ABOUT THE SPEAKER
Margaret Wertheim - Figurer
By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses.

Why you should listen

Snowflakes, fractals, the patterns on a leaf -- there's beauty to be found at the intersection of nature and physics, beauty and math. Science writer Margaret Wertheim (along with her twin sister, Christine) founded the Institute for Figuring to advance the aesthetic appreciation of scientific concepts, from the natural physics of snowflakes and fractals to human constructs such as Islamic mosaics, string figures and weaving.

The IFF's latest project is perhaps its most beguilingly strange -- a coral reef constructed entirely by crochet hook, a project that takes advantage of the happy congruence between the mathematical phenomena modeled perfectly by the creatures of the reef,  and repetitive tasks such as crocheting -- which, as it turns out, is perfectly adapted to model hyperbolic space. It is easy to sink into the kaleidoscopic, dripping beauty of the yarn-modeled reef, but the aim of the reef project is twofold: to draw attention to distressed coral reefs around the world, dying in droves from changing ocean saline levels, overfishing, and a myriad of threats; and to display a flavor of math that was previously almost impossible to picture. By modeling these complex equations in physical space, this technique can help mathematicians see patterns and make breakthroughs.

Wertheim is now working on a book about maverick scientist James Carter.

More profile about the speaker
Margaret Wertheim | Speaker | TED.com
TED2009

Margaret Wertheim: The beautiful math of coral

瑪格麗特威茲海姆與珊瑚(以及鉤針編織)中的數學

Filmed:
1,470,540 views

由瑪格麗特威茲海姆領導的一項計畫,以數學家發明的鉤針編織法重新創造出珊瑚礁,讚頌珊瑚礁的驚奇之美,並深入探討其背後的雙曲幾何學。
- Figurer
By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses. Full bio

Double-click the English transcript below to play the video.

