標是預測一個「連續的數值」，我們就把這個任務稱為「迴歸」",[12,1230,1231],{},"迴歸的核心概念，就是在茫茫的數據資料中，找出一條**「最符合趨勢的線」**（Line of Best Fit），藉此理解輸入（面積）與輸出（價格）之間的數學關係。",[12,1233,1234],{},[979,1235],{"alt":1236,"src":1237},"1.00","https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775983903268-1_N1-K-A43_98pYZ27fnupDA.webp",[781,1239,1240],{"id":1240},"數學符號約定",[12,1242,1243],{},"在深入之前，我們先來約定一下符號：",[77,1245,1246,1331,1408,1506,1533],{},[19,1247,1248,1307,1308,1330],{},[967,1249,1251],{"className":1250,"jax":971},[970],[973,1252,1257,1273],{"style":1253,"xmlns":976,"width":1254,"height":1255,"role":979,"focusable":980,"viewBox":1256,"xmlnsXLink":982},"vertical-align: -0.025ex;","3.278ex","2.046ex","0 -893.3 1449.1 904.3",[984,1258,1259,1263,1266,1270],{},[987,1260],{"id":1261,"d":1262},"MJX-2-TEX-I-1D465","M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z",[987,1264],{"id":1265,"d":990},"MJX-2-TEX-N-28",[987,1267],{"id":1268,"d":1269},"MJX-2-TEX-I-1D456","M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z",[987,1271],{"id":1272,"d":1010},"MJX-2-TEX-N-29",[1024,1274,1275],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1276,1277],{"dataMmlNode":1031},[1024,1278,1280,1287],{"dataMmlNode":1279},"msup",[1024,1281,1283],{"dataMmlNode":1282},"mi",[1036,1284],{"dataC":1285,"xLinkHref":1286},"1D465","#MJX-2-TEX-I-1D465",[1024,1288,1290,1295,1301],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},"translate(605,363) scale(0.707)",[1024,1291,1292],{"dataMmlNode":1034},[1036,1293],{"dataC":1038,"xLinkHref":1294},"#MJX-2-TEX-N-28",[1024,1296,1297],{"dataMmlNode":1282,"transform":1043},[1036,1298],{"dataC":1299,"xLinkHref":1300},"1D456","#MJX-2-TEX-I-1D456",[1024,1302,1304],{"dataMmlNode":1034,"transform":1303},"translate(734,0)",[1036,1305],{"dataC":1074,"xLinkHref":1306},"#MJX-2-TEX-N-29"," = 輸入特徵 (例如第 ",[967,1309,1311],{"className":1310,"jax":971},[970],[973,1312,1316,1321],{"style":1253,"xmlns":976,"width":1313,"height":1314,"role":979,"focusable":980,"viewBox":1315,"xmlnsXLink":982},"0.781ex","1.52ex","0 -661 345 672",[984,1317,1318],{},[987,1319],{"id":1320,"d":1269},"MJX-3-TEX-I-1D456",[1024,1322,1323],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1324,1325],{"dataMmlNode":1031},[1024,1326,1327],{"dataMmlNode":1282},[1036,1328],{"dataC":1299,"xLinkHref":1329},"#MJX-3-TEX-I-1D456"," 間房子的面積)",[19,1332,1333,1387,1388,1407],{},[967,1334,1336],{"className":1335,"jax":971},[970],[973,1337,1342,1357],{"style":1338,"xmlns":976,"width":1339,"height":1340,"role":979,"focusable":980,"viewBox":1341,"xmlnsXLink":982},"vertical-align: -0.464ex;","3.093ex","2.485ex","0 -893.3 1367.1 1098.3",[984,1343,1344,1348,1351,1354],{},[987,1345],{"id":1346,"d":1347},"MJX-4-TEX-I-1D466","M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z",[987,1349],{"id":1350,"d":990},"MJX-4-TEX-N-28",[987,1352],{"id":1353,"d":1269},"MJX-4-TEX-I-1D456",[987,1355],{"id":1356,"d":1010},"MJX-4-TEX-N-29",[1024,1358,1359],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1360,1361],{"dataMmlNode":1031},[1024,1362,1363,1369],{"dataMmlNode":1279},[1024,1364,1365],{"dataMmlNode":1282},[1036,1366],{"dataC":1367,"xLinkHref":1368},"1D466","#MJX-4-TEX-I-1D466",[1024,1370,1372,1377,1382],{"dataMmlNode":1078,"transform":1371,"dataMjxTexclass":1079},"translate(523,363) scale(0.707)",[1024,1373,1374],{"dataMmlNode":1034},[1036,1375],{"dataC":1038,"xLinkHref":1376},"#MJX-4-TEX-N-28",[1024,1378,1379],{"dataMmlNode":1282,"transform":1043},[1036,1380],{"dataC":1299,"xLinkHref":1381},"#MJX-4-TEX-I-1D456",[1024,1383,1384],{"dataMmlNode":1034,"transform":1303},[1036,1385],{"dataC":1074,"xLinkHref":1386},"#MJX-4-TEX-N-29"," = 輸出\u002F目標變數 (例如第 ",[967,1389,1391],{"className":1390,"jax":971},[970],[973,1392,1393,1398],{"style":1253,"xmlns":976,"width":1313,"height":1314,"role":979,"focusable":980,"viewBox":1315,"xmlnsXLink":982},[984,1394,1395],{},[987,1396],{"id":1397,"d":1269},"MJX-5-TEX-I-1D456",[1024,1399,1400],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1401,1402],{"dataMmlNode":1031},[1024,1403,1404],{"dataMmlNode":1282},[1036,1405],{"dataC":1299,"xLinkHref":1406},"#MJX-5-TEX-I-1D456"," 間房子的價格)",[19,1409,1410,1505],{},[967,1411,1413],{"className":1412,"jax":971},[970],[973,1414,1418,1439],{"style":975,"xmlns":976,"width":1415,"height":1416,"role":979,"focusable":980,"viewBox":1417,"xmlnsXLink":982},"9.138ex","2.587ex","0 -893.3 4038.8 1143.3",[984,1419,1420,1423,1426,1429,1432,1436],{},[987,1421],{"id":1422,"d":990},"MJX-6-TEX-N-28",[987,1424],{"id":1425,"d":1262},"MJX-6-TEX-I-1D465",[987,1427],{"id":1428,"d":1269},"MJX-6-TEX-I-1D456",[987,1430],{"id":1431,"d":1010},"MJX-6-TEX-N-29",[987,1433],{"id":1434,"d":1435},"MJX-6-TEX-N-2C","M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z",[987,1437],{"id":1438,"d":1347},"MJX-6-TEX-I-1D466",[1024,1440,1441],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1442,1443,1448,1471,1478,1500],{"dataMmlNode":1031},[1024,1444,1445],{"dataMmlNode":1034},[1036,1446],{"dataC":1038,"xLinkHref":1447},"#MJX-6-TEX-N-28",[1024,1449,1450,1455],{"dataMmlNode":1279,"transform":1043},[1024,1451,1452],{"dataMmlNode":1282},[1036,1453],{"dataC":1285,"xLinkHref":1454},"#MJX-6-TEX-I-1D465",[1024,1456,1457,1461,1466],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,1458,1459],{"dataMmlNode":1034},[1036,1460],{"dataC":1038,"xLinkHref":1447},[1024,1462,1463],{"dataMmlNode":1282,"transform":1043},[1036,1464],{"dataC":1299,"xLinkHref":1465},"#MJX-6-TEX-I-1D456",[1024,1467,1468],{"dataMmlNode":1034,"transform":1303},[1036,1469],{"dataC":1074,"xLinkHref":1470},"#MJX-6-TEX-N-29",[1024,1472,1474],{"dataMmlNode":1034,"transform":1473},"translate(1838.1,0)",[1036,1475],{"dataC":1476,"xLinkHref":1477},"2C","#MJX-6-TEX-N-2C",[1024,1479,1481,1486],{"dataMmlNode":1279,"transform":1480},"translate(2282.7,0)",[1024,1482,1483],{"dataMmlNode":1282},[1036,1484],{"dataC":1367,"xLinkHref":1485},"#MJX-6-TEX-I-1D466",[1024,1487,1488,1492,1496],{"dataMmlNode":1078,"transform":1371,"dataMjxTexclass":1079},[1024,1489,1490],{"dataMmlNode":1034},[1036,1491],{"dataC":1038,"xLinkHref":1447},[1024,1493,1494],{"dataMmlNode":1282,"transform":1043},[1036,1495],{"dataC":1299,"xLinkHref":1465},[1024,1497,1498],{"dataMmlNode":1034,"transform":1303},[1036,1499],{"dataC":1074,"xLinkHref":1470},[1024,1501,1503],{"dataMmlNode":1034,"transform":1502},"translate(3649.8,0)",[1036,1504],{"dataC":1074,"xLinkHref":1470}," = 一筆訓練樣本",[19,1507,1508,1532],{},[967,1509,1511],{"className":1510,"jax":971},[970],[973,1512,1516,1522],{"style":1253,"xmlns":976,"width":1513,"height":1514,"role":979,"focusable":980,"viewBox":1515,"xmlnsXLink":982},"1.986ex","1.025ex","0 -442 878 453",[984,1517,1518],{},[987,1519],{"id":1520,"d":1521},"MJX-7-TEX-I-1D45A","M21 287Q22 293 24 303T36 341T56 388T88 425T132 442T175 435T205 417T221 395T229 376L231 369Q231 367 232 367L243 378Q303 442 384 442Q401 442 415 440T441 433T460 423T475 411T485 398T493 385T497 373T500 364T502 357L510 367Q573 442 659 442Q713 442 746 415T780 336Q780 285 742 178T704 50Q705 36 709 31T724 26Q752 26 776 56T815 138Q818 149 821 151T837 153Q857 153 857 145Q857 144 853 130Q845 101 831 73T785 17T716 -10Q669 -10 648 17T627 73Q627 92 663 193T700 345Q700 404 656 404H651Q565 404 506 303L499 291L466 157Q433 26 428 16Q415 -11 385 -11Q372 -11 364 -4T353 8T350 18Q350 29 384 161L420 307Q423 322 423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 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也就是我們想學出來的預測器",[12,1587,1588,1589,1611,1612,1655,1656,1678],{},"我們的目標是：找到一個函數 ",[967,1590,1592],{"className":1591,"jax":971},[970],[973,1593,1597,1602],{"style":1253,"xmlns":976,"width":1594,"height":1595,"role":979,"focusable":980,"viewBox":1596,"xmlnsXLink":982},"1.303ex","1.595ex","0 -694 576 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臥室數)",[12,1842,1843,1844,1867,1868,1871,1872,1875,1876,1895],{},"這些 ",[967,1845,1847],{"className":1846,"jax":971},[970],[973,1848,1853,1858],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},"vertical-align: -0.023ex;","1.061ex","1.618ex","0 -705 469 715",[984,1854,1855],{},[987,1856],{"id":1857,"d":1714},"MJX-13-TEX-I-1D703",[1024,1859,1860],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1861,1862],{"dataMmlNode":1031},[1024,1863,1864],{"dataMmlNode":1282},[1036,1865],{"dataC":1767,"xLinkHref":1866},"#MJX-13-TEX-I-1D703"," 值被稱為",[773,1869,1870],{},"參數 (parameters)","（或",[773,1873,1874],{},"權重 weights","）。我們的工作就是要找出最準確的 ",[967,1877,1879],{"className":1878,"jax":971},[970],[973,1880,1881,1886],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},[984,1882,1883],{},[987,1884],{"id":1885,"d":1714},"MJX-14-TEX-I-1D703",[1024,1887,1888],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,1889,1890],{"dataMmlNode":1031},[1024,1891,1892],{"dataMmlNode":1282},[1036,1893],{"dataC":1767,"xLinkHref":1894},"#MJX-14-TEX-I-1D703"," 值。但該怎麼找呢？",[781,1897,1899],{"id":1898},"成本函數-the-cost-function","成本函數 (The Cost Function)",[12,1901,1902,1903],{},"我們定義了一個",[773,1904,1905],{},"最小平方法成本函",[967,1907,1909],{"className":1908,"jax":971,"display":1689},[970],[973,1910,1915,1959],{"style":1911,"xmlns":976,"width":1912,"height":1913,"role":979,"focusable":980,"viewBox":1914,"xmlnsXLink":982},"vertical-align: -2.697ex;","27.99ex","5.733ex","0 -1342 12371.4 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scale(0.707)",[1036,2030],{"dataC":1299,"xLinkHref":2031},"#MJX-15-TEX-I-1D456",[1024,2033,2035],{"dataMmlNode":1034,"transform":2034},"translate(5764.2,0)",[1036,2036],{"dataC":1038,"xLinkHref":1974},[1024,2038,2040],{"dataMmlNode":1282,"transform":2039},"translate(6153.2,0)",[1036,2041],{"dataC":1565,"xLinkHref":2042},"#MJX-15-TEX-I-210E",[1024,2044,2046],{"dataMmlNode":1034,"transform":2045},"translate(6729.2,0)",[1036,2047],{"dataC":1038,"xLinkHref":1974},[1024,2049,2051,2056],{"dataMmlNode":1279,"transform":2050},"translate(7118.2,0)",[1024,2052,2053],{"dataMmlNode":1282},[1036,2054],{"dataC":1285,"xLinkHref":2055},"#MJX-15-TEX-I-1D465",[1024,2057,2059,2063,2067],{"dataMmlNode":1078,"transform":2058,"dataMjxTexclass":1079},"translate(605,413) scale(0.707)",[1024,2060,2061],{"dataMmlNode":1034},[1036,2062],{"dataC":1038,"xLinkHref":1974},[1024,2064,2065],{"dataMmlNode":1282,"transform":1043},[1036,2066],{"dataC":1299,"xLinkHref":2031},[1024,2068,2069],{"dataMmlNode":1034,"transform":1303},[1036,2070],{"dataC":1074,"xLinkHref":1986},[1024,2072,2074],{"dataMmlNode":1034,"transform":2073},"translate(8567.3,0)",[1036,2075],{"dataC":1074,"xLinkHref":1986},[1024,2077,2079],{"dataMmlNode":1034,"transform":2078},"translate(9178.5,0)",[1036,2080],{"dataC":2081,"xLinkHref":2082},"2212","#MJX-15-TEX-N-2212",[1024,2084,2086,2091],{"dataMmlNode":1279,"transform":2085},"translate(10178.7,0)",[1024,2087,2088],{"dataMmlNode":1282},[1036,2089],{"dataC":1367,"xLinkHref":2090},"#MJX-15-TEX-I-1D466",[1024,2092,2094,2098,2102],{"dataMmlNode":1078,"transform":2093,"dataMjxTexclass":1079},"translate(523,413) scale(0.707)",[1024,2095,2096],{"dataMmlNode":1034},[1036,2097],{"dataC":1038,"xLinkHref":1974},[1024,2099,2100],{"dataMmlNode":1282,"transform":1043},[1036,2101],{"dataC":1299,"xLinkHref":2031},[1024,2103,2104],{"dataMmlNode":1034,"transform":1303},[1036,2105],{"dataC":1074,"xLinkHref":1986},[1024,2107,2109,2113],{"dataMmlNode":1279,"transform":2108},"translate(11545.8,0)",[1024,2110,2111],{"dataMmlNode":1034},[1036,2112],{"dataC":1074,"xLinkHref":1986},[1024,2114,2116],{"dataMmlNode":1042,"transform":2115},"translate(422,413) scale(0.707)",[1036,2117],{"dataC":1046,"xLinkHref":2008},[822,2119,2121,2124],{"className":2120},[825,826],[828,2122,2123],{},"公式詳解：",[832,2125,2127,2231,2302,2355,2358,2423,2426,2440,2465,2471,2513],{"className":2126},[835],[16,2128,2129],{},[19,2130,2131],{},[967,2132,2134],{"className":2133,"jax":971},[970],[973,2135,2138,2161],{"style":975,"xmlns":976,"width":2136,"height":1416,"role":979,"focusable":980,"viewBox":2137,"xmlnsXLink":982},"12.2ex","0 -893.3 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-893.3 2803.1 1143.3",[984,2241,2242,2245,2248,2251,2254],{},[987,2243],{"id":2244,"d":1547},"MJX-17-TEX-I-210E",[987,2246],{"id":2247,"d":990},"MJX-17-TEX-N-28",[987,2249],{"id":2250,"d":1262},"MJX-17-TEX-I-1D465",[987,2252],{"id":2253,"d":1269},"MJX-17-TEX-I-1D456",[987,2255],{"id":2256,"d":1010},"MJX-17-TEX-N-29",[1024,2258,2259],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2260,2261,2266,2271,2294],{"dataMmlNode":1031},[1024,2262,2263],{"dataMmlNode":1282},[1036,2264],{"dataC":1565,"xLinkHref":2265},"#MJX-17-TEX-I-210E",[1024,2267,2268],{"dataMmlNode":1034,"transform":1569},[1036,2269],{"dataC":1038,"xLinkHref":2270},"#MJX-17-TEX-N-28",[1024,2272,2273,2278],{"dataMmlNode":1279,"transform":1575},[1024,2274,2275],{"dataMmlNode":1282},[1036,2276],{"dataC":1285,"xLinkHref":2277},"#MJX-17-TEX-I-1D465",[1024,2279,2280,2284,2289],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,2281,2282],{"dataMmlNode":1034},[1036,2283],{"dataC":1038,"xLinkHref":2270},[1024,2285,2286],{"dataMmlNode":1282,"transform":1043},[1036,2287],{"dataC":1299,"xLinkHref":2288},"#MJX-17-TEX-I-1D456",[1024,2290,2291],{"dataMmlNode":1034,"transform":1303},[1036,2292],{"dataC":1074,"xLinkHref":2293},"#MJX-17-TEX-N-29",[1024,2295,2296],{"dataMmlNode":1034,"transform":2200},[1036,2297],{"dataC":1074,"xLinkHref":2293}," 是我們用公式算出來的",[773,2300,2301],{},"預測房價",[12,2303,2304,2351,2352,1108],{},[967,2305,2307],{"className":2306,"jax":971},[970],[973,2308,2309,2323],{"style":1338,"xmlns":976,"width":1339,"height":1340,"role":979,"focusable":980,"viewBox":1341,"xmlnsXLink":982},[984,2310,2311,2314,2317,2320],{},[987,2312],{"id":2313,"d":1347},"MJX-18-TEX-I-1D466",[987,2315],{"id":2316,"d":990},"MJX-18-TEX-N-28",[987,2318],{"id":2319,"d":1269},"MJX-18-TEX-I-1D456",[987,2321],{"id":2322,"d":1010},"MJX-18-TEX-N-29",[1024,2324,2325],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2326,2327],{"dataMmlNode":1031},[1024,2328,2329,2334],{"dataMmlNode":1279},[1024,2330,2331],{"dataMmlNode":1282},[1036,2332],{"dataC":1367,"xLinkHref":2333},"#MJX-18-TEX-I-1D466",[1024,2335,2336,2341,2346],{"dataMmlNode":1078,"transform":1371,"dataMjxTexclass":1079},[1024,2337,2338],{"dataMmlNode":1034},[1036,2339],{"dataC":1038,"xLinkHref":2340},"#MJX-18-TEX-N-28",[1024,2342,2343],{"dataMmlNode":1282,"transform":1043},[1036,2344],{"dataC":1299,"xLinkHref":2345},"#MJX-18-TEX-I-1D456",[1024,2347,2348],{"dataMmlNode":1034,"transform":1303},[1036,2349],{"dataC":1074,"xLinkHref":2350},"#MJX-18-TEX-N-29"," 是這間房子在現實中的",[773,2353,2354],{},"真實成交價",[12,2356,2357],{},"把它們相減，就是在算**「我們猜錯了多少錢（誤差）」**。例如，我們預測賣 50 萬，實際賣了 60 萬，誤差就是 -10 萬。",[12,2359,2360,2361],{},"2. 平方",[967,2362,2364],{"className":2363,"jax":971},[970],[973,2365,2369,2384],{"style":975,"xmlns":976,"width":2366,"height":2367,"role":979,"focusable":980,"viewBox":2368,"xmlnsXLink":982},"5.766ex","2.452ex","0 -833.9 2548.6 1083.9",[984,2370,2371,2374,2378,2381],{},[987,2372],{"id":2373,"d":990},"MJX-19-TEX-N-28",[987,2375],{"id":2376,"d":2377},"MJX-19-TEX-N-2E","M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z",[987,2379],{"id":2380,"d":1010},"MJX-19-TEX-N-29",[987,2382],{"id":2383,"d":994},"MJX-19-TEX-N-32",[1024,2385,2386],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2387,2388,2393,2399,2404,2409],{"dataMmlNode":1031},[1024,2389,2390],{"dataMmlNode":1034},[1036,2391],{"dataC":1038,"xLinkHref":2392},"#MJX-19-TEX-N-28",[1024,2394,2395],{"dataMmlNode":1034,"transform":1043},[1036,2396],{"dataC":2397,"xLinkHref":2398},"2E","#MJX-19-TEX-N-2E",[1024,2400,2402],{"dataMmlNode":1034,"transform":2401},"translate(833.7,0)",[1036,2403],{"dataC":2397,"xLinkHref":2398},[1024,2405,2407],{"dataMmlNode":1034,"transform":2406},"translate(1278.3,0)",[1036,2408],{"dataC":2397,"xLinkHref":2398},[1024,2410,2412,2417],{"dataMmlNode":1279,"transform":2411},"translate(1723,0)",[1024,2413,2414],{"dataMmlNode":1034},[1036,2415],{"dataC":1074,"xLinkHref":2416},"#MJX-19-TEX-N-29",[1024,2418,2420],{"dataMmlNode":1042,"transform":2419},"translate(422,363) scale(0.707)",[1036,2421],{"dataC":1046,"xLinkHref":2422},"#MJX-19-TEX-N-32",[12,2424,2425],{},"這裡把誤差拿來「平方」，有兩個很重要的原因：",[77,2427,2428,2434],{},[19,2429,2430,2433],{},[773,2431,2432],{},"把負數變成正數："," 如果我們高估了 10 萬（誤差 +10）或低估了 10 萬（誤差 -10），對預測來說都是一樣糟糕的。平方之後，負號就不見了，我們只看「誤差的幅度」。",[19,2435,2436,2439],{},[773,2437,2438],{},"嚴厲懲罰「大錯誤」："," 平方有一個特性，會讓越大的數字膨脹得越快（例如 2 的平方是 4，但 10 的平方是 100）。這等於是在告訴機器：「小誤差還可以接受，但如果預測錯得太離譜，你的分數會扣得非常非常重！」",[12,2441,2442,2443],{},"3. 加總",[967,2444,2446],{"className":2445,"jax":971},[970],[973,2447,2450,2456],{"style":975,"xmlns":976,"width":2448,"height":978,"role":979,"focusable":980,"viewBox":2449,"xmlnsXLink":982},"2.389ex","0 -750 1056 1000",[984,2451,2452],{},[987,2453],{"id":2454,"d":2455},"MJX-20-TEX-SO-2211","M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z",[1024,2457,2458],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2459,2460],{"dataMmlNode":1031},[1024,2461,2462],{"dataMmlNode":1034},[1036,2463],{"dataC":2024,"xLinkHref":2464},"#MJX-20-TEX-SO-2211",[12,2466,2467,2468,1108],{},"我們不能只看一間房子的誤差，而是要把資料集裡全部 47 間房子的「誤差平方」全部加起來，算出一個總分。這就是為什麼這個方法被稱為",[773,2469,2470],{},"最小平方法 (Least Squares)",[16,2472,2473],{},[19,2474,2475],{},[967,2476,2478],{"className":2477,"jax":971},[970],[973,2479,2484,2492],{"style":2480,"xmlns":976,"width":2481,"height":2482,"role":979,"focusable":980,"viewBox":2483,"xmlnsXLink":982},"vertical-align: -0.781ex;","1.795ex","2.737ex","0 -864.9 793.6 1209.9",[984,2485,2486,2489],{},[987,2487],{"id":2488,"d":1725},"MJX-21-TEX-N-31",[987,2490],{"id":2491,"d":994},"MJX-21-TEX-N-32",[1024,2493,2494],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2495,2496],{"dataMmlNode":1031},[1024,2497,2498,2504,2510],{"dataMmlNode":1995},[1024,2499,2501],{"dataMmlNode":1042,"transform":2500},"translate(220,394) scale(0.707)",[1036,2502],{"dataC":1793,"xLinkHref":2503},"#MJX-21-TEX-N-31",[1024,2505,2507],{"dataMmlNode":1042,"transform":2506},"translate(220,-345) scale(0.707)",[1036,2508],{"dataC":1046,"xLinkHref":2509},"#MJX-21-TEX-N-32",[2010,2511],{"width":2512,"height":2013,"x":2014,"y":2015},553.6,[12,2514,2515,2516,2519,2520,2551],{},"為什麼前面要乘一個二分之一？其實這只是一個",[773,2517,2518],{},"數學上的小偷吃步","。 在機器學習的下一步，我們需要用到微積分來尋找最小誤差。當平方的那個 2 掉下來相乘時，剛好可以跟 ",[967,2521,2523],{"className":2522,"jax":971},[970],[973,2524,2525,2533],{"style":2480,"xmlns":976,"width":2481,"height":2482,"role":979,"focusable":980,"viewBox":2483,"xmlnsXLink":982},[984,2526,2527,2530],{},[987,2528],{"id":2529,"d":1725},"MJX-22-TEX-N-31",[987,2531],{"id":2532,"d":994},"MJX-22-TEX-N-32",[1024,2534,2535],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2536,2537],{"dataMmlNode":1031},[1024,2538,2539,2544,2549],{"dataMmlNode":1995},[1024,2540,2541],{"dataMmlNode":1042,"transform":2500},[1036,2542],{"dataC":1793,"xLinkHref":2543},"#MJX-22-TEX-N-31",[1024,2545,2546],{"dataMmlNode":1042,"transform":2506},[1036,2547],{"dataC":1046,"xLinkHref":2548},"#MJX-22-TEX-N-32",[2010,2550],{"width":2512,"height":2013,"x":2014,"y":2015}," 抵銷掉，讓後面的計算過程變得更乾淨漂亮。它完全不會影響我們尋找最佳答案的結果。",[12,2553,2554,2599,2600,2603,2604,1108],{},[967,2555,2557],{"className":2556,"jax":971},[970],[973,2558,2561,2575],{"style":975,"xmlns":976,"width":2559,"height":978,"role":979,"focusable":980,"viewBox":2560,"xmlnsXLink":982},"4.253ex","0 -750 1880 1000",[984,2562,2563,2566,2569,2572],{},[987,2564],{"id":2565,"d":1920},"MJX-23-TEX-I-1D43D",[987,2567],{"id":2568,"d":990},"MJX-23-TEX-N-28",[987,2570],{"id":2571,"d":1714},"MJX-23-TEX-I-1D703",[987,2573],{"id":2574,"d":1010},"MJX-23-TEX-N-29",[1024,2576,2577],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2578,2579,2584,2589,2594],{"dataMmlNode":1031},[1024,2580,2581],{"dataMmlNode":1282},[1036,2582],{"dataC":1967,"xLinkHref":2583},"#MJX-23-TEX-I-1D43D",[1024,2585,2586],{"dataMmlNode":1034,"transform":1971},[1036,2587],{"dataC":1038,"xLinkHref":2588},"#MJX-23-TEX-N-28",[1024,2590,2591],{"dataMmlNode":1282,"transform":1977},[1036,2592],{"dataC":1767,"xLinkHref":2593},"#MJX-23-TEX-I-1D703",[1024,2595,2596],{"dataMmlNode":1034,"transform":1983},[1036,2597],{"dataC":1074,"xLinkHref":2598},"#MJX-23-TEX-N-29"," 越小，代表我們的模型越貼合資料。所以我們要想辦法",[773,2601,2602],{},"最小化"," ",[967,2605,2607],{"className":2606,"jax":971},[970],[973,2608,2609,2623],{"style":975,"xmlns":976,"width":2559,"height":978,"role":979,"focusable":980,"viewBox":2560,"xmlnsXLink":982},[984,2610,2611,2614,2617,2620],{},[987,2612],{"id":2613,"d":1920},"MJX-24-TEX-I-1D43D",[987,2615],{"id":2616,"d":990},"MJX-24-TEX-N-28",[987,2618],{"id":2619,"d":1714},"MJX-24-TEX-I-1D703",[987,2621],{"id":2622,"d":1010},"MJX-24-TEX-N-29",[1024,2624,2625],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2626,2627,2632,2637,2642],{"dataMmlNode":1031},[1024,2628,2629],{"dataMmlNode":1282},[1036,2630],{"dataC":1967,"xLinkHref":2631},"#MJX-24-TEX-I-1D43D",[1024,2633,2634],{"dataMmlNode":1034,"transform":1971},[1036,2635],{"dataC":1038,"xLinkHref":2636},"#MJX-24-TEX-N-28",[1024,2638,2639],{"dataMmlNode":1282,"transform":1977},[1036,2640],{"dataC":1767,"xLinkHref":2641},"#MJX-24-TEX-I-1D703",[1024,2643,2644],{"dataMmlNode":1034,"transform":1983},[1036,2645],{"dataC":1074,"xLinkHref":2646},"#MJX-24-TEX-N-29",[781,2648,2650],{"id":2649},"梯度下降-gradient-descent-尋找最佳參數","梯度下降 (Gradient Descent) — 尋找最佳參數",[12,2652,2653],{},"梯度下降是一個迭代的優化演算法。它的直觀概念是這樣的：",[16,2655,2656,2679,2725,2772],{},[19,2657,2658,2659,2678],{},"隨便猜一個 ",[967,2660,2662],{"className":2661,"jax":971},[970],[973,2663,2664,2669],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},[984,2665,2666],{},[987,2667],{"id":2668,"d":1714},"MJX-25-TEX-I-1D703",[1024,2670,2671],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2672,2673],{"dataMmlNode":1031},[1024,2674,2675],{"dataMmlNode":1282},[1036,2676],{"dataC":1767,"xLinkHref":2677},"#MJX-25-TEX-I-1D703"," 的起始值。",[19,2680,2681,2682,1108],{},"計算成本 ",[967,2683,2685],{"className":2684,"jax":971},[970],[973,2686,2687,2701],{"style":975,"xmlns":976,"width":2559,"height":978,"role":979,"focusable":980,"viewBox":2560,"xmlnsXLink":982},[984,2688,2689,2692,2695,2698],{},[987,2690],{"id":2691,"d":1920},"MJX-26-TEX-I-1D43D",[987,2693],{"id":2694,"d":990},"MJX-26-TEX-N-28",[987,2696],{"id":2697,"d":1714},"MJX-26-TEX-I-1D703",[987,2699],{"id":2700,"d":1010},"MJX-26-TEX-N-29",[1024,2702,2703],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2704,2705,2710,2715,2720],{"dataMmlNode":1031},[1024,2706,2707],{"dataMmlNode":1282},[1036,2708],{"dataC":1967,"xLinkHref":2709},"#MJX-26-TEX-I-1D43D",[1024,2711,2712],{"dataMmlNode":1034,"transform":1971},[1036,2713],{"dataC":1038,"xLinkHref":2714},"#MJX-26-TEX-N-28",[1024,2716,2717],{"dataMmlNode":1282,"transform":1977},[1036,2718],{"dataC":1767,"xLinkHref":2719},"#MJX-26-TEX-I-1D703",[1024,2721,2722],{"dataMmlNode":1034,"transform":1983},[1036,2723],{"dataC":1074,"xLinkHref":2724},"#MJX-26-TEX-N-29",[19,2726,2727,2728,2771],{},"朝著能讓 ",[967,2729,2731],{"className":2730,"jax":971},[970],[973,2732,2733,2747],{"style":975,"xmlns":976,"width":2559,"height":978,"role":979,"focusable":980,"viewBox":2560,"xmlnsXLink":982},[984,2734,2735,2738,2741,2744],{},[987,2736],{"id":2737,"d":1920},"MJX-27-TEX-I-1D43D",[987,2739],{"id":2740,"d":990},"MJX-27-TEX-N-28",[987,2742],{"id":2743,"d":1714},"MJX-27-TEX-I-1D703",[987,2745],{"id":2746,"d":1010},"MJX-27-TEX-N-29",[1024,2748,2749],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2750,2751,2756,2761,2766],{"dataMmlNode":1031},[1024,2752,2753],{"dataMmlNode":1282},[1036,2754],{"dataC":1967,"xLinkHref":2755},"#MJX-27-TEX-I-1D43D",[1024,2757,2758],{"dataMmlNode":1034,"transform":1971},[1036,2759],{"dataC":1038,"xLinkHref":2760},"#MJX-27-TEX-N-28",[1024,2762,2763],{"dataMmlNode":1282,"transform":1977},[1036,2764],{"dataC":1767,"xLinkHref":2765},"#MJX-27-TEX-I-1D703",[1024,2767,2768],{"dataMmlNode":1034,"transform":1983},[1036,2769],{"dataC":1074,"xLinkHref":2770},"#MJX-27-TEX-N-29"," 減少最多的方向（最陡的下坡方向）稍微調整 θ。",[19,2773,2774],{},"重複這個動作，直到收斂（走到谷底）。",[12,2776,2777],{},"更新規則長這樣：",[967,2779,2781],{"className":2780,"jax":971,"display":1689},[970],[973,2782,2787,2823],{"style":2783,"xmlns":976,"width":2784,"height":2785,"role":979,"focusable":980,"viewBox":2786,"xmlnsXLink":982},"vertical-align: -2.218ex;","18.205ex","5.521ex","0 -1460 8046.7 2440.2",[984,2788,2789,2792,2796,2800,2803,2806,2810,2814,2817,2820],{},[987,2790],{"id":2791,"d":1714},"MJX-28-TEX-I-1D703",[987,2793],{"id":2794,"d":2795},"MJX-28-TEX-I-1D457","M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z",[987,2797],{"id":2798,"d":2799},"MJX-28-TEX-N-3A","M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z",[987,2801],{"id":2802,"d":1018},"MJX-28-TEX-N-3D",[987,2804],{"id":2805,"d":1955},"MJX-28-TEX-N-2212",[987,2807],{"id":2808,"d":2809},"MJX-28-TEX-I-1D6FC","M34 156Q34 270 120 356T309 442Q379 442 421 402T478 304Q484 275 485 237V208Q534 282 560 374Q564 388 566 390T582 393Q603 393 603 385Q603 376 594 346T558 261T497 161L486 147L487 123Q489 67 495 47T514 26Q528 28 540 37T557 60Q559 67 562 68T577 70Q597 70 597 62Q597 56 591 43Q579 19 556 5T512 -10H505Q438 -10 414 62L411 69L400 61Q390 53 370 41T325 18T267 -2T203 -11Q124 -11 79 39T34 156ZM208 26Q257 26 306 47T379 90L403 112Q401 255 396 290Q382 405 304 405Q235 405 183 332Q156 292 139 224T121 120Q121 71 146 49T208 26Z",[987,2811],{"id":2812,"d":2813},"MJX-28-TEX-I-1D715","M202 508Q179 508 169 520T158 547Q158 557 164 577T185 624T230 675T301 710L333 715H345Q378 715 384 714Q447 703 489 661T549 568T566 457Q566 362 519 240T402 53Q321 -22 223 -22Q123 -22 73 56Q42 102 42 148V159Q42 276 129 370T322 465Q383 465 414 434T455 367L458 378Q478 461 478 515Q478 603 437 639T344 676Q266 676 223 612Q264 606 264 572Q264 547 246 528T202 508ZM430 306Q430 372 401 400T333 428Q270 428 222 382Q197 354 183 323T150 221Q132 149 132 116Q132 21 232 21Q244 21 250 22Q327 35 374 112Q389 137 409 196T430 306Z",[987,2815],{"id":2816,"d":1920},"MJX-28-TEX-I-1D43D",[987,2818],{"id":2819,"d":990},"MJX-28-TEX-N-28",[987,2821],{"id":2822,"d":1010},"MJX-28-TEX-N-29",[1024,2824,2825],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2826,2827,2840,2856,2867,2873,2880],{"dataMmlNode":1031},[1024,2828,2829,2834],{"dataMmlNode":1761},[1024,2830,2831],{"dataMmlNode":1282},[1036,2832],{"dataC":1767,"xLinkHref":2833},"#MJX-28-TEX-I-1D703",[1024,2835,2836],{"dataMmlNode":1282,"transform":1771},[1036,2837],{"dataC":2838,"xLinkHref":2839},"1D457","#MJX-28-TEX-I-1D457",[1024,2841,2843,2850],{"dataMmlNode":1034,"transform":2842},"translate(1121.1,0)",[1024,2844,2846],{"dataMmlNode":2845},"text",[1036,2847],{"dataC":2848,"xLinkHref":2849},"3A","#MJX-28-TEX-N-3A",[1024,2851,2853],{"dataMmlNode":2845,"transform":2852},"translate(278,0)",[1036,2854],{"dataC":1097,"xLinkHref":2855},"#MJX-28-TEX-N-3D",[1024,2857,2859,2863],{"dataMmlNode":1761,"transform":2858},"translate(2454.9,0)",[1024,2860,2861],{"dataMmlNode":1282},[1036,2862],{"dataC":1767,"xLinkHref":2833},[1024,2864,2865],{"dataMmlNode":1282,"transform":1771},[1036,2866],{"dataC":2838,"xLinkHref":2839},[1024,2868,2870],{"dataMmlNode":1034,"transform":2869},"translate(3520.4,0)",[1036,2871],{"dataC":2081,"xLinkHref":2872},"#MJX-28-TEX-N-2212",[1024,2874,2876],{"dataMmlNode":1282,"transform":2875},"translate(4520.7,0)",[1036,2877],{"dataC":2878,"xLinkHref":2879},"1D6FC","#MJX-28-TEX-I-1D6FC",[1024,2881,2883,2916,2933],{"dataMmlNode":1995,"transform":2882},"translate(5160.7,0)",[1024,2884,2887,2893,2899,2905,2910],{"dataMmlNode":2885,"transform":2886},"mrow","translate(220,710)",[1024,2888,2889],{"dataMmlNode":1282},[1036,2890],{"dataC":2891,"xLinkHref":2892},"1D715","#MJX-28-TEX-I-1D715",[1024,2894,2896],{"dataMmlNode":1282,"transform":2895},"translate(566,0)",[1036,2897],{"dataC":1967,"xLinkHref":2898},"#MJX-28-TEX-I-1D43D",[1024,2900,2902],{"dataMmlNode":1034,"transform":2901},"translate(1199,0)",[1036,2903],{"dataC":1038,"xLinkHref":2904},"#MJX-28-TEX-N-28",[1024,2906,2908],{"dataMmlNode":1282,"transform":2907},"translate(1588,0)",[1036,2909],{"dataC":1767,"xLinkHref":2833},[1024,2911,2913],{"dataMmlNode":1034,"transform":2912},"translate(2057,0)",[1036,2914],{"dataC":1074,"xLinkHref":2915},"#MJX-28-TEX-N-29",[1024,2917,2919,2923],{"dataMmlNode":2885,"transform":2918},"translate(738.3,-686)",[1024,2920,2921],{"dataMmlNode":1282},[1036,2922],{"dataC":2891,"xLinkHref":2892},[1024,2924,2925,2929],{"dataMmlNode":1761,"transform":2895},[1024,2926,2927],{"dataMmlNode":1282},[1036,2928],{"dataC":1767,"xLinkHref":2833},[1024,2930,2931],{"dataMmlNode":1282,"transform":1771},[1036,2932],{"dataC":2838,"xLinkHref":2839},[2010,2934],{"width":2935,"height":2013,"x":2014,"y":2015},2646,[822,2937,2939,2942],{"className":2938},[825,826],[828,2940,2941],{},"公式詳解",[832,2943,2945,2952,2959,2962,3033,3103,3192,3200,3226,3235,3239,3326,3329],{"className":2944},[835],[12,2946,2947,2951],{},[2948,2949,2950],"del",{},"其實看不懂半點"," 我盡力說說看",[12,2953,2954,2955,2958],{},"想像一個情境：",[773,2956,2957],{},"你被蒙住了雙眼，丟在一座高山上的某個地方。你的目標是「走到這座山的最低谷」。"," 你看不見，只能用腳感覺周圍地面的傾斜程度。你會怎麼做？你一定是用腳探一探，感覺哪邊是「最陡的下坡」，然後往那個方向踏出一步。接著再用腳感覺一下，再往最陡的下坡走一步。不斷重複，直到你覺得四周都平了，你就知道自己到達谷底了。",[12,2960,2961],{},"現在我們來看看我們的公式，把它拆開來看：",[2963,2964,2966,2967,2999,3000,3032],"h4",{"id":2965},"_1與準備更新位置","1. ",[967,2968,2970],{"className":2969,"jax":971},[970],[973,2971,2976,2984],{"style":2972,"xmlns":976,"width":2973,"height":2974,"role":979,"focusable":980,"viewBox":2975,"xmlnsXLink":982},"vertical-align: -0.462ex;","1.993ex","2.057ex","0 -705 881 909",[984,2977,2978,2981],{},[987,2979],{"id":2980,"d":1714},"MJX-29-TEX-I-1D703",[987,2982],{"id":2983,"d":2795},"MJX-29-TEX-I-1D457",[1024,2985,2986],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,2987,2988,2993],{"dataMmlNode":1031},[1024,2989,2990],{"dataMmlNode":1282},[1036,2991],{"dataC":1767,"xLinkHref":2992},"#MJX-29-TEX-I-1D703",[1024,2994,2996],{"dataMmlNode":1282,"transform":2995},"translate(469,0)",[1036,2997],{"dataC":2838,"xLinkHref":2998},"#MJX-29-TEX-I-1D457","​ 與 ",[967,3001,3003],{"className":3002,"jax":971},[970],[973,3004,3008,3016],{"style":3005,"xmlns":976,"width":2448,"height":3006,"role":979,"focusable":980,"viewBox":3007,"xmlnsXLink":982},"vertical-align: -0.186ex;","1.505ex","0 -583 1056 665",[984,3009,3010,3013],{},[987,3011],{"id":3012,"d":2799},"MJX-30-TEX-N-3A",[987,3014],{"id":3015,"d":1018},"MJX-30-TEX-N-3D",[1024,3017,3018],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3019,3020],{"dataMmlNode":1031},[1024,3021,3022,3027],{"dataMmlNode":1034},[1024,3023,3024],{"dataMmlNode":2845},[1036,3025],{"dataC":2848,"xLinkHref":3026},"#MJX-30-TEX-N-3A",[1024,3028,3029],{"dataMmlNode":2845,"transform":2852},[1036,3030],{"dataC":1097,"xLinkHref":3031},"#MJX-30-TEX-N-3D"," （準備更新位置）",[77,3034,3035,3068],{},[19,3036,3037,3067],{},[773,3038,3039,3066],{},[967,3040,3042],{"className":3041,"jax":971},[970],[973,3043,3044,3052],{"style":2972,"xmlns":976,"width":2973,"height":2974,"role":979,"focusable":980,"viewBox":2975,"xmlnsXLink":982},[984,3045,3046,3049],{},[987,3047],{"id":3048,"d":1714},"MJX-31-TEX-I-1D703",[987,3050],{"id":3051,"d":2795},"MJX-31-TEX-I-1D457",[1024,3053,3054],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3055,3056,3061],{"dataMmlNode":1031},[1024,3057,3058],{"dataMmlNode":1282},[1036,3059],{"dataC":1767,"xLinkHref":3060},"#MJX-31-TEX-I-1D703",[1024,3062,3063],{"dataMmlNode":1282,"transform":2995},[1036,3064],{"dataC":2838,"xLinkHref":3065},"#MJX-31-TEX-I-1D457","​："," 這是我們的「權重」（例如：面積對房價的影響力）。你可以把它想像成你現在站在山坡上的**「座標位置」**。",[19,3069,3070,3102],{},[773,3071,3072,3101],{},[967,3073,3075],{"className":3074,"jax":971},[970],[973,3076,3077,3085],{"style":3005,"xmlns":976,"width":2448,"height":3006,"role":979,"focusable":980,"viewBox":3007,"xmlnsXLink":982},[984,3078,3079,3082],{},[987,3080],{"id":3081,"d":2799},"MJX-32-TEX-N-3A",[987,3083],{"id":3084,"d":1018},"MJX-32-TEX-N-3D",[1024,3086,3087],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3088,3089],{"dataMmlNode":1031},[1024,3090,3091,3096],{"dataMmlNode":1034},[1024,3092,3093],{"dataMmlNode":2845},[1036,3094],{"dataC":2848,"xLinkHref":3095},"#MJX-32-TEX-N-3A",[1024,3097,3098],{"dataMmlNode":2845,"transform":2852},[1036,3099],{"dataC":1097,"xLinkHref":3100},"#MJX-32-TEX-N-3D","："," 在程式語言裡，這個符號唸作 \"Assign\"（賦值）。它的意思是**「把右邊算出來的新結果，取代掉左邊舊的東西」**。所以整行公式的意思是：「我的新位置，將會等於右邊算出來的結果」。",[2963,3104,3106,3107,3191],{"id":3105},"_2腳底下的坡度","2. ",[967,3108,3110],{"className":3109,"jax":971},[970],[973,3111,3116,3136],{"style":3112,"xmlns":976,"width":3113,"height":3114,"role":979,"focusable":980,"viewBox":3115,"xmlnsXLink":982},"vertical-align: -1.253ex;","4.909ex","3.622ex","0 -1047.1 2169.6 1600.8",[984,3117,3118,3121,3124,3127,3130,3133],{},[987,3119],{"id":3120,"d":2813},"MJX-33-TEX-I-1D715",[987,3122],{"id":3123,"d":1920},"MJX-33-TEX-I-1D43D",[987,3125],{"id":3126,"d":990},"MJX-33-TEX-N-28",[987,3128],{"id":3129,"d":1714},"MJX-33-TEX-I-1D703",[987,3131],{"id":3132,"d":1010},"MJX-33-TEX-N-29",[987,3134],{"id":3135,"d":2795},"MJX-33-TEX-I-1D457",[1024,3137,3138],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3139,3140],{"dataMmlNode":1031},[1024,3141,3142,3170,3188],{"dataMmlNode":1995},[1024,3143,3145,3150,3155,3160,3165],{"dataMmlNode":2885,"transform":3144},"translate(220,516.8) scale(0.707)",[1024,3146,3147],{"dataMmlNode":1282},[1036,3148],{"dataC":2891,"xLinkHref":3149},"#MJX-33-TEX-I-1D715",[1024,3151,3152],{"dataMmlNode":1282,"transform":2895},[1036,3153],{"dataC":1967,"xLinkHref":3154},"#MJX-33-TEX-I-1D43D",[1024,3156,3157],{"dataMmlNode":1034,"transform":2901},[1036,3158],{"dataC":1038,"xLinkHref":3159},"#MJX-33-TEX-N-28",[1024,3161,3162],{"dataMmlNode":1282,"transform":2907},[1036,3163],{"dataC":1767,"xLinkHref":3164},"#MJX-33-TEX-I-1D703",[1024,3166,3167],{"dataMmlNode":1034,"transform":2912},[1036,3168],{"dataC":1074,"xLinkHref":3169},"#MJX-33-TEX-N-29",[1024,3171,3173,3177],{"dataMmlNode":2885,"transform":3172},"translate(586.5,-345.6) scale(0.707)",[1024,3174,3175],{"dataMmlNode":1282},[1036,3176],{"dataC":2891,"xLinkHref":3149},[1024,3178,3179,3183],{"dataMmlNode":1761,"transform":2895},[1024,3180,3181],{"dataMmlNode":1282},[1036,3182],{"dataC":1767,"xLinkHref":3164},[1024,3184,3185],{"dataMmlNode":1282,"transform":1771},[1036,3186],{"dataC":2838,"xLinkHref":3187},"#MJX-33-TEX-I-1D457",[2010,3189],{"width":3190,"height":2013,"x":2014,"y":2015},1929.6," （腳底下的坡度）",[77,3193,3194,3197],{},[19,3195,3196],{},"這坨看起來最可怕的符號叫「偏導數」(Partial Derivative)。別管微積分了，它的白話文就叫作「坡度（slope）」。",[19,3198,3199],{},"它代表你現在腳踩的地方「有多陡」以及「哪邊是上坡」。如果山坡很陡，這個算出來的數字就很大；如果很平緩，數字就很小。",[2963,3201,3203,3204,3225],{"id":3202},"_3-減號我們要往下坡走","3. 減號 ",[967,3205,3207],{"className":3206,"jax":971},[970],[973,3208,3211,3216],{"style":3005,"xmlns":976,"width":3209,"height":3006,"role":979,"focusable":980,"viewBox":3210,"xmlnsXLink":982},"1.76ex","0 -583 778 665",[984,3212,3213],{},[987,3214],{"id":3215,"d":1955},"MJX-34-TEX-N-2212",[1024,3217,3218],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3219,3220],{"dataMmlNode":1031},[1024,3221,3222],{"dataMmlNode":1034},[1036,3223],{"dataC":2081,"xLinkHref":3224},"#MJX-34-TEX-N-2212"," （我們要往下坡走）",[77,3227,3228],{},[19,3229,3230,3231,3234],{},"剛剛說偏導數算出來的是「上坡」的方向。但我們的目標是走到谷底（減少誤差），所以我們必須在公式裡加一個",[773,3232,3233],{},"減號","，強迫機器**「反著坡度走，往下坡前進」**。",[2963,3236,3238],{"id":3237},"_4αalpha步伐大小","4. α (Alpha，步伐大小)",[77,3240,3241,3270],{},[19,3242,3243,3244,3265,3266,3269],{},"這個 ",[967,3245,3247],{"className":3246,"jax":971},[970],[973,3248,3251,3256],{"style":1253,"xmlns":976,"width":3249,"height":1514,"role":979,"focusable":980,"viewBox":3250,"xmlnsXLink":982},"1.448ex","0 -442 640 453",[984,3252,3253],{},[987,3254],{"id":3255,"d":2809},"MJX-35-TEX-I-1D6FC",[1024,3257,3258],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3259,3260],{"dataMmlNode":1031},[1024,3261,3262],{"dataMmlNode":1282},[1036,3263],{"dataC":2878,"xLinkHref":3264},"#MJX-35-TEX-I-1D6FC"," 叫作",[773,3267,3268],{},"學習率 (Learning Rate)","。在下山的故事裡，它就是你的**「步伐大小」**。",[19,3271,3272,3273],{},"機器在下山時，步伐不能亂踩。",[77,3274,3275,3301],{},[19,3276,3277,3300],{},[773,3278,3279,3280,3299],{},"如果 ",[967,3281,3283],{"className":3282,"jax":971},[970],[973,3284,3285,3290],{"style":1253,"xmlns":976,"width":3249,"height":1514,"role":979,"focusable":980,"viewBox":3250,"xmlnsXLink":982},[984,3286,3287],{},[987,3288],{"id":3289,"d":2809},"MJX-36-TEX-I-1D6FC",[1024,3291,3292],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3293,3294],{"dataMmlNode":1031},[1024,3295,3296],{"dataMmlNode":1282},[1036,3297],{"dataC":2878,"xLinkHref":3298},"#MJX-36-TEX-I-1D6FC","太大："," 你的步伐太大，可能會一腳從山谷左邊直接跨到山谷右邊，甚至越爬越高，永遠找不到最低點。",[19,3302,3303,3325],{},[773,3304,3279,3305,3324],{},[967,3306,3308],{"className":3307,"jax":971},[970],[973,3309,3310,3315],{"style":1253,"xmlns":976,"width":3249,"height":1514,"role":979,"focusable":980,"viewBox":3250,"xmlnsXLink":982},[984,3311,3312],{},[987,3313],{"id":3314,"d":2809},"MJX-37-TEX-I-1D6FC",[1024,3316,3317],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3318,3319],{"dataMmlNode":1031},[1024,3320,3321],{"dataMmlNode":1282},[1036,3322],{"dataC":2878,"xLinkHref":3323},"#MJX-37-TEX-I-1D6FC"," 太小："," 你用螞蟻的步伐下山，雖然很安全，但機器會算到天荒地老才走到谷底。",[12,3327,3328],{},"所以公式，翻譯過來大概是：",[12,3330,3331],{},"新的位置 := 舊的位置 - ( 步伐大小 × 腳底下的陡峭程度 )",[12,3333,3334,3335,3354,3355,3358],{},"這裡的 ",[967,3336,3338],{"className":3337,"jax":971},[970],[973,3339,3340,3345],{"style":1253,"xmlns":976,"width":3249,"height":1514,"role":979,"focusable":980,"viewBox":3250,"xmlnsXLink":982},[984,3341,3342],{},[987,3343],{"id":3344,"d":2809},"MJX-38-TEX-I-1D6FC",[1024,3346,3347],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,3348,3349],{"dataMmlNode":1031},[1024,3350,3351],{"dataMmlNode":1282},[1036,3352],{"dataC":2878,"xLinkHref":3353},"#MJX-38-TEX-I-1D6FC"," 是",[773,3356,3357],{},"學習率 (learning rate)","——它控制了你每次踏出的步伐有多大。步伐太大會衝過頭；太小又會走得很慢，收斂超級久。",[12,3360,3361],{},"把偏導數 (partial derivative) 展開，",[12,3363,3364],{},[979,3365],{"alt":1236,"src":3366},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775986283712-Screenshot_2026-04-12_at_5.30.47_PM.png",[12,3368,3369],{},"更新規則會變成：",[967,3371,3373],{"className":3372,"jax":971,"display":1689},[970],[973,3374,3379,3420],{"style":3375,"xmlns":976,"width":3376,"height":3377,"role":979,"focusable":980,"viewBox":3378,"xmlnsXLink":982},"vertical-align: -0.991ex;","28.915ex","3.391ex","0 -1060.7 12780.3 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這個特徵的「存在感」：",[967,4028,4030],{"className":4029,"jax":971},[970],[973,4031,4033,4050],{"style":3375,"xmlns":976,"width":1254,"height":3377,"role":979,"focusable":980,"viewBox":4032,"xmlnsXLink":982},"0 -1060.7 1449.1 1498.8",[984,4034,4035,4038,4041,4044,4047],{},[987,4036],{"id":4037,"d":1262},"MJX-45-TEX-I-1D465",[987,4039],{"id":4040,"d":990},"MJX-45-TEX-N-28",[987,4042],{"id":4043,"d":1269},"MJX-45-TEX-I-1D456",[987,4045],{"id":4046,"d":1010},"MJX-45-TEX-N-29",[987,4048],{"id":4049,"d":2795},"MJX-45-TEX-I-1D457",[1024,4051,4052],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4053,4054],{"dataMmlNode":1031},[1024,4055,4056,4061,4078],{"dataMmlNode":3548},[1024,4057,4058],{"dataMmlNode":1282},[1036,4059],{"dataC":1285,"xLinkHref":4060},"#MJX-45-TEX-I-1D465",[1024,4062,4063,4068,4073],{"dataMmlNode":1078,"transform":3556,"dataMjxTexclass":1079},[1024,4064,4065],{"dataMmlNode":1034},[1036,4066],{"dataC":1038,"xLinkHref":4067},"#MJX-45-TEX-N-28",[1024,4069,4070],{"dataMmlNode":1282,"transform":1043},[1036,4071],{"dataC":1299,"xLinkHref":4072},"#MJX-45-TEX-I-1D456",[1024,4074,4075],{"dataMmlNode":1034,"transform":1303},[1036,4076],{"dataC":1074,"xLinkHref":4077},"#MJX-45-TEX-N-29",[1024,4079,4080],{"dataMmlNode":1282,"transform":3571},[1036,4081],{"dataC":2838,"xLinkHref":4082},"#MJX-45-TEX-I-1D457",[12,4084,4085,4086,4141],{},"為什麼最後還要乘上一個 ",[967,4087,4089],{"className":4088,"jax":971},[970],[973,4090,4091,4108],{"style":3375,"xmlns":976,"width":1254,"height":3377,"role":979,"focusable":980,"viewBox":4032,"xmlnsXLink":982},[984,4092,4093,4096,4099,4102,4105],{},[987,4094],{"id":4095,"d":1262},"MJX-46-TEX-I-1D465",[987,4097],{"id":4098,"d":990},"MJX-46-TEX-N-28",[987,4100],{"id":4101,"d":1269},"MJX-46-TEX-I-1D456",[987,4103],{"id":4104,"d":1010},"MJX-46-TEX-N-29",[987,4106],{"id":4107,"d":2795},"MJX-46-TEX-I-1D457",[1024,4109,4110],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4111,4112],{"dataMmlNode":1031},[1024,4113,4114,4119,4136],{"dataMmlNode":3548},[1024,4115,4116],{"dataMmlNode":1282},[1036,4117],{"dataC":1285,"xLinkHref":4118},"#MJX-46-TEX-I-1D465",[1024,4120,4121,4126,4131],{"dataMmlNode":1078,"transform":3556,"dataMjxTexclass":1079},[1024,4122,4123],{"dataMmlNode":1034},[1036,4124],{"dataC":1038,"xLinkHref":4125},"#MJX-46-TEX-N-28",[1024,4127,4128],{"dataMmlNode":1282,"transform":1043},[1036,4129],{"dataC":1299,"xLinkHref":4130},"#MJX-46-TEX-I-1D456",[1024,4132,4133],{"dataMmlNode":1034,"transform":1303},[1036,4134],{"dataC":1074,"xLinkHref":4135},"#MJX-46-TEX-N-29",[1024,4137,4138],{"dataMmlNode":1282,"transform":3571},[1036,4139],{"dataC":2838,"xLinkHref":4140},"#MJX-46-TEX-I-1D457","​（例如這間房子的實際面積）呢？這是在計算「責任歸屬」。 想像一下，你今天預測房價大翻車，總得找個特徵來怪罪並調整吧？",[77,4143,4144,4170],{},[19,4145,4146,4147,4166,4167,1108],{},"如果這間房子的面積超大（x 數值很大），那它對這次錯誤預測的「責任」就很大。乘上這個大數字後，面積的權重 (",[967,4148,4150],{"className":4149,"jax":971},[970],[973,4151,4152,4157],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},[984,4153,4154],{},[987,4155],{"id":4156,"d":1714},"MJX-47-TEX-I-1D703",[1024,4158,4159],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4160,4161],{"dataMmlNode":1031},[1024,4162,4163],{"dataMmlNode":1282},[1036,4164],{"dataC":1767,"xLinkHref":4165},"#MJX-47-TEX-I-1D703",") 就會被",[773,4168,4169],{},"大幅度地調整",[19,4171,4172],{},"相反地，如果今天這間房子根本沒有游泳池（游泳池數量 x=0），那房價算錯關游泳池什麼事？乘上 0 之後，游泳池的權重就不會被調整。",[12,4174,4175,4176,4195],{},"也就是，我要更新這個條件的重要性 (",[967,4177,4179],{"className":4178,"jax":971},[970],[973,4180,4181,4186],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},[984,4182,4183],{},[987,4184],{"id":4185,"d":1714},"MJX-48-TEX-I-1D703",[1024,4187,4188],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4189,4190],{"dataMmlNode":1031},[1024,4191,4192],{"dataMmlNode":1282},[1036,4193],{"dataC":1767,"xLinkHref":4194},"#MJX-48-TEX-I-1D703",")。更新的幅度，取決於我這次『猜錯了多少錢』，再乘上這間房子『這個條件本身的數值有多大』。",[12,4197,4198,4199,4202],{},"這就是 ",[773,4200,4201],{},"LMS (Least Mean Squares) 更新規則","，也叫作 Widrow-Hoff 學習規則。注意看一個細節：更新的幅度跟誤差是成正比的。當預測值很接近實際值時，調整的幅度就會很微小；當誤差很大的時候，調整的幅度就會很大。",[781,4204,4206],{"id":4205},"批量-batch-vs-隨機-stochastic-梯度下降","批量 (Batch) vs 隨機 (Stochastic) 梯度下降",[12,4208,4209,4212,4213,4216],{},[773,4210,4211],{},"批量梯度下降 (Batch Gradient Descent)"," 會在做單次更新前，把",[773,4214,4215],{},"所有","訓練樣本的梯度加總起來。它很精準，但遇到大資料集的時候會跑得非常慢。",[12,4218,4219],{},[979,4220],{"alt":1236,"src":4221},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775987318720-Screenshot_2026-04-12_at_5.47.44_PM.png",[12,4223,4224,4227,4228,4231,4232,4251],{},[773,4225,4226],{},"隨機\u002F增量梯度下降 (Stochastic \u002F Incremental Gradient Descent)"," 則是每看完",[773,4229,4230],{},"一筆","訓練樣本就立刻更新一次 ",[967,4233,4235],{"className":4234,"jax":971},[970],[973,4236,4237,4242],{"style":1849,"xmlns":976,"width":1850,"height":1851,"role":979,"focusable":980,"viewBox":1852,"xmlnsXLink":982},[984,4238,4239],{},[987,4240],{"id":4241,"d":1714},"MJX-49-TEX-I-1D703",[1024,4243,4244],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4245,4246],{"dataMmlNode":1031},[1024,4247,4248],{"dataMmlNode":1282},[1036,4249],{"dataC":1767,"xLinkHref":4250},"#MJX-49-TEX-I-1D703","。它的速度快很多，在實務上通常效果也不錯，雖然走向收斂的路徑會比較曲折、充滿雜訊。",[12,4253,4254],{},[979,4255],{"alt":1236,"src":4256},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775987315179-Screenshot_2026-04-12_at_5.47.53_PM.png",[781,4258,4260],{"id":4259},"欠擬合-underfitting-vs-過擬合-overfitting","欠擬合 (Underfitting) vs 過擬合 (Overfitting)",[12,4262,4263],{},[979,4264],{"alt":1236,"src":4265},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775987112930-Screenshot_2026-04-12_at_5.44.51_PM.png",[12,4267,4268],{},"這是機器學習裡最重要的概念之一！想像一下用不同的模型來擬合我們的房價資料：",[77,4270,4271,4281,4287],{},[19,4272,4273,4274,4277,4278,1108],{},"一條",[773,4275,4276],{},"直線"," (線性擬合) 可能太簡單了——它抓不到資料的真實弧度。這叫做",[773,4279,4280],{},"欠擬合 (underfitting)",[19,4282,4283,4286],{},[773,4284,4285],{},"二次方程式"," (加上 x2) 擬合得比較好，抓到了更多結構。",[19,4288,4289,4292,4293,1108],{},[773,4290,4291],{},"五次方多項式"," 可以完美穿過每一個訓練資料點——但如果拿它來預測新房子的價格，結果一定會慘不忍睹。這叫做",[773,4294,4295],{},"過擬合 (overfitting)",[12,4297,4298,4299,4302],{},"一個只會死背訓練資料的模型，不一定是個好模型。我們要的是能對未知的新資料做出準確預測（具備",[773,4300,4301],{},"泛化能力 generalization","）的模型。",[781,4304,4306],{"id":4305},"局部加權線性迴歸-locally-weighted-linear-regression","局部加權線性迴歸 (Locally Weighted Linear Regression)",[12,4308,4309,4310,4313],{},"一般的線性迴歸是用一條全域的線來擬合所有資料。",[773,4311,4312],{},"局部加權線性迴歸 (LWLR)"," 換了個思路：在做每次預測時，它會給附近的訓練點比較大的權重，離得遠的點權重就給得比較小。",[12,4315,4316],{},"每個訓練樣本的權重通常會用高斯函數來算：",[12,4318,4319],{},[967,4320,4322],{"className":4321,"jax":971},[970],[973,4323,4328,4382],{"style":4324,"xmlns":976,"width":4325,"height":4326,"role":979,"focusable":980,"viewBox":4327,"xmlnsXLink":982},"vertical-align: -1.469ex;","22.333ex","4.07ex","0 -1149.5 9871.4 1799",[984,4329,4330,4334,4337,4340,4343,4346,4350,4354,4358,4361,4365,4368,4371,4374,4378],{},[987,4331],{"id":4332,"d":4333},"MJX-50-TEX-I-1D464","M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z",[987,4335],{"id":4336,"d":990},"MJX-50-TEX-N-28",[987,4338],{"id":4339,"d":1269},"MJX-50-TEX-I-1D456",[987,4341],{"id":4342,"d":1010},"MJX-50-TEX-N-29",[987,4344],{"id":4345,"d":1018},"MJX-50-TEX-N-3D",[987,4347],{"id":4348,"d":4349},"MJX-50-TEX-N-65","M28 218Q28 273 48 318T98 391T163 433T229 448Q282 448 320 430T378 380T406 316T415 245Q415 238 408 231H126V216Q126 68 226 36Q246 30 270 30Q312 30 342 62Q359 79 369 104L379 128Q382 131 395 131H398Q415 131 415 121Q415 117 412 108Q393 53 349 21T250 -11Q155 -11 92 58T28 218ZM333 275Q322 403 238 411H236Q228 411 220 410T195 402T166 381T143 340T127 274V267H333V275Z",[987,4351],{"id":4352,"d":4353},"MJX-50-TEX-N-78","M201 0Q189 3 102 3Q26 3 17 0H11V46H25Q48 47 67 52T96 61T121 78T139 96T160 122T180 150L226 210L168 288Q159 301 149 315T133 336T122 351T113 363T107 370T100 376T94 379T88 381T80 383Q74 383 44 385H16V431H23Q59 429 126 429Q219 429 229 431H237V385Q201 381 201 369Q201 367 211 353T239 315T268 274L272 270L297 304Q329 345 329 358Q329 364 327 369T322 376T317 380T310 384L307 385H302V431H309Q324 428 408 428Q487 428 493 431H499V385H492Q443 385 411 368Q394 360 377 341T312 257L296 236L358 151Q424 61 429 57T446 50Q464 46 499 46H516V0H510H502Q494 1 482 1T457 2T432 2T414 3Q403 3 377 3T327 1L304 0H295V46H298Q309 46 320 51T331 63Q331 65 291 120L250 175Q249 174 219 133T185 88Q181 83 181 74Q181 63 188 55T206 46Q208 46 208 23V0H201Z",[987,4355],{"id":4356,"d":4357},"MJX-50-TEX-N-70","M36 -148H50Q89 -148 97 -134V-126Q97 -119 97 -107T97 -77T98 -38T98 6T98 55T98 106Q98 140 98 177T98 243T98 296T97 335T97 351Q94 370 83 376T38 385H20V408Q20 431 22 431L32 432Q42 433 61 434T98 436Q115 437 135 438T165 441T176 442H179V416L180 390L188 397Q247 441 326 441Q407 441 464 377T522 216Q522 115 457 52T310 -11Q242 -11 190 33L182 40V-45V-101Q182 -128 184 -134T195 -145Q216 -148 244 -148H260V-194H252L228 -193Q205 -192 178 -192T140 -191Q37 -191 28 -194H20V-148H36ZM424 218Q424 292 390 347T305 402Q234 402 182 337V98Q222 26 294 26Q345 26 384 80T424 218Z",[987,4359],{"id":4360,"d":169},"MJX-50-TEX-N-2061",[987,4362],{"id":4363,"d":4364},"MJX-50-TEX-LO-28","M180 96T180 250T205 541T266 770T353 944T444 1069T527 1150H555Q561 1144 561 1141Q561 1137 545 1120T504 1072T447 995T386 878T330 721T288 513T272 251Q272 133 280 56Q293 -87 326 -209T399 -405T475 -531T536 -609T561 -640Q561 -643 555 -649H527Q483 -612 443 -568T353 -443T266 -270T205 -41Z",[987,4366],{"id":4367,"d":1955},"MJX-50-TEX-N-2212",[987,4369],{"id":4370,"d":1262},"MJX-50-TEX-I-1D465",[987,4372],{"id":4373,"d":994},"MJX-50-TEX-N-32",[987,4375],{"id":4376,"d":4377},"MJX-50-TEX-I-1D70F","M39 284Q18 284 18 294Q18 301 45 338T99 398Q134 425 164 429Q170 431 332 431Q492 431 497 429Q517 424 517 402Q517 388 508 376T485 360Q479 358 389 358T299 356Q298 355 283 274T251 109T233 20Q228 5 215 -4T186 -13Q153 -13 153 20V30L203 192Q214 228 227 272T248 336L254 357Q254 358 208 358Q206 358 197 358T183 359Q105 359 61 295Q56 287 53 286T39 284Z",[987,4379],{"id":4380,"d":4381},"MJX-50-TEX-LO-29","M35 1138Q35 1150 51 1150H56H69Q113 1113 153 1069T243 944T330 771T391 541T416 250T391 -40T330 -270T243 -443T152 -568T69 -649H56Q43 -649 39 -647T35 -637Q65 -607 110 -548Q283 -316 316 56Q324 133 324 251Q324 368 316 445Q278 877 48 1123Q36 1137 35 1138Z",[1024,4383,4384],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4385,4386,4412,4418,4435,4442],{"dataMmlNode":1031},[1024,4387,4388,4394],{"dataMmlNode":1279},[1024,4389,4390],{"dataMmlNode":1282},[1036,4391],{"dataC":4392,"xLinkHref":4393},"1D464","#MJX-50-TEX-I-1D464",[1024,4395,4397,4402,4407],{"dataMmlNode":1078,"transform":4396,"dataMjxTexclass":1079},"translate(749,363) scale(0.707)",[1024,4398,4399],{"dataMmlNode":1034},[1036,4400],{"dataC":1038,"xLinkHref":4401},"#MJX-50-TEX-N-28",[1024,4403,4404],{"dataMmlNode":1282,"transform":1043},[1036,4405],{"dataC":1299,"xLinkHref":4406},"#MJX-50-TEX-I-1D456",[1024,4408,4409],{"dataMmlNode":1034,"transform":1303},[1036,4410],{"dataC":1074,"xLinkHref":4411},"#MJX-50-TEX-N-29",[1024,4413,4415],{"dataMmlNode":1034,"transform":4414},"translate(1870.9,0)",[1036,4416],{"dataC":1097,"xLinkHref":4417},"#MJX-50-TEX-N-3D",[1024,4419,4421,4425,4430],{"dataMmlNode":1282,"transform":4420},"translate(2926.6,0)",[1036,4422],{"dataC":4423,"xLinkHref":4424},"65","#MJX-50-TEX-N-65",[1036,4426],{"dataC":4427,"xLinkHref":4428,"transform":4429},"78","#MJX-50-TEX-N-78","translate(444,0)",[1036,4431],{"dataC":4432,"xLinkHref":4433,"transform":4434},"70","#MJX-50-TEX-N-70","translate(972,0)",[1024,4436,4438],{"dataMmlNode":1034,"transform":4437},"translate(4454.6,0)",[1036,4439],{"dataC":4440,"xLinkHref":4441},"2061","#MJX-50-TEX-N-2061",[1024,4443,4445,4451,4457,4531],{"dataMmlNode":2885,"transform":4444},"translate(4621.3,0)",[1024,4446,4448],{"dataMmlNode":1034,"transform":4447},"translate(0 -0.5)",[1036,4449],{"dataC":1038,"xLinkHref":4450},"#MJX-50-TEX-LO-28",[1024,4452,4454],{"dataMmlNode":1034,"transform":4453},"translate(597,0)",[1036,4455],{"dataC":2081,"xLinkHref":4456},"#MJX-50-TEX-N-2212",[1024,4458,4460,4508,4528],{"dataMmlNode":1995,"transform":4459},"translate(1375,0)",[1024,4461,4462,4466,4487,4491,4496],{"dataMmlNode":2885,"transform":3144},[1024,4463,4464],{"dataMmlNode":1034},[1036,4465],{"dataC":1038,"xLinkHref":4401},[1024,4467,4468,4473],{"dataMmlNode":1279,"transform":1043},[1024,4469,4470],{"dataMmlNode":1282},[1036,4471],{"dataC":1285,"xLinkHref":4472},"#MJX-50-TEX-I-1D465",[1024,4474,4475,4479,4483],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,4476,4477],{"dataMmlNode":1034},[1036,4478],{"dataC":1038,"xLinkHref":4401},[1024,4480,4481],{"dataMmlNode":1282,"transform":1043},[1036,4482],{"dataC":1299,"xLinkHref":4406},[1024,4484,4485],{"dataMmlNode":1034,"transform":1303},[1036,4486],{"dataC":1074,"xLinkHref":4411},[1024,4488,4489],{"dataMmlNode":1034,"transform":1473},[1036,4490],{"dataC":2081,"xLinkHref":4456},[1024,4492,4494],{"dataMmlNode":1282,"transform":4493},"translate(2616.1,0)",[1036,4495],{"dataC":1285,"xLinkHref":4472},[1024,4497,4499,4503],{"dataMmlNode":1279,"transform":4498},"translate(3188.1,0)",[1024,4500,4501],{"dataMmlNode":1034},[1036,4502],{"dataC":1074,"xLinkHref":4411},[1024,4504,4505],{"dataMmlNode":1042,"transform":2419},[1036,4506],{"dataC":1046,"xLinkHref":4507},"#MJX-50-TEX-N-32",[1024,4509,4511,4515],{"dataMmlNode":2885,"transform":4510},"translate(1106,-377.4) scale(0.707)",[1024,4512,4513],{"dataMmlNode":1042},[1036,4514],{"dataC":1046,"xLinkHref":4507},[1024,4516,4517,4523],{"dataMmlNode":1279,"transform":1052},[1024,4518,4519],{"dataMmlNode":1282},[1036,4520],{"dataC":4521,"xLinkHref":4522},"1D70F","#MJX-50-TEX-I-1D70F",[1024,4524,4526],{"dataMmlNode":1042,"transform":4525},"translate(604,289) scale(0.707)",[1036,4527],{"dataC":1046,"xLinkHref":4507},[2010,4529],{"width":4530,"height":2013,"x":2014,"y":2015},3038.1,[1024,4532,4534],{"dataMmlNode":1034,"transform":4533},"translate(4653.1,0) translate(0 -0.5)",[1036,4535],{"dataC":1074,"xLinkHref":4536},"#MJX-50-TEX-LO-29",[822,4538,4540,4542],{"className":4539},[825,826],[828,4541,2123],{},[832,4543,4545,4548,4558,4643,4709,4747,4752,4808,4814,4840,4862,4914,4918,4925],{"className":4544},[835],[12,4546,4547],{},"這個應該不在考試範圍裡面，看個大概就行。",[12,4549,4550,4553,4554,4557],{},[773,4551,4552],{},"LWLR 就像是找了一個深耕當地的「資深房仲」","。當你要賣一間 30 坪的房子時，這位房仲不會管那些 100 坪的豪宅賣多少錢，他",[773,4555,4556],{},"只會特別去查「附近同樣也是 28 到 32 坪左右」的房子成交價","，用這些極度相似的房子來幫你估價。",[12,4559,4560,4561],{},"「差異程度」或「距離」：",[967,4562,4564],{"className":4563,"jax":971},[970],[973,4565,4568,4588],{"style":975,"xmlns":976,"width":4566,"height":1416,"role":979,"focusable":980,"viewBox":4567,"xmlnsXLink":982},"10.086ex","0 -893.3 4458.1 1143.3",[984,4569,4570,4573,4576,4579,4582,4585],{},[987,4571],{"id":4572,"d":990},"MJX-51-TEX-N-28",[987,4574],{"id":4575,"d":1262},"MJX-51-TEX-I-1D465",[987,4577],{"id":4578,"d":1269},"MJX-51-TEX-I-1D456",[987,4580],{"id":4581,"d":1010},"MJX-51-TEX-N-29",[987,4583],{"id":4584,"d":1955},"MJX-51-TEX-N-2212",[987,4586],{"id":4587,"d":994},"MJX-51-TEX-N-32",[1024,4589,4590],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4591,4592,4597,4620,4626,4631],{"dataMmlNode":1031},[1024,4593,4594],{"dataMmlNode":1034},[1036,4595],{"dataC":1038,"xLinkHref":4596},"#MJX-51-TEX-N-28",[1024,4598,4599,4604],{"dataMmlNode":1279,"transform":1043},[1024,4600,4601],{"dataMmlNode":1282},[1036,4602],{"dataC":1285,"xLinkHref":4603},"#MJX-51-TEX-I-1D465",[1024,4605,4606,4610,4615],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,4607,4608],{"dataMmlNode":1034},[1036,4609],{"dataC":1038,"xLinkHref":4596},[1024,4611,4612],{"dataMmlNode":1282,"transform":1043},[1036,4613],{"dataC":1299,"xLinkHref":4614},"#MJX-51-TEX-I-1D456",[1024,4616,4617],{"dataMmlNode":1034,"transform":1303},[1036,4618],{"dataC":1074,"xLinkHref":4619},"#MJX-51-TEX-N-29",[1024,4621,4623],{"dataMmlNode":1034,"transform":4622},"translate(2060.3,0)",[1036,4624],{"dataC":2081,"xLinkHref":4625},"#MJX-51-TEX-N-2212",[1024,4627,4629],{"dataMmlNode":1282,"transform":4628},"translate(3060.5,0)",[1036,4630],{"dataC":1285,"xLinkHref":4603},[1024,4632,4634,4638],{"dataMmlNode":1279,"transform":4633},"translate(3632.5,0)",[1024,4635,4636],{"dataMmlNode":1034},[1036,4637],{"dataC":1074,"xLinkHref":4619},[1024,4639,4640],{"dataMmlNode":1042,"transform":2419},[1036,4641],{"dataC":1046,"xLinkHref":4642},"#MJX-51-TEX-N-32",[77,4644,4645,4652,4706],{},[19,4646,4647,4648,4651],{},"x 是你",[773,4649,4650],{},"現在想估價","的房子（例如：30坪）。",[19,4653,4654,4701,4702,4705],{},[967,4655,4657],{"className":4656,"jax":971},[970],[973,4658,4659,4673],{"style":1253,"xmlns":976,"width":1254,"height":1255,"role":979,"focusable":980,"viewBox":1256,"xmlnsXLink":982},[984,4660,4661,4664,4667,4670],{},[987,4662],{"id":4663,"d":1262},"MJX-52-TEX-I-1D465",[987,4665],{"id":4666,"d":990},"MJX-52-TEX-N-28",[987,4668],{"id":4669,"d":1269},"MJX-52-TEX-I-1D456",[987,4671],{"id":4672,"d":1010},"MJX-52-TEX-N-29",[1024,4674,4675],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4676,4677],{"dataMmlNode":1031},[1024,4678,4679,4684],{"dataMmlNode":1279},[1024,4680,4681],{"dataMmlNode":1282},[1036,4682],{"dataC":1285,"xLinkHref":4683},"#MJX-52-TEX-I-1D465",[1024,4685,4686,4691,4696],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,4687,4688],{"dataMmlNode":1034},[1036,4689],{"dataC":1038,"xLinkHref":4690},"#MJX-52-TEX-N-28",[1024,4692,4693],{"dataMmlNode":1282,"transform":1043},[1036,4694],{"dataC":1299,"xLinkHref":4695},"#MJX-52-TEX-I-1D456",[1024,4697,4698],{"dataMmlNode":1034,"transform":1303},[1036,4699],{"dataC":1074,"xLinkHref":4700},"#MJX-52-TEX-N-29"," 是資料庫裡的",[773,4703,4704],{},"歷史成交房子","（例如：一間 80 坪的房子）。",[19,4707,4708],{},"把它們相減再平方，算出來的就是這兩間房子的「差距有多大」。差距越大，這個數字就越大。",[12,4710,4711,4746],{},[967,4712,4714],{"className":4713,"jax":971},[970],[973,4715,4720,4731],{"style":4716,"xmlns":976,"width":4717,"height":4718,"role":979,"focusable":980,"viewBox":4719,"xmlnsXLink":982},"vertical-align: -0.439ex;","3.457ex","1.452ex","0 -448 1528 642",[984,4721,4722,4725,4728],{},[987,4723],{"id":4724,"d":4349},"MJX-53-TEX-N-65",[987,4726],{"id":4727,"d":4353},"MJX-53-TEX-N-78",[987,4729],{"id":4730,"d":4357},"MJX-53-TEX-N-70",[1024,4732,4733],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4734,4735],{"dataMmlNode":1031},[1024,4736,4737,4740,4743],{"dataMmlNode":1282},[1036,4738],{"dataC":4423,"xLinkHref":4739},"#MJX-53-TEX-N-65",[1036,4741],{"dataC":4427,"xLinkHref":4742,"transform":4429},"#MJX-53-TEX-N-78",[1036,4744],{"dataC":4432,"xLinkHref":4745,"transform":4434},"#MJX-53-TEX-N-70"," 是指數函數（Exponential），配合前面的負號，它畫出來會是一個中間高、兩邊低的「鐘型曲線」或稱高斯曲線。",[12,4748,4749],{},[979,4750],{"alt":1236,"src":4751},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775988429324-0_9POrHcDjgD6eXS-f.webp",[12,4753,4754,4757,4758,4807],{},[773,4755,4756],{},"如果兩間房子很像（距離近）："," 算出來的權重 ",[967,4759,4761],{"className":4760,"jax":971},[970],[973,4762,4765,4779],{"style":1253,"xmlns":976,"width":4763,"height":1255,"role":979,"focusable":980,"viewBox":4764,"xmlnsXLink":982},"3.604ex","0 -893.3 1593.1 904.3",[984,4766,4767,4770,4773,4776],{},[987,4768],{"id":4769,"d":4333},"MJX-54-TEX-I-1D464",[987,4771],{"id":4772,"d":990},"MJX-54-TEX-N-28",[987,4774],{"id":4775,"d":1269},"MJX-54-TEX-I-1D456",[987,4777],{"id":4778,"d":1010},"MJX-54-TEX-N-29",[1024,4780,4781],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4782,4783],{"dataMmlNode":1031},[1024,4784,4785,4790],{"dataMmlNode":1279},[1024,4786,4787],{"dataMmlNode":1282},[1036,4788],{"dataC":4392,"xLinkHref":4789},"#MJX-54-TEX-I-1D464",[1024,4791,4792,4797,4802],{"dataMmlNode":1078,"transform":4396,"dataMjxTexclass":1079},[1024,4793,4794],{"dataMmlNode":1034},[1036,4795],{"dataC":1038,"xLinkHref":4796},"#MJX-54-TEX-N-28",[1024,4798,4799],{"dataMmlNode":1282,"transform":1043},[1036,4800],{"dataC":1299,"xLinkHref":4801},"#MJX-54-TEX-I-1D456",[1024,4803,4804],{"dataMmlNode":1034,"transform":1303},[1036,4805],{"dataC":1074,"xLinkHref":4806},"#MJX-54-TEX-N-29"," 會非常接近 1（代表重要，必須強烈參考）。",[12,4809,4810,4813],{},[773,4811,4812],{},"如果兩間房子差十萬八千里（距離遠）："," 這個函數會讓權重「墜崖式」地急速暴跌到趨近於 0。這等於房仲在說：「那間 80 坪的豪宅對我們這間 30 坪的估價毫無參考價值，直接忽略！」",[12,4815,4816,4817],{},"「參考範圍」的大小：",[967,4818,4820],{"className":4819,"jax":971},[970],[973,4821,4826,4831],{"style":4822,"xmlns":976,"width":4823,"height":4824,"role":979,"focusable":980,"viewBox":4825,"xmlnsXLink":982},"vertical-align: -0.029ex;","1.17ex","1.005ex","0 -431 517 444",[984,4827,4828],{},[987,4829],{"id":4830,"d":4377},"MJX-55-TEX-I-1D70F",[1024,4832,4833],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4834,4835],{"dataMmlNode":1031},[1024,4836,4837],{"dataMmlNode":1282},[1036,4838],{"dataC":4521,"xLinkHref":4839},"#MJX-55-TEX-I-1D70F",[12,4841,3243,4842,4861],{},[967,4843,4845],{"className":4844,"jax":971},[970],[973,4846,4847,4852],{"style":4822,"xmlns":976,"width":4823,"height":4824,"role":979,"focusable":980,"viewBox":4825,"xmlnsXLink":982},[984,4848,4849],{},[987,4850],{"id":4851,"d":4377},"MJX-56-TEX-I-1D70F",[1024,4853,4854],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4855,4856],{"dataMmlNode":1031},[1024,4857,4858],{"dataMmlNode":1282},[1036,4859],{"dataC":4521,"xLinkHref":4860},"#MJX-56-TEX-I-1D70F","是你可以自己設定的參數，它決定了房仲的「目光有多寬」。",[77,4863,4864,4889],{},[19,4865,4866,4888],{},[773,4867,3279,4868,4887],{},[967,4869,4871],{"className":4870,"jax":971},[970],[973,4872,4873,4878],{"style":4822,"xmlns":976,"width":4823,"height":4824,"role":979,"focusable":980,"viewBox":4825,"xmlnsXLink":982},[984,4874,4875],{},[987,4876],{"id":4877,"d":4377},"MJX-57-TEX-I-1D70F",[1024,4879,4880],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4881,4882],{"dataMmlNode":1031},[1024,4883,4884],{"dataMmlNode":1282},[1036,4885],{"dataC":4521,"xLinkHref":4886},"#MJX-57-TEX-I-1D70F"," 很大："," 鐘型曲線會很平緩。這代表房仲比較隨和，連 40 坪、50 坪的房子也會加減參考一下。",[19,4890,4891,4913],{},[773,4892,3279,4893,4912],{},[967,4894,4896],{"className":4895,"jax":971},[970],[973,4897,4898,4903],{"style":4822,"xmlns":976,"width":4823,"height":4824,"role":979,"focusable":980,"viewBox":4825,"xmlnsXLink":982},[984,4899,4900],{},[987,4901],{"id":4902,"d":4377},"MJX-58-TEX-I-1D70F",[1024,4904,4905],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4906,4907],{"dataMmlNode":1031},[1024,4908,4909],{"dataMmlNode":1282},[1036,4910],{"dataC":4521,"xLinkHref":4911},"#MJX-58-TEX-I-1D70F"," 很小："," 鐘型曲線會非常尖銳、極度狹窄。這代表房仲非常嚴格，只肯參考 29.5 坪到 30.5 坪的房子，只要差一點點，權重就直接給 0。",[781,4915,4917],{"id":4916},"什麼叫無母數-non-parametric","什麼叫「無母數 (non-parametric)」？",[12,4919,4920,4921,4924],{},"一般的線性迴歸，機器只要把 θ0​、θ1​、θ2​ 這三個參數學好，它就可以把那 47 間房子的歷史資料",[773,4922,4923],{},"全部刪掉","了，因為規律已經濃縮在那三個參數裡。",[12,4926,4927,4928,4931,4932,4935],{},"但 LWLR 是「無母數」的，這意味著它",[773,4929,4930],{},"沒有固定的公式參數","。它就像一個不記筆記、全靠臨時抱佛腳的學生。每次有人來問一間新房子的價格，它就必須",[773,4933,4934],{},"把那 47 間歷史資料全部拿出來重新比對一次、重新算一次附近的權重","。雖然計算量變大很多，但它的預測會比一條死板的直線靈活且準確非常多！",[12,4937,4938,4939,4958,4959,4962],{},"參數 ",[967,4940,4942],{"className":4941,"jax":971},[970],[973,4943,4944,4949],{"style":4822,"xmlns":976,"width":4823,"height":4824,"role":979,"focusable":980,"viewBox":4825,"xmlnsXLink":982},[984,4945,4946],{},[987,4947],{"id":4948,"d":4377},"MJX-59-TEX-I-1D70F",[1024,4950,4951],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4952,4953],{"dataMmlNode":1031},[1024,4954,4955],{"dataMmlNode":1282},[1036,4956],{"dataC":4521,"xLinkHref":4957},"#MJX-59-TEX-I-1D70F"," (tau) 決定了權重隨距離衰減的速度有多快。LWLR 是一種",[773,4960,4961],{},"無母數 (non-parametric)"," 的方法：它沒有一組固定的參數，而是每次有新的查詢點時，都要重新針對附近資料擬合一次。",[765,4964,4966],{"id":4965},"第三部分邏輯迴歸-logistic-regression-當輸出是離散值","第三部分：邏輯迴歸 (Logistic Regression) — 當輸出是離散值",[12,4968,4969,4970,4989,4990,5009,5010,5013],{},"前面講的都是建立在 ",[967,4971,4973],{"className":4972,"jax":971},[970],[973,4974,4975,4980],{"style":1338,"xmlns":976,"width":1661,"height":1662,"role":979,"focusable":980,"viewBox":1663,"xmlnsXLink":982},[984,4976,4977],{},[987,4978],{"id":4979,"d":1347},"MJX-60-TEX-I-1D466",[1024,4981,4982],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,4983,4984],{"dataMmlNode":1031},[1024,4985,4986],{"dataMmlNode":1282},[1036,4987],{"dataC":1367,"xLinkHref":4988},"#MJX-60-TEX-I-1D466","是連續數值的狀況。但如果 ",[967,4991,4993],{"className":4992,"jax":971},[970],[973,4994,4995,5000],{"style":1338,"xmlns":976,"width":1661,"height":1662,"role":979,"focusable":980,"viewBox":1663,"xmlnsXLink":982},[984,4996,4997],{},[987,4998],{"id":4999,"d":1347},"MJX-61-TEX-I-1D466",[1024,5001,5002],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5003,5004],{"dataMmlNode":1031},[1024,5005,5006],{"dataMmlNode":1282},[1036,5007],{"dataC":1367,"xLinkHref":5008},"#MJX-61-TEX-I-1D466"," 只能是 ",[773,5011,5012],{},"0 或 1"," 呢？（比如判斷垃圾郵件 vs 正常郵件，或是腫瘤是惡性 vs 良性）。",[12,5015,5016,5017,5020],{},"我們沒辦法用單純的線性函數，因為它有可能輸出小於 0 或大於 1 的值。所以，我們要把它包裝進 ",[773,5018,5019],{},"Sigmoid (邏輯) 函數","裡面：",[12,5022,5023],{},[967,5024,5026],{"className":5025,"jax":971},[970],[973,5027,5032,5076],{"style":5028,"xmlns":976,"width":5029,"height":5030,"role":979,"focusable":980,"viewBox":5031,"xmlnsXLink":982},"vertical-align: -1.324ex;","23.767ex","3.281ex","0 -864.9 10504.8 1450.3",[984,5033,5034,5037,5040,5043,5046,5049,5053,5056,5060,5063,5066,5070,5073],{},[987,5035],{"id":5036,"d":1547},"MJX-62-TEX-I-210E",[987,5038],{"id":5039,"d":990},"MJX-62-TEX-N-28",[987,5041],{"id":5042,"d":1262},"MJX-62-TEX-I-1D465",[987,5044],{"id":5045,"d":1010},"MJX-62-TEX-N-29",[987,5047],{"id":5048,"d":1018},"MJX-62-TEX-N-3D",[987,5050],{"id":5051,"d":5052},"MJX-62-TEX-I-1D454","M311 43Q296 30 267 15T206 0Q143 0 105 45T66 160Q66 265 143 353T314 442Q361 442 401 394L404 398Q406 401 409 404T418 412T431 419T447 422Q461 422 470 413T480 394Q480 379 423 152T363 -80Q345 -134 286 -169T151 -205Q10 -205 10 -137Q10 -111 28 -91T74 -71Q89 -71 102 -80T116 -111Q116 -121 114 -130T107 -144T99 -154T92 -162L90 -164H91Q101 -167 151 -167Q189 -167 211 -155Q234 -144 254 -122T282 -75Q288 -56 298 -13Q311 35 311 43ZM384 328L380 339Q377 350 375 354T369 368T359 382T346 393T328 402T306 405Q262 405 221 352Q191 313 171 233T151 117Q151 38 213 38Q269 38 323 108L331 118L384 328Z",[987,5054],{"id":5055,"d":1714},"MJX-62-TEX-I-1D703",[987,5057],{"id":5058,"d":5059},"MJX-62-TEX-I-1D447","M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z",[987,5061],{"id":5062,"d":1725},"MJX-62-TEX-N-31",[987,5064],{"id":5065,"d":1002},"MJX-62-TEX-N-2B",[987,5067],{"id":5068,"d":5069},"MJX-62-TEX-I-1D452","M39 168Q39 225 58 272T107 350T174 402T244 433T307 442H310Q355 442 388 420T421 355Q421 265 310 237Q261 224 176 223Q139 223 138 221Q138 219 132 186T125 128Q125 81 146 54T209 26T302 45T394 111Q403 121 406 121Q410 121 419 112T429 98T420 82T390 55T344 24T281 -1T205 -11Q126 -11 83 42T39 168ZM373 353Q367 405 305 405Q272 405 244 391T199 357T170 316T154 280T149 261Q149 260 169 260Q282 260 327 284T373 353Z",[987,5071],{"id":5072,"d":1955},"MJX-62-TEX-N-2212",[987,5074],{"id":5075,"d":169},"MJX-62-TEX-N-200B",[1024,5077,5078],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5079,5080,5085,5090,5095,5100,5105,5111,5116,5131,5136,5141,5146,5204],{"dataMmlNode":1031},[1024,5081,5082],{"dataMmlNode":1282},[1036,5083],{"dataC":1565,"xLinkHref":5084},"#MJX-62-TEX-I-210E",[1024,5086,5087],{"dataMmlNode":1034,"transform":1569},[1036,5088],{"dataC":1038,"xLinkHref":5089},"#MJX-62-TEX-N-28",[1024,5091,5092],{"dataMmlNode":1282,"transform":1575},[1036,5093],{"dataC":1285,"xLinkHref":5094},"#MJX-62-TEX-I-1D465",[1024,5096,5097],{"dataMmlNode":1034,"transform":1581},[1036,5098],{"dataC":1074,"xLinkHref":5099},"#MJX-62-TEX-N-29",[1024,5101,5102],{"dataMmlNode":1034,"transform":1755},[1036,5103],{"dataC":1097,"xLinkHref":5104},"#MJX-62-TEX-N-3D",[1024,5106,5107],{"dataMmlNode":1282,"transform":1762},[1036,5108],{"dataC":5109,"xLinkHref":5110},"1D454","#MJX-62-TEX-I-1D454",[1024,5112,5114],{"dataMmlNode":1034,"transform":5113},"translate(3736.6,0)",[1036,5115],{"dataC":1038,"xLinkHref":5089},[1024,5117,5119,5124],{"dataMmlNode":1279,"transform":5118},"translate(4125.6,0)",[1024,5120,5121],{"dataMmlNode":1282},[1036,5122],{"dataC":1767,"xLinkHref":5123},"#MJX-62-TEX-I-1D703",[1024,5125,5127],{"dataMmlNode":1282,"transform":5126},"translate(502,363) scale(0.707)",[1036,5128],{"dataC":5129,"xLinkHref":5130},"1D447","#MJX-62-TEX-I-1D447",[1024,5132,5134],{"dataMmlNode":1282,"transform":5133},"translate(5175.4,0)",[1036,5135],{"dataC":1285,"xLinkHref":5094},[1024,5137,5139],{"dataMmlNode":1034,"transform":5138},"translate(5747.4,0)",[1036,5140],{"dataC":1074,"xLinkHref":5099},[1024,5142,5144],{"dataMmlNode":1034,"transform":5143},"translate(6414.1,0)",[1036,5145],{"dataC":1097,"xLinkHref":5104},[1024,5147,5149,5155,5201],{"dataMmlNode":1995,"transform":5148},"translate(7469.9,0)",[1024,5150,5152],{"dataMmlNode":1042,"transform":5151},"translate(1340.7,394) scale(0.707)",[1036,5153],{"dataC":1793,"xLinkHref":5154},"#MJX-62-TEX-N-31",[1024,5156,5158,5162,5167],{"dataMmlNode":2885,"transform":5157},"translate(220,-527.4) scale(0.707)",[1024,5159,5160],{"dataMmlNode":1042},[1036,5161],{"dataC":1793,"xLinkHref":5154},[1024,5163,5164],{"dataMmlNode":1034,"transform":1052},[1036,5165],{"dataC":1058,"xLinkHref":5166},"#MJX-62-TEX-N-2B",[1024,5168,5170,5176],{"dataMmlNode":1279,"transform":5169},"translate(1278,0)",[1024,5171,5172],{"dataMmlNode":1282},[1036,5173],{"dataC":5174,"xLinkHref":5175},"1D452","#MJX-62-TEX-I-1D452",[1024,5177,5179,5184,5196],{"dataMmlNode":1078,"transform":5178,"dataMjxTexclass":1079},"translate(499,289) scale(0.707)",[1024,5180,5181],{"dataMmlNode":1034},[1036,5182],{"dataC":2081,"xLinkHref":5183},"#MJX-62-TEX-N-2212",[1024,5185,5187,5191],{"dataMmlNode":1279,"transform":5186},"translate(778,0)",[1024,5188,5189],{"dataMmlNode":1282},[1036,5190],{"dataC":1767,"xLinkHref":5123},[1024,5192,5194],{"dataMmlNode":1282,"transform":5193},"translate(502,289)",[1036,5195],{"dataC":5129,"xLinkHref":5130},[1024,5197,5199],{"dataMmlNode":1282,"transform":5198},"translate(2034,0)",[1036,5200],{"dataC":1285,"xLinkHref":5094},[2010,5202],{"width":5203,"height":2013,"x":2014,"y":2015},2794.9,[1024,5205,5207],{"dataMmlNode":1078,"dataMjxTexclass":1079,"transform":5206},"translate(10504.8,0)",[1024,5208,5209],{"dataMmlNode":1034},[1036,5210],{"dataC":3722,"xLinkHref":5211},"#MJX-62-TEX-N-200B",[12,5213,5214],{},"Sigmoid 函數可以把任何實數壓縮到 (0,1) 的範圍內，這樣我們就可以把它解釋成「機率」。