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TED2009

Margaret Wertheim: The beautiful math of coral

マーガレット・ワーザイム: 珊瑚と かぎ針編みに見る美しき数学の世界

February 6, 2009

マーガレット・ワーザイムは、数学者が発明したかぎ針編みの手法を用いて、珊瑚礁を再現するプロジェクトを進めています。珊瑚礁の驚くべき側面を紹介し、珊瑚をつくり出す中で見られる双曲幾何学の世界へと案内します。

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. Full bio

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Double-click the English subtitles below to play the video.
I'm here today, as June said,
私が今日
00:18
to talk about a project
お話しするのは
00:20
that my twin sister and I have been doing for the past three and half years.
私が双子の妹と3年半続けている企画に関してです
00:22
We're crocheting a coral reef.
私たちは珊瑚礁をかぎ針編みで作っています
00:26
And it's a project that we've actually
この企画は現在 世界中の
00:29
been now joined by hundreds of people around the world,
何百人という人たちが参加し
00:32
who are doing it with us. Indeed thousands of people
何千人もの人たちが
00:35
have actually been involved in this project,
この企画にいろいろな面で
00:38
in many of its different aspects.
関わっています
00:40
It's a project that now reaches across three continents,
この企画は三大陸にまたがり進められています
00:42
and its roots go into the fields of mathematics,
ルーツは 数学や海洋生物
00:45
marine biology, feminine handicraft
女性による手芸や環境活動まで
00:49
and environmental activism.
様々な分野が含まれます
00:52
It's true.
本当です
00:55
It's also a project
また この企画は
00:57
that in a very beautiful way,
地球上の
00:59
the development of this
命の進化に対して
01:01
has actually paralleled the evolution of life on earth,
理解を深めることができます
01:03
which is a particularly lovely thing to be saying
特に 2009年2月現在
01:07
right here in February 2009 --
これは最高のテーマだと思います
01:09
which, as one of our previous speakers told us,
先ほど ある方も言っていたように
01:11
is the 200th anniversary
2009年はチャールズ ダーウィンの
01:13
of the birth of Charles Darwin.
生誕200年にあたるからです
01:15
All of this I'm going to get to in the next 18 minutes, I hope.
以上のことを18分間でお伝えしますが
01:17
But let me first begin by showing you
あらましをつかむのに
01:21
some pictures of what this thing looks like.
最初に写真をお見せします
01:23
Just to give you an idea of scale,
ここに見える作品は
01:26
that installation there is about six feet across,
幅1.8mの大きさです
01:28
and the tallest models are about two or three feet high.
高さは一番丈のあるもので約60~90cmです
01:31
This is some more images of it.
こんなのも あります
01:35
That one on the right is about five feet high.
右端の作品は高さが約1.5m
01:37
The work involves hundreds of different crochet models.
かぎ針編みの珊瑚は何百種類もあって
01:39
And indeed there are now thousands and thousands of models that people
今ではこの一部として世界中から
01:43
have contributed all over the world as part of this.
かぎ針編みの珊瑚が何千と寄付されました
01:46
The totality of this project
この企画に関わる人たちの
01:49
involves tens of thousands of hours
労働時間は合計で
01:51
of human labor --
何万時間にもなり
01:53
99 percent of it done by women.
99%が女性によるものです
01:55
On the right hand side, that bit there is part of an installation
右側にあるのは 幅が約3.6mの
01:57
that is about 12 feet long.
作品の一部です
02:00
My sister and I started this project in 2005
私たち姉妹がこの企画を始めたのは2005年
02:02
because in that year, at least in the science press,
その年 少なくとも科学系の出版物には
02:05
there was a lot of talk about global warming,
地球温暖化と珊瑚礁への影響について
02:07
and the effect that global warming was having on coral reefs.
多くの記事が書かれていました
02:10
Corals are very delicate organisms,
珊瑚は非常に繊細な生物で
02:13
and they are devastated by any rise in sea temperatures.
海水温度が少しでも上昇すると死滅してしまいます
02:15
It causes these vast bleaching events
珊瑚が退色するのは
02:18
that are the first signs of corals of being sick.