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I'm here today今天, as June六月 said,
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我今天來到這裡
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to talk about a project項目
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是要談一個計畫
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that my twin雙胞胎 sister妹妹 and I have been doing for the past過去 three and half years年份.
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我和我的雙胞胎姊妹已經執行了三年半
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We're crocheting鉤針 a coral珊瑚 reef.
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我們用鉤針織出珊瑚礁
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And it's a project項目 that we've我們已經 actually其實
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而這個計畫到目前為止
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been now joined加盟 by hundreds數以百計 of people around the world世界,
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已經有從世界各地數以百計的人
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who are doing it with us. Indeed確實 thousands數千 of people
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和我們一起執行,而有數千人
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have actually其實 been involved參與 in this project項目,
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有實際參與計畫
00:40
in many許多 of its different不同 aspects方面.
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從各種不同的面向
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It's a project項目 that now reaches到達 across橫過 three continents大陸,
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現在更推行到三大洲去
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and its roots go into the fields領域 of mathematics數學,
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根基於數學
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marine海洋 biology生物學, feminine女人 handicraft手工業
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海洋生物學、婦女手工藝
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and environmental環境的 activism行動.
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以及環境運動
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It's true真正.
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沒錯
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It's also a project項目
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這也是一個
00:59
that in a very beautiful美麗 way,
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用一種很美麗的方式完成的計畫
01:01
the development發展 of this
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它的發展
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has actually其實 paralleled平行 the evolution演化 of life on earth地球,
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就和地球生物演化平行發生
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which哪一個 is a particularly尤其 lovely可愛 thing to be saying
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這件事情講起來很有趣
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right here in February二月 2009 --
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在這裡,2009年二月
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which哪一個, as one of our previous以前 speakers音箱 told us,
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前一個講者已經告訴我們
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is the 200th anniversary週年
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這是達爾文的
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of the birth分娩 of Charles查爾斯 Darwin達爾文.
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200歲誕辰
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All of this I'm going to get to in the next下一個 18 minutes分鐘, I hope希望.
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而在這接下來的18分鐘裡面,我希望可以把這些都帶過一遍
01:21
But let me first begin開始 by showing展示 you
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但首先我想先讓大家看
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some pictures圖片 of what this thing looks容貌 like.
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一些照片,了解這些東西長什麼樣子
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Just to give you an idea理念 of scale規模,
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為了讓大家對大小有個概念
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that installation安裝 there is about six feet across橫過,
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這個裝置大概有六呎寬
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and the tallest最高 models楷模 are about two or three feet high.
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最高一個大概有兩到三呎高
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This is some more images圖片 of it.
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這裡有更多照片
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That one on the right is about five feet high.
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最右邊那個大約有五呎高
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The work involves涉及 hundreds數以百計 of different不同 crochet鉤邊 models楷模.
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一共需要上百種不同的鉤針織模型
01:43
And indeed確實 there are now thousands數千 and thousands數千 of models楷模 that people
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而現在更有大半是由人們
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have contributed貢獻 all over the world世界 as part部分 of this.
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從世界各地提供的數千種模型組成的
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The totality整體 of this project項目
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這個計畫總共
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involves涉及 tens of thousands數千 of hours小時
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花費數萬小時
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of human人的 labor勞動 --
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人力
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99 percent百分 of it doneDONE by women婦女.
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而99%都是女性完成的
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On the right hand side, that bit there is part部分 of an installation安裝
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在右邊,是這個裝置的一部分
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that is about 12 feet long.
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約有12呎長
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My sister妹妹 and I started開始 this project項目 in 2005
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我的姊妹和我在2005年開始這項計畫
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because in that year, at least最小 in the science科學 press,
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因為在這一年,至少是在科學出版裡
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there was a lot of talk about global全球 warming變暖,
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有很多對全球暖化
02:10
and the effect影響 that global全球 warming變暖 was having on coral珊瑚 reefs珊瑚礁.
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以及其對珊瑚礁影響的討論
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Corals珊瑚蟲 are very delicate精巧 organisms生物,
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珊瑚是很脆弱的生物
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and they are devastated滿目瘡痍 by any rise上升 in sea temperatures溫度.
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海溫的些微上升就會造成很大傷害
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It causes原因 these vast廣大 bleaching events事件
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也就是所謂的白化現象
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that are the first signs跡象 of corals珊瑚蟲 of being存在 sick生病.
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這是珊瑚生病的第一項警訊
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And if the bleaching doesn't go away --
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如果白化一直持續
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if the temperatures溫度 don't go down -- reefs珊瑚礁 start開始 to die.
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溫度沒有下降,珊瑚礁就會開始死亡
02:28
A great deal合同 of this has been happening事件 in the Great Barrier屏障 Reef,