如果 h(x)≥0.5，我們就預測 y=1；否則就預測 y=0。",[822,5216,5218,5220],{"className":5217},[825,826],[828,5219,2941],{},[832,5221,5223,5365,5368],{"className":5222},[835],[12,5224,5225,5226,5267,5268,5364],{},"**",[967,5227,5229],{"className":5228,"jax":971},[970],[973,5230,5234,5245],{"style":1253,"xmlns":976,"width":5231,"height":5232,"role":979,"focusable":980,"viewBox":5233,"xmlnsXLink":982},"3.669ex","1.929ex","0 -841.7 1621.8 852.7",[984,5235,5236,5239,5242],{},[987,5237],{"id":5238,"d":1714},"MJX-63-TEX-I-1D703",[987,5240],{"id":5241,"d":5059},"MJX-63-TEX-I-1D447",[987,5243],{"id":5244,"d":1262},"MJX-63-TEX-I-1D465",[1024,5246,5247],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5248,5249,5261],{"dataMmlNode":1031},[1024,5250,5251,5256],{"dataMmlNode":1279},[1024,5252,5253],{"dataMmlNode":1282},[1036,5254],{"dataC":1767,"xLinkHref":5255},"#MJX-63-TEX-I-1D703",[1024,5257,5258],{"dataMmlNode":1282,"transform":5126},[1036,5259],{"dataC":5129,"xLinkHref":5260},"#MJX-63-TEX-I-1D447",[1024,5262,5264],{"dataMmlNode":1282,"transform":5263},"translate(1049.8,0)",[1036,5265],{"dataC":1285,"xLinkHref":5266},"#MJX-63-TEX-I-1D465","是什麼？**其實就是我們上面學到的計價公式的縮寫版（也就是 ",[967,5269,5271],{"className":5270,"jax":971},[970],[973,5272,5277,5297],{"style":5273,"xmlns":976,"width":5274,"height":5275,"role":979,"focusable":980,"viewBox":5276,"xmlnsXLink":982},"vertical-align: -0.375ex;","13.546ex","1.97ex","0 -705 5987.4 870.6",[984,5278,5279,5282,5285,5288,5291,5294],{},[987,5280],{"id":5281,"d":1714},"MJX-64-TEX-I-1D703",[987,5283],{"id":5284,"d":1718},"MJX-64-TEX-N-30",[987,5286],{"id":5287,"d":1002},"MJX-64-TEX-N-2B",[987,5289],{"id":5290,"d":1725},"MJX-64-TEX-N-31",[987,5292],{"id":5293,"d":1262},"MJX-64-TEX-I-1D465",[987,5295],{"id":5296,"d":2377},"MJX-64-TEX-N-2E",[1024,5298,5299],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5300,5301,5313,5319,5331,5343,5348,5354,5359],{"dataMmlNode":1031},[1024,5302,5303,5308],{"dataMmlNode":1761},[1024,5304,5305],{"dataMmlNode":1282},[1036,5306],{"dataC":1767,"xLinkHref":5307},"#MJX-64-TEX-I-1D703",[1024,5309,5310],{"dataMmlNode":1042,"transform":1771},[1036,5311],{"dataC":1774,"xLinkHref":5312},"#MJX-64-TEX-N-30",[1024,5314,5316],{"dataMmlNode":1034,"transform":5315},"translate(1127.8,0)",[1036,5317],{"dataC":1058,"xLinkHref":5318},"#MJX-64-TEX-N-2B",[1024,5320,5322,5326],{"dataMmlNode":1761,"transform":5321},"translate(2128,0)",[1024,5323,5324],{"dataMmlNode":1282},[1036,5325],{"dataC":1767,"xLinkHref":5307},[1024,5327,5328],{"dataMmlNode":1042,"transform":1771},[1036,5329],{"dataC":1793,"xLinkHref":5330},"#MJX-64-TEX-N-31",[1024,5332,5334,5339],{"dataMmlNode":1761,"transform":5333},"translate(3033.6,0)",[1024,5335,5336],{"dataMmlNode":1282},[1036,5337],{"dataC":1285,"xLinkHref":5338},"#MJX-64-TEX-I-1D465",[1024,5340,5341],{"dataMmlNode":1042,"transform":1804},[1036,5342],{"dataC":1793,"xLinkHref":5330},[1024,5344,5346],{"dataMmlNode":1034,"transform":5345},"translate(4042.1,0)",[1036,5347],{"dataC":1058,"xLinkHref":5318},[1024,5349,5351],{"dataMmlNode":1034,"transform":5350},"translate(4820.1,0)",[1036,5352],{"dataC":2397,"xLinkHref":5353},"#MJX-64-TEX-N-2E",[1024,5355,5357],{"dataMmlNode":1034,"transform":5356},"translate(5264.8,0)",[1036,5358],{"dataC":2397,"xLinkHref":5353},[1024,5360,5362],{"dataMmlNode":1034,"transform":5361},"translate(5709.4,0)",[1036,5363],{"dataC":2397,"xLinkHref":5353}," 算出來的那個直線數值）。",[12,5366,5367],{},"它就像一台「數值壓縮機」。無論你把多大或多小的數字（哪怕是 +10000 或 −10000）丟進這個公式裡，它都會把它「擠壓」成一個介於 0 到 1 之間的小數。",[12,5369,5370,5373],{},[773,5371,5372],{},"為什麼要壓在 0 到 1 之間？"," 因為這正好就是「機率」！ 如果公式算出來是 0.85，機器就是在告訴你：「我有 85% 的把握這是一封垃圾郵件（y=1）。」既然大於 0.5（50%），我們就大膽預測它是垃圾郵件。",[781,5375,5376],{"id":5376},"擬合邏輯迴歸",[12,5378,5379,5380,5383],{},"這次我們不用最小化平方誤差了，而是改用",[773,5381,5382],{},"最大概似估計 (Maximum Likelihood Estimation, MLE)","。我們的假設是：",[77,5385,5386,5525],{},[19,5387,5388],{},[967,5389,5391],{"className":5390,"jax":971},[970],[973,5392,5395,5433],{"style":975,"xmlns":976,"width":5393,"height":978,"role":979,"focusable":980,"viewBox":5394,"xmlnsXLink":982},"21.338ex","0 -750 9431.3 1000",[984,5396,5397,5401,5404,5407,5410,5413,5417,5420,5424,5427,5430],{},[987,5398],{"id":5399,"d":5400},"MJX-65-TEX-I-1D443","M287 628Q287 635 230 637Q206 637 199 638T192 648Q192 649 194 659Q200 679 203 681T397 683Q587 682 600 680Q664 669 707 631T751 530Q751 453 685 389Q616 321 507 303Q500 302 402 301H307L277 182Q247 66 247 59Q247 55 248 54T255 50T272 48T305 46H336Q342 37 342 35Q342 19 335 5Q330 0 319 0Q316 0 282 1T182 2Q120 2 87 2T51 1Q33 1 33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM645 554Q645 567 643 575T634 597T609 619T560 635Q553 636 480 637Q463 637 445 637T416 636T404 636Q391 635 386 627Q384 621 367 550T332 412T314 344Q314 342 395 342H407H430Q542 342 590 392Q617 419 631 471T645 554Z",[987,5402],{"id":5403,"d":990},"MJX-65-TEX-N-28",[987,5405],{"id":5406,"d":1347},"MJX-65-TEX-I-1D466",[987,5408],{"id":5409,"d":1018},"MJX-65-TEX-N-3D",[987,5411],{"id":5412,"d":1725},"MJX-65-TEX-N-31",[987,5414],{"id":5415,"d":5416},"MJX-65-TEX-N-2223","M139 -249H137Q125 -249 119 -235V251L120 737Q130 750 139 750Q152 750 159 735V-235Q151 -249 141 -249H139Z",[987,5418],{"id":5419,"d":1262},"MJX-65-TEX-I-1D465",[987,5421],{"id":5422,"d":5423},"MJX-65-TEX-N-3B","M78 370Q78 394 95 412T138 430Q162 430 180 414T199 371Q199 346 182 328T139 310T96 327T78 370ZM78 60Q78 85 94 103T137 121Q202 121 202 8Q202 -44 183 -94T144 -169T118 -194Q115 -194 106 -186T95 -174Q94 -171 107 -155T137 -107T160 -38Q161 -32 162 -22T165 -4T165 4Q165 5 161 4T142 0Q110 0 94 18T78 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第一個公式：預測「會發生」的機率",[832,5672,5674,5791,5796,5801,5807,5811,5944,5948,5953,5962],{"className":5673},[835],[12,5675,5676],{},[967,5677,5679],{"className":5678,"jax":971},[970],[973,5680,5681,5716],{"style":975,"xmlns":976,"width":5393,"height":978,"role":979,"focusable":980,"viewBox":5394,"xmlnsXLink":982},[984,5682,5683,5686,5689,5692,5695,5698,5701,5704,5707,5710,5713],{},[987,5684],{"id":5685,"d":5400},"MJX-67-TEX-I-1D443",[987,5687],{"id":5688,"d":990},"MJX-67-TEX-N-28",[987,5690],{"id":5691,"d":1347},"MJX-67-TEX-I-1D466",[987,5693],{"id":5694,"d":1018},"MJX-67-TEX-N-3D",[987,5696],{"id":5697,"d":1725},"MJX-67-TEX-N-31",[987,5699],{"id":5700,"d":5416},"MJX-67-TEX-N-2223",[987,5702],{"id":5703,"d":1262},"MJX-67-TEX-I-1D465",[987,5705],{"id":5706,"d":5423},"MJX-67-TEX-N-3B",[987,5708],{"id":5709,"d":1714},"MJX-67-TEX-I-1D703",[987,5711],{"id":5712,"d":1010},"MJX-67-TEX-N-29",[987,5714],{"id":5715,"d":1547},"MJX-67-TEX-I-210E",[1024,5717,5718],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5719,5720,5725,5730,5735,5740,5745,5750,5755,5760,5765,5770,5774,5779,5783,5787],{"dataMmlNode":1031},[1024,5721,5722],{"dataMmlNode":1282},[1036,5723],{"dataC":5441,"xLinkHref":5724},"#MJX-67-TEX-I-1D443",[1024,5726,5727],{"dataMmlNode":1034,"transform":5445},[1036,5728],{"dataC":1038,"xLinkHref":5729},"#MJX-67-TEX-N-28",[1024,5731,5732],{"dataMmlNode":1282,"transform":5451},[1036,5733],{"dataC":1367,"xLinkHref":5734},"#MJX-67-TEX-I-1D466",[1024,5736,5737],{"dataMmlNode":1034,"transform":5457},[1036,5738],{"dataC":1097,"xLinkHref":5739},"#MJX-67-TEX-N-3D",[1024,5741,5742],{"dataMmlNode":1042,"transform":5463},[1036,5743],{"dataC":1793,"xLinkHref":5744},"#MJX-67-TEX-N-31",[1024,5746,5747],{"dataMmlNode":1034,"transform":5469},[1036,5748],{"dataC":5472,"xLinkHref":5749},"#MJX-67-TEX-N-2223",[1024,5751,5752],{"dataMmlNode":1282,"transform":5476},[1036,5753],{"dataC":1285,"xLinkHref":5754},"#MJX-67-TEX-I-1D465",[1024,5756,5757],{"dataMmlNode":1034,"transform":5482},[1036,5758],{"dataC":5485,"xLinkHref":5759},"#MJX-67-TEX-N-3B",[1024,5761,5762],{"dataMmlNode":1282,"transform":5489},[1036,5763],{"dataC":1767,"xLinkHref":5764},"#MJX-67-TEX-I-1D703",[1024,5766,5767],{"dataMmlNode":1034,"transform":5495},[1036,5768],{"dataC":1074,"xLinkHref":5769},"#MJX-67-TEX-N-29",[1024,5771,5772],{"dataMmlNode":1034,"transform":5501},[1036,5773],{"dataC":1097,"xLinkHref":5739},[1024,5775,5776],{"dataMmlNode":1282,"transform":5506},[1036,5777],{"dataC":1565,"xLinkHref":5778},"#MJX-67-TEX-I-210E",[1024,5780,5781],{"dataMmlNode":1034,"transform":5512},[1036,5782],{"dataC":1038,"xLinkHref":5729},[1024,5784,5785],{"dataMmlNode":1282,"transform":5517},[1036,5786],{"dataC":1285,"xLinkHref":5754},[1024,5788,5789],{"dataMmlNode":1034,"transform":5522},[1036,5790],{"dataC":1074,"xLinkHref":5769},[12,5792,5793],{},[773,5794,5795],{},"白話文翻譯：",[3780,5797,5798],{},[12,5799,5800],{},"「在我們已知這筆資料 (x) 和現在的模型標準 (θ) 的條件下，這件事**『會發生 (y=1)』**的機率是多少？」",[12,5802,5803,5806],{},[773,5804,5805],{},"答案："," 就是我們的魔法壓縮機 h(x) 算出來的數字！ 例如：模型算出來 h(x)=0.8，這行公式就是在說：「這封信是垃圾郵件的機率是 80%。」",[781,5808,5810],{"id":5809},"_2-第二個公式預測不會發生的機率","2. 第二個公式：預測「不會發生」的機率",[12,5812,5813],{},[967,5814,5816],{"className":5815,"jax":971},[970],[973,5817,5818,5859],{"style":975,"xmlns":976,"width":5532,"height":978,"role":979,"focusable":980,"viewBox":5533,"xmlnsXLink":982},[984,5819,5820,5823,5826,5829,5832,5835,5838,5841,5844,5847,5850,5853,5856],{},[987,5821],{"id":5822,"d":5400},"MJX-68-TEX-I-1D443",[987,5824],{"id":5825,"d":990},"MJX-68-TEX-N-28",[987,5827],{"id":5828,"d":1347},"MJX-68-TEX-I-1D466",[987,5830],{"id":5831,"d":1018},"MJX-68-TEX-N-3D",[987,5833],{"id":5834,"d":1718},"MJX-68-TEX-N-30",[987,5836],{"id":5837,"d":5416},"MJX-68-TEX-N-2223",[987,5839],{"id":5840,"d":1262},"MJX-68-TEX-I-1D465",[987,5842],{"id":5843,"d":5423},"MJX-68-TEX-N-3B",[987,5845],{"id":5846,"d":1714},"MJX-68-TEX-I-1D703",[987,5848],{"id":5849,"d":1010},"MJX-68-TEX-N-29",[987,5851],{"id":5852,"d":1725},"MJX-68-TEX-N-31",[987,5854],{"id":5855,"d":1955},"MJX-68-TEX-N-2212",[987,5857],{"id":5858,"d":1547},"MJX-68-TEX-I-210E",[1024,5860,5861],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,5862,5863,5868,5873,5878,5883,5888,5893,5898,5903,5908,5913,5917,5922,5927,5932,5936,5940],{"dataMmlNode":1031},[1024,5864,5865],{"dataMmlNode":1282},[1036,5866],{"dataC":5441,"xLinkHref":5867},"#MJX-68-TEX-I-1D443",[1024,5869,5870],{"dataMmlNode":1034,"transform":5445},[1036,5871],{"dataC":1038,"xLinkHref":5872},"#MJX-68-TEX-N-28",[1024,5874,5875],{"dataMmlNode":1282,"transform":5451},[1036,5876],{"dataC":1367,"xLinkHref":5877},"#MJX-68-TEX-I-1D466",[1024,5879,5880],{"dataMmlNode":1034,"transform":5457},[1036,5881],{"dataC":1097,"xLinkHref":5882},"#MJX-68-TEX-N-3D",[1024,5884,5885],{"dataMmlNode":1042,"transform":5463},[1036,5886],{"dataC":1774,"xLinkHref":5887},"#MJX-68-TEX-N-30",[1024,5889,5890],{"dataMmlNode":1034,"transform":5469},[1036,5891],{"dataC":5472,"xLinkHref":5892},"#MJX-68-TEX-N-2223",[1024,5894,5895],{"dataMmlNode":1282,"transform":5476},[1036,5896],{"dataC":1285,"xLinkHref":5897},"#MJX-68-TEX-I-1D465",[1024,5899,5900],{"dataMmlNode":1034,"transform":5482},[1036,5901],{"dataC":5485,"xLinkHref":5902},"#MJX-68-TEX-N-3B",[1024,5904,5905],{"dataMmlNode":1282,"transform":5489},[1036,5906],{"dataC":1767,"xLinkHref":5907},"#MJX-68-TEX-I-1D703",[1024,5909,5910],{"dataMmlNode":1034,"transform":5495},[1036,5911],{"dataC":1074,"xLinkHref":5912},"#MJX-68-TEX-N-29",[1024,5914,5915],{"dataMmlNode":1034,"transform":5501},[1036,5916],{"dataC":1097,"xLinkHref":5882},[1024,5918,5919],{"dataMmlNode":1042,"transform":5506},[1036,5920],{"dataC":1793,"xLinkHref":5921},"#MJX-68-TEX-N-31",[1024,5923,5924],{"dataMmlNode":1034,"transform":5640},[1036,5925],{"dataC":2081,"xLinkHref":5926},"#MJX-68-TEX-N-2212",[1024,5928,5929],{"dataMmlNode":1282,"transform":5646},[1036,5930],{"dataC":1565,"xLinkHref":5931},"#MJX-68-TEX-I-210E",[1024,5933,5934],{"dataMmlNode":1034,"transform":5652},[1036,5935],{"dataC":1038,"xLinkHref":5872},[1024,5937,5938],{"dataMmlNode":1282,"transform":5657},[1036,5939],{"dataC":1285,"xLinkHref":5897},[1024,5941,5942],{"dataMmlNode":1034,"transform":5662},[1036,5943],{"dataC":1074,"xLinkHref":5912},[12,5945,5946],{},[773,5947,5795],{},[3780,5949,5950],{},[12,5951,5952],{},"「在同樣的條件下，這件事**『不會發生 (y=0)』**的機率是多少？」",[12,5954,5955,5957,5958,5961],{},[773,5956,5805],{}," 因為結果只有「是」跟「否」兩種可能，既然全部的機率加起來必須是 100%（也就是數字 1），那麼「不會發生」的機率，當然就是 ",[773,5959,5960],{},"1 減掉「會發生」的機率","！",[12,5963,5964],{},"延續上面的例子：既然是垃圾郵件的機率是 80% (0.8)，那它是正常郵件的機率就是 1−0.8=0.2 (也就是 20%)。",[12,5966,5967],{},"它的對數概似函數 (Log-likelihood) 長這樣（推導過程省略）（應該也沒什麼用，看看就好）：",[12,5969,5970],{},[967,5971,5973],{"className":5972,"jax":971},[970],[973,5974,5979,6044],{"style":5975,"xmlns":976,"width":5976,"height":5977,"role":979,"focusable":980,"viewBox":5978,"xmlnsXLink":982},"vertical-align: -0.791ex;","52.038ex","2.812ex","0 -893.3 23000.8 1242.8",[984,5980,5981,5985,5988,5991,5994,5997,6000,6003,6007,6010,6014,6018,6022,6025,6028,6031,6034,6037,6040],{},[987,5982],{"id":5983,"d":5984},"MJX-69-TEX-I-2113","M345 104T349 104T361 95T369 80T352 59Q268 -20 206 -20Q170 -20 146 3T113 53T99 104L94 129Q94 130 79 116T48 86T28 70Q22 70 15 79T7 94Q7 98 12 103T58 147L91 179V185Q91 186 91 191T92 200Q92 282 128 400T223 612T336 705Q397 705 397 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(MLE)"," 的目標，就是要「最大化」這個函數。白話來說，就是想盡辦法讓機器「對正確答案充滿自信」。",[12,6978,6979,6980,6983,6984,6987],{},"我們要想辦法",[773,6981,6982],{},"最大化","這個函數，用的方法是——你猜對了——",[773,6985,6986],{},"梯度下降","。算出來的更新規則跟線性迴歸的簡直像得出奇：",[12,6989,6990],{},[979,6991],{"alt":1236,"src":6992},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775990017729-Screenshot_2026-04-12_at_6.33.22_PM.png",[12,6994,6995],{},[967,6996,6998],{"className":6997,"jax":971},[970],[973,6999,7000,7041],{"style":3375,"xmlns":976,"width":3376,"height":3377,"role":979,"focusable":980,"viewBox":3378,"xmlnsXLink":982},[984,7001,7002,7005,7008,7011,7014,7017,7020,7023,7026,7029,7032,7035,7038],{},[987,7003],{"id":7004,"d":1714},"MJX-84-TEX-I-1D703",[987,7006],{"id":7007,"d":2795},"MJX-84-TEX-I-1D457",[987,7009],{"id":7010,"d":2799},"MJX-84-TEX-N-3A",[987,7012],{"id":7013,"d":1018},"MJX-84-TEX-N-3D",[987,7015],{"id":7016,"d":1002},"MJX-84-TEX-N-2B",[987,7018],{"id":7019,"d":2809},"MJX-84-TEX-I-1D6FC",[987,7021],{"id":7022,"d":990},"MJX-84-TEX-N-28",[987,7024],{"id":7025,"d":1347},"MJX-84-TEX-I-1D466",[987,7027],{"id":7028,"d":1269},"MJX-84-TEX-I-1D456",[987,7030],{"id":7031,"d":1010},"MJX-84-TEX-N-29",[987,7033],{"id":7034,"d":1955},"MJX-84-TEX-N-2212",[987,7036],{"id":7037,"d":1547},"MJX-84-TEX-I-210E",[987,7039],{"id":7040,"d":1262},"MJX-84-TEX-I-1D465",[1024,7042,7043],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,7044,7045,7057,7069,7079,7084,7089,7094,7117,7122,7127,7131,7152,7156,7160],{"dataMmlNode":1031},[1024,7046,7047,7052],{"dataMmlNode":1761},[1024,7048,7049],{"dataMmlNode":1282},[1036,7050],{"dataC":1767,"xLinkHref":7051},"#MJX-84-TEX-I-1D703",[1024,7053,7054],{"dataMmlNode":1282,"transform":1771},[1036,7055],{"dataC":2838,"xLinkHref":7056},"#MJX-84-TEX-I-1D457",[1024,7058,7059,7064],{"dataMmlNode":1034,"transform":2842},[1024,7060,7061],{"dataMmlNode":2845},[1036,7062],{"dataC":2848,"xLinkHref":7063},"#MJX-84-TEX-N-3A",[1024,7065,7066],{"dataMmlNode":2845,"transform":2852},[1036,7067],{"dataC":1097,"xLinkHref":7068},"#MJX-84-TEX-N-3D",[1024,7070,7071,7075],{"dataMmlNode":1761,"transform":2858},[1024,7072,7073],{"dataMmlNode":1282},[1036,7074],{"dataC":1767,"xLinkHref":7051},[1024,7076,7077],{"dataMmlNode":1282,"transform":1771},[1036,7078],{"dataC":2838,"xLinkHref":7056},[1024,7080,7081],{"dataMmlNode":1034,"transform":2869},[1036,7082],{"dataC":1058,"xLinkHref":7083},"#MJX-84-TEX-N-2B",[1024,7085,7086],{"dataMmlNode":1282,"transform":2875},[1036,7087],{"dataC":2878,"xLinkHref":7088},"#MJX-84-TEX-I-1D6FC",[1024,7090,7091],{"dataMmlNode":1034,"transform":2882},[1036,7092],{"dataC":1038,"xLinkHref":7093},"#MJX-84-TEX-N-28",[1024,7095,7096,7101],{"dataMmlNode":1279,"transform":3475},[1024,7097,7098],{"dataMmlNode":1282},[1036,7099],{"dataC":1367,"xLinkHref":7100},"#MJX-84-TEX-I-1D466",[1024,7102,7103,7107,7112],{"dataMmlNode":1078,"transform":1371,"dataMjxTexclass":1079},[1024,7104,7105],{"dataMmlNode":1034},[1036,7106],{"dataC":1038,"xLinkHref":7093},[1024,7108,7109],{"dataMmlNode":1282,"transform":1043},[1036,7110],{"dataC":1299,"xLinkHref":7111},"#MJX-84-TEX-I-1D456",[1024,7113,7114],{"dataMmlNode":1034,"transform":1303},[1036,7115],{"dataC":1074,"xLinkHref":7116},"#MJX-84-TEX-N-29",[1024,7118,7119],{"dataMmlNode":1034,"transform":3499},[1036,7120],{"dataC":2081,"xLinkHref":7121},"#MJX-84-TEX-N-2212",[1024,7123,7124],{"dataMmlNode":1282,"transform":3505},[1036,7125],{"dataC":1565,"xLinkHref":7126},"#MJX-84-TEX-I-210E",[1024,7128,7129],{"dataMmlNode":1034,"transform":3511},[1036,7130],{"dataC":1038,"xLinkHref":7093},[1024,7132,7133,7138],{"dataMmlNode":1279,"transform":3516},[1024,7134,7135],{"dataMmlNode":1282},[1036,7136],{"dataC":1285,"xLinkHref":7137},"#MJX-84-TEX-I-1D465",[1024,7139,7140,7144,7148],{"dataMmlNode":1078,"transform":1289,"dataMjxTexclass":1079},[1024,7141,7142],{"dataMmlNode":1034},[1036,7143],{"dataC":1038,"xLinkHref":7093},[1024,7145,7146],{"dataMmlNode":1282,"transform":1043},[1036,7147],{"dataC":1299,"xLinkHref":7111},[1024,7149,7150],{"dataMmlNode":1034,"transform":1303},[1036,7151],{"dataC":1074,"xLinkHref":7116},[1024,7153,7154],{"dataMmlNode":1034,"transform":3538},[1036,7155],{"dataC":1074,"xLinkHref":7116},[1024,7157,7158],{"dataMmlNode":1034,"transform":3543},[1036,7159],{"dataC":1074,"xLinkHref":7116},[1024,7161,7162,7166,7180],{"dataMmlNode":3548,"transform":3549},[1024,7163,7164],{"dataMmlNode":1282},[1036,7165],{"dataC":1285,"xLinkHref":7137},[1024,7167,7168,7172,7176],{"dataMmlNode":1078,"transform":3556,"dataMjxTexclass":1079},[1024,7169,7170],{"dataMmlNode":1034},[1036,7171],{"dataC":1038,"xLinkHref":7093},[1024,7173,7174],{"dataMmlNode":1282,"transform":1043},[1036,7175],{"dataC":1299,"xLinkHref":7111},[1024,7177,7178],{"dataMmlNode":1034,"transform":1303},[1036,7179],{"dataC":1074,"xLinkHref":7116},[1024,7181,7182],{"dataMmlNode":1282,"transform":3571},[1036,7183],{"dataC":2838,"xLinkHref":7056},[12,7185,7186,7187,7230],{},"公式長得一模一樣，但別忘了，這裡的 ",[967,7188,7190],{"className":7189,"jax":971},[970],[973,7191,7192,7206],{"style":975,"xmlns":976,"width":1540,"height":978,"role":979,"focusable":980,"viewBox":1541,"xmlnsXLink":982},[984,7193,7194,7197,7200,7203],{},[987,7195],{"id":7196,"d":1547},"MJX-85-TEX-I-210E",[987,7198],{"id":7199,"d":990},"MJX-85-TEX-N-28",[987,7201],{"id":7202,"d":1262},"MJX-85-TEX-I-1D465",[987,7204],{"id":7205,"d":1010},"MJX-85-TEX-N-29",[1024,7207,7208],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,7209,7210,7215,7220,7225],{"dataMmlNode":1031},[1024,7211,7212],{"dataMmlNode":1282},[1036,7213],{"dataC":1565,"xLinkHref":7214},"#MJX-85-TEX-I-210E",[1024,7216,7217],{"dataMmlNode":1034,"transform":1569},[1036,7218],{"dataC":1038,"xLinkHref":7219},"#MJX-85-TEX-N-28",[1024,7221,7222],{"dataMmlNode":1282,"transform":1575},[1036,7223],{"dataC":1285,"xLinkHref":7224},"#MJX-85-TEX-I-1D465",[1024,7226,7227],{"dataMmlNode":1034,"transform":1581},[1036,7228],{"dataC":1074,"xLinkHref":7229},"#MJX-85-TEX-N-29"," 已經是 Sigmoid 函數，不再是線性函數囉！（第三部分重點差不多就是這個了，上面推導過程應該不重要）",[765,7232,7233],{"id":7233},"總結",[872,7235,7236,7246],{},[875,7237,7238],{},[878,7239,7240,7243],{},[881,7241,7242],{"align":883},"主題",[881,7244,7245],{"align":883},"核心概念",[898,7247,7248,7258,7268,7278,7287,7297,7307,7317],{},[878,7249,7250,7255],{},[903,7251,7252],{"align":883},[773,7253,7254],{},"資料前處理",[903,7256,7257],{"align":883},"在訓練模型前，清理並轉換原始資料。",[878,7259,7260,7265],{},[903,7261,7262],{"align":883},[773,7263,7264],{},"線性迴歸",[903,7266,7267],{"align":883},"用線性模型來預測連續的數值。",[878,7269,7270,7275],{},[903,7271,7272],{"align":883},[773,7273,7274],{},"成本函數 (J)",[903,7276,7277],{"align":883},"衡量我們的預測錯得有多離譜。",[878,7279,7280,7284],{},[903,7281,7282],{"align":883},[773,7283,6986],{},[903,7285,7286],{"align":883},"透過迭代調整參數，想辦法把成本降到最低。",[878,7288,7289,7294],{},[903,7290,7291],{"align":883},[773,7292,7293],{},"批量 vs 隨機 GD",[903,7295,7296],{"align":883},"看完所有樣本才更新 vs 看完一筆樣本就更新。",[878,7298,7299,7304],{},[903,7300,7301],{"align":883},[773,7302,7303],{},"欠擬合 \u002F 過擬合",[903,7305,7306],{"align":883},"模型太簡單抓不到規律 vs 模型太複雜只會死背。",[878,7308,7309,7314],{},[903,7310,7311],{"align":883},[773,7312,7313],{},"局部加權 LR",[903,7315,7316],{"align":883},"預測時，給距離近的資料點比較大的影響力。",[878,7318,7319,7324],{},[903,7320,7321],{"align":883},[773,7322,7323],{},"邏輯迴歸",[903,7325,7326],{"align":883},"使用 Sigmoid 函數來分類離散的結果 (如 0 或 1)。",[7328,7329,7330],"style",{},"\nmjx-container[jax=\"SVG\"] {\n  direction: ltr;\n}\n\nmjx-container[jax=\"SVG\"] > svg {\n  overflow: visible;\n  min-height: 1px;\n  min-width: 1px;\n}\n\nmjx-container[jax=\"SVG\"] > svg a {\n  fill: blue;\n  stroke: blue;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"] {\n  display: block;\n  text-align: center;\n  margin: 1em 0;\n}\n\nmjx-container[jax=\"SVG\"][display=\"true\"][width=\"full\"] {\n  display: flex;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"left\"] {\n  text-align: left;\n}\n\nmjx-container[jax=\"SVG\"][justify=\"right\"] {\n  text-align: right;\n}\n\ng[data-mml-node=\"merror\"] > g {\n  fill: red;\n  stroke: red;\n}\n\ng[data-mml-node=\"merror\"] > rect[data-background] {\n  fill: yellow;\n  stroke: none;\n}\n\ng[data-mml-node=\"mtable\"] > line[data-line], svg[data-table] > g > line[data-line] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > rect[data-frame], svg[data-table] > g > rect[data-frame] {\n  stroke-width: 70px;\n  fill: none;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dashed, svg[data-table] > g > .mjx-dashed {\n  stroke-dasharray: 140;\n}\n\ng[data-mml-node=\"mtable\"] > .mjx-dotted, svg[data-table] > g > .mjx-dotted {\n  stroke-linecap: round;\n  stroke-dasharray: 0,140;\n}\n\ng[data-mml-node=\"mtable\"] > g > svg {\n  overflow: visible;\n}\n\n[jax=\"SVG\"] mjx-tool {\n  display: inline-block;\n  position: relative;\n  width: 0;\n  height: 0;\n}\n\n[jax=\"SVG\"] mjx-tool > mjx-tip {\n  position: absolute;\n  top: 0;\n  left: 0;\n}\n\nmjx-tool > mjx-tip {\n  display: inline-block;\n  padding: .2em;\n  border: 1px solid #888;\n  font-size: 70%;\n  background-color: #F8F8F8;\n  color: black;\n  box-shadow: 2px 2px 5px #AAAAAA;\n}\n\ng[data-mml-node=\"maction\"][data-toggle] {\n  cursor: pointer;\n}\n\nmjx-status {\n  display: block;\n  position: fixed;\n  left: 1em;\n  bottom: 1em;\n  min-width: 25%;\n  padding: .2em .4em;\n  border: 1px solid #888;\n  font-size: 90%;\n  background-color: #F8F8F8;\n  color: black;\n}\n\nforeignObject[data-mjx-xml] {\n  font-family: initial;\n  line-height: normal;\n  overflow: visible;\n}\n\nmjx-container[jax=\"SVG\"] path[data-c], mjx-container[jax=\"SVG\"] use[data-c] {\n  stroke-width: 3;\n}\n",{"title":169,"searchDepth":170,"depth":170,"links":7332},[7333,7338,7348,7351],{"id":767,"depth":170,"text":768,"children":7334},[7335,7337],{"id":783,"depth":7336,"text":784},3,{"id":1151,"depth":7336,"text":1151},{"id":1177,"depth":170,"text":1178,"children":7339},[7340,7341,7342,7343,7344,7345,7346,7347],{"id":1184,"depth":7336,"text":1184},{"id":1240,"depth":7336,"text":1240},{"id":1681,"depth":7336,"text":1682},{"id":1898,"depth":7336,"text":1899},{"id":2649,"depth":7336,"text":2650},{"id":4205,"depth":7336,"text":4206},{"id":4259,"depth":7336,"text":4260},{"id":4305,"depth":7336,"text":4306},{"id":4965,"depth":170,"text":4966,"children":7349},[7350],{"id":5376,"depth":7336,"text":5376},{"id":7233,"depth":170,"text":7233},{},{"title":760,"description":169},{"loc":753},"blog\u002F資料前處理與迴歸分析","9P3C3lZU9JjqDmxnbHCmJWv_RiKrBgoZaH1MGlxoyps",{"id":7358,"title":7359,"author":7,"body":7360,"date":7567,"description":7568,"draft":174,"edited_at":391,"extension":175,"featured_image":7569,"meta":7570,"navigation":178,"path":7571,"pinned":174,"seo":7572,"series":181,"seriesOrder":181,"sitemap":7573,"stem":7574,"tags":181,"__hash__":7575},"blog\u002Fblog\u002FMotor-Learning小兒（二）.md","Motor Learning小兒（二）",{"type":9,"value":7361,"toc":7565},[7362,7365,7371,7380,7383,7403,7406],[12,7363,7364],{},"阿對的，又要來講動作學習的定義了，雖然之前就有講過",[12,7366,7367,7368,7370],{},"那動作學習是一個過程，這個過程是借由學習或者經驗產生相當永久的動作行為(long-term effect)",[83,7369],{},"\n動作學習就是過程，而動作表現是動作做出來的結果。",[12,7372,7373,7374,7376,7377,7379],{},"而這邊講道Positive和Negative Sign",[83,7375],{},"\nPositive是指正常人沒有，但病人身上會出現的異常動作",[83,7378],{},"\nNegative則相反，正常人有的，但病人身上無法出現",[12,7381,7382],{},"對於動作學習有三大要素",[16,7384,7385,7388,7397],{},[19,7386,7387],{},"偵測練習——初期PT可以直接監測教導，而後讓病人自己監測自己動作，並且利用內在回饋方式，有利於long-term effect",[19,7389,7390,7391,7393,7394,7396],{},"動機——那對於動作的學習，肯定是動機最為重要，這樣能讓學習過程變佳，那有以下幾點可以引發動機",[83,7392],{},"\n利用喜歡的東西作為目標去做、任務是有趣的、從容易的去做起讓他們有成熟感激發動機",[83,7395],{},"\n同儕競爭互相鼓勵、最後才是給予獎勵作為誘因激發動機",[19,7398,7399,7400,7402],{},"對於目標的清淅程度——就是任務具體並且病人不會理解錯，像是抬高手拿東西而不是單純抬高手",[83,7401],{},"\n而任務越具體，更能引導寶寶產生興趣",[12,7404,7405],{},"那動作學習有以下三個考量點",[16,7407,7408,7458,7504],{},[19,7409,7410,7411,7415,7416,7420,7421,909,7426,7428,7429,7431,7432,7436,7437,7439,7440,7444,7445,7449,7450,7452,7453,7457],{},"轉移——意思是",[254,7412,7414],{"className":7413},[257,264],"相同相似的技巧","在不同情景下可以變化",[254,7417,7419],{"className":7418},[258,257],"產生新的","動作型態 (這裡也有說到 ",[49,7422,7425],{"href":7423,"rel":7424},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E5%85%AB%EF%BC%89%E7%B7%B4%E7%BF%92%E6%96%B9%E5%BC%8F-2?series=Motor%20learning",[53],"在最後一段",[83,7427],{},"\n栗子：一樣是站起來，從椅子上站起來與亞洲蹲的情況下站起來，這兩者都是Hip和Knee的Extend才能達成，當然後者更難",[83,7430],{},"\n所以我們可以借由",[254,7433,7435],{"className":7434},[264],"先學簡單","且技巧相同相似的動作，慢慢的去訓練到難的或具有功能性ADL等的動作",[83,7438],{},"\n也可以透過",[254,7441,7443],{"className":7442},[257,258],"環境改造","達成這一點，例如說寶寶的手還沒有能握住細筷子的能力，可以用",[254,7446,7448],{"className":7447},[257],"加粗","的方式讓寶寶更好握住",[83,7451],{},"\n但記得靠轉移來學習新的動作型態",[254,7454,7456],{"className":7455},[257,258],"不能一下子改太多太難","參數",[19,7459,7460,7461,486,7466,55,7470,7472,7473,7477,7478,7480,7481,7485,7487,7488,7492,7493,7495,7496,7500,7501,7503],{},"接著是練習的方式，對沒錯，之前有讀過，現在我只精簡寫一下好了，詳寫的看這兩篇（",[49,7462,7465],{"href":7463,"rel":7464},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E4%B8%83%EF%BC%89%E7%B7%B4%E7%BF%92%E6%96%B9%E5%BC%8F-1?series=Motor%20learning",[53],"一",[49,7467,7469],{"href":7423,"rel":7468},[53],"二",[83,7471],{},"\n集中VS分散，分散休息時間更長，對",[254,7474,7476],{"className":7475},[257],"學習較難或易疲勞病人","來說更佳",[83,7479],{},"\n段落VS隨機，隨機較難，但通常對",[254,7482,7484],{"className":7483},[264,257],"形成長期記憶以記轉移效果更有",[83,7486],{},"\n固定VS變異，變異在",[254,7489,7491],{"className":7490},[258,257],"轉移效果上","更佳",[83,7494],{},"\n全部VS分段，分段有",[254,7497,7499],{"className":7498},[257,258],"減負效果","，在學習較難動作時可以運用，將同一套動作數個技巧慢慢拆分練習",[83,7502],{},"\n心像練習，在腦中模擬動作型態",[19,7505,7506,7507,486,7511,486,7515,486,7520,909,7525,7527,7528,7530,7531,7533,7534,55,7538,7540,7541,7545,7546,7548,7549,7553,7554,7556,7557,7559,7560,7564],{},"最後是回饋方式，對，又來了，一樣在這裡寫精寫的，詳細看..哇，我居然分開了四篇來寫(",[49,7508,7465],{"href":7509,"rel":7510},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E4%B9%9D%EF%BC%89%E5%9B%9E%E9%A5%8B-1?series=Motor%20learning",[53],[49,7512,7469],{"href":7513,"rel":7514},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E5%8D%81%EF%BC%89%E5%9B%9E%E9%A5%8B-2-%E6%93%B4%E5%A2%9E%E6%80%A7(KR)?series=Motor%20learning",[53],[49,7516,7519],{"href":7517,"rel":7518},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E5%8D%81%E4%B8%80%EF%BC%89%E5%9B%9E%E9%A5%8B-3-%E6%93%B4%E5%A2%9E%E6%80%A7(KP)?series=Motor%20learning",[53],"三",[49,7521,7524],{"href":7522,"rel":7523},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E5%8D%81%E4%B8%80%EF%BC%89%E5%9B%9E%E9%A5%8B-4-(%E9%96%93%E9%9A%94+%E7%89%A9%E7%90%86%E5%BC%95%E5%B0%8E)?series=Motor%20learning",[53],"四",[83,7526],{},"\nKR與KP，KR效度比KP更佳",[83,7529],{},"\n總結VS延時VS立即，總結是多次動作後給予回饋，延時為動作後隔一小段時間給予回饋，這兩種都比立即回饋效果更佳",[83,7532],{},"\n（",[49,7535,7537],{"href":7522,"rel":7536},[53],"這裡第一段有提到",[83,7539],{},"\n回饋的方法，",[49,7542,7544],{"href":7513,"rel":7543},[53],"這一篇的後半段","有提到，可以再複習一下",[83,7547],{},"\n先設定一個",[254,7550,7552],{"className":7551},[264],"區間","，達到的都算得分",[83,7555],{},"\n回饋也可以做遞減，逐漸減少依賴",[83,7558],{},"\n假如病人",[254,7561,7563],{"className":7562},[258,257],"主動要求回饋","，我們再給予，也會更佳",{"title":169,"searchDepth":170,"depth":170,"links":7566},[],"2026-04-10","Motor Learning定義~結束","\u002Fimages\u002Fuploads\u002F1775875520542-37128694_p0_master1200.jpg",{},"\u002Fblog\u002Fmotor-learning",{"title":7359,"description":7568},{"loc":7571},"blog\u002FMotor-Learning小兒（二）","rQGIJJBG2JYTCd6jNzFlYufI482TpWmQ5YIfX_Gkt4s",{"id":7577,"title":7578,"author":7,"body":7579,"date":7837,"description":7838,"draft":174,"edited_at":7837,"extension":175,"featured_image":7839,"meta":7840,"navigation":178,"path":7841,"pinned":174,"seo":7842,"series":181,"seriesOrder":181,"sitemap":7843,"stem":7844,"tags":181,"__hash__":7845},"blog\u002Fblog\u002FCVA（九）復健—手部-(i).md","CVA（九）復健—手部 (i)",{"type":9,"value":7580,"toc":7835},[7581,7584,7602,7654,7717,7722,7757,7764,7781,7794,7806,7809,7832],[12,7582,7583],{},"有跑台的內容我先跳過",[12,7585,7586,7587,7589,7590,7592,7593,7595,7596,7598,7599,7601],{},"Brunnstrom說手部在中風後早期會有這五種反應",[83,7588],{},"\n本體覺牽引反應(Proprioceptive traction response)",[83,7591],{},"\n真正的抓握反射(True grasp reflex)",[83,7594],{},"\n本能性抓握反射(Instinctive grasp reaction)",[83,7597],{},"\n本能性規避反應(Instinctive avoiding reaction)",[83,7600],{},"\n索格氏手指現象(Sougue's finger phenomenon)",[12,7603,7604,7605,7607,7608,7612,7613,7617,7619,7620,7624,7628,7629,7633,7634,7636,7637,7642,7644,7645,7647,7648,7650],{},"先來講本體覺牽引反應",[83,7606],{},"\n他的機制是說，假如對上肢或者下肢的其中一個",[254,7609,7611],{"className":7610},[257,264],"關節","的屈肌肌群做",[254,7614,7616],{"className":7615},[562],"快速的牽拉或者伸展",[83,7618],{},"\n會使被",[254,7621,7623],{"className":7622},[258],"同一個肢體",[254,7625,7627],{"className":7626},[562,257],"所有關節的屈肌","一起",[254,7630,7632],{"className":7631},[264,257],"被誘發收縮","，讓整段肢體一起縮短",[83,7635],{},"\n主要會被這兩種反射",[254,7638,7641],{"className":7639},[257,7640],"bg-green-3","促進或者抑制",[83,7643],{},"\nTNR(Tonic neck reflexes)——尤其是ATNR",[83,7646],{},"\n翻正反射(Body-righting reflexes)",[83,7649],{},[254,7651,7653],{"className":7652},[258],"（利用本體感覺進行誘發）",[12,7655,7656,7657,7659,7660,7664,7665,7669,7670,7674,7675,7679,7680,7682,7683,7685,7686,7688,7689,7693,7694,7696,7697,7701,7702,7706,7707,7711,7712,7716],{},"接著是真正的抓握反射",[83,7658],{},"\n它的誘發方式是，",[254,7661,7663],{"className":7662},[264],"必須要","從",[254,7666,7668],{"className":7667},[257,258],"近端到遠端","並經過",[254,7671,7673],{"className":7672},[497],"掌心橈側部","給予",[254,7676,7678],{"className":7677},[257],"深層壓力","（利用觸覺誘發）",[83,7681],{},"\n這個反射有兩個過程",[83,7684],{},"\n首先是捕捉期，手指的屈曲會快速出現，試圖抓住物體",[83,7687],{},"\n接著是持續抓握期，這個時候屈曲會持續用力收縮，假如物體",[254,7690,7692],{"className":7691},[264],"試圖掙脫","，會讓抓握力度繼續增加（反射變強）",[83,7695],{},"\n那",[254,7698,7700],{"className":7699},[257],"掌指關節","(MP)以及",[254,7703,7705],{"className":7704},[257],"指間關節","(IP)會一起收縮並且呈現",[254,7708,7710],{"className":7709},[258],"內收(Add)","，但",[254,7713,7715],{"className":7714},[264,257],"拇指的力量是最弱","的",[12,7718,7719],{},[979,7720],{"alt":1236,"src":7721},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775725402541-Screenshot_2026-04-09_170119.png",[12,7723,7724,7725,7727,7728,7732,7736,7740,7741,7743,7744,7748,7750,7751,7753,7754,7756],{},"現在講的是本能性抓握反射",[83,7726],{},"\n那它的機制跟剛剛的真正抓握不同，不需要從近到遠，只需要",[254,7729,7731],{"className":7730},[257,258],"靜止讓",[254,7733,7735],{"className":7734},[257,497],"手掌",[254,7737,7739],{"className":7738},[257,258],"碰到","就能觸",[83,7742],{},"\n手指會不自主的握成拳頭，假如物體不拿開手是張不開的",[254,7745,7747],{"className":7746},[257],"（即使像Brunnstrom4 5期的病人能自主張開手也一樣）",[83,7749],{},"\n那有兩種方法可以釋放這個抓握",[83,7752],{},"\n刺激手背（誘發拮抗肌）",[83,7755],{},"\n腕屈曲+放在大腿上休息（因為手指在flex的情況下被帶到wrist flex, 伸肌會被拉到, 借由這個原理讓被動張力來拉開手指）",[12,7758,7759,7760],{},"那Brunnstrom覺得抓握反射也有幾個發展分期",[254,7761,7763],{"className":7762},[562],"(低階到高階)",[16,7765,7766,7769,7772,7775,7778],{},[19,7767,7768],{},"牽張反射（最原始的）——在脊髓，並且是單節段的",[19,7770,7771],{},"本體感覺牽引反射——高於脊髓，並且為多節段的（像剛說到的牽拉一個關節可以連帶誘發同一肢段的關節一起收縮）",[19,7773,7774],{},"真正的抓握反射——皮層下反應（subcortical response）",[19,7776,7777],{},"本能性抓握反射——有部份皮層使用（這裡是恢復過程重要的指標，比起真正抓握還要有功能性--by gemini）",[19,7779,7780],{},"抑制本能性抓握反射——高階皮層",[12,7782,7783,7784,7786,7787,7791,7793],{},"然後講本能性規避反應",[83,7785],{},"\n雖然它一樣從近到遠去滑動誘發，但他的前提是將手向前抬高到一定高度，這樣誘發出來的型態會變成手指拇指",[254,7788,7790],{"className":7789},[258],"hyperextension",[83,7792],{},"\n而這種反應會體現在頂葉受損的病人上",[12,7795,7796,7797,7802,7803,7805],{},"最後講的是索格氏手指現象 (",[49,7798,7801],{"href":7799,"rel":7800},"https:\u002F\u002Fwww.youtube.com\u002Fshorts\u002Fk9i59cNYq5E",[53],"這是影片","，雖然看起來沒有想象中的一下子就鬆開，但看起來也已經是不像上面第二第三點說的抓死)",[83,7804],{},"\n他提到，假如將手臂整個抬高到90度以上，可以讓手指自動出現伸展（對癱瘓的手指也有用）",[12,7807,7808],{},"Brunnstrom對於手部的功能恢復分成了七個階段",[16,7810,7811,7814,7817,7820,7823,7826,7829],{},[19,7812,7813],{},"肌腱反射回歸並且亢奮(Tendon reflexes return and become hyperactive)",[19,7815,7816],{},"痙攣與阻力增加(Spasticity and resistance develop)",[19,7818,7819],{},"借由本體覺刺激誘發手指主動屈曲(Voluntary finger flexion occurs by proprioceptive stimuli)",[19,7821,7822],{},"本體覺牽引反射出現(Proprioceptive traction response appear)",[19,7824,7825],{},"脫離本體覺刺激的手部控制(Control of hand movement without proprioceptive stimuli)",[19,7827,7828],{},"刺激掌心誘發屈曲，痙攣下降(Grasp is greatly reinforced by tactile stimuli in palm, spasticity is declining)",[19,7830,7831],{},"真正的抓握反射出現(True grasp reflex appear)",[12,7833,7834],{},"後面的我留給跑台寫好了",{"title":169,"searchDepth":170,"depth":170,"links":7836},[],"2026-04-09","講brunnstrom手指五個反應~功能恢復","\u002Fimages\u002Fuploads\u002F1775730146879-139326331_p1.png",{},"\u002Fblog\u002FCVA（九）復健—手部-(i)",{"title":7578,"description":7838},{"loc":7841},"blog\u002FCVA（九）復健—手部-(i)","iYpfITqz8NPRepIaYnPwgqVG-PFltjVz6OncktPo9X4",{"id":7847,"title":7848,"author":761,"body":7849,"date":7837,"description":169,"draft":174,"edited_at":7837,"extension":175,"featured_image":181,"meta":8517,"navigation":178,"path":8518,"pinned":174,"seo":8519,"series":181,"seriesOrder":181,"sitemap":8520,"stem":8521,"tags":181,"__hash__":8522},"blog\u002Fblog\u002FNetwork-Communication,-Chapter-1.md","Network Communication, Chapter 1",{"type":9,"value":7850,"toc":8488},[7851,7855,7862,7869,7873,7884,7887,7911,7915,7918,7922,7925,7929,7932,7957,7990,7994,7997,8017,8021,8028,8042,8045,8049,8052,8111,8115,8118,8124,8130,8134,8137,8161,8165,8169,8233,8237,8240,8260,8267,8301,8305,8308,8312,8319,8323,8326,8330,8337,8341,8348,8368,8372,8375,8407,8411,8414,8452,8456,8463,8478,8482,8485],[765,7852,7854],{"id":7853},"why-should-you-care-about-networks","Why Should You Care About Networks?",[12,7856,7857,7858,7861],{},"We live in a hyper-connected world. News travels worldwide in seconds, we store our photos and documents in the cloud, and video calls with people across the globe are just a click away. Behind all of this is one thing: ",[773,7859,7860],{},"computer networks",".",[12,7863,7864,7865,7868],{},"The idea of the ",[773,7866,7867],{},"Internet of Everything (IoE)"," captures this well — it's the convergence of people, processes, data, and things, all linked together through networked connections. Understanding how networks work is the first step to understanding the digital infrastructure that powers modern life.",[765,7870,7872],{"id":7871},"hosts-clients-and-servers","Hosts, Clients, and Servers",[12,7874,7875,7876,7879,7880,7883],{},"Every device that participates directly in network communication is called a ",[773,7877,7878],{},"host"," (or ",[773,7881,7882],{},"end device","). Your laptop, your phone, a web server — all hosts. They can send and receive messages on the network.",[12,7885,7886],{},"In modern networks, an end device can play one of three roles:",[77,7888,7889,7895,7901],{},[19,7890,7891,7894],{},[773,7892,7893],{},"Client"," — requests information or services (e.g. your browser asking for a web page).",[19,7896,7897,7900],{},[773,7898,7899],{},"Server"," — provides information or services (e.g. a machine serving that web page). Servers run specialised software for each service they offer.",[19,7902,7903,7906,7907,7910],{},[773,7904,7905],{},"Both"," — in a ",[773,7908,7909],{},"peer-to-peer (P2P) network",", a single host can act as client and server simultaneously. Think of file-sharing applications where your computer both downloads from and uploads to other users.",[765,7912,7914],{"id":7913},"network-components","Network Components",[12,7916,7917],{},"A network's infrastructure breaks down into three broad categories:",[781,7919,7921],{"id":7920},"_1-end-devices","1. End Devices",[12,7923,7924],{},"These are the devices at the \"edges\" of the network — the ones people actually interact with. Examples include laptops, smartphones, network printers, VoIP phones, security cameras, and tablets.",[781,7926,7928],{"id":7927},"_2-intermediary-devices","2. Intermediary Devices",[12,7930,7931],{},"These are the behind-the-scenes workhorses that make sure data gets where it needs to go:",[77,7933,7934,7940,7951],{},[19,7935,7936,7939],{},[773,7937,7938],{},"Switches and wireless access points"," — provide network access by connecting end devices together.",[19,7941,7942,7945,7946,7950],{},[773,7943,7944],{},"Routers"," — connect separate networks to form an ",[7947,7948,7949],"em",{},"internetwork",", directing traffic between them.",[19,7952,7953,7956],{},[773,7954,7955],{},"Firewalls"," — enforce security policies by filtering unauthorised traffic.",[822,7958,7960,7963],{"className":7959},[825,826],[828,7961,7962],{},"What's different between a Switch, Router and Modem?",[832,7964,7966],{"className":7965},[835],[16,7967,7968,7974,7984],{},[19,7969,7970,7973],{},[773,7971,7972],{},"Modem",": Your ISP sends the internet to your house via analog signals through cables (like coax, fiber optic, or phone lines). Your computers, however, only speak in digital signals (1s and 0s). The modem acts as a translator, turning the ISP's signal into a digital signal your devices can understand, and vice versa.",[19,7975,7976,7979,7980,7983],{},[773,7977,7978],{},"Router",": The router sits just inside your modem. It assigns a unique local IP address to every device in your house. When you request a webpage on your phone, the router remembers that ",[7947,7981,7982],{},"your phone"," asked for it, sends the request out through the modem, and when the website's data comes back, the router ensures it goes to your phone and not your smart TV.",[19,7985,7986,7989],{},[773,7987,7988],{},"Switch",": While a router connects your home to the outside world, a switch just links your home devices to each other. It gives you more ports to plug things in. When a computer plugged into port 1 wants to send a file to a printer plugged into port 4, the switch directs that data straight from port 1 to port 4 without bothering the rest of the network.",[781,7991,7993],{"id":7992},"_3-network-media","3. Network Media",[12,7995,7996],{},"Data needs a physical (or wireless) channel to travel through. The three common types of media are:",[77,7998,7999,8005,8011],{},[19,8000,8001,8004],{},[773,8002,8003],{},"Metallic wires"," (e.g. copper cables like Ethernet)",[19,8006,8007,8010],{},[773,8008,8009],{},"Glass or plastic fibres"," (fibre optic cables — fast and long-range)",[19,8012,8013,8016],{},[773,8014,8015],{},"Wireless transmission"," (radio waves — Wi-Fi, Bluetooth, cellular)",[765,8018,8020],{"id":8019},"network-representations-and-topologies","Network Representations and Topologies",[12,8022,8023,8024,8027],{},"When networks get large, we need diagrams to make sense of them. These ",[773,8025,8026],{},"topology diagrams"," come in two flavours:",[77,8029,8030,8036],{},[19,8031,8032,8035],{},[773,8033,8034],{},"Physical topology"," — shows where devices are physically located, which ports are in use, and how cables are actually installed.",[19,8037,8038,8041],{},[773,8039,8040],{},"Logical topology"," — shows how devices are logically connected, including their IP addresses and port assignments.",[12,8043,8044],{},"Both views are essential. The physical topology helps you troubleshoot hardware, while the logical topology helps you understand how data flows.",[765,8046,8048],{"id":8047},"types-of-networks","Types of Networks",[12,8050,8051],{},"Networks come in every size:",[872,8053,8054,8064],{},[875,8055,8056],{},[878,8057,8058,8061],{},[881,8059,8060],{"align":883},"Scale",[881,8062,8063],{"align":883},"Description",[898,8065,8066,8076,8087,8097],{},[878,8067,8068,8073],{},[903,8069,8070],{"align":883},[773,8071,8072],{},"Home network",[903,8074,8075],{"align":883},"A few devices sharing printers, files, and music.",[878,8077,8078,8084],{},[903,8079,8080,8083],{"align":883},[773,8081,8082],{},"SOHO"," (Small Office \u002F Home Office)",[903,8085,8086],{"align":883},"Supports remote work — advertising, ordering supplies, communicating with clients.",[878,8088,8089,8094],{},[903,8090,8091],{"align":883},[773,8092,8093],{},"Medium to large",[903,8095,8096],{"align":883},"Corporate or campus networks with hundreds to thousands of hosts across multiple locations.",[878,8098,8099,8104],{},[903,8100,8101],{"align":883},[773,8102,8103],{},"The Internet",[903,8105,8106,8107,8110],{"align":883},"A network ",[7947,8108,8109],{},"of"," networks, connecting hundreds of millions of computers worldwide.",[781,8112,8114],{"id":8113},"lan-vs-wan","LAN vs. WAN",[12,8116,8117],{},"The two most fundamental network types are:",[12,8119,8120,8123],{},[773,8121,8122],{},"Local Area Network (LAN)"," — covers a small geographical area like a home, school, or office building. Usually managed by a single person or organisation, and offers high-speed connections to devices within that area.",[12,8125,8126,8129],{},[773,8127,8128],{},"Wide Area Network (WAN)"," — spans large geographical areas, connecting LANs across cities, countries, or even continents. Typically managed by multiple service providers, and the links between LANs tend to be slower than what you'd get inside a LAN.",[781,8131,8133],{"id":8132},"internet-intranet-and-extranet","Internet, Intranet, and Extranet",[12,8135,8136],{},"These three terms often confuse beginners, so here's a simple breakdown:",[77,8138,8139,8145,8155],{},[19,8140,8141,8144],{},[773,8142,8143],{},"Internet"," — the global, public collection of interconnected networks using common standards.",[19,8146,8147,8150,8151,8154],{},[773,8148,8149],{},"Intranet"," — a ",[7947,8152,8153],{},"private"," network of LANs and WANs belonging to an organisation, accessible only to its members.",[19,8156,8157,8160],{},[773,8158,8159],{},"Extranet"," — like an intranet, but with controlled access granted to specific external users (e.g. suppliers or partner hospitals).",[765,8162,8164],{"id":8163},"internet-connection-types","Internet Connection Types",[781,8166,8168],{"id":8167},"for-homes-and-small-offices","For Homes and Small Offices",[872,8170,8171,8181],{},[875,8172,8173],{},[878,8174,8175,8178],{},[881,8176,8177],{"align":883},"Type",[881,8179,8180],{"align":883},"How it Works",[898,8182,8183,8193,8203,8213,8223],{},[878,8184,8185,8190],{},[903,8186,8187],{"align":883},[773,8188,8189],{},"Cable",[903,8191,8192],{"align":883},"Shares the same cable as cable TV. High bandwidth, always-on.",[878,8194,8195,8200],{},[903,8196,8197],{"align":883},[773,8198,8199],{},"DSL (Digital Subscriber Line)",[903,8201,8202],{"align":883},"Runs over copper telephone lines, with a much higher frequency than human voice. Home users typically use ADSL (faster download than upload).",[878,8204,8205,8210],{},[903,8206,8207],{"align":883},[773,8208,8209],{},"Cellular",[903,8211,8212],{"align":883},"Connects via cell towers (3G \u002F 4G \u002F 5G). Great for mobile access.",[878,8214,8215,8220],{},[903,8216,8217],{"align":883},[773,8218,8219],{},"Satellite",[903,8221,8222],{"align":883},"Useful in remote areas, but needs a clear line of sight to the satellite.",[878,8224,8225,8230],{},[903,8226,8227],{"align":883},[773,8228,8229],{},"Dial-up",[903,8231,8232],{"align":883},"Uses a phone line and modem. Very slow — mostly a relic, but still exists in some areas.",[781,8234,8236],{"id":8235},"for-businesses","For Businesses",[12,8238,8239],{},"Businesses often need faster, more reliable, and dedicated connections:",[77,8241,8242,8248,8254],{},[19,8243,8244,8247],{},[773,8245,8246],{},"Dedicated Leased Lines"," — reserved circuits rented monthly or yearly for private data\u002Fvoice networking. It guarantees 100% of the bandwidth all the time.",[19,8249,8250,8253],{},[773,8251,8252],{},"Metro Ethernet"," — Metro Ethernet takes that incredibly fast, highly reliable local network technology and stretches it across an entire city. Metro Ethernet allows a company to connect their downtown office to their suburban warehouse.",[19,8255,8256,8259],{},[773,8257,8258],{},"Business DSL (SDSL)"," — symmetric speeds (equal upload and download), unlike consumer ADSL.",[12,8261,8262,8263,8266],{},"A key modern trend is ",[773,8264,8265],{},"converged networks"," — carrying voice, video, and data all on a single network infrastructure.",[832,8268,8270,8273,8280],{"className":8269},[825,826],[12,8271,8272],{},"A note: In modern days, this (converged networks) is just standard behaviour. The note is talking about historical shift in how networks are built.",[12,8274,8275,8276,8279],{},"Imagine an office building in the 1990s. The IT and facilities teams literally had to run ",[773,8277,8278],{},"three completely separate sets of cables"," through the walls.",[16,8281,8282,8285,8288],{},[19,8283,8284],{},"Copper telephone wires to every desk just for phone calls.",[19,8286,8287],{},"Coaxial cables to conference rooms and lobbies just for video\u002Ftelevision.",[19,8289,8290,8291,8293,8295,8296,8298,8300],{},"Ethernet cables to the computers just for data and internet access.",[83,8292],{},[83,8294],{},"Eventually, engineers realised that a voice call and a video stream could just be chopped up into digital 1s and 0s, exactly like an email or a webpage.",[83,8297],{},[83,8299],{},"Once voice and video became digital data, businesses could rip out the old phone lines and TV cables. Now, they just run one single, robust Ethernet\u002FWi-Fi network. That single infrastructure carries the data, the video (like Zoom), and the voice (VoIP—Voice over Internet Protocol).",[765,8302,8304],{"id":8303},"what-makes-a-network-reliable","What Makes a Network \"Reliable\"?",[12,8306,8307],{},"Good network architecture addresses four fundamental characteristics:",[781,8309,8311],{"id":8310},"fault-tolerance","Fault Tolerance",[12,8313,8314,8315,8318],{},"A fault-tolerant network limits the damage when something breaks. The key idea is ",[773,8316,8317],{},"redundancy"," — having multiple paths between source and destination so that if one path fails, traffic is instantly rerouted through another.",[781,8320,8322],{"id":8321},"scalability","Scalability",[12,8324,8325],{},"A scalable network can grow — adding new users, devices, and services — without degrading performance for existing users. Following accepted standards and protocols is what makes this possible.",[781,8327,8329],{"id":8328},"quality-of-service-qos","Quality of Service (QoS)",[12,8331,8332,8333,8336],{},"When voice, video, and data all share the same network, congestion can happen. QoS is the mechanism that manages this by ",[773,8334,8335],{},"prioritising"," traffic. For example, a router with QoS can give voice calls priority over a large file download, so your call doesn't break up.",[781,8338,8340],{"id":8339},"security","Security",[12,8342,8343,8344,8347],{},"Network security protects both the infrastructure itself and the data flowing through it. It rests on three pillars, sometimes called the ",[773,8345,8346],{},"CIA triad",":",[16,8349,8350,8356,8362],{},[19,8351,8352,8355],{},[773,8353,8354],{},"Confidentiality"," — only authorised recipients can access the data.",[19,8357,8358,8361],{},[773,8359,8360],{},"Integrity"," — data hasn't been tampered with during transmission.",[19,8363,8364,8367],{},[773,8365,8366],{},"Availability"," — authorised users can access services when they need to.",[765,8369,8371],{"id":8370},"network-trends-to-watch","Network Trends to Watch",[12,8373,8374],{},"A few trends shaping today's networks:",[77,8376,8377,8383,8389,8395,8401],{},[19,8378,8379,8382],{},[773,8380,8381],{},"BYOD (Bring Your Own Device)"," — people use their personal devices on business and campus networks. Convenient, but raises security questions.",[19,8384,8385,8388],{},[773,8386,8387],{},"Online Collaboration"," — tools for real-time messaging, video, and file sharing (think Webex, Teams, Slack, etc.).",[19,8390,8391,8394],{},[773,8392,8393],{},"Cloud Computing"," — storing data and running applications on remote servers. Comes in four flavours: public, private, hybrid, and community clouds.",[19,8396,8397,8400],{},[773,8398,8399],{},"Smart Home Technology"," — everyday appliances connecting to the network and becoming automated.",[19,8402,8403,8406],{},[773,8404,8405],{},"Powerline Networking"," — using existing electrical wiring to carry network data, eliminating the need for extra cables.",[765,8408,8410],{"id":8409},"network-security-threats","Network Security Threats",[12,8412,8413],{},"Finally, let's talk about the bad stuff. Common external threats include:",[77,8415,8416,8422,8428,8434,8440,8446],{},[19,8417,8418,8421],{},[773,8419,8420],{},"Malware"," (viruses, worms, Trojans) — malicious code running on your device.",[19,8423,8424,8427],{},[773,8425,8426],{},"Spyware and adware"," — secretly installed software that collects your information.",[19,8429,8430,8433],{},[773,8431,8432],{},"Zero-day attacks"," — exploits that target vulnerabilities on the very day they're discovered, before patches exist.",[19,8435,8436,8439],{},[773,8437,8438],{},"Denial of Service (DoS)"," — attacks that overwhelm and crash network services.",[19,8441,8442,8445],{},[773,8443,8444],{},"Data interception and theft"," — capturing private information as it travels across the network.",[19,8447,8448,8451],{},[773,8449,8450],{},"Identity theft"," — stealing login credentials to access private data.",[781,8453,8455],{"id":8454},"how-do-we-defend-against-these","How Do We Defend Against These?",[12,8457,8458,8459,8462],{},"For home and small office networks, the basics are antivirus\u002Fantispyware software and ",[773,8460,8461],{},"firewall filtering"," to block unauthorised access.",[12,8464,8465,8466,8469,8470,8473,8474,8477],{},"Larger corporate networks add more layers: dedicated firewall systems, ",[773,8467,8468],{},"Access Control Lists (ACLs)"," for fine-grained traffic filtering, ",[773,8471,8472],{},"Intrusion Prevention Systems (IPS)"," to catch fast-spreading threats, and ",[773,8475,8476],{},"VPNs"," to give remote workers secure access.",[765,8479,8481],{"id":8480},"wrapping-up","Wrapping Up",[12,8483,8484],{},"This chapter covered the foundations: what networks are made of, how they're classified, how we connect to the internet, what makes a network reliable, and how we keep it secure. These concepts form the bedrock for everything else in networking.",[12,8486,8487],{},"In the next chapter, we'll dive deeper into how data actually moves across these networks. Stay tuned!",{"title":169,"searchDepth":170,"depth":170,"links":8489},[8490,8491,8492,8497,8498,8502,8506,8512,8513,8516],{"id":7853,"depth":170,"text":7854},{"id":7871,"depth":170,"text":7872},{"id":7913,"depth":170,"text":7914,"children":8493},[8494,8495,8496],{"id":7920,"depth":7336,"text":7921},{"id":7927,"depth":7336,"text":7928},{"id":7992,"depth":7336,"text":7993},{"id":8019,"depth":170,"text":8020},{"id":8047,"depth":170,"text":8048,"children":8499},[8500,8501],{"id":8113,"depth":7336,"text":8114},{"id":8132,"depth":7336,"text":8133},{"id":8163,"depth":170,"text":8164,"children":8503},[8504,8505],{"id":8167,"depth":7336,"text":8168},{"id":8235,"depth":7336,"text":8236},{"id":8303,"depth":170,"text":8304,"children":8507},[8508,8509,8510,8511],{"id":8310,"depth":7336,"text":8311},{"id":8321,"depth":7336,"text":8322},{"id":8328,"depth":7336,"text":8329},{"id":8339,"depth":7336,"text":8340},{"id":8370,"depth":170,"text":8371},{"id":8409,"depth":170,"text":8410,"children":8514},[8515],{"id":8454,"depth":7336,"text":8455},{"id":8480,"depth":170,"text":8481},{},"\u002Fblog\u002FNetwork-Communication,-Chapter-1",{"title":7848,"description":169},{"loc":8518},"blog\u002FNetwork-Communication,-Chapter-1","l3F_jXiYWxb4PBPJWmLT1pfypnofft-NBZFZG8f0U9w",{"id":8524,"title":8525,"author":761,"body":8526,"date":7837,"description":169,"draft":174,"edited_at":7567,"extension":175,"featured_image":181,"meta":9550,"navigation":178,"path":9551,"pinned":174,"seo":9552,"series":181,"seriesOrder":181,"sitemap":9553,"stem":9554,"tags":181,"__hash__":9555},"blog\u002Fblog\u002FNetwork-Communication,-Chapter-2.md","Network Communication, Chapter 2",{"type":9,"value":8527,"toc":9525},[8528,8532,8535,8542,8545,8571,8575,8578,8634,8638,8648,8655,8659,8666,8670,8677,8681,8684,8688,8695,8713,8716,8720,8730,8812,8819,8879,8883,8890,8916,9024,9028,9035,9046,9052,9225,9229,9232,9242,9245,9272,9276,9279,9352,9355,9359,9362,9412,9414,9418,9421,9425,9434,9438,9441,9474,9476,9480],[765,8529,8531],{"id":8530},"why-do-we-need-rules-for-communication","Why Do We Need \"Rules\" for Communication?",[12,8533,8534],{},"Think about a regular face-to-face conversation. Even without realising it, you follow a bunch of unspoken rules — you wait for your turn to speak, you use a language both sides understand, and you expect some kind of acknowledgment that the other person heard you. Networking is exactly the same.",[12,8536,8537,8538,8541],{},"In networking, these rules are called ",[773,8539,8540],{},"protocols",". Every time a message travels from a source to a destination — whether it's an email, a video call, or a simple ping — protocols govern how that happens.",[12,8543,8544],{},"For any communication to work, you need at least these things in place:",[77,8546,8547,8553,8559,8565],{},[19,8548,8549,8552],{},[773,8550,8551],{},"An identified sender and receiver"," — both ends need to be known.",[19,8554,8555,8558],{},[773,8556,8557],{},"A common language and grammar"," — otherwise the message is just noise.",[19,8560,8561,8564],{},[773,8562,8563],{},"Speed and timing of delivery"," — both sides need to agree on pacing.",[19,8566,8567,8570],{},[773,8568,8569],{},"Confirmation or acknowledgment"," — how do you know the message arrived?",[781,8572,8574],{"id":8573},"common-computer-protocol-concepts","Common Computer Protocol Concepts",[12,8576,8577],{},"Protocols in computer networks handle several key jobs:",[77,8579,8580,8586,8592,8598,8628],{},[19,8581,8582,8585],{},[773,8583,8584],{},"Message encoding"," — Converting information into a transmittable format (and decoding it on the other end). Think of it like translating your thoughts into words before speaking.",[19,8587,8588,8591],{},[773,8589,8590],{},"Message formatting and encapsulation"," — Structuring the message so the receiver knows how to read it, much like writing a letter with a proper header, body, and signature.",[19,8593,8594,8597],{},[773,8595,8596],{},"Message size"," — Just like you wouldn't dump an entire essay on someone in one breath, networks break messages into manageable chunks.",[19,8599,8600,8603,8604],{},[773,8601,8602],{},"Message timing"," — This covers three things:",[77,8605,8606,8612,8618],{},[19,8607,8608,8611],{},[773,8609,8610],{},"Flow control",": How much data can be sent, and how fast.",[19,8613,8614,8617],{},[773,8615,8616],{},"Response timeout",": How long to wait for a reply before assuming something went wrong.",[19,8619,8620,8623,8624,8627],{},[773,8621,8622],{},"Access method",": Deciding ",[7947,8625,8626],{},"when"," a device is allowed to send — you can't have everyone shouting at once.",[19,8629,8630,8633],{},[773,8631,8632],{},"Message delivery options"," — Sometimes you send to one person (unicast), sometimes to a group (multicast), and sometimes to everyone nearby (broadcast).",[765,8635,8637],{"id":8636},"network-protocols-the-common-language-of-devices","Network Protocols: The Common Language of Devices",[12,8639,8640,8641,8644,8645,7861],{},"A single message sent over a network usually involves ",[773,8642,8643],{},"multiple protocols"," working together, each handling a different part of the job. A group of these inter-related protocols is called a ",[773,8646,8647],{},"protocol suite",[12,8649,8650,8651,8654],{},"The most important protocol suite you'll encounter is ",[773,8652,8653],{},"TCP\u002FIP"," — it's the backbone of the Internet. TCP\u002FIP is implemented in software, hardware, or both on every device that connects to a network.",[781,8656,8658],{"id":8657},"the-layered-model","The Layered Model",[12,8660,8661,8662,8665],{},"To make sense of how all these protocols interact, we use a ",[773,8663,8664],{},"layered model",". The TCP\u002FIP model organises protocols into layers, where each layer has a specific role and communicates with the layers directly above and below it. This separation makes it easier to design, troubleshoot, and update networks — you can swap out a protocol at one layer without breaking everything else.",[781,8667,8669],{"id":8668},"who-makes-the-rules","Who Makes the Rules?",[12,8671,8672,8673,8676],{},"Network standards are developed by ",[773,8674,8675],{},"standards organisations"," — vendor-neutral, non-profit bodies whose job is to promote open standards so that devices from different manufacturers can all work together. You'll hear names like IEEE, IETF, and ICANN come up often in networking.",[765,8678,8680],{"id":8679},"data-encapsulation-wrapping-your-data-for-delivery","Data Encapsulation: Wrapping Your Data for Delivery",[12,8682,8683],{},"Imagine you want to send a huge video file across the Internet. Sending it as one giant uninterrupted stream would hog the entire communication channel and create massive delays for everyone else. That's clearly not practical.",[781,8685,8687],{"id":8686},"segmentation-and-multiplexing","Segmentation and Multiplexing",[12,8689,8690,8691,8694],{},"The solution is ",[773,8692,8693],{},"segmentation"," — breaking the data into smaller, more manageable pieces before sending. This has two big benefits:",[16,8696,8697,8703],{},[19,8698,8699,8702],{},[773,8700,8701],{},"Reliability"," — If one small piece gets lost, you only resend that piece, not the entire file.",[19,8704,8705,8708,8709,8712],{},[773,8706,8707],{},"Multiplexing"," — Smaller pieces from ",[7947,8710,8711],{},"different"," conversations can be interleaved on the same network, so multiple users can share the same link simultaneously.",[12,8714,8715],{},"Each segment goes through the same process to make sure it reaches the right destination and can be reassembled into the original message.",[781,8717,8719],{"id":8718},"the-encapsulation-process","The Encapsulation Process",[12,8721,8722,8723,8726,8727,8347],{},"As data travels down through the protocol layers, each layer adds its own header (and sometimes trailer) information. This is the ",[773,8724,8725],{},"encapsulation process",". At each layer, the data takes on a different form, called a ",[773,8728,8729],{},"Protocol Data Unit (PDU)",[872,8731,8732,8745],{},[875,8733,8734],{},[878,8735,8736,8739,8742],{},[881,8737,8738],{"align":883},"Layer",[881,8740,8741],{"align":883},"PDU Name",[881,8743,8744],{"align":883},"What It Represents",[898,8746,8747,8760,8773,8786,8799],{},[878,8748,8749,8752,8757],{},[903,8750,8751],{"align":883},"Application",[903,8753,8754],{"align":883},[773,8755,8756],{},"Data",[903,8758,8759],{"align":883},"The raw information from the app",[878,8761,8762,8765,8770],{},[903,8763,8764],{"align":883},"Transport",[903,8766,8767],{"align":883},[773,8768,8769],{},"Segment",[903,8771,8772],{"align":883},"Data + port info for process-to-process delivery",[878,8774,8775,8778,8783],{},[903,8776,8777],{"align":883},"Internet (Network)",[903,8779,8780],{"align":883},[773,8781,8782],{},"Packet",[903,8784,8785],{"align":883},"Segment + IP addresses for host-to-host delivery",[878,8787,8788,8791,8796],{},[903,8789,8790],{"align":883},"Network Access (Data Link)",[903,8792,8793],{"align":883},[773,8794,8795],{},"Frame",[903,8797,8798],{"align":883},"Packet + MAC addresses for hop-to-hop delivery",[878,8800,8801,8804,8809],{},[903,8802,8803],{"align":883},"Physical",[903,8805,8806],{"align":883},[773,8807,8808],{},"Bits",[903,8810,8811],{"align":883},"The actual 1s and 0s on the wire",[12,8813,8814,8815,8818],{},"When the data arrives at the destination, the reverse happens — ",[773,8816,8817],{},"de-encapsulation",". Each layer strips off its header, passing the remaining data up to the next layer until the application gets the original message.",[822,8820,8822,8825],{"className":8821},[825,826],[828,8823,8824],{},"The Encapsulation Process (Packing the Box)",[832,8826,8828],{"className":8827},[835],[77,8829,8830,8836,8846,8860,8873],{},[19,8831,8832,8835],{},[773,8833,8834],{},"Application Layer (Data):"," This is the actual birthday card and the gift you want to send. It is the raw information you care about.",[19,8837,8838,8841,8842,8845],{},[773,8839,8840],{},"Transport Layer (Segment):"," You take the gift and put it in a small inner envelope. You write *\"To John, from Jane\"*on it. In networking, this layer adds the ",[773,8843,8844],{},"port number",", which makes sure the data goes to the exact right application (John) and not someone else in the house. Because the data might be too big, this layer will also chop it up into manageable pieces (segments).",[19,8847,8848,8851,8852,8855,8856,8859],{},[773,8849,8850],{},"Internet Layer (Packet):"," You put that inner envelope inside a standard cardboard shipping box. On the outside, you write the final destination address: ",[7947,8853,8854],{},"\"123 Main St, New York, NY.\""," In networking, this layer adds the ",[773,8857,8858],{},"IP Address",", ensuring the box can navigate the global internet to find the correct final building (host-to-host delivery).",[19,8861,8862,8865,8866,8855,8869,8872],{},[773,8863,8864],{},"Network Access Layer (Frame):"," The post office takes your box and loads it into a specific local delivery truck. They stick a temporary barcode on the outside of the box that just says, ",[7947,8867,8868],{},"\"Take this to the airport depot.\"",[773,8870,8871],{},"MAC Address",". It doesn't care about the final destination in New York; it only cares about successfully moving the box to the very next local stop (hop-to-hop delivery).",[19,8874,8875,8878],{},[773,8876,8877],{},"Physical Layer (Bits):"," The truck physically drives down the road. In networking, this is the actual physical electricity pulsing over copper wires, or light flashing down a fiber optic cable, represented as 1s and 0s.",[765,8880,8882],{"id":8881},"data-access-two-kinds-of-addresses","Data Access: Two Kinds of Addresses",[12,8884,8885,8886,8889],{},"Getting data from point A to point B actually involves ",[773,8887,8888],{},"two different addressing systems"," working at different layers:",[77,8891,8892,8906],{},[19,8893,8894,8897,8898,8901,8902,8905],{},[773,8895,8896],{},"Network layer (IP) addresses"," — These are responsible for delivering the packet from the ",[7947,8899,8900],{},"original source"," to the ",[7947,8903,8904],{},"final destination",", even across different networks. Think of this as the mailing address on an envelope.",[19,8907,8908,8911,8912,8915],{},[773,8909,8910],{},"Data link layer (MAC) addresses"," — These handle delivery between one network interface card (NIC) and the next, on the ",[7947,8913,8914],{},"same local network",". Think of this as the \"hand it to the next person in the chain\" step.",[822,8917,8919,8922],{"className":8918},[825,826],[828,8920,8921],{},"MAC address vs IP address",[832,8923,8925,8931,8937,8941,8944,8948,8953,8964,8971,8974,8983,8995,9001],{"className":8924},[835],[12,8926,8927,8930],{},[773,8928,8929],{},"MAC Address = Who you are"," (Like your DNA). It is permanently burned into your device at the factory.",[12,8932,8933,8936],{},[773,8934,8935],{},"IP Address = Where you are"," (Like your street address). It changes depending on where you connect. If you take your laptop from your house to a coffee shop, your MAC address stays exactly the same, but your IP address changes because you are on a new network.",[781,8938,8940],{"id":8939},"the-ip-ban-vpns-the-network-layer","The IP Ban & VPNs (The Network Layer)",[12,8942,8943],{},"When a remote website or game server bans your IP address, they are blocking your \"street address.