病気になっている最初のサインです
02:20
And if the bleaching doesn't go away --
白化したままであったり
02:23
if the temperatures don't go down -- reefs start to die.
水温が下がらなければ 珊瑚礁は死滅に向かいます
02:25
A great deal of this has been happening in the Great Barrier Reef,
グレートバリアリーフの状況は酷く
02:28
particularly in coral reefs all over the world.
世界中の珊瑚礁が衰退しています
02:31
This is our invocation in crochet of a bleached reef.
これは白化した珊瑚礁を作品にしたものです
02:33
We have a new organization together called The Institute for Figuring,
私たちは IFFという組織を運営しており
02:37
which is a little organization we started
科学と数学の
02:40
to promote, to do projects about the
美しくてロマンチックな様相を
02:42
aesthetic and poetic dimensions of science and mathematics.
広めることを趣旨に活動しています
02:44
And I went and put a little announcement up on our site,
この企画への参加をネット上で
02:47
asking for people to join us in this enterprise.
公募したところ
02:50
To our surprise, one of the first people who called
驚いたことに アンディーウォーホル美術館から
02:52
was the Andy Warhol Museum.
連絡が来ました
02:55
And they said they were having an exhibition
地球温暖化を題材に
02:57
about artists' response to global warming,
展覧会をするので
02:59
and they'd like our coral reef to be part of it.
出展してほしい というものでした
03:01
I laughed and said, "Well we've only just started it,
私は笑って “始めたばかりだから
03:03
you can have a little bit of it."
少しだけならば” と言いました
03:05
So in 2007 we had an exhibition,
それで2007年に展覧会をしました
03:07
a small exhibition of this crochet reef.
かぎ針編み珊瑚の小さな展覧会です
03:10
And then some people in Chicago came along and they said,
その後 別の依頼がありました
03:12
"In late 2007, the theme of the Chicago Humanities Festival is
“シカゴで開催する芸術文化祭典の2007年のテーマは地球温暖化です
03:14
global warming. And we've got this 3,000 square-foot gallery
84坪のギャラリーがあるので
03:19
and we want you to fill it with your reef."
貴女が作る珊瑚礁で埋め尽くしてほしいの”
03:22
And I, naively by this stage, said, "Oh, yes, sure."
この時の私の考えは甘く “もちろんよ” と答えました
03:25
Now I say "naively" because actually
考えが甘いと言ったのは
03:28
my profession is as a science writer.
私の本職は科学作家なのです
03:30
What I do is I write books about the cultural history of physics.
物理の文化的歴史に関して執筆していて
03:32
I've written books about the history of space,
宇宙の歴史に関する本や
03:35
the history of physics and religion,
物理や宗教の歴史の本を書いてきました
03:37
and I write articles for people like the New York Times and the L.A. Times.
ニューヨークタイムズやロサンゼルスタイムズにも記事を書いています
03:39
So I had no idea what it meant to fill a 3,000 square-foot gallery.
ですから84坪を埋め尽くす大変さが分からず
03:42
So I said yes to this proposition.
二つ返事をしたのです
03:46
And I went home, and I told my sister Christine.
帰宅して 妹に伝えると
03:48
And she nearly had a fit
彼女はカンカンに怒りました
03:50
because Christine is a professor at one of
なぜなら妹は
03:52
L.A.'s major art colleges, CalArts,
カリフォルニア芸術大学で教授をしていて
03:54
and she knew exactly what it meant to fill a 3,000 square-foot gallery.
84坪を埋め尽くす大変さを知っていたからです
03:57
She thought I'd gone off my head.
妹は怒りながらも 猛烈に
04:00
But she went into crochet overdrive.
かぎ針編みを始めました
04:03
And to cut a long story short, eight months later
結論を言ってしまうと 8ヶ月後
04:05
we did fill the Chicago Cultural Center's
シカゴ文化センターの84坪のギャラリーを
04:07
3,000 square foot gallery.
埋め尽くしました
04:10
By this stage the project had taken on
この時点で この企画は
04:12
a viral dimension of its own,
想像以上に
04:14
which got completely beyond us.
どんどん広がっていきました
04:16
The people in Chicago decided
シカゴの人たちは
04:18
that as well as exhibiting our reefs, what they wanted to do
私たちの珊瑚礁の展示に加えて 彼ら自身の
04:20
was have the local people there make a reef.