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這樣的故事在很多地方都有發生,像大堡礁
02:31
particularly尤其 in coral珊瑚 reefs珊瑚礁 all over the world世界.
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還有世界各地的珊瑚礁
02:33
This is our invocation調用 in crochet鉤邊 of a bleached漂白 reef.
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這是我們用鉤針織出的白化珊瑚,為珊瑚祈禱
02:37
We have a new organization組織 together一起 called The Institute研究所 for Figuring塑造,
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我們成立了一個「圖示學院」
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which哪一個 is a little organization組織 we started開始
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宗旨是
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to promote促進, to do projects項目 about the
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推廣與承接計畫
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aesthetic審美 and poetic詩意 dimensions尺寸 of science科學 and mathematics數學.
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展示科學與數學上的美學與詩意
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And I went and put a little announcement公告 up on our site現場,
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當我公佈了聲明於網頁上
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asking for people to join加入 us in this enterprise企業.
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歡迎加入這創舉
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To our surprise, one of the first people who called
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相當意外的是一開始打來詢問的
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was the Andy安迪 Warhol沃霍爾 Museum博物館.
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是安地沃荷美術館
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And they said they were having an exhibition展覽
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說將有一展出
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about artists'藝術家 response響應 to global全球 warming變暖,
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是藝術家對全球暖化的反應
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and they'd他們會 like our coral珊瑚 reef to be part部分 of it.
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他們希望我們的珊瑚礁也能參與
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I laughed笑了 and said, "Well we've我們已經 only just started開始 it,
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我笑著回答「我們才剛剛開始
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you can have a little bit of it."
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所以只能提供一些些」
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So in 2007 we had an exhibition展覽,
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2007年我們展出
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a small exhibition展覽 of this crochet鉤邊 reef.
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只是小小的一片珊瑚礁
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And then some people in Chicago芝加哥 came來了 along沿 and they said,
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其中有些從芝加哥來的人說
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"In late晚了 2007, the theme主題 of the Chicago芝加哥 Humanities人文 Festival is
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「2007年底, 芝加哥人文藝術的主題是
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global全球 warming變暖. And we've我們已經 got this 3,000 square-foot平方英尺 gallery畫廊
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全球暖化,而我們有3000平方英呎的展場
03:22
and we want you to fill it with your reef."
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希望能全面佈置你們的珊瑚礁」
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And I, naively天真 by this stage階段, said, "Oh, yes, sure."
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我天真的就回說「好的!沒問題」
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Now I say "naively天真" because actually其實
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我說自己「天真」
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my profession職業 is as a science科學 writer作家.
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是因為我的職業是科學作家
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What I do is I write books圖書 about the cultural文化 history歷史 of physics物理.
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是寫作有關物理科學的文化歷史
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I've written書面 books圖書 about the history歷史 of space空間,
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我曾寫過太空歷史
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the history歷史 of physics物理 and religion宗教,
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物理與宗教的歷史
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and I write articles用品 for people like the New York紐約 Times and the L.A. Times.
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也為紐約時報與洛杉磯時報撰寫文章
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So I had no idea理念 what it meant意味著 to fill a 3,000 square-foot平方英尺 gallery畫廊.
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所以我根本搞不清楚填滿3000平方英呎的大小
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So I said yes to this proposition主張.
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所以我只管答應這邀請
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And I went home, and I told my sister妹妹 Christine克里斯汀.
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回家告訴我的姊妹Christine
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And she nearly幾乎 had a fit適合
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她嚇到了
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because Christine克里斯汀 is a professor教授 at one of
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因為Christine任教於
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L.A.'s major重大的 art藝術 colleges高校, CalArts加州藝術學院,
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CalArts是洛杉磯的重要藝術學院
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and she knew知道 exactly究竟 what it meant意味著 to fill a 3,000 square-foot平方英尺 gallery畫廊.
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她清楚明白什麼是3000平方英呎的展出
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She thought I'd gone走了 off my head.
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她說我瘋了
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But she went into crochet鉤邊 overdrive疲勞過度.
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但她還是加速鉤針趕進度
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And to cut a long story故事 short, eight months個月 later後來
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長話短說,8個月後
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we did fill the Chicago芝加哥 Cultural文化 Center's中心
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我們還是填滿了芝加哥文化中心
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3,000 square廣場 foot腳丫子 gallery畫廊.
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3000平方英呎的展出
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By this stage階段 the project項目 had taken採取 on
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到這一步整個計畫
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a viral病毒 dimension尺寸 of its own擁有,
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自然地進入到一重要國度
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which哪一個 got completely全然 beyond us.
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且不是我們能操控
04:18
The people in Chicago芝加哥 decided決定
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芝加哥人決定
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that as well as exhibiting參展 our reefs珊瑚礁, what they wanted to do
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除了展出我們的珊瑚
04:23
was have the local本地 people there make a reef.
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也希望當地百姓也能參與製作
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So we went and taught the techniques技術. We did workshops研討會 and lectures講座.
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所以我們前往指導技巧、接著工作坊與課程
04:28
And the people in Chicago芝加哥 made製作 a reef of their own擁有.
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芝加哥民眾也做出他們自己的珊瑚礁
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And it was exhibited展出 alongside並肩 ours我們的.