\" You turn on a VPN. A VPN acts as a middleman. You send your data to the VPN server, and the VPN server forwards it to the website. The website only sees the VPN's \"street address\" (IP address), not yours. Because your IP is hidden, you bypass the ban.",[781,8945,8947],{"id":8946},"the-mac-ban-the-data-link-layer","The MAC Ban (The Data Link Layer)",[12,8949,8950],{},[773,8951,8952],{},"MAC addresses never leave your local network.",[12,8954,8955,8956,8959,8960,8963],{},"When your computer sends a packet of data to a server in another country, it hands the packet to your home router. Your router literally ",[773,8957,8958],{},"strips off your computer's MAC address",", throws it in the trash, and slaps on the ",[7947,8961,8962],{},"router's own MAC address"," before sending it to the next stop. This happens at every single \"hop\" across the internet.",[12,8965,8966,8967,8970],{},"Because of this, ",[773,8968,8969],{},"a remote website cannot ban your MAC address over the internet because they literally cannot see it."," Only your local router can see your MAC address.",[12,8972,8973],{},"So, how do MAC bans actually work, and are they circumventable?",[12,8975,8976,8979,8980,8982],{},[773,8977,8978],{},"1. Local Network MAC Bans (The Wi-Fi Ban)"," If you misbehave at school or work, the IT admin can tell the local Wi-Fi router, \"Do not let the MAC address belonging to John's phone connect.\" Since the router is on the ",[7947,8981,8914],{}," as your phone, it sees your MAC address and blocks you.",[77,8984,8985],{},[19,8986,8987,8990,8991,8994],{},[773,8988,8989],{},"Is it circumventable? YES."," Even though the MAC address is burned into your hardware, you can use a software trick called ",[773,8992,8993],{},"MAC Spoofing",". You simply tell your phone or computer's operating system to wear a \"mask\" and broadcast a fake, randomly generated MAC address. The router sees the new fake MAC, doesn't recognize it as banned, and lets you right back on. (In fact, modern iOS and Android phones do this automatically for privacy now!).",[12,8996,8997,9000],{},[773,8998,8999],{},"2. Hardware Bans (The Anti-Cheat Ban)"," If websites can't see your MAC address over the internet, how do game developers \"hardware ban\" cheaters?",[77,9002,9003,9018],{},[19,9004,9005,9006,9009,9010,9013,9014,9017],{},"They don't do it over the internet; they do it locally. Games like ",[7947,9007,9008],{},"Valorant"," or ",[7947,9011,9012],{},"Call of Duty"," make you install aggressive Anti-Cheat software. That software runs ",[7947,9015,9016],{},"locally"," on your actual physical machine, reads your motherboard's MAC address (and serial numbers of your CPU and hard drive), and sends a list of those numbers to the game server.",[19,9019,9020,9023],{},[773,9021,9022],{},"Is it circumventable? YES, but it's much harder."," Because the anti-cheat is looking deeply at multiple pieces of hardware, simple MAC spoofing usually isn't enough. People use complex \"hardware spoofers\" to trick the anti-cheat, but it is a constant game of cat-and-mouse.",[781,9025,9027],{"id":9026},"same-network-vs-different-network","Same Network vs. Different Network",[12,9029,9030,9031,9034],{},"When sender and receiver are on the ",[773,9032,9033],{},"same network",", the frame goes directly to the destination device using its MAC address.",[12,9036,9037,9038,9041,9042,9045],{},"When they're on ",[773,9039,9040],{},"different networks",", things get more interesting. The IP addresses still point to the original source and final destination, but the frame is first sent to the ",[773,9043,9044],{},"router (default gateway)",". The router then re-wraps (re-encapsulates) the data in a new frame destined for the next hop, and so on, until the packet reaches the destination network.",[12,9047,9048,9049],{},"This is a fundamental concept: ",[773,9050,9051],{},"IP addresses stay the same end-to-end, but MAC addresses change at every hop.",[832,9053,9055,9067,9081,9094,9100,9117,9139,9151,9177,9180,9189,9194,9200,9209,9215],{"className":9054},[825,826],[12,9056,9057,9058,9062,9063,9066],{},"Let's say, you want to connect to Google (",[9059,9060,9061],"code",{},"8.8.8.8",") from your computer (",[9059,9064,9065],{},"192.168.0.15","). So, it builds an IP Packet (the cardboard shipping box).",[77,9068,9069,9075],{},[19,9070,9071,9074],{},[773,9072,9073],{},"Source IP:"," 192.168.0.15 (You)",[19,9076,9077,9080],{},[773,9078,9079],{},"Destination IP:"," 8.8.8.8 (Google)",[12,9082,9083,9084,9087,9088,9090,9091],{},"This box is now sealed. These IP addresses ",[773,9085,9086],{},"will not change"," for the entire journey. Your computer looks at Google's IP address (",[9059,9089,9061],{},") and realizes, ",[7947,9092,9093],{},"\"Google is not on my local Wi-Fi network. I need to hand this box to the router so it can leave the house.\"",[12,9095,9096,9097,9099],{},"To get the box to the router, your computer encapsulates the Packet inside a ",[773,9098,8795],{}," (the local delivery truck). It puts local MAC address labels on the outside of this truck:",[77,9101,9102,9108],{},[19,9103,9104,9107],{},[773,9105,9106],{},"Source MAC:"," Your Computer's MAC Address",[19,9109,9110,9113,9114],{},[773,9111,9112],{},"Destination MAC:"," Your Router's MAC Address ",[7947,9115,9116],{},"(Notice it does NOT use Google's MAC address!)",[12,9118,9119,9120,9123,9124,9126,9127,9130,9131,9134,9135,9138],{},"Your computer sends this Frame over the Wi-Fi or Ethernet cable. Because the Destination MAC belongs to your router, the router says, ",[7947,9121,9122],{},"\"Hey, this truck is for me!\""," and catches it. The router \"opens\" the Frame (it unloads the delivery truck). It looks at the inner IP Packet (the cardboard box) and sees the Destination IP is ",[9059,9125,9061],{}," (Google). The router says, ",[7947,9128,9129],{},"\"Okay, I need to send this to the internet provider next.\""," The router ",[773,9132,9133],{},"throws away your original Frame"," (the local truck is done with its job). The router builds a ",[773,9136,9137],{},"brand new Frame"," (a new truck) to drive the packet to the next stop (your ISP). The new Frame has:",[77,9140,9141,9146],{},[19,9142,9143,9145],{},[773,9144,9106],{}," Your Router's MAC Address",[19,9147,9148,9150],{},[773,9149,9112],{}," The ISP Router's MAC Address",[12,9152,9153,9154,9156,9157,9160,9161,9164,9165,9168,9169,9172,9173,9176],{},"It hides your local IP address (",[9059,9155,9065],{},"), and replaces your local IP with your house's ",[773,9158,9159],{},"Public IP Address"," (the single address your ISP assigned to your modem, say ",[9059,9162,9163],{},"203.0.113.5","). To remember that ",[7947,9166,9167],{},"your specific computer"," made this request, the router assigns a random, unique ",[773,9170,9171],{},"Port Number"," (let's say ",[9059,9174,9175],{},"#5001",") to the packet. The router then writes this in its NAT Table ledger:",[12,9178,9179],{},"    \"If any mail comes back from Google addressed to Port #5001, give it to the computer at 192.168.0.15.\"",[12,9181,9182,9183,9185,9186,9188],{},"Google receives the request. As far as Google is concerned, the request came from ",[9059,9184,9163],{}," on Port ",[9059,9187,9175],{},". Google has no idea your specific computer exists, nor does it know your MAC address.",[12,9190,9191,9192,7861],{},"Google packages up the webpage and sends it back to your house's Public IP, specifically tagging it for Port ",[9059,9193,9175],{},[12,9195,9196,9197],{},"The webpage arrives at your router. The router looks at the package and says, ",[7947,9198,9199],{},"\"Okay, this is from Google, and it's tagged for Port #5001.\"",[12,9201,9202,9203,9205,9206],{},"It opens up its NAT Table ledger, finds the entry for ",[9059,9204,9175],{},", and sees the note it left for itself: ",[7947,9207,9208],{},"\"Ah! Port #5001 means this belongs to 192.168.0.15.\"",[12,9210,9211,9212,9214],{},"Now that the router knows the internal IP address (",[9059,9213,9065],{},") that the data belongs to, it needs to hand the data across the house to your computer.",[12,9216,9217,9218,9220,9221,9224],{},"The router looks up your computer's IP address in its local directory to find your ",[773,9219,8871],{},". It packages Google's webpage into a brand new ",[773,9222,9223],{},"Local Frame",", slaps your computer's MAC address on the destination label, and pushes it out over the Wi-Fi. Your computer sees its MAC address, catches the frame, and loads the webpage!",[765,9226,9228],{"id":9227},"network-operating-systems","Network Operating Systems",[12,9230,9231],{},"Now that we know how data travels across networks, how do we actually control the devices—like routers and switches—that are directing all this traffic? To do that, we need to look at the software running on the hardware.",[12,9233,9234,9235,9238,9239,7861],{},"Routers, switches, and other infrastructure devices don't run Windows or macOS — they run specialised ",[773,9236,9237],{},"network operating systems",". On Cisco devices, this is the ",[773,9240,9241],{},"Cisco IOS (Internetwork Operating System)",[12,9243,9244],{},"A few key points about how IOS works:",[77,9246,9247,9254,9261],{},[19,9248,9249,9250,9253],{},"The IOS file is stored in ",[773,9251,9252],{},"flash memory"," (non-volatile, survives reboots).",[19,9255,9256,9257,9260],{},"On boot, the IOS is copied from flash into ",[773,9258,9259],{},"RAM",", where it runs while the device is operating.",[19,9262,9263,9264,9267,9268,9271],{},"Like any OS, it has a ",[773,9265,9266],{},"kernel"," (talks to hardware) and a ",[773,9269,9270],{},"shell"," (the interface you interact with), which can be a CLI or GUI.",[781,9273,9275],{"id":9274},"ways-to-access-the-cli","Ways to Access the CLI",[12,9277,9278],{},"There are several ways to get into a device's command-line interface:",[872,9280,9281,9293],{},[875,9282,9283],{},[878,9284,9285,9288,9290],{},[881,9286,9287],{"align":883},"Method",[881,9289,8177],{"align":883},[881,9291,9292],{"align":883},"Notes",[898,9294,9295,9308,9320,9337],{},[878,9296,9297,9302,9305],{},[903,9298,9299],{"align":883},[773,9300,9301],{},"Console",[903,9303,9304],{"align":883},"Out-of-band",[903,9306,9307],{"align":883},"Physical cable to the console port. Used for initial setup and maintenance. Works even if the network is down.",[878,9309,9310,9315,9317],{},[903,9311,9312],{"align":883},[773,9313,9314],{},"AUX",[903,9316,9304],{"align":883},[903,9318,9319],{"align":883},"Older method using a modem and phone line. Also doesn't require network services.",[878,9321,9322,9327,9330],{},[903,9323,9324],{"align":883},[773,9325,9326],{},"Telnet",[903,9328,9329],{"align":883},"In-band",[903,9331,9332,9333,9336],{"align":883},"Remote access over the network via a virtual interface. Requires the network to be up. ",[773,9334,9335],{},"Not secure","— data is sent in plain text.",[878,9338,9339,9344,9346],{},[903,9340,9341],{"align":883},[773,9342,9343],{},"SSH",[903,9345,9329],{"align":883},[903,9347,9348,9349],{"align":883},"Like Telnet, but with encryption and stronger authentication. ",[773,9350,9351],{},"Always prefer SSH over Telnet.",[12,9353,9354],{},"Common terminal emulator programs include PuTTY, Tera Term, SecureCRT, and the macOS Terminal.",[781,9356,9358],{"id":9357},"cli-modes","CLI Modes",[12,9360,9361],{},"The Cisco IOS CLI is organised in a hierarchy of modes, each with different levels of access:",[16,9363,9364,9374,9386,9398],{},[19,9365,9366,9369,9370,9373],{},[773,9367,9368],{},"User EXEC mode"," (",[9059,9371,9372],{},">",") — Limited monitoring commands. You land here by default.",[19,9375,9376,9369,9379,9382,9383,7861],{},[773,9377,9378],{},"Privileged EXEC mode",[9059,9380,9381],{},"#",") — Full access to monitoring and management commands. Enter with ",[9059,9384,9385],{},"enable",[19,9387,9388,9369,9391,9394,9395,7861],{},[773,9389,9390],{},"Global configuration mode",[9059,9392,9393],{},"(config)#",") — Used to make device-wide configuration changes. Enter with ",[9059,9396,9397],{},"configure terminal",[19,9399,9400,9403,9404,9407,9408,9411],{},[773,9401,9402],{},"Specific configuration modes"," — Sub-modes like interface configuration (",[9059,9405,9406],{},"(config-if)#",") or line configuration (",[9059,9409,9410],{},"(config-line)#",") for configuring specific components.",[35,9413],{},[765,9415,9417],{"id":9416},"basic-commands-securing-your-device","Basic Commands: Securing Your Device",[12,9419,9420],{},"Once you're in the CLI, some of the first things you'll want to do are give your device a name and lock it down with passwords.",[781,9422,9424],{"id":9423},"setting-a-hostname","Setting a Hostname",[12,9426,9427,9428,9431,9432,7861],{},"Hostnames help you identify devices on the network. A descriptive hostname (like ",[9059,9429,9430],{},"HQ-Router-1",") is much more useful than the default ",[9059,9433,7978],{},[781,9435,9437],{"id":9436},"passwords-you-should-know","Passwords You Should Know",[12,9439,9440],{},"Passwords are the first line of defence against unauthorised access:",[77,9442,9443,9449,9462,9468],{},[19,9444,9445,9448],{},[773,9446,9447],{},"Enable password"," — Restricts access to privileged EXEC mode (stored in plain text — avoid using this alone).",[19,9450,9451,9454,9455,9458,9459,7861],{},[773,9452,9453],{},"Enable secret"," — Same purpose as above, but the password is ",[773,9456,9457],{},"encrypted",". Always use this instead of ",[9059,9460,9461],{},"enable password",[19,9463,9464,9467],{},[773,9465,9466],{},"Console password"," — Protects the physical console port.",[19,9469,9470,9473],{},[773,9471,9472],{},"VTY password"," — Protects remote access via Telnet\u002FSSH.",[35,9475],{},[765,9477,9479],{"id":9478},"key-takeaways","Key Takeaways",[77,9481,9482,9485,9492,9501,9511,9518],{},[19,9483,9484],{},"Protocols are the rules that govern all network communication — from encoding to timing to delivery.",[19,9486,9487,9488,9491],{},"The ",[773,9489,9490],{},"TCP\u002FIP model"," organises protocols into layers, each with a distinct job.",[19,9493,9494,9497,9498,9500],{},[773,9495,9496],{},"Encapsulation"," wraps data with headers at each layer; ",[773,9499,8817],{}," unwraps them at the destination.",[19,9502,9503,9506,9507,9510],{},[773,9504,9505],{},"IP addresses"," handle end-to-end delivery; ",[773,9508,9509],{},"MAC addresses"," handle hop-by-hop delivery.",[19,9512,9513,9514,9517],{},"Network devices run specialised operating systems like ",[773,9515,9516],{},"Cisco IOS",", accessed through console, Telnet, or SSH.",[19,9519,9520,9521,9524],{},"Always ",[773,9522,9523],{},"secure your devices"," with hostnames, encrypted passwords, and SSH access.",{"title":169,"searchDepth":170,"depth":170,"links":9526},[9527,9530,9534,9538,9541,9545,9549],{"id":8530,"depth":170,"text":8531,"children":9528},[9529],{"id":8573,"depth":7336,"text":8574},{"id":8636,"depth":170,"text":8637,"children":9531},[9532,9533],{"id":8657,"depth":7336,"text":8658},{"id":8668,"depth":7336,"text":8669},{"id":8679,"depth":170,"text":8680,"children":9535},[9536,9537],{"id":8686,"depth":7336,"text":8687},{"id":8718,"depth":7336,"text":8719},{"id":8881,"depth":170,"text":8882,"children":9539},[9540],{"id":9026,"depth":7336,"text":9027},{"id":9227,"depth":170,"text":9228,"children":9542},[9543,9544],{"id":9274,"depth":7336,"text":9275},{"id":9357,"depth":7336,"text":9358},{"id":9416,"depth":170,"text":9417,"children":9546},[9547,9548],{"id":9423,"depth":7336,"text":9424},{"id":9436,"depth":7336,"text":9437},{"id":9478,"depth":170,"text":9479},{},"\u002Fblog\u002FNetwork-Communication,-Chapter-2",{"title":8525,"description":169},{"loc":9551},"blog\u002FNetwork-Communication,-Chapter-2","jWA4nQQOxUiioSIb7c07mb7ZfBAcj5wPPZjFfWkOXeQ",{"id":9557,"title":9558,"author":7,"body":9559,"date":9856,"description":9857,"draft":174,"edited_at":9856,"extension":175,"featured_image":9858,"meta":9859,"navigation":178,"path":9860,"pinned":174,"seo":9861,"series":181,"seriesOrder":181,"sitemap":9862,"stem":9863,"tags":181,"__hash__":9864},"blog\u002Fblog\u002FCVA跑台（一）.md","CVA跑台（一）",{"type":9,"value":9560,"toc":9854},[9561,9596,9641,9660,9681,9700,9724,9742,9772,9802,9815,9831],[12,9562,9563,9566,9568,9570,9571,9574,9575,9579,9580,9582,9583,9587,9588,9590,9591,9595],{},[773,9564,9565],{},"如何測試上下肢Brunnstrom stage 是否為Stage 2（第1\u002F2期區分是有無聯合動作）",[83,9567],{},[83,9569],{},"\n說話：主要是測有沒有聯合動作來區分一期或者第二期，聯合動作",[773,9572,9573],{},"上肢方向","相同，下肢除了",[254,9576,9578],{"className":9577},[257],"內收外展","其他都相反",[83,9581],{},"\n那上肢要先從",[254,9584,9586],{"className":9585},[257,258],"Extensor","測到再Flexor，讓好手用力抵抗阻力誘發壞手的動作",[83,9589],{},"\n下肢就先從",[254,9592,9594],{"className":9593},[257,264],"Flexor","先測再到Extensor，一樣是用好腳用力抵抗阻力誘發壞腳動作",[12,9597,9598,9601,9603,9605,9606,9609,9610,9612,9613,9617,9618,9622,9623,9627,9628,9632,9633,9635,9636,9640],{},[773,9599,9600],{},"測試上肢Brunnstrom stage是否為Stage 3的各項動作（紀錄角度）",[83,9602],{},[83,9604],{},"\n說話：因為要先測弱的協同動作，以及從好邊先測，所以要先從",[254,9607,9586],{"className":9608},[257],"的協同動作開始測",[83,9611],{},"\nExtensor的動作的話：患者",[254,9614,9616],{"className":9615},[257],"同側手","放在",[254,9619,9621],{"className":9620},[257],"同側大腿","上，碰",[254,9624,9626],{"className":9625},[257],"對側","膝蓋內側（",[254,9629,9631],{"className":9630},[257],"雙膝中間","）並記錄各關節角度",[83,9634],{},"\n而Flexor的動作的話：患者同側手放在同側大腿上，往上碰同側",[254,9637,9639],{"className":9638},[257],"耳垂","，並記錄各關節角度",[12,9642,9643,9646,9648,9650,9651,9653,9654,9656,9657,9659],{},[773,9644,9645],{},"測試上肢Brunnstrom stage是否為Stage 4的各項動作",[83,9647],{},[83,9649],{},"\n說話：",[83,9652],{},"\n第一個動作——手動到下背",[83,9655],{},"\n第二個動作——手向前平舉，掌心朝下",[83,9658],{},"\n第三個動作——Elbow Flex並且前臂做旋前和旋後",[12,9661,9662,9665,9667,9650,9669,9671,9672,9674,9675,9677,9678,9680],{},[773,9663,9664],{},"測試上肢Brunnstrom stage是否為Stage 5的各項動作",[83,9666],{},[83,9668],{},[83,9670],{},"\n第一個動作——手側向平舉（掌心朝下）",[83,9673],{},"\n第二個動作——手側向平舉後（掌心朝下）-->前臂旋後（掌心朝上）",[83,9676],{},"\n第三個動作——手向前平舉再往前伸（Protraction）",[83,9679],{},"\n第四個動作——手向前高舉過頭",[12,9682,9683,9686,9688,9605,9690,9693,9694,9696,9697,9699],{},[773,9684,9685],{},"測試下肢Brunnstrom stage是否為Stage 3的各項動作",[83,9687],{},[83,9689],{},[254,9691,9594],{"className":9692},[257],"協同動作開始測",[83,9695],{},"\nFlexor的動作的話——請病人supine，並嘗試讓病人膝碰胸",[83,9698],{},"\n而Extensor的話——讓病人側躺，並用Hip Knee Flex的姿勢，做Knee Extend",[12,9701,9702,9705,9707,9650,9709,9711,9712,9714,9715,9717,9718,9720,9721,9723],{},[773,9703,9704],{},"測試下肢Brunnstrom stage是否為Stage 4的各項動作",[83,9706],{},[83,9708],{},[83,9710],{},"\n第一個動作——在supine的姿勢下做hip abd",[83,9713],{},"\n第二個動作——坐姿下膝碰胸，那這個動作先測好邊再測壞邊",[83,9716],{},"\n第三個動作——坐姿下，腳踩在地上，向後滑，這個動作一樣先測好邊再測壞邊",[83,9719],{},"\n第四個動作——坐姿下，knee flex，做ankle dorsiflexion",[83,9722],{},"\n第五個動作——坐姿下，knee extend",[12,9725,9726,9729,9731,9650,9733,9735,9736,9738,9739,9741],{},[773,9727,9728],{},"測試下肢Brunnstrom stage是否為Stage 5的各項動作",[83,9730],{},[83,9732],{},[83,9734],{},"\n第一個動作——坐姿下，要knee extend到腳跟離地下，做PF\u002FDF",[83,9737],{},"\n第二個動作——坐姿下，僅腳跟碰地情況下，做eversion\u002Finversion",[83,9740],{},"\n第三個動作——站姿下，一隻腳flex並且用後跟碰臀部",[12,9743,9744,9747,9749,9751,9752,9756,9757,9759,9760,9764,9765,9767,9768,9764],{},[773,9745,9746],{},"Brunnstrom測試肩、肘、腕關節的被動動作感覺檢查",[83,9748],{},[83,9750],{},"\n說話：那等下請你",[254,9753,9755],{"className":9754},[257],"閉上眼睛","，然後我要動你的壞手，你的好手也要跟著做一樣的動作",[83,9758],{},"\n肩、肘的話——一手托住手肘，一手用兩指托住",[254,9761,9763],{"className":9762},[257],"掌心","去移動",[83,9766],{},"\n腕的話——一手托住前臂，一手用二指抓",[254,9769,9771],{"className":9770},[257],"第二及第五掌骨",[12,9773,9774,9777,9779,9781,9782,9785,9786,9790,9791,9793,9795,9796,9798,9799,9801],{},[773,9775,9776],{},"Brunnstrom測試手指Fingertip Recognition 及上肢之速度測試",[83,9778],{},[83,9780],{},"\n說話：讓病人坐著，請病人",[254,9783,9755],{"className":9784},[257],"，手放大腿上，用鉛筆的橡皮擦去碰病人的",[254,9787,9789],{"className":9788},[257],"壞側指尖","，讓他說出是碰哪一根",[83,9792],{},[83,9794],{},"\n而速度測試的話：",[83,9797],{},"\n第一個——手放大腿靠近膝蓋的地方，然後去碰下巴再回到大腿，測五秒內能來回多少次",[83,9800],{},"\n第二個——手放大腿靠近髖部的地方，然後去碰對側膝蓋再回來，測五秒內能來回多少次",[12,9803,9804,9807,9809,9811,9812,9814],{},[773,9805,9806],{},"Brunnstrom 測試足底 Sole sensation 檢查",[83,9808],{},[83,9810],{},"\n說話：坐著，將壓舌板放在足下，測",[83,9813],{},"\n不放、放腳掌（橫）、放腳跟（橫）、放小趾側（竪）、放大腳趾側（竪）",[12,9816,9817,9820,9822,9824,9825,9827,9828,9830],{},[773,9818,9819],{},"如何評估肘屈肌之肌肉痙攣（利用MAS）",[83,9821],{},[83,9823],{},"\n說話：先將手放在extend，隨後慢慢的移動到Flex再慢慢回來，之後快速的將手拉動做Flex\u002Fextend三次感受阻力",[83,9826],{},"\n0分的話無阻力、1分的話只有末端有阻力、1+的話只有後半段有阻力",[83,9829],{},"\n2的話大半段都有阻力、3分的話很難拉動要用力才能拉開、4分的話完全拉不開",[12,9832,9833,9836,9838,9840,9841,9843,9844,9848,9850,9851,9853],{},[773,9834,9835],{},"請說明如何執行及判斷Functional Reach Test",[83,9837],{},[83,9839],{},"\n說話：那首先病人要俱備這兩種能力，第一能不能獨自站立30秒以上，第二手能平舉起過90度",[83,9842],{},"\n接著就是身體直立，雙腳平行站立，握拳，手向前平舉90度，盡量讓病人向前伸，",[254,9845,9847],{"className":9846},[257],"測三次取平均值",[83,9849],{},"\n假如少於6inch的話，代表跌倒風險高",[83,9852],{},"\n假如6~10inch的話，代表跌倒風險中",{"title":169,"searchDepth":170,"depth":170,"links":9855},[],"2026-04-08","僅收錄期中李老師跑台內容 Brunnstrom~functional reach test","\u002Fimages\u002Fuploads\u002F1775616855750-143269515_p0_master1200.jpg",{},"\u002Fblog\u002FCVA跑台（一）",{"title":9558,"description":9857},{"loc":9860},"blog\u002FCVA跑台（一）","V2tMy4Ah7CXxbABDHqNIYd8xqcDM1ev6P-8O4ZJBsGU",{"id":9866,"title":9867,"author":7,"body":9868,"date":10098,"description":10099,"draft":174,"edited_at":10100,"extension":175,"featured_image":10101,"meta":10102,"navigation":178,"path":10103,"pinned":174,"seo":10104,"series":181,"seriesOrder":181,"sitemap":10105,"stem":10106,"tags":181,"__hash__":10107},"blog\u002Fblog\u002FBalance（二）前庭覺-(i).md","Balance（二）前庭覺 (i)",{"type":9,"value":9869,"toc":10096},[9870,9902,9905,9918,9954,9963,9979,9981,9996,10011,10026,10060,10070],[12,9871,9872,9873,9875,9876,9880,9882,9883,9887,9888,9890,9891,9895,9896,9898,9899,9901],{},"接著講到前庭覺",[83,9874],{},"\n它主要是提供了關於",[254,9877,9879],{"className":9878},[562],"頭部相對重力及動作的資訊",[83,9881],{},"\n那左右兩邊前庭都會提供",[254,9884,9886],{"className":9885},[562],"相同(重複)","的感覺訊息，假如一邊壞掉了，也會有另一邊做補充",[83,9889],{},"\n也是唯一能夠定義",[254,9892,9894],{"className":9893},[562],"自體有沒有動","的感覺，能分清是別人歪掉還是自己歪掉",[83,9897],{},"\n假若當視覺與軀體感覺有衝突，前庭覺就會介入並給出最終答案（但假若前庭覺壞掉了，那就會引發頭昏眼花）",[83,9900],{},"\n甚至還可以活化抗重力肌肉來提供適當的維持姿勢能力",[12,9903,9904],{},"那前庭覺也分成了周邊的跟中樞的兩個組件",[12,9906,9907,9908,9912,9913,9917],{},"先來講周邊的前庭覺，主要是前庭迷路，由",[254,9909,9911],{"className":9910},[264],"半規管","以及",[254,9914,9916],{"className":9915},[264],"內耳石","組成",[12,9919,9920,9921,9923,9924,9928,9929,9931,9932,9936,9937,9939,9940,9942,9943,9945,9946,9948,9949,9953],{},"那半規管的構造，就是一個充滿液體的環狀結構，裡面包含了纖毛細胞",[83,9922],{},"\n而這個構造能提供",[254,9925,9927],{"className":9926},[562],"頭部旋轉及角速度","的訊息",[83,9930],{},"\n而左右耳各三個半規管（前後外半規管），且彼此",[254,9933,9935],{"className":9934},[264],"互相垂直","，而分別為這樣組合來掌管不同的方向",[83,9938],{},"\n左右外半規管——左右轉頭",[83,9941],{},"\n左前+右後半規管——側前方傾斜",[83,9944],{},"\n右前+左後半規管——另一個方向的側前方傾斜",[83,9947],{},"\n而這三個平面都十分接近眼睛",[254,9950,9952],{"className":9951},[264],"外眼肌肉","，所以是容易控住外眼肌肉的路徑",[12,9955,9956,9957,9959,9960,9962],{},"而半規管的開口有一個叫壺腹，它裡面有動跟靜的纖毛，這兩個纖毛互動可以產生過極化以及去極化",[83,9958],{},"\n去極化——偵測頭部速度增加（靜纖毛靠近動纖毛）",[83,9961],{},"\n過極化——偵測頭部速度減少（靜纖毛遠離動纖毛）",[12,9964,9965,9966,9928,9970,9972,9973,9975,9976,9978],{},"那周邊前庭覺的第二個零件就是內耳石，與剛剛半規管是管旋轉的不同，它管的是",[254,9967,9969],{"className":9968},[562],"重力和直線加速度",[83,9971],{},"\n那內耳石也有兩個構造",[83,9974],{},"\n橢圓囊（管水平方向）——側彎頭部刺激最大",[83,9977],{},"\n球狀囊（管垂直方向）——前後彎頭部刺激最大",[35,9980],{},[12,9982,9983,9984,9986,9987,9991,9992],{},"接著講中樞的前庭覺",[83,9985],{},"\n那剛剛在周邊的前庭覺接收到的訊息會先經過",[254,9988,9990],{"className":9989},[7640],"前庭耳蝸腦神經","再到小腦和延腦之間的",[254,9993,9995],{"className":9994},[562],"前庭核",[12,9997,9998,9999,10001,10002,10004,10005,10007,10008,10010],{},"而前庭核一共有四顆，以下是它們的分工",[83,10000],{},"\n上&內核——主要是管眼睛，負責凝視穩定",[83,10003],{},"\n內核——還要協調眼睛跟頭部的動作，以及肢體&軀體動作感覺輸入",[83,10006],{},"\n外核——主要調控肌肉跟軀體協調（姿勢穩定）",[83,10009],{},"\n下核——連接其他神經核以及網狀系統",[12,10012,10013,10014,10016,10017,10019,10020,10022,10023,10025],{},"那前庭核接收了之後會往這四個地方發送信號",[83,10015],{},"\n動眼中心——調控VOR",[83,10018],{},"\n脊髓——分成內側前庭脊髓徑（控制頭頸部移動）和外側前庭脊髓徑（身體的移動）",[83,10021],{},"\n小腦——較正VOR",[83,10024],{},"\n大腦深處（例如網狀系統）——引發嘔吐噁心",[12,10027,10028,10029,10031,10032,10036,10038,10042,10044,10045,10049,10050,10054,10055],{},"接著講前庭的運作邏輯",[83,10030],{},"\n前庭覺它的放電一般會維持在70-100PPS，即使是",[254,10033,10035],{"className":10034},[562],"睡覺或者沒在動也不會歸零",[83,10037],{},[254,10039,10041],{"className":10040},[257],"放電的多寡取決於速度的變化",[83,10043],{},"\n且它會有",[254,10046,10048],{"className":10047},[264],"對稱性","，假如頭部的角速度或者水平速度發生改變，同側的",[254,10051,10053],{"className":10052},[258],"放電會增加","，對側的將會",[254,10056,10059],{"className":10057},[10058],"teal-3","減少",[12,10061,10062,10063,10067,10069],{},"接著來講VOR的特性——用來",[254,10064,10066],{"className":10065},[562],"維持凝視穩定",[83,10068],{},"\n它是建立在注視上面的，假如眼盯前方，頭部往左轉，那半規管就會被觸發，讓眼睛就會自動往右走",[12,10071,10072,10073,10075,10076,10081,10082,10084,10085,10088,10089,10084,10091,10095],{},"那對於轉向的速度也有三種調節能力",[83,10074],{},"\n頭部速度小於",[254,10077,10080],{"className":10078},[10079],"blue-3","每秒60度","——就是自己眼睛能夠跟上的，不需要特別調節（平滑追蹤）",[83,10083],{},"\n頭部速度大於",[254,10086,10080],{"className":10087},[258],"——需要使用VOR協助",[83,10090],{},[254,10092,10094],{"className":10093},[264],"每秒350度","——連凝視都沒辦法維持了，會採用跳視(saccade)方式",{"title":169,"searchDepth":170,"depth":170,"links":10097},[],"2026-04-06","周邊以及中樞前庭的構造及運作方式","2026-04-07","\u002Fimages\u002Fuploads\u002F1775545346184-141163959_p0.png",{},"\u002Fblog\u002Fbalance-(i)",{"title":9867,"description":10099},{"loc":10103},"blog\u002FBalance（二）前庭覺-(i)","WzTG_6oQvpepiMgcfP_Vu8sE0YSABgOg5y95C6YYnd4",{"id":10109,"title":10110,"author":7,"body":10111,"date":10098,"description":10360,"draft":174,"edited_at":10098,"extension":175,"featured_image":10361,"meta":10362,"navigation":178,"path":10363,"pinned":174,"seo":10364,"series":181,"seriesOrder":181,"sitemap":10365,"stem":10366,"tags":181,"__hash__":10367},"blog\u002Fblog\u002FCVA（七）評估-(i).md","CVA（七）評估 (i)",{"type":9,"value":10112,"toc":10358},[10113,10119,10122,10138,10147,10150,10169,10185,10208,10250,10255,10258,10305,10331,10346],[12,10114,10115,10118],{},[2948,10116,10117],{},"CVA好像有點多 看不到頭哦","  目前進度計量 76\u002F292頁",[12,10120,10121],{},"那CVA評估方向有分這幾種",[12,10123,10124,10125,10127,10131,10132,10134,10135,10137],{},"首先是評估認知跟意識的量表，包括了",[83,10126],{},[254,10128,10130],{"className":10129},[257,562],"JOMAC","——Judgment(常識\u002F判斷)、Orientation(定向感)、Memory、Abstract thinking(抽象思考)、Calculation(計算)",[83,10133],{},"\nMMSE",[83,10136],{},"\nGCS",[12,10139,10140,10141,10143,10144,10146],{},"接著是功能量表，包括了",[83,10142],{},"\nBarthel index(巴氏量表)",[83,10145],{},"\nFuntional Independent measure(FIM)——這個比巴氏量表測得還要更精細",[12,10148,10149],{},"肌張力評估，有Modified Ashworth Scale(MAS)",[12,10151,10152,10153,10155,10159,10160,10162,10163,10165,10166,10168],{},"動作功能整合測試，包括了",[83,10154],{},[254,10156,10158],{"className":10157},[257,562],"Brunnstorm Method","——分了六期 而第二期會開始出現協同動作(區分)",[83,10161],{},"\nFugl-Meyer Assessment——這個是根據布朗斯壯量表改良的",[83,10164],{},"\nMotor Assessment Scale",[83,10167],{},"\nNIH Stroke Scale",[12,10170,10171,10172,10176,10177,10181,10182,10184],{},"我們先來講布朗斯壯（跑台要跑哦）（可以再複習一下這兩份 ",[49,10173,7465],{"href":10174,"rel":10175},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%91%A8%E5%9C%8D%E7%90%86%E8%AB%96%E5%AD%B8%E6%B4%BE%EF%BC%88%E4%BA%8C%EF%BC%89%E9%9A%8E%E5%B1%A4%E7%90%86%E8%AB%96?series=Motor%20Control",[53]," ",[49,10178,7469],{"href":10179,"rel":10180},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E5%8D%81%E4%B8%89%EF%BC%89%E8%87%A8%E5%BA%8A%E6%87%89%E7%94%A8?series=Motor%20learning",[53]," 的階層理論跟布朗斯壯的描述）",[83,10183],{},"\n首先來測的是感覺，分了四種測試方向",[77,10186,10187,10193,10199,10205],{},[19,10188,10189,10190,10192],{},"被動運動覺（本體感覺）——蒙住病人眼，分別移動病人的肩、肘、前臂、腕、手指、下肢",[83,10191],{},"\n（這樣才可以知道病人需不需要一直專注看著自己腳來移動）（患測）",[19,10194,10195,10196,10198],{},"指尖辨識——蒙住病人眼，碰病人的指尖看他分不分得出來是碰哪根",[83,10197],{},"\n（測解覺跟大腦皮層的整合能力）（患測）",[19,10200,10201,10202,10204],{},"足底感覺——拿毛巾分別放在病人的前足，後足，內足，外足測他看能不能分不分得出",[83,10203],{},"\n（這跟平衡有關）（患測）",[19,10206,10207],{},"動態運動覺——蒙住病人眼，PT手抓患測帶著移動，讓病人的好手跟著這個速度跟方向跟著動",[12,10209,10210,10211,10213,10214,10216,10217,10221,10222,10226,10227,10229,10230,10235,10236,10238,10239,10241,10242,10246,10247,10249],{},"然後就是布朗斯壯的運動測試，它分成了六期，稍微解釋一下",[83,10212],{},"\n首先是第一期，沒有張力也沒有動作的",[83,10215],{},"\n第二期，它有",[254,10218,10220],{"className":10219},[562],"聯合動作出現","(伴隨協同動作)（是用來",[254,10223,10225],{"className":10224},[562],"區分第一期跟第二期","的指標），而且開始有痙攣出現，但還沒有主動動作",[83,10228],{},"\n第三期，痙攣是",[254,10231,10234],{"className":10232},[10233],"bg-yellow-3","最強","的，雖然開始有主動動作，但還是被協同動作主導",[83,10237],{},"\n第四期，這時痙攣開始下降，而且動作也開始偏離協同動作模式",[83,10240],{},"\n第五期，痙攣",[254,10243,10245],{"className":10244},[7640],"最弱","，基本上也沒有協同動作出現",[83,10248],{},"\n第六期，無痙攣，並且可以做到單關節動作，動作開始是協調的(雖然還有些笨拙)",[12,10251,10252],{},[979,10253],{"alt":1236,"src":10254},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775437999044-Gemini_Generated_Image_5mnz195mnz195mnz.png",[12,10256,10257],{},"emmm，跑台的話看後面要不要再開一章做整理好了",[12,10259,10260,10261,10263,10264,10266,10267,10271,10272,10274,10275,10279,10280,10282,10283,10287,10288,10290,10291,10293,10294,10296,10297,10299,10300,55],{},"接著講測試張力的MAS(Modified Ashworth Scale)，它分成了六個等級",[83,10262],{},"\nGrade 0  ——正常人",[83,10265],{},"\nGrade 1  ——到關節活動度",[254,10268,10270],{"className":10269},[562],"末端","才有張力出現",[83,10273],{},"\nGrade 1+  ——",[254,10276,10278],{"className":10277},[10233],"後半段","關節活動度出現張力",[83,10281],{},"\nGrade 2  ——",[254,10284,10286],{"className":10285},[7640],"大半段","活動度都有出現張力",[83,10289],{},"\nGrade 3  ——很難拉得動，但還是能拉",[83,10292],{},"\nGrade 4  ——拉不動了",[83,10295],{},"\n（補充，因為張力會受到速度影響(速度相依)，而另一個表MTS是MAS再把速度整合進去的版本）",[83,10298],{},"\n（Clasp-knife Response(摺刀反應)意思是在測試張力過程中，阻力突然消失了，代表上運動神經元受損——",[49,10301,10304],{"href":10302,"rel":10303},"https:\u002F\u002Fwww.youtube.com\u002Fwatch?v=JJ9Hg1hZS9Q",[53],"補一條影片",[12,10306,10307,10308,10310,10311,10313,10314,10316,10317,10319,10320,10324,10325,10327,10328,7611],{},"然後來講FMA，它主要看五大面向加起來113個測試項目",[83,10309],{},"\n動作功能——包括了上下肢",[83,10312],{},"\n感覺功能——分為了Light touch兩面(輕觸覺)和Position Sense八個(位置覺)",[83,10315],{},"\n平衡——七個測試（坐姿三個，站姿四個）",[83,10318],{},"\n關節活動度——",[254,10321,10323],{"className":10322},[258],"九個","關節測ROM",[83,10326],{},"\n關節疼痛——一樣是",[254,10329,10323],{"className":10330},[258],[12,10332,10333,10334,10336,10337,10339,10340,10342,10343,10345],{},"單論上肢就總分126分，包括了",[83,10335],{},"\nMotor(66)",[83,10338],{},"\nSensation(12)",[83,10341],{},"\nROM(24)",[83,10344],{},"\nPain(24)",[12,10347,10348,10349,10351,10352,10354,10355,10357],{},"那FMA的評分是0~2分來看的",[83,10350],{},"\n0分是完全沒有動作",[83,10353],{},"\n1分是能做到一部份抑或者不完美",[83,10356],{},"\n2分是流暢完美的完成",{"title":169,"searchDepth":170,"depth":170,"links":10359},[],"評估 Brunnstrom~FMA","\u002Fimages\u002Fuploads\u002F1775441596804-HE-2PhpbAAAPbL6.png",{},"\u002Fblog\u002FCVA（七）評估-(i)",{"title":10110,"description":10360},{"loc":10363},"blog\u002FCVA（七）評估-(i)","5VjlOMhJesoVA8qOO4VQLSc8-Dn-LDih6bguuuMPLJE",{"id":10369,"title":10370,"author":7,"body":10371,"date":10098,"description":10571,"draft":174,"edited_at":10098,"extension":175,"featured_image":10572,"meta":10573,"navigation":178,"path":10574,"pinned":174,"seo":10575,"series":181,"seriesOrder":181,"sitemap":10576,"stem":10577,"tags":181,"__hash__":10578},"blog\u002Fblog\u002FCVA（八）評估-(ii).md","CVA（八）評估 (ii)",{"type":9,"value":10372,"toc":10569},[10373,10376,10409,10430,10466,10475,10480,10528,10543,10563],[12,10374,10375],{},"繼續講評估",[12,10377,10378,10379,10381,10382,10384,10385,10387,10388,10390,10391,10393,10394,10396,10397,10399,10400,10402,10403,10405,10406,10408],{},"首先是Motor Assessment Scale",[83,10380],{},"\n它這個表比起上一份說的布朗斯壯（粗大動作）以及FMA（精細動作）不同",[83,10383],{},"\n這個更著重於功能性部份(ADL)，更加臨床，它分成了八個項目",[83,10386],{},"\nSupine to side lying",[83,10389],{},"\nSupine to sitting over the edge of a bed(仰躺到床緣再坐起)",[83,10392],{},"\nBalanced sitting",[83,10395],{},"\nSitting to Standing",[83,10398],{},"\nWalking",[83,10401],{},"\nUpper-arm function",[83,10404],{},"\nHand movements",[83,10407],{},"\nAdvance hand activites",[12,10410,10411,10412,10414,10415,10417,10418,10420,10421,10423,10424,10426,10427,10429],{},"接著講NIHSS的部份，它分成了11評估項目，一共42分，越高分越嚴重",[83,10413],{},"\n0分就是正常",[83,10416],{},"\n1~4分是輕度中風",[83,10419],{},"\n5~14分是中度中風",[83,10422],{},"\n15~24分是中重度重風",[83,10425],{},"\n24分以上是十分嚴重的中風",[83,10428],{},"\n（而10分以下的預後會有60%~70%機會恢復很好，20分以上預後會變十分差）",[12,10431,10432,10433,10435,10436,10438,10439,10441,10442,10444,10445,10447,10448,10450,10451,10453,10454,10456,10457,10459,10460,10462,10463,10465],{},"那十一項評分項目包括了",[83,10434],{},"\n意識——意識的評分又分成了三類（水準，問題，指令）",[83,10437],{},"\n眼球運動",[83,10440],{},"\n視野",[83,10443],{},"\n面部肌肉",[83,10446],{},"\n上肢運動",[83,10449],{},"\n下肢運動",[83,10452],{},"\n肢體運動失調",[83,10455],{},"\n感覺功能",[83,10458],{},"\n語言功能",[83,10461],{},"\n構音困難",[83,10464],{},"\n忽略症",[12,10467,10468,10469,10474],{},"下圖是來自網上抓的台中榮民總醫院的",[49,10470,10473],{"href":10471,"rel":10472},"https:\u002F\u002Fwww.vghtc.gov.tw\u002FUploadFiles\u002FWebFiles\u002FWebPagesFiles\u002FFiles\u002Ff3802ff1-0016-44af-939f-fb045f9d5a4a\u002F20190419%20NIHSS%E4%BB%8B%E7%B4%B9%E5%8F%8A%E6%87%89%E7%94%A8.pdf",[53],"NIHSS 中風量表之介紹與應用"," 雖然它這邊有分了左右的上下肢體運動 但總分一樣是42",[12,10476,10477],{},[979,10478],{"alt":1236,"src":10479},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775443710135-Screenshot_2026-04-06_103756.png",[12,10481,10482,10483,10485,10486,10488,10489,10491,10492,10494,10495,10497,10498,10500,10501,10503,10504,10506,10507,10509,10510,10512,10513,10515,10516,10518,10519,10521,10522,10524,10525,10527],{},"然後來講伯格氏平衡量表Berg Balance Scale，它原本是來預測老人的跌倒風險的，但發現用在CVA上也不錯",[83,10484],{},"\n有以下十四點",[83,10487],{},"\nSitting unsupported——不支撐坐著",[83,10490],{},"\nChange of position--sitting to standing——坐到站",[83,10493],{},"\nChange of position--standing to sitting——站到坐",[83,10496],{},"\nTransfers——轉移位",[83,10499],{},"\nStanding unsupported——不支撐站著",[83,10502],{},"\nStanding with eyes closed——閉眼站著",[83,10505],{},"\nStanding with feet together——雙腳拼攏站著",[83,10508],{},"\nTandem standing——腳尖碰腳跟站著",[83,10511],{},"\nStanding on one leg——單腳站",[83,10514],{},"\nTurning Trunk(feet fix)——轉軀幹但腳不動",[83,10517],{},"\nRetrieving objects from floor——從地上撿東西",[83,10520],{},"\nTurning 360 degrees——轉身360度",[83,10523],{},"\nStool stepping——用一個踏板輪流讓左右腳上去下來（重量轉移）",[83,10526],{},"\nReaching forward while standing——站立前往伸手",[12,10529,10530,10531,10533,10534,10536,10537,10539,10540,10542],{},"而這個表的得分會長這樣",[83,10532],{},"\n0~20分——一定會跌倒，建議坐輪椅",[83,10535],{},"\n21~40分——中度跌倒風險，建議用輔具",[83,10538],{},"\n41~56分——低跌倒風險，可以獨立行走",[83,10541],{},"\n（而老師有補充低於36分就一定會跌倒，45分以內也會高機率跌倒）",[12,10544,10545,10546,10548,10549,10553,10554,10556,10557,10559,10560,10562],{},"最後講的是Functional Reach Test，這是一個可以快速中風或者老人的跌倒風險測試",[83,10547],{},"\n那最基本測試對象",[254,10550,10552],{"className":10551},[562],"需要這兩點能力","（獨立站立30秒，肩至少能平舉90度）",[83,10555],{},"\n然後是判讀的部分",[83,10558],{},"\n假如病人能向前伸6inch(15cm)以下，代表他跌倒風險高",[83,10561],{},"\n假如病人能向前伸6~10inch(25cm)，代表跌倒風險是中",[12,10564,10565,10566,10568],{},"接下來有一大堆跑台的東西了 我之後再整理（啊好多啊~",[83,10567],{},"\n目前進度50\u002F292頁",{"title":169,"searchDepth":170,"depth":170,"links":10570},[],"Motor Assessment Scale~Functional Reach Test","\u002Fimages\u002Fuploads\u002F1775445542448-135083397_p0.png",{},"\u002Fblog\u002FCVA（八）評估-(ii)",{"title":10370,"description":10571},{"loc":10574},"blog\u002FCVA（八）評估-(ii)","F5NsFqBo4w2dGUO_7yvNf7hwpR_kEvHtkzGNRa6YWlo",{"id":10580,"title":10581,"author":7,"body":10582,"date":10098,"description":10718,"draft":174,"edited_at":10098,"extension":175,"featured_image":10719,"meta":10720,"navigation":178,"path":753,"pinned":174,"seo":10721,"series":181,"seriesOrder":181,"sitemap":10722,"stem":10723,"tags":181,"__hash__":10724},"blog\u002Fblog\u002F平衡與前庭失調（一）.md","平衡與前庭失調（一）",{"type":9,"value":10583,"toc":10716},[10584,10587,10593,10610,10622,10634,10640,10645,10648,10651,10670,10676,10684,10693,10710],[12,10585,10586],{},"小兒的Motor Learning也稍微講到一些平衡的內容，不過這一課是直接攤開來講，努力吃吧，加油",[12,10588,10589,10590,10592],{},"首先來講定義",[83,10591],{},"\n維持平衡需要持續接收整合感覺輸入，接著去制定活動的計劃並執行，以達到維持直立平衡的目標。",[12,10594,10595,10596,10598,10599,10603,10604,10606,10607,10609],{},"那平衡要達成，其實就是在處理這三個參數",[83,10597],{},"\nCOG——重心在站立時會在",[254,10600,10602],{"className":10601},[562],"S2","，且重心會按照肢體動作\u002F位置而改變",[83,10605],{},"\nBOS——這個區域當然就是越大越穩，越小越不穩（站著時是雙腳之間的範圍，坐著的是大腿和臀部構成的範圍）",[83,10608],{},"\nLOS——就是在原本BOS不變情況下，身體能在各個方向傾斜到的最遠距離",[12,10611,10612,10613,10615,10616,10618,10619,10621],{},"那維持平衡的模式，會分成三種類型（預防跌倒的三種反應模式）",[83,10614],{},"\n預期性——它是按照經驗來看的，主要是活動前會採取這個",[83,10617],{},"\n反應性——靠臨場反應",[83,10620],{},"\n適應性——主要是看任務或者環境來調整的",[12,10623,10624,10625,10627,10628,10630,10631,10633],{},"最後是環境的參數，那它會改變包括剛剛說到的最基本參數，以及因應這三個而改變",[83,10626],{},"\n地面性質——平坦草地VS沙漠",[83,10629],{},"\n視覺環境——昏暗環境VS光亮環境",[83,10632],{},"\n意圖跟選擇的任務——主動去做某些動作VS下意識（被動的，為了挽回某些情況）做的某些動作",[12,10635,10636,10637,10639],{},"那關於人類平衡的方式，這邊介紹一個觀點叫系統方式",[83,10638],{},"\n它是指說動態平衡的條件是按照這三點組成：個人、任務、環境（對 很熟悉對吧）",[12,10641,10642],{},[979,10643],{"alt":1236,"src":10644},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775460234558-Screenshot_2026-04-06_151838.png",[12,10646,10647],{},"那我就跳過講解這三要素好了，直接上圖",[12,10649,10650],{},"那接下來講周邊神經的接收，那跟姿勢控制相關的有這三個：軀體感覺、視覺、前庭覺",[12,10652,10653,10654,10658,10659,10663,10664,10666,10667,10669],{},"首先是視覺，那視角也是分成了",[254,10655,10657],{"className":10656},[258],"中間","眼睛清淅看到的，還有",[254,10660,10662],{"className":10661},[264],"周圍","不是直接注視的兩個部份",[83,10665],{},"\n那先來講中間直接注視的部份，主要是用來辦別環境方位包括",[83,10668],{},"\n判斷垂直，物體的動作（其他東西有沒有在動），環境裡的其他因素",[12,10671,10672,10673,10675],{},"然後講周圍的視角，主要是本體相對環境的的動作，包括了頭的晃動跟身體的晃動",[83,10674],{},"\n而上面就相當於視覺的本體感覺",[12,10677,10678,10679,10683],{},"那視角對於個人與",[254,10680,10682],{"className":10681},[562],"任務及環境的互動","十分重要（抓起物品，變動的環境）",[12,10685,10686,10687,10689,10690,10692],{},"那視覺評估有兩種",[83,10688],{},"\nFocal vision視銳度檢查",[83,10691],{},"\nAmbient vision視野檢查",[12,10694,10695,10696,10698,10699,9912,10703,10707,10709],{},"接著講到了軀體感覺，主要是包括了關節，肌肉，肌腱，皮膚給的訊息",[83,10697],{},"\n主要是負責",[254,10700,10702],{"className":10701},[562],"直立姿勢控制",[254,10704,10706],{"className":10705},[562],"自動姿勢反應",[83,10708],{},"\n相關的功能動作還包括了牽張反射，Flex withdraw&Crosses extensor reflex(踩到釘子，同側腳屈曲，對側腳伸直)",[12,10711,10712,10713,10715],{},"那常見會有這些病會影響軀體感覺",[83,10714],{},"\n包括了 糖尿病導致的神經病變，周邊血管疾病，SCI，截肢",{"title":169,"searchDepth":170,"depth":170,"links":10717},[],"定義~軀體感覺","\u002Fimages\u002Fuploads\u002F1775464559030-136205774_p1_master1200.jpg",{},{"title":10581,"description":10718},{"loc":753},"blog\u002F平衡與前庭失調（一）","fqsdv0C5-cbMeAawZlxu1uAaBRQ9zlXdDZaQme_epis",{"id":10726,"title":10727,"author":7,"body":10728,"date":10966,"description":10967,"draft":174,"edited_at":10100,"extension":175,"featured_image":10968,"meta":10969,"navigation":178,"path":10970,"pinned":174,"seo":10971,"series":181,"seriesOrder":181,"sitemap":10972,"stem":10973,"tags":181,"__hash__":10974},"blog\u002Fblog\u002FCVA（六）.md","CVA（六）",{"type":9,"value":10729,"toc":10964},[10730,10746,10780,10800,10802,10805,10817,10835,10844,10847,10909,10943],[12,10731,10732,10733,10735,10736,10738,10739,10741,10742],{},"那從時期來分PT能幹嘛 分成了",[83,10734],{},"\n急性期，復健期，回歸社會環境",[83,10737],{},"\n那CVA運動功能恢復時長需要數月到數年",[83,10740],{},"\n而復健黃金期只有",[254,10743,10745],{"className":10744},[562],"三到六個月",[12,10747,10748,10749,10751,10752,10756,10757,10759,10760,10764,10765,10767,10768,10772,10773,10775,10776],{},"CVA有相關的復健指標來預測",[83,10750],{},"\n第一點，假如復健期",[254,10753,10755],{"className":10754},[7640],"第一個月","表現很差，那中風後的半年的進步空間也會有限（86%）",[83,10758],{},"\n第二點，假如",[254,10761,10763],{"className":10762},[562],"前兩周內","病人上肢有回復，那代表那個病人以後上肢功能性一定會完全康復",[83,10766],{},"\n第三點，假如",[254,10769,10771],{"className":10770},[7640],"中風後24天","內沒有回復握力，這樣上肢的功能性恢復一定很差",[83,10774],{},"\n第四點，假如第一周內腿沒動作，第四周內手沒有動作，那病人預後",[254,10777,10779],{"className":10778},[562],"極差",[12,10781,10782,10783,10785,10786,10788,10789,10791,10792,10794,10795,10799],{},"從預後結果來看",[83,10784],{},"\n功能性是完全有機會康復的（只不能多次中風的話，難度會增大）",[83,10787],{},"\n就算是嚴重受損者例如包括認知功能受損，依然有機會讓他們功能性變好",[83,10790],{},"\n而且年齡不是決定預後的因素，主要要看動機以及受損程度",[83,10793],{},"\n尤其是",[254,10796,10798],{"className":10797},[7640],"年輕人","，因為年輕人在CVA上偏向出血型，出血型致死率更高",[35,10801],{},[12,10803,10804],{},"接著講損傷導致的限制跟失能部份",[12,10806,10807,10808,10810,10811,10813,10814,10816],{},"主要的損傷會以以下三點呈現",[83,10809],{},"\n第一點，癱瘓（MMT0分）或者無力",[83,10812],{},"\n第二點，高張力或低張力",[83,10815],{},"\n第三點，肌肉的啟動也有所改變",[12,10818,10819,10820,10822,10823,10825,10826,10828,10829,10831,10832,10834],{},"接著來講次級傷害，包括但不限於",[83,10821],{},"\n生理曲線與活動度改變",[83,10824],{},"\n肌肉與軟組織長度改變",[83,10827],{},"\n疼痛",[83,10830],{},"\n水腫",[83,10833],{},"\n等等等等.........",[12,10836,10837,10838,10840,10841,10843],{},"然後講動作上的問題，主要能觀察到這三種問題",[83,10839],{},"\n首先是動作喪失，異常動作模式，以及代償",[83,10842],{},"\n那這三個會漸漸影響ADL的獨立性，變得要別人來照顧",[12,10845,10846],{},"那中風病人會在復原中出現協同動作，可以分成上下肢以及屈曲伸直來看",[77,10848,10849,10861,10873,10886],{},[19,10850,10851,10852,486,10856,10860],{},"那首先是上肢的屈曲協同動作——肩胛骨後縮和上提，",[254,10853,10855],{"className":10854},[7640],"肩外轉外旋",[254,10857,10859],{"className":10858},[562],"肘屈曲","，前臂旋後，手指手腕屈曲",[19,10862,10863,10864,486,10868,10872],{},"接著是上肢的伸展協同動作——肩胛骨前伸，",[254,10865,10867],{"className":10866},[562],"肩內收內旋",[254,10869,10871],{"className":10870},[7640],"肘伸直","，前臂旋前，手腕手指屈曲",[19,10874,10875,10876,10880,10881,10885],{},"然後是下肢的屈曲協同動作——骨盤後縮上提(？)，髖",[254,10877,10879],{"className":10878},[562],"彎曲外展外旋","，膝",[254,10882,10884],{"className":10883},[7640],"彎曲90度","，踝背曲內翻，腳趾背屈",[19,10887,10888,10889,10893,10894,486,10899,10903,10904,10908],{},"最後是下肢的伸展協同動作——髖",[254,10890,10892],{"className":10891},[7640],"伸直","內旋",[254,10895,10898],{"className":10896},[10897],"bg-yellow-2","內收",[254,10900,10902],{"className":10901},[562],"膝伸直","，踝",[254,10905,10907],{"className":10906},[562],"蹠曲","內收，腳趾蹠曲",[12,10910,10911,10912,10914,10915,10919,10920,10922,10923,10927,10929,10930,10932,10933,10937,10939,10940,10942],{},"在中風病人身上還能看到聯合反應，簡單來說是病人健側用力，患側也會不自主用力",[83,10913],{},"\n上肢的話這個聯合反應是",[254,10916,10918],{"className":10917},[7640],"相同方向","的（例如我健側肘用力屈曲，患側也會肘屈曲）",[83,10921],{},"\n而下肢的則",[254,10924,10926],{"className":10925},[562],"相反（內收、外展除外",[83,10928],{},"\n也會有這三種特殊反應",[83,10931],{},"\n那打哈欠、打噴嚏、咳嗽的話，它們的",[254,10934,10936],{"className":10935},[562],"吸氣期會產生屈曲的協同動作",[83,10938],{},"\n而假如患側上肢有動作，那麼同側的下肢也會有動作（可以反過來，下肢先有動作讓上肢也有動作）(Homolateral Synkinesis)",[83,10941],{},"\n那結合剛剛上面說的因為下肢內收外展是同向，所以健側內收或外展，患側一樣是內收或外展",[12,10944,10945,10946,10948,10949,10951,10952,10954,10955,10957,10958,10960,10961,10963],{},"最後來講功能性限制，主要有以下六點",[83,10947],{},"\nADL",[83,10950],{},"\n床上活動能力",[83,10953],{},"\n轉移位",[83,10956],{},"\n平衡與姿勢控制",[83,10959],{},"\n移動能力",[83,10962],{},"\n上肢的功能性動作",{"title":169,"searchDepth":170,"depth":170,"links":10965},[],"2026-04-03","PT能幹嘛；受損導致的限制或失能","\u002Fimages\u002Fuploads\u002F1775208758679-138277104_p0_master1200.jpg",{},"\u002Fblog\u002FCVA（六）",{"title":10727,"description":10967},{"loc":10970},"blog\u002FCVA（六）","30KL8AqkEnXvxygyaPZNtTIGb4_AjMnXMhv1vHZd6bI",{"id":10976,"title":10977,"author":7,"body":10978,"date":10966,"description":11228,"draft":174,"edited_at":10100,"extension":175,"featured_image":11229,"meta":11230,"navigation":178,"path":11231,"pinned":174,"seo":11232,"series":181,"seriesOrder":181,"sitemap":11233,"stem":11234,"tags":181,"__hash__":11235},"blog\u002Fblog\u002FCVA（四）.md","CVA（五）",{"type":9,"value":10979,"toc":11226},[10980,10986,11000,11009,11024,11030,11051,11070,11097,11099,11102,11120,11138,11141,11164,11170,11187,11208,11217],[12,10981,10982,10983,10985],{},"在急性期我們能做甚麼呢，首先要看類型",[83,10984],{},"\n先來講血栓型跟TIA，接著要看的是缺血部位",[12,10987,10988,10989,10991,10992,10996,10997,10999],{},"一般來說缺血有分兩種變體 ",[83,10990],{},"\n一個叫中心區（80%～100%缺血），那這個區域細胞會在",[254,10993,10995],{"className":10994},[562],"幾分鐘內死亡","（梗塞）",[83,10998],{},"\n一個叫半影區（50%～80%缺血），這個區域的話，假如趕緊搶救，是能救得回來的（手術上也是專門搶救這個區域）",[12,11001,11002,11003,11005,11006,11008],{},"接著來看做甚麼處置 ",[83,11004],{},"\n首先是預防 預防勝於治療這是肯定的了",[83,11007],{},"\n能做的是維持血壓及血流",[12,11010,11011,11012,11014,11015,11017,11018,11020,11021,11023],{},"但假如不幸的話，有兩種手段",[83,11013],{},"\n首先是藥物 有三種類型的藥物",[83,11016],{},"\n第一類是Tissue plasminogen activator（老師給翻譯是組織性血栓溶解因子,t-PA）：在90-180分鐘內最有效",[83,11019],{},"\n第二類是抗凝血藥：有肝素，華法林",[83,11022],{},"\n第三類是抗血小板藥：有著名的阿斯匹靈",[12,11025,11026,11027,11029],{},"第二種手段就是手術，有兩種手術類型",[83,11028],{},"\n血栓內膜切開術（直接對堵住區域的斑塊\u002F血栓清理）和血管移植",[12,11031,11032,11033,11035,11036,330,11040,11042,11043,11047,11048,11050],{},"然後來看栓塞型 雖然他跟血栓型類似",[83,11034],{},"\n但主因是因為",[254,11037,11039],{"className":11038},[562],"別的地方的東西經血流漂到腦血管並堵住",[83,11041],{},"\n所以治療目的應主要放在",[254,11044,11046],{"className":11045},[562],"源頭上","例如心臟或大血管",[83,11049],{},"\n也有三種是高危險問題：心房震顫，心肌梗塞，人工瓣膜",[12,11052,11053,11054,11056,11057,11061,11062,11066,11067,11069],{},"接著是高血壓性的出血型",[83,11055],{},"\n一般來說，其實",[254,11058,11060],{"className":11059},[7640],"手術跟降壓","都",[254,11063,11065],{"className":11064},[562],"沒有很好","的對這個類型做處置",[83,11068],{},"\n所以能做得只有預防和長期控制（長期吃降血壓藥）",[12,11071,11072,11073,11075,11076,11078,11079,11087,11088,11090,11091,11093,11094,11096],{},"最後來講動脈瘤破裂的出血型 有以下幾種措施",[83,11074],{},"\n手術",[83,11077],{},"\n床上休養（",[7947,11080,11081],{},[773,11082,11083],{},[254,11084,11086],{"className":11085},[562],"絕對的床上休息","）4~6weeks",[83,11089],{},"\n降低動脈血壓",[83,11092],{},"\n抗癲癇藥物",[83,11095],{},"\n系統性抗纖維蛋白溶解劑",[35,11098],{},[12,11100,11101],{},"接著講併發症的相關處置，總得來說有七個大類",[12,11103,11104,11105,11107,11108,11112,11113,11117,11119],{},"肯定得先來講最大問題的痙攣了，也就是高張力",[83,11106],{},"\n那關於，管不管高張這個問題，其實吵了很久，因為，高張他",[254,11109,11111],{"className":11110},[264],"沒辦法做動作","，低張又軟癱也沒法",[254,11114,11116],{"className":11115},[264],"維持姿勢",[83,11118],{},"\n所以普遍會從這兩個方向去看待，影不影響動作，以及影不影響功能性（ADL）",[12,11121,11122,11123,11125,11126,11128,11129,11131,11132,11134,11135,11137],{},"那抑制痙攣有兩種手段，吃藥以及做手術",[83,11124],{},"\n首先講吃藥，用藥也分成了對周邊抑或者對中樞去作用",[83,11127],{},"\n這部份我只介紹老師打星的藥物",[83,11130],{},"\n首先對中樞的，藥名叫Diazepam，可以抑制掉整個中樞系統，但副作用有嗜睡，焦慮或者全身無力",[83,11133],{},"\n接著是周邊的，有兩種手段",[83,11136],{},"\n一種名字叫肉毒桿菌，另一種叫做脊髓內注射貝可芬（這個量極需要極小且不易嗜，效果也極佳）",[12,11139,11140],{},"手術的部份有三種，肌腱切開術，神經切除術，以後選擇性後神經根切除術",[12,11142,11143,11144,11146,11147,11151,11152,11154,11155,11157,11158,11160,11161,11163],{},"接著講第二大類，癲癇",[83,11145],{},"\n癲癇也是最麻煩的一個問題，我們給病人教導了一些東西後，遇到癲癇，教過的東西他都會",[254,11148,11150],{"className":11149},[562],"全部忘記","，相當於reset掉",[83,11153],{},"\n機率上來看，57%的病人會在第一周發生癲癇，而88%的病人會在第一年內發生癲癇",[83,11156],{},"\n類型上，血栓或者栓塞這兩個會比較早發生，而出血型會比較晚發生",[83,11159],{},"\n那治療癲癇當然就是用抗癲癇藥物了",[83,11162],{},"\n副作用的話會有：嗜睡，運動失調，注意力不集中，記憶力變差",[12,11165,11166,11167,11169],{},"第三大類，呼吸系統也會有影響",[83,11168],{},"\n主因有兩種，因為癱瘓導致的功能不全，以及因為痙攣導致的需氧增加（或者異常動作模式）",[12,11171,11172,11173,11175,11176,11178,11179,11181,11182,11186],{},"第四大類，創傷",[83,11174],{},"\n這很容易理解，中風了嘛，肯定有不穩定不平衡，抑或者不對稱姿勢導致跌導",[83,11177],{},"\n那常見的骨折部位有：肱骨，手腕，髖部",[83,11180],{},"\n這邊有小補充，偏癱病人的",[254,11183,11185],{"className":11184},[7640],"偏癱側肢體","會高機率有骨質疏鬆症（因為不常用\u002F廢用）",[12,11188,11189,11190,11192,11193,11195,11196,11198,11199,11201,11202,11204,11205,11207],{},"第五大類，血栓性靜脈炎跟深層靜脈栓塞",[83,11191],{},"\n這個問題其實在復健早期階段就會被發現了（而中風病人在中風前血管就已經有硬化或者狹窄問題）",[83,11194],{},"\n那深層靜脈栓塞成因有這幾點",[83,11197],{},"\n血流改變：流速變慢",[83,11200],{},"\n血管壁受損",[83,11203],{},"\n血流凝固時間改變：血液變稠",[83,11206],{},"\n患側姿體的不活動與垂放姿勢：不活動肌肉不收縮就沒法回流；垂放加上重力影響也沒法回流",[12,11209,11210,11211,11213,11214,11216],{},"第六大類，反射性交感神經失養症",[83,11212],{},"\n症狀有灼燒感",[83,11215],{},"\n處置上可以用交感神經阻斷劑，或者利用類固醇",[12,11218,11219,11220,11222,11223,11225],{},"最後一類，疼痛",[83,11221],{},"\n病人經常抱怨肩膀痛",[83,11224],{},"\n處置上是局部注射類固醇",{"title":169,"searchDepth":170,"depth":170,"links":11227},[],"急性期醫生能幹嘛以及併發症的相關處置","\u002Fimages\u002Fuploads\u002F1775193545170-142911098_p0_master1200.jpg",{},"\u002Fblog\u002FCVA（四）",{"title":10977,"description":11228},{"loc":11231},"blog\u002FCVA（四）","r6jrmqGHVdbIelVQZGp41itZnx8LxnparGf1IWVe11k",{"id":11237,"title":11238,"author":761,"body":11239,"date":15984,"description":15985,"draft":174,"edited_at":15986,"extension":175,"featured_image":15987,"meta":15988,"navigation":178,"path":753,"pinned":174,"seo":15989,"series":181,"seriesOrder":181,"sitemap":15990,"stem":15991,"tags":181,"__hash__":15992},"blog\u002Fblog\u002F機器學習導論.md","機器學習導論",{"type":9,"value":11240,"toc":15962},[11241,11244,11247,11250,11253,11257,11260,11267,11270,11284,11288,11291,11294,11325,11331,11334,11337,11363,11366,11369,11372,11404,11408,11411,11425,11429,11432,11452,11455,11516,11522,11525,11528,11554,11558,11561,11565,11620,11881,11927,11931,11934,12346,12349,12721,12784,12787,12794,12807,12811,12814,13260,13360,15254,15257,15268,15275,15477,15727,15736,15740,15743,15769,15784,15869,15873,15876,15902,15905,15908,15911,15925,15928,15931,15960],[765,11242,11243],{"id":11243},"前言",[12,11245,11246],{},"最近大學剛上第二學期，我發現機器學習算是挺難的一個科目。剛好我覺得可能會有人對機器學習感興趣，但不知道怎麽下手，或者想要大概看一眼機器學習是個什麽東東，再決定要不要深入學習。所以我想要基於大學講義，寫一篇對新手比較友好的文章，帶你揭開機器學習的神秘面紗~",[12,11248,11249],{},"當然，我的講義是英文寫的，在翻譯的時候難免會有錯誤。在遇到專用名詞的時候，我都會附上英文名詞，也盡量用通俗易懂的方式講解。這篇文章假設你已經有一定的編程基礎，但是不需要對機器學習方面有任何經驗。",[12,11251,11252],{},"準備好的話，我們就開始囉！",[765,11254,11256],{"id":11255},"到底什麼是學習","到底什麼是「學習」？",[12,11258,11259],{},"在開始聊「機器」學習之前，我們不妨先退一步想想：一般所謂的「學習」到底是什麼意思？",[12,11261,11262,11263,11266],{},"諾貝爾獎得主 Herbert Simon 曾給過一個很精準的定義：",[773,11264,11265],{},"「任何讓系統透過經驗，進而提升效能的過程。」"," 這句話非常直白，而且不僅適用於人類，套用在電腦上也完全講得通。",[12,11268,11269],{},"當我們希望機器去「學習」並不斷進步時，丟給它們的任務通常可以分成兩大類：",[77,11271,11272,11278],{},[19,11273,11274,11277],{},[773,11275,11276],{},"分類 (Classification)"," ： 把東西歸類到不同的標籤下（例如：「這封 email 是不是垃圾郵件？」）",[19,11279,11280,11283],{},[773,11281,11282],{},"問題解決 \u002F 規劃 \u002F 控制 (Problem solving \u002F Planning \u002F Control)"," ： 採取一連串的行動來達成某個目標（例如：「機器人該怎麼走才能離開迷宮？」）",[765,11285,11287],{"id":11286},"機器學習ai-到底差在哪","機器學習、AI 到底差在哪？",[12,11289,11290],{},"在看新聞或滑文章時，你可能常看到人工智慧 (AI)、機器學習 (ML)、深度學習 (DL) 和資料科學 (Data Science) 這幾個詞被混著用。雖然它們彼此相關，但其實不完全一樣。",[12,11292,11293],{},"你可以把它們想像成一組同心圓：",[77,11295,11296,11302,11308,11314],{},[19,11297,11298,11301],{},[773,11299,11300],{},"人工智慧 (AI)"," 是最廣泛的概念。它指的是創造能夠模仿人類智慧行為的機器。需要注意的是，AI 只在乎結果看起來聰不聰明，不在乎背後是怎麼做到的。如果你今天讓工程師寫個幾千行 if-else，那也算AI。事實上，在電腦發展的前幾十年，大家都是這樣寫 AI 的。",[19,11303,11304,11307],{},[773,11305,11306],{},"機器學習 (ML)"," 是 AI 的一個分支。跟人工手寫 if-else 規則不同，ML 是讓系統自己從資料裡面找出規律，然後用這些規律來做預測或決策。",[19,11309,11310,11313],{},[773,11311,11312],{},"深度學習 (DL)"," 又是機器學習的再往下一個分支，主要是用多層的「神經網路」來處理像影像辨識、自然語言處理等超複雜的問題。",[19,11315,11316,11319,11320,11322],{},[773,11317,11318],{},"資料科學 (Data Science)"," 則與上述所有領域都有交集。它是一門更廣的學科，涵蓋了怎麼用統計學、科學方法和演算法，從資料裡挖出有價值的資訊。",[83,11321],{},[979,11323],{"alt":1236,"src":11324},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1775145963610-Screenshot_2026-04-03_000510.png",[12,11326,11327,11328],{},"簡單來說：",[773,11329,11330],{},"機器學習的重點在於「用訓練資料建立模型來做預測」，而不是靠人去手寫規則。",[765,11332,11333],{"id":11333},"機器學習的四大種類",[12,11335,11336],{},"根據電腦系統學習的方式，我們可以把機器學習分成幾個主要類別：",[77,11338,11339,11345,11351,11357],{},[19,11340,11341,11344],{},[773,11342,11343],{},"監督式學習 (Supervised Learning)"," ： 就像你給模型看題目和標準答案。你餵給模型一堆附帶答案的範例，讓它自己去搞清楚輸入和輸出之間的關係。這包含了預測連續數字的「迴歸」(Regression，像是預測房價)，以及預測類別的「分類」(Classification，像是分辨垃圾郵件)。",[19,11346,11347,11350],{},[773,11348,11349],{},"非監督式學習 (Unsupervised Learning)"," ： 模型只拿到一堆沒有標準答案（標籤）的資料，必須自己找出裡面的架構。這裡最常見的任務是「分群」(Clustering)，把長得像的資料分在同一組。",[19,11352,11353,11356],{},[773,11354,11355],{},"強化學習 (Reinforcement Learning)"," ： 模型透過與環境互動來學習。它會採取行動，然後得到獎勵或懲罰，最後慢慢試出最好的策略。你可以想像成用零食跟指令在訓練狗狗。",[19,11358,11359,11362],{},[773,11360,11361],{},"自監督式學習 (Self-Supervised Learning)"," ： 這算是比較新的玩法。模型會根據資料本身「自己生出標籤」，幫自己出考題（例如把句子裡的某個單字挖空，然後叫模型練習預測那個字是什麼）。",[765,11364,11365],{"id":11365},"實際應用",[781,11367,11368],{"id":11368},"分類應用範例",[12,11370,11371],{},"分類在我們的日常生活中無所不在：",[77,11373,11374,11380,11386,11392,11398],{},[19,11375,11376,11379],{},[773,11377,11378],{},"醫療診斷"," ： 這張 X 光片是否有肺炎的跡象？",[19,11381,11382,11385],{},[773,11383,11384],{},"垃圾郵件過濾"," ： 這封 email 該收進收件箱還是垃圾信箱？",[19,11387,11388,11391],{},[773,11389,11390],{},"詐欺偵測"," ： 這筆信用卡交易是否可疑？",[19,11393,11394,11397],{},[773,11395,11396],{},"推薦系統"," ： 你可能會喜歡聽哪首歌、看哪部電影？",[19,11399,11400,11403],{},[773,11401,11402],{},"語音與手寫辨識"," ： 將口語或手寫文字轉換為數位文字。",[781,11405,11407],{"id":11406},"問題解決-規劃-控制範例","問題解決 \u002F 規劃 \u002F 控制範例",[12,11409,11410],{},"在這些任務中，代理程式 (Agent) 會根據環境自己採取行動來達成目標：",[77,11412,11413,11416,11419,11422],{},[19,11414,11415],{},"下西洋棋、圍棋等棋盤遊戲",[19,11417,11418],{},"開在路上的自動駕駛汽車",[19,11420,11421],{},"控制機器人或遊戲角色",[19,11423,11424],{},"無人機或直升機的自主飛行",[765,11426,11428],{"id":11427},"定義學習任務的萬用公式tpe","定義學習任務的萬用公式：T、P、E",[12,11430,11431],{},"當你想構思一個機器學習的專案時，Tom Mitchell 提出的一個框架超好用。每一個學習任務都可以用三個元素來定義：",[77,11433,11434,11440,11446],{},[19,11435,11436,11439],{},[773,11437,11438],{},"T (任務, Task)"," ： 你想讓系統嘗試做什麽？",[19,11441,11442,11445],{},[773,11443,11444],{},"P (效能, Performance)"," ： 我們應該如何衡量成功與否？",[19,11447,11448,11451],{},[773,11449,11450],{},"E (經驗, Experience)"," ： 系統要從什麼資料中學習？",[12,11453,11454],{},"這裡有幾個具體的範例：",[872,11456,11457,11470],{},[875,11458,11459],{},[878,11460,11461,11464,11467],{},[881,11462,11463],{"align":883},"任務 (T)",[881,11465,11466],{"align":883},"效能 (P)",[881,11468,11469],{"align":883},"經驗 (E)",[898,11471,11472,11483,11494,11505],{},[878,11473,11474,11477,11480],{},[903,11475,11476],{"align":883},"下西洋跳棋",[903,11478,11479],{"align":883},"贏得比賽的概率",[903,11481,11482],{"align":883},"自我對弈的練習賽",[878,11484,11485,11488,11491],{},[903,11486,11487],{"align":883},"辨識手寫單字",[903,11489,11490],{"align":883},"正確分類單字的概率",[903,11492,11493],{"align":883},"一堆有標註標準答案的手寫圖檔",[878,11495,11496,11499,11502],{},[903,11497,11498],{"align":883},"在高速公路上駕駛",[903,11500,11501],{"align":883},"發生人為判定錯誤前的平均行駛距離",[903,11503,11504],{"align":883},"記錄人類駕駛的影像與方向盤指令",[878,11506,11507,11510,11513],{},[903,11508,11509],{"align":883},"垃圾郵件分類",[903,11511,11512],{"align":883},"正確分類電子郵件的概率",[903,11514,11515],{"align":883},"帶有人工標籤的電子郵件資料庫",[12,11517,11518,11519],{},"在開始任何機器學習專案之前，這個框架非常適合用來釐清思緒。問問自己：",[7947,11520,11521],{},"我的 T、P 和 E 分別是什麼？",[765,11523,11524],{"id":11524},"設計學習系統",[12,11526,11527],{},"當你著手建立一個機器學習系統時，有四個關鍵的設計決策：",[16,11529,11530,11536,11542,11548],{},[19,11531,11532,11535],{},[773,11533,11534],{},"選擇訓練經驗"," ： 系統將從哪種資料中學習？是直接的（有標籤的輸入-輸出對），還是間接的（例如只知道一盤棋最後的輸贏，但不知道中間每一步的好壞）？",[19,11537,11538,11541],{},[773,11539,11540],{},"選擇目標函數"," ： 系統究竟應該學習什麼？以跳棋程式為例，它要學的可能是一個「評估函數」，用來給當下的棋盤局勢打分數。",[19,11543,11544,11547],{},[773,11545,11546],{},"選擇表達方式"," ：這個目標函數要長什麼樣子？可以是查詢表 (lookup tables)、線性函數 (linear function)、決策樹 (decision tree)、神經網路等 (neural network)。",[19,11549,11550,11553],{},[773,11551,11552],{},"選擇學習演算法"," ： 系統要用什麼方法去找到那個「最好的函數」？這可能是梯度下降法 (gradient decent)、動態規劃 (dynamic programming)、演化演算法等 (evolutionary algorithms)。",[765,11555,11557],{"id":11556},"具體範例教電腦下西洋跳棋","具體範例：教電腦下西洋跳棋",[12,11559,11560],{},"好，理論講了一堆，我們來把所有東西串起來。我們來看一個經典的老例子：Arthur Samuel 在 1959 年寫的跳棋程式。這可是史上最早的機器學習系統之一。",[781,11562,11564],{"id":11563},"目標函數-target-function","目標函數 (Target Function)",[12,11566,11567,11568,10176,11571,11619],{},"我們想讓系統學到一個",[773,11569,11570],{},"評估函數",[967,11572,11574],{"className":11573,"jax":971},[970],[973,11575,11578,11592],{"style":975,"xmlns":976,"width":11576,"height":978,"role":979,"focusable":980,"viewBox":11577,"xmlnsXLink":982},"4.471ex","0 -750 1976 1000",[984,11579,11580,11584,11586,11590],{},[987,11581],{"id":11582,"d":11583},"MJX-1-TEX-I-1D449","M52 648Q52 670 65 683H76Q118 680 181 680Q299 680 320 683H330Q336 677 336 674T334 656Q329 641 325 637H304Q282 635 274 635Q245 630 242 620Q242 618 271 369T301 118L374 235Q447 352 520 471T595 594Q599 601 599 609Q599 633 555 637Q537 637 537 648Q537 649 539 661Q542 675 545 679T558 683Q560 683 570 683T604 682T668 681Q737 681 755 683H762Q769 676 769 672Q769 655 760 640Q757 637 743 637Q730 636 719 635T698 630T682 623T670 615T660 608T652 599T645 592L452 282Q272 -9 266 -16Q263 -18 259 -21L241 -22H234Q216 -22 216 -15Q213 -9 177 305Q139 623 138 626Q133 637 76 637H59Q52 642 52 648Z",[987,11585],{"id":989,"d":990},[987,11587],{"id":11588,"d":11589},"MJX-1-TEX-I-1D44F","M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 114Q114 66 138 42Q154 26 178 26Q211 26 245 58Q270 81 285 114T318 219Q336 291 336 325Z",[987,11591],{"id":1009,"d":1010},[1024,11593,11594],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11595,11596,11602,11607,11614],{"dataMmlNode":1031},[1024,11597,11598],{"dataMmlNode":1282},[1036,11599],{"dataC":11600,"xLinkHref":11601},"1D449","#MJX-1-TEX-I-1D449",[1024,11603,11605],{"dataMmlNode":1034,"transform":11604},"translate(769,0)",[1036,11606],{"dataC":1038,"xLinkHref":1039},[1024,11608,11610],{"dataMmlNode":1282,"transform":11609},"translate(1158,0)",[1036,11611],{"dataC":11612,"xLinkHref":11613},"1D44F","#MJX-1-TEX-I-1D44F",[1024,11615,11617],{"dataMmlNode":1034,"transform":11616},"translate(1587,0)",[1036,11618],{"dataC":1074,"xLinkHref":1075},"，你給它一個棋盤的狀態，它就回傳一個分數，告訴你現在的局勢對我們有多有利。在理想情況下：",[77,11621,11622,11693,11774,11834],{},[19,11623,11624,11625],{},"如果這盤棋贏定了，",[967,11626,11628],{"className":11627,"jax":971},[970],[973,11629,11632,11653],{"style":975,"xmlns":976,"width":11630,"height":978,"role":979,"focusable":980,"viewBox":11631,"xmlnsXLink":982},"10.881ex","0 -750 4809.6 1000",[984,11633,11634,11637,11639,11642,11644,11647,11650],{},[987,11635],{"id":11636,"d":11583},"MJX-2-TEX-I-1D449",[987,11638],{"id":1265,"d":990},[987,11640],{"id":11641,"d":11589},"MJX-2-TEX-I-1D44F",[987,11643],{"id":1272,"d":1010},[987,11645],{"id":11646,"d":1018},"MJX-2-TEX-N-3D",[987,11648],{"id":11649,"d":1725},"MJX-2-TEX-N-31",[987,11651],{"id":11652,"d":1718},"MJX-2-TEX-N-30",[1024,11654,11655],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11656,11657,11662,11666,11671,11675,11681],{"dataMmlNode":1031},[1024,11658,11659],{"dataMmlNode":1282},[1036,11660],{"dataC":11600,"xLinkHref":11661},"#MJX-2-TEX-I-1D449",[1024,11663,11664],{"dataMmlNode":1034,"transform":11604},[1036,11665],{"dataC":1038,"xLinkHref":1294},[1024,11667,11668],{"dataMmlNode":1282,"transform":11609},[1036,11669],{"dataC":11612,"xLinkHref":11670},"#MJX-2-TEX-I-1D44F",[1024,11672,11673],{"dataMmlNode":1034,"transform":11616},[1036,11674],{"dataC":1074,"xLinkHref":1306},[1024,11676,11678],{"dataMmlNode":1034,"transform":11677},"translate(2253.8,0)",[1036,11679],{"dataC":1097,"xLinkHref":11680},"#MJX-2-TEX-N-3D",[1024,11682,11684,11687,11690],{"dataMmlNode":1042,"transform":11683},"translate(3309.6,0)",[1036,11685],{"dataC":1793,"xLinkHref":11686},"#MJX-2-TEX-N-31",[1036,11688],{"dataC":1774,"xLinkHref":11689,"transform":1052},"#MJX-2-TEX-N-30",[1036,11691],{"dataC":1774,"xLinkHref":11689,"transform":11692},"translate(1000,0)",[19,11694,11695,11696],{},"如果這盤棋輸定了，",[967,11697,11699],{"className":11698,"jax":971},[970],[973,11700,11703,11729],{"style":975,"xmlns":976,"width":11701,"height":978,"role":979,"focusable":980,"viewBox":11702,"xmlnsXLink":982},"12.642ex","0 -750 5587.6 1000",[984,11704,11705,11708,11711,11714,11717,11720,11723,11726],{},[987,11706],{"id":11707,"d":11583},"MJX-3-TEX-I-1D449",[987,11709],{"id":11710,"d":990},"MJX-3-TEX-N-28",[987,11712],{"id":11713,"d":11589},"MJX-3-TEX-I-1D44F",[987,11715],{"id":11716,"d":1010},"MJX-3-TEX-N-29",[987,11718],{"id":11719,"d":1018},"MJX-3-TEX-N-3D",[987,11721],{"id":11722,"d":1955},"MJX-3-TEX-N-2212",[987,11724],{"id":11725,"d":1725},"MJX-3-TEX-N-31",[987,11727],{"id":11728,"d":1718},"MJX-3-TEX-N-30",[1024,11730,11731],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11732,11733,11738,11743,11748,11753,11758,11763],{"dataMmlNode":1031},[1024,11734,11735],{"dataMmlNode":1282},[1036,11736],{"dataC":11600,"xLinkHref":11737},"#MJX-3-TEX-I-1D449",[1024,11739,11740],{"dataMmlNode":1034,"transform":11604},[1036,11741],{"dataC":1038,"xLinkHref":11742},"#MJX-3-TEX-N-28",[1024,11744,11745],{"dataMmlNode":1282,"transform":11609},[1036,11746],{"dataC":11612,"xLinkHref":11747},"#MJX-3-TEX-I-1D44F",[1024,11749,11750],{"dataMmlNode":1034,"transform":11616},[1036,11751],{"dataC":1074,"xLinkHref":11752},"#MJX-3-TEX-N-29",[1024,11754,11755],{"dataMmlNode":1034,"transform":11677},[1036,11756],{"dataC":1097,"xLinkHref":11757},"#MJX-3-TEX-N-3D",[1024,11759,11760],{"dataMmlNode":1034,"transform":11683},[1036,11761],{"dataC":2081,"xLinkHref":11762},"#MJX-3-TEX-N-2212",[1024,11764,11766,11769,11772],{"dataMmlNode":1042,"transform":11765},"translate(4087.6,0)",[1036,11767],{"dataC":1793,"xLinkHref":11768},"#MJX-3-TEX-N-31",[1036,11770],{"dataC":1774,"xLinkHref":11771,"transform":1052},"#MJX-3-TEX-N-30",[1036,11773],{"dataC":1774,"xLinkHref":11771,"transform":11692},[19,11775,11776,11777],{},"如果是平手，",[967,11778,11780],{"className":11779,"jax":971},[970],[973,11781,11784,11802],{"style":975,"xmlns":976,"width":11782,"height":978,"role":979,"focusable":980,"viewBox":11783,"xmlnsXLink":982},"8.619ex","0 -750 3809.6 1000",[984,11785,11786,11789,11791,11794,11796,11799],{},[987,11787],{"id":11788,"d":11583},"MJX-4-TEX-I-1D449",[987,11790],{"id":1350,"d":990},[987,11792],{"id":11793,"d":11589},"MJX-4-TEX-I-1D44F",[987,11795],{"id":1356,"d":1010},[987,11797],{"id":11798,"d":1018},"MJX-4-TEX-N-3D",[987,11800],{"id":11801,"d":1718},"MJX-4-TEX-N-30",[1024,11803,11804],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11805,11806,11811,11815,11820,11824,11829],{"dataMmlNode":1031},[1024,11807,11808],{"dataMmlNode":1282},[1036,11809],{"dataC":11600,"xLinkHref":11810},"#MJX-4-TEX-I-1D449",[1024,11812,11813],{"dataMmlNode":1034,"transform":11604},[1036,11814],{"dataC":1038,"xLinkHref":1376},[1024,11816,11817],{"dataMmlNode":1282,"transform":11609},[1036,11818],{"dataC":11612,"xLinkHref":11819},"#MJX-4-TEX-I-1D44F",[1024,11821,11822],{"dataMmlNode":1034,"transform":11616},[1036,11823],{"dataC":1074,"xLinkHref":1386},[1024,11825,11826],{"dataMmlNode":1034,"transform":11677},[1036,11827],{"dataC":1097,"xLinkHref":11828},"#MJX-4-TEX-N-3D",[1024,11830,11831],{"dataMmlNode":1042,"transform":11683},[1036,11832],{"dataC":1774,"xLinkHref":11833},"#MJX-4-TEX-N-30",[19,11835,11836,11837,11880],{},"在其他情況下，",[967,11838,11840],{"className":11839,"jax":971},[970],[973,11841,11842,11856],{"style":975,"xmlns":976,"width":11576,"height":978,"role":979,"focusable":980,"viewBox":11577,"xmlnsXLink":982},[984,11843,11844,11847,11850,11853],{},[987,11845],{"id":11846,"d":11583},"MJX-5-TEX-I-1D449",[987,11848],{"id":11849,"d":990},"MJX-5-TEX-N-28",[987,11851],{"id":11852,"d":11589},"MJX-5-TEX-I-1D44F",[987,11854],{"id":11855,"d":1010},"MJX-5-TEX-N-29",[1024,11857,11858],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11859,11860,11865,11870,11875],{"dataMmlNode":1031},[1024,11861,11862],{"dataMmlNode":1282},[1036,11863],{"dataC":11600,"xLinkHref":11864},"#MJX-5-TEX-I-1D449",[1024,11866,11867],{"dataMmlNode":1034,"transform":11604},[1036,11868],{"dataC":1038,"xLinkHref":11869},"#MJX-5-TEX-N-28",[1024,11871,11872],{"dataMmlNode":1282,"transform":11609},[1036,11873],{"dataC":11612,"xLinkHref":11874},"#MJX-5-TEX-I-1D44F",[1024,11876,11877],{"dataMmlNode":1034,"transform":11616},[1036,11878],{"dataC":1074,"xLinkHref":11879},"#MJX-5-TEX-N-29"," 就等於如果雙方都完美發揮，最後能拿到的最佳分數。",[12,11882,11883,11884,11923,11924,1108],{},"但問題來了：要算出精確的",[967,11885,11887],{"className":11886,"jax":971},[970],[973,11888,11889,11901],{"style":975,"xmlns":976,"width":11576,"height":978,"role":979,"focusable":980,"viewBox":11577,"xmlnsXLink":982},[984,11890,11891,11894,11896,11899],{},[987,11892],{"id":11893,"d":11583},"MJX-6-TEX-I-1D449",[987,11895],{"id":1422,"d":990},[987,11897],{"id":11898,"d":11589},"MJX-6-TEX-I-1D44F",[987,11900],{"id":1431,"d":1010},[1024,11902,11903],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,11904,11905,11910,11914,11919],{"dataMmlNode":1031},[1024,11906,11907],{"dataMmlNode":1282},[1036,11908],{"dataC":11600,"xLinkHref":11909},"#MJX-6-TEX-I-1D449",[1024,11911,11912],{"dataMmlNode":1034,"transform":11604},[1036,11913],{"dataC":1038,"xLinkHref":1447},[1024,11915,11916],{"dataMmlNode":1282,"transform":11609},[1036,11917],{"dataC":11612,"xLinkHref":11918},"#MJX-6-TEX-I-1D44F",[1024,11920,11921],{"dataMmlNode":1034,"transform":11616},[1036,11922],{"dataC":1074,"xLinkHref":1470},"，電腦得把整個遊戲的所有可能性都算過一遍，其運算量是天文數字。