珊瑚礁づくりをしたいと言いました
04:23
So we went and taught the techniques. We did workshops and lectures.
私たちは講習会を開いて作り方を教え
04:25
And the people in Chicago made a reef of their own.
シカゴの人たちは自ら珊瑚礁を作ったのです
04:28
And it was exhibited alongside ours.
私たちの作品と並べて展示されました
04:31
There were hundreds of people involved in that.
何百人もの人が関わりました
04:33
We got invited to do the whole thing
私たちは招待されて同じことを
04:35
in New York, and in London,
ニューヨークとロンドン
04:38
and in Los Angeles.
ロサンゼルスでも行いました
04:40
In each of these cities, the local citizens,
その各都市で何百人という
04:42
hundreds and hundreds of them, have made a reef.
地元の市民が珊瑚礁を作りました
04:44
And more and more people get involved in this,
参加者は どんどん増えています
04:46
most of whom we've never met.
大半が初対面の人たちです
04:49
So the whole thing has sort of morphed
ですから この企画は
04:51
into this organic, ever-evolving creature,
妹と私の域を超えて
04:53
that's actually gone way beyond Christine and I.
成長し続ける生命体になっています
04:55
Now some of you are sitting here thinking,
さて こう思っている方はいませんか?
04:59
"What planet are these people on?
“なぜ この人たちは
05:02
Why on earth are you crocheting a reef?
珊瑚をかぎ針編みしてるのか?
05:04
Woolenness and wetness aren't exactly
毛糸と水なんて
05:07
two concepts that go together.
ミスマッチな感じがする
05:09
Why not chisel a coral reef out of marble?
なぜ大理石を彫ったり
05:11
Cast it in bronze."
ブロンズで作らないのか?”
05:13
But it turns out there is a very good reason
それには かぎ針編みをする
05:15
why we are crocheting it
大きな理由があるのです
05:17
because many organisms in coral reefs
珊瑚礁には独特な形をした―
05:19
have a very particular kind of structure.
生き物がたくさんいます
05:21
The frilly crenulated forms that you see
珊瑚 海藻 スポンジ
05:23
in corals, and kelps, and sponges and nudibranchs,
ウミウシに見られる ひだがついた形は
05:25
is a form of geometry known as hyperbolic geometry.
双曲幾何学と呼ばれる幾何学の一種です
05:28
And the only way that mathematicians know
数学者にとって この構造を再現する―
05:31
how to model this structure
唯一の方法は かぎ針編みです
05:34
is with crochet. It happens to be a fact.
これは事実なんです
05:36
It's almost impossible to model this structure any other way,
この構造は コンピュータを含め
05:38
and it's almost impossible to do it on computers.
別の方法で作るのは ほぼ不可能です
05:41
So what is this hyperbolic geometry
では 珊瑚やウミウシが表している―
05:44
that corals and sea slugs embody?
双曲幾何学とは何かを探るため
05:46
The next few minutes is, we're all going to get raised up
次の数分 皆でレベルを上げましょう
05:49
to the level of a sea slug.
ウミウシのレベルまで
05:52
(Laughter)
(笑)
05:54
This sort of geometry revolutionized mathematics
双曲幾何学が19世紀に発見されたとき
05:55
when it was first discovered in the 19th century.
数学に大変革が起こりましたが
05:58
But not until 1997 did mathematicians actually understand
数学者は 1997年まで
06:01
how they could model it.
形に表すことができませんでした
06:04
In 1997 a mathematician
1997年にコーネル大学の
06:06
at Cornell, Daina Taimina,
数学者 デーナ タイミナが
06:08
made the discovery that this structure
この構造を編み物で再現できると
06:10
could actually be done in knitting and crochet.
発見しました
06:12
The first one she did was knitting.
彼女は最初 棒針を使いましたが
06:14
But you get too many stitches on the needle. So she quickly realized
目があまりにも多すぎるため
06:16
crochet was the better thing.
かぎ針が適していると気づきました
06:18
But what she was doing was actually making a model
彼女は再現は不可能だと言う
06:20
of a mathematical structure, that many mathematicians
数学者の概念を覆す―
06:23
had thought it was actually impossible to model.