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同時在我們的作品旁展出
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There were hundreds數以百計 of people involved參與 in that.
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數以百計的民眾參與
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We got invited邀請 to do the whole整個 thing
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我們又被邀請作同樣展出與傳授的過程
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in New York紐約, and in London倫敦,
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於紐約 倫敦
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and in Los洛杉磯 Angeles洛杉磯.
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和洛杉磯
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In each of these cities城市, the local本地 citizens公民,
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在每個地點 當地的市民
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hundreds數以百計 and hundreds數以百計 of them, have made製作 a reef.
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幾百人 一起做珊瑚
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And more and more people get involved參與 in this,
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也吸引了更多人參與
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most of whom we've我們已經 never met會見.
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都是些我們從未見過的人
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So the whole整個 thing has sort分類 of morphed演變
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所以整件事已自然的轉型
04:53
into this organic有機, ever-evolving不斷發展 creature生物,
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更有生機 更多人參與
04:55
that's actually其實 gone走了 way beyond Christine克里斯汀 and I.
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遠超過Christine和我的貢獻
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Now some of you are sitting坐在 here thinking思維,
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現在你們可能坐著想
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"What planet行星 are these people on?
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「這些人是從哪個星球來的?
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Why on earth地球 are you crocheting鉤針 a reef?
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為什麼要鉤織珊瑚
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WoolennessWoolenness and wetness aren't exactly究竟
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棉線與含水
05:09
two concepts概念 that go together一起.
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是無法相容的
05:11
Why not chisel a coral珊瑚 reef out of marble大理石?
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為什麼不用大理石雕刻珊瑚呢?
05:13
Cast it in bronze青銅."
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或是銅鑄?」
05:15
But it turns out there is a very good reason原因
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實際上 是有非常充分的理由
05:17
why we are crocheting鉤針 it
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用編織來表現珊瑚
05:19
because many許多 organisms生物 in coral珊瑚 reefs珊瑚礁
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因為每種的珊瑚
05:21
have a very particular特定 kind of structure結構體.
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多有著特別的結構
05:23
The frilly褶邊 crenulated小圓齒狀 forms形式 that you see
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這種奏摺重疊的形式
05:25
in corals珊瑚蟲, and kelps海帶, and sponges海綿 and nudibranchs海蛞蝓,
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出現在珊瑚 海帶 海綿 以及 海蛞蝓
05:28
is a form形成 of geometry幾何 known已知 as hyperbolic誇張的 geometry幾何.
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是一種幾何上稱為雙曲線的形式
05:31
And the only way that mathematicians數學家 know
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也是數學家認為唯一
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how to model模型 this structure結構體
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能展現此幾何的方式
05:36
is with crochet鉤邊. It happens發生 to be a fact事實.
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就是針織 這是個事實
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It's almost幾乎 impossible不可能 to model模型 this structure結構體 any other way,
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好像沒有其他方式能建構這樣幾何
05:41
and it's almost幾乎 impossible不可能 to do it on computers電腦.
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也好像不可能在電腦上呈現
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So what is this hyperbolic誇張的 geometry幾何
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所以到底什麼是 雙曲線幾何
05:46
that corals珊瑚蟲 and sea slugs蛞蝓 embody體現?
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在珊瑚與海蛞蝓身上?
05:49
The next下一個 few少數 minutes分鐘 is, we're all going to get raised上調 up
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接下來的幾分鐘 我們都能進化到
05:52
to the level水平 of a sea slug金屬塊.
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海蛞蝓的等級
05:54
(Laughter笑聲)
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(笑聲)
05:55
This sort分類 of geometry幾何 revolutionized革命性 mathematics數學
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在19世紀時 這種幾何的
05:58
when it was first discovered發現 in the 19th century世紀.
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出現 在數學上是革命性的
06:01
But not until直到 1997 did mathematicians數學家 actually其實 understand理解
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一直是到1997年 數學家才真正明白
06:04
how they could model模型 it.
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要如何具體模擬它
06:06
In 1997 a mathematician數學家
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1997年 一個康乃爾數學家
06:08
at Cornell康奈爾, Daina代娜 TaiminaTaimina,
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Daina Taimina
06:10
made製作 the discovery發現 that this structure結構體
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才發現這樣的結構
06:12
could actually其實 be doneDONE in knitting針織 and crochet鉤邊.
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能由針織與鉤編展現
06:14
The first one she did was knitting針織.
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她先用針織
06:16
But you get too many許多 stitches on the needle. So she quickly很快 realized實現
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但太多針了 所以立刻明白
06:18
crochet鉤邊 was the better thing.
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鉤編是更容易的
06:20
But what she was doing was actually其實 making製造 a model模型
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但她實際所為 就是完成
06:23
of a mathematical數學的 structure結構體, that many許多 mathematicians數學家
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許多數學家都難以完成的
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had thought it was actually其實 impossible不可能 to model模型.
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實體模型建構
06:28
And indeed確實 they thought that anything like this structure結構體
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多數都以為是無法
06:30
was impossible不可能 per seSE.
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達成的
06:32
Some of the best最好 mathematicians數學家 spent花費 hundreds數以百計 of years年份
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過去數百年 頂尖的數學家
06:34
trying to prove證明 that this structure結構體 was impossible不可能.
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也試著證明不可能
06:37
So what is this impossible不可能 hyperbolic誇張的 structure結構體?
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所以到底什麼是雙曲線結構?
06:40
Before hyperbolic誇張的 geometry幾何, mathematicians數學家 knew知道
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在雙曲線幾何之前 數學家慣用
06:42
about two kinds of space空間:
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兩種空間
06:44
Euclidean歐幾里德 space空間, and spherical球形 space空間.
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歐幾里得式空間與球面空間
06:47
And they have different不同 properties性能.
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各有著不同的性質
06:49
Mathematicians數學家 like to characterize表徵 things by being存在 formalist形式主義.
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數學家喜歡用形式主義來分類
06:52
You all have a sense of what a flat平面 space空間 is, Euclidean歐幾里德 space空間 is.
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你們都熟悉平整的空間 就是歐幾里得空間
06:56
But mathematicians數學家 formalize形式化 this in a particular特定 way.
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但數學家以不同的方式標記