所以我們只能退而求其次，找一個",[773,11925,11926],{},"近似值",[781,11928,11930],{"id":11929},"線性近似-linear-approximation","線性近似 (Linear Approximation)",[12,11932,11933],{},"我們可以把評估函數設計成各種「棋盤特徵」的加權總和：",[12,11935,11936],{},[967,11937,11939],{"className":11938,"jax":971},[970],[973,11940,11943,12009],{"style":975,"xmlns":976,"width":11941,"height":978,"role":979,"focusable":980,"viewBox":11942,"xmlnsXLink":982},"80.766ex","0 -750 35698.8 1000",[984,11944,11945,11948,11951,11954,11957,11960,11963,11966,11969,11972,11976,11980,11983,11987,11991,11995,11999,12002,12006],{},[987,11946],{"id":11947,"d":11583},"MJX-7-TEX-I-1D449",[987,11949],{"id":11950,"d":990},"MJX-7-TEX-N-28",[987,11952],{"id":11953,"d":11589},"MJX-7-TEX-I-1D44F",[987,11955],{"id":11956,"d":1010},"MJX-7-TEX-N-29",[987,11958],{"id":11959,"d":1018},"MJX-7-TEX-N-3D",[987,11961],{"id":11962,"d":4333},"MJX-7-TEX-I-1D464",[987,11964],{"id":11965,"d":1718},"MJX-7-TEX-N-30",[987,11967],{"id":11968,"d":1002},"MJX-7-TEX-N-2B",[987,11970],{"id":11971,"d":1725},"MJX-7-TEX-N-31",[987,11973],{"id":11974,"d":11975},"MJX-7-TEX-N-22C5","M78 250Q78 274 95 292T138 310Q162 310 180 294T199 251Q199 226 182 208T139 190T96 207T78 250Z",[987,11977],{"id":11978,"d":11979},"MJX-7-TEX-I-1D45D","M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z",[987,11981],{"id":11982,"d":994},"MJX-7-TEX-N-32",[987,11984],{"id":11985,"d":11986},"MJX-7-TEX-I-1D45F","M21 287Q22 290 23 295T28 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= 紅棋國王的數量",[19,12608,12609,12661],{},[967,12610,12612],{"className":12611,"jax":971},[970],[973,12613,12616,12630],{"style":975,"xmlns":976,"width":12614,"height":978,"role":979,"focusable":980,"viewBox":12615,"xmlnsXLink":982},"4.518ex","0 -750 1997 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= 受到威脅的黑棋數量",[19,12663,12664,12720],{},[967,12665,12667],{"className":12666,"jax":971},[970],[973,12668,12671,12688],{"style":975,"xmlns":976,"width":12669,"height":978,"role":979,"focusable":980,"viewBox":12670,"xmlnsXLink":982},"4.568ex","0 -750 2019 1000",[984,12672,12673,12676,12679,12682,12685],{},[987,12674],{"id":12675,"d":11986},"MJX-14-TEX-I-1D45F",[987,12677],{"id":12678,"d":12005},"MJX-14-TEX-I-1D461",[987,12680],{"id":12681,"d":990},"MJX-14-TEX-N-28",[987,12683],{"id":12684,"d":11589},"MJX-14-TEX-I-1D44F",[987,12686],{"id":12687,"d":1010},"MJX-14-TEX-N-29",[1024,12689,12690],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,12691,12692,12697,12702,12708,12714],{"dataMmlNode":1031},[1024,12693,12694],{"dataMmlNode":1282},[1036,12695],{"dataC":12130,"xLinkHref":12696},"#MJX-14-TEX-I-1D45F",[1024,12698,12699],{"dataMmlNode":1282,"transform":12477},[1036,12700],{"dataC":12282,"xLinkHref":12701},"#MJX-14-TEX-I-1D461",[1024,12703,12705],{"dataMmlNode":1034,"transform":12704},"translate(812,0)",[1036,12706],{"dataC":1038,"xLinkHref":12707},"#MJX-14-TEX-N-28",[1024,12709,12711],{"dataMmlNode":1282,"transform":12710},"translate(1201,0)",[1036,12712],{"dataC":11612,"xLinkHref":12713},"#MJX-14-TEX-I-1D44F",[1024,12715,12717],{"dataMmlNode":1034,"transform":12716},"translate(1630,0)",[1036,12718],{"dataC":1074,"xLinkHref":12719},"#MJX-14-TEX-N-29"," = 受到威脅的紅棋數量",[12,12722,12723,12724,12753,12754,12783],{},"這些權重（",[967,12725,12727],{"className":12726,"jax":971},[970],[973,12728,12729,12737],{"style":5273,"xmlns":976,"width":12358,"height":12359,"role":979,"focusable":980,"viewBox":12360,"xmlnsXLink":982},[984,12730,12731,12734],{},[987,12732],{"id":12733,"d":4333},"MJX-15-TEX-I-1D464",[987,12735],{"id":12736,"d":1718},"MJX-15-TEX-N-30",[1024,12738,12739],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,12740,12741],{"dataMmlNode":1031},[1024,12742,12743,12748],{"dataMmlNode":1761},[1024,12744,12745],{"dataMmlNode":1282},[1036,12746],{"dataC":4392,"xLinkHref":12747},"#MJX-15-TEX-I-1D464",[1024,12749,12750],{"dataMmlNode":1042,"transform":12047},[1036,12751],{"dataC":1774,"xLinkHref":12752},"#MJX-15-TEX-N-30"," 到 ",[967,12755,12757],{"className":12756,"jax":971},[970],[973,12758,12759,12767],{"style":5273,"xmlns":976,"width":12358,"height":12359,"role":979,"focusable":980,"viewBox":12360,"xmlnsXLink":982},[984,12760,12761,12764],{},[987,12762],{"id":12763,"d":4333},"MJX-16-TEX-I-1D464",[987,12765],{"id":12766,"d":1022},"MJX-16-TEX-N-36",[1024,12768,12769],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,12770,12771],{"dataMmlNode":1031},[1024,12772,12773,12778],{"dataMmlNode":1761},[1024,12774,12775],{"dataMmlNode":1282},[1036,12776],{"dataC":4392,"xLinkHref":12777},"#MJX-16-TEX-I-1D464",[1024,12779,12780],{"dataMmlNode":1042,"transform":12047},[1036,12781],{"dataC":1106,"xLinkHref":12782},"#MJX-16-TEX-N-36","）就是系統需要「學習」的東西。說白了，學習的過程就是在調整這些數字。",[781,12785,12786],{"id":12786},"透過間接經驗進行訓練",[12,12788,12789,12790,12793],{},"因為我們是讓電腦自己跟自己下棋，沒辦法在它每走一步時都告訴它「這步得幾分」。取而代之的是，我們用",[773,12791,12792],{},"時序差分學習 (Temporal difference 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",[967,14215,14217],{"className":14216,"jax":971},[970],[973,14218,14219,14224],{"style":1253,"xmlns":976,"width":13323,"height":1595,"role":979,"focusable":980,"viewBox":13324,"xmlnsXLink":982},[984,14220,14221],{},[987,14222],{"id":14223,"d":11589},"MJX-37-TEX-I-1D44F",[1024,14225,14226],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14227,14228],{"dataMmlNode":1031},[1024,14229,14230],{"dataMmlNode":1282},[1036,14231],{"dataC":11612,"xLinkHref":14232},"#MJX-37-TEX-I-1D44F","），你定睛一看，發現畫面上目前有 ",[773,14235,14236],{},"5 顆黑棋","，而且",[773,14239,14240],{},"沒有黑棋國王",[12,14242,14243,14244,14263],{},"那麼，對這個棋盤 ",[967,14245,14247],{"className":14246,"jax":971},[970],[973,14248,14249,14254],{"style":1253,"xmlns":976,"width":13323,"height":1595,"role":979,"focusable":980,"viewBox":13324,"xmlnsXLink":982},[984,14250,14251],{},[987,14252],{"id":14253,"d":11589},"MJX-38-TEX-I-1D44F",[1024,14255,14256],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14257,14258],{"dataMmlNode":1031},[1024,14259,14260],{"dataMmlNode":1282},[1036,14261],{"dataC":11612,"xLinkHref":14262},"#MJX-38-TEX-I-1D44F"," 來說：",[77,14265,14266,14318],{},[19,14267,14268,14269],{},"第 1 個特徵值 ",[773,14270,14271],{},[967,14272,14274],{"className":14273,"jax":971},[970],[973,14275,14278,14291],{"style":1338,"xmlns":976,"width":14276,"height":13291,"role":979,"focusable":980,"viewBox":14277,"xmlnsXLink":982},"6.245ex","0 -705 2760.1 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",[773,14322,14323],{},[967,14324,14326],{"className":14325,"jax":971},[970],[973,14327,14328,14342],{"style":1338,"xmlns":976,"width":14276,"height":13291,"role":979,"focusable":980,"viewBox":14277,"xmlnsXLink":982},[984,14329,14330,14333,14336,14339],{},[987,14331],{"id":14332,"d":13128},"MJX-40-TEX-I-1D453",[987,14334],{"id":14335,"d":11990},"MJX-40-TEX-N-33",[987,14337],{"id":14338,"d":1018},"MJX-40-TEX-N-3D",[987,14340],{"id":14341,"d":1718},"MJX-40-TEX-N-30",[1024,14343,14344],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14345,14346,14358,14363],{"dataMmlNode":1031},[1024,14347,14348,14353],{"dataMmlNode":1761},[1024,14349,14350],{"dataMmlNode":1282},[1036,14351],{"dataC":13204,"xLinkHref":14352},"#MJX-40-TEX-I-1D453",[1024,14354,14355],{"dataMmlNode":1042,"transform":13208},[1036,14356],{"dataC":12168,"xLinkHref":14357},"#MJX-40-TEX-N-33",[1024,14359,14360],{"dataMmlNode":1034,"transform":14309},[1036,14361],{"dataC":1097,"xLinkHref":14362},"#MJX-40-TEX-N-3D",[1024,14364,14365],{"dataMmlNode":1042,"transform":14314},[1036,14366],{"dataC":1774,"xLinkHref":14367},"#MJX-40-TEX-N-30",[12,14369,14370,14399,14400,10176,14420,14423],{},[967,14371,14373],{"className":14372,"jax":971},[970],[973,14374,14375,14383],{"style":1338,"xmlns":976,"width":13290,"height":13291,"role":979,"focusable":980,"viewBox":13292,"xmlnsXLink":982},[984,14376,14377,14380],{},[987,14378],{"id":14379,"d":13128},"MJX-41-TEX-I-1D453",[987,14381],{"id":14382,"d":1269},"MJX-41-TEX-I-1D456",[1024,14384,14385],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14386,14387],{"dataMmlNode":1031},[1024,14388,14389,14394],{"dataMmlNode":1761},[1024,14390,14391],{"dataMmlNode":1282},[1036,14392],{"dataC":13204,"xLinkHref":14393},"#MJX-41-TEX-I-1D453",[1024,14395,14396],{"dataMmlNode":1282,"transform":13208},[1036,14397],{"dataC":1299,"xLinkHref":14398},"#MJX-41-TEX-I-1D456"," 其實就是在問：「",[773,14401,14402,14403],{},"現在盤面上，第",[967,14404,14406],{"className":14405,"jax":971},[970],[973,14407,14408,14412],{"style":1253,"xmlns":976,"width":1313,"height":1314,"role":979,"focusable":980,"viewBox":1315,"xmlnsXLink":982},[984,14409,14410],{},[987,14411],{"id":3806,"d":1269},[1024,14413,14414],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14415,14416],{"dataMmlNode":1031},[1024,14417,14418],{"dataMmlNode":1282},[1036,14419],{"dataC":1299,"xLinkHref":3845},[773,14421,14422],{},"號特徵有幾個？","」",[781,14425,14427,14428,14455],{"id":14426},"為什麼更新公式裡需要乘上","為什麼更新公式裡需要乘上 ",[967,14429,14431],{"className":14430,"jax":971},[970],[973,14432,14433,14440],{"style":1338,"xmlns":976,"width":13290,"height":13291,"role":979,"focusable":980,"viewBox":13292,"xmlnsXLink":982},[984,14434,14435,14438],{},[987,14436],{"id":14437,"d":13128},"MJX-43-TEX-I-1D453",[987,14439],{"id":3919,"d":1269},[1024,14441,14442],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14443,14444],{"dataMmlNode":1031},[1024,14445,14446,14451],{"dataMmlNode":1761},[1024,14447,14448],{"dataMmlNode":1282},[1036,14449],{"dataC":13204,"xLinkHref":14450},"#MJX-43-TEX-I-1D453",[1024,14452,14453],{"dataMmlNode":1282,"transform":13208},[1036,14454],{"dataC":1299,"xLinkHref":3945},"？",[12,14457,14458,14459,14486],{},"了解了 ",[967,14460,14462],{"className":14461,"jax":971},[970],[973,14463,14464,14471],{"style":1338,"xmlns":976,"width":13290,"height":13291,"role":979,"focusable":980,"viewBox":13292,"xmlnsXLink":982},[984,14465,14466,14469],{},[987,14467],{"id":14468,"d":13128},"MJX-44-TEX-I-1D453",[987,14470],{"id":3974,"d":1269},[1024,14472,14473],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14474,14475],{"dataMmlNode":1031},[1024,14476,14477,14482],{"dataMmlNode":1761},[1024,14478,14479],{"dataMmlNode":1282},[1036,14480],{"dataC":13204,"xLinkHref":14481},"#MJX-44-TEX-I-1D453",[1024,14483,14484],{"dataMmlNode":1282,"transform":13208},[1036,14485],{"dataC":1299,"xLinkHref":4009}," 是什麼之後，我們回頭看 LMS 更新權重的公式，你會發現一個非常聰明的設計：",[12,14488,14489],{},[967,14490,14492],{"className":14491,"jax":971},[970],[973,14493,14494,14532],{"style":975,"xmlns":976,"width":13102,"height":978,"role":979,"focusable":980,"viewBox":13103,"xmlnsXLink":982},[984,14495,14496,14499,14501,14504,14507,14510,14513,14516,14519,14522,14525,14527,14530],{},[987,14497],{"id":14498,"d":4333},"MJX-45-TEX-I-1D464",[987,14500],{"id":4043,"d":1269},[987,14502],{"id":14503,"d":1018},"MJX-45-TEX-N-3D",[987,14505],{"id":14506,"d":1002},"MJX-45-TEX-N-2B",[987,14508],{"id":14509,"d":13121},"MJX-45-TEX-I-1D450",[987,14511],{"id":14512,"d":11975},"MJX-45-TEX-N-22C5",[987,14514],{"id":14515,"d":13128},"MJX-45-TEX-I-1D453",[987,14517],{"id":14518,"d":5069},"MJX-45-TEX-I-1D452",[987,14520],{"id":14521,"d":11986},"MJX-45-TEX-I-1D45F",[987,14523],{"id":14524,"d":6465},"MJX-45-TEX-I-1D45C",[987,14526],{"id":4040,"d":990},[987,14528],{"id":14529,"d":11589},"MJX-45-TEX-I-1D44F",[987,14531],{"id":4046,"d":1010},[1024,14533,14534],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14535,14536,14547,14552,14562,14567,14572,14577,14588,14592,14597,14602,14606,14611,14615,14619,14624],{"dataMmlNode":1031},[1024,14537,14538,14543],{"dataMmlNode":1761},[1024,14539,14540],{"dataMmlNode":1282},[1036,14541],{"dataC":4392,"xLinkHref":14542},"#MJX-45-TEX-I-1D464",[1024,14544,14545],{"dataMmlNode":1282,"transform":12047},[1036,14546],{"dataC":1299,"xLinkHref":4072},[1024,14548,14549],{"dataMmlNode":1034,"transform":13163},[1036,14550],{"dataC":1097,"xLinkHref":14551},"#MJX-45-TEX-N-3D",[1024,14553,14554,14558],{"dataMmlNode":1761,"transform":13169},[1024,14555,14556],{"dataMmlNode":1282},[1036,14557],{"dataC":4392,"xLinkHref":14542},[1024,14559,14560],{"dataMmlNode":1282,"transform":12047},[1036,14561],{"dataC":1299,"xLinkHref":4072},[1024,14563,14564],{"dataMmlNode":1034,"transform":13180},[1036,14565],{"dataC":1058,"xLinkHref":14566},"#MJX-45-TEX-N-2B",[1024,14568,14569],{"dataMmlNode":1282,"transform":13186},[1036,14570],{"dataC":13189,"xLinkHref":14571},"#MJX-45-TEX-I-1D450",[1024,14573,14574],{"dataMmlNode":1034,"transform":13193},[1036,14575],{"dataC":12074,"xLinkHref":14576},"#MJX-45-TEX-N-22C5",[1024,14578,14579,14584],{"dataMmlNode":1761,"transform":13199},[1024,14580,14581],{"dataMmlNode":1282},[1036,14582],{"dataC":13204,"xLinkHref":14583},"#MJX-45-TEX-I-1D453",[1024,14585,14586],{"dataMmlNode":1282,"transform":13208},[1036,14587],{"dataC":1299,"xLinkHref":4072},[1024,14589,14590],{"dataMmlNode":1034,"transform":13213},[1036,14591],{"dataC":12074,"xLinkHref":14576},[1024,14593,14594],{"dataMmlNode":1282,"transform":13218},[1036,14595],{"dataC":5174,"xLinkHref":14596},"#MJX-45-TEX-I-1D452",[1024,14598,14599],{"dataMmlNode":1282,"transform":13224},[1036,14600],{"dataC":12130,"xLinkHref":14601},"#MJX-45-TEX-I-1D45F",[1024,14603,14604],{"dataMmlNode":1282,"transform":13230},[1036,14605],{"dataC":12130,"xLinkHref":14601},[1024,14607,14608],{"dataMmlNode":1282,"transform":13235},[1036,14609],{"dataC":6507,"xLinkHref":14610},"#MJX-45-TEX-I-1D45C",[1024,14612,14613],{"dataMmlNode":1282,"transform":13241},[1036,14614],{"dataC":12130,"xLinkHref":14601},[1024,14616,14617],{"dataMmlNode":1034,"transform":13246},[1036,14618],{"dataC":1038,"xLinkHref":4067},[1024,14620,14621],{"dataMmlNode":1282,"transform":13251},[1036,14622],{"dataC":11612,"xLinkHref":14623},"#MJX-45-TEX-I-1D44F",[1024,14625,14626],{"dataMmlNode":1034,"transform":13257},[1036,14627],{"dataC":1074,"xLinkHref":4077},[12,14629,14630,14631,14648,14649,14682,14683,14714],{},"你看，要更新第",[967,14632,14634],{"className":14633,"jax":971},[970],[973,14635,14636,14640],{"style":1253,"xmlns":976,"width":1313,"height":1314,"role":979,"focusable":980,"viewBox":1315,"xmlnsXLink":982},[984,14637,14638],{},[987,14639],{"id":4101,"d":1269},[1024,14641,14642],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14643,14644],{"dataMmlNode":1031},[1024,14645,14646],{"dataMmlNode":1282},[1036,14647],{"dataC":1299,"xLinkHref":4130}," 個權重 (",[967,14650,14652],{"className":14651,"jax":971},[970],[973,14653,14658,14666],{"style":14654,"xmlns":976,"width":14655,"height":14656,"role":979,"focusable":980,"viewBox":14657,"xmlnsXLink":982},"vertical-align: -0.357ex;","2.36ex","1.359ex","0 -443 1043 600.8",[984,14659,14660,14663],{},[987,14661],{"id":14662,"d":4333},"MJX-47-TEX-I-1D464",[987,14664],{"id":14665,"d":1269},"MJX-47-TEX-I-1D456",[1024,14667,14668],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14669,14670],{"dataMmlNode":1031},[1024,14671,14672,14677],{"dataMmlNode":1761},[1024,14673,14674],{"dataMmlNode":1282},[1036,14675],{"dataC":4392,"xLinkHref":14676},"#MJX-47-TEX-I-1D464",[1024,14678,14679],{"dataMmlNode":1282,"transform":12047},[1036,14680],{"dataC":1299,"xLinkHref":14681},"#MJX-47-TEX-I-1D456",") 時，後面乘上了一個 ",[773,14684,14685],{},[967,14686,14688],{"className":14687,"jax":971},[970],[973,14689,14690,14698],{"style":1338,"xmlns":976,"width":13290,"height":13291,"role":979,"focusable":980,"viewBox":13292,"xmlnsXLink":982},[984,14691,14692,14695],{},[987,14693],{"id":14694,"d":13128},"MJX-48-TEX-I-1D453",[987,14696],{"id":14697,"d":1269},"MJX-48-TEX-I-1D456",[1024,14699,14700],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14701,14702],{"dataMmlNode":1031},[1024,14703,14704,14709],{"dataMmlNode":1761},[1024,14705,14706],{"dataMmlNode":1282},[1036,14707],{"dataC":13204,"xLinkHref":14708},"#MJX-48-TEX-I-1D453",[1024,14710,14711],{"dataMmlNode":1282,"transform":13208},[1036,14712],{"dataC":1299,"xLinkHref":14713},"#MJX-48-TEX-I-1D456","。為什麼要這樣做？",[12,14716,14717],{},[773,14718,14719],{},"這是一個「誰惹禍，誰負責」的機制。",[12,14721,14722,14723,14768],{},"延續上面的例子，假設這步棋我們預測錯誤了，產生了誤差 (",[967,14724,14726],{"className":14725,"jax":971},[970],[973,14727,14730,14741],{"style":1253,"xmlns":976,"width":14728,"height":1514,"role":979,"focusable":980,"viewBox":14729,"xmlnsXLink":982},"5.213ex","0 -442 2304 453",[984,14731,14732,14735,14738],{},[987,14733],{"id":14734,"d":5069},"MJX-49-TEX-I-1D452",[987,14736],{"id":14737,"d":11986},"MJX-49-TEX-I-1D45F",[987,14739],{"id":14740,"d":6465},"MJX-49-TEX-I-1D45C",[1024,14742,14743],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14744,14745,14750,14755,14759,14764],{"dataMmlNode":1031},[1024,14746,14747],{"dataMmlNode":1282},[1036,14748],{"dataC":5174,"xLinkHref":14749},"#MJX-49-TEX-I-1D452",[1024,14751,14752],{"dataMmlNode":1282,"transform":12976},[1036,14753],{"dataC":12130,"xLinkHref":14754},"#MJX-49-TEX-I-1D45F",[1024,14756,14757],{"dataMmlNode":1282,"transform":12982},[1036,14758],{"dataC":12130,"xLinkHref":14754},[1024,14760,14761],{"dataMmlNode":1282,"transform":12987},[1036,14762],{"dataC":6507,"xLinkHref":14763},"#MJX-49-TEX-I-1D45C",[1024,14765,14766],{"dataMmlNode":1282,"transform":12993},[1036,14767],{"dataC":12130,"xLinkHref":14754},")。現在演算法要來微調那些「旋鈕（權重）」了。",[16,14770,14771,14990],{},[19,14772,14773,14804,14806,14807,14852,14853,1108,14949,14951,10176,14954,14983,14984,14986,14989],{},[773,14774,14775,14776,14803],{},"黑棋國王的旋鈕 (",[967,14777,14779],{"className":14778,"jax":971},[970],[973,14780,14781,14788],{"style":5273,"xmlns":976,"width":12358,"height":12359,"role":979,"focusable":980,"viewBox":12360,"xmlnsXLink":982},[984,14782,14783,14785],{},[987,14784],{"id":4332,"d":4333},[987,14786],{"id":14787,"d":11990},"MJX-50-TEX-N-33",[1024,14789,14790],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14791,14792],{"dataMmlNode":1031},[1024,14793,14794,14798],{"dataMmlNode":1761},[1024,14795,14796],{"dataMmlNode":1282},[1036,14797],{"dataC":4392,"xLinkHref":4393},[1024,14799,14800],{"dataMmlNode":1042,"transform":12047},[1036,14801],{"dataC":12168,"xLinkHref":14802},"#MJX-50-TEX-N-33",")：",[83,14805],{},"因為盤面上根本沒有黑棋國王 (",[967,14808,14810],{"className":14809,"jax":971},[970],[973,14811,14812,14826],{"style":1338,"xmlns":976,"width":14276,"height":13291,"role":979,"focusable":980,"viewBox":14277,"xmlnsXLink":982},[984,14813,14814,14817,14820,14823],{},[987,14815],{"id":14816,"d":13128},"MJX-51-TEX-I-1D453",[987,14818],{"id":14819,"d":11990},"MJX-51-TEX-N-33",[987,14821],{"id":14822,"d":1018},"MJX-51-TEX-N-3D",[987,14824],{"id":14825,"d":1718},"MJX-51-TEX-N-30",[1024,14827,14828],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14829,14830,14842,14847],{"dataMmlNode":1031},[1024,14831,14832,14837],{"dataMmlNode":1761},[1024,14833,14834],{"dataMmlNode":1282},[1036,14835],{"dataC":13204,"xLinkHref":14836},"#MJX-51-TEX-I-1D453",[1024,14838,14839],{"dataMmlNode":1042,"transform":13208},[1036,14840],{"dataC":12168,"xLinkHref":14841},"#MJX-51-TEX-N-33",[1024,14843,14844],{"dataMmlNode":1034,"transform":14309},[1036,14845],{"dataC":1097,"xLinkHref":14846},"#MJX-51-TEX-N-3D",[1024,14848,14849],{"dataMmlNode":1042,"transform":14314},[1036,14850],{"dataC":1774,"xLinkHref":14851},"#MJX-51-TEX-N-30",")，所以公式後半段會變成： ",[967,14854,14856],{"className":14855,"jax":971},[970],[973,14857,14861,14884],{"style":3005,"xmlns":976,"width":14858,"height":14859,"role":979,"focusable":980,"viewBox":14860,"xmlnsXLink":982},"14.741ex","1.692ex","0 -666 6515.4 748",[984,14862,14863,14866,14869,14872,14875,14878,14881],{},[987,14864],{"id":14865,"d":13121},"MJX-52-TEX-I-1D450",[987,14867],{"id":14868,"d":11975},"MJX-52-TEX-N-22C5",[987,14870],{"id":14871,"d":1718},"MJX-52-TEX-N-30",[987,14873],{"id":14874,"d":5069},"MJX-52-TEX-I-1D452",[987,14876],{"id":14877,"d":11986},"MJX-52-TEX-I-1D45F",[987,14879],{"id":14880,"d":6465},"MJX-52-TEX-I-1D45C",[987,14882],{"id":14883,"d":1018},"MJX-52-TEX-N-3D",[1024,14885,14886],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14887,14888,14893,14899,14905,14910,14916,14922,14927,14933,14938,14944],{"dataMmlNode":1031},[1024,14889,14890],{"dataMmlNode":1282},[1036,14891],{"dataC":13189,"xLinkHref":14892},"#MJX-52-TEX-I-1D450",[1024,14894,14896],{"dataMmlNode":1034,"transform":14895},"translate(655.2,0)",[1036,14897],{"dataC":12074,"xLinkHref":14898},"#MJX-52-TEX-N-22C5",[1024,14900,14902],{"dataMmlNode":1042,"transform":14901},"translate(1155.4,0)",[1036,14903],{"dataC":1774,"xLinkHref":14904},"#MJX-52-TEX-N-30",[1024,14906,14908],{"dataMmlNode":1034,"transform":14907},"translate(1877.7,0)",[1036,14909],{"dataC":12074,"xLinkHref":14898},[1024,14911,14913],{"dataMmlNode":1282,"transform":14912},"translate(2377.9,0)",[1036,14914],{"dataC":5174,"xLinkHref":14915},"#MJX-52-TEX-I-1D452",[1024,14917,14919],{"dataMmlNode":1282,"transform":14918},"translate(2843.9,0)",[1036,14920],{"dataC":12130,"xLinkHref":14921},"#MJX-52-TEX-I-1D45F",[1024,14923,14925],{"dataMmlNode":1282,"transform":14924},"translate(3294.9,0)",[1036,14926],{"dataC":12130,"xLinkHref":14921},[1024,14928,14930],{"dataMmlNode":1282,"transform":14929},"translate(3745.9,0)",[1036,14931],{"dataC":6507,"xLinkHref":14932},"#MJX-52-TEX-I-1D45C",[1024,14934,14936],{"dataMmlNode":1282,"transform":14935},"translate(4230.9,0)",[1036,14937],{"dataC":12130,"xLinkHref":14921},[1024,14939,14941],{"dataMmlNode":1034,"transform":14940},"translate(4959.7,0)",[1036,14942],{"dataC":1097,"xLinkHref":14943},"#MJX-52-TEX-N-3D",[1024,14945,14947],{"dataMmlNode":1042,"transform":14946},"translate(6015.4,0)",[1036,14948],{"dataC":1774,"xLinkHref":14904},[83,14950],{},[773,14952,14953],{},"結果：",[967,14955,14957],{"className":14956,"jax":971},[970],[973,14958,14959,14967],{"style":5273,"xmlns":976,"width":12358,"height":12359,"role":979,"focusable":980,"viewBox":12360,"xmlnsXLink":982},[984,14960,14961,14964],{},[987,14962],{"id":14963,"d":4333},"MJX-53-TEX-I-1D464",[987,14965],{"id":14966,"d":11990},"MJX-53-TEX-N-33",[1024,14968,14969],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,14970,14971],{"dataMmlNode":1031},[1024,14972,14973,14978],{"dataMmlNode":1761},[1024,14974,14975],{"dataMmlNode":1282},[1036,14976],{"dataC":4392,"xLinkHref":14977},"#MJX-53-TEX-I-1D464",[1024,14979,14980],{"dataMmlNode":1042,"transform":12047},[1036,14981],{"dataC":12168,"xLinkHref":14982},"#MJX-53-TEX-N-33"," 完全不會被修改。",[83,14985],{},[773,14987,14988],{},"白話文：","「這局上面根本沒有黑棋國王，所以這次預測失準絕對不是黑棋國王害的！不要動它的旋鈕！」",[19,14991,14992,15025,15027,15028,15073,15074,1108,15147,15149,10176,15151,15180,15181,15183,15185,15186,15215],{},[773,14993,14994,14995,14803],{},"黑棋的旋鈕 (",[967,14996,14998],{"className":14997,"jax":971},[970],[973,14999,15003,15010],{"style":15000,"xmlns":976,"width":12358,"height":15001,"role":979,"focusable":980,"viewBox":15002,"xmlnsXLink":982},"vertical-align: -0.339ex;","1.342ex","0 -443 1152.6 593",[984,15004,15005,15007],{},[987,15006],{"id":4769,"d":4333},[987,15008],{"id":15009,"d":1725},"MJX-54-TEX-N-31",[1024,15011,15012],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15013,15014],{"dataMmlNode":1031},[1024,15015,15016,15020],{"dataMmlNode":1761},[1024,15017,15018],{"dataMmlNode":1282},[1036,15019],{"dataC":4392,"xLinkHref":4789},[1024,15021,15022],{"dataMmlNode":1042,"transform":12047},[1036,15023],{"dataC":1793,"xLinkHref":15024},"#MJX-54-TEX-N-31",[83,15026],{},"盤面上有 5 顆黑棋 (",[967,15029,15031],{"className":15030,"jax":971},[970],[973,15032,15033,15047],{"style":1338,"xmlns":976,"width":14276,"height":13291,"role":979,"focusable":980,"viewBox":14277,"xmlnsXLink":982},[984,15034,15035,15038,15041,15044],{},[987,15036],{"id":15037,"d":13128},"MJX-55-TEX-I-1D453",[987,15039],{"id":15040,"d":1725},"MJX-55-TEX-N-31",[987,15042],{"id":15043,"d":1018},"MJX-55-TEX-N-3D",[987,15045],{"id":15046,"d":998},"MJX-55-TEX-N-35",[1024,15048,15049],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15050,15051,15063,15068],{"dataMmlNode":1031},[1024,15052,15053,15058],{"dataMmlNode":1761},[1024,15054,15055],{"dataMmlNode":1282},[1036,15056],{"dataC":13204,"xLinkHref":15057},"#MJX-55-TEX-I-1D453",[1024,15059,15060],{"dataMmlNode":1042,"transform":13208},[1036,15061],{"dataC":1793,"xLinkHref":15062},"#MJX-55-TEX-N-31",[1024,15064,15065],{"dataMmlNode":1034,"transform":14309},[1036,15066],{"dataC":1097,"xLinkHref":15067},"#MJX-55-TEX-N-3D",[1024,15069,15070],{"dataMmlNode":1042,"transform":14314},[1036,15071],{"dataC":1050,"xLinkHref":15072},"#MJX-55-TEX-N-35",")，數字很大。公式後半段會變成：",[967,15075,15077],{"className":15076,"jax":971},[970],[973,15078,15081,15101],{"style":6423,"xmlns":976,"width":15079,"height":6425,"role":979,"focusable":980,"viewBox":15080,"xmlnsXLink":982},"10.593ex","0 -666 4681.9 688",[984,15082,15083,15086,15089,15092,15095,15098],{},[987,15084],{"id":15085,"d":13121},"MJX-56-TEX-I-1D450",[987,15087],{"id":15088,"d":11975},"MJX-56-TEX-N-22C5",[987,15090],{"id":15091,"d":998},"MJX-56-TEX-N-35",[987,15093],{"id":15094,"d":5069},"MJX-56-TEX-I-1D452",[987,15096],{"id":15097,"d":11986},"MJX-56-TEX-I-1D45F",[987,15099],{"id":15100,"d":6465},"MJX-56-TEX-I-1D45C",[1024,15102,15103],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15104,15105,15110,15115,15120,15124,15129,15134,15138,15143],{"dataMmlNode":1031},[1024,15106,15107],{"dataMmlNode":1282},[1036,15108],{"dataC":13189,"xLinkHref":15109},"#MJX-56-TEX-I-1D450",[1024,15111,15112],{"dataMmlNode":1034,"transform":14895},[1036,15113],{"dataC":12074,"xLinkHref":15114},"#MJX-56-TEX-N-22C5",[1024,15116,15117],{"dataMmlNode":1042,"transform":14901},[1036,15118],{"dataC":1050,"xLinkHref":15119},"#MJX-56-TEX-N-35",[1024,15121,15122],{"dataMmlNode":1034,"transform":14907},[1036,15123],{"dataC":12074,"xLinkHref":15114},[1024,15125,15126],{"dataMmlNode":1282,"transform":14912},[1036,15127],{"dataC":5174,"xLinkHref":15128},"#MJX-56-TEX-I-1D452",[1024,15130,15131],{"dataMmlNode":1282,"transform":14918},[1036,15132],{"dataC":12130,"xLinkHref":15133},"#MJX-56-TEX-I-1D45F",[1024,15135,15136],{"dataMmlNode":1282,"transform":14924},[1036,15137],{"dataC":12130,"xLinkHref":15133},[1024,15139,15140],{"dataMmlNode":1282,"transform":14929},[1036,15141],{"dataC":6507,"xLinkHref":15142},"#MJX-56-TEX-I-1D45C",[1024,15144,15145],{"dataMmlNode":1282,"transform":14935},[1036,15146],{"dataC":12130,"xLinkHref":15133},[83,15148],{},[773,15150,14953],{},[967,15152,15154],{"className":15153,"jax":971},[970],[973,15155,15156,15164],{"style":15000,"xmlns":976,"width":12358,"height":15001,"role":979,"focusable":980,"viewBox":15002,"xmlnsXLink":982},[984,15157,15158,15161],{},[987,15159],{"id":15160,"d":4333},"MJX-57-TEX-I-1D464",[987,15162],{"id":15163,"d":1725},"MJX-57-TEX-N-31",[1024,15165,15166],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15167,15168],{"dataMmlNode":1031},[1024,15169,15170,15175],{"dataMmlNode":1761},[1024,15171,15172],{"dataMmlNode":1282},[1036,15173],{"dataC":4392,"xLinkHref":15174},"#MJX-57-TEX-I-1D464",[1024,15176,15177],{"dataMmlNode":1042,"transform":12047},[1036,15178],{"dataC":1793,"xLinkHref":15179},"#MJX-57-TEX-N-31"," 會被大幅度修改。",[83,15182],{},[773,15184,14988],{},"「畫面上有一大堆黑棋，結果我們分數還估錯，那『黑棋分數 (",[967,15187,15189],{"className":15188,"jax":971},[970],[973,15190,15191,15199],{"style":15000,"xmlns":976,"width":12358,"height":15001,"role":979,"focusable":980,"viewBox":15002,"xmlnsXLink":982},[984,15192,15193,15196],{},[987,15194],{"id":15195,"d":4333},"MJX-58-TEX-I-1D464",[987,15197],{"id":15198,"d":1725},"MJX-58-TEX-N-31",[1024,15200,15201],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15202,15203],{"dataMmlNode":1031},[1024,15204,15205,15210],{"dataMmlNode":1761},[1024,15206,15207],{"dataMmlNode":1282},[1036,15208],{"dataC":4392,"xLinkHref":15209},"#MJX-58-TEX-I-1D464",[1024,15211,15212],{"dataMmlNode":1042,"transform":12047},[1036,15213],{"dataC":1793,"xLinkHref":15214},"#MJX-58-TEX-N-31",")』這個旋鈕肯定設錯了，趕快用力調一下！」",[12,15217,15218,15219,10176,15250,15253],{},"總結來說，",[773,15220,15221],{},[967,15222,15224],{"className":15223,"jax":971},[970],[973,15225,15226,15234],{"style":1338,"xmlns":976,"width":13290,"height":13291,"role":979,"focusable":980,"viewBox":13292,"xmlnsXLink":982},[984,15227,15228,15231],{},[987,15229],{"id":15230,"d":13128},"MJX-59-TEX-I-1D453",[987,15232],{"id":15233,"d":1269},"MJX-59-TEX-I-1D456",[1024,15235,15236],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15237,15238],{"dataMmlNode":1031},[1024,15239,15240,15245],{"dataMmlNode":1761},[1024,15241,15242],{"dataMmlNode":1282},[1036,15243],{"dataC":13204,"xLinkHref":15244},"#MJX-59-TEX-I-1D453",[1024,15246,15247],{"dataMmlNode":1282,"transform":13208},[1036,15248],{"dataC":1299,"xLinkHref":15249},"#MJX-59-TEX-I-1D456",[773,15251,15252],{},"就是告訴電腦：「在這個回合裡，這項特徵參與度有多高。」"," 參與度越高的特徵，如果最後發現預測錯誤，它的權重就會被修正得越明顯。",[12,15255,15256],{},"直覺上很簡單：",[77,15258,15259,15262,15265],{},[19,15260,15261],{},"如果預測正確 → 不改變權重",[19,15263,15264],{},"如果預測太高 → 按比例減少權重",[19,15266,15267],{},"如果預測太低 → 按比例增加權重",[12,15269,15270,15271,15274],{},"在合理的情況下，LMS 保證能慢慢收斂，找到能讓",[773,15272,15273],{},"均方誤差 (Mean Squared Error, MSE)"," 降到最低的那組權重：",[12,15276,15277],{},[967,15278,15280],{"className":15279,"jax":971},[970],[973,15281,15286,15335],{"style":15282,"xmlns":976,"width":15283,"height":15284,"role":979,"focusable":980,"viewBox":15285,"xmlnsXLink":982},"vertical-align: -0.798ex;","25.71ex","3.176ex","0 -1051 11364 1403.8",[984,15287,15288,15292,15296,15300,15303,15306,15309,15312,15315,15318,15322,15325,15329,15332],{},[987,15289],{"id":15290,"d":15291},"MJX-60-TEX-I-1D440","M289 629Q289 635 232 637Q208 637 201 638T194 648Q194 649 196 659Q197 662 198 666T199 671T201 676T203 679T207 681T212 683T220 683T232 684Q238 684 262 684T307 683Q386 683 398 683T414 678Q415 674 451 396L487 117L510 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447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z",[987,15301],{"id":15302,"d":1018},"MJX-60-TEX-N-3D",[987,15304],{"id":15305,"d":1725},"MJX-60-TEX-N-31",[987,15307],{"id":15308,"d":12851},"MJX-60-TEX-I-1D45B",[987,15310],{"id":15311,"d":2455},"MJX-60-TEX-SO-2211",[987,15313],{"id":15314,"d":1269},"MJX-60-TEX-I-1D456",[987,15316],{"id":15317,"d":990},"MJX-60-TEX-N-28",[987,15319],{"id":15320,"d":15321},"MJX-60-TEX-I-1D44C","M66 637Q54 637 49 637T39 638T32 641T30 647T33 664T42 682Q44 683 56 683Q104 680 165 680Q288 680 306 683H316Q322 677 322 674T320 656Q316 643 310 637H298Q242 637 242 624Q242 619 292 477T343 333L346 336Q350 340 358 349T379 373T411 410T454 461Q546 568 561 587T577 618Q577 634 545 637Q528 637 528 647Q528 649 530 661Q533 676 535 679T549 683Q551 683 578 682T657 680Q684 680 713 681T746 682Q763 682 763 673Q763 669 760 657T755 643Q753 637 734 637Q662 632 617 587Q608 578 477 424L348 273L322 169Q295 62 295 57Q295 46 363 46Q379 46 384 45T390 35Q390 33 388 23Q384 6 382 4T366 1Q361 1 324 1T232 2Q170 2 138 2T102 1Q84 1 84 9Q84 14 87 24Q88 27 89 30T90 35T91 39T93 42T96 44T101 45T107 45T116 46T129 46Q168 47 180 50T198 63Q201 68 227 171L252 274L129 623Q128 624 127 625T125 627T122 629T118 631T113 633T105 634T96 635T83 636T66 637Z",[987,15323],{"id":15324,"d":1955},"MJX-60-TEX-N-2212",[987,15326],{"id":15327,"d":15328},"MJX-60-TEX-N-5E","M112 560L249 694L257 686Q387 562 387 560L361 531Q359 532 303 581L250 627L195 580Q182 569 169 557T148 538L140 532Q138 530 125 546L112 560Z",[987,15330],{"id":15331,"d":1010},"MJX-60-TEX-N-29",[987,15333],{"id":15334,"d":994},"MJX-60-TEX-N-32",[1024,15336,15337],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15338,15339,15345,15352,15359,15365,15382,15415,15421,15435,15441,15464],{"dataMmlNode":1031},[1024,15340,15341],{"dataMmlNode":1282},[1036,15342],{"dataC":15343,"xLinkHref":15344},"1D440","#MJX-60-TEX-I-1D440",[1024,15346,15348],{"dataMmlNode":1282,"transform":15347},"translate(1051,0)",[1036,15349],{"dataC":15350,"xLinkHref":15351},"1D446","#MJX-60-TEX-I-1D446",[1024,15353,15355],{"dataMmlNode":1282,"transform":15354},"translate(1696,0)",[1036,15356],{"dataC":15357,"xLinkHref":15358},"1D438","#MJX-60-TEX-I-1D438",[1024,15360,15362],{"dataMmlNode":1034,"transform":15361},"translate(2737.8,0)",[1036,15363],{"dataC":1097,"xLinkHref":15364},"#MJX-60-TEX-N-3D",[1024,15366,15368,15374,15379],{"dataMmlNode":1995,"transform":15367},"translate(3793.6,0)",[1024,15369,15371],{"dataMmlNode":1042,"transform":15370},"translate(255.4,394) 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scale(0.707)",[1036,15434],{"dataC":1299,"xLinkHref":15404},[1024,15436,15438],{"dataMmlNode":1034,"transform":15437},"translate(8630.3,0)",[1036,15439],{"dataC":2081,"xLinkHref":15440},"#MJX-60-TEX-N-2212",[1024,15442,15444,15460],{"dataMmlNode":1761,"transform":15443},"translate(9630.5,0)",[1024,15445,15446],{"dataMmlNode":1078,"dataMjxTexclass":1079},[1024,15447,15449,15453],{"dataMmlNode":15448},"mover",[1024,15450,15451],{"dataMmlNode":1282},[1036,15452],{"dataC":15428,"xLinkHref":15429},[1024,15454,15456],{"dataMmlNode":1034,"transform":15455},"translate(427,257) translate(-250 0)",[1036,15457],{"dataC":15458,"xLinkHref":15459},"5E","#MJX-60-TEX-N-5E",[1024,15461,15462],{"dataMmlNode":1282,"transform":15432},[1036,15463],{"dataC":1299,"xLinkHref":15404},[1024,15465,15467,15472],{"dataMmlNode":1279,"transform":15466},"translate(10538.5,0)",[1024,15468,15469],{"dataMmlNode":1034},[1036,15470],{"dataC":1074,"xLinkHref":15471},"#MJX-60-TEX-N-29",[1024,15473,15474],{"dataMmlNode":1042,"transform":2419},[1036,15475],{"dataC":1046,"xLinkHref":15476},"#MJX-60-TEX-N-32",[832,15478,15481],{"className":15479},[825,15480],"info-box-warning",[12,15482,15483,15484,15516,15517,15600,15601,15644,15645,1108,15688,15726],{},"註：公式裡的 ",[967,15485,15487],{"className":15486,"jax":971},[970],[973,15488,15492,15500],{"style":14654,"xmlns":976,"width":15489,"height":15490,"role":979,"focusable":980,"viewBox":15491,"xmlnsXLink":982},"2.054ex","1.902ex","0 -683 908 840.8",[984,15493,15494,15497],{},[987,15495],{"id":15496,"d":15321},"MJX-61-TEX-I-1D44C",[987,15498],{"id":15499,"d":1269},"MJX-61-TEX-I-1D456",[1024,15501,15502],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15503,15504],{"dataMmlNode":1031},[1024,15505,15506,15511],{"dataMmlNode":1761},[1024,15507,15508],{"dataMmlNode":1282},[1036,15509],{"dataC":15428,"xLinkHref":15510},"#MJX-61-TEX-I-1D44C",[1024,15512,15513],{"dataMmlNode":1282,"transform":15432},[1036,15514],{"dataC":1299,"xLinkHref":15515},"#MJX-61-TEX-I-1D456"," 就是我們剛剛作為目標的 ",[967,15518,15520],{"className":15519,"jax":971},[970],[973,15521,15522,15549],{"style":975,"xmlns":976,"width":12829,"height":978,"role":979,"focusable":980,"viewBox":12830,"xmlnsXLink":982},[984,15523,15524,15527,15530,15533,15536,15539,15542,15544,15547],{},[987,15525],{"id":15526,"d":11583},"MJX-62-TEX-I-1D449",[987,15528],{"id":15529,"d":12005},"MJX-62-TEX-I-1D461",[987,15531],{"id":15532,"d":11986},"MJX-62-TEX-I-1D45F",[987,15534],{"id":15535,"d":12845},"MJX-62-TEX-I-1D44E",[987,15537],{"id":15538,"d":1269},"MJX-62-TEX-I-1D456",[987,15540],{"id":15541,"d":12851},"MJX-62-TEX-I-1D45B",[987,15543],{"id":5039,"d":990},[987,15545],{"id":15546,"d":11589},"MJX-62-TEX-I-1D44F",[987,15548],{"id":5045,"d":1010},[1024,15550,15551],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15552,15553,15587,15591,15596],{"dataMmlNode":1031},[1024,15554,15555,15560],{"dataMmlNode":1761},[1024,15556,15557],{"dataMmlNode":1282},[1036,15558],{"dataC":11600,"xLinkHref":15559},"#MJX-62-TEX-I-1D449",[1024,15561,15562,15567,15572,15577,15582],{"dataMmlNode":1078,"transform":12872,"dataMjxTexclass":1079},[1024,15563,15564],{"dataMmlNode":1282},[1036,15565],{"dataC":12282,"xLinkHref":15566},"#MJX-62-TEX-I-1D461",[1024,15568,15569],{"dataMmlNode":1282,"transform":12880},[1036,15570],{"dataC":12130,"xLinkHref":15571},"#MJX-62-TEX-I-1D45F",[1024,15573,15574],{"dataMmlNode":1282,"transform":12704},[1036,15575],{"dataC":12888,"xLinkHref":15576},"#MJX-62-TEX-I-1D44E",[1024,15578,15579],{"dataMmlNode":1282,"transform":12892},[1036,15580],{"dataC":1299,"xLinkHref":15581},"#MJX-62-TEX-I-1D456",[1024,15583,15584],{"dataMmlNode":1282,"transform":12897},[1036,15585],{"dataC":12900,"xLinkHref":15586},"#MJX-62-TEX-I-1D45B",[1024,15588,15589],{"dataMmlNode":1034,"transform":12904},[1036,15590],{"dataC":1038,"xLinkHref":5089},[1024,15592,15593],{"dataMmlNode":1282,"transform":12909},[1036,15594],{"dataC":11612,"xLinkHref":15595},"#MJX-62-TEX-I-1D44F",[1024,15597,15598],{"dataMmlNode":1034,"transform":12915},[1036,15599],{"dataC":1074,"xLinkHref":5099},"，而 ",[967,15602,15604],{"className":15603,"jax":971},[970],[973,15605,15608,15619],{"style":14654,"xmlns":976,"width":15489,"height":15606,"role":979,"focusable":980,"viewBox":15607,"xmlnsXLink":982},"2.735ex","0 -1051 908 1208.8",[984,15609,15610,15613,15616],{},[987,15611],{"id":15612,"d":15321},"MJX-63-TEX-I-1D44C",[987,15614],{"id":15615,"d":15328},"MJX-63-TEX-N-5E",[987,15617],{"id":15618,"d":1269},"MJX-63-TEX-I-1D456",[1024,15620,15621],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15622,15623],{"dataMmlNode":1031},[1024,15624,15625,15639],{"dataMmlNode":1761},[1024,15626,15627],{"dataMmlNode":1078,"dataMjxTexclass":1079},[1024,15628,15629,15634],{"dataMmlNode":15448},[1024,15630,15631],{"dataMmlNode":1282},[1036,15632],{"dataC":15428,"xLinkHref":15633},"#MJX-63-TEX-I-1D44C",[1024,15635,15636],{"dataMmlNode":1034,"transform":15455},[1036,15637],{"dataC":15458,"xLinkHref":15638},"#MJX-63-TEX-N-5E",[1024,15640,15641],{"dataMmlNode":1282,"transform":15432},[1036,15642],{"dataC":1299,"xLinkHref":15643},"#MJX-63-TEX-I-1D456"," 則是我們當前的預測值 ",[967,15646,15648],{"className":15647,"jax":971},[970],[973,15649,15650,15664],{"style":975,"xmlns":976,"width":11576,"height":978,"role":979,"focusable":980,"viewBox":11577,"xmlnsXLink":982},[984,15651,15652,15655,15658,15661],{},[987,15653],{"id":15654,"d":11583},"MJX-64-TEX-I-1D449",[987,15656],{"id":15657,"d":990},"MJX-64-TEX-N-28",[987,15659],{"id":15660,"d":11589},"MJX-64-TEX-I-1D44F",[987,15662],{"id":15663,"d":1010},"MJX-64-TEX-N-29",[1024,15665,15666],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15667,15668,15673,15678,15683],{"dataMmlNode":1031},[1024,15669,15670],{"dataMmlNode":1282},[1036,15671],{"dataC":11600,"xLinkHref":15672},"#MJX-64-TEX-I-1D449",[1024,15674,15675],{"dataMmlNode":1034,"transform":11604},[1036,15676],{"dataC":1038,"xLinkHref":15677},"#MJX-64-TEX-N-28",[1024,15679,15680],{"dataMmlNode":1282,"transform":11609},[1036,15681],{"dataC":11612,"xLinkHref":15682},"#MJX-64-TEX-I-1D44F",[1024,15684,15685],{"dataMmlNode":1034,"transform":11616},[1036,15686],{"dataC":1074,"xLinkHref":15687},"#MJX-64-TEX-N-29",[967,15689,15691],{"className":15690,"jax":971},[970],[973,15692,15696,15707],{"style":6423,"xmlns":976,"width":15693,"height":15694,"role":979,"focusable":980,"viewBox":15695,"xmlnsXLink":982},"5.566ex","1.645ex","0 -705 2460 727",[984,15697,15698,15701,15704],{},[987,15699],{"id":15700,"d":15291},"MJX-65-TEX-I-1D440",[987,15702],{"id":15703,"d":15295},"MJX-65-TEX-I-1D446",[987,15705],{"id":15706,"d":15299},"MJX-65-TEX-I-1D438",[1024,15708,15709],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,15710,15711,15716,15721],{"dataMmlNode":1031},[1024,15712,15713],{"dataMmlNode":1282},[1036,15714],{"dataC":15343,"xLinkHref":15715},"#MJX-65-TEX-I-1D440",[1024,15717,15718],{"dataMmlNode":1282,"transform":15347},[1036,15719],{"dataC":15350,"xLinkHref":15720},"#MJX-65-TEX-I-1D446",[1024,15722,15723],{"dataMmlNode":1282,"transform":15354},[1036,15724],{"dataC":15357,"xLinkHref":15725},"#MJX-65-TEX-I-1D438"," 其實就是把每次的誤差平方後加總平均。",[832,15728,15730,15733],{"className":15729},[825,826],[12,15731,15732],{},"想像你面前有一台電腦，上面有七個旋鈕（分別對應黑棋數量、紅棋數量等等）。",[12,15734,15735],{},"電腦一開始是瞎猜的。我們讓電腦給旋鈕亂填幾個數字。假設電腦預測這盤棋的局勢能拿 80 分，結果實際打完發現只有 50 分（預測太高了）。LMS 演算法其實就是一個**「旋鈕微調機制」**：它會告訴電腦，「你分數估太高了，去把剛才轉太高的那幾個旋鈕往回轉一點點」。每一次下棋都在微調旋鈕，下了幾萬盤之後，旋鈕就會被調到一個「預測最準」的位置。這就是 LMS 在做的事。",[765,15737,15739],{"id":15738},"訓練資料從哪來","訓練資料從哪來？",[12,15741,15742],{},"訓練資料的來源和品質非常重要，常見的來源有這幾種：",[77,15744,15745,15751,15757,15763],{},[19,15746,15747,15750],{},[773,15748,15749],{},"環境提供的隨機範例","（實務上最常見）",[19,15752,15753,15756],{},[773,15754,15755],{},"教師挑選的範例","，專門挑最有學習價值的資料（例如「差一點就猜對」的例子）",[19,15758,15759,15762],{},[773,15760,15761],{},"主動學習 (Active learning)","，模型遇到不確定的題目時，主動去問人類專家標準答案",[19,15764,15765,15768],{},[773,15766,15767],{},"自主實驗 (Self-directed experimentation)","，學習系統自己設計實驗來找答案",[12,15770,15771,15772,15775,15776,15779,15780,15783],{},"做機器學習時有一個很大的假設，就是訓練資料和未來要預測的測試資料必須是",[773,15773,15774],{},"獨立同分布 (Independently and Identically Distributed, IID)"," 的——白話文就是「它們必須來自同一個同溫層」。如果這個假設不成立，你就得用到像",[773,15777,15778],{},"遷移學習 (Transfer learning)"," 或",[773,15781,15782],{},"集體分類 (Collective Classification)"," 等更進階的技巧了。",[822,15785,15787,15790],{"className":15786},[825,826],[828,15788,15789],{},"補充説明：什麽是IID？",[832,15791,15793,15803,15805,15810,15813,15816,15830,15833,15838,15840,15843,15845,15850,15853,15856,15858,15863,15866],{"className":15792},[835],[12,15794,15795,15796,15799,15800,1108],{},"我們把這個詞拆成兩半來看：",[773,15797,15798],{},"「獨立 (Independent)」"," 和 ",[773,15801,15802],{},"「同分布 (Identically Distributed)」",[35,15804],{},[12,15806,15807],{},[773,15808,15809],{},"同分布 (Identically Distributed)",[12,15811,15812],{},"打個比方：訓練題庫和最終考試的「範圍與難度」必須一樣。",[12,15814,15815],{},"機器學習就像是一個準備大考的學生。",[77,15817,15818,15824],{},[19,15819,15820,15823],{},[773,15821,15822],{},"訓練資料"," = 你平常寫的模擬考題。",[19,15825,15826,15829],{},[773,15827,15828],{},"測試資料"," = 你最終去考的學測或統測。",[12,15831,15832],{},"如果你的模擬考題都是「高中數學」，而最終的大考也是考「高中數學」，我們就說這兩批資料是**「同分布」**的。因為它們背後出題的規則、範圍、難度都是一致的。學生（機器學習模型）只要平常練習得夠好，大考就能考高分。",[12,15834,15835],{},[773,15836,15837],{},"什麼情況下是「不同分布」？",[83,15839],{},[12,15841,15842],{}," 假設你平常寫的模擬考題都是「小學算術」（訓練資料），結果大考當天發下來的考卷是「大學微積分」（測試資料）。 這時學生絕對會考零分，因為考題的「分布（規則與環境）」完全改變了。",[83,15844],{},[12,15846,15847],{},[773,15848,15849],{},"獨立 (Independent)",[12,15851,15852],{},"每一筆資料都是相互獨立的，不會互相抄襲或影響。",[12,15854,15855],{},"想像一下你丟硬幣。你前一次丟出正面，會影響下一次丟出反面的機率嗎？不會。每一次丟硬幣都是一個全新的幾率，這就叫做**「獨立」**。",[83,15857],{},[12,15859,15860],{},[773,15861,15862],{},"什麼情況下是「不獨立」？",[12,15864,15865],{},"想像你在預測明天的天氣或明天的股票價格。 明天的天氣，絕對跟「今天的天氣」有高度關聯；明天的台積電股價，絕對跟「今天的台積電股價」息息相關。",[12,15867,15868],{},"在這種情況下，資料點和資料點之間是「互相影響」的。如果你把這些資料打亂順序隨便餵給 AI，AI 會學得一塌糊塗，因為它忽略了資料之間「時間上的因果關係」。",[765,15870,15872],{"id":15871},"目標函數可以長什麼樣","目標函數可以長什麼樣？",[12,15874,15875],{},"不同的表達方式各有優缺點，主要就是在「表達能力」跟「好不好學」之間做取捨：",[77,15877,15878,15884,15890,15896],{},[19,15879,15880,15883],{},[773,15881,15882],{},"數值函數"," ： 線性迴歸、神經網路、支援向量機 (SVM)。這些非常擅長捕捉平滑、連續的模式。",[19,15885,15886,15889],{},[773,15887,15888],{},"符號函數"," ： 決策樹、邏輯規則。這種生出來的模型人類比較看得懂。",[19,15891,15892,15895],{},[773,15893,15894],{},"基於實例的函數"," ： 最近鄰演算法 (Nearest-neighbor)、基於案例的推理。它遇到新問題時，會去翻舊筆記，找最像的範例來參考。",[19,15897,15898,15901],{},[773,15899,15900],{},"機率圖模型"," ： 貝氏分類器 (Naïve Bayes)、貝氏網路、隱馬可夫模型。這類方法可以直接把變數之間的不確定性跟依賴關係建進模型裡。",[12,15903,15904],{},"一個模型的表達能力越強，能處理的問題就越複雜，但也代表你需要餵給它更多的資料，它才能學得準確。這是機器學習裡永遠逃不掉的取捨。",[765,15906,15907],{"id":15907},"評估學習系統",[12,15909,15910],{},"訓練完一個模型之後，你怎麼知道它到底行不行？主要有兩種方法：",[77,15912,15913,15919],{},[19,15914,15915,15918],{},[773,15916,15917],{},"實驗評估"," ： 拿一組標準的資料集，用交叉驗證 (Cross-validation) 來做對照實驗。看的指標包括測試準確率、訓練時間、預測速度等等。然後用統計檢定來確認不同方法之間的差異到底是真的還是碰巧。",[19,15920,15921,15924],{},[773,15922,15923],{},"理論分析"," ： 用數學去證明這個演算法的能耐。例如它的運算複雜度、擬合能力、樣本複雜度 (Sample complexity)（到底需要多少資料才能學得夠好） 等等。",[12,15926,15927],{},"實務上，大部分 ML 工作兩種都會用到。",[765,15929,15930],{"id":15930},"重點回顧",[16,15932,15933,15939,15945,15951,15954],{},[19,15934,15935,15938],{},[773,15936,15937],{},"機器學習是關於從經驗中學習"," ： 使用資料來逼近函數，而不是靠人工編寫規則。",[19,15940,15941,15944],{},[773,15942,15943],{},"所有機器學習問題都能拆成 T、P、E","：任務、效能指標、經驗。",[19,15946,15947,15950],{},[773,15948,15949],{},"設計系統的四個選擇","：訓練經驗、目標函數、表達方式、學習演算法。",[19,15952,15953],{},"模型的表達能力越強，需要的資料量就越大。",[19,15955,15956,15959],{},[773,15957,15958],{},"評估是關鍵","：模型到底好不好，取決於它面對「沒看過的資料」時表現得怎樣。",[7328,15961,7330],{},{"title":169,"searchDepth":170,"depth":170,"links":15963},[15964,15965,15966,15967,15968,15972,15973,15974,15980,15981,15982,15983],{"id":11243,"depth":170,"text":11243},{"id":11255,"depth":170,"text":11256},{"id":11286,"depth":170,"text":11287},{"id":11333,"depth":170,"text":11333},{"id":11365,"depth":170,"text":11365,"children":15969},[15970,15971],{"id":11368,"depth":7336,"text":11368},{"id":11406,"depth":7336,"text":11407},{"id":11427,"depth":170,"text":11428},{"id":11524,"depth":170,"text":11524},{"id":11556,"depth":170,"text":11557,"children":15975},[15976,15977,15978,15979],{"id":11563,"depth":7336,"text":11564},{"id":11929,"depth":7336,"text":11930},{"id":12786,"depth":7336,"text":12786},{"id":12809,"depth":7336,"text":12810},{"id":15738,"depth":170,"text":15739},{"id":15871,"depth":170,"text":15872},{"id":15907,"depth":170,"text":15907},{"id":15930,"depth":170,"text":15930},"2026-04-02","基於 WIA1006\u002FWID3006 機器學習 — 馬來亞大學，2025\u002F2026 學年第 2 學期","2026-04-04","\u002Fimages\u002Fuploads\u002F1775143473434-G-LPXbYa0AMCyl5.jpg",{},{"title":11238,"description":15985},{"loc":753},"blog\u002F機器學習導論","jHDwYa3SCOhqDuN7DAltQSTwyWboPj5ud_hnWi3VKQg",{"id":15994,"title":15995,"author":7,"body":15996,"date":16095,"description":16096,"draft":174,"edited_at":16095,"extension":175,"featured_image":16097,"meta":16098,"navigation":178,"path":16099,"pinned":174,"seo":16100,"series":181,"seriesOrder":181,"sitemap":16101,"stem":16102,"tags":181,"__hash__":16103},"blog\u002Fblog\u002FCVA（三）血管症候群-i.md","CVA（三）血管症候群 (i)",{"type":9,"value":15997,"toc":16093},[15998,16007,16016,16034,16052,16068,16071,16076],[12,15999,16000,16001,16003,16004,16006],{},"決定受損程度有兩個因素",[83,16002],{},"\n第一 受傷區域的大小還有位置，等下會重點說明這一塊",[83,16005],{},"\n第二 側支循環的量：就是備用小路，假如這條路徑良好 可以減少神經系統受損程度",[12,16008,16009,16010,16012,16013,16015],{},"假如以血管來看",[83,16011],{},"\n頸動脈堵住的話，會呈現單側偏癱，因為頸動脈分左右，堵住一邊，另一住還能流通",[83,16014],{},"\n但基底動脈的話，因為它是由兩條椎動脈匯流而程一條 再從這裡分出包括PCA在內的一堆血管 所以會呈現雙側偏癱",[12,16017,16018,16019,16021,16022,16024,16025,16027,16028,16030,16031,16033],{},"接下來講一下威氏環",[83,16020],{},"\n先來講由頸內動脈分出來的血管它們分別是",[83,16023],{},"\nMCA、ACA、還有連接ACA之間的前交通支、最後就是後交通支",[83,16026],{},"\n接著來講椎動脈出來的，包括了",[83,16029],{},"\n基底動脈及PCA",[83,16032],{},"\n（僅講義重點標注 不代表沒有其他）",[12,16035,16036,16037,16039,16040,16042,16043,16045,16046,16048,16049,16051],{},"那從以上這些血管假如出狀況了，會演變到以下的症候群",[83,16038],{},"\nACA症候群",[83,16041],{},"\nMCA症候群",[83,16044],{},"\n內頸動脈症候群",[83,16047],{},"\nPCA症候群",[83,16050],{},"\n椎動脈症候群",[12,16053,16054,16055,16057,16058,16060,16061,16064,16065,16067],{},"先來講ACA Syndromes ",[83,16056],{},"\nACA的血主要供應兩個區域",[83,16059],{},"\n首先是大腦半球內側，會供應額葉（",[773,16062,16063],{},"初級運動皮層","）以及頂葉（初級本體感覺皮質區）",[83,16066],{},"\n接著也會往裡面跑，供應基底核（前內囊以及尾狀核下部）、穹隆前部、胼胝體前4\u002F5",[12,16069,16070],{},"那假如ACA出狀況了 會有以下癥狀",[77,16072,16073],{},[19,16074,16075],{},"對側偏癱（下肢比上肢嚴重）————初級運動區域受影響",[77,16077,16078,16081,16084,16087,16090],{},[19,16079,16080],{},"對側感覺喪失（下肢比下肢嚴重）——初級感覺區域受影響",[19,16082,16083],{},"尿失禁————額葉的後內側受影響",[19,16085,16086],{},"失用症及雙手協調問題————胼胝體受影響",[19,16088,16089],{},"意志喪失\u002F動作遲緩（冷漠）————額葉內側受影響",[19,16091,16092],{},"一些原始反射如抓握\u002F吸吮反射再現——額葉受影響",{"title":169,"searchDepth":170,"depth":170,"links":16094},[],"2026-04-01","臨床表現與病灶位置的關係~ACA","\u002Fimages\u002Fuploads\u002F1775007735475-127888519_p0_master1200.jpg",{},"\u002Fblog\u002FCVA（三）血管症候群-i",{"title":15995,"description":16096},{"loc":16099},"blog\u002FCVA（三）血管症候群-i","LmlGapSdVYDl0s3SusHWhzCgok2UmU776EQkVj7y-pw",{"id":16105,"title":16106,"author":7,"body":16107,"date":16095,"description":16281,"draft":174,"edited_at":10966,"extension":175,"featured_image":16282,"meta":16283,"navigation":178,"path":16284,"pinned":174,"seo":16285,"series":181,"seriesOrder":181,"sitemap":16286,"stem":16287,"tags":181,"__hash__":16288},"blog\u002Fblog\u002FCVA（四）血管症候群-(ii).md","CVA（四）血管症候群 (ii)",{"type":9,"value":16108,"toc":16279},[16109,16128,16131,16163,16172,16178,16201,16204,16224,16230,16236,16242,16262,16265],[12,16110,16111,16112,16114,16115,16117,16118,16122,16124,16125,16127],{},"接著來講MCA Syndromes",[83,16113],{},"\n一樣先講他的供應部位",[83,16116],{},"\n它一部份會跑到大腦表層，供應",[254,16119,16121],{"className":16120},[258],"前、頂還有顳葉",[83,16123],{},"\n而另一部則會跑到基底核供應裏面的結構包括了",[83,16126],{},"\n後內囊、放射冠、殼核、尾狀核，以及蒼白球外側",[12,16129,16130],{},"假如MCA出狀況 就會有以下癥狀",[77,16132,16133,16136,16139,16142,16145,16148,16151,16154,16157,16160],{},[19,16134,16135],{},"對側偏癱（上肢比下肢嚴重）———初級運動皮質區受影響",[19,16137,16138],{},"對側感覺喪失（上肢比下肢嚴重）——初級感覺皮質區受影響",[19,16140,16141],{},"運動型失語症（吞吞吐吐，能理解）——Broca's 區受影響（優勢大腦半球）",[19,16143,16144],{},"理解型失語症（講話流暢 ，但答非所問）——Wernicke's 區受影響（優勢大腦半球）",[19,16146,16147],{},"全面性失語症（既說不了也理解不了）———額葉以及顳葉大面積受損（優勢大腦半球）",[19,16149,16150],{},"知覺障礙（失認症、空間感喪失、半側忽略）——右側頂葉受影響",[19,16152,16153],{},"對側同側偏盲（左腦受損，那兩隻眼的右半邊都看不見）——內囊的視角放射纖維受影響",[19,16155,16156],{},"喪失對側共軛注視（左腦損傷，無法看向右側）———額葉眼動區受影響",[19,16158,16159],{},"肢體運動性失用症（無法精細動作，肌力尚在）———後內囊上部受影響",[19,16161,16162],{},"感覺性運動失調（因失去本體感覺而運動不穩）———頂葉受影響",[12,16164,16165,16166,16168,16169,16171],{},"然後來講PCA Syndromes",[83,16167],{},"\n它會供應到",[83,16170],{},"\n枕葉（視皮質）、內側及下部顳葉、1\u002F5胼胝體、上腦幹、中腦、後間腦及大部份的視丘",[12,16173,16174,16175,16177],{},"假如PCA出狀況 ",[83,16176],{},"\n它分成了兩個區域 首先是周邊區域就會有以下癥狀",[77,16179,16180,16183,16186,16189,16192,16195,16198],{},[19,16181,16182],{},"對側同側偏盲（左腦受損，那兩隻眼的右半邊都看不見）——初級視覺皮質區或者視放射受影響",[19,16184,16185],{},"雙側偏盲但黃斑部(中心)不受影響（兩邊都盲但只有中間看得到）——禽距皮質受影響（但黃斑部由MCA供血 不受影響）",[19,16187,16188],{},"視覺失認症（知覺看到，但到了認知理解不了）————左枕葉受影響",[19,16190,16191],{},"臉盲症（無法用眼分辨人臉）————視覺聯合皮質區受損",[19,16193,16194],{},"失讀症（沒有失寫症）（會寫字但不知道自己寫甚麼）———優勢腦（左腦）禽距或後胼胝體受影響",[19,16196,16197],{},"記憶缺損（失憶）————顳葉內（包括海馬體）受影響",[19,16199,16200],{},"地形定向障礙（失去地圖感，再熟悉也會迷路）————非優勢腦（右腦）初級視覺皮質區受影響",[12,16202,16203],{},"接著是中心區域就會有以下癥狀",[77,16205,16206,16212,16215,16218,16221],{},[19,16207,16208,16209,16211],{},"視丘疼痛症候群、感覺缺失、感覺障礙————視丘的腹後外側核(VPL)受影響",[83,16210],{},"\n視丘疼痛症候群有（自發性對側疼痛、灼燒感、輕輕碰到也會很痛）",[19,16213,16214],{},"不自主運動（舞蹈症、意向顫抖、半身不自主亂揮）———下視丘核受影響",[19,16216,16217],{},"對側偏癱————中腦的腦角受影響",[19,16219,16220],{},"韋伯氏症候群（眼睛無法轉向同側+對側半身偏癱）————第三對腦神經和大腦同時受影響",[19,16222,16223],{},"眼睛無法垂直轉動、瞳孔反應遲鈍、眼瞼下垂————第三對腦神經的核上纖維受影響",[12,16225,16226,16227,16229],{},"最後講到椎基底動脈症候群",[83,16228],{},"\n將兩個血管分開來看它們分別的供應區域",[12,16231,16232,16233,16235],{},"首先是椎動脈 它分別供應了小腦跟延腦",[83,16234],{},"\n接著是基底動脈 它分別供應了橋腦、內耳以及小腦",[12,16237,16238,16239,16241],{},"接著分別來講椎動脈和基底動腦出狀況會有哪些癥狀",[83,16240],{},"\n先來講椎動脈 有延腦外側症候群 包括以下癥狀",[77,16243,16244,16247,16250,16253,16256,16259],{},[19,16245,16246],{},"同側臉部溫覺以痛覺————三叉神經受影響",[19,16248,16249],{},"小腦型共濟失調（走路不穩，肢體不協調）————小腦受影響",[19,16251,16252],{},"眩暈、噁心、嘔吐、眼球震顫————前庭神經核受影響",[19,16254,16255],{},"霍納氏症候群（瞳孔縮小、眼瞼下垂、無汗）———下行交感神經纖維受影響",[19,16257,16258],{},"吞嚥與發聲困難（嘔吐反射喪失）————第九第十對腦神經受影響",[19,16260,16261],{},"對側身體超過50%痛溫覺受損————脊髓視丘束受影響",[12,16263,16264],{},"接著講基底動脈，有閉鎖症候群（LIS），包括以下癥狀",[77,16266,16267,16270,16273,16276],{},[19,16268,16269],{},"四肢癱瘓————雙側皮質脊髓束受影響",[19,16271,16272],{},"雙側腦神經痲痺（眼睛能上下動及眨眼）————雙側腦神經的長束（Long tract）",[19,16274,16275],{},"昏迷————網狀活化系統（假如這裡沒有受傷就是清醒的LIS）",[19,16277,16278],{},"認知功能保留（知道發生了甚麼，但無法回應）",{"title":169,"searchDepth":170,"depth":170,"links":16280},[],"MCA PCA 椎基底動脈 症候群","\u002Fimages\u002Fuploads\u002F1775182252893-HE0KsPOaYAAB8aI.jpg",{},"\u002Fblog\u002Fcva-(ii)",{"title":16106,"description":16281},{"loc":16284},"blog\u002FCVA（四）血管症候群-(ii)","_5ShwehuGVaShPi8yChu2vBIIHOqAlhyC5rG0orFn7Q",{"id":16290,"title":16291,"author":7,"body":16292,"date":16752,"description":16753,"draft":174,"edited_at":7567,"extension":175,"featured_image":16754,"meta":16755,"navigation":178,"path":7571,"pinned":174,"seo":16756,"series":181,"seriesOrder":181,"sitemap":16757,"stem":16758,"tags":181,"__hash__":16759},"blog\u002Fblog\u002FMotor-Learning.md","Motor Learning小兒（一）",{"type":9,"value":16293,"toc":16750},[16294,16297,16306,16315,16333,16342,16351,16367,16376,16404,16478,16493,16496,16538,16544,16592,16638,16679,16682,16719,16734],[12,16295,16296],{},"那這一節課著重在動態模組理論，跟黃老師教的是互通的",[12,16298,16299,16300,16302,16303,16305],{},"那首先是講感覺統合的部份",[83,16301],{},"\n意思是指 知覺+大腦以往的經歷 結合成為認知的這麼一個過程",[83,16304],{},"\n而感覺統合就是結合的過程 認知是結果這樣(這跟神經物治講的動作控制學雷同)",[12,16307,16308,16309,16311,16312,16314],{},"而接下來講到動作的發展",[83,16310],{},"\n那老師用的理論是動態模組理論",[83,16313],{},"\n假如還記得黃老師的Motor Control最後一課講的應該不難吃",[12,16316,16317,16318,16320,16321,16323,16324,16326,16327,16329,16330,16332],{},"不過我還是先列出來老師PPT裡的五個角度",[83,16319],{},"\n第一 動作技巧的顯現",[83,16322],{},"\n第二 動作型態的精準度",[83,16325],{},"\n第三 動作成果(可從評估表推估) ",[83,16328],{},"\n第四 組合技巧的獲得(次系統組合的結果)",[83,16331],{},"\n第五 對環境適應力的增強",[12,16334,16335,16336,16338,16339,16341],{},"我們現在來講平衡系統的發展",[83,16337],{},"\n1)平衡系統有三個人一起負責 迷路系統 本體覺與觸覺 視角",[83,16340],{},"\n以站立來形容的話",[12,16343,16344,16345,16347,16348,16350],{},"2)人類的重心(COM)基本會在S2 ",[83,16346],{},"\n那壓力中心(COP)是動態的 他會因應COM的改變而改變",[83,16349],{},"\n那底面積(BOS)就是兩隻腳踩在地面的距離",[12,16352,16353,16354,16358,16359,16361,16362,16366],{},"3)那平衡的演化 在早期 小孩會",[254,16355,16357],{"className":16356},[258,257],"極度依賴視角","來判斷",[83,16360],{},"\n但在成熟的過程中 我們會",[254,16363,16365],{"className":16364},[562],"越來越傾向用本體感覺","去判斷",[12,16368,16369,16370,16372,16373,16375],{},"4)穩定極限(LOS) 他把我們人類想象成一個倒立的三角錐",[83,16371],{},"\n在不移動的情況下身體能偏多少(前6度 側8度 後4度)",[83,16374],{},"\n因為前面有腳趾輔助 而且側邊是比較寛 但後面甚麼都沒有 所以角度就變成這樣了(可以看游老師的講義)",[12,16377,16378,16379,16381,16382,16386,16387,16391,16392,16394,16395,16399,16400],{},"5)承受外力時的反應時 人類會有兩種變化",[83,16380],{},"\n第一種就是假如這",[254,16383,16385],{"className":16384},[257,264],"外力少到一定範圍"," 就只會用",[254,16388,16390],{"className":16389},[7640],"姿勢穩定反應","來做調整",[83,16393],{},"\n另一種則是假如外力",[254,16396,16398],{"className":16397},[257,258],"超過姿勢穩定反應可以調整的程度"," 就會產生",[254,16401,16403],{"className":16402},[562],"保護性姿勢",[12,16405,16406,16407,16409,16410,16412,16413,16415,16416,16420,16422,16423,16427,16431,16433,16434,16436,16438,16439,16443,16444,16446,16447,7716,16451,16453,16454,16456,16458,16459,16461,16462,16464,16465,16469,16470,16472,16474,16475,16477],{},"6)",[83,16408],{},"\ni) 我們在平衡反應上還有兩種策略可以選 一種是固定BOS的 一種是改變BOS的",[83,16411],{},"\n首先是固定的一類 最熟悉的就是我們的踝策略和髖策略",[83,16414],{},"\n那一般而言 越成熟的人 會越偏好用",[254,16417,16419],{"className":16418},[258],"踝策略",[83,16421],{},"\n而目前比較新的提出 就是",[254,16424,16426],{"className":16425},[497,257],"抓握",[254,16428,16430],{"className":16429},[497],"是一種不算策略(Strategy)的方法",[83,16432],{},"\n例如老人在快摔倒時握緊拐仗穩定好自己 這也是一種功能性向的反應",[83,16435],{},[83,16437],{},"\nii) 而另一點則是改變BOS的 例子就有跨步策略 身體是",[254,16440,16442],{"className":16441},[258],"被迫做出","的 伸手出去支撐也是如此",[83,16445],{},"\n那在發展過程中 而在",[254,16448,16450],{"className":16449},[258],"方向性上也是有順序",[83,16452],{},"\n往前大概在6個月大才學會 而側向是8個月大 最後才是後向10個月大",[83,16455],{},[83,16457],{},"\niii) 那在臨床上 有些病人可能會因為關節或肌肉力量的原因 ",[83,16460],{},"\n我們會教導他們去利用拐仗 來增加BOS的大小 這樣他的LOS也會變大",[83,16463],{},"\n我們",[254,16466,16468],{"className":16467},[257],"可以通過適度的給他們外力","訓練他們",[83,16471],{},[83,16473],{},"\niv) 目前 reach test 是最好用來測病人靜態以及半靜態平衡的方法",[83,16476],{},"\n盡可能讓病人手伸出去多一點 那假如伸得遠出去 平衡就越好",[12,16479,16480,16481,16483,16484,16486,16487,16489,16490,16492],{},"那對於小兒的發展議題，主要有這幾個",[83,16482],{},"\ni)——新形式的起源(The origin of new form)",[83,16485],{},"\nii)——連續性與非連續性(Continuity vs discontinuity)",[83,16488],{},"\niii)——變異性(Variability)",[83,16491],{},"\niv)——生物與環境的影響(Biological vs. environmental influence)",[12,16494,16495],{},"那動態模組理論是經歷過以下發展而來的",[16,16497,16498,16505,16525],{},[19,16499,16500,16501],{},"那首先是小兒痲痺(1910s)——當年的理念是哪邊無力練哪邊",[254,16502,16504],{"className":16503},[257,562],"(肌肉再教育 muscle re-education)",[19,16506,16507,16508,16512,16513,16515,16516,16518,16519,16521,16522,16524],{},"接著是1950s——當年他們開始著重以神經成熟理論為基礎學派，著重在",[254,16509,16511],{"className":16510},[562,257],"感覺輸入","促進正常的動作以及動作發展",[83,16514],{},"\n神經成熟理論(1945s)由Gesell和McGraw提出，他們的關鍵理念有如下",[83,16517],{},"\nCNS髓鞘化(Increased myelination of CNS)",[83,16520],{},"\n皮質抑制皮質下中心(Inhibition of the subcortical centers by the higher cerebral cortex)",[83,16523],{},"\n層級控制(Hierarchical control)",[19,16526,16527,16528,16532,16533,16537],{},"最後來講到階層理論的雛型(1980s)——當年他們覺得動作發展",[254,16529,16531],{"className":16530},[257],"不只單一的神經支配","，把",[254,16534,16536],{"className":16535},[257,258],"其他的系統、環境","一併整合進來",[12,16539,16540,16541,16543],{},"那神經成熟理論貢獻有兩點，正常的發展與病理的進程，以及反射到動作里程碑的評估",[83,16542],{},"\n那它有三個假設",[16,16545,16546,16557,16576],{},[19,16547,16548,16549,16551,16552,16556],{},"從反射到隨意動作——意思是剛出生只有原始反射，但隨著大腦成熟這些反射會被抑制",[83,16550],{},"\n但在1979s有學者提出說，其實原始反射對於每個寶寶來說",[254,16553,16555],{"className":16554},[258],"變異性","也很大",[19,16558,16559,16560,16562,16563,16567,16568,7711,16572],{},"頭尾走向——意思是身體的發展一定是從頭到胸到骨盤再到下肢的發展",[83,16561],{},"\n但在1976s有學者發現到，南非的寶寶被家長",[254,16564,16566],{"className":16565},[257],"直立抱法或者練習坐","，會比美國寶寶",[254,16569,16571],{"className":16570},[258],"更快發展出下肢動作",[254,16573,16575],{"className":16574},[264],"爬和翻身較慢",[19,16577,16578,16579,16581,16582,16586,16587,16591],{},"最後是近端到遠端——意思是身體發展要先學會控制近端(肩、軀幹)，而後才能控制遠端(手指)",[83,16580],{},"\n但在1988s有學者提出，寶寶的",[254,16583,16585],{"className":16584},[264],"伸手以及操作","的發展在近端遠端上是",[254,16588,16590],{"className":16589},[257,258],"同時存在","的(同步進行發展，並沒有明確上下關係)",[12,16593,16594,16595,16597,16598,16602,16603,16607,16609,16610,16614,16615,16617,16618,16622,16623,16627,16628,16632,16634,16635,16637],{},"那每個人在做動作時一定會受到自身物理特性影響例如關節角度、肌肉長度等因素",[83,16596],{},"\n那協調就是將這些複雜的東西，透過",[254,16599,16601],{"className":16600},[258],"降低自由度","，來",[254,16604,16606],{"className":16605},[264],"產生平滑的動作",[83,16608],{},"\n那降低自由度的策略會牽涉到一個叫",[254,16611,16613],{"className":16612},[562],"自我組織","的東西，那它的核心理念是說",[83,16616],{},"\n動作是有",[254,16619,16621],{"className":16620},[562],"適應性","的，次系統會根據",[254,16624,16626],{"className":16625},[257,258],"環境任務","等因素做調整，",[254,16629,16631],{"className":16630},[264],"再拼湊起來",[83,16633],{},"\n(舉例來說，即使一樣是走路，在光亮的環境和在昏暗的環境下，也會做一些微調)（Bernstein提出）",[83,16636],{},"\n有提到三個重點",[16,16639,16640,16646,16662],{},[19,16641,16642,16643,16645],{},"次序參數——它探討的是關節之間的協同",[83,16644],{},"\n例如在同一個動作型態上，做不同的任務，力度或關節角度也稍微不同，但假如相對時間相同，就能利用次序參數說明",[19,16647,16648,16649,16653,16654,16656,16657,16661],{},"那個體在發展過程中會因應不同的任務去做動作調整，而通常會採取",[254,16650,16652],{"className":16651},[257,562],"最省力、自然以及方便","的動作型態",[83,16655],{},"\n那假如這個動作達到了上述說的型態，便是",[254,16658,16660],{"className":16659},[258,257],"最穩定型態","，即使會因應任務去做改變也是十分穩定的",[19,16663,16664,16665,16667,16668,16672,16673,16675,16676,16678],{},"相移現象——意思就是說原本在做著一個穩定的動作型態",[83,16666],{},"\n因為一些",[254,16669,16671],{"className":16670},[258],"因素所干擾","，就會變成另一個動作型態",[83,16674],{},"\n(例如速度的改變從走路變成跑步，相對時間不同，所以是另一個型態，不適應次序參數)",[83,16677],{},"\n（對 黃老師教動態系統理論也提到過這個）",[12,16680,16681],{},"最後講兩個實驗",[16,16683,16684,16705],{},[19,16685,16686,16687,16689,16690,16692,16693,558,16697,16701,16702,16704],{},"第一個是關於踏步反射的實驗，那踏步反射在作原始反射，在第四周會消失，但在一歲時又會再次出現",[83,16688],{},"\n而神經成熟理論認為，是因為大腦成熟了，讓高階抑制了低階",[83,16691],{},"\n但動態模組理論發現，其實是因為在第四周寶寶",[254,16694,16696],{"className":16695},[257,258],"長脂肪比長肌肉快",[254,16698,16700],{"className":16699},[264],"力量不足","做不出來",[83,16703],{},"\n將寶寶放在水中利用浮力降低脂肪重量，踏步反射就可以又被誘發出來",[19,16706,16707,16708,16710,16711,16713,16714,16718],{},"第二個實驗，是觀察青蛙生長的環境與發育的關係",[83,16709],{},"\n青蛙需要水跟泥土的環境才能發育健全，假如只給水不給泥土的環境，就會讓發育有缺陷",[83,16712],{},"\n所以神經成熟是可以讓動作型態形成，但必須得加上",[254,16715,16717],{"className":16716},[257,258],"環境，時間以及個體本身條件","才能讓型態表現更好",[12,16720,16721,16722,16724,16725,16727,16728,16730,16731,16733],{},"那在臨床意義上有以下幾點",[83,16723],{},"\n分散式控制(Distributed control)",[83,16726],{},"\n控制參數可能來自兒童或者環境(Control parameter may be from the child or from the environment)",[83,16729],{},"\n由兒童主導(Active role of the child)",[83,16732],{},"\n個體差異的訊息(variability provides important information)",[12,16735,16736,16737,16741,16742,16746,16747,16749],{},"評估",[254,16738,16740],{"className":16739},[257,7640],"不應只侷限在探討神經發展過程","，而是要根據",[254,16743,16745],{"className":16744},[562,257],"多個系統，家庭因素","等問題",[83,16748],{},"\n(之前聽到的例子，有一個治療師說家長假如一直給小兒玩手機沒讓他們多動，確實會讓發展遲緩)",{"title":169,"searchDepth":170,"depth":170,"links":16751},[],"2026-03-31","感覺統合~三個協調的重點","\u002Fimages\u002Fuploads\u002F1775795013607-141589321_p0.jpg",{},{"title":16291,"description":16753},{"loc":7571},"blog\u002FMotor-Learning","WfAalY0VpEvjA4FEwqJIqFvJHZ0cmvKnrpM76PAKB1U",{"id":16761,"title":16762,"author":7,"body":16763,"date":17019,"description":17020,"draft":174,"edited_at":17019,"extension":175,"featured_image":17021,"meta":17022,"navigation":178,"path":17023,"pinned":174,"seo":17024,"series":181,"seriesOrder":181,"sitemap":17025,"stem":17026,"tags":17027,"__hash__":17029},"blog\u002Fblog\u002F腦性痲痺-CP.md","腦性痲痺 CP",{"type":9,"value":16764,"toc":17017},[16765,16768,16805,16817,16820,16872,16904,16934,16946,16972,16998,17003,17008],[12,16766,16767],{},"以下根據余老師做的總結來編寫",[12,16769,16770,16771,16773,16774,16778,16779,16783,16784,16786,16787,16791,16792,16796,16798,16799,16801,16802,16804],{},"首先是定義 ",[83,16772],{},"\n在大腦",[254,16775,16777],{"className":16776},[562],"未成熟","的階段 因為",[254,16780,16782],{"className":16781},[562],"腦傷而導致的動作障礙","為主的症候群",[83,16785],{},"\n而CP有",[254,16788,16790],{"className":16789},[258],"三個非","合併導致",[254,16793,16795],{"className":16794},[258],"發展遲緩",[83,16797],{},"\n非進行性(傷口不會再惡化) ",[83,16800],{},"\n非暫時性(腦傷不會好)",[83,16803],{},"\n非單純性(有機會響影到多個區域 症狀會有例如智能不足等)",[12,16806,16807,16808,16810,16811,16813,16814,16816],{},"影響區域有三種區分",[83,16809],{},"\n單側麻痺(Hemiplegia)(患側手腳無力)",[83,16812],{},"\n雙側麻痺(Diplegia)(通常雙腿影響比雙手明顯)",[83,16815],{},"\n四肢麻痺(Quadriplegia)(四肢 但上肢影響程度比下肢大)",[12,16818,16819],{},"我們現在來講三大分類",[12,16821,16822,16823,16825,16826,16830,16831,16833,16834,16838,16839,16841,16845,16846,16848,16849,16854,16855,16859,16860,16862,16863,16865,16866,16868,16869,16871],{},"首先是痙攣型(Spasticity) 也是最大宗的一類(70%)",[83,16824],{},"\n傷到了",[254,16827,16829],{"className":16828},[562],"錐狀束","(錐體路徑 Pyramidal Tract)",[83,16832],{},"\n而四肢張力都會變大 ",[254,16835,16837],{"className":16836},[562],"上肢比下肢","還要嚴重",[83,16840],{},[254,16842,16844],{"className":16843},[257],"上肢為Flex協同動作 下肢為Exten協同動作","(詳細請見李老師CVA中的表)",[83,16847],{},"\n併發症有 ",[254,16850,16853],{"className":16851},[16852],"green-5","斜視","(70%) ",[254,16856,16858],{"className":16857},[16852],"癲癇","(50%)",[83,16861],{},"\n治療重點有",[83,16864],{},"\n增加中軸張力(核心穩定)",[83,16867],{},"\n降低肢體張力",[83,16870],{},"\n提升抗重力能力",[12,16873,16874,16875,16825,16877,16881,16882,16884,16885,16889,16890,16892,16893,16895,16896,16862,16898,16900,16901,16903],{},"接著講徐動型(Athethoid)",[83,16876],{},[254,16878,16880],{"className":16879},[562],"基底核黃核","部位",[83,16883],{},"\n張力",[254,16886,16888],{"className":16887},[258],"時大時小","(有時候很硬 有時候很軟)",[83,16891],{},"\n而頭部控制差 上肢較下肢嚴重 且有不隨意扭動",[83,16894],{},"\n併發症有 聽覺障礙(高頻聽不見) 語言障礙",[83,16897],{},[83,16899],{},"\n對稱協調控制",[83,16902],{},"\n雙側控制",[12,16905,16906,16907,16825,16909,16913,16915,16916,16918,16919,16921,16922,16924,16925,16927,16928,16930,16931,16933],{},"最後來講失調型(Ataxia)",[83,16908],{},[254,16910,16912],{"className":16911},[562],"小腦",[83,16914],{},"\n張力小",[83,16917],{},"\n特徵有 步幅大(怕跌倒) 意向性震顫(手主動靠近目標 手越抖)",[83,16920],{},"\n併發有 平衡 感覺統合 知覺都會較差",[83,16923],{},"\n在治療重點上",[83,16926],{},"\n會給他們穿加壓衣(增加感統知覺) ",[83,16929],{},"\n穩定與張力提升",[83,16932],{},"\n承重(增加感統知覺)",[12,16935,16936,16937,16939,16940,16942,16943,16945],{},"還有一些小分類 簡單帶過一下",[83,16938],{},"\n首先是僵直型 這個是比痙攣型張力還要再強",[83,16941],{},"\n接著是顫抖型 這個與失調型的意向性震顫不同 在靜止時也會自己節律的抖動",[83,16944],{},"\n最後是低張型 名稱軟寶寶 多為一歲前會觀察到 到兩三歲會再發展成痙攣型抑或者徐動型",[12,16947,16948,16949,16951,16952,16954,16955,16957,16958,16960,16961,16963,16964,16966,16967,16971],{},"接著來講治療原則 主要有五點",[83,16950],{},"\n早期教育(早療 黃金期)",[83,16953],{},"\n個別化(畢竟每一個孩子的症狀都不盡相同 要針對他們的症狀計劃)",[83,16956],{},"\n治療項目盡量以ADL為主",[83,16959],{},"\n日常活動(結合孩子一天的作息去制定訓練 回家訓練)",[83,16962],{},"\n感官輸入(如本體感覺 觸覺)",[83,16965],{},"\n老師有圈了個重點 ",[254,16968,16970],{"className":16969},[258],"張力 並不等於 肌力","(張力很大 但肌力通常低下 要控制張力同時訓練肌力)",[12,16973,16974,16975,16977,16978,16982,16983,16977,16985,16989,16990,16992,16993,16997],{},"最後來講預後",[83,16976],{},"\n假如 ",[254,16979,16981],{"className":16980},[257],"2歲前","的寶寶能自行坐起來 未來100%能夠自行走動",[83,16984],{},[254,16986,16988],{"className":16987},[257],"4歲的","寶寶還不會自行坐起來 未來不會走",[83,16991],{},"\n假如 是",[254,16994,16996],{"className":16995},[257],"偏癱","的寶寶 未來100%能夠自行走動",[12,16999,17000],{},[979,17001],{"alt":1236,"src":17002},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774841979537-Screenshot_20260330_100529_Gallery.png",[12,17004,17005],{},[979,17006],{"alt":1236,"src":17007},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774842001784-Screenshot_20260330_100531_Gallery.png",[12,17009,17010,17011,17013],{},"一些講義的內容 我隨後會在另一篇裡加上 ",[83,17012],{},[254,17014,17016],{"className":17015},[562],"讀英文！！！",{"title":169,"searchDepth":170,"depth":170,"links":17018},[],"2026-03-30","按余老師給的總結懶人包做填寫","\u002Fimages\u002Fuploads\u002F1774842345403-129630217_p0_master1200.jpg",{},"\u002Fblog\u002F腦性痲痺-CP",{"title":16762,"description":17020},{"loc":17023},"blog\u002F腦性痲痺-CP",[17028],"小兒PT","VRwnEKZEYqmW7o2UAStJ5mCqG7YSqw_jRSxAkVYjn34",{"id":17031,"title":17032,"author":7,"body":17033,"date":17193,"description":17194,"draft":174,"edited_at":16095,"extension":175,"featured_image":17195,"meta":17196,"navigation":178,"path":17197,"pinned":174,"seo":17198,"series":181,"seriesOrder":181,"sitemap":17199,"stem":17200,"tags":181,"__hash__":17201},"blog\u002Fblog\u002FCVA（二）.md","CVA（二）",{"type":9,"value":17034,"toc":17191},[17035,17047,17068,17071,17096,17111,17129,17144,17147,17159,17175],[12,17036,17037,17038,17040,17041,17043,17044,17046],{},"現在我們來講分類 從病理上分成了三種",[83,17039],{},"\n血栓型(60%) 栓塞型(20%) 出血型(5%)",[83,17042],{},"\n而從發展進程來看又分成了三種(15%)",[83,17045],{},"\n完全型 發展型 短暫性腦缺血發作(TIA)",[12,17048,17049,17050,17052,17053,17055,17056,17058,17059,17061,17062,17064,17065,17067],{},"我們首先來講血栓型(Thrombotic Infarction)",[83,17051],{},"\n主要由粥狀動脈硬化斑塊和高血壓交互形成",[83,17054],{},"\n多發生在血管彎曲處積累班塊(多數為腦動脈第一主要分支處)",[83,17057],{},"\n而它是進行式的 所以在中風之前 多數患者都不清楚斑塊積累已深",[83,17060],{},"\n關於TIA這個前置警訊 它會誘發兩個機制",[83,17063],{},"\n腦血管痙攣--因血管突然收縮 導致原本就狹窄的血管完全被阻斷",[83,17066],{},"\n暫時性全身血壓過低--原本就狹窄 血壓還突然下降 導致血液供給不足",[12,17069,17070],{},"那來講機制 簡單就是血塊在斑塊中破開 觸發凝血因子 導致血栓(新民老師有專門講過 maybe重要)",[12,17072,17073,17074,17076,17077,17079,17080,17082,17083,17085,17086,17088,17089,10176,17093,17095],{},"接著講栓塞型(Embolic Infarction)",[83,17075],{},"\n栓塞型是說有栓子在血液中流血最終塞到血管",[83,17078],{},"\n通常栓子有三種來源",[83,17081],{},"\n心臟 頸內動脈血栓 頸動脈竇的粥狀斑塊",[83,17084],{},"\n而最常發生在MCA處",[83,17087],{},"\n而比起血栓型 栓塞型",[254,17090,17092],{"className":17091},[562],"更加致命",[83,17094],{},"\n因為血栓型是發展型的(慢慢堵住) 而栓塞型是完全型的(突然有一塊東西堵住)",[12,17097,17098,17099,17101,17102,17104,17105,17107,17108,17110],{},"然後講有一個比較特殊的變體 叫空隙性中風(小洞中風 Lacunar Infarction)",[83,17100],{},"\n是一些近乎90度分出來的微小管血處發生 通常影響這三個部位",[83,17103],{},"\n基底核--在MCA的M1處 ",[83,17106],{},"\n腦幹--在基底動脈處",[83,17109],{},"\n視丘--在PCA的P1\u002FP2處",[12,17112,17113,17114,17116,17117,17119,17120,17122,17123,17125,17126,17128],{},"最後我們來講出血型(Hemorrhage)",[83,17115],{},"\n分成腦內出血跟蜘蛛膜下腔出血",[83,17118],{},"\n腦內出血就是指血管破裂 血跑到並壓迫腦實質空間",[83,17121],{},"\n而蜘蛛膜下腔出血通常是腦動脈瘤破裂",[83,17124],{},"\n而患者通常會說有以下徵狀",[83,17127],{},"\n劇烈頭痛(這輩子最痛的) 噁心嘔吐 脖子僵硬 意識昏迷",[12,17130,17131,17132,17134,17135,17137,17138,17140,17141,17143],{},"而出血型通常有這四種損傷機制",[83,17133],{},"\n第一點 血會被噴出來 擠壓到周邊神經組織",[83,17136],{},"\n第二點 腦內壓升高(ICP)",[83,17139],{},"\n第三點 腦疝脫 是指血塊搶佔了空間 把正常腦組織推走(mass effect)",[83,17142],{},"\n第四點 周圍血流減少 意思是不只佔了腦組織空間 還從血管外壓到血管 導致供血不能",[12,17145,17146],{},"通常有這三種原因導致腦中風",[12,17148,17149,17150,17152,17153,17155,17156,17158],{},"第一種 高血壓 分成了三個要點",[83,17151],{},"\n長期的高血壓會對血管管壁造成損傷(因長期承受高壓力沖刷導致管壁失去彈性)",[83,17154],{},"\n跟小洞中風一樣 都是微小血管問題(區別在一個堵住一個破開)",[83,17157],{},"\n高血壓性小腦出血",[12,17160,17161,17162,17164,17165,17167,17168,17172,17174],{},"第二種 囊狀動脈瘤",[83,17163],{},"\n也是因為長期被沖刷 導致內壁被過度拉伸",[83,17166],{},"\n好發在威氏環",[254,17169,17171],{"className":17170},[257],"前半部",[83,17173],{},"\n通常為8~10mm",[12,17176,17177,17178,17180,17181,17183,17184,17186,17187],{},"最後一種是 AVM 動靜脈畸型",[83,17179],{},"\n這一個是天生的 比較難辦 意思是動靜脈直接對接 中間並沒有微血管",[83,17182],{},"\n而靜脈沒有辦法承受來自動脈的血壓 導致破裂",[83,17185],{},"\n好發在大腦",[254,17188,17190],{"className":17189},[257],"後半部",{"title":169,"searchDepth":170,"depth":170,"links":17192},[],"2026-03-26","CVA分類","\u002Fimages\u002Fuploads\u002F1774515663816-IMG_20200709_193107.jpg",{},"\u002Fblog\u002FCVA（二）",{"title":17032,"description":17194},{"loc":17197},"blog\u002FCVA（二）","apEyOXViAqwKG6XZaxqVBHM60bPSkudeJMWzzy-eIXM",{"id":17203,"title":17204,"author":7,"body":17205,"date":17301,"description":17302,"draft":174,"edited_at":17193,"extension":175,"featured_image":17303,"meta":17304,"navigation":178,"path":17305,"pinned":174,"seo":17306,"series":181,"seriesOrder":181,"sitemap":17307,"stem":17308,"tags":181,"__hash__":17309},"blog\u002Fblog\u002F腦血管病變（CVA）（中風）(一).md","腦血管病變（CVA）（中風）(一)",{"type":9,"value":17206,"toc":17299},[17207,17210,17231,17252,17258,17260,17263,17272,17275,17278,17284,17290,17293,17296],[12,17208,17209],{},"好了同學們 我們來讀CVA",[12,17211,17212,17213,17215,17216,17218,17219,17221,17222,17224,17225,17227,17228,17230],{},"從成因上能分成 梗塞性(Infarction) 和出血性(hemorrhage)",[83,17214],{},"\n那主要徵狀有",[83,17217],{},"\n偏癱",[83,17220],{},"\n感覺異常",[83,17223],{},"\n失語症\u002F構音困難",[83,17226],{},"\n視野缺損",[83,17229],{},"\n認知及智力受損",[12,17232,17233,17234,17236,17237,17239,17240,17242,17243,17245,17246,17248,17249,17251],{},"流行病學上 ",[83,17235],{},"\nCVA在美國都排第三第四名 台灣排第二第三名",[83,17238],{},"\n年齡也是重要因素 大多數CVA都在65歲以上",[83,17241],{},"\n而到了55歲 那麼每十年 患CVA的機率就會翻一倍",[83,17244],{},"\n男性比女性更容易患上",[83,17247],{},"\n黑人比白人更容易患上",[83,17250],{},"\n梗塞性佔所有類型70~85%",[12,17253,17254,17255,17257],{},"然後有三種高風險因素",[83,17256],{},"\n高血壓 糖尿病 心臟病",[35,17259],{},[12,17261,17262],{},"以下補充一下來自物治精選神經的內容 可看可不看",[12,17264,17265,17266,17268,17269,17271],{},"除了這些還有其他高危因子",[83,17267],{},"\n膽固醇過高 運動量不足 過重 抽煙 或有CVA家族史",[83,17270],{},"\n上述八種有其三 屬高危族群",[12,17273,17274],{},"在國民健康署給了六項建議預防中風",[12,17276,17277],{},"定期健檢",[12,17279,17280,17281,17283],{},"血壓測量722原則--18歲以上每年至少在家量一次血壓 並按照以下組數測量",[83,17282],{},"\n7天連續量 一天早晚量一次共2次 每次量2遍取平均值 (建議血壓值在120\u002F80mmHg)",[12,17285,17286,17287,17289],{},"三高異常辨識--血壓在120\u002F80mmHg以下 ",[83,17288],{},"\n空腹血糖值在70~99mg\u002FdL LDL(低密度膽固醇)維持在130mg\u002FdL以下",[12,17291,17292],{},"科學算病管評估中心--利用 科學算病館 網站",[12,17294,17295],{},"維持良好習慣--如作息 運動 飲食(三低一高) 及情緒穩定",[12,17297,17298],{},"中風跡象--看微笑 看舉手 說你好",{"title":169,"searchDepth":170,"depth":170,"links":17300},[],"2026-03-24","CVACVACVACVA~(路人可只看底下橫線的內容)","\u002Fimages\u002Fuploads\u002F1774504345861-IMG_20200706_025803.jpg",{},"\u002Fblog\u002F腦血管病變（CVA）（中風）(一)",{"title":17204,"description":17302},{"loc":17305},"blog\u002F腦血管病變（CVA）（中風）(一)","WAWJvtEAtJQSFAIChqC7ABykN4jeGw5TIvYG1DaHZLM",{"id":17311,"title":17312,"author":7,"body":17313,"date":17479,"description":17480,"draft":174,"edited_at":17301,"extension":175,"featured_image":17481,"meta":17482,"navigation":178,"path":17483,"pinned":174,"seo":17484,"series":181,"seriesOrder":181,"sitemap":17485,"stem":17486,"tags":181,"__hash__":17487},"blog\u002Fblog\u002F動作學習（十）回饋-2-擴增性(KR).md","動作學習（十）回饋-2-擴增性(KR)",{"type":9,"value":17314,"toc":17477},[17315,17321,17359,17381,17387,17399,17414,17423,17441,17459,17465,17471],[12,17316,17317,17318,17320],{},"接下來到了動作過程中~動作結束這兩個階段的感覺回饋",[83,17319],{},"\n分成了固有回饋(內發 個體本身的) 和擴增性回饋(外在的 旁人給的)",[12,17322,17323,17324,17326,17327,17329,17330,17334,17335,17339,17340,17342,17343,17347,17348,17352,17353,17355,17356,17358],{},"我們來講擴增性回饋 ",[83,17325],{},"\n時間點上也是分成在動作過程中給他回饋 跟結束給他回饋",[83,17328],{},"\n而結束的時間點上還能分成",[254,17331,17333],{"className":17332},[562],"立刻","給他回饋 和",[254,17336,17338],{"className":17337},[562],"過一陣子","再給他回饋",[83,17341],{},"\n再頻率上還能分成 ",[254,17344,17346],{"className":17345},[562],"做完一次","給一次回饋(單次) 和",[254,17349,17351],{"className":17350},[562],"做完幾次","後才給一次回饋(累積)",[83,17354],{},"\n例如 心率監測器(一直跳多少一直變化一直調整給你看)",[83,17357],{},"\n抑或者跑步APP裡記錄的全程心跳過程(整組一次過統計平均給你看)",[12,17360,17361,17362,17364,17365,17367,17368,17372,17373,17377,17378,17380],{},"剛說完時間上 接著講特質上",[83,17363],{},"\n分成了口語化跟非口語化",[83,17366],{},"\n而口語化上又分成了 ",[254,17369,17371],{"className":17370},[562],"講結果","(KR) 跟",[254,17374,17376],{"className":17375},[562],"講表現","(KP)",[83,17379],{},"\n而非口語化上意思是例如給一些特定的訊號讓他知道(會意)自己剛剛的行為",[12,17382,17383,17384,17386],{},"KR像剛說的直接講結果 從結果上讓接收者去做調整",[83,17385],{},"\n例如說 投那顆球 差兩公分就進了 抑或者 沒進 沒中",[12,17388,17389,17390,17392,17393,17395,17396,17398],{},"KR在回饋的內容上 像剛剛的例子來看",[83,17391],{},"\n直接數值(差公分)的叫量化回饋 而講二分法(中 沒中)的叫質性回饋",[83,17394],{},"\n僅從表現結果來看",[83,17397],{},"\n量化＞質性＞不給回饋＞亂給回饋",[12,17400,17401,17402,17404,17405,17407,17408,17410,17411,17413],{},"在回饋頻率上也分成了 絕對回饋 跟相對回饋",[83,17403],{},"\n絕對回饋意思是 在一整組的動作裡 給了多少次回饋",[83,17406],{},"\n而相對回饋 就是用絕對回饋 除以練習次數",[83,17409],{},"\n例子 在一整組動作裡 給了50次回饋 那絕對回饋頻率=50",[83,17412],{},"\n而假如這整組動作裡做了100次動作 那相對回饋頻率就是50\u002F100=50%",[12,17415,17416,17417,17419,17420,17422],{},"而在KR上 相對回饋頻率的%數減少 能有效促進學習",[83,17418],{},"\n分別有以下做法",[83,17421],{},"\n帶狀回饋 消褪回饋 總結回饋 平均回饋",[12,17424,17425,17426,17428,17429,17431,17432,17434,17435,17437,17438,17440],{},"首先來講帶狀回饋 意思是假如病人在做動作的過程中",[83,17427],{},"\n設定一個範圍 給他空間自己調整",[83,17430],{},"\n假如說 太嚴苛(精準到0.