数学的構造を作り上げました
06:25
And indeed they thought that anything like this structure
本来 この種の構造は
06:28
was impossible per se.
無理だと考えられていました
06:30
Some of the best mathematicians spent hundreds of years
数学の権威と言われる人たちも
06:32
trying to prove that this structure was impossible.
不可能性を証明するのに何百時間と費やしました
06:34
So what is this impossible hyperbolic structure?
双曲構造の何がそうさせるのでしょう?
06:37
Before hyperbolic geometry, mathematicians knew
双曲幾何学が出てくる前
06:40
about two kinds of space:
数学者が認識していた二つの空間は
06:42
Euclidean space, and spherical space.
ユークリッド空間と球状空間で
06:44
And they have different properties.
どちらも異なる特質をもっています
06:47
Mathematicians like to characterize things by being formalist.
数学者は形式主義者なので 特徴づけが好きです
06:49
You all have a sense of what a flat space is, Euclidean space is.
皆さんは平面 いわゆるユークリッド空間の意味はわかりますね?
06:52
But mathematicians formalize this in a particular way.
でも 数学者は平行線の概念を使って
06:56
And what they do is, they do it through the concept
ユークリッド空間を
06:59
of parallel lines.
定義します
07:01
So here we have a line and a point outside the line.
ここに直線があり その上に点があります
07:03
And Euclid said, "How can I define parallel lines?
ユークリッドの定義で質問します
07:06
I ask the question, how many lines can I draw through
この点を通過しつつ 直線に
07:09
the point but never meet the original line?"
交わらない線は 何本?
07:12
And you all know the answer. Does someone want to shout it out?
どなたか答えてくれますか?
07:14
One. Great. Okay.
そう 1です
07:17
That's our definition of a parallel line.
それが平行線の定義で
07:19
It's a definition really of Euclidean space.
ユークリッド空間の定義ですが
07:21
But there is another possibility that you all know of:
他の可能性もあります
07:24
spherical space.
球状空間です
07:26
Think of the surface of a sphere --
ビーチボールや地球のような
07:28
just like a beach ball, the surface of the Earth.
球の表面を考えてください
07:30
I have a straight line on my spherical surface.
球の表面に直線が引いてあり
07:32
And I have a point outside the line. How many straight lines
その上に点があります この点を通過しつつ
07:35
can I draw through the point
直線に交わらない線は
07:37
but never meet the original line?
何本あるでしょう?
07:39
What do we mean to talk about
丸みを帯びた表面における
07:41
a straight line on a curved surface?
直線とはどういう意味か―
07:43
Now mathematicians have answered that question.
数学者が答えを出しています
07:46
They've understood there is a generalized concept
直線を一般化した―
07:49
of straightness, it's called a geodesic.
測地線と呼ばれるものがあり
07:51
And on the surface of a sphere,
球の表面に描ける
07:53
a straight line is the biggest possible circle you can draw.
最長の円が直線です
07:55
So it's like the equator or the lines of longitude.
赤道や経線を想像してください
07:58
So we ask the question again,
もう一度質問します
08:02
"How many straight lines can I draw through the point,
点を通りつつ 元の線に
08:04
but never meet the original line?"
交わらない線は何本?
08:06
Does someone want to guess?
どなたか当ててくれますか?
08:08
Zero. Very good.
そうですね 0です
08:11
Now mathematicians thought that was the only alternative.
数学者はそれが唯一の選択肢だと思っていました
08:13
It's a bit suspicious isn't it? There is two answers to the question so far,
この二つの答えは少し疑わしいですね
08:15
Zero and one.
0と1です
08:18
Two answers? There may possibly be a third alternative.
三つめの答えがあるかもしれません
08:20
To a mathematician if there are two answers,
数学者が答えを導き
08:22
and the first two are zero and one,
それが0と1ならば
08:24
there is another number that immediately suggests itself
即座に提案できる 三つめの
08:26
as the third alternative.
選択肢があります
08:28
Does anyone want to guess what it is?
どなたか当ててくれますか?
08:30
Infinity. You all got it right. Exactly.