06:59
And what they do is, they do it through通過 the concept概念
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他們的作法是利用
07:01
of parallel平行 lines.
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平行線條的概念
07:03
So here we have a line and a point outside the line.
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所以 假設一條直線 與直線外的一個點
07:06
And Euclid歐幾里得 said, "How can I define確定 parallel平行 lines?
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歐幾里得就問:「如何定義平行線?」
07:09
I ask the question, how many許多 lines can I draw through通過
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我問一下 我能畫出幾條平行線
07:12
the point but never meet遇到 the original原版的 line?"
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能經過那點 又不與原來的直線相交
07:14
And you all know the answer回答. Does someone有人 want to shout it out?
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你們都知道這個答案 有人願意喊出來嗎?
07:17
One. Great. Okay.
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一個 對! OK
07:19
That's our definition定義 of a parallel平行 line.
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那就是我們定義的平行線
07:21
It's a definition定義 really of Euclidean歐幾里德 space空間.
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那就是歐幾里得空間
07:24
But there is another另一個 possibility可能性 that you all know of:
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但也有另一種可能
07:26
spherical球形 space空間.
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球面空間
07:28
Think of the surface表面 of a sphere領域 --
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想想一個球面的表面
07:30
just like a beach海灘 ball, the surface表面 of the Earth地球.
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就像是海灘球 就像是地球表面
07:32
I have a straight直行 line on my spherical球形 surface表面.
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我有一個在球表面上的直線
07:35
And I have a point outside the line. How many許多 straight直行 lines
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和一個線外的點 那有多少直線
07:37
can I draw through通過 the point
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通過那點 又不會
07:39
but never meet遇到 the original原版的 line?
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與原始直線相交?
07:41
What do we mean to talk about
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到底什麼叫作
07:43
a straight直行 line on a curved彎曲 surface表面?
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曲面上的直線呢?
07:46
Now mathematicians數學家 have answered回答 that question.
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數學家已經定義
07:49
They've他們已經 understood了解 there is a generalized一般性 concept概念
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共通概念的曲面上之
07:51
of straightness, it's called a geodesic.
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直線性 就叫作 測地線
07:53
And on the surface表面 of a sphere領域,
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若是在球面上
07:55
a straight直行 line is the biggest最大 possible可能 circle you can draw.
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直線就是最大能畫出的圓
07:58
So it's like the equator赤道 or the lines of longitude經度.
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所以 就像是赤道 或是南北方向的緯線
08:02
So we ask the question again,
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所以 再問一次問題
08:04
"How many許多 straight直行 lines can I draw through通過 the point,
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「我能畫出多少直線 經過那點
08:06
but never meet遇到 the original原版的 line?"
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又不與原直線相交?」
08:08
Does someone有人 want to guess猜測?
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有人要猜嗎?
08:11
Zero. Very good.
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零 非常好
08:13
Now mathematicians數學家 thought that was the only alternative替代.
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數學家以為只有這另一個答案
08:15
It's a bit suspicious可疑 isn't it? There is two answers答案 to the question so far,
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有些可疑不是嗎? 能有兩個答案:
08:18
Zero and one.
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零或一
08:20
Two answers答案? There may可能 possibly或者 be a third第三 alternative替代.
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兩個解答 也有可能有第三個答案
08:22
To a mathematician數學家 if there are two answers答案,
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對於數學家來說 若有兩個答案
08:24
and the first two are zero and one,
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首先的回答 就是 零 與 一
08:26
there is another另一個 number that immediately立即 suggests提示 itself本身
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同時 也自然而然 會以為
08:28
as the third第三 alternative替代.
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有第三種可能
08:30
Does anyone任何人 want to guess猜測 what it is?
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有人要猜嗎?
08:33
Infinity無窮. You all got it right. Exactly究竟.
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無限多 的確 你們都答對
08:36
There is, there's a third第三 alternative替代.
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有第三個解答
08:38
This is what it looks容貌 like.
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這就是圖形表示
08:40
There's a straight直行 line, and there is an infinite無窮 number of lines
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有一條直線 以及無線多條直線
08:43
that go through通過 the point and never meet遇到 the original原版的 line.
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通過那一點 又不會與原始線相交會
08:45
This is the drawing畫畫.
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是這樣畫的
08:47
This nearly幾乎 drove開車 mathematicians數學家 bonkers瘋狂的
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這幾乎逼數學家發瘋
08:49
because, like you, they're sitting坐在 there feeling感覺 bamboozled迷惑.
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因為 像你們一般 他們覺得被搞糊塗了
08:52
Thinking思維, how can that be? You're cheating作弊. The lines are curved彎曲.
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想一想 怎麼可能? 你是在作弊 這些直線是彎曲的
08:55
But that's only because I'm projecting突出 it onto a
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只因為我將這些直線 投射在
08:57
flat平面 surface表面.
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平坦表面
08:59
Mathematicians數學家 for several一些 hundred years年份
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數學家歷經幾百年
09:01
had to really struggle鬥爭 with this.
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的掙扎困惑
09:03
How could they see this?
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怎麼能明白呢?
09:05
What did it mean to actually其實 have a physical物理 model模型
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怎樣能有一實際的具體模型
09:08
that looked看著 like this?
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能展現這樣的理論呢?
09:10
It's a bit like this: imagine想像 that we'd星期三 only ever encountered遇到 Euclidean歐幾里德 space空間.
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像這樣 想像我們只理解與經歷 歐式幾何空間
09:13
Then our mathematicians數學家 come along沿
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然後 我們的數學家過來說
09:15
and said, "There's this thing called a sphere領域,
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"有一種球面空間
09:17
and the lines come together一起 at the north and south pole."
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線條伸展南北極後 會重合
09:19
But you don't know what a sphere領域 looks容貌 like.
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但你不明白球面的長相
09:21
And someone有人 that comes along沿 and says, "Look here's這裡的 a ball."
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另一個人走來說 「看! 這就是個球」
09:24
And you go, "Ah! I can see it. I can feel it.
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你就會「啊! 我懂了 我能感受了
09:26
I can touch觸摸 it. I can play with it."
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我能觸摸 也能翻弄」
09:29
And that's exactly究竟 what happened發生
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這就是1997年
09:31
when Daina代娜 TaiminaTaimina
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當 Daina Taimina
09:33
in 1997, showed顯示 that you could crochet鉤邊 models楷模
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以鉤織品展示了
09:37
in hyperbolic誇張的 space空間.
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雙曲面空間
09:39
Here is this diagram in crochetnesscrochetness.