幾公分那種) 比較不適合他去學習",[83,17433],{},"\n(過於精確的回饋對學習無益)",[83,17436],{},"\n比較建議是錯的太離譜才去給回饋",[83,17439],{},"\n(我自己理解--可能可以因應表現隨時調整範圍 讓病人的動作品質上升?)",[12,17442,17443,17444,17446,17447,17449,17450,17452,17453,17455,17456,17458],{},"而接下來消褪回饋 跟剛剛帶狀回饋一樣設一個範圍",[83,17445],{},"\n也是不到範圍內去給回饋",[83,17448],{},"\n而消褪比較偏向是頻率減少的部份 讓我自己去抓那個正確(動作及格)的範圍",[83,17451],{},"\n例如我第一次做 四次不達標 給我四次回饋-->下次做兩次不達標 給兩次回饋",[83,17454],{},"\n最後全部達標 不給回饋這樣",[83,17457],{},"\n(我自己理解--目的應該是更偏向病人自己抓感覺?)",[12,17460,17461,17462,17464],{},"接下來講結回饋 就是一組結束後再給他講分數 屬於是累積回饋的分類",[83,17463],{},"\n頻率可以因應難度而定(例如簡單的動作可以給更少的回饋)",[12,17466,17467,17468,17470],{},"最後講平均回饋 就是給他講一組的平均分 一樣是累積回饋",[83,17469],{},"\n例如 這組比上組平均高了幾分",[12,17472,17473],{},[254,17474,17476],{"className":17475},[562],"而研究指出 學習者主動要求何時獲得回饋可有利學習",{"title":169,"searchDepth":170,"depth":170,"links":17478},[],"2026-03-23","擴增性KR","\u002Fimages\u002Fuploads\u002F1774235040613-IMG_20201025_201029.jpg",{},"\u002Fblog\u002F動作學習（十）回饋-2-擴增性(KR)",{"title":17312,"description":17480},{"loc":17483},"blog\u002F動作學習（十）回饋-2-擴增性(KR)","qqeXPcncJn8IYdH_37DfUGfApRtccKu_ljcsag3r6Gg",{"id":17489,"title":17490,"author":7,"body":17491,"date":17479,"description":17637,"draft":174,"edited_at":17301,"extension":175,"featured_image":17638,"meta":17639,"navigation":178,"path":17640,"pinned":174,"seo":17641,"series":181,"seriesOrder":181,"sitemap":17642,"stem":17643,"tags":181,"__hash__":17644},"blog\u002Fblog\u002F動作學習（十一）回饋-3-擴增性(KP).md","動作學習（十一）回饋-3-擴增性(KP)",{"type":9,"value":17492,"toc":17635},[17493,17499,17505,17537,17551,17577,17592,17617],[12,17494,17495,17496,17498],{},"我們接著講KP 它是從動作的形態上 動作層面上的 偏向接收者要去腦內想畫面",[83,17497],{},"\n例如 你剛剛手抬不夠高 你剛剛投籃出手可以直一點",[12,17500,17501,17502,17504],{},"而KP也有一下四種回饋做法",[83,17503],{},"\n影像示範回饋 動態學回饋 生物回饋 動力學回饋",[12,17506,17507,17508,17510,17511,17515,17516,17518,17519,17521,17522,17526,17527,17529,17530,17534,17536],{},"先來講示範回饋 ",[83,17509],{},"\n示範回饋比不是",[254,17512,17514],{"className":17513},[562],"漫無目的","地做整套動作讓病人自己吸收",[83,17517],{},"\n在這個基礎上還可以分成兩個時間段 ",[83,17520],{},"\n第一是示範前 引導病人去看 ",[254,17523,17525],{"className":17524},[562],"局部的 關鍵的"," 動作形態",[83,17528],{},"\n第二則是示範過程中~結束 偏向讓病人去看哪裡有不對 提示他下次",[254,17531,17533],{"className":17532},[562],"糾正",[83,17535],{},"\n有研究指示 有糾正的看示範會比只引導的看示範來的更有效",[12,17538,17539,17540,17542,17543,17545,17546,909],{},"這裡有兩點是之前提到的 再申一次",[83,17541],{},"\n第一點 因為病人的注意力有限 所以得讓病的注意力放在局部的 關鍵的地方上",[83,17544],{},"\n第二點 就是看別人做錯的事能促進學習(",[49,17547,17550],{"href":17548,"rel":17549},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E4%B9%9D%EF%BC%89%E5%9B%9E%E9%A5%8B-1",[53],"也是之前提到的",[12,17552,17553,17554,17556,17557,17559,17560,17562,17563,17565,17566,17570,17571,17573,17574,17576],{},"接著來講動態學回饋",[83,17555],{},"\n是著重在動作軌跡 形態上的 而不是關注出多少力 ",[83,17558],{},"\n關注的點可以從角度 時間 速度 協調等 ",[83,17561],{},"\n例如 你手可以抬高點\u002F抬高30度",[83,17564],{},"\n(這個跟",[254,17567,17569],{"className":17568},[562],"KR的直講結果上的數據","不一樣哦 這是在動作層面上的 不要搞混了)",[83,17572],{},"\n這裡也說了假如我們給甚麼樣的回饋 病人的成果會更偏向達成我們給予的回饋",[83,17575],{},"\n例如 只跟他講注意步距 步距的改善就會比協調的改善還要來得更好",[12,17578,17579,17580,17582,17583,17585,17586,17588,17589,17591],{},"然後來講生物回饋",[83,17581],{},"\n他會偏向讓病人看到生理上數值的變化 例如肌電圖 ",[83,17584],{},"\n他就按著肌電圖的改變 去調整自己的動作",[83,17587],{},"\n另一種則是給予聾啞人看聲波圖 也可以讓他們注意到聲波的變化",[83,17590],{},"\n讓他們盡量以達到跟聲波圖上的圖形重合 來讓他們嘗試發音",[12,17593,17594,17595,17597,17598,17602,17603,17605,17606,17610,17611,17613,17614,17616],{},"最後來講動力學回饋",[83,17596],{},"\n他跟動態動講動作軌跡 形態上有所不同 他關注的是",[254,17599,17601],{"className":17600},[562],"肌肉使用上","的多少",[83,17604],{},"\n但也指出 實際讓他知道出力的",[254,17607,17609],{"className":17608},[7640],"具體參數","會不好",[83,17612],{},"\n直接在他出力的同時跟他說 大力了一點 小力了一點 這種讓他自己意會 動腦去想的 會更優",[83,17615],{},"\n而降低回饋頻率也能促進學習",[12,17618,17619,17620,17622,17623,17625,17626,17628,17629,17631,17632,17634],{},"那麼最後總結一下 臨床上按照以上回饋方式可以得出以下總結",[83,17621],{},"\n第一 在學新動作之前 可以示範一次給病人看 有利於在腦中構築動作型態",[83,17624],{},"\n第二 指導 示範 回饋的資訊不是越多越好",[83,17627],{},"\n第三 示範不必是正確的",[83,17630],{},"\n第四 假如病人在學習過程中能自行找出錯誤 可以減少回饋",[83,17633],{},"\n第五 回饋的頻率不要過高",{"title":169,"searchDepth":170,"depth":170,"links":17636},[],"擴增性KP","\u002Fimages\u002Fuploads\u002F1774238705780-IMG_20201030_204929.jpg",{},"\u002Fblog\u002F動作學習（十一）回饋-3-擴增性(KP)",{"title":17490,"description":17637},{"loc":17640},"blog\u002F動作學習（十一）回饋-3-擴增性(KP)","D3kBGFVuaKo5hkO06V1-EMKNnFjWcPi3g9F26PWN5jE",{"id":17646,"title":17647,"author":7,"body":17648,"date":17479,"description":17781,"draft":174,"edited_at":17301,"extension":175,"featured_image":17782,"meta":17783,"navigation":178,"path":17784,"pinned":174,"seo":17785,"series":181,"seriesOrder":181,"sitemap":17786,"stem":17787,"tags":181,"__hash__":17788},"blog\u002Fblog\u002F動作學習（十一）回饋-4-(間隔+物理引導).md","動作學習（十二）回饋-4-(間隔+物理引導)",{"type":9,"value":17649,"toc":17779},[17650,17653,17667,17689,17698,17715,17718,17724,17730,17739,17745,17754,17776],[12,17651,17652],{},"終於要結束回饋了",[12,17654,17655,17656,17658,17659,17661,17662,17666],{},"在回饋的延時上有兩種區分",[83,17657],{},"\n一種是回饋間隔 就是動作結束後 隔多久才給予回饋",[83,17660],{},"\n另一種是回饋後間隔 就是給完回饋後 隔了多久",[254,17663,17665],{"className":17664},[562],"消化","完開始下一次動作的時間段",[12,17668,17669,17670,17674,17675,17677,17678,909,17683,17685,17686,17688],{},"而在回饋間隔上 ",[254,17671,17673],{"className":17672},[562],"不宜在動作結束","立即給予回饋 ",[83,17676],{},"\n因為會中斷基模自行修正 不利於基模的建立 (",[49,17679,17682],{"href":17680,"rel":17681},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%8B%95%E4%BD%9C%E5%AD%B8%E7%BF%92%EF%BC%88%E4%BA%94%EF%BC%89%E7%90%86%E8%AB%96-2",[53],"引用基模理論",[83,17684],{},"\n所以應當延時3~8秒才給予回饋",[83,17687],{},"\n(應當讓內在基模修正 而後以外在回饋方式進一步改進基模)",[12,17690,17691,17692,17694,17695,17697],{},"接著來講練習間隔 練習間隔是把 回饋間隔 與回饋後間隔 組合在一起",[83,17693],{},"\n而多數學者認為這個練習間隔越長 效果越佳",[83,17696],{},"\n(因為間隔長了 代表不記得先前的動作方式 讓大腦重新想一次動作程式)",[12,17699,17700,17701,17705,17706,17708,17709,17711],{},"而在動作練習組數之間還可以給予",[254,17702,17704],{"className":17703},[562],"空白間隔"," (比較適用在組內在做同一種動作)",[83,17707],{},"\n例如第一組練習後給了回饋 在做二~五組時不給回饋 在做完第六組後再給回饋",[83,17710],{},[254,17712,17714],{"className":17713},[562],"可以減少依賴 強化內在基模",[12,17716,17717],{},"在回饋間隔裡的活動 大概有兩種 一種是干擾活動 一種是主觀判斷",[12,17719,17720,17721,17723],{},"干擾活動中 在後續測驗表現會比較差 ",[83,17722],{},"\n因為大腦處理能力有限 假如還要給病人加重負擔 會不利於學習",[12,17725,17726,17727,17729],{},"而主觀判斷的意思是 在回饋的間隔中 ",[83,17728],{},"\n提醒病人以主觀判斷自己做的動作對不對(主動強化修正基模)",[12,17731,17732,17733,17735,17736,17738],{},"接著來講物理引導上 對於學習上也是有一定幫助的",[83,17734],{},"\n比較多用在一些很需要抓感覺的動作",[83,17737],{},"\n例如騎腳踏車 裝輔助輪跟我扶著 都是物理引導 在學會之前也是要抓平衡感(感覺)",[12,17740,17741,17742,17744],{},"而怎麼利用物理引導呢 像很常說的 手把手教真的學不會",[83,17743],{},"\n那麼有以下幾點",[12,17746,17747,17748,17750,17751,17753],{},"第一 穿插練習 例如10次動作裡 第 1 4 7次做引導 其他七次讓他自己做(減少依賴)",[83,17749],{},"\n第二 在最開始 陌生的時候給予引導 讓他先在大腦裡構建自己的模版",[83,17752],{},"\n第三 而在速度方面 指導的越慢 效果越好 反之亦然",[12,17755,17756,17757,17759,17760,17762,17763,17765,17766,17768,17769,17771,17772],{},"總結一下四種核心",[83,17758],{},"\n在最開始給予觀念",[83,17761],{},"\n慢速指導會更好",[83,17764],{},"\n可以預防受傷",[83,17767],{},"\n降低恐懼感",[83,17770],{},"\n但是最主要的 ",[254,17773,17775],{"className":17774},[562],"不能代替主動學習",[12,17777,17778],{},"哇哈哈 還有100頁就結束啦",{"title":169,"searchDepth":170,"depth":170,"links":17780},[],"間隔+物理引導","\u002Fimages\u002Fuploads\u002F1774240031787-IMG_20201101_110456.jpg",{},"\u002Fblog\u002F動作學習（十一）回饋-4-(間隔+物理引導)",{"title":17647,"description":17781},{"loc":17784},"blog\u002F動作學習（十一）回饋-4-(間隔+物理引導)","tB8GftJUcLZ3arjfJShfzGcViWaQG6gfgd0MzSqEnIc",{"id":17790,"title":17791,"author":7,"body":17792,"date":17479,"description":18156,"draft":174,"edited_at":17301,"extension":175,"featured_image":18157,"meta":18158,"navigation":178,"path":18159,"pinned":174,"seo":18160,"series":181,"seriesOrder":181,"sitemap":18161,"stem":18162,"tags":181,"__hash__":18163},"blog\u002Fblog\u002F動作學習（十三）臨床應用.md","動作學習（十五）臨床應用",{"type":9,"value":17793,"toc":18154},[17794,17797,17812,17845,17864,17867,17876,17906,17935,17975,17996,18001,18004,18036,18048,18051,18073,18078,18081,18112,18133,18151],[12,17795,17796],{},"加油 剩80頁PPT不到了",[12,17798,17799,17800,17802,17803,17805,17806,17808,17809,17811],{},"接下來講臨床應用部份",[83,17801],{},"\n分成三個大方向 ",[83,17804],{},"\n肌肉再教育",[83,17807],{},"\n神經誘發",[83,17810],{},"\n任務取向模式",[12,17813,17814,17815,17819,17820,17822,17823,17825,17826,17828,17829,17831,17832,17834,17835,17839,17841,17842,17844],{},"先來講肌肉再教育 背景是因應",[254,17816,17818],{"className":17817},[562],"小兒麻痺大流行","而受推廣",[83,17821],{},"\n治療重點包括",[83,17824],{},"\n評估:徒手肌力測試",[83,17827],{},"\n處置:對較弱的肌肉做訓練 維持ROM完整 避免固定不動",[83,17830],{},"\n強調病人主動參與 預防併發症",[83,17833],{},"\n必要時",[254,17836,17838],{"className":17837},[562],"可用輔具協助",[83,17840],{},"\n限制:因為日常生活並非由單一肌肉達成 而是靠協同 只專注在單一肌肉上成效不佳",[83,17843],{},"\nUMN lesion患者無法做出單關節動作",[12,17846,17847,17848,17822,17850,17852,17853,17855,17856,909,17861,17863],{},"接著來講神經誘發 針對剛提到的UMNL病人發展而來",[83,17849],{},[83,17851],{},"\n評估:反射動作",[83,17854],{},"\n處置:以感覺回饋修改反射動作 亦鼓勵高階控制動作練習 重複練習正確動作(無意外應該是",[49,17857,17860],{"href":17858,"rel":17859},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E5%91%A8%E5%9C%8D%E7%90%86%E8%AB%96%E5%AD%B8%E6%B4%BE%EF%BC%88%E4%BA%8C%EF%BC%89%E9%9A%8E%E5%B1%A4%E7%90%86%E8%AB%96",[53],"階層理論",[83,17862],{},"\n強調抑制異常動作與痙攣 誘發正常動作 並透過反覆練習使動作自動化與習慣化",[12,17865,17866],{},"神經誘發還分成六個學派...........",[12,17868,17869,17870,17872,17873,17875],{},"首先來講第一個......感覺統合(SI)",[83,17871],{},"\n它認為 是感知或知覺受影響 而不是動作上有問題",[83,17874],{},"\n所以會結合多感觀刺激輸入以訓練 強調感覺回饋及重複練習",[12,17877,17878,17879,17822,17881,17883,17884,17886,17887,17889,17890,17892,17893,17895,17896,17898,17899,17903,17905],{},"接著講.......Brunnstorm的理論 由治療偏癱發展而來",[83,17880],{},[83,17882],{},"\n初期可利用反射誘發動作發生",[83,17885],{},"\n依患者恢復程度加以訓練",[83,17888],{},"\n逐一打破協同動作引導自主性動作(Brunnstorm分期表 可見新民老師講義裡的表)",[83,17891],{},"\n促進手部功能",[83,17894],{},"\n行走前需要準備運動的練習",[83,17897],{},"\n治療目的:以感覺刺激輸入訊息給患者在訓練過程中正向加強 提升",[254,17900,17902],{"className":17901},[562],"主動控制協同動作的能力",[83,17904],{},"\n強調站及步態訓練",[12,17907,17908,17909,17911,17912,17914,17915,17920,17921,17923,17924,17926,17927,17931,17932,17934],{},"接著來講Bobath的NDT...... 他是階層理論來解釋嬰兒CP的不正常姿勢反射(較適合在嬰兒評估治療)",[83,17910],{},"\n治療重點:使用擺位產生正常 從而抑制不正常的動作 也靠抑制不正常動作抑制異常張力",[83,17913],{},"\n而且按照",[254,17916,17919],{"className":17917},[17918],"bg-orange-3","正常發展程序","(近端到遠近的控制順序)",[83,17922],{},"\n與關鍵點控制(近端keypoint控制張力 遠端keypoint控制精細動作)",[83,17925],{},"\n而Bobath認為不該以使用",[254,17928,17930],{"className":17929},[562],"反射及聯合動作","(會加重痙攣)訓練及不做肌肉訓練(讓肢體變硬)",[83,17933],{},"\n在動作控制時不應過度用力(他認為會引起不正常反射)",[12,17936,17937,17938,17940,17941,17943,17944,17948,17949,17951,17952,17954,17955,17959,17960,17962,17963,17967,17968,17970,17971],{},"而在最新的Bobath理論又更新出五點面向",[83,17939],{},"\n第一點 多重任務導向 不只是身體本身 還探討了任務本身及環境因素",[83,17942],{},"\n第二點 功能導向 以改善",[254,17945,17947],{"className":17946},[7640],"功能性動作","為主(以達成任務為主) 並更貼合ADL ",[83,17950],{},"\n第三點 動作學習 意思是除了在治療過程中學到的 ",[83,17953],{},"\n_在",[254,17956,17958],{"className":17957},[7640],"治療外的時間點","會不會讓學習更有益(即日常主動解決事情) 望求達到最佳效",[83,17961],{},"\n第四點 動作分析 這邊就是",[254,17964,17966],{"className":17965},[7640],"考我們PT的功力","了 不只要看出動作上有啥問題 更要看仔細一點 例如肌肉力量",[83,17969],{},"\n第五點 附加治療 需要時可與各種療法並用 例如副木 跑步機 ",[254,17972,17974],{"className":17973},[7640],"肌力訓練",[12,17976,17977,17978,17980,17981,17985,17987,17988,17992,17993,17995],{},"還有三個......理論 接著講Johnstone的 他更偏向治療CVA",[83,17979],{},"\n他也是用階層理論 亦支持剛剛講Bobath時提到的 ",[254,17982,17984],{"className":17983},[17918],"正常發展程式",[83,17986],{},"\n他提出可以用",[254,17989,17991],{"className":17990},[562],"填充空氣的塑料副木","控制病人的肢體姿勢 以達到正常擺位和避免肩關節疼痛等",[83,17994],{},"\n(可以參考一下Gemini)",[12,17997,17998],{},[979,17999],{"alt":1236,"src":18000},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774260332783-Screenshot_2026-03-23_180500.png",[12,18002,18003],{},"還有 兩個 理論(咳血)",[12,18005,18006,18007,18009,18010,7716,18013,18015,18016,18018,18019,18023,18024,18026,18027,18029,18030,18032,18033,18035],{},"接著講PNF 大二下基物二都跑過台的了 對角線動作跟訓練 ",[83,18008],{},"\n他也是強調",[254,18011,17984],{"className":18012},[17918],[83,18014],{},"\n(但不要因為PNF D1 D2先從遠端開始動就覺得他是反過來的 ",[83,18017],{},"\n只是因為",[254,18020,18022],{"className":18021},[562],"旋轉能給予本體感覺"," 可帶動整段肢體)",[83,18025],{},"\n而他治療重點包括",[83,18028],{},"\n本體感覺刺激 只需要給一些小阻力或者牽拉 誘發動作",[83,18031],{},"\n神經肌肉控制正常化 引導肌肉主動或被動收縮或放鬆 讓神經和肌肉控制機制變正常",[83,18034],{},"\n功能改善:由上述過程 增加肌力 增加ROM",[12,18037,18038,18039,18041,18042,18044,18045,18047],{},"他提到治療師應靈活應用多重感覺刺激輸入引導或強化動作",[83,18040],{},"\n觸覺:治療師的接觸與引導(例 教導病人PNF的二指握法)",[83,18043],{},"\n聽覺:聲音指令和音量控制",[83,18046],{},"\n本體覺:誘發牽張反射",[12,18049,18050],{},"他還提到了善用擴散現象 意思是對健側邊施最大阻力 可誘發其他的肌肉收縮與動作產生",[12,18052,18053,18054,18056,18057,18061,18063,18064,18066,18067,18069,18070,18072],{},"結束 理論 啦......我們最後來講ROOD",[83,18055],{},"\n他一樣強調感覺輸入 而且是 ",[254,18058,18060],{"className":18059},[562],"外在的感覺輸入直接導入動作輸出",[83,18062],{},"\n且動作本身也是感覺 會形成一個感知迴路",[83,18065],{},"\n治療重點十分重視感覺輸入(輕撫 刷擦 冷刺激 按壓 牽張 輕叩)",[83,18068],{},"\n而正常的發展進行這一點在小兒余亮老師有提到就是",[83,18071],{},"\n先有動作 再穩定 接著在穩定的姿勢下轉移重心 最後是重心轉移下做動作",[12,18074,18075],{},[979,18076],{"alt":1236,"src":18077},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774263529039-Screenshot_2026-03-23_185830.png",[12,18079,18080],{},"我們來講最後一個大方向(沒錯 是不是忘記了是三種教法)",[12,18082,18083,18084,18086,18087,18091,18093,18094,18096,18097,18099,18100,18102,18103,18105,18106,18108,18109,18111],{},"最後一個是任務導向模式 它認為動作是靠 個人 任務 環境三者互動起來自然呈現的結果",[83,18085],{},"\n動作由目標而發 且感覺系統在動作控上不僅是反射刺激的關係 而",[254,18088,18090],{"className":18089},[562],"用於動作之預測和適應",[83,18092],{},"\n治療重點如下",[83,18095],{},"\n任務評估跟目標設定",[83,18098],{},"\n強調患者主動參與及自我修正",[83,18101],{},"\n特定任務訓練與高劑量練習",[83,18104],{},"\n善用練習的變異性",[83,18107],{},"\n多感覺擴增性回饋",[83,18110],{},"\n個別化設計",[12,18113,18114,18115,18117,18118,18120,18121,18123,18124,18126,18127,18129,18130,18132],{},"而他認為 任務導向是唯一 專一的",[83,18116],{},"\n即要學開車就在車上練開車 而不是踩腳踏車",[83,18119],{},"\n在步態學習上",[83,18122],{},"\n應該以最小化損傷 是身體限制 那就修好它 例如牽拉 肌肉訓練",[83,18125],{},"\n最大化步態策略 練出最省力 有效的做法(CVA病人比較常見到甩腿這麼費力的動作)",[83,18128],{},"\n和環境適應力 應對各種環境",[83,18131],{},"\n這三做結合",[12,18134,18135,18136,18138,18139,18141,18142,18144,18145,18147,18148,18150],{},"而有人提出動作再學習模式",[83,18137],{},"\n有四步",[83,18140],{},"\n第一步 評估分析任務",[83,18143],{},"\n第二步 練習缺乏的動作成份",[83,18146],{},"\n第三步 直接練習該任務",[83,18149],{},"\n第四步 訓練不同情境下的動作",[12,18152,18153],{},"剩不到 五十頁 加 油.....",{"title":169,"searchDepth":170,"depth":170,"links":18155},[],"第四份PPT","\u002Fimages\u002Fuploads\u002F1774265882810-10575241i.jpg",{},"\u002Fblog\u002F動作學習（十三）臨床應用",{"title":17791,"description":18156},{"loc":18159},"blog\u002F動作學習（十三）臨床應用","vf881gktEM2lq8t9C3Y7nCna6fnYJ4HdNpcQ_HFclyc",{"id":18165,"title":18166,"author":7,"body":18167,"date":17479,"description":18351,"draft":174,"edited_at":17301,"extension":175,"featured_image":18352,"meta":18353,"navigation":178,"path":18354,"pinned":174,"seo":18355,"series":181,"seriesOrder":181,"sitemap":18356,"stem":18357,"tags":181,"__hash__":18358},"blog\u002Fblog\u002F動作學習（十二）神經可塑性.md","動作學習（十三）神經可塑性",{"type":9,"value":18168,"toc":18349},[18169,18172,18198,18220,18223,18226,18276,18288,18291,18318,18324,18327,18333,18338,18344],[12,18170,18171],{},"我們現在來講在學習時神經會有啥變化",[12,18173,18174,18175,18177,18178,18182,18183,18185,18186,18188,18189,18191,18192,18194,18195,18197],{},"先來描述一下神經系統 它是可以被修改的 ",[83,18176],{},"\n而神經系統的改變 ",[254,18179,18181],{"className":18180},[562],"約等於","行為\u002F心理上的改變",[83,18184],{},"\n假如我們看到有一個人的行為發生改變 那他大概有以一下幾點物理變化",[83,18187],{},"\n學習\u002F記憶",[83,18190],{},"\n發育",[83,18193],{},"\n成癮",[83,18196],{},"\n恢復",[12,18199,18200,18201,18203,18204,18208,18209,18211,18212,18216,18217,18219],{},"而假如將神經從生物體觀察上 有兩種分期",[83,18202],{},"\n一種是短期功能性上的塑性 簡單來說就是",[254,18205,18207],{"className":18206},[562],"神經元傳導","變得更有效更高效了",[83,18210],{},"\n而另一種則是結構上的塑性 意思是從",[254,18213,18215],{"className":18214},[7640],"數量或結構","上發生了改變",[83,18218],{},"\n而有一個重點 動作的學習是以上兩種情況加在一起 是自然呈現的結果",[12,18221,18222],{},"而在神經塑性有分了三個時期",[12,18224,18225],{},"首先是發展時期的神經塑性",[12,18227,18228,18229,18231,18232,18234,18235,18239,18240,18242,18243,18247,18248,18250,18251,18253,18254,18258,18259,18261,18262,18264,18265,18267,18268,18272,18273,18275],{},"先來講標的細胞 這個東西會決定神細元存活的數目",[83,18230],{},"\n有人做過研究 分別對雞胚胎移植移除標的細胞",[83,18233],{},"\n發現",[254,18236,18238],{"className":18237},[562],"移除","標的細胞的胚胎那一個區域的神經元明顯下降",[83,18241],{},"\n而",[254,18244,18246],{"className":18245},[7640],"移植","了標的細胞的胚胎神經元則明顯增加",[83,18249],{},"\n所以讓神經元存活的關鍵",[83,18252],{},"\n就是看",[254,18255,18257],{"className":18256},[562],"突觸前神經元與標的細胞","有沒有互動",[83,18260],{},"\n假如沒有跟標的細胞互動的 就會流失掉",[83,18263],{},"\n而在發展期 一個標的細胞會同時連接多個神經元",[83,18266],{},"\n但在成熟後 會變成",[254,18269,18271],{"className":18270},[562],"一個標的細胞連接一個神經元"," 其他會被淘汰",[83,18274],{},"\n(競爭是重要的)",[12,18277,18278,18279,18281,18282,18284,18285,18287],{},"接著來講受傷時期的神經塑性",[83,18280],{},"\n在受傷後 運動功能多少會被影響",[83,18283],{},"\n而神經重塑的程度 決定了受傷後復原的運動能力",[83,18286],{},"\n而重塑也受環境與經驗影響",[12,18289,18290],{},"那麼先來講PNS的神經受傷生理變化的過程",[12,18292,18293,18294,18296,18297,18301,18303,18304,18308,18309,18311,18312,18314,18315,18317],{},"那先來講受傷處的近端",[83,18295],{},"\n細胞本體會腫大 細胞核移到周邊位置並發生",[254,18298,18300],{"className":18299},[10233],"溶解現象",[83,18302],{},"\n然後講遠端 會發生一種叫 ",[254,18305,18307],{"className":18306},[562],"瓦勒式變性現象"," 的改變",[83,18310],{},"\n意思是細胞核遠端的軸突跟髓鞘發生溶解 破碎 最後被吞噬",[83,18313],{},"\n最後 受傷的上下游也會有兩種變化",[83,18316],{},"\n受傷部位的上游會發生 而受傷部位的下遊則發生前溯變化",[12,18319,18320,18321,18323],{},"而受傷之後他們會開始復原 而且通常復原機會良好 稱為重生",[83,18322],{},"\n而通常會在軸突再次出芽生長",[12,18325,18326],{},"首先第一種叫再生性出芽生長 直在在軸突末端長出新的軸突",[12,18328,18329,18330,18332],{},"第二種叫代償性出芽生長",[83,18331],{},"\n意思是有標的細胞因神經受損空著沒人佔據 而附近沒有受傷的神經元軸突會生長並佔據",[12,18334,18335],{},[979,18336],{"alt":1236,"src":18337},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774251258882-Screenshot_2026-03-23_153408.png",[12,18339,18340,18341,18343],{},"最後代償性出芽生長 簡單來說就是遠端軸突受傷 ",[83,18342],{},"\n那麼近端假如還能長那就在近端長出來(都是在同一個神經元上)",[12,18345,18346],{},[979,18347],{"alt":1236,"src":18348},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774251534288-Screenshot_2026-03-23_153759.png",{"title":169,"searchDepth":170,"depth":170,"links":18350},[],"第五份PPT 介紹~CNS","\u002Fimages\u002Fuploads\u002F1774251705899-IMG_20200616_205324.jpg",{},"\u002Fblog\u002F動作學習（十二）神經可塑性",{"title":18166,"description":18351},{"loc":18354},"blog\u002F動作學習（十二）神經可塑性","T9UVZ_5iZ4Fy3NX42VOGPKy3sVVcdiTZq2IlEUo4_AU",{"id":18360,"title":18361,"author":7,"body":18362,"date":17479,"description":18461,"draft":174,"edited_at":17301,"extension":175,"featured_image":18462,"meta":18463,"navigation":178,"path":18464,"pinned":174,"seo":18465,"series":181,"seriesOrder":181,"sitemap":18466,"stem":18467,"tags":181,"__hash__":18468},"blog\u002Fblog\u002F動作學習（十二）神經可塑性2.md","動作學習（十四）神經可塑性2",{"type":9,"value":18363,"toc":18459},[18364,18367,18395,18401,18407,18413,18419,18441,18447,18450],[12,18365,18366],{},"我們接著來講CNS上的重塑",[12,18368,18369,18370,18372,18373,18377,18379,18380,18382,18383,18385,18386,18388,18389,18391,18392,18394],{},"而CNS上的受損 通常無法像PNS那樣重生 ",[83,18371],{},"\n但是復原後 還是被受損時期功能性還要好 不是因為",[254,18374,18376],{"className":18375},[562],"生長了啥 重生了啥",[83,18378],{},"\n而是因為以下幾點",[83,18381],{},"\n水腫消除",[83,18384],{},"\n殘存的細胞恢復活力",[83,18387],{},"\n休克過後恢復",[83,18390],{},"\n原本意義不明的區域被徵召",[83,18393],{},"\n使用某些路線平替",[12,18396,18397,18398,18400],{},"雖然CNS沒有重生 但還是會有出芽生長的情形 形成新的軸突聯結",[83,18399],{},"\n但目前臨床應用上還不夠明顯",[12,18402,18403,18404,18406],{},"而CNS受損後 神經會有三種恢復時間段",[83,18405],{},"\n神經休克-->去神經化過敏感性-->側枝生長",[12,18408,18409,18410,18412],{},"去神經化過敏感性 意思是受傷後 剩下的神經纖維會對神經傳導物質變得敏感",[83,18411],{},"\n激活相關通路 讓功能恢復",[12,18414,18415,18416,18418],{},"最後我們來講學習跟經驗引起的神經塑性",[83,18417],{},"\n會圍繞這四點來討論",[12,18420,18421,18422,18424,18425,18429,18430,18432,18433,18437,18438,18440],{},"首先是習慣化",[83,18423],{},"\n習慣化分成兩種 一種是",[254,18426,18428],{"className":18427},[562],"功能性(短期習慣化)","(降低感覺) ",[83,18431],{},"\n一種是",[254,18434,18436],{"className":18435},[562],"結構化(長期習慣化)","(直接讓通路消失)",[83,18439],{},"\n習慣化會使多數突觸喪失功能(突觸數量減少)",[12,18442,18443,18444,18446],{},"第二種 敏感化 就是習慣化反過來 ",[83,18445],{},"\n突觸傳導變多 會導致突觸數量變多",[12,18448,18449],{},"第三 重複刺激 意思是反複的刺激同一個區域 他在腦部的皮質區會增大",[12,18451,18452,18453,18455,18456,18458],{},"第四 減少使用 會讓腦部的皮質區變小",[83,18454],{},"\n以研究為例 把猴子的三四指縫起來成同一隻以減少使用",[83,18457],{},"\n過了一段時間觀察腦部皮質區變更模糊",{"title":169,"searchDepth":170,"depth":170,"links":18460},[],"CNS ~第五份PPT 完","\u002Fimages\u002Fuploads\u002F1774254235999-IMG_20200616_205906.jpg",{},"\u002Fblog\u002F動作學習（十二）神經可塑性2",{"title":18361,"description":18461},{"loc":18464},"blog\u002F動作學習（十二）神經可塑性2","uuesqAFo6zj_Qm-1P_gNe3_JNwA5YO9WQGW3RyeKFns",{"id":18470,"title":18471,"author":7,"body":18472,"date":17479,"description":18705,"draft":174,"edited_at":17301,"extension":175,"featured_image":18706,"meta":18707,"navigation":178,"path":18708,"pinned":174,"seo":18709,"series":181,"seriesOrder":181,"sitemap":18710,"stem":18711,"tags":181,"__hash__":18712},"blog\u002Fblog\u002F動作學習（十五）影響表現的因素.md","動作學習（十七）影響表現的因素",{"type":9,"value":18473,"toc":18703},[18474,18477,18483,18489,18498,18507,18516,18531,18540,18558,18561,18567,18572,18581,18590,18596,18599,18602,18607,18613,18616,18634,18637,18655,18682,18700],[12,18475,18476],{},"同學 撐過這裡 就結束了 小考加油",[12,18478,18479,18480,18482],{},"那表現之前說過了 是來推估動作學到了多少",[83,18481],{},"\n但這個表現 會被暫時性的因素所影響 例如疲勞",[12,18484,18485,18486,18488],{},"那在動作學習上 就是相當永久的的改變",[83,18487],{},"\n那麼影響動作學習的因素就有 像練習 或者回饋",[12,18490,18491,18492,18494,18495,18497],{},"而這兩個分別代表暫時性跟永久性的被影響的差異",[83,18493],{},"\n那這裡有共通的被影響特點",[83,18496],{},"\n個人能力 注意力 警醒程度與焦慮 動機",[12,18499,18500,18501,18503,18504,18506],{},"個人能力呢 也可以叫說資質 也可以用悟性來講",[83,18502],{},"\n基本上屬於先天性的",[83,18505],{},"\n他不太會因為被學習跟經驗而改變",[12,18508,18509,18510,18512,18513,18515],{},"那在能力上也分成兩種 一種叫通用動作能力",[83,18511],{},"\n它認為 假如你平衡感好 那你協調跟反應也一定很快",[83,18514],{},"\n不過很多研究都證明說它還是不對的",[12,18517,18518,18519,18521,18522,18524,18525,18527,18528,18530],{},"而另一個 動作能力特效性假說",[83,18520],{},"\n他則因為 能力不只這麼大範疇就能被概括(The number of motor abilities was very large)",[83,18523],{},"\n像是手部的控制就能被拆分成精細度 協調能力 靈巧度 手指速度等等",[83,18526],{},"\n然後 每種動作能力都是相互獨立的",[83,18529],{},"\n最後 任務是由大量的能力組合在一起的",[12,18532,18533,18534,18536,18537,18539],{},"接著來講注意力 他有以下特點",[83,18535],{},"\n串聯 容量有限 費力的 ",[83,18538],{},"\n還有限制同時進行多種任務的能力 會干援訊息處理的反應選擇(怎麼動)跟反應程式期(下命令)",[12,18541,18542,18543,18545,18546,18548,18549,18551,18552,18554,18555,18557],{},"而下命令也分了五種類型",[83,18544],{},"\n第一種 集中注意力 比較偏向反應一類",[83,18547],{},"\n第二種 持續注意力 在警醒度上比較有關聯",[83,18550],{},"\n第三種 選擇注意力 就是能不能不被某些事干擾的能力",[83,18553],{},"\n第四種 交替注意力 就是將原本的注意力轉移到新的事情上 也比較屬於反應一類",[83,18556],{},"\n第五種 分隔注意力 就是同時處理幾件不同範疇的能力 類似邊開車邊聽電話",[12,18559,18560],{},"而注意力有四種理論模型",[12,18562,18563,18564,18566],{},"第一種 濾管理論 他的理論是人的注意力有限的 像東西穿過瓶口",[83,18565],{},"\n所以也須要選擇甚麼東西進去(選擇注意力)",[12,18568,18569],{},[979,18570],{"alt":1236,"src":18571},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774282019738-Screenshot_2026-03-24_000646.png",[12,18573,18574,18575,18577,18578,18580],{},"第二種 注意力容量彈性論 他認為注意力不是固定容量",[83,18576],{},"\n而是會根據任務的難度 增加容量 以應付",[83,18579],{},"\n但假如當任務太難 那麼會導致過載 表現變差",[12,18582,18583,18584,18586,18587,18589],{},"第三種 多階段注意理論",[83,18585],{},"\n他認為假如是兩種不同範疇任務上 例如邊織毛衣邊說話",[83,18588],{},"\n抑或者在兩種不同階段的認為上 例如看著琴譜彈鋼琴",[12,18591,18592,18593,18595],{},"而行動選擇論 他認為 注意力的分配 是我個人想優先選擇做哪些任務先",[83,18594],{},"\n所以注意力分配看的是結果而不是原因",[12,18597,18598],{},"而在注意力上還有這些現象可以看到這些",[12,18600,18601],{},"像下圖 比較反直覺(非認明刺激)可直接理解 這個叫Stroop effect",[12,18603,18604],{},[979,18605],{"alt":1236,"src":18606},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774282805876-Screenshot_2026-03-24_001953.png",[12,18608,18609,18610,18612],{},"第二個 雞尾酒現象 就像是你在跟別人專心聊天時 ",[83,18611],{},"\n即時背景有三到四個人聊天 你也聽不出來背景的人說甚麼(解釋了選擇注意力)",[12,18614,18615],{},"第三個 訊息越有意義 注意力就越集中(Von restorff effect)",[12,18617,18618,18619,18621,18622,18624,18625,18627,18628,18630,18631,18633],{},"接著講第三個特點 警醒程度跟焦慮",[83,18620],{},"\n警醒程度是偏向生理上的(或多或少會有指標參數) 簡單來說是我們有多活躍",[83,18623],{},"\n然後是焦慮 他是偏向心因性 那焦慮還分成兩種",[83,18626],{},"\n一種是天生的(特質焦慮)",[83,18629],{},"\n一種是因為某些事導致的(情境焦慮)",[83,18632],{},"\n而研究中表示 覺醒程度過高也不好 有可能會是極端焦慮 過低也不好(嗜睡)",[12,18635,18636],{},"最後是動機 就是讓他做的任務的驅動力",[12,18638,18639,18640,18642,18643,18645,18646,18648,18649,18651,18652,18654],{},"動機有以下理論",[83,18641],{},"\n第一種 因為需要 所以想要",[83,18644],{},"\n第二種 想活下去 那就去工作(被接納 認可) 那工作需要知識(學習) (Tolman三階層需要)",[83,18647],{},"\n第三種 為了爽跟避免痛苦是最大動機(享樂理論)",[83,18650],{},"\n第四種 人類有與環境互動的最基本需求(容量取決理論)",[83,18653],{},"\n第五點 人就是為了獲得成就感跟避免失誤(成就需求理論)",[12,18656,18657,18658,18660,18661,18663,18664,18666,18667,18669,18670,18672,18673,18675,18676,18678,18679,18681],{},"那增加動機有這些方法",[83,18659],{},"\n本身就有趣",[83,18662],{},"\n社會的期許(被壓力)",[83,18665],{},"\n鼓勵性質給分",[83,18668],{},"\n給錢獎勵",[83,18671],{},"\n表現的重要性",[83,18674],{},"\n相互競爭的社會動機",[83,18677],{},"\n進步本身有獎賞作用",[83,18680],{},"\n退步會有罰",[12,18683,18684,18685,18687,18688,18690,18691,18693,18694,18696,18697,18699],{},"而臨床上增加動機的方法有",[83,18686],{},"\n注意病人的警醒度適中",[83,18689],{},"\n配合疲勞調整",[83,18692],{},"\n提起 可能失敗 引起動機",[83,18695],{},"\n給口頭或實際的獎懲",[83,18698],{},"\n告知任務有何實際幫助",[12,18701,18702],{},"晚安各位孩子 該睡了",{"title":169,"searchDepth":170,"depth":170,"links":18704},[],"恭喜同學結束了 小考加油","\u002Fimages\u002Fuploads\u002F1774274522604-10576526i.jpg",{},"\u002Fblog\u002F動作學習（十五）影響表現的因素",{"title":18471,"description":18705},{"loc":18708},"blog\u002F動作學習（十五）影響表現的因素","ZHGAd7STb4uXj0Fo8Z0JKU9fAV629Yp_hClf0TYFLPU",{"id":18714,"title":18715,"author":7,"body":18716,"date":17479,"description":18961,"draft":174,"edited_at":17301,"extension":175,"featured_image":18962,"meta":18963,"navigation":178,"path":18964,"pinned":174,"seo":18965,"series":181,"seriesOrder":181,"sitemap":18966,"stem":18967,"tags":181,"__hash__":18968},"blog\u002Fblog\u002F動作學習（十四）記憶.md","動作學習（十六）記憶",{"type":9,"value":18717,"toc":18957},[18718,18721,18739,18751,18756,18777,18782,18804,18813,18844,18852,18857,18867,18882,18888,18906,18918,18927,18951],[12,18719,18720],{},"加油加油一起加油",[12,18722,18723,18724,18726,18727,18729,18730,18732,18733,18735,18736,18738],{},"這下我們來探討一下記憶",[83,18725],{},"\n先來講記憶的種類",[83,18728],{},"\n分成了斜述性(外顯性)記憶 即可以說出來 ",[83,18731],{},"\n又可以分成了情節記憶(自傳式) 跟語意知識(一般性知識)",[83,18734],{},"\n還有程式性(內隱性)記憶 即技巧",[83,18737],{},"\n在腦子裡知道怎麼去做的記憶",[12,18740,18741,18742,18744,18745,18747,18748,18750],{},"那記憶以時間段又分成了三種",[83,18743],{},"\n立刻記憶 又稱感觀記憶 以秒為單位",[83,18746],{},"\n短期記憶 又稱工作記憶 以分鐘到幾天為單位 ",[83,18749],{},"\n長期記憶 以日~年為單位 經定型的過程 在神經網絡上會有結構的改變",[12,18752,18753],{},[979,18754],{"alt":1236,"src":18755},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774268317554-Screenshot_2026-03-23_201822.png",[12,18757,18758,18759,18761,18762,18764,18765,18767,18768,18770,18771,18773,18774,18776],{},"而記憶會經歷這三種歷程",[83,18760],{},"\n首先是登錄 立刻記憶被轉為短期記憶",[83,18763],{},"\n然後是留存 是發生在記短期記憶的過程",[83,18766],{},"\n一般會進行歸檔 覆誦 譯碼 和決定等處理 保存下來",[83,18769],{},"\n最後是提取 是指經過登錄 譯碼過後的訊息 會被與長期記憶做比較的過程",[83,18772],{},"\n包括回憶 起來某些事(主動)",[83,18775],{},"\n和再認 當時情重現時 會被想起來(被動)",[12,18778,18779],{},[979,18780],{"alt":1236,"src":18781},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774268686265-Screenshot_2026-03-23_202432.png",[12,18783,18784,18785,18787,18788,18792,18793,18795,18796,18800,18801,18803],{},"接下來講記憶元素理論",[83,18786],{},"\n它提到 大腦會依據",[254,18789,18791],{"className":18790},[562],"重要性","來選擇 像是考試重點 你就記得很清楚",[83,18794],{},"\n記憶不是全有全無 當某個意識積累到到了",[254,18797,18799],{"className":18798},[562],"最低門檻","就會被想起來",[83,18802],{},"\n而競爭機制就是說 意識A比意識B要深刻 那在想起來的速度肯定是A先出來",[12,18805,18806,18807,18809,18810,18812],{},"那失憶的部份可以用時間來區分兩種類別",[83,18808],{},"\n一種是記不住新的東西 叫前向性失憶",[83,18811],{},"\n一種是記不起來以前的東西 叫回溯性記憶",[12,18814,18815,18816,18818,18819,18821,18822,18824,18825,18827,18828,18830,18831,18833,18834,18838,18839,18843],{},"而遺忘有分成這幾個理論",[83,18817],{},"\n第一種是記憶轉變論 因為長期沒用 導致變形 再忘掉(哎喲真的太久了我都給忘記具體東西了)",[83,18820],{},"\n第二種是干擾理論 還分成了兩種時間性",[83,18823],{},"\n一種是舊的東西干擾到新的東西 叫前向干擾",[83,18826],{},"\n另一種是新的東西干擾到舊的東西 叫回溯干擾",[83,18829],{},"\n最後一種是永久記憶及附屬理論",[83,18832],{},"\n他提出記憶形成就會是",[254,18835,18837],{"className":18836},[10233],"永久"," 只是變得",[254,18840,18842],{"className":18841},[10233],"次要","才不容易被想起來",[781,18845,18847,18848],{"id":18846},"注意-右上角的是要改成阿茲海默症","注意 右上角的是要改成",[254,18849,18851],{"className":18850},[562],"阿茲海默症",[12,18853,18854],{},[979,18855],{"alt":1236,"src":18856},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774269914781-Screenshot_2026-03-23_204430.png",[12,18858,18859,18860,18862,18863],{},"在記憶網絡裡頭",[83,18861],{},"\n記憶不只存在於單一區域 而是",[254,18864,18866],{"className":18865},[562],"遍佈整個大腦",[12,18868,18869,18870,18872,18873,18875,18876,18878,18879,18881],{},"接著來講兩種記憶類型會在哪裡建立",[83,18871],{},"\n首先來講敍述性記憶 那新的敍述性記憶會產生至海馬迴",[83,18874],{},"\n而像是辨識人臉 事件 空間等敍述性記憶 高度依賴內側顳葉(海馬迴與杏仁體)",[83,18877],{},"\n接著講程序性記憶 因為他偏向技巧 所以是發生在大腦皮層跟基底核",[83,18880],{},"\n而傳統制約反應就與小腦有關",[12,18883,18884,18885,18887],{},"記憶從短期記憶變成長期記憶也需要用到海馬回",[83,18886],{},"\n而這個過程需要時間 被稱作定型或記憶固化",[12,18889,18890,18891,18893,18894,18896,18897,18899,18900,18902,18903,18905],{},"而促進學習有這幾種",[83,18892],{},"\n第一是適合在腦傷病人上的",[83,18895],{},"\n主要看他左腦還是右腦受傷",[83,18898],{},"\n左腦 是邏輯腦 但是受傷了 所以要用右腦來訓練 ",[83,18901],{},"\n而右腦是圖像腦 抽象腦 可以多給他視覺輸入 或者心像練習",[83,18904],{},"\n反過來是右腦受傷了的話 那就用節拍 口訣一類的去練 用語言邏輯補回來",[12,18907,18908,18909,18911,18912,18914,18915,18917],{},"第二 鼓勵過度學習 即使學會了也要再額外練",[83,18910],{},"\n第三 事件分類記憶",[83,18913],{},"\n第四 利用近期-初始效應 因為干擾少 便方便記",[83,18916],{},"\n第五 回饋給予原則",[12,18919,18920,18921,18923,18924,18926],{},"展開一下來講近期-初始效應",[83,18922],{},"\n初始效應可以利用在剛開始學 干擾不多的情況下 這樣更容易形成記憶",[83,18925],{},"\n而近期效應 就是說剛做完這件事 我過了半會還記得",[12,18928,18929,18930,18932,18933,18935,18936,18938,18939,18941,18942,18944,18945,18947,18948,18950],{},"目前有七種學習方式來增強記憶形成",[83,18931],{},"\n無錯練習",[83,18934],{},"\n比喻練習",[83,18937],{},"\n雙項式練習",[83,18940],{},"\n發現練習",[83,18943],{},"\n觀察練習",[83,18946],{},"\n試行錯誤練習",[83,18949],{},"\n心像練習",[12,18952,18953,18954,18956],{},"那外顯性可以促記憶的 可以試講把東西講出來 自己把東西講細節 順序都講出來",[83,18955],{},"\n那內隱式可以用 無錯練習的方式去練 因為這東西基本上是技巧 那用無錯練習可以把它練更優",{"title":169,"searchDepth":170,"depth":170,"links":18958},[18959],{"id":18846,"depth":7336,"text":18960},"注意 右上角的是要改成阿茲海默症","還有不到五十頁 同學加油","\u002Fimages\u002Fuploads\u002F1774272957036-10477521i.jpg",{},"\u002Fblog\u002F動作學習（十四）記憶",{"title":18715,"description":18961},{"loc":18964},"blog\u002F動作學習（十四）記憶","LWBQGomO5XLKaAD02oFnhvlE1f5IIEqBH-TgfdM7kj4",{"id":18970,"title":18971,"author":7,"body":18972,"date":19144,"description":19145,"draft":174,"edited_at":19144,"extension":175,"featured_image":19146,"meta":19147,"navigation":178,"path":19148,"pinned":174,"seo":19149,"series":181,"seriesOrder":181,"sitemap":19150,"stem":19151,"tags":181,"__hash__":19152},"blog\u002Fblog\u002F動作學習（七）練習方式-1.md","動作學習（七）練習方式-1",{"type":9,"value":18973,"toc":19142},[18974,18977,18980,19007,19025,19040,19055,19058,19064,19076,19085,19094,19106,19115,19121],[12,18975,18976],{},"好好好 終於要輪到怎麼學習了",[12,18978,18979],{},"我先在這一篇講 集中分散 固定變異 還隨機段落",[12,18981,18982,18983,18985,18986,18988,18989,18991,18992,18994,18995,18997,18998,19000,19001,19003,19004,19006],{},"先來比較集中練習跟分散練習",[83,18984],{},"\n集中練習是練習時間＞休息時間 而分散練是休息時間＞練習時間",[83,18987],{},"\n集中練習比較適用在 ",[83,18990],{},"\n簡單的內容",[83,18993],{},"\n快速 離散的動作 意思是 動作開始跟結束有明顯段落 像投籃 打哥爾夫球",[83,18996],{},"\n那分散練習比較適用在",[83,18999],{},"\n危險的任務(例如需要高度集中的任務)",[83,19002],{},"\n複雜的內容(訊息量過多)",[83,19005],{},"\n長時間 連續性的動作(容易疲勞) 例如游泳 跑步等",[12,19008,19009,19010,19012,19013,19015,19016,19018,19019,19021,19022,19024],{},"而第二類 固定練習跟變異練習做比較",[83,19011],{},"\n固定練習就是指參數全部一致的情況下做重複的訓練",[83,19014],{},"\n而變異練習則是指在一種或以上的參數不同情況下做訓練",[83,19017],{},"\n拿籃球做例子 你當然可以一個一直站在三分線上投籃",[83,19020],{},"\n但實際出來的效果可能不如 我在跟別人實際比賽練出來的本領強",[83,19023],{},"\n而變異練習還有一個特點 就是可以訓練概化能力(即之前提到的舉一反三能力)",[12,19026,19027,19028,19030,19031,19033,19034,19036,19037,19039],{},"第三類來到了 段落練習跟隨機練習",[83,19029],{},"\n段落練習在練習上沒有變化 例如  AA BB CC 這樣練",[83,19032],{},"\n相對單調且簡單 適合新人 但效果沒有隨機練習好",[83,19035],{},"\n而隨機練習就是混著來 ACB BAC ABC CBA  這樣練",[83,19038],{},"\n組合複雜且隨機 相對進階 且時間會相較段落練習高 但在運用上會更優",[12,19041,19042,19043,19045,19046,19048,19049,19051,19052,19054],{},"在情境干擾(CI)上也能解釋段落練習跟隨機練習的差異",[83,19044],{},"\n那low CI代表基本上沒有變化 基本上可以重複的做同一件事(計算low)",[83,19047],{},"\n(只有一種任務重複實行)",[83,19050],{},"\n而higi CI代表著一直變 開始需要隨機應變了(計算up)",[83,19053],{},"\n(即多種任務需要交替進行)",[12,19056,19057],{},"而這裡有五種假說分別說出為甚麼隨機練習比段落練習好",[12,19059,19060,19061,19063],{},"第一種處理階層假說 他意思是段落思考不需要動腦想 只需要從短期記憶裡翻記錄就好",[83,19062],{},"\n而隨機練習因為所有預設都不一樣 所以不用直接沿用短期記憶 得自己動腦得出結果",[12,19065,19066,19067,19069,19070,19072,19073,19075],{},"第二種遺忘學說 他們認為學習就是一直在做運算才能變好",[83,19068],{},"\n而隨機練習的過程 每一次做事都不一樣 ",[83,19071],{},"\n做新的事就會忘記舊的事 且重新運算 如此類推 所以學得更好",[83,19074],{},"\n段落練習則相反 每次做得事都一樣 沒有重新運算 所以學不好",[12,19077,19078,19079,19081,19082,19084],{},"第三種基模假說 就是認為任務像公式",[83,19080],{},"\n段落練習只是用一種公式一直練 例如1+1不會解微積分",[83,19083],{},"\n而隨機練習則代表一直變換公式 這個公式裡面的參數會不斷被調整 這樣你會學得更多",[12,19086,19087,19088,19090,19091,19093],{},"第四種詳述假說 他說大腦一定要多分析才能有效學習",[83,19089],{},"\n而段落練習只能分析一件事 重複的",[83,19092],{},"\n而隨機練習是同時分析不同的單項任務 而不同的任務間還可以做歸納 比較 更有利學習",[12,19095,19096,19097,19099,19100,19102,19103,19105],{},"第五種回溯抑制假說 他的意思是後面學的會抑制(稀釋掉)前面學到的東西",[83,19098],{},"\n段落練習為例 AAABBBCCC 而到了C之後就開始抑制A的練習",[83,19101],{},"\n但隨機練習因為隨機不重複的運算 不太容易被相互抑制導致忘掉",[83,19104],{},"\n而他這個假說可以解釋為甚麼在保留測驗過程中段落練習出來的分數較差",[12,19107,19108,19109,19111,19112,19114],{},"但隨機學很慢很痛苦 段落太簡單又學不到甚麼 在介於兩者之間出現了序列訓練",[83,19110],{},"\n結合了可預測性跟不重複性 即 ABC ABC ABC ABC",[83,19113],{},"\n(有研究指出序列練習跟隨機練習在得分上幾乎相同)",[12,19116,19117,19118,19120],{},"他再指出 練習表現好 不代表 你真的學得好",[83,19119],{},"\n段落練習學得快 精準度高 但在隨後的保留測驗中其實不如隨機測驗",[12,19122,19123,19124,19126,19127,19129,19130,19132,19133,19135,19136,19138,19139,19141],{},"最後提到隨機練習的具以下特性",[83,19125],{},"\n第一 隨機練具備更強的適應性",[83,19128],{},"\n第二 困難的任務用隨機練效果更好",[83,19131],{},"\n簡單的任務用隨機練沒有明顯優勢",[83,19134],{},"\n第三 因應技巧程度定制",[83,19137],{},"\n假如是技巧不多的人 可以利用段落跟序列練習",[83,19140],{},"\n而當技巧十分高 則可以利用隨機練習",{"title":169,"searchDepth":170,"depth":170,"links":19143},[],"2026-03-22","集中分散 固定變異 隨機段落","\u002Fimages\u002Fuploads\u002F1774164465962-IMG_20200617_181520.jpg",{},"\u002Fblog\u002F動作學習（七）練習方式-1",{"title":18971,"description":19145},{"loc":19148},"blog\u002F動作學習（七）練習方式-1","OfRGjr037349Irr2cLrPYSaV1-jG3JRJnXLuGwkMdO4",{"id":19154,"title":19155,"author":7,"body":19156,"date":19144,"description":19302,"draft":174,"edited_at":19144,"extension":175,"featured_image":19303,"meta":19304,"navigation":178,"path":19305,"pinned":174,"seo":19306,"series":181,"seriesOrder":181,"sitemap":19307,"stem":19308,"tags":181,"__hash__":19309},"blog\u002Fblog\u002F動作學習（三）Measurement-of-learning.md","動作學習（三）Measurement of learning",{"type":9,"value":19157,"toc":19300},[19158,19173,19183,19201,19204,19213,19219,19225,19238,19253,19271,19280],[12,19159,19160,19161,19163,19164,19166,19167,19169,19170,19172],{},"我們的學習成果 可以被兩種表現曲線所推估",[83,19162],{},"\n一種是成就曲線 (Achievement Curve)",[83,19165],{},"\n簡單來說就是得分計量 你學了一天的得分 會跟你學了十天的得分不一樣",[83,19168],{},"\n而另一種是錯誤曲線 (Error Curve)",[83,19171],{},"\n以剛剛的例子來看 你第一天學錯的多 但你學了十天錯得會比第一天少",[12,19174,19175,19176,19180,19182],{},"但這裡有個大誤區 ",[254,19177,19179],{"className":19178},[562],"表現曲線 不代表 學習曲線",[83,19181],{},"\n因為學習沒有辦法被直接測量 所以只能靠對錯的程度來猜測 進步了多少",[12,19184,19185,19186,19188,19189,19191,19192,19194,19195,19197,19198,19200],{},"而在測量學習的過程中有兩個容易失真的情況",[83,19187],{},"\n一個是天花板效應 (Ceiling effects)",[83,19190],{},"\n意思就是 今天你的能力明顯比測驗內容還要高出好多 你也拿到了滿分 但不代表你進步了",[83,19193],{},"\n另一個是地板效應 (Floor effects)",[83,19196],{},"\n就是剛剛的反過來 測驗難度明顯比你的能力還要高 ",[83,19199],{},"\n那你會拿到很低分 也測不出進步 但不代表你實際沒有任何進步",[12,19202,19203],{},"雖然學習沒有辦法直接被測量 但還是有判斷的標準",[12,19205,19206,19207,19209,19210,19212],{},"第一是留存現象 像第一節課講到的相當永久的特性",[83,19208],{},"\n這代表著假如有學到點甚麼 就一定會稍微存起來 ",[83,19211],{},"\n可以隔一天再讓你做測驗來判斷有沒有學起來\u002F進步",[12,19214,19215,19216,19218],{},"第二是概化現象 相當於舉一反三",[83,19217],{},"\n簡單來說今天我學到了扔棒球 那你可能也會用差不多的姿勢來扔其他球類例如壘球",[12,19220,19221,19222,19224],{},"第三是改變了情境還能做出差不多表現動作的能力",[83,19223],{},"\n例如我在室內學會了走路 來到戶外人行道 我也能走",[12,19226,19227,19228,19230,19231,19235,19237],{},"還有一點可以用來測量的是 轉移(Transfer)",[83,19229],{},"\n意思是今天學到的一樣東西 或多或少會對另外一些技巧有 ",[254,19232,19234],{"className":19233},[562],"好 或者 不好 的影響",[83,19236],{},"\n而兩樣東西越像 關聯越多 轉移就更多",[12,19239,19240,19241,19243,19244,19246,19247,19249,19250,19252],{},"先來介紹第一種轉移 正轉移跟負轉移",[83,19242],{},"\n正轉移意思 學到了A 在做B的時候多少有些幫助 ",[83,19245],{},"\n例如 會騎腳踏車的人 更容易學會騎機車",[83,19248],{},"\n而負轉移就反過來 例如我本身就會打網球 但學了打羽球後 我打網球的實力下降",[83,19251],{},"\n因為手感不一樣",[12,19254,19255,19256,19258,19259,19261,19262,19264,19265,19267,19268,19270],{},"而第二種轉移 近轉移跟遠轉移",[83,19257],{},"\n先來講近轉移 意思是訓練內容跟實際的情況相差不大",[83,19260],{},"\n在室內訓練他 他學會了 把他扔到平原上 他也能做出差不多表現",[83,19263],{},"\n而另一種遠轉移 則是說雖然練的跟實際情況看似很大 但本質上是雷同的",[83,19266],{},"\n例如 今天教他站起身的同時教他重心轉移的技巧",[83,19269],{},"\n那麼他今天向前彎伸手抓取東西時的重心轉移 也會有所提升",[12,19272,19273,19274,19276,19277,19279],{},"而第三種轉移 對測轉移(交叉轉移)",[83,19275],{},"\n意思是你右手學會了某個字 左手也能寫出同一個字",[83,19278],{},"\n就像之前講通用動作程式時提到的一樣 不同的器官能夠做出同樣的動作 差別在完美度",[12,19281,19282,19283,19285,19286,19290,19292,19293,19295,19296],{},"最後用來測量學習表現的指標 背景轉換阻⼒(resistance to contextual change)",[83,19284],{},"\n我把他理解成 換了環境 動作表現有沒有大的改變 用來測量",[254,19287,19289],{"className":19288},[562],"下限值",[83,19291],{},"\n因為學到的東西不能只對單一環境有表現 ",[83,19294],{},"\n所以要靠變換不同的變數來實際驗證 靠的就是",[254,19297,19299],{"className":19298},[562],"適應性跟轉移",{"title":169,"searchDepth":170,"depth":170,"links":19301},[],"在嘗試成為知識焚化爐的路上","\u002Fimages\u002Fuploads\u002F1774146343774-20201202_121856.jpg",{},"\u002Fblog\u002F動作學習（三）Measurement-of-learning",{"title":19155,"description":19302},{"loc":19305},"blog\u002F動作學習（三）Measurement-of-learning","D2QibQoGGvqaZDkyDOTMILw5xdYtOJMbrPP-drXb-KE",{"id":19311,"title":19312,"author":7,"body":19313,"date":19144,"description":19433,"draft":174,"edited_at":17479,"extension":175,"featured_image":19434,"meta":19435,"navigation":178,"path":19436,"pinned":174,"seo":19437,"series":181,"seriesOrder":181,"sitemap":19438,"stem":19439,"tags":181,"__hash__":19440},"blog\u002Fblog\u002F動作學習（九）回饋-1.md","動作學習（九）回饋-1",{"type":9,"value":19314,"toc":19431},[19315,19318,19321,19326,19329,19338,19347,19355,19364,19370,19388,19404,19413],[12,19316,19317],{},"讓我盡量有三篇內容解決你吧 哈哈哈哈哈哈",[12,19319,19320],{},"感覺的訊息如下圖",[12,19322,19323],{},[979,19324],{"alt":1236,"src":19325},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774168154011-Screenshot_2026-03-22_162846.png",[12,19327,19328],{},"先來講動作前給的感覺訊息 包括了口語教導跟口語提示",[12,19330,19331,19332,19334,19335,19337],{},"口語教導(Verbal instruction)是動作出來前給予的",[83,19333],{},"\n教怎麼做這個動作(描述特性 順序 目標) ",[83,19336],{},"\n但不要描述具體至參數等 會使動作變得遲緩僵硬",[12,19339,19340,19341,19343,19344,19346],{},"口語提示 (Verbal Cue)是在動作過程中給予的",[83,19342],{},"\n只需要短又精準的語句引導即可(以讓整體動作變得更省力\u002F效率為主)",[83,19345],{},"\n假如像最常聽到的挺胸收腹",[12,19348,19349,19350,19354],{},"假如在",[254,19351,19353],{"className":19352},[562],"探索式情境學習","中 不給指導會比起給予指導來得更要好",[12,19356,19357,19358,19360,19361,19363],{},"而在給口頭語句時也更偏向讓一些情境給他 而不是直接講怎麼動",[83,19359],{},"\n例如說 大腿抬起起來幾度 這樣病人可能會要想一下",[83,19362],{},"\n但假如直接講 用膝蓋往上頂 他會更加快的出來",[12,19365,19366,19367,19369],{},"而且人的注意力是有限的",[83,19368],{},"\n在講的時候 講一兩個簡單直接的指令 會比你直接講一大串文字教他怎麼動會更好",[12,19371,19372,19373,19375,19376,19378,19379,19381,19382,19384],{},"在學習剛開始 先看到榜樣的動作會比聽別人口述標準還要有效",[83,19374],{},"\n口述是從語言轉化成動作 會相較於看別人的視覺轉化成動作還要來得慢",[83,19377],{},"\n而且讓他先看一套榜樣動作 可以在腦內先有個大概",[83,19380],{},"\n這樣即使手還沒有開始動之前 腦內也可以先進行模擬",[83,19383],{},[254,19385,19387],{"className":19386},[562],"可以不用做最完美的動作來做榜樣",[12,19389,19390,19391,19393,19394,19396,19397,19399,19400],{},"而有一位學者做了研究指出 新手之間互相觀察彼此動作會比新手看專家還要有效",[83,19392],{},"\n因為在AB都新手的情況下 B起拿對照表看著A做得如何",[83,19395],{},"\n這樣A會被B嚴格觀察並且記錄下來(B也會相對重視起A會錯的那些)",[83,19398],{},"\n這樣交互觀察 ",[254,19401,19403],{"className":19402},[562],"能有效促進主動解決問題的決策過程",[12,19405,19406,19407,19409,19410,19412],{},"說完了視覺回饋 接下來講聽覺回饋",[83,19408],{},"\n聽覺回饋有一個特點 就是他很能抓時間 ",[83,19411],{},"\n假如那個動作對時間精準有要求 那就盡量用聽覺回饋",[12,19414,19415,19416,19418,19419,19421,19422,19424,19425,19427,19428,19430],{},"而聽覺回饋有兩種",[83,19417],{},"\n第一種是音樂動作回饋(MMF)",[83,19420],{},"\n意思是可以將音樂與動作組合在一起 ",[83,19423],{},"\n例如跳舞 聽著歌來跳會比不聽歌跳來得要有趣跟投入(情緒上)",[83,19426],{},"\n第二種是規律聽覺刺激(RAS)",[83,19429],{},"\n即聽著節拍讓動作組合在一起",{"title":169,"searchDepth":170,"depth":170,"links":19432},[],"口頭+視覺回饋","\u002Fimages\u002Fuploads\u002F1774175583479-IMG_20200617_181537.jpg",{},"\u002Fblog\u002F動作學習（九）回饋-1",{"title":19312,"description":19433},{"loc":19436},"blog\u002F動作學習（九）回饋-1","BhvlfI_C_36MJiWnFUPMTi1aDUwClNVcN0ymyPEcnIg",{"id":19442,"title":19443,"author":7,"body":19444,"date":19144,"description":19595,"draft":174,"edited_at":17301,"extension":175,"featured_image":19596,"meta":19597,"navigation":178,"path":19598,"pinned":174,"seo":19599,"series":181,"seriesOrder":181,"sitemap":19600,"stem":19601,"tags":181,"__hash__":19602},"blog\u002Fblog\u002F動作學習（二）form-of-learning.md","動作學習（二）forms of learning",{"type":9,"value":19445,"toc":19593},[19446,19452,19466,19475,19487,19493,19499,19504,19510,19525,19530,19536,19557,19567],[12,19447,19448,19449,19451],{},"現在來講動作學習的形式",[83,19450],{},"\n首先來介紹關聯性跟非關聯性",[12,19453,19454,19455,19457,19458,19460,19462,19463,19465],{},"非關聯性 意思是 只針對單一刺激輸入的部份 從而對那個刺激的接收強度發生變化",[83,19456],{},"\n因為他只針對單一刺激輸入 假如換成別的刺激輸入就要重新適應(無法舉一反三)",[83,19459],{},[83,19461],{},"\n可以讓刺激輸入分辨有沒有害",[83,19464],{},"\n使神經系統對這刺激做兩種演化 一種是習慣化 一種是敏感化",[12,19467,19468,19469,19471,19472,19474],{},"先來講習慣化 就是習慣了 讓那個刺激輸入對我而言變得平淡(被人打多了習慣痛了的意思)",[83,19470],{},"\n在臨床應用上 前庭病變的病人會因為頭部轉動而發生不適 ",[83,19473],{},"\n而我們可以多給他刺激到會產生不適的地方 讓他習慣 讓不適感降低(脫敏訓練)",[12,19476,19477,19478,19480,19481,19483,19484,19486],{},"而敏感化 就是更加有感覺 對我而言刺激輸入比以往來得更明顯(剛剛出完車禍 後面會更加注意駕駛)",[83,19479],{},"\n在臨床應用上 跌倒對PT來說是大忌 我們要訓練讓病人不容易跌倒",[83,19482],{},"\n在訓練的過程中加入一些模仿跌倒的環節 讓他的刺激輸入更加敏感 ",[83,19485],{},"\n以求日後他能知道跌倒的前兆 減少跌倒的風險",[12,19488,19489,19490,19492],{},"接著來到關聯性 意思是看到前兆就知道肯定後發生甚麼(因果關係)(舉一反三)",[83,19491],{},"\n這個也有兩種演化 一種是傳統制約反應 一種是操作制約反應",[12,19494,19495,19496,19498],{},"傳統制約反應 就是將刺激輸入跟結果緊緊捆綁(有前兆就有結果)(A是刺激輸入)",[83,19497],{},"\n最典型的例子 有A+B就有得吃 假如只有A 那他也以為有得吃",[12,19500,19501],{},[979,19502],{"alt":1236,"src":19503},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774089362522-Screenshot_2026-03-21_183544.png",[12,19505,19506,19507,19509],{},"在臨床應用上 可以給病人先對刺激輸入與結果做連結",[83,19508],{},"\n例如 口頭提示(起來)+操作(拉他起來)=引導他站起來 假若沒有操作介入他也能站起來",[12,19511,19512,19513,19515,19516,19518,19519,19521,19522,19524],{},"那麼操作制約反應 就是做A才會有B B才是刺激輸入 ",[83,19514],{},"\n這裡有兩種刺激輸入可以做改變 一個是正向 一個是負面",[83,19517],{},"\n例子 開車沒扣安全帶 會有警示燈 ",[83,19520],{},"\n在臨床應用上 可以利用生物回饋(Biofeedback)",[83,19523],{},"\n這裡我直接偷懶引用gemini了",[12,19526,19527],{},[979,19528],{"alt":1236,"src":19529},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774091802836-Screenshot_2026-03-21_191304.png",[12,19531,19532,19533,19535],{},"接下來講第二類學習的形式",[83,19534],{},"\n敍述性跟非敍述性",[12,19537,19538,19539,19541,19542,19544,19545,19547,19548,19550,19551,19553,19554,19556],{},"先來講敍述性 又叫做外顯性的認知",[83,19540],{},"\n就像是你玩教別人玩遊戲 變強的竅門 可以被說出來的就是敍述性",[83,19543],{},"\n而敍述性也代表著需要專心 要意識參與",[83,19546],{},"\n也可以被描述 ",[83,19549],{},"\n可以因被別人重複描述而轉化成自己的程序性記憶",[83,19552],{},"\n但有些腦傷的病人可能在認知方面有缺失 所以沒有辦法利用這點",[83,19555],{},"\n而心像練習也算是一種敍述性",[12,19558,19559,19560,19562,19563],{},"而非敍述性 又叫做內隱性的認知",[83,19561],{},"\n就像是你不太可能教別人玩遊戲 把一些肌肉記憶 而不用",[254,19564,19566],{"className":19565},[562],"刻意回想",[12,19568,19569,19570,19575,19577,19578,19580,19581,19583,19584,19586,19587,19589,19590,19592],{},"而非敍述性有一個小分類叫做",[254,19571,19574],{"className":19572},[19573],"bg-green-4","程式學習",[83,19576],{},"\n意思就是一直練一直練練到會",[83,19579],{},"\n這點玩遊戲的同學就很有感受了 菜就多練 但這種沒辦法教給別人 ",[83,19582],{},"\n有這些特徵",[83,19585],{},"\n因重複學習而獲得行為表現的進步",[83,19588],{},"\n不需要經過思考就能做出來(像是所謂的肌肉記憶)",[83,19591],{},"\n在臨床上可以練像是轉移位的動作",{"title":169,"searchDepth":170,"depth":170,"links":19594},[],"絕讚啃書中","\u002Fimages\u002Fuploads\u002F1774142429929-20201202_121927.jpg",{},"\u002Fblog\u002F動作學習（二）form-of-learning",{"title":19443,"description":19595},{"loc":19598},"blog\u002F動作學習（二）form-of-learning","x2bFbTiOsnoUgBZITdniNxrY_PolASWVthT3sqOkDjs",{"id":19604,"title":19605,"author":7,"body":19606,"date":19144,"description":19752,"draft":174,"edited_at":17479,"extension":175,"featured_image":19753,"meta":19754,"navigation":178,"path":19755,"pinned":174,"seo":19756,"series":181,"seriesOrder":181,"sitemap":19757,"stem":19758,"tags":181,"__hash__":19759},"blog\u002Fblog\u002F動作學習（五）理論-2.md","動作學習（五）理論-2",{"type":9,"value":19607,"toc":19750},[19608,19611,19637,19655,19678,19683,19688,19690,19702,19720,19744],[12,19609,19610],{},"阿巴阿巴阿巴 我們繼續來講理論",[12,19612,19613,19614,19616,19617,19619,19620,19624,19625,19630,19631,19633,19634,19636],{},"現在我們來講基模理論",[83,19615],{},"\n他認為 學到的經驗 是概念 是規則 是關係 ",[83,19618],{},"\n而學習是具",[254,19621,19623],{"className":19622},[562],"開放鏈","性質(",[49,19626,19629],{"href":19627,"rel":19628},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E9%80%B2%E9%9A%8E%E6%8E%A7%E5%88%B6%E5%88%B6%E5%88%B6%E5%88%B6",[53],"引見此篇內的開放式回路",")(會自己修正)",[83,19632],{},"\n動作程式理面的東西是抽象的 不是模版 也並不唯一",[83,19635],{},"\n而我們學一個新的程式 學的不是細節 學的的本質",[12,19638,19639,19640,19642,19643,19645,19646,19648,19649,19651,19652,19654],{},"而基模包含以下四點內容 ",[83,19641],{},"\n起始狀態",[83,19644],{},"\n預期的動作結果",[83,19647],{},"\n動作變數",[83,19650],{},"\n感覺結果",[83,19653],{},"\n這四點組合在一起變成抽象的概念或者記憶",[12,19656,19657,19658,19660,19661,19663,19664,19668,19670,19671,19673,19674],{},"而這四種內容又會組合成兩種基模",[83,19659],{},"\n召還基模 即知道做一個動作需要甚麼參數",[83,19662],{},"\n構成召還基模的有 起始狀態 預期的動作結果 ",[254,19665,19667],{"className":19666},[7640],"動作變數",[83,19669],{},"\n再認基模 意思是還沒做出來之前就猜到了會有啥結果",[83,19672],{},"\n構成召還基模的則有 起始狀態 預期的動作結果 ",[254,19675,19677],{"className":19676},[562],"感覺結果",[12,19679,19680],{},[979,19681],{"alt":1236,"src":19682},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774152546064-Screenshot_2026-03-22_120449.png",[12,19684,19685],{},[979,19686],{"alt":1236,"src":19687},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774242658032-Screenshot_2026-03-23_131009.png",[83,19689],{},[12,19691,19692,19693,19695,19696,19698,19699,19701],{},"接下來講生態學習論",[83,19694],{},"\n提到 學習這個過程包含三點 練習 環境限制 為了完成任務而尋找最佳策略",[83,19697],{},"\n而在尋找最佳的過程中包含 感知線索(perceptual cues) 及 動作反應(motor response)",[83,19700],{},"\n當認知與動作結合的過程 是找出完成任務的最佳解",[12,19703,19704,19705,19707,19708,19710,19711,19713,19714,19716,19717,19719],{},"先來講感知線索他分成了三個要素",[83,19706],{},"\nPrescriptive role(處方的角色) 那我理解成理解題目並構思答案",[83,19709],{},"\n(understanding the goal of the task and the movements to be learned)",[83,19712],{},"\nFeedback role(回饋的角色) ",[83,19715],{},"\n在動作過程中(KP)和動作結果(KR) 都有回饋以修正",[83,19718],{},"\n組織的角色 他可以將認知跟動作組合在一起 而這個組合經過篩選 已是最佳解",[12,19721,19722,19723,19725,19726,19728,19729,19731,19732,10176,19736,10176,19740,909],{},"他還認為 學習的這個過程 不是重複單一學習一種技巧",[83,19724],{},"\n是在特定工作目標下 將感知跟動作結合在一起不斷修正優化 ",[83,19727],{},"\n而不是基模理論的增強動作的規則",[83,19730],{},"\n所以這個理論會更加注重在我們動作控制的前三堂講(",[49,19733,7465],{"href":19734,"rel":19735},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E6%8E%A7%E5%88%B6%E8%87%AA%E5%B7%B1-Be-water-my-friend",[53],[49,19737,7469],{"href":19738,"rel":19739},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E6%8E%A7%E5%88%B6%E8%87%AA%E5%B7%B1-Be-water-my-friend%EF%BC%88%E4%BA%8C%EF%BC%89",[53],[49,19741,7519],{"href":19742,"rel":19743},"https:\u002F\u002Fblog.chinono.dev\u002Fblog\u002F%E6%8E%A7%E5%88%B6%E8%87%AA%E5%B7%B1-Be-water-my-friend%EF%BC%88%E4%B8%89%EF%BC%89",[53],[12,19745,19746,19747,19749],{},"看下來 生態學習論一樣強調感覺刺激的回饋",[83,19748],{},"\n但他應該是更偏向主動對刺激的應對 而不是像之前提到的因應刺激輸入做改變",{"title":169,"searchDepth":170,"depth":170,"links":19751},[],"基模理論和生態學習論","\u002Fimages\u002Fuploads\u002F1774151870253-IMG_20200616_205821.jpg",{},"\u002Fblog\u002F動作學習（五）理論-2",{"title":19605,"description":19752},{"loc":19755},"blog\u002F動作學習（五）理論-2","27kBlBuSNfZg0TKmRj0UzSKFgOoc4JUZIIiNn5KPbjk",{"id":19761,"title":19762,"author":7,"body":19763,"date":19144,"description":19866,"draft":174,"edited_at":17301,"extension":175,"featured_image":19867,"meta":19868,"navigation":178,"path":19869,"pinned":174,"seo":19870,"series":181,"seriesOrder":181,"sitemap":19871,"stem":19872,"tags":181,"__hash__":19873},"blog\u002Fblog\u002F動作學習（八）練習方式-2.md","動作學習（八）練習方式-2",{"type":9,"value":19764,"toc":19864},[19765,19783,19792,19795,19804,19816,19819,19828,19834,19843,19846,19849,19855,19861],[12,19766,19767,19768,19770,19771,19773,19774,19776,19777,19779,19780,19782],{},"到了心象練習 在內心想 結合自己平時的經驗\u002F記憶 在腦海裡優化 這樣下一次做就會更好",[83,19769],{},"\n不管是正常人 還是病人(中風 SCI 帕金森氏症等)都能這樣重複在腦海裡練",[83,19772],{},"\n而這只是輔助 是互補 而不是替代 ",[83,19775],{},"\n他不能實際讓你動作一下子只腦海模擬那樣做完美 ",[83,19778],{},"\n但例如用的力度 肢體角度做優化 讓整套動作來得有效率 ",[83,19781],{},"\n(這是真的有用 因為我玩快打旋風之前腦海裡平時沒事做都在想怎麼搓招接招 實際玩下來是有用的)",[12,19784,19785,19786,19788,19789,19791],{},"最後到了全部練習跟部份練習",[83,19787],{},"\n全部練習意思是從頭學到尾 沒有停不會變 ",[83,19790],{},"\n部份練習也叫分解練習 就是把一段東西拆開了練",[12,19793,19794],{},"他有兩種情境讓我們區分怎麼用全部或者部份練習",[12,19796,19797,19798,19800,19801,19803],{},"首先是任務的本質 ",[83,19799],{},"\n假如整套任務的動作都是合在一起才能做到那就不要拆開 例如投籃",[83,19802],{},"\n但像是整套任務的動作可以分開互不干預那就可以拆開看 例如穿衣服+扣扭扣",[12,19805,19806,19807,19809,19810,19812,19813,19815],{},"其次是時間跟動作類型",[83,19808],{},"\n再拿投籃為例 舉手再到投出去不到1秒時間可以做完那就不要拆開來練 用全部練習",[83,19811],{},"\n抑或者像走路那樣 只練一隻腳伸直腳屈曲腳是沒意義 只能用全部練習",[83,19814],{},"\n而像是跳舞 由多個動作組合的 那就適合部份練習",[12,19817,19818],{},"而分解練習也分成三種形式",[12,19820,19821,19822,19824,19825,19827],{},"第一種單獨分解練習",[83,19823],{},"\n他的意思是將複雜的動作拆分成兩部份或以上單獨訓練 ",[83,19826],{},"\n例如剛學泳游的我們會用浮板代替手部划水 而腳在後面蹬腳踩水這樣",[12,19829,19830,19831,19833],{},"第二種漸進分解練習 由簡單的部份遞進 會比先從困難部份開始學好",[83,19832],{},"\n例如籃球運球上籃 從運球 變成運球+拿起籃球走兩步 再變成運球+拿起籃球走兩步+跳起來出手",[12,19835,19836,19837,19839,19840,19842],{},"第三種則是簡化分解練習 例如說讓籃球在指尖上轉很難 那我就先利用書本來轉 學習找中心點",[83,19838],{},"\n也可以放慢速度來練 例如像剛剛運球上籃為例 假如走兩步沒辦法快速走 那就從慢走兩步練",[83,19841],{},"\n在室內練習也相當於是戶外任務的簡化",[12,19844,19845],{},"最後轉到了轉移效果 把動作分解成零件來看 怎麼拆才合理",[12,19847,19848],{},"他用互動性來區分",[12,19850,19851,19852,19854],{},"假設前者零件跟後者零件要一起運作才是連貫的動作 那就代表他這互動性強",[83,19853],{},"\n例子有棒球 你可以純空揮 但對於你擊球效果來說肯定沒這麼有效 要把揮球+擊球才有用",[12,19856,19857,19858,19860],{},"而互動性弱 就代表零件之間拆開來也不唐突",[83,19859],{},"\n例如跳舞 我轉體後再跳躍 很明顯可以拆開來 先練轉體 再練跳躍",[12,19862,19863],{},"好耶 終於可以下一章了 還有150頁 加油加油",{"title":169,"searchDepth":170,"depth":170,"links":19865},[],"心像練習 全部部份","\u002Fimages\u002Fuploads\u002F1774167633805-IMG_20200617_182035.jpg",{},"\u002Fblog\u002F動作學習（八）練習方式-2",{"title":19762,"description":19866},{"loc":19869},"blog\u002F動作學習（八）練習方式-2","XxX7Tu1YkgrWuObT9mpo_PmoGqymRIXz97YYigdHCIU",{"id":19875,"title":19876,"author":7,"body":19877,"date":19144,"description":19946,"draft":174,"edited_at":19144,"extension":175,"featured_image":19947,"meta":19948,"navigation":178,"path":19949,"pinned":174,"seo":19950,"series":181,"seriesOrder":181,"sitemap":19951,"stem":19952,"tags":181,"__hash__":19953},"blog\u002Fblog\u002F動作學習（六）理論-3.md","動作學習（六）理論-3",{"type":9,"value":19878,"toc":19944},[19879,19882,19894,19897,19906,19912,19915,19920,19929,19941],[12,19880,19881],{},"阿巴阿巴 理論到頭了",[12,19883,19884,19885,19887,19888,19890,19891,19893],{},"現在來講 Bernstein 提出的動作學習三階段論",[83,19886],{},"\n他把動作學習的過程用身體自由度來解釋動作學習的進程",[83,19889],{},"\n他提出有三個過程",[83,19892],{},"\n凍結自由度 釋放與重組 善⽤機械特性",[12,19895,19896],{},"我們來滑雪做例子",[12,19898,19899,19900,19902,19903,19905],{},"先來講凍結自由度 意思是在學滑雪的開始 ",[83,19901],{},"\n我們會先學好站穩 再看能不能動起來 ",[83,19904],{},"\n這時候我們的關緊肯定是鎖最緊的",[12,19907,19908,19909,19911],{},"第二點 釋放與重組 這時候我們滑雪可以滑一段距離且不太會跌",[83,19910],{},"\n關節比起剛學要更輕鬆 開始有協調動作",[12,19913,19914],{},"第三點 善用機械特性 就是已經會了滑雪了 利用物理特性來滑得更好更快",[12,19916,19917],{},[979,19918],{"alt":1236,"src":19919},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774158176692-Screenshot_2026-03-22_134239.png",[12,19921,19922,19923,19925,19926,19928],{},"最後我們來講 訊息理論之最佳挑戰觀點",[83,19924],{},"\n他認為 學習過程伴隨訊息消化 假如訊息複雜或者大量 會影響消化",[83,19927],{},"\n而這個消化的能力是跟 我們的技巧跟任務的難度 掛勾",[12,19930,19931,19932,19934,19935,19937,19938,19940],{},"但他也同時說了訊息的內容決定了學習時長 假設如下",[83,19933],{},"\n沒有訊息就沒有辦法產生學習效應",[83,19936],{},"\n太難或太簡單會影響學習速度",[83,19939],{},"\n任何動作技巧學習都有相對應的最佳訊息量",[12,19942,19943],{},"理論 結束啦 啊嗚嗚嗚",{"title":169,"searchDepth":170,"depth":170,"links":19945},[],"Bernstein的動作學習三階段 及 訊息理論之最佳挑戰觀點","\u002Fimages\u002Fuploads\u002F1774159201152-IMG_20200616_205416.jpg",{},"\u002Fblog\u002F動作學習（六）理論-3",{"title":19876,"description":19946},{"loc":19949},"blog\u002F動作學習（六）理論-3","oZZbX4P3fzbqMrbpatOZ9oUcgNPO4Rh4tTEI0EIVTmQ",{"id":19955,"title":19956,"author":7,"body":19957,"date":19144,"description":20112,"draft":174,"edited_at":19144,"extension":175,"featured_image":20113,"meta":20114,"navigation":178,"path":20115,"pinned":174,"seo":20116,"series":181,"seriesOrder":181,"sitemap":20117,"stem":20118,"tags":181,"__hash__":20119},"blog\u002Fblog\u002F動作學習（四）理論.md","動作學習（四）理論",{"type":9,"value":19958,"toc":20110},[19959,19962,20010,20015,20020,20026,20041,20050,20061,20074,20091],[12,19960,19961],{},"好好好 終於要來講理論了",[12,19963,19964,19965,19967,19968,19970,19971,19973,19974,19976,19977,19979,19980,19982,19983,19987,19988,19992,19993,19995,19996,20000,20001,20003,20004,20009],{},"先來講 Three-stage model (動作分期說)",[83,19966],{},"\n這個理論動作的學習分成三個時期",[83,19969],{},"\n認知期 (此階段停留時間短) ",[83,19972],{},"\n連結期 (此階段停留時間中等)",[83,19975],{},"\n自動化期 (此階段因已學會所以停留最長)",[83,19978],{},"\n這邊直接上圖表並且講解",[83,19981],{},"\n我們可以看到 認知期 就是剛開始學習 這時候動作表現",[254,19984,19986],{"className":19985},[562],"最差"," 而且需要",[254,19989,19991],{"className":19990},[562],"高度注意力 無法分心"," 依賴回饋",[83,19994],{},"\n而到了連結期 算是對學到的動作理解了 開始",[254,19997,19999],{"className":19998},[7640],"精進的過程"," 錯誤比前者少 注意力也可以少一點 分心一點",[83,20002],{},"\n最後到了自動化期 這時候已經到達了",[254,20005,20008],{"className":20006},[20007],"bg-blue-3","專精"," 錯誤極少 也可以分心 例如聊天或者想其他事",[12,20011,20012],{},[979,20013],{"alt":1236,"src":20014},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774146845133-Screenshot_2026-03-22_103304.png",[12,20016,20017],{},[979,20018],{"alt":1236,"src":20019},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774147172273-Screenshot_2026-03-22_103918.png",[12,20021,20022,20023,20025],{},"接下來講另一個動作分期說 由Gentile提出 叫Gentile’s two-stage model",[83,20024],{},"\n把動作學習分成兩種時期",[12,20027,20028,20029,20031,20032,20034,20035,20037,20038,20040],{},"第一期是 調控跟非調控 就像是Motor control 裡頭講的須調整跟不須調整環境",[83,20030],{},"\n就像杯子的大小 會影響我手張多開 這個叫調控",[83,20033],{},"\n但就像標子的顏色就算五顏六色 也不會影響我手張多開 這就是非調控",[83,20036],{},"\n而第一期他提到有三個重要的特徵",[83,20039],{},"\n理解任務要求 發展基本的動作協調模式 區辨環境特徵",[12,20042,20043,20044,20046,20047,20049],{},"第二期 他覺得學到的東西會有兩種變體",[83,20045],{},"\n一種是專注化 意思是同一件事得分率提升",[83,20048],{},"\n一種是多樣化 在地鐵站上的逆著人流走 跟在廣場上逆著人流走 使用的動作大差不差",[12,20051,20052,20053,20055,20056,20060],{},"這篇最後教的理論是閉鎖式動作學習",[83,20054],{},"\n他主張 大腦必須要有一個",[254,20057,20059],{"className":20058},[562],"正確的標準"," 這樣在學習的過程中才會按照這個標準作修正",[12,20062,20063,20064,20066,20067,20069,20070,909],{},"他表示學的過程中有兩個重要的特徵",[83,20065],{},"\n第一是記憶痕跡 動作開始之前 選一個之前學到的正確的標準 做準備",[83,20068],{},"\n第二是感知痕跡 在做動作的時候 會比對那個正確的標準 隨時修正(即",[254,20071,20073],{"className":20072},[562],"強調回饋",[12,20075,20076,20077,20079,20080,20082,20083,20085,20086,20090],{},"他的理論強調這三點",[83,20078],{},"\n第一 感知痕跡可以被訓練",[83,20081],{},"\n第二 感知痕跡會因為訓練次數會越來越敏感(練到第一百次 即使你閉著眼彈錯一個琴鍵 你也感覺得到",[83,20084],{},"\n第三 強調",[254,20087,20089],{"className":20088},[562],"重複練習相同且正確","的動作",[12,20092,20093,20094,20096,20097,20101,20102,20104,20105,20109],{},"但他的理論也有限制",[83,20095],{},"\n首先是回饋部份 像",[254,20098,20100],{"className":20099},[7640],"CPG","裡頭就有提到 在沒有回饋的情況下 也能做得到動作 甚至能學到某些內容",[83,20103],{},"\n第二點 根據現在的研究指出 ",[254,20106,20108],{"className":20107},[7640],"變異多樣化","的學習 比起只學正確單一重複 還要更有效果",{"title":169,"searchDepth":170,"depth":170,"links":20111},[],"動作分期說到閉鏈式學習理論","\u002Fimages\u002Fuploads\u002F1774150308835-IMG_20200616_135236.jpg",{},"\u002Fblog\u002F動作學習（四）理論",{"title":19956,"description":20112},{"loc":20115},"blog\u002F動作學習（四）理論","N39J5ssKpgFiAcpBYZ_bjqFHChJaMcK7bBKZ0cZpDDw",{"id":20121,"title":20122,"author":7,"body":20123,"date":20263,"description":20264,"draft":174,"edited_at":17019,"extension":175,"featured_image":20265,"meta":20266,"navigation":178,"path":20267,"pinned":174,"seo":20268,"series":181,"seriesOrder":181,"sitemap":20269,"stem":20270,"tags":181,"__hash__":20271},"blog\u002Fblog\u002F中樞理論學派（二）Motor-Program.md","中樞理論學派（二）Motor Program",{"type":9,"value":20124,"toc":20261},[20125,20148,20151,20157,20169,20184,20196,20199,20202,20208,20211,20217,20226,20235,20240,20258],[12,20126,20127,20128,20130,20131,20133,20134,20138,20139,20141,20142,20144,20145,20147],{},"現在來到了Motor Program的部份 大家看到Program這個詞很容易聯想到 程式 代碼之類",[83,20129],{},"\n沒錯 他這個就是指說在動作產生前 腦子已經想好一套流程 它就是Motor Program",[83,20132],{},"\n而因為這一套流程是先想好的 一樣",[254,20135,20137],{"className":20136},[258],"不需要透過感覺回饋"," 就能產生動作",[83,20140],{},"\n他這個Program包括了 肌肉收縮順序 產生的力量等等 ",[83,20143],{},"\n而感覺回饋僅用來糾錯調整 不是用來刺激動作產生的",[83,20146],{},"\n而Program一但被執行 就必須被完成",[12,20149,20150],{},"以下將用動作程式代指Motor Program",[12,20152,20153,20154,20156],{},"那通用動作有三個理論 ",[83,20155],{},"\n1. 開鏈式系統 2. 通用動作程式 3. 階層特性",[12,20158,20159,20160,20162,20163,20165,20166,20168],{},"先來講開鏈式系統 像剛描述到的 一被執行則必須被完成 ",[83,20161],{},"\n而他的特性就是 在動作結束前 都沒有回饋 達成後才有回饋",[83,20164],{},"\n對 這裡的特性就跟 \u003C\u003C第六課>> 文中的開放式回路相似",[83,20167],{},"\n而這個系統在穩定且可預測的環境中最有效",[12,20170,20171,20172,20174,20175,20177,20178,20180,20181,20183],{},"接下來到通用動作程式 顧名思義 就是他把動作拆分成各個參數 ",[83,20173],{},"\n而有些是不可變的參數 裡面有1. 順序 2. 相對間隔\u002F相對時間(比例) 3. 相對力量(比例)",[83,20176],{},"\n這三個不可變的參數構成通用動作程式",[83,20179],{},"\n假若有兩種動作的這三個不可變參數皆相同 那他們所使用的通用動作程式就是同一個",[83,20182],{},"\n即使有任一不可變參數不同 那兩者的通用動作程式也不一樣",[12,20185,20186,20187,20189,20190,20192,20193,20195],{},"舉一個例子 土跟士這兩個字 別看這兩字僅上下橫線長度不一樣",[83,20188],{},"\n但土字在寫字裡上橫比下橫用力 士則相反 下橫比上橫用力 ",[83,20191],{},"\n即使順序(筆畫)跟相對間隔一樣 但兩者相對力量也不一樣",[83,20194],{},"\n所以是兩種通用動作程式",[12,20197,20198],{},"來突擊問一下 跑步跟走路兩種通用動作程式一樣嗎",[12,20200,20201],{},"而在通用動作程式裡可以改的參數",[12,20203,20204,20205,20207],{},"第一點 肌肉(部位) 意思就是 右撇子的你用左手寫同一個字 雖然字是比較醜 ",[83,20206],{},"\n但同一個字的不變參數相同 不影響同一個通用動作程式在不同部位的應用",[12,20209,20210],{},"第二點 總力量 今天你拿毛筆寫字 你寫的總力度變大 但同一個字的相對力量比例不變 亦適用通用動作程式",[12,20212,20213,20214,20216],{},"第三點 總時間間隔 今天寫同一個字 把他寫大一點佔多點位置 但時長用更長",[83,20215],{},"\n而寫小一個字 佔的位置小 整體時間比例也會縮短",[12,20218,20219,20220,20222,20223,20225],{},"而最後講到階層特性 他跟前面周圍理論學派的階層理論不同",[83,20221],{},"\n這邊的階層是指說 今天我要做一個任務例如拿水杯 就會讓小的動作程式組合成拿水杯的任務",[83,20224],{},"\n動作程式如下",[12,20227,20228,20229,20231,20232,20234],{},"1)身體前彎的動作程式 2) 手臂往前伸的動作程式 3) 手指打開的動作程式 ",[83,20230],{},"\n4) 抓握水杯的動作程式 5) 手臂回來的動作程式 ",[83,20233],{},"\n這樣把一套動作所需的動作程式串聯在一起 就是階層特性",[12,20236,20237],{},[979,20238],{"alt":1236,"src":20239},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774062985971-Screenshot_2026-03-21_111610.png",[12,20241,20242,20243,20245,20246,20248,20249,20251,20252,20254,20255,20257],{},"臨床上 會注意不要打斷病人的動作 尤其是快速的動作",[83,20244],{},"\n且鼓勵病人自動的做出來(利用開鏈式)",[83,20247],{},"\n但當預到環境會變化的情境 則鼓勵利用閉鏈式(即\u003C\u003C第六課>>的閉鎖式回路 注重感覺回饋以調整糾錯",[83,20250],{},"\n假若病人因中風偏癱 動作程式沒有缺失情況下 可訓練病人用另一側肢體肌肉以執行動作程式",[83,20253],{},"\n可以在原本的動作程式中修改 不需要重新構築新的動作程式",[83,20256],{},"\n鼓勵善用階層特性",[12,20259,20260],{},"還有 三個理論...就結束...動作控制學了.....(吐血",{"title":169,"searchDepth":170,"depth":170,"links":20262},[],"2026-03-21","越讀越爽了 哈嘶哈嘶哈嘶","\u002Fimages\u002Fuploads\u002F1774063674180-EhtmpujU4AAFKcy.jpg",{},"\u002Fblog\u002F中樞理論學派（二）Motor-Program",{"title":20122,"description":20264},{"loc":20267},"blog\u002F中樞理論學派（二）Motor-Program","N-slccQC119sWUXM2BsVRPoGjSTYQvkPZgDYzDCz-i8",{"id":20273,"title":20274,"author":7,"body":20275,"date":20263,"description":20356,"draft":174,"edited_at":17019,"extension":175,"featured_image":20357,"meta":20358,"navigation":178,"path":20359,"pinned":174,"seo":20360,"series":181,"seriesOrder":181,"sitemap":20361,"stem":20362,"tags":181,"__hash__":20363},"blog\u002Fblog\u002F動作學習（一）介紹.md","動作學習（一）介紹",{"type":9,"value":20276,"toc":20354},[20277,20305],[12,20278,20279,20280,20282,20283,20285,20286,20290,20291,20293,20294,20296,20297,20301,20302,20304],{},"動作學習 它的定義是 動作 藉由學習或者經驗產生的這個能力 是相當之永久的改變過程",[83,20281],{},"\n而我們把他拆分成三段",[83,20284],{},"\n手段: 靠",[254,20287,20289],{"className":20288},[562],"學習或經驗","產生的",[83,20292],{},"\n結果: 學到了=變成本領",[83,20295],{},"\n特性: ",[254,20298,20300],{"className":20299},[562],"相當永久","的改變過程-->意思練完之後 回到家忘記怎麼做了 那就不算是學",[83,20303],{},"\n而當他真的學會了 假如許久不未碰 讓他再做同樣的動作 他一樣能完成(只是可能跟以前比不算完美)",[12,20306,20307,20308,20310,20311,20315,20316,20318,20319,20321,20323,20324,20326,20328,20329,20331,20332,20334,20336,20337,20339,20340,20342,20343,20345,20346,20350,20351,20353],{},"而動作學習有四大特徵",[83,20309],{},"\n第一點 學習是獲得 ",[254,20312,20314],{"className":20313},[562],"執行技巧的能力"," 的過程 ",[83,20317],{},"\n是一種能力上的改變 是內在的 可以理解成下限",[83,20320],{},[83,20322],{},"\n第二點 學習意味著經驗與練習",[83,20325],{},[83,20327],{},"\n第三點 學習無法被測量 只能靠行為上推演",[83,20330],{},"\n例如 我今天耍雜技比昨天好 那只能代表我昨天有好好學習\u002F或學到甚麼小竅門",[83,20333],{},[83,20335],{},"\n第四點 學習到的技巧是 相對永久 的變化",[83,20338],{},"\n因為提到學習到的技巧是內在的 是下限",[83,20341],{},"\n但假如因為其他因素存在 而做得出來 這不叫做學會",[83,20344],{},"\n所以",[254,20347,20349],{"className":20348},[562],"排除","一些其他的因素 依然做得出來 這個才叫學會",[83,20352],{},"\n(其他因素包括但不限於 疲勞 情緒 動機 干擾等)",{"title":169,"searchDepth":170,"depth":170,"links":20355},[],"好了 這下連教人類怎麼學習動作都出來了","\u002Fimages\u002Fuploads\u002F1774140403310-EnL1WTpVEAAuJgW.jpg",{},"\u002Fblog\u002F動作學習（一）介紹",{"title":20274,"description":20356},{"loc":20359},"blog\u002F動作學習（一）介紹","VuzRhI3y52uHobkhlE2kgafcotN8m_pAxgBq5yhFEp4",{"id":20365,"title":20366,"author":7,"body":20367,"date":20263,"description":20450,"draft":174,"edited_at":17019,"extension":175,"featured_image":20451,"meta":20452,"navigation":178,"path":20453,"pinned":174,"seo":20454,"series":181,"seriesOrder":181,"sitemap":20455,"stem":20456,"tags":181,"__hash__":20457},"blog\u002Fblog\u002F動態模組理論.md","動態模組理論",{"type":9,"value":20368,"toc":20448},[20369,20378,20381,20401,20410,20425,20431,20440,20445],[12,20370,20371,20372,20374,20375,20377],{},"動態系統理論認為 動作的產生經由次系統",[83,20373],{},"\n而次系統負責選用徵召哪些部位實行 哪些部位限制 再協同完成",[83,20376],{},"\n次系統就是剛剛系統理論提到的中樞系統 肌肉骨骼系統 感覺系統 外部因素",[12,20379,20380],{},"次系統有以下幾點特徵",[12,20382,20383,20384,20388,20389,20393,20395,20396,20400],{},"自我重組 他描述著 只要一個動作包含的",[254,20385,20387],{"className":20386},[562],"次系統(零件)","達到了",[254,20390,20392],{"className":20391},[562],"臨界點(critical level of skill)",[83,20394],{},"\n那麼 動作就會",[254,20397,20399],{"className":20398},[562],"自然產生出來"," 不用被教會 亦適於用嬰兒",[12,20402,20403,20404,20406,20407,20409],{},"非線性發展 每個次系統發展都不一樣 且不是線性 ",[83,20405],{},"\n所以每個個體達成某些動作的時間都不一樣 ",[83,20408],{},"\n例如嬰兒獨立行走出現的時間 發展較慢的個體會影響獨立行走出現的時間",[12,20411,20412,20413,20415,20416,20418,20419,20421,20422,20424],{},"相移現象",[83,20414],{},"\n動作系統結構的改變非線性",[83,20417],{},"\n假如當變換某些次系統的控制參數 到達臨界",[83,20420],{},"\n動作將會以新的形態出現",[83,20423],{},"\n且不會出現介於兩個動作形態之間不穩定動作形態",[12,20426,20427,20428,20430],{},"而這套理論講述著 某一動作 所有的次系統皆成熟起來 動作才會發生 ",[83,20429],{},"\n所以穩定性極佳 且生物體會偏向做出 最省能量且效率最高的動作形態",[12,20432,20433,20434,20436,20437,20439],{},"而臨床應用上 應為他把動作描述為 次系統到達臨界點並組合而成的產物",[83,20435],{},"\n所以可以觀察病人 若某些動作無法達成時 注意他們的次系統 並加以訓練 已達成臨界點產生動作",[83,20438],{},"\n而速度也是一種動作形態的變因",[12,20441,20442],{},[979,20443],{"alt":1236,"src":20444},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774079521551-Screenshot_2026-03-21_155143.png",[12,20446,20447],{},"很好 動作控制終於讀完了 該開始下一堂課了",{"title":169,"searchDepth":170,"depth":170,"links":20449},[],"結束 啦！！！！！！！！！","\u002Fimages\u002Fuploads\u002F1774079542057-10558485i.jpg",{},"\u002Fblog\u002F動態模組理論",{"title":20366,"description":20450},{"loc":20453},"blog\u002F動態模組理論","I4ys8eyisD-8ty9AakYCbLK7yRk_0I1FIg4g6aHXPSE",{"id":20459,"title":20460,"author":7,"body":20461,"date":20263,"description":20553,"draft":174,"edited_at":17019,"extension":175,"featured_image":20554,"meta":20555,"navigation":178,"path":20556,"pinned":174,"seo":20557,"series":181,"seriesOrder":181,"sitemap":20558,"stem":20559,"tags":181,"__hash__":20560},"blog\u002Fblog\u002F模組理論.md","模組理論",{"type":9,"value":20462,"toc":20551},[20463,20469,20477,20493,20499,20511,20530,20533,20542,20548],[12,20464,20465,20466,20468],{},"模組理論是把腦子切分成不同區域 不同區域負責計算自己內容 例如 ",[83,20467],{},"\n負責杯子在多遠的距離的部門 杯子多大手要張開多大部門等等",[12,20470,20471,20473,20474,20476],{},[83,20472],{},"\n而不同模組計算出來的東西能彼此利用 例如",[83,20475],{},"\n我A區計算完杯子的距離 可以傳給B區口頭講給別人聽 不需要重新再計算",[12,20478,20479,20480,20482,20483,20485,20486,20488,20489],{},"在不同的任務裡 都會去計算他們共同的參數 裡面包括",[83,20481],{},"\n選擇(選擇的部位) 順序 時間 力量",[83,20484],{},"\n這裡有點像中樞理論系統的通用動作程式",[83,20487],{},"\n還是有不同的地方是 ",[254,20490,20492],{"className":20491},[562],"有沒有硬性要求部位",[12,20494,20495,20496,20498],{},"模組理論是探究大腦分部門後 每個部門得出的共同數值會與互相傳達 節省算力",[83,20497],{},"\n而通用動作程式是探究動作本身的不可變參數 使動作可以在不同部位裡做出相約的事情",[12,20500,20501,20502,20504,20505,20507,20508,20510],{},"而這邊提到了動作處理有某些重要的部門 ",[83,20503],{},"\n副皮質運動區(SMA) 處理動作的順序計算",[83,20506],{},"\n小腦 計算動作的時長",[83,20509],{},"\n基底核 計算力的分配",[12,20512,20513,20514,20518,20520,20521,20523,20524,20526,20527,20529],{},"小腦的計算部門分成了內外小腦 ",[254,20515,20517],{"className":20516},[562],"這兩個部門算力是獨立進行的",[83,20519],{},"\n外小腦是用來計算時間的 中樞系統裡頭的時鐘",[83,20522],{},"\n內小腦則是運動部門 負責將指令傳達給肌肉",[83,20525],{},"\n因為兩個區域是獨立的 假若外小腦受損而內小腦完整 則會影響動作的節奏 抑或分便不出誰長短(時間上",[83,20528],{},"\n反之 動作整體時間相同 但因為運動部門受損 導致動作整體不佳(如抖動 不協調)",[12,20531,20532],{},"臨床上 可以靠這個理論來評估病人為哪個區域受損",[12,20534,20535,20536,20538,20539,20541],{},"而治療應用上 假如小腦受損 可以利用身體其他運動器官隨節拍拍打 而後彼此傳輸參數",[83,20537],{},"\n例如 手跟著拍節拍打 然後讓腳試著跟著同樣的節拍 最後再訓練說話的節奏",[83,20540],{},"\n用這種不同器官互相傳遞共用數據的方式訓練",[12,20543,20544,20545,20547],{},"但仍有些許限制",[83,20546],{},"\n例如無法解釋小腦病變病患者同時有低張力問題",[12,20549,20550],{},"要到頭了... 