無限大 皆さん正解です
08:33
There is, there's a third alternative.
三つめの選択肢は
08:36
This is what it looks like.
このように見えます
08:38
There's a straight line, and there is an infinite number of lines
直線があり 無限の線が点を通り
08:40
that go through the point and never meet the original line.
直線とは交ることはありません
08:43
This is the drawing.
これは その図形です
08:45
This nearly drove mathematicians bonkers
さすがに 数学者たちは頭を抱えました
08:47
because, like you, they're sitting there feeling bamboozled.
線が弧を描いていることから
08:49
Thinking, how can that be? You're cheating. The lines are curved.
だまされたように感じていたのです
08:52
But that's only because I'm projecting it onto a
でも それは単に平面に
08:55
flat surface.
映し出しているからです
08:57
Mathematicians for several hundred years
数学者は数百年間
08:59
had to really struggle with this.
どうやってこれを
09:01
How could they see this?
形に出来るか格闘しました
09:03
What did it mean to actually have a physical model
図形しかなければ想像するのも大変ですが
09:05
that looked like this?
このように考えてください
09:08
It's a bit like this: imagine that we'd only ever encountered Euclidean space.
ユークリッド空間しか知らない人に
09:10
Then our mathematicians come along
北極点と南極点で
09:13
and said, "There's this thing called a sphere,
必ず直線が交わる―
09:15
and the lines come together at the north and south pole."
球の存在を話したとします
09:17
But you don't know what a sphere looks like.
どんな形なのか教えるために
09:19
And someone that comes along and says, "Look here's a ball."
ボールを見てごらん と言ってあげれば
09:21
And you go, "Ah! I can see it. I can feel it.
視覚や触覚から
09:24
I can touch it. I can play with it."
球とは何かを理解できるのです
09:26
And that's exactly what happened
それがまさに1997年に
09:29
when Daina Taimina
デーナ タイミナがやってみせたことです
09:31
in 1997, showed that you could crochet models
彼女はかぎ針編みで双曲線空間を
09:33
in hyperbolic space.
形成できると証明しました
09:37
Here is this diagram in crochetness.
これがかぎ針編みで表した図解です
09:39
I've stitched Euclid's parallel postulate on to the surface.
表面にユークリッド幾何学の平行線公準を縫いました
09:42
And the lines look curved.
線はカーブしているように見えますが
09:46
But look, I can prove to you that they're straight
直線だということを証明できます
09:48
because I can take any one of these lines,
線を一つ選んで
09:51
and I can fold along it.
それに沿って折ると
09:53
And it's a straight line.
直線が現れます
09:56
So here, in wool,
数学で最も名高い公準が
09:58
through a domestic feminine art,
間違っていることを
10:01
is the proof that the most famous postulate
女性による手芸が
10:03
in mathematics is wrong.
毛糸で証明しました
10:05
(Applause)
(拍手)
10:08
And you can stitch all sorts of mathematical
このような表面には
10:14
theorems onto these surfaces.
様々な数学の定理を縫えます
10:16
The discovery of hyperbolic space ushered in the field of mathematics
双曲線空間の発見は非ユークリッド幾何学と呼ばれる―
10:19
that is called non-Euclidean geometry.
数学の分野をもたらしました
10:22
And this is actually the field of mathematics
これは一般相対性理論の
10:24
that underlies general relativity
基礎となる数学の分野で
10:26
and is actually ultimately going to show us
宇宙の形がどのようになっているのか
10:28
about the shape of the universe.
見せてくれるのです
10:30
So there is this direct line
女性による手芸から
10:32
between feminine handicraft,
ユークリッド そして
10:34
Euclid and general relativity.
一般相対性理論へと順行しています
10:36
Now, I said that mathematicians thought that this was impossible.
数学者が無理だと言っていたことは触れました
10:39
Here's two creatures who've never heard of Euclid's parallel postulate --
平行線公準なんて知らない2種類の生き物がいます
10:42
didn't know it was impossible to violate,
問題になっているとも知らずに
10:46
and they're simply getting on with it.
暮らしてきた生き物で
10:48
They've been doing it for hundreds of millions of years.