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這是以鉤織品來展現
09:42
I've stitched縫合 Euclid's歐幾里得 parallel平行 postulate假定 on to the surface表面.
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我已將歐式的平行線設在這個表面
09:46
And the lines look curved彎曲.
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線條看起來是彎曲的
09:48
But look, I can prove證明 to you that they're straight直行
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我能證明這是一條線
09:51
because I can take any one of these lines,
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因為我能以任一條線
09:53
and I can fold along沿 it.
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沿著它折
09:56
And it's a straight直行 line.
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是一條直線
09:58
So here, in wool羊毛,
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所以呢 經由一
10:01
through通過 a domestic國內 feminine女人 art藝術,
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家庭婦女的藝術棉織品
10:03
is the proof證明 that the most famous著名 postulate假定
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證明數學界最有名的假設
10:05
in mathematics數學 is wrong錯誤.
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(無法建出雙曲面模型) 是錯的
10:08
(Applause掌聲)
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(掌聲)
10:14
And you can stitch all sorts排序 of mathematical數學的
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你能鉤織各式的數學定理
10:16
theorems定理 onto these surfaces.
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在這些表面上顯現
10:19
The discovery發現 of hyperbolic誇張的 space空間 ushered迎來 in the field領域 of mathematics數學
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而雙曲面引領了其他數學
10:22
that is called non-Euclidean非歐幾里得 geometry幾何.
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稱為 非歐式幾何
10:24
And this is actually其實 the field領域 of mathematics數學
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這類數學也是
10:26
that underliesunderlies general一般 relativity相對論
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廣義相對論的基礎
10:28
and is actually其實 ultimately最終 going to show顯示 us
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終極地為我們
10:30
about the shape形狀 of the universe宇宙.
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引導出宇宙的形狀
10:32
So there is this direct直接 line
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所以有一直接關聯線
10:34
between之間 feminine女人 handicraft手工業,
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連結女性手工藝
10:36
Euclid歐幾里得 and general一般 relativity相對論.
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歐基里得 與 廣義相對論
10:39
Now, I said that mathematicians數學家 thought that this was impossible不可能.
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我剛說數學家原本認為是不可能
10:42
Here's這裡的 two creatures生物 who've誰一直 never heard聽說 of Euclid's歐幾里得 parallel平行 postulate假定 --
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這裡有兩種生物從來沒有聽過 歐基里得 的平行假設
10:46
didn't know it was impossible不可能 to violate違反,
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也就不知道不能違反
10:48
and they're simply只是 getting得到 on with it.
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它們卻與 非歐幾何 相處融洽
10:50
They've他們已經 been doing it for hundreds數以百計 of millions百萬 of years年份.
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他們已存在 數億年之久
10:54
I once一旦 asked the mathematicians數學家 why it was
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我曾問過數學家怎麼會這樣
10:56
that mathematicians數學家 thought this structure結構體 was impossible不可能
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數學專家沒能具體建構的模型
10:59
when sea slugs蛞蝓 have been doing it since以來 the Silurian志留紀 age年齡.
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而海蛞蝓 卻已經從志留纪就擁有著
11:02
Their answer回答 was interesting有趣.
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他們的回答是有趣的
11:04
They said, "Well I guess猜測 there aren't that many許多 mathematicians數學家
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他們說「可能沒有足夠的數學家
11:06
sitting坐在 around looking at sea slugs蛞蝓."
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四處坐著看到海蛞蝓」
11:08
And that's true真正. But it also goes deeper更深 than that.
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或許是 但這件事也能更深入
11:11
It also says a whole整個 lot of things
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也說明 整體數學家
11:13
about what mathematicians數學家 thought mathematics數學 was,
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以為的數學是什麼
11:16
what they thought it could and couldn't不能 do,
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以為數學能做到與做不到
11:18
what they thought it could and couldn't不能 represent代表.
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以為數學能呈現到與不能呈現
11:20
Even mathematicians數學家, who in some sense
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就連數學家 在某些角度
11:22
are the freest自由 of all thinkers思想家,
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是最自由的思考者
11:24
literally按照字面 couldn't不能 see
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沒能看到
11:26
not only the sea slugs蛞蝓 around them,
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身旁的海蛞蝓
11:28
but the lettuce生菜 on their plate盤子 --
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也沒留意到 餐盤中的 萵苣
11:30
because lettuces生菜, and all those curly捲曲 vegetables蔬菜,
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因為 像萵苣這些彎曲的蔬菜
11:32
they also are embodiments實施例 of hyperbolic誇張的 geometry幾何.
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都是雙曲面幾何的體現
11:36
And so in some sense they literally按照字面,
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某種程度數學家
11:39
they had such這樣 a symbolic象徵 view視圖 of mathematics數學,
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他們有著對數學的符號式的觀點
11:41
they couldn't不能 actually其實 see what was going on
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卻不能察覺
11:44
on the lettuce生菜 in front面前 of them.
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在眼前的萵苣
11:47
It turns out that the natural自然 world世界 is full充分 of hyperbolic誇張的 wonders奇蹟.
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事實上 自然界中 充滿著太多符號式 驚奇
11:51
And so, too, we've我們已經 discovered發現
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基於此 我們也發現
11:53
that there is an infinite無窮 taxonomy分類
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有無限多分類
11:55
of crochet鉤邊 hyperbolic誇張的 creatures生物.
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來鉤織雙曲面的生物
11:57
We started開始 out, Chrissy克麗絲 and I and our contributors貢獻者,
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我們姊妹加上其他參與者 開始
12:00
doing the simple簡單 mathematically數學 perfect完善 models楷模.
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作出簡單數學上的完美模型
12:02
But we found發現 that when we deviated偏離 from the specific具體
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我們發現當我們偏離特定
12:06
setnesssetness of the mathematical數學的 code
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數學符號設定
12:09
that underliesunderlies it -- the simple簡單 algorithm算法
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就是原本簡單的規律:
12:11
crochet鉤邊 three, increase增加 one --
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鉤織三針 加一針
12:13
when we deviated偏離 from that and made製作 embellishments裝飾 to the code,
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當我們偏離 做了些規律上的額外裝飾變化
12:16
the models楷模 immediately立即 started開始 to look more natural自然.
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模型立即呈現更佳的自然
12:20
And all of our contributors貢獻者, who are an amazing驚人
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所有來自世界各地的參與者
12:22
collection採集 of people around the world世界,
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無不覺得驚奇
12:24
do their own擁有 embellishments裝飾.
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也開始了他們的裝飾變化
12:26
As it were, we have this ever-evolving不斷發展,
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就這樣 我們開始了
12:28
crochet鉤邊 taxonomic分類 tree of life.
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鉤織品物種族譜的生命演化
12:30
Just as the morphology形態學
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就像是地球生物
12:32
and the complexity複雜 of life on earth地球 is never ending結尾,
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生生不息的變化與複雜化
12:34