剩30頁就結束這節課了...",{"title":169,"searchDepth":170,"depth":170,"links":20552},[],"啊！！！！！！！快 結束 一節課啦","\u002Fimages\u002Fuploads\u002F1774068417258-10543846i.jpg",{},"\u002Fblog\u002F模組理論",{"title":20460,"description":20553},{"loc":20556},"blog\u002F模組理論","TRicAqv9iHmP32tMjQt12xsxsdwvXq3rHpPxBDFq1So",{"id":20562,"title":20563,"author":7,"body":20564,"date":20263,"description":20714,"draft":174,"edited_at":17019,"extension":175,"featured_image":20715,"meta":20716,"navigation":178,"path":20717,"pinned":174,"seo":20718,"series":181,"seriesOrder":181,"sitemap":20719,"stem":20720,"tags":181,"__hash__":20721},"blog\u002Fblog\u002F系統理論.md","系統理論",{"type":9,"value":20565,"toc":20712},[20566,20580,20585,20623,20626,20641],[12,20567,20568,20569,20571,20572,20574,20575,20579],{},"系統理論認為動作不只是單一系統控制\u002F產生的  ",[83,20570],{},"\n中樞系統 肌肉骨骼系統 感覺系統 外部因素 ",[83,20573],{},"\n這四點一起作用下的結果",[254,20576,20578],{"className":20577},[562],"浮現","(意指共同作用交織下自然發生)",[12,20581,20582],{},[979,20583],{"alt":1236,"src":20584},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774069493665-Screenshot_2026-03-21_130425.png",[12,20586,20587,20588,20590,20591,20593,20595,20596,20598,20600,20601,20603,20604,20606,20607,20609,20611,20612,20614,20615,20617,20619,20620,20622],{},"此理論主要觀點有",[83,20589],{},"\n第一點 將身體作用在機械系統 那麼神經系統就不可以想出違反物理原則的動作",[83,20592],{},[83,20594],{},"\n第二點 動作產生不是反應的結果 而是我們主動活動而產生的現象 所以動物才要靠持續感知而修改行為",[83,20597],{},[83,20599],{},"\n第三點 就像是做一些很多個關節一起動的動作 假如腦子要每個獨立思考運算會很佔算力",[83,20602],{},"\n所以他提出來協調結構(coordinative structure) ",[83,20605],{},"\n意思是大腦會讓肌肉組成一個小組 對小組下達指令 讓他們共同作用",[83,20608],{},[83,20610],{},"\n第四點 生物體能活用多餘的自由度",[83,20613],{},"\n意思就是 將多個單關節的組合在一起 高效且流暢的完成動作",[83,20616],{},[83,20618],{},"\n第五點 大腦會把要做的動作做好參數 然後發到脊髓處 讓脊髓來完成動作 ",[83,20621],{},"\n那大腦只需要負責計算 脊髓則實行起來 減少大腦的負荷 稱最小互動原則",[12,20624,20625],{},"也有一個特性是分佈控制 意思就是做一件動作 同時發到給不同的小組 讓他們彼此做自己的份內事",[12,20627,20628,20629,20631,20632,20634,20635,20637,20638,20640],{},"系統模式有兩種假設",[83,20630],{},"\n第一種 神經系統要做的不是對小組指導他們做甚麼 ",[83,20633],{},"\n而是讓他們以完成工作為目的 他們自行分配身體的資源達成目的",[83,20636],{},"\n第二種 神經系統會依照肌肉骨骼系統所擁有的資源 預測動作的方式 ",[83,20639],{},"\n並且在過程中不斷適合(優化資源分配)已達成最有效工作方式",[12,20642,20643,20644,20646,20647,20649,20650,20652,20654,20655,20657,20659,20660,20662,20663,20665,20667,20668,20670,20671,20673,20674,20676,20678,20679,20681,20682,20684,20685,20687,20688,20690,20691,20693,20694,20696,20697,20699,20700,20702,20703,20705,20706,20708,20709,20711],{},"臨床應用上 主要有以下幾點",[83,20645],{},"\n第一點 動作是為了達成目的而產生 所以盡量訓練功能性動作主為 ",[83,20648],{},"\n避免單純的練神經反射或者動作的型態(動作怎麼動)",[83,20651],{},[83,20653],{},"\n第二點 可以加入不同環境 姿勢起始 視覺環境來訓練預測和適應性",[83,20656],{},[83,20658],{},"\n第三點 教導病人以不同小組為主進行訓練",[83,20661],{},"\n假若有些慣用小組受損 那麼我們應該引導病人嘗試他們目前最有效的小組 並且加以訓練",[83,20664],{},[83,20666],{},"\n第四點 他強調 腦傷的病人的動作障礙雖有別於常人 ",[83,20669],{},"\n但仍然是大腦已結合自身僅有的東西組合而成的結果",[83,20672],{},"\n例如中風病人步態雖一拐一拐 但為了極力保持能動跟相對不容易跌倒 這是好的結果",[83,20675],{},[83,20677],{},"\n第五點 他強調動作的形成可以是動態的 並不單一",[83,20680],{},"\n動作會因為目標和環境而改變",[83,20683],{},"\n例如 今天打球 ",[83,20686],{},"\n有人傳球給你(環境刺激)",[83,20689],{},"\n目標A: 投籃",[83,20692],{},"\n目標B: 運球",[83,20695],{},"\n這兩個動作在刺激一樣上 得到兩個不同的結果 原因在目標上 ",[83,20698],{},"\n而另一個例子 今天我在公車上",[83,20701],{},"\n要站穩(目的)",[83,20704],{},"\n刺激A: 公車煞車",[83,20707],{},"\n刺激B: 有人推撞",[83,20710],{},"\n而這兩個刺激在這個動作的產生上是相同的 都是抓住扶手或者踏步來穩住身體",{"title":169,"searchDepth":170,"depth":170,"links":20713},[],"要到頭 啦！！！！！！！！！！！！","\u002Fimages\u002Fuploads\u002F1774074083123-10496727i.jpg",{},"\u002Fblog\u002F系統理論",{"title":20563,"description":20714},{"loc":20717},"blog\u002F系統理論","qpQyAhP6Fom4SoH0Uzl0hbEwDdMMOyR7nCmyBI8amho",{"id":20723,"title":20724,"author":7,"body":20725,"date":20814,"description":20815,"draft":174,"edited_at":17019,"extension":175,"featured_image":20816,"meta":20817,"navigation":178,"path":20818,"pinned":174,"seo":20819,"series":181,"seriesOrder":181,"sitemap":20820,"stem":20821,"tags":181,"__hash__":20822},"blog\u002Fblog\u002F中樞理論學派（一）CPG.md","中樞理論學派（一）CPG",{"type":9,"value":20726,"toc":20812},[20727,20739,20748,20760,20772,20775,20784,20789,20794,20797,20806,20809],[12,20728,20729,20730,20732,20733,20735,20736,20738],{},"中樞理論與剛剛的周圍理論是相反的",[83,20731],{},"\n他們主張動作只由大腦傳達指令 不需要感覺刺激 自發的完成動作",[83,20734],{},"\n而他們有兩種理論",[83,20737],{},"\n1. CPG(中央行式產生器) 2. Motor Program",[12,20740,20741,20742,20744,20745,20747],{},"首先來講CPG",[83,20743],{},"\nCPG就是能在沒有周圍感覺輸入狀況下 規律或交替的完成動作型態的神經網絡",[83,20746],{},"\n存在於脊髓之中",[12,20749,20750,20751,20753,20754,20756,20757,20759],{},"有兩種特點",[83,20752],{},"\n第一種就是與生俱來 因為CPG是存在於脊髓 不用教也不用刻意管控",[83,20755],{},"\n第二種是Phasic(陣發性) 以走路為例 以周圍理論來說就是因感覺輸入後才會產生交替動作",[83,20758],{},"\n但CPG則認為即使沒有感覺輸入 也能一步一步走",[12,20761,20762,20763,20765,20766,20768,20769,20771],{},"而CPG理論有三種模型 ",[83,20764],{},"\n雙半中心模型 ",[83,20767],{},"\n閉鏈式迴路模型 ",[83,20770],{},"\n節律器模型",[12,20773,20774],{},"雙半串心模型簡單來說就是一組半中心組在一起 而這個半中心互為拮抗肌 以達成自動交替動作",[12,20776,20777,20778,20780,20781,20783],{},"而閉鎖是具校正功能 路徑是先從脊髓發出指令 ",[83,20779],{},"\n而一部份則會回傳回脊髓 用下圖來看就是中途拐彎  拐彎回去過程再加入其他感覺輸入 繼續迴圈",[83,20782],{},"\n其中就包括了 肌梭在走過的過程中會一直回傳感覺輸入給CPG讓他可以自行調整",[12,20785,20786],{},[979,20787],{"alt":1236,"src":20788},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774058007726-Screenshot_2026-03-21_095315.png",[12,20790,20791],{},[979,20792],{"alt":1236,"src":20793},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774056138600-Screenshot_2026-03-21_092144.png",[12,20795,20796],{},"最後節律器模型就是認為 神經元可以像心臟一樣自律跳動 活化且產生肌肉收縮後 還能再被自動活化",[12,20798,20799,20800,20802,20803,20805],{},"在臨床的應用上 因為CPG是存在於脊髓上 而SCI病人是脊髓路徑受損 ",[83,20801],{},"\n不存在像階層理論說的傳不上去高中階無法被抑制\u002F誘發 ",[83,20804],{},"\n所以CPG還是能被自動誘發做節律交替作(如行走)",[12,20807,20808],{},"簡單來說 CPG的特性可以幫助大腦達成自主自動 且節律交替有規則的動作 為大腦節省算力(如走路)",[12,20810,20811],{},"越讀越爽 我是不是這輩子有了",{"title":169,"searchDepth":170,"depth":170,"links":20813},[],"2026-03-20","啊~~~~~殺了我吧","\u002Fimages\u002Fuploads\u002F1774056557316-EhtmqMpUcAIrzEc.jpg",{},"\u002Fblog\u002F中樞理論學派（一）CPG",{"title":20724,"description":20815},{"loc":20818},"blog\u002F中樞理論學派（一）CPG","rxOrmk1NQ58VeZD0fm637kOAXkHdWxuV69XwXe1qc6U",{"id":20824,"title":20825,"author":7,"body":20826,"date":20814,"description":20933,"draft":174,"edited_at":17019,"extension":175,"featured_image":20934,"meta":20935,"navigation":178,"path":753,"pinned":174,"seo":20936,"series":181,"seriesOrder":181,"sitemap":20937,"stem":20938,"tags":181,"__hash__":20939},"blog\u002Fblog\u002F周圍理論學派（一）反射理論.md","周圍理論學派（一）反射理論",{"type":9,"value":20827,"toc":20931},[20828,20834,20846,20855,20861,20866,20872,20884,20887,20890,20893,20902,20920,20925],[12,20829,20830,20831,20833],{},"周圍理論學派他們主張感覺是動作啟動到完成最重要 必要的條件 ",[83,20832],{},"\n而裡面有兩個理論 第一個是反射鏈理論 而另一個則是階層理論",[12,20835,20836,20837,20839,20840,20842,20843,20845],{},"先來講反射鏈理論 誰提出我不想鳥了",[83,20838],{},"\n他們主張動作是由感覺引發肌肉產生的 不論是外在還是內發的",[83,20841],{},"\n而這些動作包括了 視覺 前庭覺 體感",[83,20844],{},"\n複雜的動作由多個簡單的反射組成 故稱為反射鏈",[12,20847,20848,20849,20851,20852,20854],{},"反射會有閾值 意思是到達最基本刺激點會起反應 ",[83,20850],{},"\n例如 閾值是3 即使在怎麼往上給刺激 也只會到3的程度 往上加不會反應形態",[83,20853],{},"\n但假如只給到了2以則不會產生任何反應",[12,20856,20857,20858,20860],{},"而身體上會有感覺接收區 現稱為皮質感覺區(Dermatome)",[83,20859],{},"\n運動神經元只會對他該出的感覺刺激做出反應",[12,20862,20863],{},[979,20864],{"alt":1236,"src":20865},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773995822036-Screenshot_2026-03-20_163641.png",[12,20867,20868,20869,20871],{},"而所有動作指令會被傳送到脊髓前角的alpha-motor neuron才會被引起肌肉收縮",[83,20870],{},"\n而alpha-motor neuron被稱為最終共同路徑",[12,20873,20874,20875,20877,20878,20880,20881,20883],{},"感覺訊息可以分為",[83,20876],{},"\n內在的訊息 即臟器的感覺",[83,20879],{},"\n身體表面感覺到的訊息 如體感覺(觸 壓 溫度) 和 前庭覺",[83,20882],{},"\n身體外的事物感受到的訊息 如視覺",[12,20885,20886],{},"而反射之間也有三個作用",[12,20888,20889],{},"第一個就是在促進 我給予病人外在的刺激例如拍打該區以強調力量產生能促進肌力增加",[12,20891,20892],{},"第二是互相抑制 只是利用了拮抗肌的效果 例如病人肱二頭肌力量過大 我便拍打肱三減少肱二用力",[12,20894,20895,20896,20898,20899,20901],{},"第三是發散作用 這種大家比較有感覺 踢到桌角或者踩到釘子 我們都會把受傷腳提起來 而另一隻角就伸直",[83,20897],{},"\n受傷腳踩到釘子 受傷腳是主要感覺的區域 ",[83,20900],{},"\n但非受傷腳沒有感覺也會自己有動作(伸直) 非受傷腳採取的的動作就是發散作用",[12,20903,20904,20905,20907,20908,20910,20911,20913,20914,20916,20917,20919],{},"但反射理論也有他解釋不到的地方",[83,20906],{},"\n首先是他沒有辦法解釋自發(從思考 內心而發 有感而發)的動作",[83,20909],{},"\n第二點就是沒有感覺刺激下也能產生動作 例如把感覺路徑去掉 動作雖然變得笨拙但不代表做不出來",[83,20912],{},"\n第三點是快速的動作無法解釋 例如打字1秒十下 但按照反射從感覺到動作產生只能做到1秒三下(生理)",[83,20915],{},"\n第四點是無法解釋同樣刺激會有多種\u002F不同的動作反應 像剛剛發散作用的例子另一隻腳會被伸直 但當假如另一隻腳是殘廢的 則會抑制伸直的動作",[83,20918],{},"\n第五點就是沒有辦法解釋動作怎麼學習的",[12,20921,20922],{},[979,20923],{"alt":1236,"src":20924},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773998047912-Screenshot_2026-03-20_171344.png",[12,20926,20927,20928,20930],{},"臨床上我們可以透過反射理論來評估病人預後",[83,20929],{},"\n可以在訓練期間使用反射促進或抑制使病人訓練更佳",{"title":169,"searchDepth":170,"depth":170,"links":20932},[],"開始理論啦！！！","\u002Fimages\u002Fuploads\u002F1774000375308-EjZb4n1U8AAOBtz.jpg",{},{"title":20825,"description":20933},{"loc":753},"blog\u002F周圍理論學派（一）反射理論","GdliWJu_WSgMuh7_qxFfs7EOMWSIyI4IqN3N6zZFtFE",{"id":20941,"title":20942,"author":7,"body":20943,"date":20814,"description":21006,"draft":174,"edited_at":17019,"extension":175,"featured_image":21007,"meta":21008,"navigation":178,"path":21009,"pinned":174,"seo":21010,"series":181,"seriesOrder":181,"sitemap":21011,"stem":21012,"tags":181,"__hash__":21013},"blog\u002Fblog\u002F周圍理論學派（二）階層理論.md","周圍理論學派（二）階層理論",{"type":9,"value":20944,"toc":21004},[20945,20966,20971,20977,20986,20998],[12,20946,20947,20948,20950,20951,20953,20954,20956,20957,20959,20960,20962,20963,20965],{},"階層理論最核心的點是 自主動作與自動動作是被各個階層所管理",[83,20949],{},"\n簡單講解一下 自主動作是我想個人出來的想去做的",[83,20952],{},"\n而自動動作是由不需要我去想就能自己做出來的動作 例如呼吸 走路等 不用自己去想怎麼提腳那種",[83,20955],{},"\n存在三種層級",[83,20958],{},"\n高階中心(聯合皮質區)",[83,20961],{},"\n中階中心(運動皮質區)",[83,20964],{},"\n初級中心(脊髓)",[12,20967,20968],{},[979,20969],{"alt":1236,"src":20970},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1774001045510-Screenshot_2026-03-20_180349.png",[12,20972,20973,20974,20976],{},"高階可以誘發或抑制低階的動作",[83,20975],{},"\n且同樣注重周圍的感覺回饋",[12,20978,20979,20980,20982,20983,20985],{},"階層理論有以下特點",[83,20981],{},"\n1. 上往下的控制 意思就是 低一階只可以被它的上一階所控制 而高一階的也只能控制它的下一階",[83,20984],{},"\n2. 反向演化 正常而言 反射的動作會因為被其高一階所抑制 但假若高階受損 低階的反射動作將會出現",[12,20987,20988,20989,20991,20992,20994,20995,20997],{},"當牽張反射產生 會先引起低階動作 如膝跳反射 即初階中心 ",[83,20990],{},"\n會慢慢回傳到中階中心 最後才會到大腦皮質區如運動及聯合皮質區",[83,20993],{},"\n但假若病人為SCI(脊髓損傷病人) 則只有低階產生 不會傳至中高級",[83,20996],{},"\n亦會使低階變強 因沒有中階所抑制",[12,20999,21000,21001,21003],{},"臨床應用上 因為這個理論提及高階受損低階被誘發或被增強 ",[83,21002],{},"\n所以可以用來評估腦損傷程度",{"title":169,"searchDepth":170,"depth":170,"links":21005},[],"繼續理論！！","\u002Fimages\u002Fuploads\u002F1774002644179-IMG_20201115_202140.jpg",{},"\u002Fblog\u002F周圍理論學派（二）階層理論",{"title":20942,"description":21006},{"loc":21009},"blog\u002F周圍理論學派（二）階層理論","PZ674c1uH2GjG4eQxF4zf9J3l53yEn-YZjyNUQB0054",{"id":21015,"title":21016,"author":7,"body":21017,"date":20814,"description":21119,"draft":174,"edited_at":17019,"extension":175,"featured_image":21120,"meta":21121,"navigation":178,"path":21122,"pinned":174,"seo":21123,"series":181,"seriesOrder":181,"sitemap":21124,"stem":21125,"tags":181,"__hash__":21126},"blog\u002Fblog\u002F控制自己-Be-water-my-friend.md","Motor Control（一）",{"type":9,"value":21018,"toc":21117},[21019,21022,21025,21028,21031,21034,21037,21043,21048,21051,21054,21060,21063,21069,21075,21081,21087,21096,21111],[12,21020,21021],{},"早安各位孩子 我是你們的黑奴前領導人之一",[12,21023,21024],{},"今天我是來為大家講解我們PT的其中一個負責領域 神經領域的入門",[12,21026,21027],{},"大家可能會好奇動作控制不是人類隨隨便便都能做到的嗎 研究來幹嘛",[12,21029,21030],{},"是沒錯但 當假如你今天被上了多個debuff再加上一堆場地陷阱卡時做著雜技 你也能隨便實現嗎",[12,21032,21033],{},"很顯然不行 就算今天只是發個燒也能讓你頭昏眼花躺死在床",[12,21035,21036],{},"所以我就來簡單講述一下動作科學裡的第一大類————動作控制",[12,21038,21039,21040,21042],{},"動作控制最基本也分了三個大類",[83,21041],{},"\n1. 個體(Individual) 2. 任務(Task) 3. 環境(Environment)",[12,21044,21045],{},[979,21046],{"alt":1236,"src":21047},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773978076463-movernment.png",[12,21049,21050],{},"這三個會構成我們的動作的產生條件\u002F變數",[12,21052,21053],{},"我先來描述個體 就是自己個體本身在決定動作內容的內在變數",[12,21055,21056,21057,21059],{},"有三種狀況會影響自己在決定動作內容的變數",[83,21058],{},"\n1. 知覺(Perception) 2.認知(Cognition) 3. 行動(Action or Activities)",[12,21061,21062],{},"我來用群友最愛的例子來解釋這三個狀況",[12,21064,21065,21066,21068],{},"今天你被蒙上眼睛",[83,21067],{},"\n被人用某種棒狀物觸碰著並有人在你耳邊說話",[12,21070,21071,21072,21074],{},"知覺就是用身體上所有的感覺辨識 包括視嗅聽味觸",[83,21073],{},"\n你知道被碰觸 知道這東西的質感 大小等一切條件",[12,21076,21077,21078,21080],{},"認知就是結合腦中整合知覺產生的東西 你突然驚覺這硬硬的 長長的 但沒有溫度 表面平滑 ",[83,21079],{},"\n有人拿著棍子在碰我 或者想對我做些甚麼",[12,21082,21083,21084,21086],{},"並且認知也是想做甚麼並且下達指令給行動產生動作的一環",[83,21085],{},"\n欸 有人拿著棍子蒙著我眼睛想幹嘛 有種不好的預感 我想要脫下眼罩 站起來跟他對峙",[12,21088,21089,21090,21092,21093,21095],{},"而行動就是實行認知給的指令的環節",[83,21091],{},"\n我伸手把眼罩拿下來 並且站起身看起來張開眼看向他 ",[83,21094],{},"\n的這系列所有肌肉調動 全都是行動做的事",[12,21097,21098,21099,21101,21102,21104,21105,21107,21108,21110],{},"好 這裡給同學提問",[83,21100],{},"\n當我假如用眼睛目視到那根棍子跟一個男人 是哪一類",[83,21103],{},"\n我分辨出來那跟棍子是球棒跟他是群友 是哪一類",[83,21106],{},"\n我看到這般情景想要懇求群友不要把我抓回去逆當黑奴 是哪一類",[83,21109],{},"\n我實際說出懇求的話 是哪一類",[12,21112,21113,21114,21116],{},"同學也可以自行給出例子寫到下面來",[83,21115],{},"\n有補充或者有大佬留言糾正就不吝留言",{"title":169,"searchDepth":170,"depth":170,"links":21118},[],"來給對PT有興趣的路人們簡單講解一下學渣對這門課的理解","\u002Fimages\u002Fuploads\u002F1773978280816-20201130_205814.jpg",{},"\u002Fblog\u002F控制自己-Be-water-my-friend",{"title":21016,"description":21119},{"loc":21122},"blog\u002F控制自己-Be-water-my-friend","kqsIZx8wrVBi0WhyeCuJw0LedfojQFxXzGUZf7a9UUU",{"id":21128,"title":21129,"author":7,"body":21130,"date":20814,"description":21119,"draft":174,"edited_at":17019,"extension":175,"featured_image":21173,"meta":21174,"navigation":178,"path":21175,"pinned":174,"seo":21176,"series":181,"seriesOrder":181,"sitemap":21177,"stem":21178,"tags":181,"__hash__":21179},"blog\u002Fblog\u002F控制自己-Be-water-my-friend（三）.md","Motor Control（三）",{"type":9,"value":21131,"toc":21171},[21132,21138,21153,21165,21168],[12,21133,21134,21135,21137],{},"終於來到了最後的環境一類了",[83,21136],{},"\n而這裡的環境是指會不會影響我的動作的部份",[12,21139,21140,21141,21143,21144,21146,21147,21149,21150,21152],{},"分為了須調整和不須調整",[83,21142],{},"\n須調整就是 他一定會影響你動作變化",[83,21145],{},"\n例如握住杯子 用的是手指 手指在剛剛說了是小的 算精細動作",[83,21148],{},"\n但杯子的大小也會影響手指張開多大",[83,21151],{},"\n這種不是自己能改變的就叫須調整",[12,21154,21155,21156,21158,21159,21161,21162,21164],{},"不須調整就是怎麼影響你也不會影響做事情本身的動作",[83,21157],{},"\n例如 噪音 有人正在G8你 或者光線的顏色 環境音",[83,21160],{},"\n這些在去掉心理因素時所影響的變量本身對我握住杯子沒有任何影響",[83,21163],{},"\n這種叫在不須調整",[12,21166,21167],{},"以上包括前兩篇提到的都是 調控任何動作行為任務的一切參數",[12,21169,21170],{},"這篇先寫短一點 等下還有一長串東西呢 草",{"title":169,"searchDepth":170,"depth":170,"links":21172},[],"\u002Fimages\u002Fuploads\u002F1773982753027-IMG_20200623_142022.jpg",{},"\u002Fblog\u002F控制自己-Be-water-my-friend（三）",{"title":21129,"description":21119},{"loc":21175},"blog\u002F控制自己-Be-water-my-friend（三）","uJQYlQNYdvpwJG5q7K_yrcT4iXjmBJeb-Ri1jrSp968",{"id":21181,"title":21182,"author":7,"body":21183,"date":20814,"description":21119,"draft":174,"edited_at":17019,"extension":175,"featured_image":21320,"meta":21321,"navigation":178,"path":21322,"pinned":174,"seo":21323,"series":181,"seriesOrder":181,"sitemap":21324,"stem":21325,"tags":181,"__hash__":21326},"blog\u002Fblog\u002F控制自己-Be-water-my-friend（二）.md","Motor Control（二）",{"type":9,"value":21184,"toc":21318},[21185,21188,21191,21203,21208,21214,21223,21232,21244,21262,21274,21280,21286,21292,21309],[12,21186,21187],{},"上回說了個體本身對動作產生的影響會怎樣",[12,21189,21190],{},"而接下來便到了任務(Task)的部份",[12,21192,21193,21194,21196,21197,21199,21200,21202],{},"任務也分成了三種大變數",[83,21195],{},"\n1. 封閉或開放式動作",[83,21198],{},"\n2. 連續不連續串聯動作",[83,21201],{},"\n3. 粗大動作\u002F精細動作",[12,21204,21205],{},[979,21206],{"alt":1236,"src":21207},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773981198506-Screenshot_2026-03-20_123256.png",[12,21209,21210,21211,21213],{},"那我先來講第一點",[83,21212],{},"\nWhat is封閉 Whats is 開放",[12,21215,21216,21217,21219,21220,21222],{},"封閉意思是指任務本身所有變量不變",[83,21218],{},"\n重複的定點投籃 在家中拿起在桌上的杯子 在只有自己的房間扣鈕扣",[83,21221],{},"\n這種只需要專注在一件事情上的我們叫在封閉",[12,21224,21225,21226,21228,21229,21231],{},"而開放式代表著一堆變化的參數影響著做任務本身的你",[83,21227],{},"\n踢球 打網球 擊打投手投來的棒球 想要接住被擊飛在空中準備落下的棒球的你",[83,21230],{},"\n這種無法自己全部掌握需要一直變化著思緒策略或者力度的行為叫做開放式",[12,21233,21234,21235,21237,21238,21240,21241,21243],{},"到了連續跟不連續動作與串聯動作",[83,21236],{},"\n連續是指沒有明確段落或開始結束的行為",[83,21239],{},"\n例子有走路 跑步 遊泳 ",[83,21242],{},"\n你可以隨意的變換目的類型",[12,21245,21246,21247,21249,21250,21252,21253,21255,21256,21258,21259,21261],{},"可能這邊開始有些抽象 那我拿不連續當反例",[83,21248],{},"\n不連續就指說有明確段落或開始結束",[83,21251],{},"\n例子有開關燈 敲打一個鋼琴鍵",[83,21254],{},"\n像是開關 按到一半鬆開手 然後燈沒開或者沒關 一直這樣按一半鬆手這種毫無意思的抽象行為沒意義",[83,21257],{},"\n只有讓開關整個按下去 觸發電流 讓燈開起來\u002F關燈",[83,21260],{},"\n所以不連續就是達成某些段落才有意義的行為",[12,21263,21264,21265,21267,21268,21270,21271,21273],{},"而串聯性動作就是指多個不連續的動作組合在一起的行為",[83,21266],{},"\n例如彈鋼琴一首曲子 用鍵盤打字",[83,21269],{},"\n鋼琴也是一樣要按鋼琴鍵到聽到聲音才有意義 ",[83,21272],{},"\n那麼我要彈一首曲子就是我按著譜子去敲打鋼琴鍵 也是把不連續串起來",[12,21275,21276,21277,21279],{},"好了好了知道有人快要睡著了最後了",[83,21278],{},"\n最後一個任務本身會影響的參數是粗大動作和精細動作",[12,21281,21282,21283,21285],{},"粗大動作就是 對 大的肌肉動起來的動作 動起來很明顯的動作",[83,21284],{},"\n走跑跳 揮拳伸懶腰那些",[12,21287,21288,21289,21291],{},"反過來精細動作就是小的動作 整體動起來不會有明顯驅體變化的動作",[83,21290],{},"\n講話 手指動來動去 眨眼 咀嚼 這些都是精細動作",[12,21293,21294,21295,21297,21298,21300,21302,21303,21305,21306,21308],{},"好 提問環節到了",[83,21296],{},"\n分辨以下動作是封閉開放 是精細粗大 是連續還不連續還串聯",[83,21299],{},[83,21301],{},"\n我對著琴譜彈鋼琴",[83,21304],{},"\n運球上籃",[83,21307],{},"\n對著節拍哼聲",[12,21310,21311,21312,21314,21315,21317],{},"還有大概一百五十頁PPT的內容呢 尼馬",[83,21313],{},"\n一周能噴出200頁PPT 一次考要諗約600~900頁PPT",[83,21316],{},"\n我以後還碰國戰遊戲被推上當領導我原地自刎歸天",{"title":169,"searchDepth":170,"depth":170,"links":21319},[],"\u002Fimages\u002Fuploads\u002F1773981453970-IMG_20200616_135133.jpg",{},"\u002Fblog\u002F控制自己-Be-water-my-friend（二）",{"title":21182,"description":21119},{"loc":21322},"blog\u002F控制自己-Be-water-my-friend（二）","1xyRKMzmzEWCC1vYZbva0W6WNZOy52_U8fW2dO6zSRM",{"id":21328,"title":21329,"author":7,"body":21330,"date":20814,"description":21119,"draft":174,"edited_at":17019,"extension":175,"featured_image":21400,"meta":21401,"navigation":178,"path":21402,"pinned":174,"seo":21403,"series":181,"seriesOrder":181,"sitemap":21404,"stem":21405,"tags":181,"__hash__":21406},"blog\u002Fblog\u002F控制自己-Be-water-my-friend（五）.md","Motor Control（五）",{"type":9,"value":21331,"toc":21398},[21332,21347,21362,21374,21377,21382,21387,21390,21395],[12,21333,21334,21335,21337,21338,21340,21341,21343,21344,21346],{},"書接上回",[83,21336],{},"\n現在來到了功能分類 是指說我們人在執行動作時有沒有動",[83,21339],{},"\n一樣分了兩類",[83,21342],{},"\n固定不變穩定的還是會動來動去的",[83,21345],{},"\n有操作就是沒操作的",[12,21348,21349,21350,21352,21353,21355,21356,21358,21359,21361],{},"那先來第一類 Stability 和 Transport",[83,21351],{},"\nStability我就把他理解成固定的不動的",[83,21354],{},"\n顧名思義 站立不動 坐著不動 躺著不動 這些都叫固定",[83,21357],{},"\n那Transport我就解釋成移動",[83,21360],{},"\n走路 跑步 泳遊 跳",[12,21363,21364,21365,21367,21368,21370,21371,21373],{},"而第二類有沒有操作",[83,21366],{},"\n最基本理解就是手部有沒有被分心出去做事",[83,21369],{},"\n射箭 有操作 滑手機 有操作 擦槍 有操作 ",[83,21372],{},"\n而啥也沒幹的就是無操作",[12,21375,21376],{},"所以 對 又被分成了這兩表格",[12,21378,21379],{},[979,21380],{"alt":1236,"src":21381},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773985015794-Screenshot_2026-03-20_133628.png",[12,21383,21384],{},[979,21385],{"alt":1236,"src":21386},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773985083041-Screenshot_2026-03-20_133751.png",[12,21388,21389],{},"結果 按照環境的兩大類跟身體動作的兩大類 我們就能變出上一節課講的4X4表格",[12,21391,21392],{},[979,21393],{"alt":1236,"src":21394},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773985213471-Screenshot_2026-03-20_133959.png",[12,21396,21397],{},"歡迎發揮你們抽象的想法在最後一張圖挑幾個留言分享",{"title":169,"searchDepth":170,"depth":170,"links":21399},[],"\u002Fimages\u002Fuploads\u002F1773985655349-___.jpg",{},"\u002Fblog\u002F控制自己-Be-water-my-friend（五）",{"title":21329,"description":21119},{"loc":21402},"blog\u002F控制自己-Be-water-my-friend（五）","nwscu9L858J9Sf1TVzkbJzlYD-_wCdk1kgwa1OVTPwo",{"id":21408,"title":21409,"author":7,"body":21410,"date":20814,"description":21119,"draft":174,"edited_at":17019,"extension":175,"featured_image":21499,"meta":21500,"navigation":178,"path":21501,"pinned":174,"seo":21502,"series":181,"seriesOrder":181,"sitemap":21503,"stem":21504,"tags":181,"__hash__":21505},"blog\u002Fblog\u002F控制自己-Be-water-my-friend（四）.md","Motor Control（四）",{"type":9,"value":21411,"toc":21497},[21412,21418,21436,21448,21457,21472,21484,21487,21492],[12,21413,21414,21415,21417],{},"很好各位同學 假如你們看完剛剛三篇一定是對動作控制稍微理解",[83,21416],{},"\n也相信你們不是對PT感興趣就是抖M才點進來這裡對吧",[12,21419,21420,21421,21423,21424,21426,21427,21429,21430,21432,21433,21435],{},"而這裡有個大聰明把剛剛所有的東西用一個4X4的大表格列完出來",[83,21422],{},"\n對 沒想到居然有這麼大個表格是吧",[83,21425],{},"\n由這三點變出來的不同任務描寫對我們自己身體調控參數的影響",[83,21428],{},"\n• 依據環境 (environment) 分類 ",[83,21431],{},"\n• 依據行動的功能 (function of action) 分類 ",[83,21434],{},"\n• 任務的綜合分類",[12,21437,21438,21439,21441,21442,21444,21445,21447],{},"那先來講述環境分類",[83,21440],{},"\n環境分成兩類",[83,21443],{},"\n1. 動態與靜態",[83,21446],{},"\n2. 一致與變化",[12,21449,21450,21451,21453,21454,21456],{},"先來講環境的第一類",[83,21452],{},"\n動態靜態就是指說場地本身會不會動",[83,21455],{},"\n例如搭電扶梯 電扶梯是動的 走在平原 平原是靜的 搭電梯 動的 坐在咖啡廳裡 靜的",[12,21458,21459,21460,21462,21463,21465,21466,21468,21469,21471],{},"而第二類一致與變化",[83,21461],{},"\n一致是指做每一次動作都不會有環境變化 可預測的地方",[83,21464],{},"\n在啥也沒有的平原上來回走動",[83,21467],{},"\n按著距離等長的三角椎繞行來回",[83,21470],{},"\n這些本身不會被動的 做幾次都不會有環境變化",[12,21473,21474,21475,21477,21478,21480,21481,21483],{},"而變化就是每做一次都會隨機變化 不可預測的地方",[83,21476],{},"\n擁擠人潮裡走動",[83,21479],{},"\n凹突不平的路面走動",[83,21482],{},"\n這些每次都有變化抑或者不可預測的情形就是變化的",[12,21485,21486],{},"然後整合這兩類就會得到這兩個表",[12,21488,21489],{},[979,21490],{"alt":1236,"src":21491},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773983922403-Screenshot_2026-03-20_131746.png",[12,21493,21494],{},[979,21495],{"alt":1236,"src":21496},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773984031992-Screenshot_2026-03-20_132002.png",{"title":169,"searchDepth":170,"depth":170,"links":21498},[],"\u002Fimages\u002Fuploads\u002F1773983954366-IMG_20200722_231036.jpg",{},"\u002Fblog\u002F控制自己-Be-water-my-friend（四）",{"title":21409,"description":21119},{"loc":21501},"blog\u002F控制自己-Be-water-my-friend（四）","8QeeOssnCAv_7wtm5j0muuf6DezeqJHDIzyKpBGl4Jc",{"id":21507,"title":21508,"author":7,"body":21509,"date":20814,"description":21709,"draft":174,"edited_at":17019,"extension":175,"featured_image":21710,"meta":21711,"navigation":178,"path":21712,"pinned":174,"seo":21713,"series":181,"seriesOrder":181,"sitemap":21714,"stem":21715,"tags":181,"__hash__":21716},"blog\u002Fblog\u002F進階控制制制制.md","Motor Control（六）",{"type":9,"value":21510,"toc":21707},[21511,21526,21541,21546,21558,21561,21566,21578,21584,21611,21620,21623,21650,21653,21656,21662,21667,21670,21675,21681,21687,21692,21698,21704],[12,21512,21513,21514,21516,21517,21519,21520,21522,21523,21525],{},"關於在我們動作產生到完成時 我們的大腦一定不是空的 ",[83,21515],{},"\n而是聚焦在這三點",[83,21518],{},"\n訊息理論 ",[83,21521],{},"\n反應時間 ",[83,21524],{},"\n閉鎖式回路與開放式回路",[12,21527,21528,21529,21531,21532,21534,21535,21537,21538,21540],{},"首先來講訊息理論 由一個荷蘭人提出",[83,21530],{},"\n他說我們在做動作時會經歷這三個階段",[83,21533],{},"\n認明刺激(Stimulus Identification)",[83,21536],{},"\n反應選擇(Response Selection) ",[83,21539],{},"\n反應程式組合(Response Programming)",[12,21542,21543],{},[979,21544],{"alt":1236,"src":21545},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773990603831-Screenshot_2026-03-20_150938.png",[12,21547,21548,21549,21551,21552,21554,21555,21557],{},"其實內容與第一~三堂講的內容相似",[83,21550],{},"\n認明刺激就是認知在對知覺加工的過程",[83,21553],{},"\n反應選擇就是認知",[83,21556],{},"\n反應程式組合就是生成整套動作的內容 例如拿起前方50cm杯子 要身體前彎 伸出手 張開手 握住杯 拿回來",[12,21559,21560],{},"而反應時間就是知覺偵測到開始變成認知再產生動作產生的過程",[12,21562,21563],{},[979,21564],{"alt":1236,"src":21565},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773991127457-Screenshot_2026-03-20_151747.png",[12,21567,21568,21569,21571,21572,21574,21575,21577],{},"賽車的五盞紅燈亮起來是預警期 ",[83,21570],{},"\n轉綠燈再到你開始踩油門的瞬間 這麼短的過程就是反應時間",[83,21573],{},"\n動作時間就是你開始踩到真踩到油門的時長",[83,21576],{},"\n而回應時間就是將反應時間和動作時間加在一起",[12,21579,21580,21581,21583],{},"這種反應時間會因為知覺認知配對的組合增加而變長 且呈線性增長 這就是亥可定律",[83,21582],{},"\n給你個例子 講出以下顏色",[12,21585,21586,21590,21591,21595,21596,21601,21602,21595,21607],{},[254,21587,21589],{"className":21588},[16852],"紅","                      ",[254,21592,21594],{"className":21593},[258],"黃","                       ",[254,21597,21600],{"className":21598},[21599],"purple-3","藍","                        ",[254,21603,21606],{"className":21604},[21605],"yellow-1","紫",[254,21608,21610],{"className":21609},[10079],"綠",[12,21612,21613,21614,21616,21617,21619],{},"這種就是比較典型的反應時間會增",[83,21615],{},"\n原因為是因為刺激與反應配對數目增加",[83,21618],{},"\n(代表知覺被觸發到認知的辨認結束 因為不是很直覺得辨認需要被拖長而理解)",[12,21621,21622],{},"但是這不符合亥可定律",[12,21624,21625,21628,21590,21631,21634,21601,21637,21640,21643,21644,21643,21647],{},[254,21626,21589],{"className":21627},[258],[254,21629,169],{"className":21630},[16852],[254,21632,21594],{"className":21633},[21605],[254,21635,169],{"className":21636},[258],[254,21638,21600],{"className":21639},[10079],[254,21641,169],{"className":21642},[21599],"                         ",[254,21645,21606],{"className":21646},[21599],[254,21648,21610],{"className":21649},[264],[12,21651,21652],{},"因為他並沒有讓配對組合增加(沒有反直覺)",[12,21654,21655],{},"而最後就是閉鎖式跟開放式回路的對比",[12,21657,21658,21659,21661],{},"先來講閉鎖式的回路",[83,21660],{},"\n簡單來說就是在持續的動作中不斷回傳讓自己可以持續調整",[12,21663,21664],{},[979,21665],{"alt":1236,"src":21666},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773992386445-Screenshot_2026-03-20_153850.png",[12,21668,21669],{},"而我們PT可以在這時給予例如像口頭的回饋給病人聽讓他改進動作內容",[12,21671,21672],{},[979,21673],{"alt":1236,"src":21674},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773992691800-Screenshot_2026-03-20_154139.png",[12,21676,21677,21678,21680],{},"到了開放式回路",[83,21679],{},"\n就是讓整套動作做完結束之後才得到回饋 與閉鏈式相比無法在得知事情結束前更改",[12,21682,21683,21684,21686],{},"但開放式回路卻有一種叫做輸出副本的東西",[83,21685],{},"\n他可以在認知將想做的傳達到給動作前一刻 先傳回去給腦子 讓我們有個預期可以會變成怎樣",[12,21688,21689],{},[979,21690],{"alt":1236,"src":21691},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1773993075653-Screenshot_2026-03-20_155057.png",[12,21693,21694,21695,21697],{},"再申 這個輸出副本只是在腦子裡有個模擬事情會怎樣過程怎樣完成",[83,21696],{},"\n而與閉鎖式回饋不同是在動作進行中持續調整修改",[12,21699,21700,21701,21703],{},"很好 這麼多才16頁內容 ",[83,21702],{},"\n卒",[12,21705,21706],{},"歡迎大佬補充糾正",{"title":169,"searchDepth":170,"depth":170,"links":21708},[],"以達進階 小心食用 噎到不會幫你叫救護車","\u002Fimages\u002Fuploads\u002F1773993528425-77896396_p0_master1200.jpg",{},"\u002Fblog\u002F進階控制制制制",{"title":21508,"description":21709},{"loc":21712},"blog\u002F進階控制制制制","4l_X7jv7IMLIi-2lqyDUlDzieoP36ARTVg3EsYZS0Wo",{"id":21718,"title":21719,"author":21720,"body":21721,"date":21743,"description":21744,"draft":174,"edited_at":21743,"extension":175,"featured_image":21745,"meta":21746,"navigation":178,"path":21747,"pinned":174,"seo":21748,"series":181,"seriesOrder":181,"sitemap":21749,"stem":21750,"tags":181,"__hash__":21751},"blog\u002Fblog\u002F一隻小花妖.md","一隻小花妖","花夜",{"type":9,"value":21722,"toc":21741},[21723,21726,21729,21732,21735,21738],[12,21724,21725],{},"啊......已經開始了嗎?",[12,21727,21728],{},"大家好我是花夜，是一隻小花妖，已成功地融入現代社會之中，或許某一天你們能在街頭的某個角落看到我?",[12,21730,21731],{},"喜歡的東西有點多，例如電動、漫畫、動畫、歷史等等，涉獵範圍廣但不深，拜託了不要嗆我我只是一個小菜雞｡ﾟヽ(ﾟ´Д`)ﾉﾟ｡",[12,21733,21734],{},"順帶一提，本人是遊戲王愛好者，之後會在這裡做各種雜七雜八的遊戲王OCG介紹，歡迎大家一起討論",[12,21736,21737],{},"無論你們身在何處，我永遠在這裡靜候你們的到來",[12,21739,21740],{},"寫這篇的時候眼睛受傷，盯著螢幕好不舒服，祝你們一輩子健康無慮",{"title":169,"searchDepth":170,"depth":170,"links":21742},[],"2026-03-05","讓你們淺淺的認識我","\u002Fimages\u002Fuploads\u002F1772722320083-791_20260218161129.png",{},"\u002Fblog\u002F一隻小花妖",{"title":21719,"description":21744},{"loc":21747},"blog\u002F一隻小花妖","9Ujqk6jczQOVHug_pVFEuWzMY7Q6weFqUWnBrga_6QI",{"id":21753,"title":21754,"author":761,"body":21755,"date":22627,"description":22628,"draft":174,"edited_at":181,"extension":175,"featured_image":22629,"meta":22630,"navigation":178,"path":22631,"pinned":174,"seo":22632,"series":181,"seriesOrder":181,"sitemap":22633,"stem":22634,"tags":181,"__hash__":22635},"blog\u002Fblog\u002F紀錄一次Discord機器人的開發過程.md","紀錄一次Discord機器人的開發過程",{"type":9,"value":21756,"toc":22622},[21757,21764,21767,21770,21777,21786,21790,21793,21823,21826,21846,21850,21856,21873,21876,21880,21883,21890,21898,21901,21904,21909,21920,21929,22607,22610,22616,22619],[21758,21759,21761],"h6",{"id":21760},"每次都要找些好看的封面圖還挺麻煩的就當是美圖分享吧",[2948,21762,21763],{},"每次都要找些好看的封面圖還挺麻煩的，就當是美圖分享吧",[12,21765,21766],{},"最近假期在家真的閒到發慌。家裡管得嚴，加上妹妹正在準備升學考試，為了不吵到她，我在家也不太好意思一直打遊戲。結果呢，唯一的娛樂活動反而變成了寫程式~~（蛤~~",[12,21768,21769],{},"剛好，把我這個小破站翻新完之後，突然覺得有點空虛，沒有什麼別的事要做了。於是，在發呆了一下午之後還是決定：不如再來試著重新寫一次 Discord 音樂機器人好了。",[12,21771,21772,21773,21776],{},"寫音樂機器人這件事我在中學時就做過一次了。當時花了我好幾個月的時間，寫了一個能24\u002F7在線的音樂機器人。",[2948,21774,21775],{},"至今還記得音樂開始播放的時候有多興奮","。所以這一次不是簡單的做一個會播歌機器人就好，那也太無聊了。我想要來寫點好玩的：給我的機器人加一個可以互動的網頁介面。",[832,21778,21780],{"className":21779},[825,15480],[12,21781,21782,21783],{},"請注意：這篇不是那種按部就班的「保姆級教學文」喔...我只想在這裡紀錄開發歷程，並且盡我所能解釋其背後的工作原理。",[2948,21784,21785],{},"想找教程可以出門左轉去谷歌上找(x",[765,21787,21789],{"id":21788},"_1-介紹","1. 介紹",[12,21791,21792],{},"如果你在 2026 年還想弄一個能在 Discord 語音頻道裡播歌的機器人，查完資料你就會發現，這是一件苦差事。",[12,21794,21795,21796,21806,21807,21814,21815,21822],{},"自從 Groovy 和 Rythm 在 2021 年被 YouTube 官方強制下線後，開發音樂機器人就成了一場開發者與YouTube 的軍備競賽。以前方便好用的 ",[773,21797,21798,21805],{},[49,21799,21802],{"href":21800,"rel":21801},"https:\u002F\u002Fgithub.com\u002Ffent\u002Fnode-ytdl-core",[53],[9059,21803,21804],{},"node-ytdl-core","在2024年就掛掉了","，而其他的替代品 ：",[49,21808,21811],{"href":21809,"rel":21810},"https:\u002F\u002Fgithub.com\u002Fplay-dl\u002Fplay-dl",[53],[9059,21812,21813],{},"play-dl","和",[49,21816,21819],{"href":21817,"rel":21818},"https:\u002F\u002Fgithub.com\u002Fdistubejs\u002Fytdl-core",[53],[9059,21820,21821],{},"ytdl-core","也紛紛停止開發了。",[12,21824,21825],{},"想用以前的老套路，硬找個還活著的 package 來下載 YouTube 音源再塞給 Discord，你會遇到一堆問題：",[77,21827,21828,21834,21840],{},[19,21829,21830,21833],{},[773,21831,21832],{},"極度脆弱："," YouTube 現在會主動打擊爬蟲。他們會頻繁更改客戶端、加密演算法，甚至對資料中心的 IP 進行嚴格的限流。這意味著機器人可能昨天還好好的，今天早上起來就滿地報錯。",[19,21835,21836,21839],{},[773,21837,21838],{},"效能問題："," Node.js 是一個單執行緒（Single-threaded）的執行環境，不是設計來做繁重媒體處理的。讓它一邊下載音訊、解碼，還要重新編碼並即時推送到 Discord，只要同時服務幾個不同的伺服器，CPU 就要撐不住開始哀嚎了。",[19,21841,21842,21845],{},[773,21843,21844],{},"職責過載："," 機器人要負責監聽 Discord 訊息事件、爬取 YouTube、處理音軌，還要維持語音頻道的串流。只要其中一個環節崩潰，整個機器人就會直接斷線，聽歌聽到一半的朋友大概會氣死。",[765,21847,21849],{"id":21848},"_2-lavalink","2. Lavalink",[12,21851,21852,21853],{},"如果 Node.js 處理音訊這麼痛苦，那答案很簡單：",[773,21854,21855],{},"不要讓你的機器人碰音訊。",[12,21857,21858,21859,21868,21869,21872],{},"解決這個問題的其中一個方法就是使用 ",[773,21860,21861],{},[49,21862,21865],{"href":21863,"rel":21864},"https:\u002F\u002Fgithub.com\u002Flavalink-devs\u002FLavalink",[53],[9059,21866,21867],{},"Lavalink","。它是一個專門為 Discord 機器人打造的獨立 Java 音訊伺服器。機器人只負責接收使用者的指令（例如 ",[9059,21870,21871],{},"\u002Fplay","），Lavalink 則扛下所有髒活：解析 YouTube 網址、繞過限制、解碼音訊，並直接把串流送到 Discord 的語音頻道裡。兩者之間只透過 WebSocket 和 REST API 進行溝通。",[12,21874,21875],{},"這樣一來，如果機器人因為某些 Bug 當機重啟了，Lavalink 依然會在背景繼續播歌，完全不影響正在聽音樂的使用者。",[765,21877,21879],{"id":21878},"_3-代碼結構","3. 代碼結構",[12,21881,21882],{},"所以說了這麼多，機器人應該長什麼樣？",[12,21884,21885,21886,21889],{},"我這裡選用的是 ",[773,21887,21888],{},"Deno + Svelte + Lavalink"," 的組合。整個專案包含了三個伺服器，資料夾結構大概長這樣：",[21891,21892,21896],"pre",{"className":21893,"code":21895,"language":2845},[21894],"language-text","Music-bot\u002F\n├── deno.json                  # 配置文件\n├── .gitignore\n├── bot-backend\u002F               # 機器人本體\n│   ├── main.ts                \n│   ├── deploy-commands.ts     \n│   └── .env\n├── lavalink-engine\u002F           # Lavalink\n│   ├── Lavalink.jar           \n│   ├── application.yml        \n│   └── plugins\u002F               \n└── web-dashboard\u002F             # SvelteKit 網頁前端\n",[9059,21897,21895],{"__ignoreMap":169},[12,21899,21900],{},"這個專案裡包含了三個伺服器：網頁後端，Lavalink伺服器和機器人。",[12,21902,21903],{},"運行邏輯大約是這樣的：",[12,21905,21906],{},[979,21907],{"alt":1236,"src":21908},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1771778271569-Screenshot_2026-02-23_at_12.36.38_AM.png",[12,21910,21911,21912,21915,21916,21919],{},"機器人代碼意外的非常簡單。只需要用到 ",[9059,21913,21914],{},"Shoukaku","（負責跟 Lavalink 溝通）和 ",[9059,21917,21918],{},"discord.js","（負責跟 Discord 溝通），就可以開始動工了。",[12,21921,21922,21923,15799,21925,21928],{},"一個最基本~~（陽春）~~的機器人代碼（只有",[9059,21924,21871],{},[9059,21926,21927],{},"\u002Fstop","指令）：",[21891,21930,21934],{"className":21931,"code":21932,"language":21933,"meta":169,"style":169},"language-JavaScript shiki shiki-themes github-light github-dark","import {\n  Client,\n  GatewayIntentBits,\n  type ChatInputCommandInteraction,\n} from \"discord.js\";\nimport { Shoukaku, Connectors, LoadType } from \"shoukaku\";\nimport \"@std\u002Fdotenv\u002Fload\";\n\nconst client = new Client({\n  intents: [\n    GatewayIntentBits.Guilds,\n    GatewayIntentBits.GuildVoiceStates,\n  ],\n});\n\n\u002F\u002F Shoukaku 初始化\n\nconst nodes = [\n  {\n    name: \"main\",\n    url: `${Deno.env.get(\"LAVALINK_HOST\")}:${Deno.env.get(\"LAVALINK_PORT\")}`,\n    auth: Deno.env.get(\"LAVALINK_PASSWORD\")!,\n  },\n];\n\nconst shoukaku = new Shoukaku(new Connectors.DiscordJS(client), nodes, {\n  reconnectTries: 10,\n  reconnectInterval: 3000,\n});\n\nshoukaku.on(\"error\", (_, error) => console.error(\"Shoukaku error:\", error));\nshoukaku.on(\"ready\", (name) => console.log(`Lavalink node \"${name}\" connected`));\nshoukaku.on(\"disconnect\", (name, reason) =>\n  console.warn(`Lavalink node \"${name}\" disconnected — ${reason ?? \"unknown reason\"}. Reconnecting...`)\n);\n\n\u002F\u002F ====================\n\nclient.once(\"clientReady\", () => {\n  console.log(`Logged in as ${client.user?.tag}`);\n});\n\nclient.on(\"interactionCreate\", async (interaction) => {\n  if (!interaction.isChatInputCommand()) return;\n\n  switch (interaction.commandName) {\n    case \"play\":\n      await handlePlay(interaction);\n      break;\n    case \"stop\":\n      await handleStop(interaction);\n      break;\n  }\n});\n\nasync function handlePlay(interaction: ChatInputCommandInteraction) {\n  const member = await interaction.guild?.members.fetch(interaction.user.id);\n  const voiceChannel = member?.voice.channel;\n\n  if (!voiceChannel) {\n    await interaction.reply({\n      content: \"需要加入語音頻道才能播放音樂。\",\n      ephemeral: true,\n    });\n    return;\n  }\n\n  await interaction.deferReply();\n\n  const query = interaction.options.getString(\"query\", true);\n  const node = shoukaku.options.nodeResolver(shoukaku.nodes);\n\n  if (!node) {\n    await interaction.editReply(\"找不到Lavalink節點。\");\n    return;\n  }\n\n  const isUrl = query.startsWith(\"http:\u002F\u002F\") || query.startsWith(\"https:\u002F\u002F\");\n  const result = await node.rest.resolve(isUrl ? query : `ytsearch:${query}`);\n\n  if (!result || result.loadType === LoadType.EMPTY || result.loadType === LoadType.ERROR) {\n    await interaction.editReply(\"找不到任何結果。\");\n    return;\n  }\n\n  const track = result.loadType === LoadType.SEARCH || result.loadType === LoadType.PLAYLIST\n    ? result.data[0]\n    : result.data;\n\n  let player = shoukaku.players.get(interaction.guildId!);\n  if (!player) {\n    player = await shoukaku.joinVoiceChannel({\n      guildId: interaction.guildId!,\n      channelId: voiceChannel.id,\n      shardId: 0,\n    });\n  }\n\n  await player.playTrack({ track: { encoded: track.encoded } });\n\n  await interaction.editReply(`Now playing: **${track.info.title}**`);\n}\n\nasync function handleStop(interaction: ChatInputCommandInteraction) {\n  const player = shoukaku.players.get(interaction.guildId!);\n\n  if (!player) {\n    await interaction.reply({\n      content: \"目前沒有播放音樂。\",\n      ephemeral: true,\n    });\n    return;\n  }\n\n  await shoukaku.leaveVoiceChannel(interaction.guildId!);\n  await interaction.reply(\"停止播放並退出語音頻道。\");\n}\n\nclient.login(Deno.env.get(\"DISCORD_TOKEN\"));\n","JavaScript",[9059,21935,21936,21943,21948,21953,21959,21965,21971,21977,21983,21989,21995,22001,22007,22013,22019,22024,22030,22035,22041,22047,22053,22059,22065,22071,22077,22082,22088,22094,22100,22105,22110,22116,22122,22128,22134,22140,22145,22151,22156,22162,22168,22173,22178,22184,22190,22195,22201,22207,22213,22219,22225,22231,22236,22242,22247,22252,22258,22264,22270,22275,22280,22286,22292,22298,22304,22310,22315,22320,22326,22331,22337,22343,22348,22354,22360,22365,22370,22375,22381,22387,22392,22398,22404,22409,22414,22419,22425,22431,22437,22442,22448,22454,22460,22466,22472,22478,22483,22488,22493,22499,22504,22510,22516,22521,22527,22533,22538,22543,22548,22554,22559,22564,22569,22574,22579,22585,22591,22596,22601],{"__ignoreMap":169},[254,21937,21940],{"class":21938,"line":21939},"line",1,[254,21941,21942],{},"import {\n",[254,21944,21945],{"class":21938,"line":170},[254,21946,21947],{},"  Client,\n",[254,21949,21950],{"class":21938,"line":7336},[254,21951,21952],{},"  GatewayIntentBits,\n",[254,21954,21956],{"class":21938,"line":21955},4,[254,21957,21958],{},"  type ChatInputCommandInteraction,\n",[254,21960,21962],{"class":21938,"line":21961},5,[254,21963,21964],{},"} from \"discord.js\";\n",[254,21966,21968],{"class":21938,"line":21967},6,[254,21969,21970],{},"import { Shoukaku, Connectors, LoadType } from \"shoukaku\";\n",[254,21972,21974],{"class":21938,"line":21973},7,[254,21975,21976],{},"import \"@std\u002Fdotenv\u002Fload\";\n",[254,21978,21980],{"class":21938,"line":21979},8,[254,21981,21982],{"emptyLinePlaceholder":178},"\n",[254,21984,21986],{"class":21938,"line":21985},9,[254,21987,21988],{},"const client = new Client({\n",[254,21990,21992],{"class":21938,"line":21991},10,[254,21993,21994],{},"  intents: [\n",[254,21996,21998],{"class":21938,"line":21997},11,[254,21999,22000],{},"    GatewayIntentBits.Guilds,\n",[254,22002,22004],{"class":21938,"line":22003},12,[254,22005,22006],{},"    GatewayIntentBits.GuildVoiceStates,\n",[254,22008,22010],{"class":21938,"line":22009},13,[254,22011,22012],{},"  ],\n",[254,22014,22016],{"class":21938,"line":22015},14,[254,22017,22018],{},"});\n",[254,22020,22022],{"class":21938,"line":22021},15,[254,22023,21982],{"emptyLinePlaceholder":178},[254,22025,22027],{"class":21938,"line":22026},16,[254,22028,22029],{},"\u002F\u002F Shoukaku 初始化\n",[254,22031,22033],{"class":21938,"line":22032},17,[254,22034,21982],{"emptyLinePlaceholder":178},[254,22036,22038],{"class":21938,"line":22037},18,[254,22039,22040],{},"const nodes = [\n",[254,22042,22044],{"class":21938,"line":22043},19,[254,22045,22046],{},"  {\n",[254,22048,22050],{"class":21938,"line":22049},20,[254,22051,22052],{},"    name: \"main\",\n",[254,22054,22056],{"class":21938,"line":22055},21,[254,22057,22058],{},"    url: `${Deno.env.get(\"LAVALINK_HOST\")}:${Deno.env.get(\"LAVALINK_PORT\")}`,\n",[254,22060,22062],{"class":21938,"line":22061},22,[254,22063,22064],{},"    auth: Deno.env.get(\"LAVALINK_PASSWORD\")!,\n",[254,22066,22068],{"class":21938,"line":22067},23,[254,22069,22070],{},"  },\n",[254,22072,22074],{"class":21938,"line":22073},24,[254,22075,22076],{},"];\n",[254,22078,22080],{"class":21938,"line":22079},25,[254,22081,21982],{"emptyLinePlaceholder":178},[254,22083,22085],{"class":21938,"line":22084},26,[254,22086,22087],{},"const shoukaku = new Shoukaku(new Connectors.DiscordJS(client), nodes, {\n",[254,22089,22091],{"class":21938,"line":22090},27,[254,22092,22093],{},"  reconnectTries: 10,\n",[254,22095,22097],{"class":21938,"line":22096},28,[254,22098,22099],{},"  reconnectInterval: 3000,\n",[254,22101,22103],{"class":21938,"line":22102},29,[254,22104,22018],{},[254,22106,22108],{"class":21938,"line":22107},30,[254,22109,21982],{"emptyLinePlaceholder":178},[254,22111,22113],{"class":21938,"line":22112},31,[254,22114,22115],{},"shoukaku.on(\"error\", (_, error) => console.error(\"Shoukaku error:\", error));\n",[254,22117,22119],{"class":21938,"line":22118},32,[254,22120,22121],{},"shoukaku.on(\"ready\", (name) => console.log(`Lavalink node \"${name}\" connected`));\n",[254,22123,22125],{"class":21938,"line":22124},33,[254,22126,22127],{},"shoukaku.on(\"disconnect\", (name, reason) =>\n",[254,22129,22131],{"class":21938,"line":22130},34,[254,22132,22133],{},"  console.warn(`Lavalink node \"${name}\" disconnected — ${reason ?? \"unknown reason\"}. Reconnecting...`)\n",[254,22135,22137],{"class":21938,"line":22136},35,[254,22138,22139],{},");\n",[254,22141,22143],{"class":21938,"line":22142},36,[254,22144,21982],{"emptyLinePlaceholder":178},[254,22146,22148],{"class":21938,"line":22147},37,[254,22149,22150],{},"\u002F\u002F ====================\n",[254,22152,22154],{"class":21938,"line":22153},38,[254,22155,21982],{"emptyLinePlaceholder":178},[254,22157,22159],{"class":21938,"line":22158},39,[254,22160,22161],{},"client.once(\"clientReady\", () => {\n",[254,22163,22165],{"class":21938,"line":22164},40,[254,22166,22167],{},"  console.log(`Logged in as ${client.user?.tag}`);\n",[254,22169,22171],{"class":21938,"line":22170},41,[254,22172,22018],{},[254,22174,22176],{"class":21938,"line":22175},42,[254,22177,21982],{"emptyLinePlaceholder":178},[254,22179,22181],{"class":21938,"line":22180},43,[254,22182,22183],{},"client.on(\"interactionCreate\", async (interaction) => {\n",[254,22185,22187],{"class":21938,"line":22186},44,[254,22188,22189],{},"  if (!interaction.isChatInputCommand()) return;\n",[254,22191,22193],{"class":21938,"line":22192},45,[254,22194,21982],{"emptyLinePlaceholder":178},[254,22196,22198],{"class":21938,"line":22197},46,[254,22199,22200],{},"  switch (interaction.commandName) {\n",[254,22202,22204],{"class":21938,"line":22203},47,[254,22205,22206],{},"    case \"play\":\n",[254,22208,22210],{"class":21938,"line":22209},48,[254,22211,22212],{},"      await handlePlay(interaction);\n",[254,22214,22216],{"class":21938,"line":22215},49,[254,22217,22218],{},"      break;\n",[254,22220,22222],{"class":21938,"line":22221},50,[254,22223,22224],{},"    case \"stop\":\n",[254,22226,22228],{"class":21938,"line":22227},51,[254,22229,22230],{},"      await handleStop(interaction);\n",[254,22232,22234],{"class":21938,"line":22233},52,[254,22235,22218],{},[254,22237,22239],{"class":21938,"line":22238},53,[254,22240,22241],{},"  }\n",[254,22243,22245],{"class":21938,"line":22244},54,[254,22246,22018],{},[254,22248,22250],{"class":21938,"line":22249},55,[254,22251,21982],{"emptyLinePlaceholder":178},[254,22253,22255],{"class":21938,"line":22254},56,[254,22256,22257],{},"async function handlePlay(interaction: ChatInputCommandInteraction) {\n",[254,22259,22261],{"class":21938,"line":22260},57,[254,22262,22263],{},"  const member = await interaction.guild?.members.fetch(interaction.user.id);\n",[254,22265,22267],{"class":21938,"line":22266},58,[254,22268,22269],{},"  const voiceChannel = member?.voice.channel;\n",[254,22271,22273],{"class":21938,"line":22272},59,[254,22274,21982],{"emptyLinePlaceholder":178},[254,22276,22277],{"class":21938,"line":2013},[254,22278,22279],{},"  if (!voiceChannel) {\n",[254,22281,22283],{"class":21938,"line":22282},61,[254,22284,22285],{},"    await interaction.reply({\n",[254,22287,22289],{"class":21938,"line":22288},62,[254,22290,22291],{},"      content: \"需要加入語音頻道才能播放音樂。\",\n",[254,22293,22295],{"class":21938,"line":22294},63,[254,22296,22297],{},"      ephemeral: true,\n",[254,22299,22301],{"class":21938,"line":22300},64,[254,22302,22303],{},"    });\n",[254,22305,22307],{"class":21938,"line":22306},65,[254,22308,22309],{},"    return;\n",[254,22311,22313],{"class":21938,"line":22312},66,[254,22314,22241],{},[254,22316,22318],{"class":21938,"line":22317},67,[254,22319,21982],{"emptyLinePlaceholder":178},[254,22321,22323],{"class":21938,"line":22322},68,[254,22324,22325],{},"  await interaction.deferReply();\n",[254,22327,22329],{"class":21938,"line":22328},69,[254,22330,21982],{"emptyLinePlaceholder":178},[254,22332,22334],{"class":21938,"line":22333},70,[254,22335,22336],{},"  const query = interaction.options.getString(\"query\", true);\n",[254,22338,22340],{"class":21938,"line":22339},71,[254,22341,22342],{},"  const node = shoukaku.options.nodeResolver(shoukaku.nodes);\n",[254,22344,22346],{"class":21938,"line":22345},72,[254,22347,21982],{"emptyLinePlaceholder":178},[254,22349,22351],{"class":21938,"line":22350},73,[254,22352,22353],{},"  if (!node) {\n",[254,22355,22357],{"class":21938,"line":22356},74,[254,22358,22359],{},"    await interaction.editReply(\"找不到Lavalink節點。\");\n",[254,22361,22363],{"class":21938,"line":22362},75,[254,22364,22309],{},[254,22366,22368],{"class":21938,"line":22367},76,[254,22369,22241],{},[254,22371,22373],{"class":21938,"line":22372},77,[254,22374,21982],{"emptyLinePlaceholder":178},[254,22376,22378],{"class":21938,"line":22377},78,[254,22379,22380],{},"  const isUrl = query.startsWith(\"http:\u002F\u002F\") || query.startsWith(\"https:\u002F\u002F\");\n",[254,22382,22384],{"class":21938,"line":22383},79,[254,22385,22386],{},"  const result = await node.rest.resolve(isUrl ? query : `ytsearch:${query}`);\n",[254,22388,22390],{"class":21938,"line":22389},80,[254,22391,21982],{"emptyLinePlaceholder":178},[254,22393,22395],{"class":21938,"line":22394},81,[254,22396,22397],{},"  if (!result || result.loadType === LoadType.EMPTY || result.loadType === LoadType.ERROR) {\n",[254,22399,22401],{"class":21938,"line":22400},82,[254,22402,22403],{},"    await interaction.editReply(\"找不到任何結果。\");\n",[254,22405,22407],{"class":21938,"line":22406},83,[254,22408,22309],{},[254,22410,22412],{"class":21938,"line":22411},84,[254,22413,22241],{},[254,22415,22417],{"class":21938,"line":22416},85,[254,22418,21982],{"emptyLinePlaceholder":178},[254,22420,22422],{"class":21938,"line":22421},86,[254,22423,22424],{},"  const track = result.loadType === LoadType.SEARCH || result.loadType === LoadType.PLAYLIST\n",[254,22426,22428],{"class":21938,"line":22427},87,[254,22429,22430],{},"    ? result.data[0]\n",[254,22432,22434],{"class":21938,"line":22433},88,[254,22435,22436],{},"    : result.data;\n",[254,22438,22440],{"class":21938,"line":22439},89,[254,22441,21982],{"emptyLinePlaceholder":178},[254,22443,22445],{"class":21938,"line":22444},90,[254,22446,22447],{},"  let player = shoukaku.players.get(interaction.guildId!);\n",[254,22449,22451],{"class":21938,"line":22450},91,[254,22452,22453],{},"  if (!player) {\n",[254,22455,22457],{"class":21938,"line":22456},92,[254,22458,22459],{},"    player = await shoukaku.joinVoiceChannel({\n",[254,22461,22463],{"class":21938,"line":22462},93,[254,22464,22465],{},"      guildId: interaction.guildId!,\n",[254,22467,22469],{"class":21938,"line":22468},94,[254,22470,22471],{},"      channelId: voiceChannel.id,\n",[254,22473,22475],{"class":21938,"line":22474},95,[254,22476,22477],{},"      shardId: 0,\n",[254,22479,22481],{"class":21938,"line":22480},96,[254,22482,22303],{},[254,22484,22486],{"class":21938,"line":22485},97,[254,22487,22241],{},[254,22489,22491],{"class":21938,"line":22490},98,[254,22492,21982],{"emptyLinePlaceholder":178},[254,22494,22496],{"class":21938,"line":22495},99,[254,22497,22498],{},"  await player.playTrack({ track: { encoded: track.encoded } });\n",[254,22500,22502],{"class":21938,"line":22501},100,[254,22503,21982],{"emptyLinePlaceholder":178},[254,22505,22507],{"class":21938,"line":22506},101,[254,22508,22509],{},"  await interaction.editReply(`Now playing: **${track.info.title}**`);\n",[254,22511,22513],{"class":21938,"line":22512},102,[254,22514,22515],{},"}\n",[254,22517,22519],{"class":21938,"line":22518},103,[254,22520,21982],{"emptyLinePlaceholder":178},[254,22522,22524],{"class":21938,"line":22523},104,[254,22525,22526],{},"async function handleStop(interaction: ChatInputCommandInteraction) {\n",[254,22528,22530],{"class":21938,"line":22529},105,[254,22531,22532],{},"  const player = shoukaku.players.get(interaction.guildId!);\n",[254,22534,22536],{"class":21938,"line":22535},106,[254,22537,21982],{"emptyLinePlaceholder":178},[254,22539,22541],{"class":21938,"line":22540},107,[254,22542,22453],{},[254,22544,22546],{"class":21938,"line":22545},108,[254,22547,22285],{},[254,22549,22551],{"class":21938,"line":22550},109,[254,22552,22553],{},"      content: \"目前沒有播放音樂。\",\n",[254,22555,22557],{"class":21938,"line":22556},110,[254,22558,22297],{},[254,22560,22562],{"class":21938,"line":22561},111,[254,22563,22303],{},[254,22565,22567],{"class":21938,"line":22566},112,[254,22568,22309],{},[254,22570,22572],{"class":21938,"line":22571},113,[254,22573,22241],{},[254,22575,22577],{"class":21938,"line":22576},114,[254,22578,21982],{"emptyLinePlaceholder":178},[254,22580,22582],{"class":21938,"line":22581},115,[254,22583,22584],{},"  await shoukaku.leaveVoiceChannel(interaction.guildId!);\n",[254,22586,22588],{"class":21938,"line":22587},116,[254,22589,22590],{},"  await interaction.reply(\"停止播放並退出語音頻道。\");\n",[254,22592,22594],{"class":21938,"line":22593},117,[254,22595,22515],{},[254,22597,22599],{"class":21938,"line":22598},118,[254,22600,21982],{"emptyLinePlaceholder":178},[254,22602,22604],{"class":21938,"line":22603},119,[254,22605,22606],{},"client.login(Deno.env.get(\"DISCORD_TOKEN\"));\n",[12,22608,22609],{},"如你所見，複雜的處理音頻 \u002F 連接語音頻道代碼都被外包給了 Shoukaku 和 Lavalink。整個機器人的代碼非常簡潔，只有一百多行。當然，這仍不包含更複雜的其他音樂控制指令。但是，有了這個基本框架，想要繼續擴展控制指令就很方便了。",[12,22611,22612,22613],{},"而關於網頁控制頁面，目前我也還沒有開發完成前端，也不知道具體會長什麼樣。",[2948,22614,22615],{},"不如就把它留到下一篇文章再聊吧（挖坑",[12,22617,22618],{},"感謝你看到這裡！趁著假期我想多用部落格練練手，多寫點文章紀錄學習過程，順便練習一下如何把問題給講解清楚。如果你有任何問題，或者是文中有出錯的地方，都歡迎留言告訴我！",[7328,22620,22621],{},"html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":169,"searchDepth":170,"depth":170,"links":22623},[22624,22625,22626],{"id":21788,"depth":170,"text":21789},{"id":21848,"depth":170,"text":21849},{"id":21878,"depth":170,"text":21879},"2026-02-22","閒著沒事幹當作練習～","\u002Fimages\u002Fuploads\u002F1771752251524-108199050_p0.jpg",{},"\u002Fblog\u002F紀錄一次Discord機器人的開發過程",{"title":21754,"description":22628},{"loc":22631},"blog\u002F紀錄一次Discord機器人的開發過程","qgEP2b9vyFHgKsiQba6oX2kd0qbGockMyyjkH61rHAk",{"id":22637,"title":22638,"author":761,"body":22639,"date":22627,"description":22853,"draft":174,"edited_at":22854,"extension":175,"featured_image":22855,"meta":22856,"navigation":178,"path":22857,"pinned":174,"seo":22858,"series":181,"seriesOrder":181,"sitemap":22859,"stem":22860,"tags":181,"__hash__":22861},"blog\u002Fblog\u002F紀錄一次Discord機器人的開發過程（2）.md","紀錄一次Discord機器人的開發過程（2）",{"type":9,"value":22640,"toc":22843},[22641,22646,22652,22655,22658,22661,22667,22670,22676,22679,22693,22702,22708,22711,22728,22734,22740,22743,22746,22754,22761,22767,22770,22773,22776,22782,22785,22788,22791,22798,22801,22804,22807,22810,22815,22818,22830,22833,22836],[21758,22642,22644],{"id":22643},"就說我很認真在選封面圖片嘛",[2948,22645,22643],{},[765,22647,22649],{"id":22648},"_4-網頁控制面板",[773,22650,22651],{},"4. 網頁控制面板",[12,22653,22654],{},"上一篇文章結尾我自己挖的坑：「網頁控制面板留到下一篇」，現在該來乖乖填坑了。",[12,22656,22657],{},"我想要做的很簡單：打開網頁，用 Discord 帳號登入，選一個機器人所在的伺服器，然後就可以在網頁上搜尋歌曲、暫停、跳過、查看播放佇列——所有你在 Discord 裡用斜槓指令能做的事，都能在網頁上完成，而且是即時同步的。",[12,22659,22660],{},"既然是自己做著好玩的專案，我索性選了個沒用過的新玩具：SvelteKit 來當前端框架，順便學點新東西。",[781,22662,22664],{"id":22663},"_41-sveltekit的路由",[773,22665,22666],{},"4.1 SvelteKit 的路由",[12,22668,22669],{},"SvelteKit 的路由系統挺好懂的，基本上就是資料夾長怎樣，網址就長怎樣。舉個例子：",[21891,22671,22674],{"className":22672,"code":22673,"language":2845},[21894],"src\u002Froutes\u002F\n├── +page.svelte                          → \u002F\n├── dashboard\u002F\n│   ├── +page.svelte                      → \u002Fdashboard\n│   └── [guildId]\u002F\n│       └── +page.svelte                  → \u002Fdashboard\u002Fabc123\n└── auth\u002F\n    ├── login\u002F+server.ts                  → \u002Fauth\u002Flogin\n    ├── callback\u002F+server.ts               → \u002Fauth\u002Fcallback\n    └── logout\u002F+server.ts                 → \u002Fauth\u002Flogout\n",[9059,22675,22673],{"__ignoreMap":169},[12,22677,22678],{},"每個路由可以有兩個搭檔文件：",[77,22680,22681,22687],{},[19,22682,22683,22686],{},[9059,22684,22685],{},"+page.server.ts","：在伺服器端執行，負責載入資料（例如查詢資料庫、呼叫 API）。它回傳的資料會自動傳給對應的 .svelte 頁面。",[19,22688,22689,22692],{},[9059,22690,22691],{},"+page.svelte","：在瀏覽器端渲染的 UI 元件，透過 $props() 就能拿到伺服器端載入的資料。",[12,22694,22695,22696,22701],{},"另外還有一種叫 ",[773,22697,22698],{},[9059,22699,22700],{},"+server.ts","，它不負責畫畫面，純粹用來處理後端的 API 請求。我們接下來要講的Discord 登入，就是靠它來搞定的。",[781,22703,22705],{"id":22704},"_42-discordoauth2-登入",[773,22706,22707],{},"4.2 Discord OAuth2 登入",[12,22709,22710],{},"要讓大家在網頁上控制機器人，第一步總得先知道「你是誰」對吧？這時候就遇到了第一個大難題：標準的 OAuth2 登入流程。聽起來好像很複雜，其實就是三步：",[16,22712,22713,22719,22725],{},[19,22714,22715,22718],{},[773,22716,22717],{},"點擊「用 Discord 登入」","，網頁把你重新導向到 Discord 的授權頁面，問你：「這個應用程式想看你的大頭貼和伺服器清單，可以嗎？」",[19,22720,22721,22724],{},[773,22722,22723],{},"使用者按下同意","，Discord 就會把你送回我的網站，並且在網址上塞給你一個「一次性授權碼」。",[19,22726,22727],{},"我的網頁後端拿到這個碼，跑去跟 Discord 換真正的「Access Token」，然後查出你的名字和頭像，最後發一個簽名過的 Cookie 給你，這樣就算登入成功啦！",[12,22729,22730,22731],{},"這裡所有的 Token 交換都發生在伺服器端，瀏覽器永遠不會碰到 Access Token。",[2948,22732,22733],{},"文檔看了好久才搞定這個破登入",[781,22735,22737],{"id":22736},"_43-伺服器選擇器",[773,22738,22739],{},"4.3 伺服器選擇器",[12,22741,22742],{},"登入之後，使用者會看到一個伺服器選擇頁面。但這裡有個問題：我總不能把你加入的所有私人伺服器都列出來吧？我只能顯示你跟機器人同時都在的伺服器。",[12,22744,22745],{},"所以載入這個頁面時，後端會做兩件事：",[16,22747,22748,22751],{},[19,22749,22750],{},"用你的的 Access Token 去問 Discord：「他加入了哪些伺服器？」",[19,22752,22753],{},"透過 WebSocket 去問機器人：「你現在在哪些伺服器裡？」",[12,22755,22756,22757,22760],{},"然後取兩個清單的",[773,22758,22759],{},"交集","——只顯示使用者和機器人同時都在的伺服器。點擊任意一個伺服器卡片，就會進入該伺服器的音樂控制頁面。",[781,22762,22764],{"id":22763},"_44-即時音樂控制",[773,22765,22766],{},"4.4 即時音樂控制",[12,22768,22769],{},"這才是整個網頁面板最好玩的部分。",[12,22771,22772],{},"進入控制頁面之後，頁面會直接從瀏覽器跟機器人的 WebSocket 伺服器建立連線，並且「訂閱」這個伺服器的狀態更新。一旦訂閱成功，機器人就會把當前的播放狀態推送過來：正在播什麼歌、佇列裡有什麼、有沒有暫停、播到哪了。",[12,22774,22775],{},"之後，不管狀態怎麼變化——不管是有人在 Discord 裡打了 \u002Fskip，還是有人在網頁上按了暫停，機器人都會把最新的狀態推送給所有訂閱了這個伺服器的瀏覽器。",[781,22777,22779],{"id":22778},"_45-事件匯流排event-bus",[773,22780,22781],{},"4.5 事件匯流排（Event Bus）",[12,22783,22784],{},"那怎麼讓 Discord 指令和網頁控制互相同步？",[12,22786,22787],{},"舉個例子：我在 Discord 打了 \u002Fpause，網頁上的暫停按鈕也應該要跟著變。反過來，我在網頁上按了跳過，Discord 裡的播放佇列也要跟著更新。",[12,22789,22790],{},"我一開始忘了處理這個同步問題，導致在 Discord 裡暫停音樂後，網頁完全沒反應——因為斜槓指令只是直接操作了播放器，沒有通知任何人「我改了狀態」。",[12,22792,22793,22794,22797],{},"解決方法是加一個簡單的",[773,22795,22796],{},"事件匯流排（Event Bus）","。不管狀態是從哪裡被改變的（Discord 指令、網頁按鈕、歌曲自然播完），都會經過同一個通知機制。WebSocket 伺服器監聽這個事件，然後把最新狀態廣播給所有訂閱中的瀏覽器。",[12,22799,22800],{},"Discord 指令 ──→ 改變佇列狀態 ──→ 發送事件 ──→ 廣播給網頁",[12,22802,22803],{},"網頁控制按鈕 ──→ 改變佇列狀態 ──→ 發送事件 ──→ 廣播給網頁",[12,22805,22806],{},"歌曲自然播完 ──→ 改變佇列狀態 ──→ 發送事件 ──→ 廣播給網頁",[12,22808,22809],{},"所有的路徑最終都匯聚到同一個出口，這就保證了不管變化從哪裡來，所有的客戶端都會同步更新。",[765,22811,22813],{"id":22812},"結語",[773,22814,22812],{},[12,22816,22817],{},"到這裡，一個帶有網頁控制面板的 Discord 音樂機器人就基本成形了。",[12,22819,22820],{},[22821,22822,22823,22826],"figure",{},[979,22824],{"alt":1236,"src":22825},"https:\u002F\u002Fraw.githubusercontent.com\u002FChinHongTan\u002Fblog\u002Fmain\u002Fpublic\u002Fimages\u002Fuploads\u002F1771778325963-Screenshot_2026-02-22_at_10.03.25_PM.webp",[22827,22828,22829],"figcaption",{},"給你看一眼這個超醜的介面～",[12,22831,22832],{},"回頭看，其實整個專案最有趣的部分不是寫 UI~~（其實也沒寫多少）~~，而是搞清楚這些不同的系統之間要怎麼溝通：機器人怎麼跟 Lavalink 溝通、網頁怎麼跟機器人溝通、Discord 指令和網頁操作怎麼互相同步。",[12,22834,22835],{},"目前的介面還很陽春，功能上也還有不少可以改進的地方（例如搜尋結果列表、拖曳排序佇列、音量調整等等）。也許之後有興趣了，可以再回來改進一下UI介面設計。",[12,22837,22838,22839,22842],{},"能有耐心看到這裡的話...",[2948,22840,22841],{},"我真的好愛你","！感謝您看到這裡！如果你也在折騰類似的，希望這篇文章能給你一些靈感。有任何問題都歡迎留言！",{"title":169,"searchDepth":170,"depth":170,"links":22844},[22845,22852],{"id":22648,"depth":170,"text":22651,"children":22846},[22847,22848,22849,22850,22851],{"id":22663,"depth":7336,"text":22666},{"id":22704,"depth":7336,"text":22707},{"id":22736,"depth":7336,"text":22739},{"id":22763,"depth":7336,"text":22766},{"id":22778,"depth":7336,"text":22781},{"id":22812,"depth":170,"text":22812},"講講寫網頁控制面板的那些事","2026-02-24","\u002Fimages\u002Fuploads\u002F1771775949773-69618131_p0.jpg",{},"\u002Fblog\u002F紀錄一次Discord機器人的開發過程（2）",{"title":22638,"description":22853},{"loc":22857},"blog\u002F紀錄一次Discord機器人的開發過程（2）","IQQgJmMxvEJkaDKs9ZgdG0dboMrMOHcUbi9kJG0VsJk",{"id":22863,"title":22864,"author":761,"body":22865,"date":23101,"description":23102,"draft":174,"edited_at":181,"extension":175,"featured_image":23103,"meta":23104,"navigation":178,"path":23105,"pinned":174,"seo":23106,"series":181,"seriesOrder":181,"sitemap":23107,"stem":23108,"tags":181,"__hash__":23109},"blog\u002Fblog\u002F部落格架站指南.md","部落格架站指南",{"type":9,"value":22866,"toc":23090},[22867,22872,22874,22877,22881,22884,22887,22893,22897,22900,22904,22911,22914,22917,22921,22924,22927,22930,22933,22937,22940,22950,22953,22956,22961,22965,22968,22978,22981,22984,22986,22989,23084,23087],[21758,22868,22870],{"id":22869},"配上好看的圖把人騙進來再說",[2948,22871,22869],{},[765,22873,11243],{"id":11243},[12,22875,22876],{},"這是一篇寫給對架設、設計部落格有興趣的朋友的文章，希望能幫到未來的你。這篇文章會把重點放在「設計」與「框架選擇」的層面，帶你了解市場上的不同方案該如何挑選。如果有說錯的地方，也請多多指教！",[765,22878,22880],{"id":22879},"部落格是怎麼運作的","部落格是怎麼運作的？",[12,22882,22883],{},"歸根結底，部落格就是一個非常簡單的網站。你完全可以用最基礎的HTML，CSS，JavaScript三件套來手刻自己的部落格。",[12,22885,22886],{},"但現實是，一個完整的部落格不僅僅有文章，還要有橫幅、目錄、頂部導航、留言區等固定的介面格式。寫部落格的時候，人們當然首先要考慮的是文章內容，而不是網站的排版。試想一下：當你終於擠出一點時間，想坐下來好好寫一篇文章時，如果還要分心去搞定網頁排版、文字大小這些瑣事，等一切調整完畢，寫作靈感大概也消失殆盡了。",[12,22888,22889,22890,1108],{},"為了讓創作者能專注於「內容」本身，這時候我們就要請出另外一個非常好用的工具：",[773,22891,22892],{},"部落格框架",[765,22894,22896],{"id":22895},"部落格框架該怎麼選","部落格框架該怎麼選？",[12,22898,22899],{},"根據用戶需求與技術背景的不同，市場上有幾種主流的選擇：",[781,22901,22903],{"id":22902},"wordpress傳統動態-cms","WordPress（傳統動態 CMS）",[12,22905,22906,22907,22910],{},"作為世界上最受歡迎的部落格系統，WordPress的優點非常明顯：",[773,22908,22909],{},"開箱即用","。它擁有海量的外掛和佈景主題。你幾乎可以不寫一行程式碼，就把網站架起來。但隨著時間推移，它的缺點也會慢慢浮現。它是一個相對龐大且「笨重」的系統，一旦你對排版有強迫症，比如想要像素級地修改某個區塊的設計，你會發現自己必須鑽進一堆複雜的 PHP 程式碼裡。對於喜歡完全掌控視覺設計的人來說，這有時候會讓人感到相當綁手綁腳。",[12,22912,22913],{},"雖然 WordPress 號稱免費開源，但對於我們這種想白嫖到底的「免費仔」來說，它其實隱藏著不少成本。首先，它需要傳統的伺服器（Hosting）和 MySQL 資料庫來運行，這意味著你每個月都要掏出真金白銀來付主機費。",[12,22915,22916],{},"其次，就是著名的外掛地獄。想要SEO好一點？裝個外掛；想要網站跑快一點？裝個快取外掛；想要防止被駭客攻擊？再裝個資安外掛。這些好用的外掛往往都是採用訂閱制收費的。當你把網站拼湊成你想要的樣子時，不僅網站變得臃腫無比，載入速度變慢，每個月的開銷也可能是一筆不小的數目。這也是為什麼，很多懂一點技術的人，最終都會選擇逃離WordPress。",[781,22918,22920],{"id":22919},"靜態網站生成器ssg","靜態網站生成器（SSG）",[12,22922,22923],{},"於是，這些受夠了笨重系統的開發者們，轉向了另一個極致：像Hexo、Hugo或Astro這樣的「靜態網站生成器」。",[12,22925,22926],{},"SSG允許你自己設計部落格的外觀。如果覺得自己設計不好，社區也有大量的主題可供使用。它的運作邏輯非常純粹：你只需要在本地端用Markdown寫作，然後在終端機敲幾行指令，框架就會把你的文字編譯成輕量、響應速度快的純HTML網頁。",[12,22928,22929],{},"這樣做的一大好處是，你可以免費部署在很多的網頁託管服務上。大多數的託管服務（如 GitHub Pages、Cloudflare Pages、Vercel 等）針對純靜態網頁都有很寬裕的免費額度。你甚至可以設定自動化腳本（CI\u002FCD），只要推送 Markdown 檔案上去，伺服器就會自動幫你編譯更新。這種網頁速度快、沒有資料庫被駭的風險，省心又省事。",[12,22931,22932],{},"但痛點來了： 每次寫文章都要打開VS Code，沒有那個我們熟悉好用的視覺化後台。如果你今天出門在外，突然想用手機改文章裡的一個錯字；又或者是你想邀請不懂 Markdown 的朋友一起共筆......那就麻煩了。",[781,22934,22936],{"id":22935},"headless-cms無頭內容管理系統","Headless CMS（無頭內容管理系統）",[12,22938,22939],{},"難道我們不能同時擁有靜態網站的自由與速度加上好用的後台管理介面嗎？這時候，時代的解藥出現了——Headless CMS。",[12,22941,22942,22943,15799,22946,22949],{},"什麼是「無頭」？簡單來說，它把網站的 ",[773,22944,22945],{},"前台視覺設計",[773,22947,22948],{},"後台內容管理"," 徹底切開了。後台只負責儲存你的文章和圖片資料，而網站要長成圓的還是扁的，完全是你自己說了算。Headless CMS會提供三樣東西：內容管理（新增\u002F刪除文章）、文字編輯器，以及內容儲存API。",[12,22951,22952],{},"當然，天下沒有白吃的午餐。如果你想當個免費仔，通常會選擇GitHub作為文章的儲存庫（Git-based CMS）。但 GitHub 作為儲存方案有個致命傷：如果兩個人同時編輯同一篇文章，缺乏即時同步機制的 Git 就會發生衝突（Git conflict），不僅可能導致心血白費，網站管理員處理起來更是頭痛。為了解決這個痛點，許多好用的 CMS 都會改用傳統的雲端資料庫來支援多人即時協作——當然，這也意味著它們必須開始向你收費了。",[12,22954,22955],{},"另一方面，完全免費的開源 CMS（如 Decap CMS、Sveltia CMS），其內建的編輯器又著實不太好用。CMS 為了兼顧所有用戶，通常會做出許多妥協：塞滿你不需要的功能，但你想客製化的特殊功能它又做不到。",[3780,22957,22958],{},[12,22959,22960],{},"私心插一嘴：SveltiaCMS其實是個很優秀的開源專案，介面現代且完全免費。但致命傷在於，它不支援客製化的實時預覽（WYSIWYG）。如果我想在編輯器裡直接預覽LaTeX數學公式或是特殊的自定義組件，它完全做不到。這對我來說是個硬傷。或許未來它更新後會是個完美的解決方案，但現在，我只能繼續尋找別的出路。",[781,22962,22964],{"id":22963},"全部客製化web框架-編輯器","全部客製化：Web框架 + 編輯器",[12,22966,22967],{},"前面的那麼多選擇，對於我這個免費仔來說都有各種各樣的缺點~~（要錢！）~~。在經過了很長一段時間的開發後，我終於受不了了，決定自己從頭做一個後台。",[12,22969,22970,22971,15799,22974,22977],{},"我此前最大的抱怨就是編輯器實在是不好用，但很幸運的是，開源界有很多超好用的神級編輯器框架，例如 ",[773,22972,22973],{},"TipTap",[773,22975,22976],{},"Milkdown","。 他們最大的好處在，只提供插件。你可以根據自己的需求，拿著這些插件隨心所欲的組裝自己想要的編輯器。想要什麼客製化的功能？想要適配特定的格式？沒問題，自己動手就好了！",[12,22979,22980],{},"一般很少會有人走到像我這一步：又要多人協作，又要GitHub儲存，又要有預覽功能的編輯器，還不能收費。我早期開發部落格，在上網研究的時候，完全沒見到有這種組合方法，只能想盡辦法繞過各種CMS的限制。直到偶然發現可以單獨把Milkdown這類編輯器抽出來，結合Web框架自己寫介面，才讓我重新把擱置了幾個月的部落格拿出來大改。",[12,22982,22983],{},"雖然這條路一開始最難走，但看著一個完全免費、有著好用實時預覽，且100%自己設計的部落格後台在手中誕生，那種成就感，絕對是任何現成框架都給不了的。",[765,22985,7233],{"id":7233},[12,22987,22988],{},"如果看到這裡，你還是不太確定應該怎麼選，可以參考以下表格：",[872,22990,22991,23015],{},[875,22992,22993],{},[878,22994,22995,23000,23005,23010],{},[881,22996,22997],{"align":883},[773,22998,22999],{},"方案",[881,23001,23002],{"align":883},[773,23003,23004],{},"最大優點",[881,23006,23007],{"align":883},[773,23008,23009],{},"致命痛點",[881,23011,23012],{"align":883},[773,23013,23014],{},"適合對象",[898,23016,23017,23033,23049,23065],{},[878,23018,23019,23024,23027,23030],{},[903,23020,23021],{"align":883},[773,23022,23023],{},"WordPress",[903,23025,23026],{"align":883},"開箱即用、生態系龐大",[903,23028,23029],{"align":883},"笨重、主機成本、外掛地獄",[903,23031,23032],{"align":883},"想快速建站、無技術背景者",[878,23034,23035,23040,23043,23046],{},[903,23036,23037],{"align":883},[773,23038,23039],{},"SSG 靜態生成",[903,23041,23042],{"align":883},"免費託管、載入快",[903,23044,23045],{"align":883},"缺乏視覺化後台、需依賴終端機",[903,23047,23048],{"align":883},"習慣本地Markdown寫作的開發者",[878,23050,23051,23056,23059,23062],{},[903,23052,23053],{"align":883},[773,23054,23055],{},"Headless CMS",[903,23057,23058],{"align":883},"前後端分離、自訂性高",[903,23060,23061],{"align":883},"多人協作與複雜功能多需付費",[903,23063,23064],{"align":883},"需要管理介面且有預算的團隊",[878,23066,23067,23072,23075,23078],{},[903,23068,23069],{"align":883},[773,23070,23071],{},"自製後台",[903,23073,23074],{"align":883},"完全免費、100%客製化",[903,23076,23077],{"align":883},"開發成本高、需從零打造",[903,23079,23080,23081,55],{"align":883},"追求自由的開發者（",[2948,23082,23083],{},"或者像我一樣的免費仔",[12,23085,23086],{},"希望這篇文章，能為正在猶豫如何架設部落格的你帶來一些收穫！也許之後我會再開一個新的文章，聊聊設計心得、或是開發教程之類的東西。但是嘛...