何億年もこの形をしています
10:50
I once asked the mathematicians why it was
私は以前 数学者に
10:54
that mathematicians thought this structure was impossible
なぜ この構造が不可能だと思ったのか 尋ねました
10:56
when sea slugs have been doing it since the Silurian age.
ウミウシはシルル紀からこの形のままです
10:59
Their answer was interesting.
彼らの回答は面白くて
11:02
They said, "Well I guess there aren't that many mathematicians
ウミウシをじっと観察する数学者は
11:04
sitting around looking at sea slugs."
少ないからではないか と言われました
11:06
And that's true. But it also goes deeper than that.
もっともな意見ですが それよりも重大なのは
11:08
It also says a whole lot of things
数学者たちの
11:11
about what mathematicians thought mathematics was,
数学に対する捉え方を物語っていることです
11:13
what they thought it could and couldn't do,
彼らが出来る と思っていたことや
11:16
what they thought it could and couldn't represent.
再現出来ないと思っていたことです
11:18
Even mathematicians, who in some sense
数学者は 思索家の中でも
11:20
are the freest of all thinkers,
一番自由な思想をもつ人たちですが
11:22
literally couldn't see
彼らでさえ
11:24
not only the sea slugs around them,
ウミウシだけではなく
11:26
but the lettuce on their plate --
レタスにも気づきませんでした
11:28
because lettuces, and all those curly vegetables,
ひだ状になっている野菜は
11:30
they also are embodiments of hyperbolic geometry.
双曲線幾何学をかたどっています
11:32
And so in some sense they literally,
ある意味 彼らは数学における
11:36
they had such a symbolic view of mathematics,
記号的な見方を持っていますが
11:39
they couldn't actually see what was going on
目の前にあるレタスには
11:41
on the lettuce in front of them.
気がつかなかったのです
11:44
It turns out that the natural world is full of hyperbolic wonders.
自然界は双曲線の神秘に満ちています
11:47
And so, too, we've discovered
かぎ針で編めば
11:51
that there is an infinite taxonomy
異なる形の双曲生物を
11:53
of crochet hyperbolic creatures.
無限につくれることもわかりました
11:55
We started out, Chrissy and I and our contributors,
私たち姉妹と企画の参加者たちは 数学的に
11:57
doing the simple mathematically perfect models.
シンプルで正確なモデルに取りかかりました
12:00
But we found that when we deviated from the specific
でも 私たちがその具体的な数学的コードの
12:02
setness of the mathematical code
一式から外れると
12:06
that underlies it -- the simple algorithm
根底にあるのは
12:09
crochet three, increase one --
3回編んで 一目増やすという
12:11
when we deviated from that and made embellishments to the code,
シンプルな演算法だとわかり
12:13
the models immediately started to look more natural.
急にそのモデルが自然に見え始めました
12:16
And all of our contributors, who are an amazing
世界中から参加してくれる
12:20
collection of people around the world,
素晴らしい人たちは
12:22
do their own embellishments.
彼ら独自の作品を作っています
12:24
As it were, we have this ever-evolving,
いわば 私たちは未だかつてない
12:26
crochet taxonomic tree of life.
かぎ針編みの系統樹を進化させています
12:28
Just as the morphology
形態学や地球上の
12:30
and the complexity of life on earth is never ending,
生命体の複雑さには終わりがないように
12:32
little embellishments and complexifications
遺伝子コードに含まれる
12:34
in the DNA code
潤色や複素化が
12:37
lead to new things like giraffes, or orchids --
新しい生き物を生み出します
12:39
so too, do little embellishments in the crochet code
同様に わずかなひねりが
12:42
lead to new and wondrous creatures
作品の進化系統樹に
12:45
in the evolutionary tree of crochet life.
新しくて不思議な生き物を生み出すのです
12:48
So this project really has
ですから この企画はまさに
12:51
taken on this inner organic life of its own.
内に秘めた有機的な命をもつようになりました
12:53
There is the totality of all the people who have come to it.
参加した人 全員の集合性です
12:56
And their individual visions,
そして彼らの個人的なビジョンと
12:59
and their engagement with this mathematical mode.
この数学的方法との結びつきです
13:01
We have these technologies. We use them.
かぎ針編みを用いる―
13:04
But why? What's at stake here? What does it matter?