little embellishments裝飾 and complexificationscomplexifications
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基因些微的變化與複雜
12:37
in the DNA脫氧核糖核酸 code
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才演化出
12:39
lead to new things like giraffes長頸鹿, or orchids蘭花 --
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長頸鹿 或是 蘭花
12:42
so too, do little embellishments裝飾 in the crochet鉤邊 code
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同樣地 鉤織中小小裝飾變化
12:45
lead to new and wondrous奇妙 creatures生物
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產出了全新的品種
12:48
in the evolutionary發展的 tree of crochet鉤邊 life.
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鉤織品物種族譜的生命演化
12:51
So this project項目 really has
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所以這個計畫
12:53
taken採取 on this inner organic有機 life of its own擁有.
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真的開始其內在的有機生命
12:56
There is the totality整體 of all the people who have come to it.
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統整了所有參與者的
12:59
And their individual個人 visions願景,
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各自願景
13:01
and their engagement訂婚 with this mathematical數學的 mode模式.
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加上各自以數學形式的參與
13:04
We have these technologies技術. We use them.
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我們已有各式科技 能被使用
13:06
But why? What's at stake賭注 here? What does it matter?
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那為什麼要用手工呢? 有什麼重要的?
13:09
For Chrissy克麗絲 and I, one of the things that's important重要 here
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對我們姊妹而言 最重要的一點是
13:12
is that these things suggest建議
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這樣的實作顯示出
13:14
the importance重要性 and value of embodied體現 knowledge知識.
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將內隱知識的具體展現 之重要性與價值
13:17
We live生活 in a society社會
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我們生活在這樣的社會
13:19
that completely全然 tends趨向 to valorize穩定物價
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總是傾向於使用
13:21
symbolic象徵 forms形式 of representation表示 --
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象徵符號的表達
13:23
algebraic代數 representations交涉,
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如代數
13:25
equations方程, codes代碼.
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函數式 程式 等
13:27
We live生活 in a society社會 that's obsessed痴迷
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我們著魔於
13:29
with presenting呈現 information信息 in this way,
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將資訊如此表達
13:31
teaching教學 information信息 in this way.
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也傳授資訊用這樣的方式
13:34
But through通過 this sort分類 of modality形態,
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但是利用鉤織的形式
13:37
crochet鉤邊, other plastic塑料 forms形式 of play --
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或是其他種遊戲
13:41
people can be engaged訂婚 with the most abstract抽象,
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人們能更體會最抽象的
13:44
high-powered高功率, theoretical理論 ideas思路,
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最高層的 理論的概念
13:46
the kinds of ideas思路 that normally一般 you have to go
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而這些概念 通常都是要
13:48
to university大學 departments部門 to study研究 in higher更高 mathematics數學,
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就學於高等教育才會聽到
13:51
which哪一個 is where I first learned學到了 about hyperbolic誇張的 space空間.
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那也是我過去第一次 學到雙曲面空間 的地方
13:54
But you can do it through通過 playing播放 with material材料 objects對象.
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但是 你可以經由操弄實體物質了
13:58
One of the ways方法 that we've我們已經 come to think about this
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在我們的數字研究中心
14:00
is that what we're trying to do with the Institute研究所 for Figuring塑造
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我們也想出一套邏輯去實踐
14:03
and projects項目 like this, we're trying to have
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就是設計出
14:05
kindergarten幼兒園 for grown-ups大人.
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成人式的幼稚園
14:07
And kindergarten幼兒園 was actually其實 a very formalized形式化
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幼稚園事實上是一個非常制式的
14:09
system系統 of education教育,
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教育系統
14:11
established既定 by a man named命名 Friedrich弗里德里希 Froebel福祿貝爾,
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當初創始的是 Friedrich Froebel
14:13
who was a crystallographer晶體學 in the 19th century世紀.
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而他原本是19世紀的結晶學家
14:15
He believed相信 that the crystal水晶 was the model模型
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他認為 結晶結構
14:17
for all kinds of representation表示.
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是所有事務的規律表現
14:19
He developed發達 a radical激進 alternative替代 system系統
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他也就發展出嶄新不同既往
14:22
of engaging the smallest最少 children孩子
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的幼兒教育系統
14:24
with the most abstract抽象 ideas思路
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經由身體操作的遊戲
14:26
through通過 physical物理 forms形式 of play.
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試著傳遞抽象意念
14:28
And he is worthy值得 of an entire整個 talk on his own擁有 right.
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他這個題材故事 本身就值得另闢一場演講
14:30
The value of education教育
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Froebel 引領的
14:32
is something that Froebel福祿貝爾 championed倡導,
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教育價值的傳遞
14:35
through通過 plastic塑料 modes模式 of play.
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是經由 物質模式的遊戲
14:37
We live生活 in a society社會 now
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現今的社會
14:39
where we have lots of think tanks坦克,
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我們有一大堆的 智庫
14:41
where great minds頭腦 go to think about the world世界.
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有著一群聰明腦袋 為世界想像
14:44
They write these great symbolic象徵 treatises論文
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撰述許多偉大的抽象論文
14:46
called books圖書, and papers文件,
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像 書籍 論文
14:48
and op-ed專欄 articles用品.
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專欄 等等
14:50
We want to propose提出, Chrissy克麗絲 and I,
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我們姊妹倆 想提議
14:52
through通過 The Institute研究所 for Figuring塑造, another另一個 alternative替代 way of doing things,
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經由 數字研究中心 的提倡 另一種不同的作法
14:55
which哪一個 is the play tank坦克.
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就是 「玩庫」
14:58
And the play tank坦克, like the think tank坦克,
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玩庫 就像是智庫一般
15:00
is a place地點 where people can go
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是個人們可聚集
15:02
and engage從事 with great ideas思路.
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激發出偉大想法
15:04
But what we want to propose提出,
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但我們要強調的是
15:06
is that the highest最高 levels水平 of abstraction抽象化,
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最抽象的學問
15:08
things like mathematics數學, computing計算, logic邏輯, etc等等. --
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像 數學 電腦 邏輯 等等
15:11
all of this can be engaged訂婚 with,
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不只能
15:13
not just through通過 purely純粹 cerebral顱內 algebraic代數
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靠純粹的智力演算
15:15
symbolic象徵 methods方法,
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抽象符號
15:17
but by literally按照字面, physically物理 playing播放 with ideas思路.
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也能用玩的方式 產出想法
15:21
Thank you very much.
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謝謝
15:23
(Applause掌聲)
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(掌聲)
Translated by K. C. Peng
Reviewed by Joan Liu