我也還不清楚應該要從哪裡開始說就是了。",[12,23088,23089],{},"非常感謝你願意花時間看到這裡！",{"title":169,"searchDepth":170,"depth":170,"links":23091},[23092,23093,23094,23100],{"id":11243,"depth":170,"text":11243},{"id":22879,"depth":170,"text":22880},{"id":22895,"depth":170,"text":22896,"children":23095},[23096,23097,23098,23099],{"id":22902,"depth":7336,"text":22903},{"id":22919,"depth":7336,"text":22920},{"id":22935,"depth":7336,"text":22936},{"id":22963,"depth":7336,"text":22964},{"id":7233,"depth":170,"text":7233},"2026-02-21","這麼多框架應該怎麼選？","\u002Fimages\u002Fuploads\u002F1771647859909-99136266_p9.png",{},"\u002Fblog\u002F部落格架站指南",{"title":22864,"description":23102},{"loc":23105},"blog\u002F部落格架站指南","-D7hYwY30M42dspcpk3pQU-35RuAbDkoFmXANuwyDP8",{"id":23111,"title":23112,"author":23113,"body":23114,"date":23155,"description":23156,"draft":174,"edited_at":181,"extension":175,"featured_image":23157,"meta":23158,"navigation":178,"path":23159,"pinned":174,"seo":23160,"series":181,"seriesOrder":181,"sitemap":23161,"stem":23162,"tags":23163,"__hash__":23164},"blog\u002Fblog\u002F北冰洋漂流記.md","北冰洋漂流記","灰海獅",{"type":9,"value":23115,"toc":23153},[23116,23126,23129,23132,23136,23146],[12,23117,23118,23121,23122,23125],{},[2948,23119,23120],{},"在經歷了一段時間的拖稿後決定寫出這篇了","，首先呢，做個簡單的自我介紹，這裡是灰海獅，正在北冰洋漂流中，也有人會叫我寒潮或",[2948,23123,23124],{},"蒙蒙","，總之呢，情況就是這麼個情況。",[12,23127,23128],{},"本人是動漫宅，同時也涉獵一些雜七雜八的東西，包括但不限於:布袋戲、歷史、宗教等等的。",[12,23130,23131],{},"平時閒來無事也會寫小說，把我腦中那些天馬行空的想法寫出來，雖然常常因為懶得動而無限期擱置(至於文筆稀爛又是另一回事了)，但我還是很享受寫小說的時光的。",[23133,23134,23135],"h1",{"id":23135},"名字的由來",[12,23137,23138,23139,23142,23143],{},"好吧，名字好像沒有甚麼特別的由來XD，會有這名字是因為我小時候有隻很喜歡的布偶，就是隻灰色的海豹，沒錯，海豹，",[2948,23140,23141],{},"只是我當初不知道它是海豹，還以為是海獅","，於是這名字就一路用到現在了，寒潮的話，是我在自己小說裡給自己的名字，而蒙蒙...",[2948,23144,23145],{},"這名字的由來改天再分享。",[12,23147,23148,23149,23152],{},"大致就是這樣了，謝謝願意在這忙碌的世界留下一點時間看這篇文章的你，",[2948,23150,23151],{},"也許改天我會開始分享我寫的小說(?","，總之就是這樣~ 我要繼續回去漂流了(x",{"title":169,"searchDepth":170,"depth":170,"links":23154},[],"2026-02-06","淺淺的自我介紹","\u002Fimages\u002Fuploads\u002Fimg_4487.jpg",{},"\u002Fblog\u002F{{slug}}",{"title":23112,"description":23156},{"loc":23159},"blog\u002F北冰洋漂流記",[],"b-Guen-vKEHEhtCEEsIerPTxyTXMd6hS9q8dx75T70o",{"id":23166,"title":23167,"author":23168,"body":23169,"date":26763,"description":26764,"draft":174,"edited_at":23101,"extension":175,"featured_image":26765,"meta":26766,"navigation":178,"path":26767,"pinned":174,"seo":26768,"series":181,"seriesOrder":181,"sitemap":26769,"stem":26770,"tags":26771,"__hash__":26777},"blog\u002Fblog\u002F清華大學電機系-大一雜魚修課心得-總結.md","清華大學電機系 - 大一雜魚修課心得 & 總結","mahiro",{"type":9,"value":23170,"toc":26744},[23171,23176,23178,23181,23184,23187,23189,23194,23198,23202,23205,23208,23211,23214,23217,23411,23414,23741,23744,23747,23780,23791,23795,23798,23803,23812,23815,23818,23822,23855,23858,23861,23864,23885,23889,23893,23896,23902,23906,23909,23912,23916,23919,23922,23925,23928,23932,23935,23939,23943,23947,23951,23954,23956,23959,23987,24025,24029,24032,24035,24039,24042,24045,24049,24053,24060,24064,24068,24071,24074,24076,24082,24085,24094,24098,24129,24133,24136,24139,24142,24145,24149,24152,24155,24158,24178,24181,24184,24232,24236,24240,24243,24247,24250,24253,24257,24260,24264,24267,24271,24276,24280,24289,24292,24298,24300,24303,24332,24384,24386,24389,24392,24396,24399,24402,24404,24407,24410,24413,24415,24418,24421,24423,24430,24438,24441,24444,24447,24450,24453,24494,24497,24567,24571,24574,24578,24582,24585,24588,24591,24594,24598,24601,24604,24608,24612,24615,24618,24620,24623,24657,24718,24721,24728,24739,24744,24747,24752,24757,24760,24763,24768,24777,24786,24789,24794,24797,24803,24806,24842,24846,24849,24868,24871,24875,24878,24882,24885,24889,24892,24896,24900,24911,24917,24921,24925,24928,24935,24940,24942,24945,24972,24976,24979,24982,25045,25048,25062,25065,25076,25084,25092,25095,25098,25101,25103,25109,25112,25133,25136,25139,25142,25145,25149,25152,25156,25159,25163,25166,25169,25173,25176,25179,25183,25187,25190,25192,25195,25231,25252,25256,25259,25262,25265,25268,25271,25274,25277,25280,25286,25290,25332,25336,25388,25391,25394,25397,25400,25405,25409,25412,25417,25421,25424,25451,25454,25457,25487,25491,25494,25529,25561,25564,25572,25576,25580,25583,25586,25589,25592,25595,25598,25601,25604,25607,25611,25615,25618,25620,25623,25653,25658,25668,25671,25674,25677,25680,25683,25686,25689,25692,25695,25698,25704,25707,25710,25737,25740,25743,25746,25749,25752,25756,25759,25763,25766,25769,25772,25775,25778,25782,25785,25788,25792,25795,25798,25802,25805,25808,25811,25814,25817,25820,25823,25826,25835,25837,25840,25866,25888,25891,25894,25897,25900,25903,25906,25909,25912,25915,25918,25925,25929,25932,25968,25971,25998,26002,26005,26040,26043,26046,26056,26059,26073,26076,26079,26083,26110,26113,26116,26120,26124,26127,26130,26133,26136,26139,26142,26146,26150,26153,26157,26160,26163,26166,26168,26171,26196,26199,26202,26204,26207,26210,26212,26215,26218,26221,26223,26226,26229,26232,26234,26237,26240,26243,26246,26249,26252,26258,26261,26265,26268,26273,26276,26301,26304,26318,26321,26335,26338,26352,26355,26358,26360,26363,26366,26369,26372,26375,26378,26381,26384,26388,26392,26396,26399,26404,26407,26410,26412,26415,26439,26443,26446,26450,26456,26460,26466,26470,26474,26480,26483,26489,26493,26535,26539,26543,26546,26549,26552,26555,26559,26563,26568,26570,26573,26595,26598,26601,26604,26607,26610,26613,26619,26623,26626,26673,26675,26678,26681,26685,26688,26691,26694,26698,26701,26708,26712,26715,26718,26721,26724,26727,26730,26733,26736,26739,26742],[23172,23173,23175],"h5",{"id":23174},"歌愛雪鎮樓求你保佑我這樣的小雜魚","歌愛雪鎮樓~求你保佑我這樣的小雜魚。",[765,23177,11243],{"id":11243},[12,23179,23180],{},"不管是什麼風、還是演算法的小巧思帶你來到這邊。總之，很感謝你點開這篇文章。",[12,23182,23183],{},"這裡是撐了一個學期後的我，在寒假利用空餘時間寫的、本學期的選課紀錄與心得。",[12,23185,23186],{},"如果你正苦苦尋求著什麼關鍵字、或哪堂課的評價，希望這篇能幫到你~",[35,23188],{},[12,23190,23193],{"className":23191},[23192],"indent","高中在鄉下小學校廢了三年後，到大學馬上迎來的是一週接一週、不間斷的月考、各種報告及考試，以及一次比一次差的段考成績。尤其是我又很不知死活地參考卷哥心得選了25學分，搞得這半年十分甚至九分地累，甚至還遠超我準備學測的那半年，真的不知道我怎麼活下來的…\n",[12,23195,23197],{"className":23196},[23192],"總之現在撐過來、撐到寒假了，考慮到過去受前人修課心得獲益良多，但電機系這邊的選課心得真的特別少，因此決定也來試試寫一份自己的修課心得吧。除了方便未來回憶我這學期修25學分有多累人之外，也能作為未來學生的選課參考~雖然可能沒人會看到就是。\n",[12,23199,23201],{"className":23200},[23192],"本來打算在二選之前打完的，沒想到一拖就拖到了三選之後.....拖延症真糟糕啊我。\n",[12,23203,23204],{},"另外，本學期選課選得有億點多，甚至還不知死活地選了第二外語，導致代價就是累成狗，成績單也不好看。所以千萬建議學弟妹選課須謹慎…當然你是卷哥卷姊的話就另當別論了。",[765,23206,23207],{"id":23207},"選課列表",[12,23209,23210],{},"基本上，大一課表上是以必修課為主，沒有什麼加選修課的空間",[12,23212,23213],{},"通識的部分因為一選二選大多都被搶完了，輪到新生選課時名額也沒剩多少，因此加退選通常才是主要戰場。大一上的體育課則不能選，而由班級決定。",[12,23215,23216],{},"(可點擊藍色字體，跳轉到該章節)",[872,23218,23219,23235],{},[875,23220,23221],{},[878,23222,23223,23226,23229,23232],{},[881,23224,23225],{},"學分類型",[881,23227,23228],{},"科目名稱",[881,23230,23231],{},"授課教師",[881,23233,23234],{},"學分",[898,23236,23237,23254,23269,23285,23300,23316,23333,23349,23365,23380,23396],{},[878,23238,23239,23242,23248,23251],{},[903,23240,23241],{},"EE必修（大一上）",[903,23243,23244],{},[49,23245,23247],{"href":23246},"#%E8%A8%88%E7%AE%97%E6%A9%9F%E7%A8%8B%E5%BC%8F%E8%A8%AD%E8%A8%88","計算機程式設計",[903,23249,23250],{},"張彌彰",[903,23252,23253],{},"3",[878,23255,23256,23258,23264,23267],{},[903,23257,23241],{},[903,23259,23260],{},[49,23261,23263],{"href":23262},"#%E9%82%8F%E8%BC%AF%E8%A8%AD%E8%A8%88","邏輯設計",[903,23265,23266],{},"馬席彬",[903,23268,23253],{},[878,23270,23271,23273,23279,23282],{},[903,23272,23241],{},[903,23274,23275],{},[49,23276,23278],{"href":23277},"#%E5%BE%AE%E7%A9%8D%E5%88%86%EF%BC%A1%E4%B8%80","微積分Ａ一",[903,23280,23281],{},"江金城",[903,23283,23284],{},"4",[878,23286,23287,23289,23295,23298],{},[903,23288,23241],{},[903,23290,23291],{},[49,23292,23294],{"href":23293},"#%E6%99%AE%E9%80%9A%E7%89%A9%E7%90%86%EF%BC%A2%E4%B8%80","普通物理Ｂ一",[903,23296,23297],{},"鄭宏泰",[903,23299,23253],{},[878,23301,23302,23304,23310,23313],{},[903,23303,23241],{},[903,23305,23306],{},[49,23307,23309],{"href":23308},"#%E6%99%AE%E9%80%9A%E7%89%A9%E7%90%86%E5%AF%A6%E9%A9%97%E4%B8%80","普通物理實驗一",[903,23311,23312],{},"戴明鳳",[903,23314,23315],{},"1",[878,23317,23318,23321,23327,23330],{},[903,23319,23320],{},"校定必修（英文領域）",[903,23322,23323],{},[49,23324,23326],{"href":23325},"#%E4%B8%AD%E9%AB%98%E7%B4%9A%E8%8B%B1%E6%96%87%E4%B8%89-%E9%96%B1%E8%AE%80","中高級英文三-閱讀",[903,23328,23329],{},"劉文貞",[903,23331,23332],{},"2",[878,23334,23335,23338,23344,23347],{},[903,23336,23337],{},"校定必修（第二外語）",[903,23339,23340],{},[49,23341,23343],{"href":23342},"#%E5%88%9D%E7%B4%9A%E5%BE%B7%E8%AA%9E%E4%B8%80","初級德語一",[903,23345,23346],{},"韓佩雯",[903,23348,23253],{},[878,23350,23351,23354,23360,23363],{},[903,23352,23353],{},"一般通識",[903,23355,23356],{},[49,23357,23359],{"href":23358},"#%E7%95%B6%E4%BB%A3%E5%9C%8B%E9%9A%9B%E8%AD%B0%E9%A1%8C%E7%A0%94%E7%A9%B6","當代國際議題研究",[903,23361,23362],{},"方天賜",[903,23364,23332],{},[878,23366,23367,23369,23375,23378],{},[903,23368,23353],{},[903,23370,23371],{},[49,23372,23374],{"href":23373},"#%E6%81%90%E6%80%96%E4%B8%BB%E7%BE%A9%E8%88%87%E5%8F%8D%E6%81%90","恐怖主義與反恐",[903,23376,23377],{},"侍建宇",[903,23379,23332],{},[878,23381,23382,23385,23391,23394],{},[903,23383,23384],{},"校定必修",[903,23386,23387],{},[49,23388,23390],{"href":23389},"#%E5%A4%A7%E5%AD%B8%E4%B8%AD%E6%96%87","大學中文",[903,23392,23393],{},"王達甫",[903,23395,23332],{},[878,23397,23398,23400,23406,23409],{},[903,23399,23384],{},[903,23401,23402],{},[49,23403,23405],{"href":23404},"#%E5%A4%A7%E4%B8%80%E9%AB%94%E8%82%B2","大一體育",[903,23407,23408],{},"戴偉國",[903,23410,1027],{},[765,23412,23413],{"id":23413},"課表",[872,23415,23416,23439],{},[875,23417,23418],{},[878,23419,23420,23424,23427,23430,23433,23436],{},[881,23421,23422],{},[83,23423],{},[881,23425,23426],{},"Mon.",[881,23428,23429],{},"Tue.",[881,23431,23432],{},"Wed.",[881,23434,23435],{},"Thu.",[881,23437,23438],{},"Fri.",[898,23440,23441,23467,23491,23518,23542,23571,23596,23623,23648,23673,23695,23716],{},[878,23442,23443,23445,23450,23455,23459,23463],{},[903,23444,23315],{},[903,23446,23447,23449],{},[49,23448,23247],{"href":23246},"EE 231001",[903,23451,23452,23454],{},[49,23453,23294],{"href":23293},"PHYS113304",[903,23456,23457],{},[83,23458],{},[903,23460,23461,23449],{},[49,23462,23247],{"href":23246},[903,23464,23465,23454],{},[49,23466,23294],{"href":23293},[878,23468,23469,23471,23475,23479,23483,23487],{},[903,23470,23332],{},[903,23472,23473,23449],{},[49,23474,23247],{"href":23246},[903,23476,23477,23454],{},[49,23478,23294],{"href":23293},[903,23480,23481],{},[83,23482],{},[903,23484,23485,23449],{},[49,23486,23247],{"href":23246},[903,23488,23489,23454],{},[49,23490,23294],{"href":23293},[878,23492,23493,23495,23499,23504,23509,23513],{},[903,23494,23253],{},[903,23496,23497],{},[83,23498],{},[903,23500,23501,23503],{},[49,23502,23278],{"href":23277},"MATH101007",[903,23505,23506,23508],{},[49,23507,23326],{"href":23325},"LANG103025",[903,23510,23511,23503],{},[49,23512,23278],{"href":23277},[903,23514,23515,23517],{},[49,23516,23374],{"href":23373},"GE 144300",[878,23519,23520,23522,23526,23530,23534,23538],{},[903,23521,23284],{},[903,23523,23524],{},[83,23525],{},[903,23527,23528,23503],{},[49,23529,23278],{"href":23277},[903,23531,23532,23508],{},[49,23533,23326],{"href":23325},[903,23535,23536,23503],{},[49,23537,23278],{"href":23277},[903,23539,23540,23517],{},[49,23541,23374],{"href":23373},[878,23543,23544,23547,23552,23557,23562,23566],{},[903,23545,23546],{},"5",[903,23548,23549,23551],{},[49,23550,23309],{"href":23308},"PHYS101001",[903,23553,23554,23556],{},[49,23555,23263],{"href":23262},"EECS101002",[903,23558,23559,23561],{},[49,23560,23359],{"href":23358},"GE 158400",[903,23563,23564,23556],{},[49,23565,23263],{"href":23262},[903,23567,23568,23570],{},[49,23569,23390],{"href":23389},"CL 101051",[878,23572,23573,23576,23580,23584,23588,23592],{},[903,23574,23575],{},"6",[903,23577,23578,23551],{},[49,23579,23309],{"href":23308},[903,23581,23582,23556],{},[49,23583,23263],{"href":23262},[903,23585,23586,23561],{},[49,23587,23359],{"href":23358},[903,23589,23590,23556],{},[49,23591,23263],{"href":23262},[903,23593,23594,23570],{},[49,23595,23390],{"href":23389},[878,23597,23598,23601,23605,23609,23613,23618],{},[903,23599,23600],{},"7",[903,23602,23603,23551],{},[49,23604,23309],{"href":23308},[903,23606,23607],{},[83,23608],{},[903,23610,23611],{},[83,23612],{},[903,23614,23615,23617],{},[49,23616,23343],{"href":23342},"FL 204107",[903,23619,23620,23622],{},[49,23621,23405],{"href":23404},"PE 111039",[878,23624,23625,23628,23632,23636,23640,23644],{},[903,23626,23627],{},"8",[903,23629,23630,23551],{},[49,23631,23309],{"href":23308},[903,23633,23634],{},[83,23635],{},[903,23637,23638],{},[83,23639],{},[903,23641,23642,23617],{},[49,23643,23343],{"href":23342},[903,23645,23646,23622],{},[49,23647,23405],{"href":23404},[878,23649,23650,23653,23657,23661,23665,23669],{},[903,23651,23652],{},"9",[903,23654,23655],{},[83,23656],{},[903,23658,23659],{},[83,23660],{},[903,23662,23663],{},[83,23664],{},[903,23666,23667,23617],{},[49,23668,23343],{"href":23342},[903,23670,23671],{},[83,23672],{},[878,23674,23675,23677,23680,23684,23687,23691],{},[903,23676,49],{},[903,23678,23679],{},"邏輯設計（TA hour）",[903,23681,23682],{},[83,23683],{},[903,23685,23686],{},"微積分Ａ一（演習課）",[903,23688,23689],{},[83,23690],{},[903,23692,23693],{},[83,23694],{},[878,23696,23697,23700,23702,23706,23708,23712],{},[903,23698,23699],{},"b",[903,23701,23679],{},[903,23703,23704],{},[83,23705],{},[903,23707,23686],{},[903,23709,23710],{},[83,23711],{},[903,23713,23714],{},[83,23715],{},[878,23717,23718,23721,23725,23729,23733,23737],{},[903,23719,23720],{},"c",[903,23722,23723],{},[83,23724],{},[903,23726,23727],{},[83,23728],{},[903,23730,23731],{},[83,23732],{},[903,23734,23735],{},[83,23736],{},[903,23738,23739],{},[83,23740],{},[765,23742,23743],{"id":23743},"修課心得",[781,23745,23746],{"id":23247},"計算機程式設計 Introduction to Programming",[832,23748,23750,23759,23762,23765,23768,23771,23777],{"className":23749},[825,826],[12,23751,23752,23755,23756],{},[773,23753,23754],{},"科號："," 11410EE 231001\n開課教師：張彌彰  \u002F\u002F ",[2948,23757,23758],{},"名字可以倒過來唸",[12,23760,23761],{},"課程學分：3",[12,23763,23764],{},"課程類型： 電機系必修（大一上）",[12,23766,23767],{},"上課時間：M1M2 R1R2 \u002F\u002F 大一的第一堂課…",[12,23769,23770],{},"修課人數：76 -> 64 \u002F20(新生20) 容量 139  ",[12,23772,23773,23774],{},"上課教材：C Programming: A Modern Approach\n",[979,23775],{"alt":169,"src":23776},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%871.jpg",[12,23778,23779],{},"需要原文書嗎？ 上機考可以翻，所以建議買，不過我期中之後就沒再翻過就是。",[832,23781,23783,23788],{"className":23782},[825,15480],[12,23784,23785],{},[773,23786,23787],{},"範圍：",[12,23789,23790],{},"C語言，從 Ch 1 ~ Ch 20：Input\u002Foutput; Variables and data types; expressions & operators;\nConditional (if-else\u002Fswitch-case); Iteration(for\u002Fwhile); Arrays; Functions;\nPointers; String; Bitwise, Link list…等",[2963,23792,23794],{"id":23793},"心得待補充","心得：(待補充)",[12,23796,23797],{},"我覺得這堂課完全值得我另外開一篇文介紹。",[12,23799,23800],{},[979,23801],{"alt":1236,"src":23802},"https:\u002F\u002Ftruth.bahamut.com.tw\u002Fs01\u002F202601\u002Fc3fe429536e05b78d51e2c4447eaee42.PNG",[2963,23804,23806,23807],{"id":23805},"點名方式-每堂點名","點名方式： ",[254,23808,23811],{"className":23809},[23810],"red","每堂點名",[12,23813,23814],{},"上課時講到一半會隨機點人回答問題，發現有人沒到就會全班點名。就算沒有也可能會點。",[12,23816,23817],{},"每缺席一次-1分，事前須請假寄信，事後只接受病假，且須附上相關證明。",[2963,23819,23821],{"id":23820},"成績算法","成績算法：",[872,23823,23824,23840],{},[875,23825,23826],{},[878,23827,23828,23831,23834,23837],{},[881,23829,23830],{},"作業（Lab）（每次4% 共12次）",[881,23832,23833],{},"Quiz （每次4% 共3次）",[881,23835,23836],{},"Midterm（上機10% + 筆試10%）",[881,23838,23839],{},"Final（上機10% + 筆試10%）",[898,23841,23842],{},[878,23843,23844,23847,23850,23853],{},[903,23845,23846],{},"48%",[903,23848,23849],{},"12%",[903,23851,23852],{},"20%",[903,23854,23852],{},[12,23856,23857],{},"小考(Quiz 1 ~ Quiz 3)和段考的滿分皆為110分。",[12,23859,23860],{},"期末 20% (皆為上機10% + 筆試10%)",[12,23862,23863],{},"另外，今年有額外的加分小考。",[872,23865,23866,23876],{},[875,23867,23868],{},[878,23869,23870,23873],{},[881,23871,23872],{},"Quiz 4（極難，滿分100）",[881,23874,23875],{},"Survey（期末問卷）",[898,23877,23878],{},[878,23879,23880,23883],{},[903,23881,23882],{},"+4",[903,23884,23882],{},[2963,23886,23888],{"id":23887},"調分嗎不調別想了孩子","調分嗎？不調，別想了孩子。",[2963,23890,23892],{"id":23891},"給加簽嗎部分加簽","給加簽嗎？部分加簽：",[12,23894,23895],{},"限電機\u002F電資院大一學生，學期前寄信加簽",[12,23897,23898,23899],{},"沒上就只能去隔壁班",[2948,23900,23901],{},"逃過一劫",[2963,23903,23905],{"id":23904},"涼度","涼度：★★☆☆☆",[12,23907,23908],{},"如果0基礎來上的話，雖然應該能聽到會，但肯定得更吃力些",[12,23910,23911],{},"此外後期作業難度相當大也極度耗時，debug容易會瘋掉",[2963,23913,23915],{"id":23914},"甜度","甜度：★☆☆☆☆",[12,23917,23918],{},"隔壁班62人裡面20個A+，將近30%，",[12,23920,23921],{},"這邊我期末上機全對被手改後的分數跟期中錯一題一樣低",[12,23923,23924],{},"我真的是跟我大學生活過不去才會選這班",[12,23926,23927],{},"推薦度：",[2963,23929,23931],{"id":23930},"想學好程式尤其c","想學好程式(尤其C) ★★★★⯪ ",[12,23933,23934],{},"(上課很扎實，不過比較趕的關係，有些像file read\u002Fwrite的部分就沒講)",[2963,23936,23938],{"id":23937},"有考古或學長姐","有考古或學長姐：★★★★★",[2963,23940,23942],{"id":23941},"看重gpa","看重GPA：★☆☆☆☆",[2963,23944,23946],{"id":23945},"總結如果時間倒轉我想重上一次因為我作業分數被扣爛幹","總結：如果時間倒轉，我想重上一次！因為我作業分數被扣爛幹",[2963,23948,23950],{"id":23949},"成績分布-待補","成績分布： (待補)",[12,23952,23953],{},"μ = 77.14 σ  = 10.84",[35,23955],{},[781,23957,23958],{"id":23263},"邏輯設計 Logic Design",[832,23960,23962,23967,23970,23972,23975,23978,23981,23984],{"className":23961},[825,826],[12,23963,23964],{},[773,23965,23966],{},"科號：11410EECS101002\t",[12,23968,23969],{},"  \u003Cp>\n開課教師：馬席彬",[12,23971,23761],{},[12,23973,23974],{},"課程類型：電機系必修（大一上）",[12,23976,23977],{},"上課時間：T5T6 R5R6",[12,23979,23980],{},"修課人數：177 -> 167 \u002F20 (新生20) 容量170 (旺宏懷樸)",[12,23982,23983],{},"上課教材：自編講義",[12,23985,23986],{},"需要原文書嗎？ 完全不用",[832,23988,23990,23994,23997],{"className":23989},[825,15480],[12,23991,23992],{},[773,23993,23787],{},[12,23995,23996],{},"  \u003Cp>",[16,23998,23999,24002,24005,24008,24011,24017,24020],{},[19,24000,24001],{},"數位系統與2\u002F8\u002F16進位",[19,24003,24004],{},"Boolean Algebra, Boolean Function, Logic Gates(AND OR)",[19,24006,24007],{},"Simplify Boolean Function (用K-Map)",[19,24009,24010],{},"Combinational Logic ----一段範圍(~乘法器)----",[19,24012,24013,24014,24016],{},"Synchronous Sequential Logic (有Feedback)",[83,24015],{},"----二段範圍----",[19,24018,24019],{},"Registers & Counter",[19,24021,24022,24023],{},"Memory & Programmable Logic",[83,24024],{},[2963,24026,24028],{"id":24027},"心得","心得：",[12,24030,24031],{},"前排提醒：據說跟歷屆相比，今年題目特別簡單又過於甜。",[12,24033,24034],{},"由於第一堂課隔壁班英文授課聽不太懂，長跑到懷樸後聽課有種豁然開朗的感覺，於是果斷加簽這班。",[12,24036,24038],{"className":24037},[23192],"這堂課不點名，自從113年改16週開始也沒作業了，不過eeclass仍會附上前四屆的作業，不計分，但小考題型幾乎都來自這些作業的題目(有時甚至數值都一樣)。\n",[12,24040,24041],{},"而教授在課後會把每一堂課錄影放到eeclass，因此理論上你也可以考試到場就好，其他時候看線上影片+講義自己讀或補眠。",[12,24043,24044],{},"而教室也的確只有在考試時才會坐滿人，有一次下大雨時教室甚至空了一半以上。",[12,24046,24048],{"className":24047},[23192],"不過因為課綱差異，有些作業題目換到這屆並不會考(或教授會在課上強調不考)，這點可以問教授或TA hour問助教確認。\n",[12,24050,24052],{"className":24051},[23192],"上課方式是照著自己編的講義教(所以不用原文書)，從介紹數位與進位系統、Boolean代數等，一路組合、進階到後面回授邏輯等，每一章節都是前一章的延伸。\n",[12,24054,24056,24057,24059],{"className":24055},[23192],"1~5章的前半段通常是廣泛的入門介紹，主要考點則大部分在後半段。\n教授課上會把各個概念介紹得很詳細，如果都聽懂的話作業題目應該是都沒問題的(不過有些題目倒是要看一遍解答才會)。\n",[83,24058],{},"\n ",[12,24061,24063],{"className":24062},[23192],"值得注意的是：從第五章涉及feedback開始，總體課程難度會陡升，而Quiz 5也似乎是唯一沒人提前交卷的小考(不過反而不是平均最低分的一次)。\n",[12,24065,24067],{"className":24066},[23192],"儘管如此，如果對上課內容、作業有疑問或不清楚的話，可以下課後去問教授，也可以每週一晚上7:00~9:00的TA hour去問助教(但我通常只有考試那個禮拜才去啦)。\n",[12,24069,24070],{},"這堂課最大的難點大概就是它排在中午後一節，剛吃完飯血糖上升之外，因為懷樸不通風、冷氣又強，教授聲音還十分有磁性很催眠，因此很容易就恍神…然後一回神就突然跟不上進度了。",[12,24072,24073],{},"這點教授本人也有提過他上課聲音會讓人想睡就是。好在恍神的話還有上課影片可以補進度。",[83,24075],{},[12,24077,24078,24079],{},"課堂上不能發出聲響、聊天及睡覺，教授很看重這些。\n",[2948,24080,24081],{},"不過我還是看過有在課堂上開筆電看棒球的。",[12,24083,24084],{},"這堂課的內容將會在下學期的邏輯設計實驗中付諸實作，屆時再補充吧(前提是我有選到)。",[2963,24086,24088,24089],{"id":24087},"點名方式不點名","點名方式：",[254,24090,24093],{"className":24091},[24092],"green","不點名",[2963,24095,24097],{"id":24096},"成績算法考多少拿多少","成績算法：考多少拿多少",[872,24099,24100,24116],{},[875,24101,24102],{},[878,24103,24104,24107,24110,24113],{},[881,24105,24106],{},"Quiz （7次）",[881,24108,24109],{},"Midterm 1（1~4章）",[881,24111,24112],{},"Midterm 2（4~5章）",[881,24114,24115],{},"Final（6~7章）",[898,24117,24118],{},[878,24119,24120,24123,24125,24127],{},[903,24121,24122],{},"25%",[903,24124,24122],{},[903,24126,24122],{},[903,24128,24122],{},[2963,24130,24132],{"id":24131},"小考形式","小考形式：",[12,24134,24135],{},"預先公布在eeclass，範圍是前一個章節。",[12,24137,24138],{},"一般排在章節教完後的下堂第二節課小考，如果進度落後則會順延。",[12,24140,24141],{},"由於大多都是作業題型(甚至可能數值都沒換)，講義+4屆作業做完就差不多了。",[12,24143,24144],{},"分數就是很暴力的七次取平均。七次Quiz平均如圖",[2963,24146,24148],{"id":24147},"段考形式","段考形式：",[12,24150,24151],{},"相比起小考的作業題型，會多一些活用題，部分題目的解題思路也會比較刁鑽一些，但總體還是上課時的概念。",[12,24153,24154],{},"由於各章節是層層堆疊，以及有時段考出前面單元的題目(如期末直接出)，因此要確保前面的單元能讀懂。",[12,24156,24157],{},"小考與段考的時間基本上都偏充裕，最多壓線完成，不會寫不完。",[77,24159,24160,24163,24166,24169,24172,24175],{},[19,24161,24162],{},"段考似乎跟劉班是共同出題？",[19,24164,24165],{},"三次平均80.67\u002F91.02\u002F83.30",[19,24167,24168],{},"標準差17.16\u002F12.74\u002F18.25",[19,24170,24171],{},"Midterm 2滿分105，其餘滿分100",[19,24173,24174],{},"一段原本平均好像67，題目爭議的關係有重改",[19,24176,24177],{},"Quiz考卷可保留，但期中\u002F期末考卷會收回",[12,24179,24180],{},"值得注意的是，往年期中平均才約50，甚至有一半二退的紀錄...(見補充)",[12,24182,24183],{},"但抱怨一下，馬班助教改考卷都特別慢，一段考卷在二段考前才出來、而隔壁班二段一週後就出來。然後Quiz 5期末當週才出來，而二段、Quiz 6、Quiz 7 跟Final甚至都到期末後一個禮拜才改好...\n不過助教人很好，改考卷也不刁難人，所以...好啦，可以原諒。",[12,24185,24186,24187,24231],{},"另外建議not A寫成",[967,24188,24190],{"className":24189,"jax":971},[970],[973,24191,24195,24205],{"style":6545,"xmlns":976,"width":24192,"height":24193,"role":979,"focusable":980,"viewBox":24194,"xmlnsXLink":982},"1.697ex","2.337ex","0 -1033 750 1033",[984,24196,24197,24201],{},[987,24198],{"id":24199,"d":24200},"MJX-1-TEX-I-1D434","M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z",[987,24202],{"id":24203,"d":24204},"MJX-1-TEX-S4-2013","M0 248V285H499V248H0Z",[1024,24206,24207],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,24208,24209],{"dataMmlNode":1031},[1024,24210,24211,24217],{"dataMmlNode":15448},[1024,24212,24213],{"dataMmlNode":1282},[1036,24214],{"dataC":24215,"xLinkHref":24216},"1D434","#MJX-1-TEX-I-1D434",[1024,24218,24220],{"dataMmlNode":1034,"transform":24219},"translate(0,648)",[973,24221,24226],{"width":24222,"height":24223,"x":1027,"y":24224,"viewBox":24225},750,237,"148","187.5 148 750 237",[1036,24227],{"dataC":24228,"xLinkHref":24229,"transform":24230},"2013","#MJX-1-TEX-S4-2013","scale(2.25,1)","  ( A上一橫線)而不是A’，避免計算時漏看(血的教訓…)",[2963,24233,24235],{"id":24234},"調分嗎a太多就沒調","調分嗎？A+太多就沒調",[2963,24237,24239],{"id":24238},"給加簽嗎全簽","給加簽嗎？全簽：",[12,24241,24242],{},"第一堂到課加簽，電機\u002F電資院優先。不過最後有座位就給簽就是",[2963,24244,24246],{"id":24245},"涼度-1","涼度：★★★★⯪",[12,24248,24249],{},"懷樸冷氣每次都開超強",[12,24251,24252],{},"沒作業，成績完全取決於小考。不過小考題基本上都跟歷屆作業差不多就是",[2963,24254,24256],{"id":24255},"甜度-1","甜度：★★★★★",[12,24258,24259],{},"53.9% A+，平均85.9，邏設開通識課了？\n聽說歷屆平均沒那麼高的說...",[2963,24261,24263],{"id":24262},"推薦度推-見補充","推薦度：推？   見補充",[12,24265,24266],{},"總結：感謝教授這屆大發慈悲、感謝今年助教大發慈悲",[2963,24268,24270],{"id":24269},"成績分布-μ-8590-σ-1275","成績分布： μ = 85.90 σ  = 12.75",[12,24272,24273],{},[979,24274],{"alt":1236,"src":24275},"https:\u002F\u002Fmegapx-assets.dcard.tw\u002Fimages\u002Fb2950511-f4d1-43f1-86fb-a454645229f2\u002F1280.webp",[2963,24277,24279],{"id":24278},"補充","補充：",[12,24281,24282,24283,24288],{},"根據",[49,24284,24287],{"href":24285,"rel":24286},"https:\u002F\u002Fwww.dcard.tw\u002Ff\u002Fnthu\u002Fp\u002F260615470",[53],"前幾屆大二、大三的學長姐所述的慘況","，去年(113)同教授的邏設期中平均僅40~50分，二退人數更達到70人(快一半)；兩年前 (112) 調分(好像調3~5分)前甚至不到10個A+、三年前(111)期中考平均50，最終成績分布如下方附圖。",[12,24290,24291],{},"相比起來，今年完全通識課難度，最後也只退10人，幾乎可以說是邏輯設計趣談了。我本來還想推薦資工系來修，但現在我完全不敢保證下一屆是否仍舊這種甜涼度...",[12,24293,24294,24295],{},"附上三年前(111)同教授的成績分布(來源dcard)給未來選課的參考一下\n",[979,24296],{"alt":169,"src":24297},"https:\u002F\u002Fmegapx-assets.dcard.tw\u002Fimages\u002F80028095-9c12-4cea-9d58-dee39d50aece\u002F1280.webp",[35,24299],{},[781,24301,24302],{"id":23278},"微積分Ａ一 Calculus I",[832,24304,24306,24311,24312,24315,24318,24320,24323,24326,24329],{"className":24305},[825,826],[12,24307,24308],{},[773,24309,24310],{},"科號：11410MATH101007","  ",[12,24313,24314],{},"開課教師：江金城 ",[12,24316,24317],{},"課程學分：4",[12,24319,23974],{},[12,24321,24322],{},"上課時間：T3T4 R3R4 + WaWb（演習課）",[12,24324,24325],{},"修課人數：117 -> 116 \u002F120 (新生95)  容量139",[12,24327,24328],{},"上課教材：Calculus 9\u002Fe Stewart (我不確定是哪個封面)",[12,24330,24331],{},"需要原文書嗎？上課基本用不到，但課本習題對小考很有用。",[832,24333,24335,24340,24342,24345,24348,24351,24354,24357,24361,24364,24370,24375,24378,24381],{"className":24334},[825,15480],[12,24336,24337],{},[773,24338,24339],{},"範圍： ",[12,24341,23996],{},[12,24343,24344],{},"1.\tfunctions and limits;",[12,24346,24347],{},"2.\tderivatives; ----一段範圍(~2-4)----",[12,24349,24350],{},"4.\tintegrals;",[12,24352,24353],{},"5.\tapplications of integration; (旋轉體體積)",[12,24355,24356],{},"6.\tinverse, logarithmic, exponential ----二段範圍(~6-3)----",[12,24358,24360],{"className":24359},[23192],"and inverse trigonometric functions; ",[12,24362,24363],{},"7.\ttechniques of integration;",[12,24365,24366],{},[254,24367,24369],{"className":24368},[23810],"9.\tDifferential Equations;",[16,24371,24372],{},[19,24373,24374],{},"Parametric Equations and Polar Coordinates",[12,24376,24377],{},"範圍理論上應該只到積分應用，但後面為了趕課在下學期早點進入多變數",[12,24379,24380],{},"從原定第7章飆去10章參數式…",[12,24382,24383],{},"\u003C\u002Fp>",[12,24385,24028],{},[12,24387,24388],{},"江教授以往大多都是在數學系開課，教數學系的微積分、高等微積分為主。這次算是難得開微積分A的課，更難得來電機系開課。不過我是選了課之後才知道他是數學系系主任...",[12,24390,24391],{},"上課方式是依照原文書內容寫英文版書、以及講解部分例題。基本上全部抄下來後，再寫一些原文書後面的例題就足夠了。",[12,24393,24395],{"className":24394},[23192],"前期主要考 epsilon – delta (極限證明)的部分，也有大量的證明題以及定理推導，這也是前期微積分困難的地方。只是畢竟不是數學系，教授也提過證明題比例不會超過三分之一。\n",[12,24397,24398],{},"而且這些證明大多僅限於第一次段考範圍 (1~2章) ，從第五、六章開始證明題就少很多了，取而代之的是計算為主的題目。",[12,24400,24401],{},"雖然這麼說，但中後期課上有些定義(如微積分基本定理、黎曼和與積分定義、曲線算法)可能會直接作為段考考題要你寫出來，有背就有分(偏偏我沒背到，導致分數直接跳水)",[83,24403],{},[12,24405,24406],{},"前4章基礎的極限、微分、積分部分還可以吃高中的老本，越往後就越多新東西，難度也會逐漸升高。",[12,24408,24409],{},"中期開始課程進度相當之快，幾乎一週一個新章節。後期為了讓我們在下學期進早點進入多變數函數的部分，因此雖然課綱只到第七章(積分方法)，但後來還是趕著教到微分方程與參數式，使得最後一次段考的範圍相當之大。",[12,24411,24412],{},"不過教授人很好，二段的時候直接在課上讓我們舉手決定考試範圍到哪裡。最後我們為了壓證明題的比例，決定到6-3，而期末的範圍似乎也凸顯了這是正確的決定；後來二段出題不小心總分只配90分時，那10分更直接白送。",[83,24414],{},[12,24416,24417],{},"另外，每週三19:00會有微積分演習課+小考，講課部分是助教講解一些課本例題(當然有不少人都在讀自己的書)，小考難度稍高，方式在下方。",[12,24419,24420],{},"而段考部分題目大都不太會出過於刁鑽的題目；但只要有認真聽課，基本上都可以有足夠扎實的微積分基本功(一些證明除外，我恨 epsilon – delta)",[83,24422],{},[12,24424,24425,24426,24429],{},"因為個人微積分因為某些奇怪的原因",[2948,24427,24428],{},"其實就是太菜","幾乎都沒考到很好，教授真的救了我的微積分成績QQ",[2963,24431,23806,24433],{"id":24432},"點名方式-偶爾點名",[254,24434,24437],{"className":24435},[24436],"orange","偶爾點名",[12,24439,24440],{},"點名沒到會扣出席成績。",[12,24442,24443],{},"前期點過兩次名，中間為了趕課沒點名，後面近學期末又點了兩次",[12,24445,24446],{},"不過因為每次都只點一部分人(估計20~30個)，而且優先點上次缺席的人",[12,24448,24449],{},"所以我直到學期末都沒被點到就是",[2963,24451,23821],{"id":24452},"成績算法-1",[872,24454,24455,24477],{},[875,24456,24457],{},[878,24458,24459,24462,24465,24468,24471,24474],{},[881,24460,24461],{},"Quiz（共12次）",[881,24463,24464],{},"作業（共14次）",[881,24466,24467],{},"出席（點名）",[881,24469,24470],{},"Midterm 1（1 ~ 2-4）",[881,24472,24473],{},"Midterm 2（2-5 ~ 6-3）",[881,24475,24476],{},"Final（6-4 ~ 10-3）",[898,24478,24479],{},[878,24480,24481,24484,24486,24488,24490,24492],{},[903,24482,24483],{},"10%",[903,24485,24483],{},[903,24487,24483],{},[903,24489,24122],{},[903,24491,24122],{},[903,24493,24122],{},[12,24495,24496],{},"(沒錯，滿分105)",[77,24498,24499,24513,24521,24547],{},[19,24500,24501,24502],{},"作業：在線上答題平台上，當週(週二、週四)上課內容。",[77,24503,24504,24507,24510],{},[19,24505,24506],{},"通常20~30題計算題，填答題為主，難度不一。",[19,24508,24509],{},"最多曾出到57題，有時則是20題但計算量大。",[19,24511,24512],{},"另外線上平台要額外付700~900。記得付錢，否則到時做不了作業，還得自行連絡書商購買授權。",[19,24514,24515,24516],{},"出席：被點名缺席就會扣分",[77,24517,24518],{},[19,24519,24520],{},"如果全學期沒被點過名，也是10%全拿",[19,24522,24523,24524],{},"小考方式：每週三7:00~8:00演習課時小考，共12次(排除段考後)。",[77,24525,24526,24529,24532,24535,24538,24541,24544],{},[19,24527,24528],{},"但比重不重，目的也是以弄清概念為主。",[19,24530,24531],{},"每次3題，滿分30，題型大都來自課本習題",[19,24533,24534],{},"捨去最低兩次後，以滿分300分計算。",[19,24536,24537],{},"範圍通常是上週上課內容。",[19,24539,24540],{},"題目比段考難，常考些較刁鑽的題目，時間也相對較趕。",[19,24542,24543],{},"部分題目跟課本習題差不多。",[19,24545,24546],{},"不要太混的話最低拿18分以上(60%)應該還是可以的",[19,24548,24549,24550],{},"段考共三次",[77,24551,24552,24555,24558,24561,24564],{},[19,24553,24554],{},"每次7~8大題(其中1~3小題)。",[19,24556,24557],{},"時間100分鐘",[19,24559,24560],{},"時間跟難度都比小考寬裕許多，寫完一次大概還會剩20分鐘可以檢查。",[19,24562,24563],{},"三次平均73.36\u002F70.3=>80.3\u002F80",[19,24565,24566],{},"標準差14.3\u002F14.4\u002F(未知)\n小考不要太混基本上都能拿到6分以上，作業出席的部分更可說是白送\n可以發現：比起一些小考段考各占25%的教授，這邊相當於直接白送20分，總分還溢出5分。所以",[2963,24568,24570],{"id":24569},"調分嗎-不調分這給分還不夠甜嗎","調分嗎？ 不調分，這給分還不夠甜嗎",[12,24572,24573],{},"(據說出席夠高的話快被當教授會撈...不過微A這邊要被當應該很難)",[2963,24575,24577],{"id":24576},"給加簽嗎系統寫不接受但第一堂下課後讓加簽的找他我猜是給簽吧","給加簽嗎？系統寫不接受，但第一堂下課後讓加簽的找他，我猜是給簽…吧？",[2963,24579,24581],{"id":24580},"涼度-2","涼度：★★★☆☆",[12,24583,24584],{},"相比隔壁韓國教授10題證明 + 負向調分到沒人A+",[12,24586,24587],{},"排除掉微積分這科本身的難度來看，這邊簡直是新手村",[2963,24589,24256],{"id":24590},"甜度-2",[12,24592,24593],{},"我沒拿到A+是我太混，不是教授給分不夠甜，我愧對教授",[2963,24595,24597],{"id":24596},"推薦度","推薦度：★★★★★",[12,24599,24600],{},"不過電機微積分教授每年輪換，明年應該也選不到他了",[12,24602,24603],{},"如果之後他回去教數學系，系上微A又都是大刀的話或許可以考慮？",[2963,24605,24607],{"id":24606},"總結-江大佛名不虛傳","總結： 江大佛名不虛傳",[2963,24609,24611],{"id":24610},"成績分布不公開","成績分布：不公開",[12,24613,24614],{},"不過54個A+，共46.6%，",[12,24616,24617],{},"μ = 86.55， σ  = 11.5",[35,24619],{},[781,24621,24622],{"id":23294},"普通物理Ｂ一 General Physics B I",[832,24624,24626,24631,24634,24636,24638,24641,24644,24647,24652,24655],{"className":24625},[825,826],[12,24627,24628],{},[773,24629,24630],{},"科號：11410PHYS113304\t",[12,24632,24633],{},"  \u003Cp>開課教師：鄭弘泰",[12,24635,23761],{},[12,24637,23974],{},[12,24639,24640],{},"上課時間：T1T2 F1F2",[12,24642,24643],{},"修課人數：173 -> 161 \u002F140 (新生120)  容量150",[12,24645,24646],{},"上課教材：Essential University Physics (4th Global Edition), Richard Wolfson",[12,24648,24649],{},[979,24650],{"alt":1236,"src":24651},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%874.jpg",[12,24653,24654],{},"需要原文書嗎？搞個林志明的講義比較重要。",[12,24656,24383],{},[832,24658,24660,24665,24668,24671,24674,24677,24680,24683,24686,24689,24692,24695,24698,24701,24703,24706,24709,24712,24715],{"className":24659},[825,15480],[12,24661,24662],{},[773,24663,24664],{},"範圍",[12,24666,24667],{},"  \u003Cp>Ch 05 - Newton's Laws Applications 牛頓定律的應用",[12,24669,24670],{},"Ch 06 - Work, Energy & Power 功，能和功率",[12,24672,24673],{},"Ch 07 - Conservation of Energy 能量守恆",[12,24675,24676],{},"Ch 08 - Gravity 重力",[12,24678,24679],{},"Ch 09 - Systems of Particles 多質點系统",[12,24681,24682],{},"----一段範圍----",[12,24684,24685],{},"Ch 10 - Rotational Motion 轉動",[12,24687,24688],{},"Ch 11 - Rotational Vectors & Angular Momentum 轉動向量和角動量",[12,24690,24691],{},"Ch 12 - Static Equilibrium 靜力平衡",[12,24693,24694],{},"Ch 13 - Oscillatory Motion 振盪性運動 (振動)",[12,24696,24697],{},"Ch 14 - Wave Motion 波動",[12,24699,24700],{},"Ch 32 - Interference & Diffraction 干涉和繞射",[12,24702,24016],{},[12,24704,24705],{},"Ch 15 - Fluid Motion 流體力學",[12,24707,24708],{},"Ch 16 - Temperature and Heat 温度和熱量",[12,24710,24711],{},"Ch 17 - The Thermal Behavior of Matter 物質的熱行為",[12,24713,24714],{},"Ch 18 - Heat, Work, and the First Law of Thermodynamics 熱，功，和熱力學第一定律",[12,24716,24717],{},"Ch 19 - The Second Law of Thermodynamics 熱力學第二定律",[2963,24719,24028],{"id":24720},"心得-1",[12,24722,24724,24725,24727],{"className":24723},[23192],"上課方法基本上就是照著課本念與寫板書，以及寫一些例題的方式。出於這個原因，如果有林志明講義的話，會發現他的上課順序和講義完全相同。\n",[83,24726],{},"\n\t",[12,24729,24731,24732,24734,24735,24737],{"className":24730},[23192],"相比其他教授，這堂課沒有小考也不點名，平時分數也完全來自elearn上面的題目。考慮到這堂是早八，所以可以明顯看見每過一堂課，到課的人會越來越少...\n",[83,24733],{},"\n儘管loading小，但這堂課(據說)是普物調分數一數二多的，學期末更直接平調15分。\n",[83,24736],{},[83,24738],{},[12,24740,24741,24743],{},[83,24742],{},"\n上課是先從1~4章開始講，而1~4章幾乎全是高中內容，會讓人產生普物難度很低的錯覺，使得許多人前3天才開始讀一段範圍。",[12,24745,24746],{},"但因為1~4章不考(不考幹嘛教...)，而5~8的難度又跟1~4差上不少，導致最後一群不努力的人被第一次段考送下去，包括我。",[12,24748,24749,24751],{},[83,24750],{},"\n考題是所有教授共同命題，因此可以自由選普物B教授旁聽。雖說都是特定的例題，不過範圍很廣、難度也不低。好就在幾乎每屆的普物都是差不多的題型，因此建議備考的時候多寫幾屆普物考古題(可以不用計時，熟悉題型為優先)。",[12,24753,24754,24756],{},[83,24755],{},"\n第一次段考力學的部分跟高中實際上有非常多重複，只是要改成用微積分的形式(但這時候也還沒教積分，所以積分題目大多都是舉例帶過而已)；",[12,24758,24759],{},"二段範圍同時包含轉動、簡協、波動、光學等範圍，難度也是這幾次裡面最高的。",[12,24761,24762],{},"期末熱力學就相對仁慈許多了，難度回歸正常水準。",[12,24764,24765,24767],{},[83,24766],{},"\n第一次段考的平均偏低(這邊後來有51，不過我看其他班好像是45左右)，第二次因為範圍極大(加上轉動慣量這個全新的概念)平均也差不多，期末熱力學難度則有明顯的降低。",[12,24769,24770,24772,24773,24776],{},[83,24771],{},"\n相比起普A，普物B會更看重在用公式的部分，因此只要公式全背起來、題型熟悉就行。",[2948,24774,24775],{},"也可以叫AI幫你為這本書生一份公式整理","；然後推導的部分不要記，什麼偏微分體積分環場積都看過去就好，微積分沒教就別理他。",[12,24778,24779,24781,24782,24785],{},[83,24780],{},"\n而複習的時候比起啃原文書，拿個林志明的講義自己念會有效率不少。也可以買一本",[773,24783,24784],{},"大學物理學精要","來讀(考研究所用的參考書，被稱為物理科聖經。)",[12,24787,24788],{},"不過這些講義的內容不一定是普物B會考的的內容，像二段我還以為要算面積分\u002F體積分，浪費了四天讀... (實際上會旋轉體就差不多了)",[12,24790,24791,24793],{},[83,24792],{},"\n也聽說很多電機系的同學會自己回家啃原文書\u002F拿林志明講義來讀。不過我資質愚鈍所以最後還是早八乖乖爬起來。",[12,24795,24796],{},"不過如果要聽普物，可以考慮去校門口化工館旁聽劉怡維上課，概念講得十分清楚(但他較少講例題，講課順序也跟林志明講義不同。)",[2963,24798,24088,24800],{"id":24799},"點名方式不點名-1",[254,24801,24093],{"className":24802},[24092],[2963,24804,23821],{"id":24805},"成績算法-2",[872,24807,24808,24827],{},[875,24809,24810],{},[878,24811,24812,24815,24818,24821,24824],{},[881,24813,24814],{},"平時 （作業）",[881,24816,24817],{},"Midterm 1",[881,24819,24820],{},"Midterm 2",[881,24822,24823],{},"Final",[881,24825,24826],{},"調分",[898,24828,24829],{},[878,24830,24831,24833,24835,24837,24839],{},[903,24832,24122],{},[903,24834,24122],{},[903,24836,24122],{},[903,24838,24122],{},[903,24840,24841],{},"+15",[2963,24843,24845],{"id":24844},"作業在elearn上每次段考範圍一份","作業：在elearn上，每次段考範圍一份。",[12,24847,24848],{},"因為沒有小考，所以平時成績完全來自作業",[77,24850,24851,24862,24865],{},[19,24852,24853,24854],{},"每章6題，每題可以作答3次。",[77,24855,24856,24859],{},[19,24857,24858],{},"建議算錯一次之後就拍下來丟AI了，否則要是答錯，分數影響不小。",[19,24860,24861],{},"時間從上次段考截止到下次段考前一天晚上11:50，但有時會更早，這點要注意。",[19,24863,24864],{},"如果調完差5分以內及格的話，教授會仁慈幫你撈到60。",[19,24866,24867],{},"要拿到A+的話需要三次段考總和198~200+",[12,24869,24870],{},"三次段考平均：51.14\u002F40.85\u002F58.37",[2963,24872,24874],{"id":24873},"調分嗎-爆調15分","調分嗎？   爆調15分",[12,24876,24877],{},"似乎是調最多的，調分完之後距離及格縣5分內會撈。",[2963,24879,24881],{"id":24880},"給加簽嗎第一堂課到課加簽","給加簽嗎？第一堂課到課加簽",[12,24883,24884],{},"好像簽20個左右吧，但要簽的人非常多。",[2963,24886,24888],{"id":24887},"涼度-3","涼度：★★★★★",[12,24890,24891],{},"不用點名、不用小考，也不用到課",[2963,24893,24895],{"id":24894},"甜度-3","甜度：★★★⯪☆",[2963,24897,24899],{"id":24898},"推薦度無腦推","推薦度：無腦推",[77,24901,24902,24905,24908],{},[19,24903,24904],{},"想衝GPA：★★★★★",[19,24906,24907],{},"求輕鬆過：★★★★★",[19,24909,24910],{},"想睡掉早八：★★★★★",[12,24912,24913,24914,24916],{},"想早八爬起來、認真在課上學懂普物：★★★★★",[83,24915],{},"\n（不點名、不小考所以自己也能自己選教授旁聽。但這種人存在嗎?）",[2963,24918,24920],{"id":24919},"總結調分魔術師","總結：調分魔術師",[2963,24922,24924],{"id":24923},"成績分布不公開但會附上全班成績excel","成績分布：不公開，但會附上全班成績Excel",[12,24926,24927],{},"μ = 78.61 σ = 14.00",[22821,24929,24930,24931],{},"\n  ",[979,24932],{"src":24933,"alt":24934},"\u002Fimages\u002Fuploads\u002F圖片6.png","undefined",[22821,24936,24930,24937],{},[979,24938],{"src":24939,"alt":24934},"\u002Fimages\u002Fuploads\u002F圖片5.png",[35,24941],{},[781,24943,24944],{"id":23309},"普通物理實驗一 General Physics Laboratory I",[832,24946,24948,24953,24956,24959,24961,24964,24967,24970],{"className":24947},[825,826],[12,24949,24950],{},[773,24951,24952],{},"科號：11410PHYS101002",[12,24954,24955],{},"  \u003Cp>開課教師：戴明鳳 （實際上多是助教帶）",[12,24957,24958],{},"課程學分：1  \u002F\u002F 幹 破課",[12,24960,23764],{},[12,24962,24963],{},"上課時間： M5M6M7M8",[12,24965,24966],{},"修課人數：53  \u002F58 （新生58）",[12,24968,24969],{},"範圍：同普通物理B一（力學&熱力學）",[12,24971,24383],{},[2963,24973,24975],{"id":24974},"心得-excel應用實驗一","心得：   Excel應用實驗一",[12,24977,24978],{},"電機系（其實好像全校都這樣）人見人幹的破課。",[12,24980,24981],{},"分為講解課（L+講）、實驗課與演示實驗（報告）。",[77,24983,24984,24995,25006,25017,25025,25042],{},[19,24985,24986,24987],{},"講解課就是解釋實驗原理",[77,24988,24989,24992],{},[19,24990,24991],{},"但對實驗的幫助不大，原因見下。",[19,24993,24994],{},"好處就在講解課通常下午三點半就下課，以及回答問題可以加分。",[19,24996,24997,24998],{},"實驗課內容通常會配合當學期的普通物理範圍",[77,24999,25000,25003],{},[19,25001,25002],{},"所以普物實驗一就是力學、轉動、波動、熱力學",[19,25004,25005],{},"是的，全是這些電機系完全用不到的東西。",[19,25007,25008,25009],{},"實驗前會先有一次 open-book 課前小考，範圍就是當次實驗內容",[77,25010,25011,25014],{},[19,25012,25013],{},"可以自己印預報來看。",[19,25015,25016],{},"個人建議將講義內容貼到預報裡面，考題重複性很高。",[19,25018,25019,25020],{},"考完後，講師會講解實驗內容與操作",[77,25021,25022],{},[19,25023,25024],{},"然後你會發現實驗內容跟你預報看到的八竿子打不著，所以實驗都以現場講師為主。",[19,25026,25027,25028],{},"做完實驗收集完數據、在Excel算出要求的數值後給實驗助教檢查，才能離開。",[77,25029,25030,25033,25036,25039],{},[19,25031,25032],{},"數據的部分據說有些助教會要求誤差需要小於5%\u002F20%之類才能離開，不然就需要重做；",[19,25034,25035],{},"不過每次實驗的助教都不同人，所以標準也各有不同",[19,25037,25038],{},"但我們這屆的助教對這方面要求都寬鬆許多，實驗數據合理、做得出結報就行。",[19,25040,25041],{},"真的要感謝這一屆的實驗助教，謝謝你們救了我們寶貴的肝。",[19,25043,25044],{},"之後再依照這些數據做一份結報出來，下周一之前交，這次實驗才算完成。",[12,25046,25047],{},"出於上述原因、以及實驗光是器材架設就很耗時，實驗大部分都做不完：",[77,25049,25050,25053,25056,25059],{},[19,25051,25052],{},"第一次實驗滑車做到快7點",[19,25054,25055],{},"第二次因為各組排隊等蓋格計數器，三點做完實驗還排隊等到六點。",[19,25057,25058],{},"不過之後實驗室都改為6點就清場了，只是後期實驗大多也得做到5點半左右。",[19,25060,25061],{},"但做實驗的速度是會隨著操作逐漸變快的，到後面幾次最快4點就全員離場了，難得做完實驗天還是亮的。",[12,25063,25064],{},"演示實驗課則是助教會給你一個實驗器材，你需要提前做好ppt介紹器材、以及它的原理及應用，並在演示實驗課當天上台報告，報告完根據建議改ppt後再交一份修改版。",[77,25066,25067,25070,25073],{},[19,25068,25069],{},"但我們一班大概有23組，所以一般建議壓在5~10分鐘內。",[19,25071,25072],{},"只是講到一半戴教授常常補充一些阿里阿雜的東西，導致每次演示實驗都拖到6:30左右才能離場==；",[19,25074,25075],{},"通常前幾組報告還會有人專心聽，到後面幾乎都死一片了。",[12,25077,25078,25079,25081,25083],{},"出於以上原因，這堂課離場時間平均至少5:30，最晚6:30~7:00，所以實驗課當天晚上還是千萬不要排課（但是戴明鳳開在當天晚上的通識可能可以啦）。",[83,25080],{},[83,25082],{},"\n要早點離場的話，個人建議一定要搞到家傳：因為實驗內容每屆幾乎都大同小異， Excel 裡面的公式改一改，套實驗的數據進就能用，可以讓你省下不少寫公式、測數據的時間；",[12,25085,25086,25087,25089,25091],{},"而測出來的數據不準的時候，也有補救方法，不用花半天重建那一堆實驗器材；而結報也有一個格式可以參考，更不容易需要熬夜。",[83,25088],{},[83,25090],{},"\n預報的部分基本上都是去普物實驗室網站複製貼上，結報要不要參考家傳就見仁見智了；",[12,25093,25094],{},"但說真的，除非你是天生不用讀書的卷哥卷姊，否則我建議能混就混、別花太多時間熬夜在這1學分的破課上面，因為會壓縮到睡眠以及讀其他科目的時間。",[12,25096,25097],{},"加上課程內容以及實驗做的力學、熱力學對未來幫助也不大（普物實驗二的電磁、電路學反而比較相關，但（幸好）必修沒物理實驗二）、甚至對學普物B一也沒太大幫助（頂多就是學到些Excel技巧）。",[12,25099,25100],{},"喔對，這學期周一放假放掉兩次實驗課，還把碰撞實驗給放掉了，結報-2，爽。",[83,25102],{},[2963,25104,23806,25106],{"id":25105},"點名方式-每堂點名-1",[254,25107,23811],{"className":25108},[23810],[2963,25110,23821],{"id":25111},"成績算法-3",[872,25113,25114,25123],{},[875,25115,25116],{},[878,25117,25118,25121],{},[881,25119,25120],{},"平時成績",[881,25122,24823],{},[898,25124,25125],{},[878,25126,25127,25130],{},[903,25128,25129],{},"70%",[903,25131,25132],{},"30%",[12,25134,25135],{},"平時成績包含每次實驗報告、實驗前考試、演示實驗報告等分數，以及講解課回答加分",[12,25137,25138],{},"結報可以把問題與討論、心得都寫一寫，但也不用太努力拚加分啦，因為怎麼加都加不到期末的那30%裡面==",[12,25140,25141],{},"期末前半部分是考實驗操作器材、用途與方法（如游標卡尺、向心力機器）跟實驗內容，跟實驗前小考的內容有些重疊；後半部分則是講解實驗課的器材，比例分別60%跟40%。我是建議專心讀前者就好。",[12,25143,25144],{},"另外戴班不會有助教連連看，所以別想背助教了。",[2963,25146,25148],{"id":25147},"調分嗎大調","調分嗎？大調",[12,25150,25151],{},"最後班平均調到82多，戴班最後沒意外都A\u002FA+",[2963,25153,25155],{"id":25154},"給加簽嗎-好問題","給加簽嗎？ 好問題",[12,25157,25158],{},"第一節課有要求工學院去其他班，所以這班應該是只留給電機系",[2963,25160,25162],{"id":25161},"涼度-4","涼度：⯪☆☆☆☆",[12,25164,25165],{},"一學分的破課，5學分的loading",[12,25167,25168],{},"做到半夜，帶你熬夜",[2963,25170,25172],{"id":25171},"甜度-4","甜度：★★★☆☆",[12,25174,25175],{},"考前30分鐘才發現可以帶大抄==",[2963,25177,25178],{"id":24596},"推薦度：   ☆☆☆☆☆",[2963,25180,25182],{"id":25181},"總結-我很感謝我的組員帶飛","總結：  我很感謝我的組員帶飛",[2963,25184,25186],{"id":25185},"成績分布不公開-1","成績分布：不公開。",[12,25188,25189],{},"μ = 82.13 σ  = 6.26  ，",[35,25191],{},[781,25193,25194],{"id":23326},"中高級英文三-閱讀 Upper-Intermediate English III：Reading",[832,25196,25198,25203,25206,25209,25212,25215,25218,25221,25226,25229],{"className":25197},[825,826],[12,25199,25200],{},[773,25201,25202],{},"科號：11410LANG103025\t",[12,25204,25205],{},"  \u003Cp>開課教師：劉文貞",[12,25207,25208],{},"課程學分：2",[12,25210,25211],{},"課程類型：校定必修（英文）",[12,25213,25214],{},"上課時間： W3W4",[12,25216,25217],{},"修課人數：AA -> BB \u002F30 （新生30）, 容量50",[12,25219,25220],{},"上課教材：自製簡報 + Pathways：Reading，Writing，and CriticalThinking （4） 3\u002Fe",[12,25222,25223],{},[979,25224],{"alt":1236,"src":25225},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%877.jpg",[12,25227,25228],{},"需要原文書嗎？   必需（水木書店有賣）",[12,25230,24383],{},[832,25232,25234,25238,25241,25244,25247,25250],{"className":25233},[825,15480],[12,25235,25236],{},[773,25237,23787],{},[12,25239,25240],{},"  \u003Cp>\nUnit 1 The Changing Workplace",[12,25242,25243],{},"Unit 4 Rethinking Transport",[12,25245,25246],{},"Unit 8 Living Longer",[12,25248,25249],{},"Unit 6 Why Language Matters (須自己讀)",[12,25251,24383],{},[2963,25253,25255],{"id":25254},"心得-2","心得：  ",[12,25257,25258],{},"就...很標準的高中英文課，例如隨堂點名、分組加分、不准用電子產品等等。大概就只跟高中差在全英授課，文章比較長、難度比較高（C1難度）、以及要求上課都用全英對話這點了。",[12,25260,25261],{},"上課會先分組，然後從組別間英文自我介紹開始講起。開始上課後，回答問題搶答可以加分，有時上課也會有些小組團隊合作回答問題、或玩kahoot!的環節。最後學期末似乎會算小組總分。",[12,25263,25264],{},"上課內容則是從閱讀技巧講起，然後用自製的簡報來帶課文，並有時會發學習單，讓學生以教過的閱讀技巧（Summarize 、Outline、picturing等）去分析、理解該篇比高中課本還長上數倍的課文；",[12,25266,25267],{},"回家作業則是將單字與解釋連接起來，上課檢討，不過不算分。",[12,25269,25270],{},"全學期有算分的回家作業大概只有一次，在運動會週。那週有傳影片要求自學。不過作業也是很簡單的文章分析而已，eeclass上繳交。",[12,25272,25273],{},"如果高中英文課就有學過相關閱讀技巧的話，由於幾乎沒有回家作業，這堂課頂多就是Quiz與小組報告前會稍忙一些，其餘應該沒太多課後負擔要做。",[12,25275,25276],{},"另外，雖然是全英上課，不過老師的英文沒有什麼口音，反而聽到她講中文時會有外國人講中文的感覺；",[12,25278,25279],{},"此外，上課時後老師會時不時補充些在國外的生活經驗、或引用生活例子來解釋課文內容。",[2963,25281,23806,25283],{"id":25282},"點名方式-每堂點名-2",[254,25284,23811],{"className":25285},[23810],[2963,25287,25289],{"id":25288},"成績算法總分可達105","成績算法：總分可達105",[872,25291,25292,25313],{},[875,25293,25294],{},[878,25295,25296,25299,25302,25305,25308,25311],{},[881,25297,25298],{},"出席（平時）",[881,25300,25301],{},"上課作業（學習單）",[881,25303,25304],{},"回家作業（只有一次）",[881,25306,25307],{},"分組報告",[881,25309,25310],{},"Quiz（多次）",[881,25312,24823],{},[898,25314,25315],{},[878,25316,25317,25320,25322,25325,25328,25330],{},[903,25318,25319],{},"15~20%",[903,25321,23852],{},[903,25323,25324],{},"5%",[903,25326,25327],{},"15%",[903,25329,25327],{},[903,25331,25132],{},[2963,25333,25335],{"id":25334},"出席分數算法","出席分數算法：",[872,25337,25338,25348],{},[875,25339,25340],{},[878,25341,25342,25345],{},[881,25343,25344],{},"評分項目",[881,25346,25347],{},"分數",[898,25349,25350,25357,25365,25373,25381],{},[878,25351,25352,25355],{},[903,25353,25354],{},"初始分數",[903,25356,23652],{},[878,25358,25359,25362],{},[903,25360,25361],{},"全勤",[903,25363,25364],{},"+2",[878,25366,25367,25370],{},[903,25368,25369],{},"遲到",[903,25371,25372],{},"-2",[878,25374,25375,25378],{},[903,25376,25377],{},"缺席",[903,25379,25380],{},"-5",[878,25382,25383,25386],{},[903,25384,25385],{},"在課堂上從事無關活動",[903,25387,25372],{},[12,25389,25390],{},"若為負分，將併入學期成績計算；若累積達 20 分，則學期成績額外加 5 分，也就是說總成績的出席項會拿到20分。",[12,25392,25393],{},"這一項我估計是以課堂參與度下去評分的，小組分數似乎也是記到這邊。",[12,25395,25396],{},"不確定前半學期跟後半的出席分是算總和還是算平均。",[12,25398,25399],{},"上課作業：發學習單，以教過的技巧分組去分析文章。",[77,25401,25402],{},[19,25403,25404],{},"有時也會玩kahoot!",[2963,25406,25408],{"id":25407},"回家作業","回家作業：",[12,25410,25411],{},"只有一份。是運動會那週的閱讀分析作業",[77,25413,25414],{},[19,25415,25416],{},"內容和上課學習單大同小異，eeclass線上繳交。",[2963,25418,25420],{"id":25419},"分組報告-pair-article-presentation","分組報告( Pair Article Presentation )：",[12,25422,25423],{},"期初二人分組，選擇給定文章中的一篇，並在指定的時段以英文上台報告該指定長文。",[77,25425,25426,25429,25432,25440,25443],{},[19,25427,25428],{},"分析的部分不難，比較難的是口說的部份。",[19,25430,25431],{},"這部分建議選擇前期一點的組別（最好在10月初以前），這樣期末就可以少一項負擔；",[19,25433,25434,25435],{},"加上分組報告後提出問題是可以加分的。",[77,25436,25437],{},[19,25438,25439],{},"我塞在期末趕太多報告，在這部分沒準備好直接炸開...",[19,25441,25442],{},"報告完後，老師會給一份挺詳細的報告分析表以及改善建議，十分用心~",[19,25444,25445,25446],{},"然後絕對不要帶僥倖心態用AI生成報告，期末有不少人被抓包。",[77,25447,25448],{},[19,25449,25450],{},"僅允許AI部分潤飾報告文筆及抓錯，不過有許多特殊規定要遵守。",[2963,25452,24132],{"id":25453},"小考形式-1",[12,25455,25456],{},"有兩次在表上的小考，一次範圍通常是一篇課文",[77,25458,25459,25462,25479],{},[19,25460,25461],{},"兩次表上的小考各5%，共占10%，可以當作兩次期中。",[19,25463,25464,25465],{},"分為三個部分：單字與片語、課文閱讀理解、閱讀技巧",[77,25466,25467,25470,25473,25476],{},[19,25468,25469],{},"會提前給單字表，通常20~30個，建議考前狂抄單字來練習。",[19,25471,25472],{},"閱讀理解部分為open-book，範圍是關於上課內容的課文",[19,25474,25475],{},"基本上內容都跟之前學習單帶過的題目大同小異",[19,25477,25478],{},"閱讀技巧則是給一篇新的文章，要用課上教的技巧去分析該文章。",[19,25480,25481,25482],{},"此外，通常在分組報告前，課堂上可能有報告範圍的pop-Quiz。",[77,25483,25484],{},[19,25485,25486],{},"這部分共占5%",[2963,25488,25490],{"id":25489},"final形式","Final形式：",[12,25492,25493],{},"英文課共同命題，難度較高；範圍則是上課教過的課文。",[77,25495,25496,25510,25518,25526],{},[19,25497,25498,25499],{},"題型跟小考大同小異，只是還多一份申論（作文）",[77,25500,25501,25504,25507],{},[19,25502,25503],{},"題目是關於段考的文章內容",[19,25505,25506],{},"要求180字以上",[19,25508,25509],{},"寫起來感覺比學測簡單",[19,25511,25512,25513],{},"閱讀理解部分同樣是問課文，但close-book。",[77,25514,25515],{},[19,25516,25517],{},"不過也不會像小考問得那麼細節。",[19,25519,25520,25521],{},"單字有將近240個，可能要花點時間準備",[77,25522,25523],{},[19,25524,25525],{},"可以提前整理一遍單字-字意表，再重點標記不熟的單字",[19,25527,25528],{},"估計Final平均分應該也沒到太好。",[872,25530,25531,25547],{},[875,25532,25533],{},[878,25534,25535,25538,25541,25544],{},[881,25536,25537],{},"單字",[881,25539,25540],{},"閱讀理解（課文）",[881,25542,25543],{},"申論（作文）",[881,25545,25546],{},"長文閱讀",[898,25548,25549],{},[878,25550,25551,25553,25556,25558],{},[903,25552,25132],{},[903,25554,25555],{},"20~30%",[903,25557,24483],{},[903,25559,25560],{},"30~40%",[12,25562,25563],{},"BONUS：參加培力英文測驗：共+4",[77,25565,25566,25569],{},[19,25567,25568],{},"報名聽+讀 or 說+寫，可各拿到一分(共+2)",[19,25570,25571],{},"聽+讀 or 說+寫 達到B2等級，可再各拿一分(共+2)。",[2963,25573,25575],{"id":25574},"調分嗎-全班平調3分","調分嗎？   全班平調+3分。",[2963,25577,25579],{"id":25578},"給加簽嗎-似乎不給","給加簽嗎？    似乎不給",[2963,25581,24581],{"id":25582},"涼度-5",[12,25584,25585],{},"上課規矩限制、以及要做的事情不少，還挺忙的",[12,25587,25588],{},"不過幾乎沒回家作業，不會占花太多課後時間。",[12,25590,25591],{},"一半一半吧。",[2963,25593,24895],{"id":25594},"甜度-5",[12,25596,25597],{},"加分機會很多，建議全部拿滿",[2963,25599,23927],{"id":25600},"推薦度-1",[12,25602,25603],{},"因為新生保留，新生可以選，如果缺英文學分的話也很推薦選這堂；",[12,25605,25606],{},"但如果要考免修的話不建議花時間來修",[2963,25608,25610],{"id":25609},"總結-中高英裡面非常推薦的一堂課","總結： 中高英裡面非常推薦的一堂課！",[2963,25612,25614],{"id":25613},"成績分布不公開-2","成績分布：不公開，",[12,25616,25617],{},"μ = 84.13  σ  = 8.54，",[35,25619],{},[781,25621,25622],{"id":23343},"初級德語一 Beginning German I",[832,25624,25626,25631,25634,25636,25639,25642,25645,25648,25651],{"className":25625},[825,826],[12,25627,25628],{},[773,25629,25630],{},"科號：11410FL 204107\t",[12,25632,25633],{},"  \u003Cp>開課教師：韓佩雯",[12,25635,23761],{},[12,25637,25638],{},"課程類型：第二外語（抵英文學分）",[12,25640,25641],{},"上課時間：R7R8R9",[12,25643,25644],{},"修課人數：40 -> 36 \u002F42",[12,25646,25647],{},"上課教材：Das Leben - Kurs- und Übungsbuch - A1",[12,25649,25650],{},"需要原文書嗎？ 必需（水木書店有賣）",[12,25652,24383],{},[12,25654,25655],{},[979,25656],{"alt":1236,"src":25657},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%878.jpg",[832,25659,25661,25665],{"className":25660},[825,15480],[12,25662,25663],{},[773,25664,23787],{},[12,25666,25667],{},"  \u003Cp>德文字母、課本1~6課。\u003C\u002Fp>",[2963,25669,24028],{"id":25670},"心得-3",[12,25672,25673],{},"第一堂課會先從德文的26+4個（三個變音+ ß ）德文字母發音開始教，之後開始教單字。",[12,25675,25676],{},"由於老師幾乎不用電子產品（不過不像程設課那樣完全禁用），因此筆記部分需要上課時自己抄下來（或拍下來）。而習題、考卷解答也是完全手寫、傳下去給同學自行拍照。",[12,25678,25679],{},"上課會先從單字開始講起，之後進到課本課文，從課文帶到各個單字與例句，並依照課本例題去講解德文的一些文法與用例。老師基本上會把每個用例都講清楚講明白。",[12,25681,25682],{},"雖然這麼說，不過德文文法部分真的特別搞剛：除了動詞現在式有六種變化態、受詞（目前）有兩種等等規則之外，名詞不只分陰陽性，連複數型也是不規則的。因此就算英文底子好，學德文也難免會被這些規則卡住。",[12,25684,25685],{},"我是修了之後，才知道原來德文是文法最複雜的語言之一...這點老師也承認德文真的很難、學習門檻不低。",[12,25687,25688],{},"不過德文發音是完全按照字母念的，這點算是德文比英文好的一點就是，一些外來字也是按讀音改寫法。只是因為德文字母與英文重疊，但又常有很多念法上的異同（聽看看das Restaurant就知道了），這點頗需要適應。",[12,25690,25691],{},"老師有時也會分享一些以前她在德文系就讀、以及之前在歐洲、德國的許多生活習慣與經驗，再加上歐洲的一些節慶、歷史故事、王室或介紹一座城市。",[12,25693,25694],{},"也因此，這堂課上不只可以學到德文，也能學到不少課本上讀不到的，德國與歐洲的人文歷史小知識。因為我個人暑假剛去過德國與瑞士，所以聽到老師分享這些在歐洲的生活經驗時，總有種親切感。",[12,25696,25697],{},"雖然第一堂課老師看起來十分嚴格，不過隨著課程進行，會發現其實老師其實蠻和善的、也蠻可愛的ww，有德文的相關問題也可以下課去請教，雖然好像因為班上都是電神很少人會提問就是。",[2963,25699,24088,25701],{"id":25700},"點名方式偶爾點名",[254,25702,24437],{"className":25703},[24436],[12,25705,25706],{},"全學期只點過三次，兩次在前幾堂課，中期趕課，剩下一次在最後一堂",[2963,25708,23821],{"id":25709},"成績算法-4",[872,25711,25712,25725],{},[875,25713,25714],{},[878,25715,25716,25719,25722],{},[881,25717,25718],{},"Quiz （1次）",[881,25720,25721],{},"Midterm（1~2課）",[881,25723,25724],{},"Final（3~6課）",[898,25726,25727],{},[878,25728,25729,25731,25734],{},[903,25730,25327],{},[903,25732,25733],{},"35%",[903,25735,25736],{},"50%",[12,25738,25739],{},"小考形式是聽寫單字與句子，基本上只是為了熟悉考試方法而已。",[12,25741,25742],{},"之後與下學期也不會有其他次小考。",[12,25744,25745],{},"不過後來有允許用期末的分數補期中。",[12,25747,25748],{},"BONUS：全勤+1分",[12,25750,25751],{},"有抓到教授上課講錯\u002F寫錯+1分（不過最後好像兩三個人拿到而已...）",[2963,25753,25755],{"id":25754},"調分嗎不調","調分嗎？不調",[12,25757,25758],{},"不過這次有改成績算法（我直接被救起來）",[2963,25760,25762],{"id":25761},"給加簽嗎不接受加簽不過加退選上的機率很高","給加簽嗎？不接受加簽，不過加退選上的機率很高",[12,25764,25765],{},"第一節課後的加退選，通常會有名額出來",[12,25767,25768],{},"因此想選可以第一堂就開始旁聽，兩週內應該會有名額。",[2963,25770,23905],{"id":25771},"涼度-6",[12,25773,25774],{},"這是我期末花最多時間讀的科目。",[12,25776,25777],{},"到底誰修課心得填說這是五星輕鬆甜涼課…",[2963,25779,25781],{"id":25780},"甜度-6","甜度：★★★★☆",[12,25783,25784],{},"考試每格扣分大概只扣0.幾",[12,25786,25787],{},"上課聽得懂+有認真讀，應該是不難拿分的（這不是我）",[2963,25789,25791],{"id":25790},"推薦度不建議大一修","推薦度：不建議大一修",[12,25793,25794],{},"推薦給想花時間學好德文、或有德文底子的",[12,25796,25797],{},"但如果時間不多、還不適應大學生活、或語言底子弱的話，就建議大二再說",[2963,25799,25801],{"id":25800},"總結-德文真的很難但肯努力學肯定能學到不少東西not-me","總結：  德文真的很難，但肯努力學，肯定能學到不少東西（not me）。",[2963,25803,24611],{"id":25804},"成績分布不公開-3",[12,25806,25807],{},"μ = 85.03 σ  = 11.76",[2963,25809,24279],{"id":25810},"補充-1",[12,25812,25813],{},"我是怎麼敢在日文平假名都花一年才背起來的情況下來修德文的啊...",[12,25815,25816],{},"因為輕忽語言課，看有空堂就選了，使得最後把這堂課排在有早八的週四，跑去挑戰人家外語系的必修。偏偏當天從1~6節都是主科（程設+邏設+微積分...），使得我整個學期上課幾乎恍神、直到最後一個月才聽懂課上內容...最後在這堂課的表現真的不太好，學習成果也不佳。",[12,25818,25819],{},"大一對環境不熟悉的情況下，除了卷哥卷姊，否則真的完全不建議修第二外語，尤其是在對一個語言完全不熟悉的情況下：因為相關單字、語法是很大的額外負擔。",[12,25821,25822],{},"除非是本來就有該語言基礎（如日文），不然在需要占用大量專業科目複習時間的情況下，語言課修下去真的可說是成績炸彈。",[12,25824,25825],{},"總之，考慮到下學期專業科目較多，我自己是學乖了，初德二大概得等二年級課業較輕的時候再繼續修了...",[12,25827,25828,25829,25834],{},"估計",[49,25830,25833],{"href":25831,"rel":25832},"https:\u002F\u002Fblog.chinono.dev\u002F?author=%E6%B3%95%E6%B3%95",[53],"法法","的德文都比混了一個學期的我還強了。",[35,25836],{},[781,25838,25839],{"id":23359},"當代國際議題研究 Current important issues in international Relations",[832,25841,25843,25848,25851,25853,25856,25859,25862,25864],{"className":25842},[825,826],[12,25844,25845],{},[773,25846,25847],{},"科號：11410GE 158400",[12,25849,25850],{},"  \u003Cp>開課教師：方天賜",[12,25852,25208],{},[12,25854,25855],{},"課程類型：一般通識（社會領域）",[12,25857,25858],{},"上課時間：W5W6",[12,25860,25861],{},"修課人數：57 \u002F60 容量77",[12,25863,23983],{},[12,25865,24383],{},[832,25867,25869,25874,25877,25880,25883,25886],{"className":25868},[825,15480],[12,25870,25871],{},[773,25872,25873],{},"內容：",[12,25875,25876],{},"  \u003Cp>國際關係的意義（基本政治概念）、大國角力、",[12,25878,25879],{},"領土爭端、民族主義、宗教衝突、外交實務（演講）、",[12,25881,25882],{},"民主發展、軍備管制、恐怖主義、小國外交、人類安全、",[12,25884,25885],{},"中小國外交。",[12,25887,24383],{},[2963,25889,24028],{"id":25890},"心得-4",[12,25892,25893],{},"算是十分搶手的一堂輕鬆通識，我自己也是在加退選才偶然選上，加上本來就對國際議題有點研究才選。",[12,25895,25896],{},"上課一開始會先從一些基礎的政治學概念講起，之後的上課內容則藉著近代的大國政治與時事，藉以講解主題以及複雜的國際關係。不過今年因為川普上台的關係，美國的部分占的篇幅相當大，而教授也有對川普的外交手法進行分析。",[12,25898,25899],{},"而教授作為前駐印度外交官，不只有時會分享過去派駐印度的經驗，課上有時也會拿印度來當例子。像是前期介紹大國政治的時候，教授就有拿印度總理莫迪與川普、對台灣的互動做舉例。也因為他在印度待了好幾年，教授更是強調別請他吃咖哩或印度料理ww",[12,25901,25902],{},"除此之外，每堂課剛開始上課時，會鼓勵同學上台發表、分享當週的國際大事。而教授也會自製ppt，分享該週有哪些國際大事。不過可能大學生都不太敢發表，全學期有上台過的大概就3~4個，而且大多都在前半學期。",[12,25904,25905],{},"也因為教授曾在外交部工作過，每個學期會邀請一位外交相關的專家來演講，像是這學期就邀請了以前台灣駐沙烏地阿拉伯的大使（過去有正式邦交關係時的那種）來分享外交工作以及派駐經驗。",[12,25907,25908],{},"另外，到最後一堂課，教授還會做一部影片來回顧整學期的上課內容、帶過上課的每一個主題，可以說十分用心，甚至讓大家不自覺全場鼓掌~而學期也有邀請大家加入時事與印度議題的兩個討論群組。",[12,25910,25911],{},"教授雖然看起來很嚴肅，實際上人很好。上課時要求不多，期末作業前也是開放大家跟他討論題目。除此之外，教授更可說是冷面笑匠，雖然總是一臉正經，講話卻有時很好笑，使得雖然國際關係很複雜，上課卻一點也不枯燥。",[12,25913,25914],{},"儘管教授對於國際關係與政治有著自己的一套看法，但他也很十分歡迎不同意見，在這方面上不會太刁難學生。所以作業的部分不必太拘謹或擔心需要討好，專心發表自己的想法即可~",[12,25916,25917],{},"正如第一堂課所說，教授希望讓每個人能培養「國際觀」；而這堂課整學期下來，不論本來是否有在關注時事議題，對於國際議題肯定都會有新的一層理解。",[2963,25919,23806,25921,25924],{"id":25920},"點名方式-每堂點名簽到單",[254,25922,23811],{"className":25923},[23810],"（簽到單）",[2963,25926,25928],{"id":25927},"成績算法不考試只有作業與期末報告未來可能更動","成績算法：不考試，只有作業與期末報告（未來可能更動！）",[12,25930,25931],{},"備註：似乎因為AI問題，這堂課之後應該也會全面改成考試形式了。",[872,25933,25934,25953],{},[875,25935,25936],{},[878,25937,25938,25941,25944,25947,25950],{},[881,25939,25940],{},"出席",[881,25942,25943],{},"國際大事分享",[881,25945,25946],{},"綜合表現",[881,25948,25949],{},"平時作業",[881,25951,25952],{},"期末報告",[898,25954,25955],{},[878,25956,25957,25959,25961,25963,25966],{},[903,25958,24483],{},[903,25960,25324],{},[903,25962,24483],{},[903,25964,25965],{},"45%",[903,25967,24122],{},[12,25969,25970],{},"國際大事分享：可選擇在課程開頭口頭報告，或在LINE群組內分享時事新聞。",[77,25972,25973,25981,25984,25987,25995],{},[19,25974,25975,25976],{},"分享「過去一週內」發生的國際新聞大事",[77,25977,25978],{},[19,25979,25980],{},"不一定限於國際政治，像是Gemini 3剛推出的時候，教授就有介紹",[19,25982,25983],{},"口頭報告大概2~3分鐘，並大致介紹事件背景與經過",[19,25985,25986],{},"傳在LINE群組，則是上傳相關新聞與約100字的短評與心得分析",[19,25988,25989,25990],{},"前8週（半學期）繳交就能5分拿滿，之後會以2週為單位遞減。",[77,25991,25992],{},[19,25993,25994],{},"畢竟之前教授發現同學會堆在期末才發表...",[19,25996,25997],{},"分享一次即可。",[2963,25999,26001],{"id":26000},"平時作業45","平時作業：45%",[12,26003,26004],{},"裡面含5項作業 ；此外還有期末報告一份，皆為個人作業：",[872,26006,26007,26026],{},[875,26008,26009],{},[878,26010,26011,26014,26017,26020,26023],{},[881,26012,26013],{},"選課調查",[881,26015,26016],{},"大國政治",[881,26018,26019],{},"領土爭議",[881,26021,26022],{},"演講心得",[881,26024,26025],{},"軍備管制",[898,26027,26028],{},[878,26029,26030,26032,26034,26036,26038],{},[903,26031,25324],{},[903,26033,24483],{},[903,26035,24483],{},[903,26037,24483],{},[903,26039,24483],{},[12,26041,26042],{},"BONUS： 演講提問有加分",[12,26044,26045],{},"平時作業的話共有4次，每次10%，通常是關於當週上課內容的主題",[77,26047,26048],{},[19,26049,26050,26051],{},"沒有限定字數，闡述觀點即可",[77,26052,26053],{},[19,26054,26055],{},"我自己是寫少則600，多則1500字都有",[12,26057,26058],{},"四項平時作業的主題分別是：",[16,26060,26061,26064,26067,26070],{},[19,26062,26063],{},"大國政治（Q：請問你認為美中衝突是否不可避免?）",[19,26065,26066],{},"領土爭議（Q：台灣應該放棄對南海的主權主張（十一段線、U型線）嗎?  ）",[19,26068,26069],{},"演講心得（沙烏地阿拉伯大使演講）",[19,26071,26072],{},"軍備管制（Q：台灣應該發展核子武器嗎?）",[12,26074,26075],{},"（第四次作業出這樣的主題，真的蠻佩服教授的...）",[12,26077,26078],{},"儘管教授會在課堂上對該議題發表自己的看法，但每一項作業都沒有標準答案。回答的觀點與教授不同更完全ok，只要論述充足就行。像是據教授說，第四次作業最後結果就是各半。",[2963,26080,26082],{"id":26081},"期末報告至少3000字以上","期末報告：至少3000字以上",[77,26084,26085,26088,26093,26096,26099,26102,26105],{},[19,26086,26087],{},"距離期限兩週之前可以找教授討論題目。",[19,26089,26090],{},[2948,26091,26092],{},"如果你想挑戰自我的話，可以寫印度，挑戰教授最擅長的領域",[19,26094,26095],{},"期末當週同時 eeclass上繳交word檔以及課上繳交紙本。",[19,26097,26098],{},"參考來源不可引自維基（但可以用上面的CC共享圖片），通常參考國內外的新聞報導即可",[19,26100,26101],{},"3000字看起來很多，實際寫起來會發現很輕鬆就能達標。像我本來花了幾小時寫本文，結果後來發現文句潤飾一下、把心得結語加上去後，再把註腳跟參考資料加完，就已經超過8000了...",[19,26103,26104],{},"至於格式的部分，剛好直接把大學中文的格式規範拿來用就好了。總體看下來可能我這門課的報告完成度還比中文課高...",[19,26106,26107],{},[2948,26108,26109],{},"然後我現在一想，幹早知道就一份報告兩邊交==",[12,26111,26112],{},"另外，有做課上筆記、或聽相關演講的話，也可以在期末週給教授查閱，聽說也有加分。",[12,26114,26115],{},"不過每項評分細項、作業批改結果全都不公開，所以也不知道具體拿多少。只是最後看下來，評分應該都給得不錯。",[2963,26117,26119],{"id":26118},"給加簽嗎應該給簽但最後也沒滿","給加簽嗎？應該給簽，但最後也沒滿。",[2963,26121,26123],{"id":26122},"涼度-7","涼度：",[12,26125,26126],{},"常關注國際議題者：★★★★★\n除了做期末報告時特別忙，可能會花好幾天，其他時間都挺閒的\n不過期末報告再麻煩也沒中文報告難寫又耗時",[12,26128,26129],{},"沒接觸過、想了解國際議題者：★★★⯪☆\n如果都沒接觸過相關概念，那可能要花點時間研究上課內容以及作業之類",[12,26131,26132],{},"甜度：★★★★☆？\n不清楚成績分布，也不知道給分，估計期末報告跟課堂參與占大項",[2963,26134,23927],{"id":26135},"推薦度-2",[12,26137,26138],{},"對國際政治感興趣者：必須選",[12,26140,26141],{},"沒接觸過、想了解國際議題者：大推，不過可能得花點時間去理解",[2963,26143,26145],{"id":26144},"總結-負擔很輕又能學到東西對國際政治有興趣的可謂必選","總結：  負擔很輕又能學到東西，對國際政治有興趣的可謂必選",[2963,26147,26149],{"id":26148},"成績分布-不公開作業分數也是不公開","成績分布：  不公開。（作業分數也是不公開）",[12,26151,26152],{},"μ = 86.25 σ  = 5.27",[2963,26154,26156],{"id":26155},"備註","備註：",[12,26158,26159],{},"儘管教授有政黨背景，上課也會對各項議題發表些自己的觀點，",[12,26161,26162],{},"不過他不會強求你接受他的觀點，作業也不會因此差別給分(像是核武議題)，課堂包容性非常高。",[12,26164,26165],{},"但如果對這方面還是有點芥蒂的話，選課時可能就得多加考慮。",[35,26167],{},[781,26169,26170],{"id":23374},"恐怖主義與反恐 Terrorism and Anti-Terrorism",[832,26172,26174,26179,26182,26184,26186,26189,26191,26194],{"className":26173},[825,826],[12,26175,26176],{},[773,26177,26178],{},"科號：11410GE 144300",[12,26180,26181],{},"  \u003Cp>開課教師：侍建宇",[12,26183,25208],{},[12,26185,25855],{},[12,26187,26188],{},"上課時間：F3F4",[12,26190,25861],{},[12,26192,26193],{},"上課教材：自編講義（會放在eeclass）",[12,26195,24383],{},[2963,26197,24028],{"id":26198},"心得-5",[12,26200,26201],{},"課上會先從恐怖主義開始講解，一路往下講解到一些恐怖主義相關的概念，以及用以色列&巴勒斯坦、蓋達組織、ISIS、以及中國新疆等議題做舉例講解。",[83,26203],{},[12,26205,26206],{},"課上講義會放在eeclass，用的是全英文，所以如果不熟悉相關概念的話，可能會比較看不懂。不過教授上課是用中文講解，因此問題不大。（學期結束會取消分享，要存的記得。）",[12,26208,26209],{},"上課的時候不太點名，也很少管底下在幹嘛，加上或許是上課語調比較平的關係，所以可以看到很多人都沒在專心聽，甚至在打報告或滑手機...到後面很多人甚至沒來上課，使得50多人的教室只剩下20多人，而教授這時候就常常直接點名了。",[83,26211],{},[12,26213,26214],{},"有時教授會在上課找紀錄片來播，並在播完後問大家有沒有心得。不過就如上面所述的，大學大多數時候都是沒人敢舉手（或是都在滑手機），然後教授就會稍微對參與度的部分發牢騷而已。",[12,26216,26217],{},"教授對新疆、維吾爾議題特別有研究，曾在數十年前去過新疆當地田野調查，也常去參加相關議題訪談。而教授過去也是在香港大學任教，他也常常分享他以前在香港的教書經歷，尤其是在看到我們上課幾乎都沒互動的時候（不過好像香港大學那邊也是同樣的情況。）",[12,26219,26220],{},"不過教授有時補充會講嗨忘記時間，像是講香港大學的經歷或提巴勒斯坦問題的時候，常常一講就是十幾分鐘。這也讓課程內容有時會有點跳tone難以聽懂。",[83,26222],{},[12,26224,26225],{},"如上面所述，教授有時在到課人數太少時會突襲點名。所以期末的時候，估計大家很怕突然點名，才全部到課（難得看到教室坐滿），結果教授反而看大家都來了就沒點名了（教授也知道大家是來期末點名的）",[12,26227,26228],{},"另外學期中，教授有邀請一位與他同屬國安研究院的專家來演講國家監控與個人（恐怖組織）逃脫相關議題，而其中一份作業也是寫演講心得。但作業中除了學到的東西之外，如果有，教授也鼓勵我們指出該講師的演講不足之處。",[12,26230,26231],{},"不過可能因為講者是國安研究院的，有點講嗨了，演講內容更多是聚焦在國安議題，反而恐怖主義的部分講蠻少...",[83,26233],{},[12,26235,26236],{},"上課作業很少，除了一份上述演講心得外，其餘作業內容通常依照給定的一段訪談或新聞，並回答申論題，大概1000~2000字。",[12,26238,26239],{},"不過整學期只派過四次作業，其中兩次還是在期末之後。所以換算下來學期內只有兩份作業，涼到怕。",[12,26241,26242],{},"而且作業有交就有分，所以教授鼓勵就算遲交也盡量交。",[12,26244,26245],{},"而教授也鼓勵我們在群組內分享恐怖主義發展相關新聞，這也會記入平時考量之內。\n雖然教授有時在課上會小小抱怨我們貼的內容，但也不會因此刁難人或不給分。",[12,26247,26248],{},"值得注意的是：這堂課不下課，是直接1小時50分鐘不中斷的。不過也沒啥特別勞累的活動，所以差別不大就是。",[12,26250,26251],{},"另外，這學期因為週五放兩次假，加上教授有時又會去美國演講的關係，換算下來大概少了四堂課。",[2963,26253,24088,26255],{"id":26254},"點名方式偶爾點名-1",[254,26256,24437],{"className":26257},[24436],[12,26259,26260],{},"人太少的時候會點名，總共點過兩三次而已",[2963,26262,26264],{"id":26263},"成績算法好吧其實我有點忘記算法了","成績算法：好吧，其實我有點忘記算法了",[12,26266,26267],{},"只有4份作業，沒有考試，沒有期末報告",[12,26269,26270],{},[773,26271,26272],{},"但是這堂是16 + 2，代表有期末後作業。",[12,26274,26275],{},"根據課綱：",[872,26277,26278,26290],{},[875,26279,26280],{},[878,26281,26282,26284,26287],{},[881,26283,25940],{},[881,26285,26286],{},"平時",[881,26288,26289],{},"作業",[898,26291,26292],{},[878,26293,26294,26296,26298],{},[903,26295,24483],{},[903,26297,25132],{},[903,26299,26300],{},"60%",[12,26302,26303],{},"平時部分：",[77,26305,26306,26309,26312,26315],{},[19,26307,26308],{},"可在LINE群組分享關於恐怖主義發展的新聞",[19,26310,26311],{},"時間不限定",[19,26313,26314],{},"每次1分，至多15分",[19,26316,26317],{},"其餘應該是依照發言、上課參與度去評",[12,26319,26320],{},"作業部份：依據恐怖主義相關內容（新聞\u002F訪談\u002F紀錄片），寫課後心得報告。 -",[77,26322,26323,26326,26329,26332],{},[19,26324,26325],{},"長度為1000-2000字。",[19,26327,26328],{},"每次作業期限大概給到20天以上，也寬限遲交（會不會扣分就不知道了）",[19,26330,26331],{},"有時會需要看1小時以上的訪談或紀錄片，這點須注意",[19,26333,26334],{},"一般大概一天內可以完成（但最後一項作業花我三天）",[12,26336,26337],{},"四次主題分別是：",[16,26339,26340,26343,26346,26349],{},[19,26341,26342],{},"定義恐怖主義（從以哈戰爭，探討恐怖主義的定義）",[19,26344,26345],{},"國家恐怖主義與中國（從新疆問題探討國家恐怖主義的定義）",[19,26347,26348],{},"演講心得（演講完好像一兩週後才派這份作業...）",[19,26350,26351],{},"穆斯林兄弟會紀錄片",[12,26353,26354],{},"（5%去哪了？？？？）",[12,26356,26357],{},"後兩次作業在期末後2週各一份。",[12,26359,26115],{},[12,26361,26362],{},"給加簽嗎？應該全簽，但最後也沒滿",[2963,26364,24888],{"id":26365},"涼度-8",[12,26367,26368],{},"上課很輕鬆",[12,26370,26371],{},"前兩次作業一天內能完成，最後一次作業花了我三天...",[12,26373,26374],{},"不過期限十分長，教授也有把最後兩次作業的時間也有延長到期末之後",[2963,26376,25781],{"id":26377},"甜度-7",[12,26379,26380],{},"課堂參與度高點、上課多發言，教授給分也不會太刁難。",[12,26382,26383],{},"不過這學期這堂課平均比歷屆高了快5分，似乎是課上參與度比較好的關係？",[2963,26385,26387],{"id":26386},"推薦度-甜涼好課對相關議題有興趣更推薦","推薦度： 甜涼好課，對相關議題有興趣更推薦",[2963,26389,26391],{"id":26390},"總結-教授人很好但多給教授點回應真的不要去教室滑手機啦","總結：  教授人很好~但多給教授點回應，真的不要去教室滑手機啦",[2963,26393,26395],{"id":26394},"成績分布歷年好像比較多都81左右-但標準差大","成績分布：（歷年好像比較多都81左右 但標準差大）",[12,26397,26398],{},"μ =85.32 σ  = 3.96",[12,26400,26401],{},[979,26402],{"alt":1236,"src":26403},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%879.png",[2963,26405,24279],{"id":26406},"補充-2",[12,26408,26409],{},"沒想到這學期搶到的兩堂通識都剛好是政治類的...不知道該說是有緣嗎？雖然兩堂還是都修得很快樂、成績也不低就是。",[35,26411],{},[781,26413,26414],{"id":23390},"大學中文 \t College Chinese",[832,26416,26418,24311,26423,26426,26428,26431,26434,26437],{"className":26417},[825,826],[12,26419,26420],{},[773,26421,26422],{},"科號：11410CL 101051\t",[12,26424,26425],{},"開課教師：王達甫 ",[12,26427,25208],{},[12,26429,26430],{},"課程類型：校定必修",[12,26432,26433],{},"上課時間：F5F6",[12,26435,26436],{},"修課人數：25->24 \u002F25（新生保留25）",[12,26438,26193],{},[2963,26440,26442],{"id":26441},"心得懲罰你國文沒考15級分的課","心得：懲罰你國文沒考15級分的課。",[12,26444,26445],{},"學測國文沒有15級分的學生都得修這堂課。如果說普通物理實驗是Excel使用訓練課，那麼這堂課就是Word實作練習課。",[12,26447,26449],{"className":26448},[23192],"這堂課跟高中的國文課十分不一樣。上課最開始會先講一些有趣的古文，以及討論一些相關的論文研究，之後帶到一些論文寫作規範、寫作技巧。然後則需要依照這些技巧，一步一步根據課上的論文格式教學，從前言、大綱到內容、結論逐漸寫出一篇完整的、5000字以上的個人報告。如果高中有寫過小論文的話，這堂或許會比較輕鬆。\n",[12,26451,26453,26454],{"className":26452},[23192],"雖然教授常常嚇人，讓人以為他很嚴厲、甚至第一堂課還鼓勵大家退掉選其他教授；不過實際上教授人很nice，文章有時找不到方向時也開放和他討論。中間有幾次發現作業太趕的時候，更是開放延長期限到假日，讚啦。\n",[83,26455],{},[12,26457,26459],{"className":26458},[23192],"此外，開學的時候就會分小組，並且古文介紹相關的課時會有一些小組活動、互相提問與討論。而後面也會有一次小組報告，讓小組做一篇簡報去講解一份論文（剛好跟物理段考撞在同一週，裂開），並且互相提問。不過也只是用來算小組參與度分數，最後個人報告還是各做各的。\n",[12,26461,26463,26464],{"className":26462},[23192],"上課討論的加分機會千萬要拿好，另外組長分數會往上調一個級距（A變A+等），建議主動爭取，尤其是大一的時候、大部分人還不熟環境而不敢自告奮勇時。\n",[83,26465],{},[12,26467,26469],{"className":26468},[23192],"這一班大學中文報告的題目是自己定，但可以找教授討論、以抓一個大致的方向。有時候有幾節課是這樣子的一對一討論課，上課前寫黑板決定討論順序，討論完就可以回去打報告了（但沒用，下一節還是有體育課...）\n",[12,26471,26473],{"className":26472},[23192],"中後期會有一次格式教學課，需要按照格式規範將文章的標點符號、參考資料、縮排、字體與格式在上課時改好。不過每一屆的結果都是上課時進度爆炸改不完，最後放學生回家改就是了，所以這點不必太擔心。由於太繁雜，基本上建議把格式規定跟文章丟給AI幫你抓。\t\n",[12,26475,26477,26478],{"className":26476},[23192],"除此之外，後期文章將近完成時，也會有一次類似口試的、約6分鐘的上台報告。這點千萬要注意別超時。\n",[83,26479],{},[12,26481,26482],{},"雖然講了這麼多，教授人也很nice，但他課上也提到之後應該也不會帶大學中文課了，實在可惜。",[2963,26484,23806,26486],{"id":26485},"點名方式-每堂點名-3",[254,26487,23811],{"className":26488},[23810],[2963,26490,26492],{"id":26491},"成績算法-期末報告5000字以上沒交死當","成績算法： 期末報告5000字以上，沒交死當。",[872,26494,26495,26517],{},[875,26496,26497],{},[878,26498,26499,26501,26504,26507,26510,26513,26515],{},[881,26500,11243],{},[881,26502,26503],{},"期中大綱",[881,26505,26506],{},"小組導讀",[881,26508,26509],{},"稿件修改（格式）",[881,26511,26512],{},"個人簡報（口試）",[881,26514,25952],{},[881,26516,26286],{},[898,26518,26519],{},[878,26520,26521,26523,26525,26527,26529,26531,26533],{},[903,26522,24483],{},[903,26524,23852],{},[903,26526,24483],{},[903,26528,25324],{},[903,26530,24483],{},[903,26532,23852],{},[903,26534,25327],{},[2963,26536,26538],{"id":26537},"調分嗎-不調因為我就差一分","調分嗎？ 不調，因為我就差一分==",[2963,26540,26542],{"id":26541},"給加簽嗎-不給簽","給加簽嗎？ 不給簽",[2963,26544,26545],{"id":23904},"涼度： ★★⯪☆☆",[12,26547,26548],{},"上課負擔不重，基本上負擔幾乎全部來自於個人報告",[2963,26550,25172],{"id":26551},"甜度-8",[12,26553,26554],{},"差一分A+ （我算了一下，好像甚至是零點多分） ，幹",[2963,26556,26558],{"id":26557},"總結excel有普物實驗word有大學中文","總結：Excel有普物實驗，Word有大學中文",[2963,26560,26562],{"id":26561},"成績分布-μ-8304-σ-1770","成績分布： μ = 83.04 σ  = 17.70",[12,26564,26565],{},[979,26566],{"alt":1236,"src":26567},"\u002Fimages\u002Fuploads\u002F%E5%9C%96%E7%89%8710.png",[35,26569],{},[781,26571,26572],{"id":23405},"大一體育 Physical Education",[832,26574,26576,26581,26584,26587,26589,26592],{"className":26575},[825,826],[12,26577,26578],{},[773,26579,26580],{},"11410PE 111039",[12,26582,26583],{},"  \u003Cp>開課教師：戴偉國",[12,26585,26586],{},"課程學分：0",[12,26588,26430],{},[12,26590,26591],{},"上課時間：F7F8",[12,26593,26594],{},"修課人數：56 ",[2963,26596,24028],{"id":26597},"心得-6",[12,26599,26600],{},"上課地點會前堂課email或體幹公布。基本上同一班（清班\u002F華班）會是同一個體育老師。",[12,26602,26603],{},"每堂課都是不同的運動內容，會一堂一堂帶我們造訪全校的各個體育設施，帶同學熟悉環境的同時，也讓大家能為未來五次的體育必修志願填寫做準備。",[12,26605,26606],{},"另外，雖然體育老師人看起來很嚴肅，不過其實人很好，有時上課講話也常逗笑大家。",[12,26608,26609],{},"雖然0學分，電機系的同學真的得好好珍惜這堂課，因為從期中開始，這大概是唯一可以活動筋骨的時間了。",[12,26611,26612],{},"期末測驗就是一些關於學校設施&運動姿勢的選擇題，5分鐘就能完成，比重也很輕，這大概是我上大學後第一次寫到選擇題...",[2963,26614,23806,26616],{"id":26615},"點名方式-每堂點名-4",[254,26617,23811],{"className":26618},[23810],[2963,26620,26622],{"id":26621},"成績算法憑記憶","成績算法：(憑記憶)",[12,26624,26625],{},"每個大一需要參加運動會項目",[872,26627,26628,26649],{},[875,26629,26630],{},[878,26631,26632,26635,26638,26641,26644,26646],{},[881,26633,26634],{},"體適能",[881,26636,26637],{},"運動會（個人）",[881,26639,26640],{},"運動會（團體）",[881,26642,26643],{},"游泳（6~7章）",[881,26645,25940],{},[881,26647,26648],{},"Midterm（4~5章）",[898,26650,26651],{},[878,26652,26653,26655,26660,26664,26666,26671],{},[903,26654,24483],{},[903,26656,26657,26659],{},[2948,26658,24483],{}," （取消）",[903,26661,26662,26659],{},[2948,26663,24483],{},[903,26665,24483],{},[903,26667,26668,26670],{},[2948,26669,25736],{}," 70%",[903,26672,24483],{},[83,26674],{},[12,26676,26677],{},"由於運動會取消（感謝颱風），原本運動會分數併入出席分。",[12,26679,26680],{},"不過有參加預賽仍然每個項目加2~3分",[2963,26682,26684],{"id":26683},"給加簽嗎不確定","給加簽嗎？不確定",[12,26686,26687],{},"不過有4~5個本系大二生（似乎是轉學生）   ",[2963,26689,24888],{"id":26690},"涼度-9",[12,26692,26693],{},"有到就會過，取消運動會之後就沒啥要做的事情了  ",[2963,26695,26697],{"id":26696},"甜度-9","甜度：★★★★☆   ",[12,26699,26700],{},"不過0學分也沒差  ",[2963,26702,26704,26705],{"id":26703},"總結-健身熟悉環境-讓你沒辦法三點回家","總結：  健身+熟悉環境+ ",[2948,26706,26707],{},"讓你沒辦法三點回家",[2963,26709,26711],{"id":26710},"成績分布-不公開","成績分布：  不公開   ",[12,26713,26714],{},"μ = 4.08(GPA，對應91.93) ， σ  = 0.24",[765,26716,26717],{"id":26717},"小結",[12,26719,26720],{},"修完有獎勵，修不完有懲罰。",[12,26722,26723],{},"選課須適度，參考須謹慎。尤其是千萬別盡信GPA 4.3的卷哥卷姐的心得，很容易一不小心就翻車。",[12,26725,26726],{},"這學期從微積分A開頭之後，從9\u002F30~11\u002F20，段考幾乎就沒有中斷過，一週接一週，我的活動範圍也幾乎只剩下教室與圖書館。",[12,26728,26729],{},"一堂課究竟如何、loading多重，還是要自己去修才知道。有時看著前人修著輕鬆，但自己去選也可能完全不是那樣。",[12,26731,26732],{},"另外，這學期各科的給分，真的無處不反映了「選擇大於努力」：不論是程式設計、微積分A、邏輯設計甚至是線性代數，兩位教授的給分真的可說天壤之別。希望下學期能保持這樣的選課運吧。",[12,26734,26735],{},"嘛，不過對於這學期，講的還是太多了，未來估計開別篇文再詳細講講吧。",[12,26737,26738],{},"至於未來還會不會寫大一下、大二大三......那就得看我經過三電的洗禮後，還有沒有餘力了。但首先，拜託保佑我選到電路學。",[12,26740,26741],{},"不管如何，如果你有幸看到這篇文，感謝願意你看到這邊。有閒之時，也歡迎去看看本部落格的其他文章~",[7328,26743,7330],{},{"title":169,"searchDepth":170,"depth":170,"links":26745},[26746,26747,26748,26749,26762],{"id":11243,"depth":170,"text":11243},{"id":23207,"depth":170,"text":23207},{"id":23413,"depth":170,"text":23413},{"id":23743,"depth":170,"text":23743,"children":26750},[26751,26752,26753,26754,26755,26756,26757,26758,26759,26760,26761],{"id":23247,"depth":7336,"text":23746},{"id":23263,"depth":7336,"text":23958},{"id":23278,"depth":7336,"text":24302},{"id":23294,"depth":7336,"text":24622},{"id":23309,"depth":7336,"text":24944},{"id":23326,"depth":7336,"text":25194},{"id":23343,"depth":7336,"text":25622},{"id":23359,"depth":7336,"text":25839},{"id":23374,"depth":7336,"text":26170},{"id":23390,"depth":7336,"text":26414},{"id":23405,"depth":7336,"text":26572},{"id":26717,"depth":170,"text":26717},"2026-01-21","一個雜魚，在充滿怪物的學校中前半年的生存狀況","https:\u002F\u002Ftruth.bahamut.com.tw\u002Fs01\u002F202601\u002Ff2c1c67681cab28e27fe24104ceae821.JPG",{},"\u002Fblog\u002F清華大學電機系 - 大一雜魚修課心得 & 總結",{"title":23167,"description":26764},{"loc":26767},"blog\u002F清華大學電機系-大一雜魚修課心得-總結",[23743,26772,26773,26774,26775,26776,3771],"清華大學","電機","反思","大一","新生","TgVrp2ntuVSjMacKflrTMFER8Lg1cxV719DsEBISyno",{"id":26779,"title":26780,"author":26781,"body":26782,"date":26843,"description":26844,"draft":174,"edited_at":181,"extension":175,"featured_image":26845,"meta":26846,"navigation":178,"path":26847,"pinned":174,"seo":26848,"series":181,"seriesOrder":181,"sitemap":26849,"stem":26850,"tags":26851,"__hash__":26852},"blog\u002Fblog\u002F小紅書被封禁究竟是濫權還是無視法規呢.md","小紅書被封禁究竟是濫權還是無視法規呢?","osborrrrn",{"type":9,"value":26783,"toc":26841},[26784,26825,26834],[12,26785,26786,26787,26789,26790,26792,26793,26795,26796,26798,26799,26801,26802,26804,26805,26807,26809,26810,26812,26813,26816,26817,26819,26821,26822,26824],{},"小紅書為近年風靡於台灣女性與學生團體，但在2025年12月4日由內政部與刑事警察局聯合通過記者會公布為期一年的禁令，同時要求網路業者立即封鎖小紅書的域名和伺服器。",[83,26788],{},"\n小紅書在台擁有超過300萬人使用然而經國家安全局資安檢測，15項指標均未符合標準，且該軟體自113年起涉入1706件詐騙案件造成國民損失約為2億4,768萬餘元\n執法機關偵辦犯罪時面臨重大困難，形成實質法律真空。而內政部為保障台灣用戶隱私安全於2025年10月14日海基會函請小紅書母公司中國行吟信息科技（上海）有限公司依法提出具體改善作為，但迄今業者無任何回應。試圖迴避中華民國法律管轄。且放任詐騙與其他違法行為置之不理故依照《詐欺犯罪危害防制條例》第42條「詐欺犯罪防制緊急事件」規定，將對「小紅書」APP發布網際網路停止解析或限制接取之命令，暫定期間一年；後續將視該公司是否善意回應、主動配合我國相關法規並確保國人數位安全，再研議後續處置。",[83,26791],{},"\n(節取於內政部守護民眾資訊安全 對涉詐高風險APP發布暫行措施114-12-04)",[83,26794],{},"\n對於此事件許多民眾在網路反映：",[83,26797],{},"\n1.是否違反憲法",[83,26800],{},"\n2.政府為何不去封禁FACEBOOK(Meta)、LINE 、TikTok",[83,26803],{},"\n3.政治因素。",[83,26806],{},[83,26808],{},"\n而我對於此事件的想法",[83,26811],{},"\n1.來討論是否違反憲法：網民認為說，直接封禁過度限制了人民言論與資訊自由。然而此次封禁由內政部新聞稿知是違反了《詐欺犯罪危害防制條例》，而內政部依法行政並要求ISP也就是",[773,26814,26815],{},"網際網路服務供應商","封鎖小紅書的域名和伺服器，此APP造成許多危害且不願意在台設立據點提供檢方調查犯罪，而現今我國與中國沒有合適的共同反詐管道，因此無法有效限制詐騙故直接封禁。可能符合憲法中的必要性與比例原則。",[83,26818],{},[83,26820],{},"\n2.政府為何不去封禁FACEBOOK(Meta)和LINE、TikTok等等國際平台：上述平台同樣充斥著詐騙如以Meta為例：Meta2025一月至4月共撤銷了430萬則詐騙廣告數億新台幣的損失，為何Meta不必被封禁呢因為Meta在台北南山廣場大樓具有營運地點，也有提供過詐騙分子IP與行為訊號協助警方打擊詐騙並快速移除冒名詐騙貼文，然而Meta仍然充斥著詐騙因此被數發部多次開罰。而LINE在台同樣擁有據點為在台北市宏匯瑞光大樓。