動機や重要性は何かと言うと
13:06
For Chrissy and I, one of the things that's important here
これらの事柄が
13:09
is that these things suggest
体系化した知識の重要性や
13:12
the importance and value of embodied knowledge.
価値を表している事です
13:14
We live in a society
私たちが住む社会とは
13:17
that completely tends to valorize
記号化した表現方法を
13:19
symbolic forms of representation --
非常に評価する傾向にあります
13:21
algebraic representations,
代数による表現や
13:23
equations, codes.
方程式や記号などです
13:25
We live in a society that's obsessed
私たちの住む世界とは
13:27
with presenting information in this way,
情報の表し方や教え方が
13:29
teaching information in this way.
型にはまっています
13:31
But through this sort of modality,
でも かぎ針編みや
13:34
crochet, other plastic forms of play --
形を造る遊びを利用すれば
13:37
people can be engaged with the most abstract,
最も抽象的で活動的で理論的な考えと
13:41
high-powered, theoretical ideas,
関係性をもてるのです
13:44
the kinds of ideas that normally you have to go
普通ならば大学に進んで
13:46
to university departments to study in higher mathematics,
高級数学で学ぶような事柄です
13:48
which is where I first learned about hyperbolic space.
私が初めて双曲線空間を学んだのも大学でした
13:51
But you can do it through playing with material objects.
でも物を使った遊びでも同じことはできます
13:54
One of the ways that we've come to think about this
遊びと結びつけた方法の一つを
13:58
is that what we're trying to do with the Institute for Figuring
私たちは IFFで実現させようとしており
14:00
and projects like this, we're trying to have
大人向けの幼稚園の中に
14:03
kindergarten for grown-ups.
取り入れようとしています
14:05
And kindergarten was actually a very formalized
幼稚園は非常に一定の
14:07
system of education,
形をもつ教育システムで
14:09
established by a man named Friedrich Froebel,
フリードリッヒ フレーベルが確立しました
14:11
who was a crystallographer in the 19th century.
彼は19世紀の結晶学者で
14:13
He believed that the crystal was the model
結晶が全ての表現の
14:15
for all kinds of representation.
モデルであると信じていました
14:17
He developed a radical alternative system
彼は急進的なやり方で
14:19
of engaging the smallest children
幼い子どもが 物を使って
14:22
with the most abstract ideas
最も抽象的な概念を体感できる―
14:24
through physical forms of play.
システムを発展させました
14:26
And he is worthy of an entire talk on his own right.
彼の功績は素晴らしいものです
14:28
The value of education
フレーベルは
14:30
is something that Froebel championed,
形を造る遊びを通した教育に
14:32
through plastic modes of play.
価値があると提唱しました
14:35
We live in a society now
私たちが現在住む世界には
14:37
where we have lots of think tanks,
シンクタンクが沢山あって
14:39
where great minds go to think about the world.
世界について考える偉大な人が大勢います
14:41
They write these great symbolic treatises
彼らは 本や新聞や
14:44
called books, and papers,
論評といった
14:46
and op-ed articles.
表象的なものを書きますが
14:48
We want to propose, Chrissy and I,
私たち姉妹は
14:50
through The Institute for Figuring, another alternative way of doing things,
IFFを通して 別の方法を提案したいのです
14:52
which is the play tank.
それは プレイタンク
14:55
And the play tank, like the think tank,
プレイタンクはシンクタンクのように
14:58
is a place where people can go
素晴らしいアイデアを
15:00
and engage with great ideas.
分かち合える場所です
15:02
But what we want to propose,
でも 私たちが提案するのは
15:04
is that the highest levels of abstraction,
最高レベルの抽象概念です
15:06
things like mathematics, computing, logic, etc. --
数学や情報処理や
15:08
all of this can be engaged with,
数理論理学などは
15:11
not just through purely cerebral algebraic
難しい代数や
15:13
symbolic methods,
記号解法だけではなく
15:15
but by literally, physically playing with ideas.
遊びを通じて体感できるのです
15:17
Thank you very much.
どうもありがとう
15:21
(Applause)
(拍手)
15:23
Translator:Takako Sato
Reviewer:Aiko McLean

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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.

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