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ABOUT THE SPEAKER
Margaret Wertheim - Figurer
By masterminding a project to model a coral reef armed only with crochet hooks, Margaret Wertheim hopes to bring some of the most complicated mathematical models embodied in our universe into the minds (and hands) of the masses.

Why you should listen

Snowflakes, fractals, the patterns on a leaf -- there's beauty to be found at the intersection of nature and physics, beauty and math. Science writer Margaret Wertheim (along with her twin sister, Christine) founded the Institute for Figuring to advance the aesthetic appreciation of scientific concepts, from the natural physics of snowflakes and fractals to human constructs such as Islamic mosaics, string figures and weaving.

The IFF's latest project is perhaps its most beguilingly strange -- a coral reef constructed entirely by crochet hook, a project that takes advantage of the happy congruence between the mathematical phenomena modeled perfectly by the creatures of the reef,  and repetitive tasks such as crocheting -- which, as it turns out, is perfectly adapted to model hyperbolic space. It is easy to sink into the kaleidoscopic, dripping beauty of the yarn-modeled reef, but the aim of the reef project is twofold: to draw attention to distressed coral reefs around the world, dying in droves from changing ocean saline levels, overfishing, and a myriad of threats; and to display a flavor of math that was previously almost impossible to picture. By modeling these complex equations in physical space, this technique can help mathematicians see patterns and make breakthroughs.

Wertheim is now working on a book about maverick scientist James Carter.

More profile about the speaker
Margaret Wertheim | Speaker | TED.com