TikTok雖並未在台有據點然而平台在台灣有配合法規設置法律代表人也推出防詐宣導活動，並且有提供資料給予警方調查詐騙。\n",[83,26823],{},"\n3.政治因素：名面上政府是以反詐為由來封禁小紅書然而是否因政治因素無從得知故本文不多做評論。",[12,26826,26827,26828,26830,26831,26833],{},"結論",[83,26829],{},"\n這篇文章僅為個人薄見若有錯誤歡迎討論。而這次的行動也是台灣首次大規模封禁社群平台，看到了許多人的討論和觀點，是否違憲我也說不準只能表達我個人的觀點以及等待憲法法庭釋憲。而許多人利用這平台來學習美妝、調查觀光景點，學習知識甚至是家居裝潢是個具有多功能的平台失去了這個程式對於部分人來說十分重大，而後續的處理辦法也值得我們持續觀察。",[83,26832],{},"\n若釋憲最終推翻了我所描述的內容我將刪除此篇文章，感謝你看到這裡。",[12,26835,26836,26837],{},"封面來自於中央社2025 12\u002F6\u002F19:50 ",[49,26838,26839],{"href":26839,"rel":26840},"https:\u002F\u002Fwww.cna.com.tw\u002Fnews\u002Faipl\u002F202512060192.aspx",[53],{"title":169,"searchDepth":170,"depth":170,"links":26842},[],"2025-12-07","小紅書被台灣政府暫時封禁一年，其原由是否合乎法規與具備正當理由，並反思其所造成之影響。","\u002Fimages\u002Fuploads\u002F小紅書封禁.jpg",{},"\u002Fblog\u002F小紅書被封禁究竟是濫權還是無視法規呢?",{"title":26780,"description":26844},{"loc":26847},"blog\u002F小紅書被封禁究竟是濫權還是無視法規呢",[26774],"1rNZbL-QE9_cDaCX-Ey3O7qZWO37cyCDmJzA15ZK4AU",{"id":26854,"title":26855,"author":25833,"body":26856,"date":26890,"description":26891,"draft":174,"edited_at":181,"extension":175,"featured_image":181,"meta":26892,"navigation":178,"path":26893,"pinned":174,"seo":26894,"series":181,"seriesOrder":181,"sitemap":26895,"stem":26896,"tags":181,"__hash__":26897},"blog\u002Fblog\u002F2025數學回顧.md","2025數學回顧",{"type":9,"value":26857,"toc":26888},[26858,26861,26864,26867,26870,26873,26876,26879,26882,26885],[12,26859,26860],{},"2025對我來說可能是挑戰特別多的一年，很不幸的，這些挑戰都是來自生活、家人之類的，和數學無關，所以自然也壓縮到我讀書的時間，所以在年初時我直接開啟了gap year的模式，雖然學到的東西也蠻多的。",[12,26862,26863],{},"今年主要的讀書方向還是代數幾何，但是因為興趣的關係，我並沒有走向複幾何跟雙有理之類的偏代幾自身的研究方向，主要還是關注特定的問題所需要的代幾工具，就像仔細run一次étale cohomology是我今年的主要目標。這部分我是先讀了Poonen的Rational points on variety，大概在年初花了1個月看了第一次全書，最近準備看第二次跟習題，這也很符合我的讀書習慣，我常常用最短時間先抓各章的大致目標、重點以及難度，這樣可以方便我真的需要時比較輕鬆的掌握，在一些論文需要時也能很直接的接受那些我不知道怎麼證的結論。在這本書中，能看到蠻多的老朋友，比如fppf fpqc morphism之類的，之後還有Weil conjecture的一些東西之類的，最後一章是一些曲面理論，目前還沒用到，但是我預計會讀一下，最近和蠻多人討論還有在知乎逛到一些雙有理的在講一些曲面分類的東西，感覺就特別有趣。講到fppf fpqc morphism就會想到年初我也讀了FGA Explain 裡面很多目前被我當作black box的東西，比如Hilbert scheme，我是預計明年上半年就解決這本書，目前的記憶是它沒有習題，可能要找一些習題來練筆。",[12,26865,26866],{},"講到代幾就想到今年雙十一買了中國那邊給大學生的代數幾何書，主要內容還是老生常談的variety跟曲線論之類的，以Riemann-Roch 作為最終目標，有趣的是裡面蠻多的結果是我沒看過的，這讓我想起去年讀Weil的代幾書，展示了Grothendieck scheme理論之前的代幾模樣，也就是義大利學派他們的一些代數曲面分類的一些基礎跟相關的結果(至於核心的分類結果我不知道，所以就不多說什麼了XD)。今年也看了陳志杰的模、範疇、同調代數與層，這本書我認為是最棒的給要讀代幾的人的同調代數教材，一方面我們並不需要太多的同調代數知識，比如Kan decomposition，另一方面這本書用相對薄的厚度把代幾需要的同調代數都包含了進來，是一本我難得會翻下去想一看再看的中文數學書！",[12,26868,26869],{},"講到這裡就想到最近剛出版的Rising sea，這本書可以說是非常多人推薦的一本教科書，雖然我不是用這本書入門的，但是因為很多人都引用了這本前身的講義，所以就花了1800左右買下了。我目前仔細看了5章，也就是到Scheme自身的一些property，沒記錯的話應該是只有local的部分，整體來講沒有說特別符合我的胃口，誠然裡面的敘述是那種很苦口婆心式的敘述方法，但是裡面很多定義其實蠻口語化的，強調幾何的直觀。可能是習慣GTM52那種formal definition後再直觀，所以跟我不合，但是根據大家都看到一定程度，我自己還是會找時間看完它ww",[12,26871,26872],{},"和代幾相關但是也沒有太多相關的是暑假讀的K theory，我讀的是黎景輝的書，主要是代數詮釋的K theory，裡面的內容我查不多忘光了，但是最有趣的還是一些K group的認識，比如Grothendieck group跟Milner group，如果明年有空應該會再看一次，目標是把scheme的K theory給吃掉。",[12,26874,26875],{},"和自己方向相關還要讀的書大概是代數數論的部分，因為自己其實不需要特別多這方面的知識，因此看的書偏向一些比較基礎的書，比如Neukirch Marcus之類的書，Marcus是年初買的書，在最近才把它大致看完跟寫習題，除此之外我還買了馮克勤的代數數論，只剩下最後的Class field theory因為可能不需要就放著不看了。其實在讀馮的書到解析理論時，我突然發現那些東西特別好玩，所以現在我的購物車裡面放了很多解析數論的書，而且這些書都好貴，果然是高貴的數論(X",[12,26877,26878],{},"再來是一些被我當作”閒書“的數學書，今年的這類閒書真的蠻多的簡單講幾本好了。",[12,26880,26881],{},"我第一個想到的是一位跟我不錯的幾何分析教授推薦給我的一本GSM的extrinsic geometric flows，他給我的意見是可以看看前三章，也就是一些PDE的結果跟curve shortening flow，這本書很符合我對幾何分析的刻板印象，內容一堆不等式估計，有些upper bound的結果蠻醜的w 不過裡面的一些漂亮結果是書的後面才證的，主要是mean curvature flow的結果，至於有沒有機會繼續讀基本是看緣分了。",[12,26883,26884],{},"再來是Spectral geometry，也是上述教授推薦給我的，他自己也想要嘗試往這個方向，所以丟了一個40幾頁的note給我看。這個方向主要是考慮manifold上的laplacian operator，有些問題比如根據旋律去判斷鼓的形狀也是這個方向的問題之一，這部分的推廣形式會用到moduli space，是我第一次看見微幾根代幾的相交部分，雖然有聽過spectral algebraic geometry，但是這部分好像是代數拓撲那邊的東西，所以關於spectral geometry這個方向，我應該會找時間和教授討論一下要不要一起讀。",[12,26886,26887],{},"最後看了一下自己打的東西，注意到基本上都是講書，沒有論文之類的。我自己的理由應該是因為書給我的啟發比較多，因為目前的階段看書還是比較重要的一環，論文的話，我目前應該只能看出作者做了啥，沒有一個完整的圖像在我腦海裡，應該再幾年就能講一篇論文然後結合看過的相關資料講一些東西了XD",{"title":169,"searchDepth":170,"depth":170,"links":26889},[],"2025-12-05","上課無聊來隨便寫一下",{},"\u002Fblog\u002F2025數學回顧",{"title":26855,"description":26891},{"loc":26893},"blog\u002F2025數學回顧","bCmUt1pBpHXsHKJ4Lilknz6MU1c6DMUCt1p_umlgfOg",{"id":26899,"title":26900,"author":761,"body":26901,"date":28456,"description":28457,"draft":174,"edited_at":181,"extension":175,"featured_image":28458,"meta":28459,"navigation":178,"path":28460,"pinned":174,"seo":28461,"series":181,"seriesOrder":181,"sitemap":28462,"stem":28463,"tags":28464,"__hash__":28465},"blog\u002Fblog\u002Flatex-example.md","LaTeX Example",{"type":9,"value":26902,"toc":28454},[26903,26963,26970,27116,27122,27197,27204,27370,27377,27546,27803,27813,28097,28104,28304,28313,28452],[12,26904,26905,26906,26962],{},"Here is some inline math: ",[967,26907,26909],{"className":26908,"jax":971},[970],[973,26910,26914,26929],{"style":3005,"xmlns":976,"width":26911,"height":26912,"role":979,"focusable":980,"viewBox":26913,"xmlnsXLink":982},"8.699ex","2.072ex","0 -833.9 3845.1 915.9",[984,26915,26916,26919,26921,26924,26927],{},[987,26917],{"id":26918,"d":15299},"MJX-1-TEX-I-1D438",[987,26920],{"id":1017,"d":1018},[987,26922],{"id":26923,"d":1521},"MJX-1-TEX-I-1D45A",[987,26925],{"id":26926,"d":13121},"MJX-1-TEX-I-1D450",[987,26928],{"id":993,"d":994},[1024,26930,26931],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,26932,26933,26938,26943,26949],{"dataMmlNode":1031},[1024,26934,26935],{"dataMmlNode":1282},[1036,26936],{"dataC":15357,"xLinkHref":26937},"#MJX-1-TEX-I-1D438",[1024,26939,26941],{"dataMmlNode":1034,"transform":26940},"translate(1041.8,0)",[1036,26942],{"dataC":1097,"xLinkHref":1098},[1024,26944,26946],{"dataMmlNode":1282,"transform":26945},"translate(2097.6,0)",[1036,26947],{"dataC":1530,"xLinkHref":26948},"#MJX-1-TEX-I-1D45A",[1024,26950,26952,26957],{"dataMmlNode":1279,"transform":26951},"translate(2975.6,0)",[1024,26953,26954],{"dataMmlNode":1282},[1036,26955],{"dataC":13189,"xLinkHref":26956},"#MJX-1-TEX-I-1D450",[1024,26958,26960],{"dataMmlNode":1042,"transform":26959},"translate(466,363) scale(0.707)",[1036,26961],{"dataC":1046,"xLinkHref":1047},". This is a classic.",[12,26964,26965,26966,26969],{},"Now, let's look at the ",[773,26967,26968],{},"Quadratic Formula"," as a display equation:",[12,26971,26972],{},[967,26973,26975],{"className":26974,"jax":971},[970],[973,26976,26981,27012],{"style":26977,"xmlns":976,"width":26978,"height":26979,"role":979,"focusable":980,"viewBox":26980,"xmlnsXLink":982},"vertical-align: -0.797ex;","14.815ex","3.262ex","0 -1089.5 6548.3 1441.6",[984,26982,26983,26985,26987,26990,26992,26996,27000,27003,27006,27009],{},[987,26984],{"id":1261,"d":1262},[987,26986],{"id":11646,"d":1018},[987,26988],{"id":26989,"d":1955},"MJX-2-TEX-N-2212",[987,26991],{"id":11641,"d":11589},[987,26993],{"id":26994,"d":26995},"MJX-2-TEX-N-B1","M56 320T56 333T70 353H369V502Q369 651 371 655Q376 666 388 666Q402 666 405 654T409 596V500V353H707Q722 345 722 333Q722 320 707 313H409V40H707Q722 32 722 20T707 0H70Q56 7 56 20T70 40H369V313H70Q56 320 56 333Z",[987,26997],{"id":26998,"d":26999},"MJX-2-TEX-N-221A","M95 178Q89 178 81 186T72 200T103 230T169 280T207 309Q209 311 212 311H213Q219 311 227 294T281 177Q300 134 312 108L397 -77Q398 -77 501 136T707 565T814 786Q820 800 834 800Q841 800 846 794T853 782V776L620 293L385 -193Q381 -200 366 -200Q357 -200 354 -197Q352 -195 256 15L160 225L144 214Q129 202 113 190T95 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scale(0.707)",[1024,27032,27033],{"dataMmlNode":1034},[1036,27034],{"dataC":2081,"xLinkHref":27035},"#MJX-2-TEX-N-2212",[1024,27037,27038],{"dataMmlNode":1282,"transform":5186},[1036,27039],{"dataC":11612,"xLinkHref":11670},[1024,27041,27043],{"dataMmlNode":1034,"transform":27042},"translate(1207,0)",[1036,27044],{"dataC":27045,"xLinkHref":27046},"B1","#MJX-2-TEX-N-B1",[1024,27048,27051,27089,27096],{"dataMmlNode":27049,"transform":27050},"msqrt","translate(1985,0)",[1024,27052,27054,27066,27071,27077,27083],{"transform":27053},"translate(853,0)",[1024,27055,27056,27060],{"dataMmlNode":1279},[1024,27057,27058],{"dataMmlNode":1282},[1036,27059],{"dataC":11612,"xLinkHref":11670},[1024,27061,27063],{"dataMmlNode":1042,"transform":27062},"translate(462,289) scale(0.707)",[1036,27064],{"dataC":1046,"xLinkHref":27065},"#MJX-2-TEX-N-32",[1024,27067,27069],{"dataMmlNode":1034,"transform":27068},"translate(865.6,0)",[1036,27070],{"dataC":2081,"xLinkHref":27035},[1024,27072,27074],{"dataMmlNode":1042,"transform":27073},"translate(1643.6,0)",[1036,27075],{"dataC":12218,"xLinkHref":27076},"#MJX-2-TEX-N-34",[1024,27078,27080],{"dataMmlNode":1282,"transform":27079},"translate(2143.6,0)",[1036,27081],{"dataC":12888,"xLinkHref":27082},"#MJX-2-TEX-I-1D44E",[1024,27084,27086],{"dataMmlNode":1282,"transform":27085},"translate(2672.6,0)",[1036,27087],{"dataC":13189,"xLinkHref":27088},"#MJX-2-TEX-I-1D450",[1024,27090,27092],{"dataMmlNode":1034,"transform":27091},"translate(0,88.9)",[1036,27093],{"dataC":27094,"xLinkHref":27095},"221A","#MJX-2-TEX-N-221A",[2010,27097],{"width":27098,"height":27099,"x":27100,"y":27101},3105.6,42.4,"853","846.5",[1024,27103,27105,27109],{"dataMmlNode":2885,"transform":27104},"translate(1957.6,-345) scale(0.707)",[1024,27106,27107],{"dataMmlNode":1042},[1036,27108],{"dataC":1046,"xLinkHref":27065},[1024,27110,27111],{"dataMmlNode":1282,"transform":1052},[1036,27112],{"dataC":12888,"xLinkHref":27082},[2010,27114],{"width":27115,"height":2013,"x":2014,"y":2015},4402.7,[12,27117,27118,27119,8347],{},"We can also write ",[773,27120,27121],{},"Euler's Identity",[12,27123,27124],{},[967,27125,27127],{"className":27126,"jax":971},[970],[973,27128,27132,27152],{"style":3005,"xmlns":976,"width":27129,"height":27130,"role":979,"focusable":980,"viewBox":27131,"xmlnsXLink":982},"10.751ex","2.064ex","0 -830.4 4752 912.4",[984,27133,27134,27137,27139,27143,27146,27148,27150],{},[987,27135],{"id":27136,"d":5069},"MJX-3-TEX-I-1D452",[987,27138],{"id":1320,"d":1269},[987,27140],{"id":27141,"d":27142},"MJX-3-TEX-I-1D70B","M132 -11Q98 -11 98 22V33L111 61Q186 219 220 334L228 358H196Q158 358 142 355T103 336Q92 329 81 318T62 297T53 285Q51 284 38 284Q19 284 19 294Q19 300 38 329T93 391T164 429Q171 431 389 431Q549 431 553 430Q573 423 573 402Q573 371 541 360Q535 358 472 358H408L405 341Q393 269 393 222Q393 170 402 129T421 65T431 37Q431 20 417 5T381 -10Q370 -10 363 -7T347 17T331 77Q330 86 330 121Q330 170 339 226T357 318T367 358H269L268 354Q268 351 249 275T206 114T175 17Q164 -11 132 -11Z",[987,27144],{"id":27145,"d":1002},"MJX-3-TEX-N-2B",[987,27147],{"id":11725,"d":1725},[987,27149],{"id":11719,"d":1018},[987,27151],{"id":11728,"d":1718},[1024,27153,27154],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,27155,27156,27176,27182,27187,27192],{"dataMmlNode":1031},[1024,27157,27158,27163],{"dataMmlNode":1279},[1024,27159,27160],{"dataMmlNode":1282},[1036,27161],{"dataC":5174,"xLinkHref":27162},"#MJX-3-TEX-I-1D452",[1024,27164,27166,27170],{"dataMmlNode":1078,"transform":27165,"dataMjxTexclass":1079},"translate(499,363) scale(0.707)",[1024,27167,27168],{"dataMmlNode":1282},[1036,27169],{"dataC":1299,"xLinkHref":1329},[1024,27171,27172],{"dataMmlNode":1282,"transform":15407},[1036,27173],{"dataC":27174,"xLinkHref":27175},"1D70B","#MJX-3-TEX-I-1D70B",[1024,27177,27179],{"dataMmlNode":1034,"transform":27178},"translate(1418.2,0)",[1036,27180],{"dataC":1058,"xLinkHref":27181},"#MJX-3-TEX-N-2B",[1024,27183,27185],{"dataMmlNode":1042,"transform":27184},"translate(2418.4,0)",[1036,27186],{"dataC":1793,"xLinkHref":11768},[1024,27188,27190],{"dataMmlNode":1034,"transform":27189},"translate(3196.2,0)",[1036,27191],{"dataC":1097,"xLinkHref":11757},[1024,27193,27195],{"dataMmlNode":1042,"transform":27194},"translate(4252,0)",[1036,27196],{"dataC":1774,"xLinkHref":11771},[12,27198,27199,27200,27203],{},"Here is a ",[773,27201,27202],{},"summation"," (Sigma):",[12,27205,27206],{},[967,27207,27209],{"className":27208,"jax":971},[970],[973,27210,27215,27245],{"style":27211,"xmlns":976,"width":27212,"height":27213,"role":979,"focusable":980,"viewBox":27214,"xmlnsXLink":982},"vertical-align: -0.816ex;","21.589ex","3.185ex","0 -1047.1 9542.4 1407.7",[984,27216,27217,27220,27223,27225,27227,27229,27232,27234,27237,27240,27242],{},[987,27218],{"id":27219,"d":2455},"MJX-4-TEX-SO-2211",[987,27221],{"id":27222,"d":12851},"MJX-4-TEX-I-1D45B",[987,27224],{"id":1353,"d":1269},[987,27226],{"id":11798,"d":1018},[987,27228],{"id":11801,"d":1718},[987,27230],{"id":27231,"d":994},"MJX-4-TEX-N-32",[987,27233],{"id":1350,"d":990},[987,27235],{"id":27236,"d":1002},"MJX-4-TEX-N-2B",[987,27238],{"id":27239,"d":1725},"MJX-4-TEX-N-31",[987,27241],{"id":1356,"d":1010},[987,27243],{"id":27244,"d":1022},"MJX-4-TEX-N-36",[1024,27246,27247],{"stroke":1026,"fill":1026,"stroke-width":1027,"transform":1028},[1024,27248,27249,27277,27290,27295],{"dataMmlNode":1031},[1024,27250,27251,27256,27263],{"dataMmlNode":15384},[1024,27252,27253],{"dataMmlNode":1034},[1036,27254],{"dataC":2024,"xLinkHref":27255},"#MJX-4-TEX-SO-2211",[1024,27257,27258],{"dataMmlNode":1078,"transform":15393,"dataMjxTexclass":1079},[1024,27259,27260],{"dataMmlNode":1282},[1036,27261],{"dataC":12900,"xLinkHref":27262},"#MJX-4-TEX-I-1D45B",[1024,27264,27265,27269,27273],{"dataMmlNode":1078,"transform":6088,"dataMjxTexclass":1079},[1024,27266,27267],{"dataMmlNode":1282},[1036,27268],{"dataC":1299,"xLinkHref":1381},[1024,27270,27271],{"dataMmlNode":1034,"transform":15407},[1036,27272],{"dataC":1097,"xLinkHref":11828},[1024,27274,27275],{"dataMmlNode":1042,"transform":15412},[1036,27276],{"dataC":1774,"xLinkHref":11833},[1024,27278,27280,27284],{"dataMmlNode":1279,"transform":27279},"translate(2453.3,0)",[1024,27281,27282],{"dataMmlNode":1282},[1036,27283],{"dataC":1299,"xLinkHref":1381},[1024,27285,27287],{"dataMmlNode":1042,"transform":27286},"translate(378,363) 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example on how to write latex on this blog.","\u002Fimages\u002Fuploads\u002Flatex.png",{},"\u002Fblog\u002Flatex-example",{"title":26900,"description":28457},{"loc":28460},"blog\u002Flatex-example",[1031],"tXXxVl19h6hE_ldOS6b7BbnzZ-2dRdzZOE86ZGnD1kU",{"id":28467,"title":28468,"author":25833,"body":28469,"date":28456,"description":28598,"draft":174,"edited_at":181,"extension":175,"featured_image":28599,"meta":28600,"navigation":178,"path":28601,"pinned":174,"seo":28602,"series":181,"seriesOrder":181,"sitemap":28603,"stem":28604,"tags":28605,"__hash__":28607},"blog\u002Fblog\u002F微積分隨筆-未完成版.md","微積分隨筆",{"type":9,"value":28470,"toc":28592},[28471,28474,28482,28486,28489,28492,28495,28499,28502,28507,28510,28513,28518,28521,28524,28527,28530,28533,28536,28539,28542,28545,28548,28551,28554,28557,28562,28566,28571,28574,28577,28580,28583,28586,28589],[12,28472,28473],{},"這篇我應該主要講的是一些回頭看自己學習微積分or to say 分析的歷程，講一些自己想講的東西。而因為自己基本上都是在讀代數相關的東西，分析很久沒有碰，所以可能講的不是特別好。",[3780,28475,28476,28479],{},[12,28477,28478],{},"首先，這裡的微積分的定義有點模糊，因為我自己是直接看Baby Rudin學微積分的，然後再在大一的微積分課程補了一下自己的計算能力不足，所以我打算講到啥就講啥，不想太嚴格。",[12,28480,28481],{},"再來，以下可能會出現3種語言，中文、英文 and 台語。",[765,28483,28485],{"id":28484},"why-we-learn-calculus","Why we learn Calculus",[12,28487,28488],{},"對非數學系的人來說，微積分是一個語言，它是用來描述那些連續相關性質的語言，比如自然界中的種種現象，我們可以用微分方程去描述，而微分方程的基礎語言就是微積分，而對於統計機率來說，微積分也很重要，這是因為考慮連續的分佈(distribution)，我們要看那些random variable是遵循什麼樣的分佈時，就會利用微積分的語言了。",[12,28490,28491],{},"在數學系的視角來看，微積分就是一個很基礎的理論，它可以讓你第一次從高中那種比較不嚴格的論述走向嚴格論述，這也是數學系新生可能第一次面對到的困難–epsilon-delta定義。",[12,28493,28494],{},"在這之後的章節大概就是微積分的幾個topic了，定義連續、連續函數、連續函數的幾大定理、定義微分及微分的性質blabla，其中我覺得比較重要的是隱函數定理(Implicit Function Theorem)。在幾何中，隱函數定理很常出現，我記得在去年讀Loring W. Tu的那本manifold中，突然出現了隱函數定理，然後去問了系上做幾何分析的教授，才發現隱函數定理大有學問，這也讓我想到自己在代數路上走太深了，沒有怎麼注意其他方向的有趣東西，真是慚愧。",[765,28496,28498],{"id":28497},"some-topics-of-calculus","Some topics of Calculus",[12,28500,28501],{},"這邊我想要講一下微積分的看點，會粗略分為計算跟理論兩個部分。",[77,28503,28504],{},[19,28505,28506],{},"計算",[12,28508,28509],{},"計算這部分真的算老生常談，首先是計算能力。計算能力需要一次又一次的練習去練起來，根據我的經驗，無論是教授或是身邊同學，大家都這樣講的，所以還是不要像我一樣，都看題目然後想到方法就不動手算。",[12,28511,28512],{},"第二部分是積分法則。這部分我還記得大一時我覺得非常無聊，因為我實在懶得因為考試去背這些東西ww，但是和同學討論後，他給我了一個我覺得很棒的理由，他叫我給出有理函數都是可積的證明，而這個就是你可以在微積分課本上看到那些長長的公式的理論基礎。而這些積分法則在計算上真的很方便，這在有上到常微分方程課程的科系就能知道的事實。",[77,28514,28515],{},[19,28516,28517],{},"理論",[12,28519,28520],{},"這部分我覺得可以講幾個有趣的看點",[12,28522,28523],{},"首先是實數，這部分在大一時基本不會遇到，除非你是數學系，尤其是國外的數學系學生。實數定義本身就很有趣，在分析上，我有看過用公理直接定義的(比如Zorich那本數學分析書)、用Dedekind cut定義(大部分書籍都這樣定義)以及用Cantor sequence定義(Tao以及Amann -Escher裡面有）。不同方法代表了作者的品味，比如公理法就是簡單粗暴，我很喜歡這種風格，另外兩種是比較符合數學那種定義定理證明的調調，但是都需要花一個大篇幅去講，除非像Rudin直接塞在習題那就沒差了XD",[12,28525,28526],{},"第二個看點我覺得是微積分基本定理",[12,28528,28529],{},"微積分基本定理作為一個現在高中生都知道的定理，但是它背後藏了很多很深的東西，這些東西可以顯現數學家為了一般化，所以去設計出後續的很多理論，而微積分基本定理是一個引入Lebesgue Integral的一個很好的motivation。",[12,28531,28532],{},"在一般的書籍中，我們能看見這樣的微積分基本定理的條件：",[12,28534,28535],{},"F(x)可導、f(x)可積、F'(x)=f(x)",[12,28537,28538],{},"這個形式我記得跟高中不同，因為F的導數不一定可基以及f不一定可導，所以我們不要求f一定是F的導數，也就是這個形式是比高中時還要強的。",[12,28540,28541],{},"除此之外我們還有其他更強的形式，但是都得不到像高中那種簡潔的形式，這是因為Riemann積分的侷限性，而為了解決這個問題，我們可以引入Lebesgue積分，而這部分就是其他故事了，以後有機會再講。",[12,28543,28544],{},"第三個看點是隱函數定理，而它的重要性前面已經講過了，這邊稍微講一下證明它的幾個方法。",[12,28546,28547],{},"第一個方法是傳統的解方程，也就是做消元，之後做歸納，這個方法你能在100多年前的分析書找到，真的很傳統。第二個方法是找extreme value，這個方法我瞭解的不多，因為這是當初同學報告時給的酷東西，大概的難點是要找到一個函數去幫助你做出一些東西以及這個方法不能推廣到更一般的space，只能在歐式空間。第三個是現代最常見的方法，大家是叫它不動點法，它只需要一些前置知識比如metric space跟Banach不動點定理，就可以很漂亮的解決，而且在這個證明下，我們可以得知隱函數定理在一般的Banach space也是valid的。",[12,28549,28550],{},"最後一個看點我想要講的是一些作者會把拓撲、實分析、複分析以及流形之類的知識塞進課本中。",[12,28552,28553],{},"這部分有的人會覺得很討厭，因為課程安排可能會重疊，比如Courant-John的那三本Introduction to Calculus and Analysis中，塞了非常多東西，導致在之後的課程要上分析時，會重疊到，而且在那三本中的敘述就已經很嚴格了，並不只是單純的topic重疊。",[12,28555,28556],{},"對我來說，我覺得把一些高級的知識放進大一大二的課程中是可行的，因為那些知識雖然說是高級，只不過是一些常見的東西抽象化之後的產物，而且這個抽象化沒有特別抽象。比如metric space，只要對real spce有最簡單的理解，就可以用類比的方式去看它。",[3780,28558,28559],{},[12,28560,28561],{},"這邊還有一個看點超級重要，這邊因為我不想講所以跳過。如果說看一本分析書要看哪裡，就是要看它對於重積分換元定理的證明長什麼樣。這個定理要完完全全的證明可能要7 8頁正文，有些書是很含糊的就帶過。",[765,28563,28565],{"id":28564},"ways-to-learn-calculus","Ways to learn Calculus",[12,28567,28568],{},[773,28569,28570],{},"實踐是檢驗真理的唯一標準",[12,28572,28573],{},"數學這個科目不可避免的要做題目，但是要根據自己的胃口去寫多少以及怎麼樣的題目。這部分我的大致建議是一個章節盡量不要超過10題，選題方法可以去問看看自己的老師或是教授，甚至是去問AI，主要是問哪些題目是經典的題目就行了。",[12,28575,28576],{},"再來是選書，以非數學系的學生來講，只要找到一本最適合自己的書就好了，這部分可以去網路找看看自己相同科系或者背景的人的心得。",[12,28578,28579],{},"而對於數學系的學生，我認為除了一本最適合自己的書外，還要找好幾本參考書做參考。以我為例子好了，我當初是Baby Rudin當精讀，Zorich以及Amann-Escher當作參考書，而其中後者第三卷也是我精讀的，這是因為Baby Rudin最後講了Lebesgue theory ，但是大家的共識跟我自己也覺得寫的不是特別好，所以就用其他書了。",[12,28581,28582],{},"最後是心態，學習數學本身就是挫折滿滿，這是不管在哪個階段都會遇到的，對於挫折這件事，應該是要根據個人而去找方法解決，我自己是本身就習慣了這種挫折，所以才一直學數學到現在並且未來還想繼續走這條路下去。",[765,28584,28585],{"id":28585},"後記",[12,28587,28588],{},"這是我第一次寫這種文章，歡迎指出缺點。",[12,28590,28591],{},"以前都會覺得這種科普文章沒什麼，但是現在發現要給一些不是數學領域的人知道數學的一些東西，不是特別容易的事哈哈哈。",{"title":169,"searchDepth":170,"depth":170,"links":28593},[28594,28595,28596,28597],{"id":28484,"depth":170,"text":28485},{"id":28497,"depth":170,"text":28498},{"id":28564,"depth":170,"text":28565},{"id":28585,"depth":170,"text":28585},"應該高中生能看懂吧","\u002Fimages\u002Fuploads\u002Fscreenshot_20251104_160859_onedrive.jpg",{},"\u002Fblog\u002F微積分隨筆",{"title":28468,"description":28598},{"loc":28601},"blog\u002F微積分隨筆-未完成版",[28606],"隨筆","tNfb15uAkCM6eV6w55U2ekd-YqhQ3SoHdJQAVjJKn08",{"id":28609,"title":28610,"author":28611,"body":28612,"date":28846,"description":28847,"draft":174,"edited_at":181,"extension":175,"featured_image":28848,"meta":28849,"navigation":178,"path":28850,"pinned":174,"seo":28851,"series":181,"seriesOrder":181,"sitemap":28852,"stem":28853,"tags":28854,"__hash__":28856},"blog\u002Fblog\u002Fptau217-marks-tau-seeding-hotspots-in-early-alzheimer’s-cortex.md","pTau217 Marks Tau Seeding Hotspots in Early Alzheimer’s Cortex","automata",{"type":9,"value":28613,"toc":28835},[28614,28618,28621,28629,28632,28643,28646,28651,28655,28660,28664,28667,28670,28679,28683,28686,28689,28698,28702,28705,28713,28719,28728,28731,28742,28747,28751,28757,28760,28780,28786,28791,28795,28798,28801,28805,28811,28816,28830],[765,28615,28617],{"id":28616},"introduction","Introduction",[12,28619,28620],{},"阿茲海默症（Alzheimer’s disease, AD）是一種神經退行性疾病，其典型特徵包含 β-類澱粉蛋白（amyloid-β, Aβ）沉積與 tau 病理的累積。tau 病理不僅表現為神經元內神經纖維纏結（neurofibrillary tangles, NFTs），也出現為可驅動聚集的種子型 tau（seeding-competent tau），而這種 seeding activity 被認為與病理向不同腦區擴散相關。",[12,28622,28623,28626,28628],{},[773,28624,28625],{},"臨床與病理研究長期觀察到一個現象：AD 並非所有腦區同時、等量地受影響。",[83,28627],{},"\n相反地，一些區域（例如 entorhinal cortex, ENT 和 inferior temporal gyrus, ITG）在疾病早期就累積 tau 病理並表現強烈的退化跡象，而其他區域（例如cerebellum, CER）相對保留較長的時間。這種「區域差異」（regional variation）可能反映了兩件事：1. 某些腦區較早、較強地承受 tau 病理壓力。2. 某些 tau 分子型態（例如特定位點的p-tau）或 seeding activity，在不同腦區中本身就不一樣。",[12,28630,28631],{},"本研究的核心目標，是同時比較多個腦區的 tau 特性，包括：",[77,28633,28634,28637,28640],{},[19,28635,28636],{},"tau 播種活性（seeding activity）",[19,28638,28639],{},"特定位點磷酸化 tau（例如 pTau217, pTau262, pTau396 等）",[19,28641,28642],{},"tau 蛋白的整體含量",[12,28644,28645],{},"並將這些分子層級指標，對照這些腦區在阿茲海默症病程中所扮演的角色。",[3780,28647,28648],{},[12,28649,28650],{},"換句話說，問題不是單純「AD 腦有沒有 tau」，而是「哪一塊腦最早出現具播種能力的 tau？那一塊腦的 tau 長什麼生化樣態？這種 tau 樣態是否對應到可臨床量測的生物標記（例如 pTau217）？」",[765,28652,28654],{"id":28653},"background-and-rationale","Background and Rationale",[3780,28656,28657],{},[12,28658,28659],{},"這邊在論文架構上是不存在的，但我覺得需要補充一下資訊，以防有人看不懂 w",[781,28661,28663],{"id":28662},"_1-tau-and-phosphorylated-tau","1. Tau and phosphorylated tau",[12,28665,28666],{},"Tau 是一種 microtubule-associated protein，在成熟神經元特別是 axon 中，協助穩定 microtubules ，維持細胞骨架與軸突內物質運輸的完整性（Hardy and Selkoe 2002）。在阿茲海默症中，tau 分子會發生過度磷酸化（hyperphosphorylation），使 tau 從微管上解離，並逐步聚集成高度有序的 β-摺疊纖維，最終形成 NFTs，而 NFTs 是阿茲海默症病理診斷的經典標誌之一（Hardy and Selkoe 2002）",[12,28668,28669],{},"所謂磷酸化 tau（phosphorylated tau, p-tau）指的是 tau 在特定胺基酸殘基（通常是 Ser 或 Thr）上被磷酸化後的特定構型。不同位點的磷酸化定義出不同的 p-tau ，如 pTau217（Thr217 磷酸化）、pTau181（Thr181）、pTau262（Ser262 附近）、pTau396（Ser396\u002FSer404 區域）等。這些位點並非可互相取代：以 pTau217 為例，它在臨床研究中被證明在 AD 患者腦部和血漿中都顯著上升，並能將 AD 與其他失智症形式區隔，甚至在臨床症狀尚不嚴重的階段亦有區辨力（Palmqvist et al. 2020）",[22821,28671,24930,28672,24930,28676],{},[979,28673],{"src":28674,"alt":28675},"\u002Fimages\u002Fuploads\u002F螢幕擷取畫面-2025-11-02-163341.png","Intracellular neuronal aggregates in tauopathies",[22827,28677,28678],{},"Figure1. Tau phosphorylation, detachment from microtubules, and aggregation into neurofibrillary pathology. (a) In healthy neurons, tau binds to and stabilizes axonal microtubules, which are cylindrical polymers of α- and β-tubulin. Tau contains microtubule-binding repeats and additional domains (proline-rich region, projection domain) that help maintain microtubule structure. (b) Hyperphosphorylation of tau at multiple serine\u002Fthreonine sites by kinases such as GSK3β, CDK5, and ERK2 reduces tau’s affinity for microtubules, destabilizing the microtubule network. (c) Abnormally phosphorylated tau dissociates from microtubules and forms paired helical filaments (PHFs), which are heavily phosphorylated and often ubiquitinated. (d) Further processing and aggregation of tau yields oligomers and neurofibrillary tangles (NFTs), changes that are associated with neuronal dysfunction and ultimately cell death. Source: Mazanetz MP & Fischer PM, 2007, \\\\\\\\\\\\\\\\\\*Nature Reviews Drug Discovery\\\\\\\\\\\\\\\\\\* 6:464–479.",[781,28680,28682],{"id":28681},"_2-tau-seeding-activity","2. Tau seeding activity",[12,28684,28685],{},"Tau seeding activity 為描述一種「模板驅動聚集」的行為：已經錯誤折疊、並形成聚集核心的 tau（seed），能夠促使原本可溶性的 tau 轉換為相同β-摺疊聚集構型，並往外延伸成纖維狀聚集體。這代表 tau 病理不只是「自己累積變多」，而是具有可擴散的構形訊號（Kraus et al. 2019; Orrù et al. 2017）",[12,28687,28688],{},"在實驗上，這項播種活性可用 real-time quaking-induced conversion (RT-QuIC) 測量。RT-QuIC 將可能含有播種活性的腦組織均質液（brain homogenate）與重組 tau 底物共同孵育，並在週期性震盪條件下促進聚集。如果樣本中真的含有播種活性，則聚集會加速發生，並可用螢光染劑 Thioflavin T (ThT) 的訊號上升速率、終點強度、lag time（起始延遲時間）等指標來量化。此法也可計算 SD50（引發 50% 反應孔出現陽性訊號所需的稀釋度），作為播種活性強度的功能性指標（Kraus et al. 2019; Orrù et al. 2017）",[22821,28690,24930,28691,24930,28695],{},[979,28692],{"src":28693,"alt":28694},"\u002Fimages\u002Fuploads\u002F螢幕擷取畫面-2025-11-02-164733.png","The most promising techniques for the quantitation of tau seeding activity in human biofluid",[22827,28696,28697],{},"Figure 2. Quantifying tau seeding activity using biosensor cells and RT-QuIC. (A) In a cell-based biosensor assay, a sample containing tau seeds is applied to a reporter cell line overexpressing tau repeat domains fused to fluorescent proteins (e.g., CFP\u002FYFP). Seed-competent tau from the sample is taken up by the cells and induces intracellular tau aggregation. Aggregation brings the tagged tau molecules into close proximity, producing a FRET signal that can be quantified by flow cytometry as integrated FRET density (combining %FRET-positive cells and median FRET intensity). (B) In RT-QuIC, a seed-containing sample is incubated with excess recombinant tau substrate and thioflavin T (ThT) under shaking\u002Fincubation cycles. Seed-competent tau drives templated aggregation of the substrate, generating a characteristic ThT fluorescence trace: an initial lag phase followed by a rapid aggregation phase and plateau. The ThT kinetics provide a quantitative readout of tau seeding activity in biofluids such as CSF. Source: Lathuiliere A. & Hyman B.T., 2021, Frontiers in Neuroscience 15:654176.",[781,28699,28701],{"id":28700},"_3-braak-staging-thal-staging","3. Braak staging \u002F Thal staging",[12,28703,28704],{},"阿茲海默症病理的「空間 - 時間順序」可以用兩個常用分期系統來描述 :",[3780,28706,28707],{},[12,28708,28709,28710,28712],{},"這邊我們著重於 Braak staging，因為它在描述 tau上與本研究比較有關連 ; ",[83,28711],{},"\n有興趣可以去查另一個 Thal staging，描述 β-amyloid 沉積的範圍與分布廣度",[12,28714,28715,28716,28718],{},"Braak staging：描述 tau 病理（特別是 NFTs）如何在大腦中依序出現與擴散。",[83,28717],{},"\n典型順序是：最早在 entorhinal cortex 與內側顳葉（包括海馬相關迴路）觀察到高度 tau 病理；接著外側顳葉皮質，包括 inferior temporal gyrus (ITG)、middle temporal gyrus (MTG)、superior temporal gyrus (STG)；最後擴散到更廣泛的新皮質聯合區域。cerebellum (CER, 小腦) 在典型 AD 病程中通常相對少見明顯 tau 纖維性病變（Braak and Braak 1991; Braak and Braak 1995; Braak et al. 2006）。",[22821,28720,24930,28721,24930,28725],{},[979,28722],{"src":28723,"alt":28724},"\u002Fimages\u002Fuploads\u002Ftau-tracer-uptake-patterns-resemble-ex-vivo-braak-stages-a-schematic-display-of-braak.png","Figure 3. Braak stages of tau pathology in Alzheimer’s disease and their in vivo PET correlates.",[22827,28726,28727],{},"Figure 3. Braak stages of tau pathology in Alzheimer’s disease and their in vivo PET correlates. (A) Schematic post mortem staging of Alzheimer’s disease tau pathology (neurofibrillary tangles composed of hyperphosphorylated tau). Earliest involvement (Braak stages I\u002FII) is localized to the transentorhinal \u002F entorhinal cortex and adjacent medial temporal structures. Intermediate stages (III\u002FIV) involve limbic regions, including medial temporal lobe and parts of medial parietal cortex. Late stages (V\u002FVI) show widespread neocortical involvement. (B) Tau PET tracer uptake patterns in vivo (e.g., \\\\\\\\\\\\\\[¹⁸F]Flortaucipir) recapitulate this hierarchical progression: signal first appears in entorhinal \u002F medial temporal cortex, then spreads to inferior and lateral temporal cortex and medial parietal regions, and finally becomes widespread across association neocortex. These PET patterns provide living-brain support for Braak’s ex vivo staging of tau pathology. Source: Adapted from “Biomarkers for tau pathology,” Schöll M. et al., 2018, Molecular and Cellular Neuroscience.",[12,28729,28730],{},"本研究特別挑選多個腦區（ENT、ITG、MTG、STG、CER 等）來比較播種活性與 tau 分子狀態，這些腦區並不是隨機抽樣，而是涵蓋：",[77,28732,28733,28736,28739],{},[19,28734,28735],{},"典型 AD 病程中「早期高風險、最先累積 tau 病理」的區域（ENT、ITG）",[19,28737,28738],{},"進一步受累的外側顳葉皮質（MTG、STG）",[19,28740,28741],{},"以及對照用的、在典型 Braak 分期中較少 tau 聚集的小腦（CER）",[3780,28743,28744],{},[12,28745,28746],{},"透過橫跨這些腦區，本研究在測試「Braak staging 的時序 ≈ seeding activity 的梯度」",[781,28748,28750],{"id":28749},"_4-rt-quic","4. RT-QuIC",[12,28752,28753,28754,28756],{},"Real-time quaking-induced conversion (RT-QuIC) 是一個高靈敏度的體外偵測方法。",[83,28755],{},"\n最初用於朊毒蛋白（prion）類疾病，後來擴展至 α-synuclein、tau 等可產生 seeding activity 的錯誤折疊蛋白（Orrù et al. 2017）。本研究利用 RT-QuIC 來問：不同腦區的 AD 樣本，其播種活性是否同樣強？是否和 Braak staging 順序吻合？是否與特定 p-tau 物種（例如 pTau217）對應？",[12,28758,28759],{},"RT-QuIC 的量測重點指標包含：",[77,28761,28762,28768,28774],{},[19,28763,28764,28767],{},[773,28765,28766],{},"lag time","：螢光訊號（ThT）開始上升前的延遲時間，越短代表播種引發聚集的速度越快",[19,28769,28770,28773],{},[773,28771,28772],{},"end-point ThT fluorescence","：反應終點的螢光強度，代表最終聚集程度",[19,28775,28776,28779],{},[773,28777,28778],{},"SD50","：引發 50% 反應孔出現陽性的劑量",[12,28781,28782,28783,28785],{},"重點是，RT-QuIC 測到的是「功能性 seeding activity」，而不是單純的「total tau 」。",[83,28784],{},"\n也就是說，就算兩個腦區的 tau 含量類似，它們的 seeding activity 仍可能不同。",[3780,28787,28788],{},[12,28789,28790],{},"如果對於 RT-QuIC 有興趣可自行上網搜尋相關步驟，這邊偷懶省略方法學",[781,28792,28794],{"id":28793},"_5-clinical-biomarker-relevance-of-ptau217","5. Clinical biomarker relevance of pTau217",[12,28796,28797],{},"臨床上，pTau217 已被提出為具高潛力的 AD marker，包含腦脊髓液與血漿檢測。研究顯示，血漿 pTau217 在區分典型 AD 與其他失智症型態時具高敏感度與高特異度，甚至在臨床症狀尚未完全明顯之前已可異常（Palmqvist et al. 2020；Jack et al. 2024）。",[12,28799,28800],{},"本研究將這個臨床層訊號往回對照腦內：pTau217 是否在 AD 早期最脆弱、最早受累積的皮質區域（例如 ITG、ENT）顯著集中？這些同時又是否是 seeding activity 最強的腦區？如果答案是肯定的，那麼 pTau217可能反映了特定腦區內、 tau 本身的狀態。",[765,28802,28804],{"id":28803},"methods","Methods",[12,28806,28807,28808,28810],{},"對於方法學有興趣的可以去讀一下原論文，它放在 Discussion下面。",[83,28809],{},"\n這邊我將 Methods 提前說明，配合 Results 的實驗結果。",[12,28812,28813],{},[773,28814,28815],{},"超簡單版方法學 :",[16,28817,28818,28821,28824,28827],{},[19,28819,28820],{},"使用已確診阿茲海默症病例的死後人類腦組織，切片+免疫染色後掃描",[19,28822,28823],{},"將各腦區的腦漿稀釋後，加入含有 tau 的多孔板，在震盪\u002F孵育條件下進行 RT-QuIC",[19,28825,28826],{},"跑 Western blotting，採用密度分析法測定 tau protein 強度，進行定量分析",[19,28828,28829],{},"將 AD 患者和非 AD 對照組的腦漿拿去跑液相層析質譜 (LC-MS) 分析",[3780,28831,28832],{},[12,28833,28834],{},"ps. 這篇的大腦來源是北京和湖南長沙，看起來是南昌大學醫學院主導的",{"title":169,"searchDepth":170,"depth":170,"links":28836},[28837,28838,28845],{"id":28616,"depth":170,"text":28617},{"id":28653,"depth":170,"text":28654,"children":28839},[28840,28841,28842,28843,28844],{"id":28662,"depth":7336,"text":28663},{"id":28681,"depth":7336,"text":28682},{"id":28700,"depth":7336,"text":28701},{"id":28749,"depth":7336,"text":28750},{"id":28793,"depth":7336,"text":28794},{"id":28803,"depth":170,"text":28804},"2025-11-02","論文整理小筆記 (可能適合?對於生物醫學有興趣的人閱讀)","\u002Fimages\u002Fuploads\u002F螢幕擷取畫面-2025-11-02-145011.png",{},"\u002Fblog\u002Fptau217-marks-tau-seeding-hotspots-in-early-alzheimer's-cortex",{"title":28610,"description":28847},{"loc":28850},"blog\u002Fptau217-marks-tau-seeding-hotspots-in-early-alzheimer’s-cortex",[28855],"Research notes","drSy8mt-fC88DVATF_184V4CS3ul99GxeOC0OvZO4CE",{"id":28858,"title":28859,"author":28611,"body":28860,"date":29483,"description":29484,"draft":174,"edited_at":181,"extension":175,"featured_image":29485,"meta":29486,"navigation":178,"path":29487,"pinned":174,"seo":29488,"series":181,"seriesOrder":181,"sitemap":29489,"stem":29490,"tags":29491,"__hash__":29493},"blog\u002Fblog\u002Fstability-instead-of-revenge-a-reconstruction-strategy-for-post-world-war-i-germany-1919-1935.md","Stability Instead of Revenge: A Reconstruction Strategy for Post-World War I Germany, 1919-1935",{"type":9,"value":28861,"toc":29466},[28862,28866,28869,28871,28879,28882,28885,28888,28891,28895,28898,28901,28904,28907,28910,28914,28917,28920,28923,28926,28929,28933,28938,28941,28944,28947,28950,28953,28961,28965,28968,28973,28976,28979,28982,28986,28989,28994,28997,29005,29010,29013,29018,29021,29026,29029,29032,29036,29039,29042,29050,29053,29056,29060,29063,29068,29071,29076,29079,29084,29087,29090,29094,29097,29100,29103,29107,29110,29113,29116,29119,29123,29126,29129,29418,29422,29428,29434,29437,29443,29449,29451],[765,28863,28865],{"id":28864},"abstract","Abstract",[12,28867,28868],{},"本文將論證，德國在 World War I 戰敗後 (1919-1935) 並非只能在被凡爾賽條約長期壓制與走向法西斯主義擴張之間二選一。相反的，1919年至1929年之間確實存在一條穩定化重建路線：以跨派系的文人聯合政府、賠款-貨幣重組與外資帶動工業復甦、防禦導向而受政府監督的軍隊、社會安全網與公共工程吸收失業人口、以及將德國高技術工業定位為歐洲復興工廠，而非侵略工具。¹ 本文指出，這套路線在1924-1929年的德國局部實現過，並一度成功讓德國恢復貨幣穩定、重返國際金融、獲得部分外交正常化，甚至暫時壓低極端主義吸引力。² 然而，該路線並未在1920年代以制度（社會保險、政府節制軍權、危機時的公共就業機制）形式被保留；因此，當1929年全球經濟崩盤、外資抽離、德國失業激增至數百萬時，政治中心沒有緩衝能力，極端民族主義遂乘虛而入，最終在1933年奪權。³ 本文主張，威瑪共和國的悲劇不在於從未有機會，而在於曾經接近成功，卻未能將短暫的穩定變成結構性的常態。",[765,28870,28617],{"id":28616},[22821,28872,24930,28873,24930,28876],{},[979,28874],{"src":28875,"alt":24934},"\u002Fimages\u002Fuploads\u002Fsignatures_du_traité_de_versailles_28_juin_1919_-_page_213.jpg",[22827,28877,28878],{},"fac-simile des trois pages de signature du traité de Versailles ,Amalgamated press Ltd",[12,28880,28881],{},"1918年11月，德國在 WW1 中求和，帝國倒台，威瑪共和國成立。⁴ 隨後的《凡爾賽條約》強制德國接受全部「戰爭罪責」、割讓領土、喪失殖民地，並將其陸軍限制在10萬人，同時禁止坦克、重砲、潛艦與軍用飛機，要求解散總參謀部。此外，條約在賠款問題上採取懲罰性設計，最終以1320億金馬克的天文數額呈現；協約國亦保留以軍事占領方式強制徵收的權利。⁵ 這些條件不只重創德國經濟結構與軍事威信，也使新生的議會政體在國內缺乏正當性，被廣泛視為受監管的戰敗政權，而非能保護國家利益的主權政府。⁶",[12,28883,28884],{},"傳統論述往往把德國的命運描述為宿命式的二擇一：第一是屈從於凡爾賽秩序、在外力操控下的共和國；第二是走向民族復仇主義與極端威權統治，即納粹主導的軍事再擴張帝國。⁷ 本文將提出第三條路線的存在：1919-1929年間，德國在結構上其實有一個政治與經濟的穩定化方案，能在不立即求戰的前提下，逐步恢復主權談判能力、貨幣信用、社會秩序與產業競爭力。這條路線的本質不是引起戰爭轉移國內焦點，也不是肅清左右極端份子，而是以國家主導的秩序與社會安全作為生存工具。",[12,28886,28887],{},"本文的核心論點如下：德國在戰後真正需要、而且在部分時期曾經短暫擁有的，是一套以五大支柱構成的穩定化戰略：(1) 跨派系的重建型文人內閣，壓制左右極端武裝、確立文人節制武力；(2) 將賠款由懲罰機制轉化為外資、工業復甦的長期重建機制，同時提前穩定貨幣；(3) 以防禦導向、專業化、政府監督的小型軍隊作為外交籌碼，而非立即擴張；(4) 把失業保險、公共工程與工人制度化參與視為國安緩衝，而非慈善；(5) 把德國的高端化工、機械、電氣工程產業視為德國整體重建不可或缺的關鍵點，以產業互賴取代領土擴張。",[12,28889,28890],{},"本文將依照時間脈絡與主題層面證明，這套方案在1924-1929年曾局部落地，卻未能制度化，因此在1929年全球經濟衝擊下崩解，讓極端主義接收一切。",[765,28892,28894],{"id":28893},"historiographical-background","Historiographical Background",[12,28896,28897],{},"戰後德國的崩壞與納粹上台，長久以來在史學上有幾種主要解讀。",[12,28899,28900],{},"Richard J. Evans 代表的解釋，強調威瑪共和國一出生便被內部暴力政治侵蝕：政府在1919-1920年仰賴右翼準軍事部隊（自由軍團）鎮壓左翼革命，但事後並未真正將武力壟斷收回國家，反而讓軍國民族主義勢力保留武裝自主性，進一步破壞了議會體制的正當性。依此觀點，威瑪的軟弱、菁英階層對民主的半心半意、以及1930年代初期的大規模失業，塑造了極端民族主義成為唯一有力方案的氛圍。⁸",[12,28902,28903],{},"Adam Tooze 則將經濟－金融結構視為關鍵：德國的貨幣信用在1922-1923年間幾近毀滅，1923年魯爾工業區被法國與比利時佔領，柏林政府以消極抵抗配合印鈔補貼工人，導致惡性通膨摧毀了中產階級的儲蓄與對政府的信任；德國後來雖靠《道威斯計畫》(1924) 和《楊格計畫》(1929) 爭取重新融入國際金融體系，卻因此對外資與出口過度依賴。當美國在1929年後抽走資金時，德國經濟瞬間崩盤，失業暴增，政治因此坍塌。⁹",[12,28905,28906],{},"Margaret MacMillan 則從國際秩序角度強調，《凡爾賽條約》不只是處罰性的和平條件，而是一套長期監管機制：它限制德國軍力，保留盟國對德國工業心臟地帶動武索賠的正當性，並透過賠款架構將戰敗德國鎖在一個受監督的次等國地位。凡爾賽因此在心理與制度層面同時引發國恥與必須突破的國內敘事。¹⁰",[12,28908,28909],{},"本文介入的角度是：上述觀點對威瑪為何失敗的描述相當有力，但它們往往把失敗看成一條直線。本文將主張，1924-1929年間其實出現過一個「幾乎可行」的折衷模式：外交上用合作談判取代立即復仇、金融上用國際貸款換取賠款分期、軍事上用防禦導向取信鄰國、國內用公共工程與社會安全網抑制失業激進化。而這套模式之所以沒能避免1933年的極權化，不是因為它過於理想化，而是因為它沒有被及時制度化成持久的政策。¹¹",[765,28911,28913],{"id":28912},"methodology-and-scope","Methodology and Scope",[12,28915,28916],{},"本文的論證結合兩種層次。",[12,28918,28919],{},"第一，本文採用傳統敘事史料與權威次級史料（Evans、Tooze、MacMillan 等）來重構1918-1935年間的德國：惡性通膨、魯爾佔領、《道威斯計畫》與《楊格計畫》、1925年《洛迦諾條約》、德國1926年進入國際聯盟、1929年美資抽離後的失業潮與政治極端化。¹²",[12,28921,28922],{},"第二，本文採用反事實測試（counterfactual testing），但以非常有限且可驗證的方式進行。本文並不空想一個完全不同的德國，而是以假設：「如果已在1924-1929年短暫出現的做法（例如：用外資重組賠款、穩定貨幣並恢復工業、以合作外交換取撤軍、在城市層級實施公共工程）能夠在1919-1923年更早被啟動，並在1920年代中期就被立法固化成制度，那麼1929-1932年全球衰退是否仍會必然導向極端民族主義的勝利？」這種推論並非「許願」，而是把歷史上確實存在的政策片段往前推幾年，並問它們是否有現實的政治－外交條件可以提前出現。¹³",[12,28924,28925],{},"本研究的侷限也在此，1929年的全球金融崩潰與美資撤離並非德國可以單方面避免的衝擊；即使德國在1920年代中期就完成經濟制度與軍隊管理，也不能保證納粹不會崛起。",[12,28927,28928],{},"本文的主張較為溫和：不是「希特勒一定消失」，而是威瑪共和國其實有一個窄而真實的生存窗口，且它幾乎成功了，但沒能建立起制度。",[765,28930,28932],{"id":28931},"i-the-postwar-crisis-structural-constraints","I. The Postwar Crisis: Structural Constraints",[12,28934,28935],{},[773,28936,28937],{},"1918-1923年的德國同時面臨四個危機，而且這四個危機互相強化彼此。",[12,28939,28940],{},"首先是財政與貨幣的崩潰。戰爭主要靠舉債支撐的德意志帝國在戰敗後不但要面對本身龐大債務，還要負擔賠款。1923年，法國與比利時為強行收取煤炭和工業產出，直接佔領魯爾工業區；柏林政府呼籲工人消極抵抗，並以印鈔補貼他們不工作的收入。結果是惡性通膨在1922-1923年全面爆發，馬克幾乎失去價值，中產階級的畢生積蓄在數月間蒸發。這一事件摧毀了社會對威瑪政府「至少能保護你的財產」的信任。¹⁴",[12,28942,28943],{},"第二是內部武裝政治。1919年1月柏林的左翼革命嘗試建立評議會式政權，卻被政府授權的右翼自由軍團（Freikorps）所鎮壓。這些自由軍團並不效忠議會民主，而是民族主義、反共主義的半獨立武裝。結果，威瑪政府一開始就把國家軍事外包給一群其實也想推翻體制的人，等於告訴社會：「政治靠槍，不靠憲法。」¹⁵",[12,28945,28946],{},"第三是外交上的受監管地位。《凡爾賽條約》不但限制軍備，還授權協約國在德國境內以占領、查驗裁軍等手段執行戰後和平。德國失去殖民地、重裝軍力與威懾力，變成一個可以被隨時施壓的工業國。¹⁶",[12,28948,28949],{},"第四是大規模失業與社會挫敗。戰後復員釋放出大量失業退伍軍人，魯爾停工又使經濟中樞停擺。年輕勞工、退伍士兵、低階中產失去收入與尊嚴，開始把希望投向極端勢力—左派是革命化的工人組織，右派是民族羞辱敘事下的準軍事團體。¹⁷",[12,28951,28952],{},"這四重危機構成一個惡性迴路：經濟毀滅感、外來占領的羞辱、政治暴力的常態化、與失業的絕望感互相疊加，讓威瑪政府的正常議會政治顯得無能而軟弱。¹⁸",[22821,28954,24930,28955,24930,28958],{},[979,28956],{"src":28957,"alt":169},"\u002Fimages\u002Fuploads\u002Fgermany_hyperinflation.svg.png",[22827,28959,28960],{},"Logarithmic chart of German Hyperinflation. Based on the values in Table IV (page 441) of The Economics of Inflation by Costantino Bresciani-Turroni, published 1937.",[765,28962,28964],{"id":28963},"ii-political-consolidation-a-reconstruction-cabinet","II. Political Consolidation: A Reconstruction Cabinet",[12,28966,28967],{},"若要讓德國不在1919-1920年就走向內戰，需要立即讓國內停火，也就是建立一個跨派系的重建內閣。這個內閣必須同時吸納溫和社會民主派（SPD）、天主教中間政黨（Zentrum）、自由派資產階級與務實保守派官僚／工業界代表，並對外聲明：此政府的優先目標是國家穩定，而非階級清算或民族復仇。¹⁹",[12,28969,28970],{},[773,28971,28972],{},"這樣的重建內閣必須同時完成三個條件。",[12,28974,28975],{},"第一個交換：彼此承諾不打內戰。 溫和左派同意暫不推行全面評議會革命，而接受議會制度；溫和保守派與工商菁英同意不再縱容自由軍團等右翼私兵作為警察替代品。換句話說，政府不得再用「一邊的民兵」去屠殺「另一邊的民兵」，卻又不把武力收回國家。Evans 指出，威瑪在1919-1920年的最大錯誤，正是用右翼私軍去鎮壓左翼，卻沒有在事後國家化右翼武力，導致雙方都不再信任共和國的中立性。²⁰",[12,28977,28978],{},"第二個交換：把全部武裝力量國家化並置於政府監督。 所有準軍事組織：左翼工人武裝、右翼自由軍團，都應在1919-1920年被編入「國家治安與邊境防衛部隊」，同時在法理上接受國會監督，仿照軍事專業加政治監督的雙軌模式。這樣的目的，是阻止「平行軍閥國」在德國內部持續存在。²¹",[12,28980,28981],{},"第三個交換：對外給出一致、務實、可談判的訊號。 重建內閣必須在1919-1920年對英國與美國釋放明確訊號：「德國希望以談判重訂賠款的支付方式與占領條件，而非以短期軍事報復行動推翻凡爾賽秩序。」這個訊號並非投降，而是一種拉攏：英國與美國本身就擔心法國對魯爾的強硬占領會導致全歐洲不穩，而不穩會威脅英美資本的安全。若柏林能從一開始就主打「我要求生存空間，而不是立刻打仗」，它在國際金融與外交上更容易獲得緩衝，換取之後的賠款重談。²²",[765,28983,28985],{"id":28984},"iii-reparations-currency-and-industrial-recovery","III. Reparations, Currency, and Industrial Recovery",[12,28987,28988],{},"若無法處理賠款制度、貨幣信用與工業復甦，德國無法持續存在為一個可治理的現代國家。",[12,28990,28991],{},[773,28992,28993],{},"賠款重組：從國際懲罰轉為分期＋外資＋工業復甦。",[12,28995,28996],{},"1924年的《道威斯計畫》將原本幾乎不可支付的賠款重新包裝：美國與其他貸款向德國注入資本，以恢復其工業生產；德國則以恢復後的出口收入，按年、分期支付較低的賠款，並以此換取法國1925年逐步撤出魯爾。到1929年，《楊格計畫》更嘗試將賠款總額下修、付款期延長，並逐漸撤除對德國內政的直接監管。這相當於把懲罰性賠款變成分期付款的迴路。²³",[22821,28998,24930,28999,24930,29002],{},[979,29000],{"src":29001,"alt":24934},"\u002Fimages\u002Fuploads\u002Fdawesplan.webp",[22827,29003,29004],{},"The Dawes Plan-Chapter 15 – Years of Crisis. Mrs. Tucker World History Victor Valley High School. Main Points. Postwar Uncertainty Worldwide Depression Fascism Rising in Europe Aggressors Invade Nations.",[12,29006,29007],{},[773,29008,29009],{},"(1) 貨幣穩定化（1923 年後的倫滕馬克改革）",[12,29011,29012],{},"惡性通膨是威瑪合法性的致命傷。1922-1923年間，政府為了補貼魯爾工業區的消極抵抗，用印鈔撐住工人的生活，結果貨幣價值崩毀，德國中產階級的存款化為廢紙。這讓數百萬人相信：共和國無法保護你的基本財產。真正可行的穩定方案是停止用印鈔當社會安撫工具，改用稅收與國內公債、讓魯爾重新運轉來恢復稅基、並在1923年底以倫滕馬克（以工業資產為擔保）重建貨幣信用。這些措施在史實中確實止住了惡性通膨，但它們是在經濟已經全毀後才被迫上線，而不是在1921-1922年就被主動採取。²⁴",[12,29014,29015],{},[773,29016,29017],{},"(2) 把德國的高技術工業當成談判籌碼",[12,29019,29020],{},"德國在化工、染料、藥品、精密機械、電氣工程、光學儀器等領域的技術力，在1920年代中後期迅速恢復並成為歐洲重建所需要的關鍵供應來源。德國可以（在1924-1929年部分確實這樣做）向英法表示：「你們想要恢復自己的現代工業，就需要穩定、運作中的德國重工與化工。要達到這點，你們必須允許我脫離被占領狀態，並把賠款轉成可行的長期分期。」把工業復甦轉換成外交籌碼，而非軍事威脅。²⁵",[12,29022,29023],{},[773,29024,29025],{},"(3) 風險：對外資的高度依賴",[12,29027,29028],{},"這條重建路線有一個致命弱點：它嚴重依賴美國資本。當美國在1929年後金融崩盤並抽回資金時，德國外匯斷裂，工廠倒閉，失業數百萬人，整個社會再次陷入絕望，而極端政黨正是在這個真空期迅速坐大。²⁶",[12,29030,29031],{},"統整以上資料分析，賠款重組＋工業復甦買到的其實是一段黃金緩衝期，而不是永久解答。這段緩衝期只對德國有用，前提是它用來重建社會安全網、政府節制軍權、公共工程就業保險化，讓金融衝擊不會直接使德國崩盤。²⁷",[765,29033,29035],{"id":29034},"iv-military-and-diplomacy-using-a-defensive-army-as-a-negotiating-tool","IV. Military and Diplomacy: Using a Defensive Army as a Negotiating Tool",[12,29037,29038],{},"《凡爾賽條約》將德國陸軍限縮為10萬人的國防軍，禁止重裝武器、坦克、潛艦、軍機，並解散總參謀部，目的就是讓德國喪失重新發動大規模歐陸戰爭的能力。²⁸ 德國菁英在1920年代有兩種本能反應：一是祕密規避條約（例如在蘇俄境內試驗裝甲戰術與航空訓練）；二是鼓吹「凡爾賽就是國恥，必須以武力打破」。²⁹",[12,29040,29041],{},"穩定化策略的替代方案，則是把軍事限制本身轉化成外交籌碼。也就是說：德國公開承諾維持小型、專業、明確防禦導向、受政府監督的軍隊，並以此要求法國撤出魯爾工業區、要求停止「佔領式討債」、要求德國被承認為「正常歐洲國家」，而不再是永久的戰犯監管對象。這個邏輯在1925年《洛迦諾條約》中開始具體化：德國與法國、比利時互保西部邊界的現狀，英國與義大利作為保證國，德國藉此逐步恢復外交主體資格，並在1926年加入國際聯盟。³⁰",[22821,29043,24930,29044,24930,29047],{},[979,29045],{"src":29046,"alt":24934},"\u002Fimages\u002Fuploads\u002Fwar_ensign_of_germany_-1921–1933-.svg.png",[22827,29048,29049],{},"War flag of Weimar Republic with iron cross (1921–1933) ,Jwnabd",[12,29051,29052],{},"然而，這要求國防軍（Reichswehr）接受兩件在普魯士軍事文化裡並不自然的事：(1) 服從文人政府，而不是把自己視為「真正的國家」；(2) 把任務定義為防禦與內部秩序維持，而非準備下一場復仇戰爭。³¹",[12,29054,29055],{},"Evans 指出，1920年代的國防軍仍保留高度專業自豪感，並非納粹式黨軍；它轉向侵略與意識形態戰爭的徹底化，是1933年後才發生的事。也就是說，如果威瑪政府能在1920年代中期就將防禦導向、政府監督的軍隊用憲政形式限制，國防軍可能成為秩序維持者，而非未來極權政權的工具。³²",[765,29057,29059],{"id":29058},"v-social-stability-as-national-security-unemployment-insurance-public-works-and-worker-participation","V. Social Stability as National Security: Unemployment Insurance, Public Works, and Worker Participation",[12,29061,29062],{},"1932年時，德國失業人口被估計在六百萬上下，約接近總勞動力三成，這種規模的失業讓無數工人、店員、店主、退伍兵相信國家已經徹底失能。在這樣的心理氣候下，任何承諾立刻採取強力行動、恢復秩序與尊嚴的勢力，無論是革命左派或極端民族主義右派，都會看起來比沉悶的議會政黨更現實。穩定化路線因此把社會政策視為穩定國安，而不是慈善事業。³³",[12,29064,29065],{},[773,29066,29067],{},"(1) 失業保險與最低生存線。",[12,29069,29070],{},"1920年代的德國政府若能提早（在景氣尚可的1924-1929年間）用稅收與長期內債建立全國性的失業保險、基本糧食與住房補助制度，失業者在景氣下滑時就不會瞬間掉到今天沒飯吃的深淵。這會直接降低因失業而轉變為暴力動員的效率。失業保險在此是國家安全閥，而非單純社福。³⁴",[12,29072,29073],{},[773,29074,29075],{},"(2) 公共工程作為就業緩衝池。",[12,29077,29078],{},"威瑪時期的地方政府其實已經在做市政現代化、公共住宅、都市基礎建設、電氣化、自來水與下水道。如果中央政府在1920年代中後期就把這些工程制度化，那麼1929年全球衰退來臨時，數十萬甚至百萬失業者就可以被短期吸收進去，而不是被丟回街頭流浪。這一步等於把「經濟危機 → 大規模失業 → 極端政黨壯大」的鏈條切斷。³⁵",[12,29080,29081],{},[773,29082,29083],{},"(3) 制度化工人參與，讓衝突走法律管道而非街頭武裝。",[12,29085,29086],{},"若能讓工廠層級的「勞資協商委員會」取得法定地位（工時、安全、解僱、資訊透明），工人便不必把希望全部押在街頭暴力或全面革命；同時，資方可以在法律程序中處理勞資爭議，而非每逢罷工就請右翼武裝回廠維持秩序。³⁶",[12,29088,29089],{},"對1920年代的工業資本家來說，這聽起來像把企業主權稀釋。但以歷史角度來看會發現：拒絕讓步的後果，就是1933年之後的軍備國家。名義上企業仍屬私人，但實質生產、投資方向、勞動結構全由極權國家決定。從長期風險角度，1920年代就接受「福利國家＋工人制度化參與」對資本家反而是較小的痛苦。³⁷",[765,29091,29093],{"id":29092},"vi-technology-and-industry-making-europe-dependent-on-germany-instead-of-germany-conquering-europe","VI. Technology and Industry: Making Europe “Dependent on Germany” Instead of “Germany Conquering Europe”",[12,29095,29096],{},"德國在戰前即是世界級的化工、藥品、合成染料、精密光學、機械加工、電氣工程強國。在1920年代後半，隨著貨幣穩定與外資注入，這些高附加價值產業快速恢復出口，重新成為歐洲現代化所仰賴的供應來源。³⁸",[12,29098,29099],{},"穩定化戰略的第五支柱，就是把這件事升級成國家級外交框架：「歐洲的再工業化需要德國產能；要獲得這個產能，歐洲列強必須停止把德國當作永久罪犯並解除佔領式壓制，轉而接受一個合作式的、長期的賠款與安全架構。」換句話說，德國不是用坦克，而是用機械、電力系統、化學肥料與工業零件來綁住對手的經濟復甦。這種「產業互賴」的邏輯，在1924-1929年已經隱約出現。³⁹",[12,29101,29102],{},"此路線的弱點很明顯：它將德國的命運綁在國際經濟循環上，因此在1929年全球金融崩盤時，德國首當其衝。⁴⁰",[765,29104,29106],{"id":29105},"vii-feasibility-and-structural-fragility-the-19241929-golden-window-and-its-collapse","VII. Feasibility and Structural Fragility: The 1924–1929 Golden Window and Its Collapse",[12,29108,29109],{},"1924-1929年的德國，事實上已經短暫展現了這條穩定化路線的雛形。史特雷澤曼的外交推動《道威斯計畫》（1924），促使法國1925年撤出魯爾；《洛迦諾條約》（1925）讓德國－西歐邊界關係走向互保；德國於1926年加入國際聯盟。惡性通膨在1923年底後被壓制，貨幣重新取得信用；外資貸款湧入工業與市政建設；出口產業（化工、機械、電氣）恢復動能；城市生活與文化活力在黃金二十年代中繁榮起來。這一切說明：德國確實可以在不立刻求戰的前提下，逐步恢復外交主體、經濟活力與社會穩定。⁴¹",[12,29111,29112],{},"然而，這個黃金窗口並未被用來建立穩定制度。失業保險並未全面法制化成聯邦級安全網；公共工程沒有被寫成「一旦景氣下跌就自動啟動」的緩衝機制；工人參與和勞資協商權並未以國家層級保障；國防軍的政府監督與防禦定位也沒有被憲政化，而仍保留「我們才是國家」的菁英自我意識。⁴²",[12,29114,29115],{},"因此，當1929年全球大蕭條爆發，美國資金抽離，德國出口需求斷崖式下跌，失業者在短時間內暴增至數百萬，國家並沒有現成的安全閥。群眾對議會民主的信任在數季之內瓦解，轉而支持那些承諾「立刻行動、恢復尊嚴、打破凡爾賽」的極端民族主義者。1933年，極端民族主義政權正式奪權。⁴³",[12,29117,29118],{},"換句話說，不是穩定化路線從來不存在，而是路線存在並曾運作，但它被當成過渡性權宜之計，沒有被制度化；因此一遇到全球級外生衝擊，它瞬間瓦解。",[765,29120,29122],{"id":29121},"conclusion","Conclusion",[12,29124,29125],{},"本文已論證，威瑪共和國的失敗並非單純注定，而是因為一個幾乎完成、卻沒完成的穩定化工程。1919-1929年之間，德國其實有機會在五個面向上打造一個不以侵略為前提的復甦方案：(1) 政治上，以跨派系的重建內閣終止內戰化，並把所有武裝力量國家化，置於政府監督；(2) 經濟與金融上，以《道威斯計畫》式的模式，將賠款轉為長期、外資支撐的重建迴路，並以魯爾工業區生產恢復稅基、穩定貨幣；(3) 軍事與外交上，將小而防禦導向的國防軍本身當成外交籌碼，透過《洛迦諾條約》與進入國際聯盟換取撤軍與地位正常化，而不是立刻重整大軍；(4) 社會結構上，把失業保險、公共工程與工人制度化參與當作國安閥，以阻止失業潮直接投向極端主義；(5) 產業與科技上，把德國在化工、機械、電氣等高附加價值出口部門視為歐洲整體復甦的必要條件，以「產業互賴」取代「領土擴張」作為國力來源。這套方案並非烏托邦，它在1924-1929年其實大半存在；但它沒有被法制化成「自動啟動的安全網」，因此在1929年衝擊下瓦解，為1933年的奪權鋪路。⁴⁴",[765,29127,9292],{"id":29128},"notes",[16,29130,29131,29142,29152,29162,29167,29174,29181,29188,29193,29199,29204,29212,29224,29227,29238,29244,29248,29255,29263,29268,29272,29276,29283,29291,29298,29302,29306,29313,29317,29321,29325,29334,29341,29349,29356,29362,29371,29378,29382,29386,29390,29394,29404,29412],{},[19,29132,29133,29134,29137,29138,29141],{},"Margaret MacMillan, ",[7947,29135,29136],{},"Paris 1919: Six Months That Changed the World"," (New York: Random House, 2001), 389–391, 404–406, 480; Richard J. Evans, ",[7947,29139,29140],{},"The Coming of the Third Reich"," (New York: Penguin, 2004), 13–17.",[19,29143,29144,29145,29148,29149,29151],{},"Adam Tooze, ",[7947,29146,29147],{},"The Wages of Destruction: The Making and Breaking of the Nazi Economy"," (London: Allen Lane, 2006), 37–38, 43–44, 95–107; Evans, ",[7947,29150,29140],{},", 280–284.",[19,29153,29154,29155,29157,29158,29161],{},"Evans, ",[7947,29156,29140],{},", 80–84, 88; Tooze, ",[7947,29159,29160],{},"The Wages of Destruction",", 173–174, 189–190.",[19,29163,29154,29164,29166],{},[7947,29165,29140],{},", 13–17.",[19,29168,29169,29170,29173],{},"MacMillan, ",[7947,29171,29172],{},"Paris 1919",", 389–391, 404–406.",[19,29175,29169,29176,29178,29179,29166],{},[7947,29177,29172],{},", 404–406, 480; Evans, ",[7947,29180,29140],{},[19,29182,29154,29183,29157,29185,29187],{},[7947,29184,29140],{},[7947,29186,29160],{},", 95–107.",[19,29189,29154,29190,29192],{},[7947,29191,29140],{},", 52–53, 80–84, 88.",[19,29194,29195,29196,29198],{},"Tooze, ",[7947,29197,29160],{},", 37–38, 43–44, 95–107, 173–174, 189–190.",[19,29200,29169,29201,29203],{},[7947,29202,29172],{},", 389–391, 404–406, 480.",[19,29205,29154,29206,29208,29209,29211],{},[7947,29207,29140],{},", 280–284; Tooze, ",[7947,29210,29160],{},", 37–38, 43–44, 95–107.",[19,29213,29154,29214,29216,29217,29219,29220,29223],{},[7947,29215,29140],{},", 13–17, 280–284; MacMillan, ",[7947,29218,29172],{},", 404–406; Tooze, ",[7947,29221,29222],{},"The Wages of Destruction,"," 37–38, 43–44, 95–107, 173–174, 189–190.",[19,29225,29226],{},"Hamilton College Writing Center, “Writing a Good History Paper” (Clinton, NY: Hamilton College Writing Center, n.d.).",[19,29228,29195,29229,29231,29232,29234,29235,29237],{},[7947,29230,29160],{},", 37–38, 43–44; MacMillan, ",[7947,29233,29172],{},", 404–406; Evans, ",[7947,29236,29140],{},", 52–53.",[19,29239,29240,29241,29243],{},"Richard J. Evans, ",[7947,29242,29140],{}," (New York: Penguin, 2004), 52–53.",[19,29245,29169,29246,29203],{},[7947,29247,29172],{},[19,29249,29144,29250,29252,29253,29237],{},[7947,29251,29147],{}," (London: Allen Lane, 2006), 37–38, 43–44; Evans, ",[7947,29254,29140],{},[19,29256,29154,29257,29259,29260,29262],{},[7947,29258,29140],{},", 13–17; Tooze, ",[7947,29261,29160],{},", 37–38, 43–44.",[19,29264,29154,29265,29267],{},[7947,29266,29140],{},", 13–17, 52–53.",[19,29269,29154,29270,29237],{},[7947,29271,29140],{},[19,29273,29154,29274,29237],{},[7947,29275,29140],{},[19,29277,29169,29278,29280,29281,29262],{},[7947,29279,29172],{},", 404–406, 480; Tooze, ",[7947,29282,29160],{},[19,29284,29195,29285,29287,29288,29290],{},[7947,29286,29160],{},", 37–38, 43–44, 95–107; Margaret MacMillan, ",[7947,29289,29136],{}," (New York: Random House, 2001), 404–406.",[19,29292,29195,29293,29295,29296,29237],{},[7947,29294,29160],{},", 37–38, 43–44; Evans, ",[7947,29297,29140],{},[19,29299,29195,29300,29187],{},[7947,29301,29160],{},[19,29303,29195,29304,29161],{},[7947,29305,29160],{},[19,29307,29195,29308,29310,29311,29151],{},[7947,29309,29160],{},", 95–107; Evans, ",[7947,29312,29140],{},[19,29314,29169,29315,29173],{},[7947,29316,29172],{},[19,29318,29154,29319,29151],{},[7947,29320,29140],{},[19,29322,29154,29323,29151],{},[7947,29324,29140],{},[19,29326,29154,29327,29329,29330,29333],{},[7947,29328,29140],{},", 280–284; Richard J. Evans, ",[7947,29331,29332],{},"The Third Reich in Power",", 1933–1939 (New York: Penguin, 2005), 18–21.",[19,29335,29154,29336,29338,29339,29151],{},[7947,29337,29332],{},", 1933–1939, 18–21; Evans, ",[7947,29340,29140],{},[19,29342,29195,29343,29345,29346,29348],{},[7947,29344,29160],{},", 173–174, 189–190; Evans, ",[7947,29347,29140],{},", 80–84, 88.",[19,29350,29195,29351,29295,29353,29355],{},[7947,29352,29160],{},[7947,29354,29140],{},", 80–84.",[19,29357,29154,29358,29208,29360,29187],{},[7947,29359,29140],{},[7947,29361,29160],{},[19,29363,29154,29364,29366,29367,29370],{},[7947,29365,29140],{},", 52–53, 80–84; Evans, ",[7947,29368,29369],{},"The Third Reich in Power,"," 1933–1939, 18–21.",[19,29372,29154,29373,29375,29376,29187],{},[7947,29374,29369],{}," 1933–1939, 18–21; Tooze, ",[7947,29377,29160],{},[19,29379,29195,29380,29187],{},[7947,29381,29160],{},[19,29383,29195,29384,29187],{},[7947,29385,29160],{},[19,29387,29195,29388,29161],{},[7947,29389,29160],{},[19,29391,29195,29392,29211],{},[7947,29393,29160],{},[19,29395,29154,29396,29398,29399,29401,29402,29187],{},[7947,29397,29140],{},", 280–284; Evans, ",[7947,29400,29332],{},", 1933–1939, 18–21; Tooze, ",[7947,29403,29160],{},[19,29405,29406,29407,29345,29410,29348],{},"Tooze, T",[7947,29408,29409],{},"he Wages of Destruction",[7947,29411,29140],{},[19,29413,29154,29414,29208,29416,29187],{},[7947,29415,29140],{},[7947,29417,29160],{},[765,29419,29421],{"id":29420},"bibliography","Bibliography",[12,29423,29424,29425,29427],{},"Evans, Richard J. ",[7947,29426,29140],{},". New York: Penguin, 2004.",[12,29429,29424,29430,29433],{},[7947,29431,29432],{},"The Third Reich in Power, 1933–1939",". New York: Penguin, 2005.",[12,29435,29436],{},"Hamilton College Writing Center. “Writing a Good History Paper.” Clinton, NY: Hamilton College Writing Center, n.d.",[12,29438,29439,29440,29442],{},"MacMillan, Margaret. ",[7947,29441,29136],{},". New York: Random House, 2001.",[12,29444,29445,29446,29448],{},"Tooze, Adam. ",[7947,29447,29147],{},". London: Allen Lane, 2006.",[765,29450,28585],{"id":28585},[12,29452,29453,29454,29456,29457,29459,29460,29462,29463,29465],{},"這是一篇莫名其妙就生成出來的...偽歷史論文?",[83,29455],{},"\n我也不知道為何一頓飯的時間就討論出這些奇妙東西，人生真是奇妙對吧。",[83,29458],{},"\n如有任何錯誤或遺漏，請寄email到我的信箱~也歡迎指教~",[83,29461],{},"\n(註 : 此文有使用chatGTP進行文獻搜索與文字潤飾)",[83,29464],{},"\n感謝您長達30分鐘的觀看XD",{"title":169,"searchDepth":170,"depth":170,"links":29467},[29468,29469,29470,29471,29472,29473,29474,29475,29476,29477,29478,29479,29480,29481,29482],{"id":28864,"depth":170,"text":28865},{"id":28616,"depth":170,"text":28617},{"id":28893,"depth":170,"text":28894},{"id":28912,"depth":170,"text":28913},{"id":28931,"depth":170,"text":28932},{"id":28963,"depth":170,"text":28964},{"id":28984,"depth":170,"text":28985},{"id":29034,"depth":170,"text":29035},{"id":29058,"depth":170,"text":29059},{"id":29092,"depth":170,"text":29093},{"id":29105,"depth":170,"text":29106},{"id":29121,"depth":170,"text":29122},{"id":29128,"depth":170,"text":9292},{"id":29420,"depth":170,"text":29421},{"id":28585,"depth":170,"text":28585},"2025-10-31","一篇在吃飯時莫名討論出的偽論文 (Chicago Manual of Style)\n備註 : 目前引用文獻頁碼錯誤極多，但觀點大致無誤，修正中","\u002Fimages\u002Fuploads\u002Fatlas_van_der_hagen-kw1049b10_047-s._imperium_romano-germanicum_oder_deutschland_mit_seinen_angräntzenden_königreichen_und_provincien_neulich_entworffen_und_theils_gezeichnet_durch_iulium_reichelt_chur_pfal.jpg",{},"\u002Fblog\u002Fstability-instead-of-revenge-a-reconstruction-strategy-for-post-world-war-i-germany-1919-1935",{"title":28859,"description":29484},{"loc":29487},"blog\u002Fstability-instead-of-revenge-a-reconstruction-strategy-for-post-world-war-i-germany-1919-1935",[29492],"World War II conjecture","y_XCN15_pSc6wwNQ5309Lb_XtmrzEdYY1EH6pL2yNwg",{"id":29495,"title":29496,"author":761,"body":29497,"date":29483,"description":29599,"draft":174,"edited_at":29600,"extension":175,"featured_image":29601,"meta":29602,"navigation":178,"path":29603,"pinned":174,"seo":29604,"series":181,"seriesOrder":181,"sitemap":29605,"stem":29606,"tags":29607,"__hash__":29609},"blog\u002Fblog\u002F根本沒人在乎你的部落格.md","根本沒人在乎你的部落格",{"type":9,"value":29498,"toc":29595},[29499,29501,29504,29511,29513,29516,29542,29545,29589,29592],[765,29500,11243],{"id":11243},[12,29502,29503],{},"今天在網絡上無意間翻到了這篇文章。十分認同作者的觀點。我嘗試建立部落格已經一個多月，和大部分我見到的人一樣，部落格建立好之後草草寫一個Hello World就放著好幾天沒動了。僅僅是在想著各種設計、外觀、參考別人的部落格就花費了許多時間，彷彿這才是部落格的真正意義。當終於設計好部落格，架在伺服器上了，反而不知道要寫什麼。直到我看了這篇文章，才明白部落格的意義何在，於是決定翻譯分享出來.",[12,29505,29506,29507],{},"文章來自Alex Molas，連接：",[49,29508,29509],{"href":29509,"rel":29510},"https:\u002F\u002Fwww.alexmolas.com\u002F2023\u002F07\u002F15\u002Fnobody-cares-about-your-blog.html",[53],[765,29512,29496],{"id":29496},[12,29514,29515],{},"我幾年前開始寫部落格，從那時起，我就有過無數個想放棄的理由。以下就來列舉，為什麼根本沒人在乎你的部落格：",[16,29517,29518,29524,29530,29536],{},[19,29519,29520,29523],{},[773,29521,29522],{},"你的部落格毫無原創性。"," 外面有成千上萬的部落格，你憑什麼覺得自己的與眾不同？你很可能只是在拾人牙慧，重複你在別處看來的東西。",[19,29525,29526,29529],{},[773,29527,29528],{},"你根本不是你那個領域的專家。"," 否則，你早就去寫論文、接受採訪了，哪還會在這裡發部落格。",[19,29531,29532,29535],{},[773,29533,29534],{},"你只是在向全世界秀下限，顯得你有多蠢。"," 如果你說的話還不如保持沉默，那你最好閉嘴。",[19,29537,29538,29541],{},[773,29539,29540],{},"就算哪天真的有人在乎你的部落格，那也只是為了來批評你。"," 你的作品就是垃圾，把它公諸於世只會讓人們發現，你本人也是個垃圾。",[12,29543,29544],{},"但這一切根本不是問題，因為你壓根就不該在乎別人是怎麼想的。以下才是我認為你應該在乎（你自己的）部落格的真正理由：",[16,29546,29547,29553,29559,29565,29571,29577,29583],{},[19,29548,29549,29552],{},[773,29550,29551],{},"你可以把它當成寫給未來自己的筆記。"," 幾年後，你就會擁有一本很棒的日誌，記錄著你這些年來的進化。重讀你過去的文字，就像在與過去的自己對話。",[19,29554,29555,29558],{},[773,29556,29557],{},"釋放你腦中那些需要傾瀉而出的想法。"," 即使沒有人在乎這些想法，把它們寫下來本身就是一種心靈的宣洩過程。",[19,29560,29561,29564],{},[773,29562,29563],{},"學習如何寫作和表達複雜的概念。"," 最好的學習方式就是教學（即便根本沒有讀者）。正如保羅·格雷厄姆 (Paul Graham) 所說，親自動筆去寫一件事，即便是你自認很熟的事。通常你會發現，你其實並不像自己想像的那麼了解它。",[19,29566,29567,29570],{},[773,29568,29569],{},"就算你分享給世界的觀點並非原創，你也可以用你個人的視角來豐富它們。"," 如同比爾·瑟斯頓 (Bill Thurson) 所言，我們每個人都只對少數事物有清晰的理解，而對更多的概念則模糊不清。這世上永遠不缺需要被釐清的想法。",[19,29572,29573,29576],{},[773,29574,29575],{},"如果你曾花費大把時間解決某個超級特定的問題，那你更該把它寫下來。"," 說不定哪天，你就會因此成為別人的英雄。也可能，未來你會再次遇到同樣的問題，到那時，你就是你自己的英雄。",[19,29578,29579,29582],{},[773,29580,29581],{},"維護一個部落格是件很酷的事，哪怕只是從技術角度來看。"," 這種對某樣東西擁有完全所有權的感覺真的很有成就感，即使它只是這個虛無飄渺的世界中，遠端伺服器上的幾個位元組。",[19,29584,29585,29588],{},[773,29586,29587],{},"你想他媽的寫什麼都行。"," 這是你的部落格，你不需要遵守任何規則。我剛才就飆髒話了，而你拿我一點辦法也沒有，因為這是我的部落格，老子愛怎樣就怎樣。這種自由感真的超酷（恕我直言）。",[12,29590,29591],{},"P.S. 我本來正要發布這篇文章，但那時我突然開始想：「我為什麼要發這篇文？誰會浪費時間來讀這堆狗屁？」",[12,29593,29594],{},"但你知道嗎？我才不在乎你怎麼想，文章我照發，你照樣拿我沒轍 :)",{"title":169,"searchDepth":170,"depth":170,"links":29596},[29597,29598],{"id":11243,"depth":170,"text":11243},{"id":29496,"depth":170,"text":29496},"看到了一篇寫的很棒的文章，決定翻譯之後轉發一下。","2026-02-16","\u002Fimages\u002Fuploads\u002F__plana_and_arona_blue_archive__sample-3e0b6caf7810576f0fd6c98c77565758.jpg",{},"\u002Fblog\u002F根本沒人在乎你的部落格",{"title":29496,"description":29599},{"loc":29603},"blog\u002F根本沒人在乎你的部落格",[29608],"日誌觀點","0s1UXD4XQeYpOtDHP8ShiyqMYPwcpCGopLa4UN25yS4",{"id":29611,"title":29612,"author":25833,"body":29613,"date":29708,"description":29709,"draft":174,"edited_at":181,"extension":175,"featured_image":29710,"meta":29711,"navigation":178,"path":29712,"pinned":174,"seo":29713,"series":181,"seriesOrder":181,"sitemap":29714,"stem":29715,"tags":29716,"__hash__":29718},"blog\u002Fblog\u002F早安-午安-晚安.md","早安 午安 晚安",{"type":9,"value":29614,"toc":29704},[29615,29618,29621,29625,29628,29631,29634,29637,29640,29643,29647,29650,29676,29679,29686,29694,29697],[12,29616,29617],{},"您好、Hello、Guten Tag。",[12,29619,29620],{},"我是法法，很高興有人打開這個文章。先祝你今天平安，have a nice day.",[765,29622,29624],{"id":29623},"who-am-i","Who Am I?",[12,29626,29627],{},"我是台灣嘉義人，是個分享欲有點重的人，目前在跟數學展開一個愛恨情仇的故事，希望這個故事有個美好結局XD",[12,29629,29630],{},"我的名字一開始叫做大法，是一個遊戲我取的網名，後面被當時的熟人稱為法法，因此就用到現在了。",[12,29632,29633],{},"為什麼不用大法呢? 對我來說，那個遊戲是一個敏感遊戲，因此我不可避免地做了一些去識別化，而在這邊我想要多做一點真正的自己，所以就選擇了法法這個名字了w",[12,29635,29636],{},"興趣的話，由於我是那種天然對知識就有興趣的人，所以我自己涉略的領域有一點多。不過! 數學是永遠的愛(雖然它也給我了很多挫折ww",[12,29638,29639],{},"簡單來講，我看了一些心理學和社會學等的教科書，也看了一些哲學和女性主義的書籍，這些都是當時的我因為某些契機讀的。因為說到底還是一個門外漢，所以如果你對以上領域有興趣的話，歡迎跟我交流喔!",[12,29641,29642],{},"除了這些硬硬的知識之外，我也喜歡自己一個人旅行跟吃美食。",[765,29644,29646],{"id":29645},"something-i-can-bring-here","Something I Can Bring Here",[12,29648,29649],{},"既然跟糯糯拿到了權限，我覺得自己應該要做出一些東西才是XD",[77,29651,29652,29658,29664,29670],{},[19,29653,29654,29655,29657],{},"一些數學筆記",[83,29656],{},"這部分本來是我平常讀書或是paper時隨筆寫下的一些東西，我覺得可以整理一下，然後利用純文字的方式給出自己的理解。",[19,29659,29660,29661,29663],{},"日常生活",[83,29662],{},"比如一些美食照之類的w",[19,29665,29666,29667,29669],{},"人類觀察",[83,29668],{},"自從在今年把部分把精力放在線上遊戲之後，發現網路正常人真的是不可多得，因此想寫一些東西當作給自己的警戒或者是發牢騷。",[19,29671,29672,29673,29675],{},"書籍分享",[83,29674],{},"正如我在前面講的，我看了很多領域的書籍，而在打到這裡的當下，我身邊還有很多非數學書在讀，這些書感覺是可以分享的。",[12,29677,29678],{},"最後來簡單介紹圖片好了",[12,29680,29681,29682,29685],{},"This diagram is the expression of ",[773,29683,29684],{},"snake lemma."," Snake lemma is valid in every abelian category, and it's a important tool  in homological algebra.",[12,29687,29688,29693],{},[7947,29689,29690],{},[773,29691,29692],{},"Snake lemma."," See diagram above, consider second and third row, they composed a diagram which is commutative. Moreover, they are exact and 0 is zero object. Then there exists a morphism d such that d connects first row and forth row is exact.",[12,29695,29696],{},"The rest of the proof is left as an exercise to the reader XDDD.",[12,29698,29699,29700],{},"The diagram comes from ",[49,29701,29702],{"href":29702,"rel":29703},"https:\u002F\u002Fupload.wikimedia.org\u002Fwikipedia\u002Fcommons\u002Fthumb\u002F9\u002F9d\u002FSnake_lemma_complete.svg\u002F1920px-Snake_lemma_complete.svg.png",[53],{"title":169,"searchDepth":170,"depth":170,"links":29705},[29706,29707],{"id":29623,"depth":170,"text":29624},{"id":29645,"depth":170,"text":29646},"2025-10-28","想說的一些話","\u002Fimages\u002Fuploads\u002Fsnake_lemma_complete.svg.png",{},"\u002Fblog\u002F早安 午安 晚安",{"title":29612,"description":29709},{"loc":29712},"blog\u002F早安-午安-晚安",[29717],"介紹","PzGpMYMivOVxJPlZqRIk8D1fPMYWLILGOLeNkLLS3hc",{"id":29720,"title":29721,"author":26781,"body":29722,"date":29708,"description":29776,"draft":174,"edited_at":181,"extension":175,"featured_image":29777,"meta":29778,"navigation":178,"path":29779,"pinned":174,"seo":29780,"series":181,"seriesOrder":181,"sitemap":29781,"stem":29782,"tags":29783,"__hash__":29784},"blog\u002Fblog\u002F走進、走近、走盡.md","走進、走近、走盡",{"type":9,"value":29723,"toc":29771},[29724,29727,29730,29733,29736,29739,29743,29746,29750],[12,29725,29726],{},"Hello 你好 Bonjour\n我是風玄也可以叫我Osborn，感謝你點開這篇文章，希望你今天過得愉快",[765,29728,29729],{"id":29623},"Who am I",[12,29731,29732],{},"我是風玄來自台灣新北人幹話特別多",[12,29734,29735],{},"網名一開始叫風影但由於太過中二所以改名風玄雖然還是一樣中二w，Osborn則是來自於之前玩遊戲跟朋友互取英文名子時想到，其來自於北歐神話涵義神聖的武士或是神熊!?",[12,29737,29738],{},"興趣是打遊戲和看書涉及的種類蠻多元的有關法律，歷史和人文類的也會看些輕小說。打遊戲喜歡fps和養成類遊戲，非常喜歡賽馬娘裡的東海帝王，原型是來自日本1990年代的賽馬真實故事十分精采，馬生有過三次骨折，最後成功康復並奪得1993有馬紀念頭馬，故事讓人憐惜與敬佩。對於歷史與法律有所興趣。歷史對於我來說是個警惕自我的鏡子，法律則是從小對於不公正的事會想要試圖導正，然而因為能力不足無法有所作為。我很喜歡一句話：法律是保護懂法律的人。我希望自己能夠利用個人的能力來幫助他人。",[765,29740,29742],{"id":29741},"why-am-i-here","Why am I here",[12,29744,29745],{},"聽說七糯糯建設了一個有趣的網站，若能成為我幫助他人的第一步就太有意思了，時間會沖淡記憶但文字卻是永恆的，我或許不能幫助到100%的人但如果可以幫助到那1%的人也不虛此行，雖然不是最專業但會盡量保持正確度，若有錯誤歡迎指正與討論。",[765,29747,29749],{"id":29748},"program","Program",[77,29751,29752,29759,29765],{},[19,29753,29754,29758],{},[781,29755,29757],{"id":29756},"thread上或是新聞上的法律謬誤","Thread上或是新聞上的法律謬誤","時常看到一些錯誤的法律言論誤導大眾，希望能透過棉薄之力來導正",[19,29760,29761,29764],{},[781,29762,29763],{"id":29763},"書籍閱讀心得","去分享一些有趣的書與分享內心的感悟",[19,29766,29767,29770],{},[781,29768,29769],{"id":29769},"生活瑣事","可能是美食照或是風景照!?",{"title":169,"searchDepth":170,"depth":170,"links":29772},[29773,29774,29775],{"id":29623,"depth":170,"text":29729},{"id":29741,"depth":170,"text":29742},{"id":29748,"depth":170,"text":29749},"希望能讓大家了解我","\u002Fimages\u002Fuploads\u002Fimg_3171.jpeg",{},"\u002Fblog\u002F走進、走近、走盡",{"title":29721,"description":29776},{"loc":29779},"blog\u002F走進、走近、走盡",[29717],"11-VMjMzUSrlYsDRq9-CUo8Aq-1M1GVNZtL-Ld-nqKM",{"id":29786,"title":29787,"author":28611,"body":29788,"date":29855,"description":29856,"draft":174,"edited_at":181,"extension":175,"featured_image":29857,"meta":29858,"navigation":178,"path":29859,"pinned":174,"seo":29860,"series":181,"seriesOrder":181,"sitemap":29861,"stem":29862,"tags":29863,"__hash__":29864},"blog\u002Fblog\u002F一個漂流到地球的故事.md","一個漂流到地球的故事",{"type":9,"value":29789,"toc":29850},[29790,29799,29802,29809,29816,29825,29828,29831,29834,29836,29847],[12,29791,29792,29793,29795,29796,29798],{},"Hello、你好、Salvēte、こんにちは。",[83,29794],{},"\n在82億人之中，我們相遇了，或許認識，或許不是很熟，但歡迎你的到來。",[83,29797],{},"\nI am Automata，你也可以叫我天喵，我們有很多時間能互相認識。",[765,29800,29801],{"id":29623},"Who Am I ?",[12,29803,29804,29805,29808],{},"產地 : 臺灣、屬名 : Homo sapiens、性別 : ",[773,29806,29807],{},"_"," (自由填入)",[12,29810,29811,29812,29815],{},"天喵起源於一款幻想歷史遊戲，當時想叫天可汗 (因為他打跑蒙古人XD)，但因為這名字太無聊了，想多一點變化，便加入了貓咪元素，於是搖身一變成就了\"天喵汗\" ",[773,29813,29814],{},";"," 而 Automata則是來源於 NieR:Automata 這部作品，我很喜歡那種破碎、荒廢、未來都市的感覺。",[12,29817,29818,29819,29821,29822,29824],{},"興趣 : 醫學、旅遊、滑雪、美食、酒精、Formula One (害我想買方向盤)",[83,29820],{},"\n正在坐牢 : Immunology、Embryology (後悔中)",[83,29823],{},"\ncancer research (終極大坐牢)",[12,29826,29827],{},"喜歡冬天去日本自由旅行，享受滑雪時在雪上飛的感受，拉麵、溫泉、雪地都是我的最愛。對於酒精也略有研究，紅酒、清酒、琴酒、威士忌、蘭姆酒，有時會去酒展和酒吧逛逛~ (註 : 理性飲酒，理性醉)",[765,29829,29830],{"id":29741},"Why am I here ?",[12,29832,29833],{},"當時聽說七糯糯想要創立blog，臨機一動就想說可以一起寫寫看，分享一些生活中的趣事、知識、或單純練習一下文筆，讓生活能留下一些痕跡，讓一些想法能以文筆互相交流，友誼可能會隨著時間沖淡，但遺留在這邊的回憶永存 (直到網站被關掉為止XD)，或許回頭一看，會覺得當年的自己很酷呢~",[765,29835,29749],{"id":29748},[16,29837,29838,29841,29844],{},[19,29839,29840],{},"生活趣事 (不定時更新，可能是研究生小八卦，或是美食評價)",[19,29842,29843],{},"生醫筆記 (可能會更新論文review)",[19,29845,29846],{},"滑雪日記 (或許哪天可以跟七糯糯一起去滑雪? )",[12,29848,29849],{},"可能就這樣吧XD，畢竟寫文章也是需要精力的~感謝你願意花時間閱讀啦~",{"title":169,"searchDepth":170,"depth":170,"links":29851},[29852,29853,29854],{"id":29623,"depth":170,"text":29801},{"id":29741,"depth":170,"text":29830},{"id":29748,"depth":170,"text":29749},"2025-10-26","Toast、biomedicine and snowboard","\u002Fimages\u002Fuploads\u002Fhasan-almasi-5ddkjb6fgtq-unsplash.jpg",{},"\u002Fblog\u002F一個漂流到地球的故事",{"title":29787,"description":29856},{"loc":29859},"blog\u002F一個漂流到地球的故事",[29717],"hHh1FNhPliIskcFcdLVmg-gkyhGapO5NP0E6vZyQF0Y",{"id":29866,"title":29867,"author":761,"body":29868,"date":29999,"description":30000,"draft":174,"edited_at":30001,"extension":175,"featured_image":30002,"meta":30003,"navigation":178,"path":30004,"pinned":178,"seo":30005,"series":181,"seriesOrder":181,"sitemap":30006,"stem":30007,"tags":30008,"__hash__":30009},"blog\u002Fblog\u002F你好，世界。.md","你好，世界。",{"type":9,"value":29869,"toc":29990},[29870,29873,29876,29879,29893,29896,29900,29903,29910,29913,29916,29919,29922,29925,29928,29931,29934,29937,29940,29943,29946,29949,29952,29955,29958,29961,29964,29967,29970,29973,29976,29979,29981,29984,29987],[12,29871,29872],{},"首先，致所有讀者：歡迎來到「星谷雜貨店」！",[12,29874,29875],{},"經過一番（慘痛的）折騰和無數次的「為什麼這破程式碼又壞了」之後，這個專屬於我們的小角落終於正式上線了。",[12,29877,29878],{},"在這裡，你可以：",[77,29880,29881,29884,29887,29890],{},[19,29882,29883],{},"分享你最近在追的劇、聽的歌、玩的遊戲。",[19,29885,29886],{},"寫下你在生活中遇到的趣事或牢騷。",[19,29888,29889],{},"貼一張你拍到（或在網路上看到）的圖片。",[19,29891,29892],{},"分享你任何的奇思妙想！",[12,29894,29895],{},"總之，這是一個沒有壓力、沒有主題限制的共享空間。",[765,29897,29899],{"id":29898},"我是誰","我是誰？",[12,29901,29902],{},"天天躲在家裡的宅，馬來亞大學軟件工程系學生。名字的話，我也忘記是誰給我取的了。我以前叫智乃乃，因為自己很喜歡「請問您今天要來點兔子嗎？」裡面的香風智乃（超級可愛啊啊啊啊），又想要一個可愛一點的名字，就這麼取了。英文自然就選了Kafuu Chino裡的Chino，所以叫Chinono. 後來有個友人玩笑間把我叫成了七糯糯。我一下子就愛上了這個超可愛的名字。",[12,29904,29905,29906,29909],{},"之前是讀醫學系的",[2948,29907,29908],{},"不過被當掉了","。然後因為對電腦超級感興趣，所以有的時候癮上來，考試前連休息都不用了，讀完書就去寫電腦程式，寫了幾個小時才發現好像要來不及讀書了。",[12,29911,29912],{},"愛好的話，當然是電腦程式啦！在這個之外我也有很多愛好，比如我是小小的手辦收藏家，之前也有迷戀過機械鍵盤，耳機，模型車之類的。所以房間裡堆著很多其實我都用不太到的東西。因為有好的耳機，所以我也喜歡經常聽歌，經常會一個人安靜的坐在房間裡閉上眼專心聽歌。",[12,29914,29915],{},"我大部分的電腦程式技能都是靠著自學來的。我不覺得自己的技術很好，也不知道自己學的方法對不對。但是當我看著自己寫了好幾個星期的作品運行起來，那種成就感真的是太棒了。因為是自學的，我對於很多技術原理，專有名詞並不熟悉。我的學習方法都是想好自己想做什麼，閱讀文檔，查詢資料，然後就直接下場開始實作了。",[765,29917,29918],{"id":29918},"創作部落格的目的",[12,29920,29921],{},"我從來沒有寫過部落格，也不知道寫這個好不好玩。但是，我有過幾次自己架設網站的經驗，也希望能通過架設部落格學習新的東西。",[12,29923,29924],{},"部落格的大部分代碼，都是我自己慢慢查文檔，排查錯誤，設計網站，慢慢做出來的。過程很漫長，但是成功之後也很開心！這個網站也是我自費（其實大部分都是免費服務）架起來的。這裡是一個真正屬於我們的空間，不受平台政策，廣告的煩擾、可以隨心所欲客製化的小空間。",[12,29926,29927],{},"最近我見到我的一位網友，退出了discord平台，剛剛用WordPress製作了一個新的個人部落格。我覺得，這未嘗也不是一種能自由表達自己的方法。我在這裡可以不受任何約束，不顧任何人的眼光，寫我想寫的，說我想說的話。",[12,29929,29930],{},"我開始研究架設部落格幾天後，分享給了我的朋友天喵。他當時就覺得說，那不如你做一個部落格，讓我也能加入一起寫吧。我覺得這也是個好主意，就採納了建議。",[12,29932,29933],{},"所以嘛，這個部落格才會用到“我們”，因為我打算開放給我的幾個朋友一起編輯，體驗一下寫部落格的感受。如果你也想加入我們，歡迎來我的discord找我提出來。只不過，如果我不認識你的話，很抱歉我可能不會接受，所以不妨先讓我認識你！",[765,29935,29936],{"id":29936},"盯著螢幕的空虛感",[12,29938,29939],{},"不知道你們有沒有這種體驗：有些天，在夜深人靜的時候，我經常會盯著手機螢幕，打開各種社交軟件，看看有沒有人在線、有沒有人看過我分享的東西、有沒有人想找我...即使是半夜兩三點，我的朋友們都不在線，我仍然會拿著我的手機，到處翻找。",[12,29941,29942],{},"即使我很不想承認，但是有的時候，我會躺在床上，盯著手機螢幕，讀完網友們的每一條訊息紀錄，把自己身邊發生的所有事情都分享出來，只想得到朋友們的一點點關注，害怕自己落下什麼沒跟上...時間久了，真的會感覺很空虛。",[765,29944,29945],{"id":29945},"網路與現實的失衡",[12,29947,29948],{},"用了太多的社交媒體，也讓我的社交關係變得很糟糕。前年，我剛剛進入大學的時候，很怕生，不知道該找誰說話。社交媒體給了我很大的安慰。我無聊的時候就可以打開dc，看看朋友們又說了些啥。",[12,29950,29951],{},"但是...時間久了，我發現，我越來越依賴著社交媒體。我沒有幾個現實的朋友，因為我幾乎都不會去主動找人交談。我的時間都花在了社交媒體上。我不知道這是不是一件好事，但是我其實內心不敢和我的家人和現實朋友們分享我和網友們的事。在網絡上的我，其實和現實的我相差很大。",[12,29953,29954],{},"我越孤單，就越會盯著手機看。",[12,29956,29957],{},"我沒有朋友的情況，也間接導致了我的成績一落千丈。",[12,29959,29960],{},"醫學，靠自己一個人真的讀不過來。",[765,29962,29963],{"id":29963},"從醫學到軟件工程",[12,29965,29966],{},"在今年，我從醫學系轉到了軟件工程。原因有很多，但是最主要的還是...我對醫學其實並不是很感興趣。",[12,29968,29969],{},"我身邊的同學們感覺都超級熱愛醫學，但是我不知道為什麼我要讀醫學。我讀下去只是為了考得好，以後找一份安穩的，高薪的工作。",[12,29971,29972],{},"很多人大概會指責我的想法，但我確實是這麼想的。但不一樣的是，我真的真的很喜歡軟件工程。當我寫的代碼在電腦上，經過無數次debug，終於運行起來的時候，那種成就感是無法比擬的。所以，去年得知我考試考不過的時候，我就和父母提出想要轉系了。父母大致上還是理解我的，雖然覺得很可惜，但我至少沒有選擇躺平。能讀自己真正喜歡的科系也好，而且未來工作應該也不會太難找。",[765,29974,29975],{"id":29975},"我的希望",[12,29977,29978],{},"今年，我已經嘗試在減少discord的使用時間了。我開始和室友們相處、交談、打遊戲、出去玩。我希望能在網絡世界和現實世界找到一個新的平衡點。我希望的是，我可以養成一個寫部落格的習慣，讓我在空閒的時候，不要一直想著去看手機，打開discord毫無目的的到處翻找。這部落格對我來說，就像是一個日記，只不過更加先進。",[765,29980,28585],{"id":28585},[12,29982,29983],{},"不知不覺就寫了一個半小時的文章。",[12,29985,29986],{},"我還是第一次，花了這麼長的時間，把自己最真誠的一面展現出來。希望我的朋友們，有看完這篇文章的話，能更好地認識我！",[12,29988,29989],{},"那麼，今天就寫這麼多了，謝謝你讀到這裡，也再一次歡迎各位！",{"title":169,"searchDepth":170,"depth":170,"links":29991},[29992,29993,29994,29995,29996,29997,29998],{"id":29898,"depth":170,"text":29899},{"id":29918,"depth":170,"text":29918},{"id":29936,"depth":170,"text":29936},{"id":29945,"depth":170,"text":29945},{"id":29963,"depth":170,"text":29963},{"id":29975,"depth":170,"text":29975},{"id":28585,"depth":170,"text":28585},"2025-10-24","關於我和這個部落格，以及一些自己的反思。","2026-02-18","\u002Fimages\u002Fuploads\u002F84017469_p0.jpg",{},"\u002Fblog\u002F你好，世界。",{"title":29867,"description":30000},{"loc":30004},"blog\u002F你好，世界。",[29717,26774],"hNFfUYc0nCBT-EUMhpiUbdp5yQJcDIB6x9jv9YTdOLc",{"id":30011,"extension":30012,"meta":30013,"series":30014,"stem":30052,"__hash__":30053},"series\u002Fseries.json","json",{},{"微積分教學":30015,"生活紀錄":30017,"Motor 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