Margaret Wertheim: The beautiful math of coral (and crochet)

翻译人员: lin qiang 校对人员: Tony Yet

I'm here today, as June said,

我今天在此，就如琼所说，

to talk about a project

要讲述一个我和同胞姐姐

that my twin sister and I have been doing for the past three and half years.

做了三年半时间的项目。

We're crocheting a coral reef.

我们在编织一个珊瑚礁。

And it's a project that we've actually

实际上，现在已经有成百上千，来自世界各地的人们

been now joined by hundreds of people around the world,

加入到我们的行列中，

who are doing it with us. Indeed thousands of people

他们和我们一起工作，事实上，

have actually been involved in this project,

成千上万的人们，已经通过各种各样的方式

in many of its different aspects.

参与到这个项目中。

It's a project that now reaches across three continents,

这个项目现在已经扩展到三个大陆。

and its roots go into the fields of mathematics,

它的基础涉及数学，

marine biology, feminine handicraft

海洋生物学，女性手工艺品

and environmental activism.

和环保主义。

It's true.

是这样的。

It's also a project

这同时也是一个

that in a very beautiful way,

十分美妙的项目，

the development of this

因为项目在进行的同时

has actually paralleled the evolution of life on earth,

也与地球生命进化的脉络并行，

which is a particularly lovely thing to be saying

这是个很可爱的话题，

right here in February 2009 --

2009年2月，

which, as one of our previous speakers told us,

就如之前有位演讲者所说，

is the 200th anniversary

是查尔斯·达尔文的

of the birth of Charles Darwin.

200周年诞辰。

All of this I'm going to get to in the next 18 minutes, I hope.

这就是接下来18分钟内，我所想要与你们分享的。

But let me first begin by showing you

但首先请我给你们

some pictures of what this thing looks like.

展示一些这些东西的图片。

Just to give you an idea of scale,

为使你们对大小有个概念，

that installation there is about six feet across,

那个作品大概6英尺宽，

and the tallest models are about two or three feet high.

而最高的模型大约2到3英尺高。

This is some more images of it.

这是它的另一些图片。

That one on the right is about five feet high.

右边的那个大约有5英尺高。

The work involves hundreds of different crochet models.

整个作品包含了数百件不同的针织模型。

And indeed there are now thousands and thousands of models that people

事实上，类似这样的模型，现在已经有数千件，

have contributed all over the world as part of this.

都来自世界各地人们的捐献。

The totality of this project

整个项目

involves tens of thousands of hours

包含了成千上万个小时

of human labor --

的人力劳动——

99 percent of it done by women.

99%是有妇女完成的。

On the right hand side, that bit there is part of an installation

在右手边，那是一个大约12英尺长

that is about 12 feet long.

的作品的一部分。

My sister and I started this project in 2005

我和姐姐在2005年开始了这个项目，

because in that year, at least in the science press,

因为那一年，至少在科学出版上，

there was a lot of talk about global warming,

出现了很多有关全球变暖的讨论，

and the effect that global warming was having on coral reefs.

而全球变暖将对珊瑚礁产生影响。

Corals are very delicate organisms,

珊瑚是非常脆弱的生物。

and they are devastated by any rise in sea temperatures.

海水温度稍一上升就会对它们产生致命的影响。

It causes these vast bleaching events

这也导致了这些大规模的白化现象，

that are the first signs of corals of being sick.

而这正是珊瑚生病的第一个征兆。

And if the bleaching doesn't go away --

如果白化不能够消失，

if the temperatures don't go down -- reefs start to die.

如果温度不下降，珊瑚礁就会开始死去。

A great deal of this has been happening in the Great Barrier Reef,

在大堡礁已经有许多这样的情形出现，

particularly in coral reefs all over the world.

全世界的珊瑚礁也同样如此。

This is our invocation in crochet of a bleached reef.

这个白化珊瑚礁的针织模型寄托了我们的祈祷。

We have a new organization together called The Institute for Figuring,

我们还一起成立了一个新的组织，称作计算研究所，

which is a little organization we started

这是个小组织，目的是

to promote, to do projects about the

促进并从事有关

aesthetic and poetic dimensions of science and mathematics.

表现科学和数学中美学和诗意方面的项目。

And I went and put a little announcement up on our site,

在我们的网站上我做了个小小的声明，

asking for people to join us in this enterprise.

希望人们加入到这项事业中。

To our surprise, one of the first people who called

出乎我们意料，首先打电话过来的

was the Andy Warhol Museum.

竟是安迪·沃霍尔博物馆。

And they said they were having an exhibition

他们说要举办一个有关

about artists' response to global warming,

艺术家们对全球变暖作何反应的展览，

and they'd like our coral reef to be part of it.

并希望我们的珊瑚礁能成为其中一部分。

I laughed and said, "Well we've only just started it,

我笑了，说：“我们才刚刚开始，

you can have a little bit of it."

你们可以拿一小部分去。”

So in 2007 we had an exhibition,

因此2007年我们就办了个展览，

a small exhibition of this crochet reef.

一次这种编织珊瑚的小展览。

And then some people in Chicago came along and they said,

然后有些从芝加哥过来参观的人就说，

"In late 2007, the theme of the Chicago Humanities Festival is

“2007年底，芝加哥人文艺术节的主题就是全球变暖，

global warming. And we've got this 3,000 square-foot gallery

我们有3000平方英尺的展厅，

and we want you to fill it with your reef."

希望你们用珊瑚礁来填满它。”

And I, naively by this stage, said, "Oh, yes, sure."

而我，天真得很，说，“噢，好的，没问题。”

Now I say "naively" because actually

我说“天真”其实是因为

my profession is as a science writer.

我的职业是科学作家。

What I do is I write books about the cultural history of physics.

我所做的是写有关物理学文化历史的书籍。

I've written books about the history of space,

我已经写过有关太空历史、

the history of physics and religion,

物理学和宗教历史的书，

and I write articles for people like the New York Times and the L.A. Times.

我也为纽约时报和洛杉矶时报之类撰写文章。

So I had no idea what it meant to fill a 3,000 square-foot gallery.

所以我对填满3000平方英尺的展厅没有丝毫概念。

So I said yes to this proposition.

所以我就答应了这个提议。

And I went home, and I told my sister Christine.

回家之后，我告诉了姐姐克里斯汀，

And she nearly had a fit

她几乎大发雷霆，

because Christine is a professor at one of

因为她在洛杉矶最主要的艺术学院，

L.A.'s major art colleges, CalArts,

加州艺术学院里当教授，

and she knew exactly what it meant to fill a 3,000 square-foot gallery.

十分清楚填满3000平方英尺的展厅是什么概念。

She thought I'd gone off my head.

她认为我是发疯了。

But she went into crochet overdrive.

但她还是加紧投入了编织中。

And to cut a long story short, eight months later

长话短说，八个月之后，

we did fill the Chicago Cultural Center's

我们真的把芝加哥文化中心3000平方英尺

3,000 square foot gallery.

的展厅填满了。

By this stage the project had taken on

通过这次展示，我们的项目

a viral dimension of its own,

出现了“病毒式传播”的效应，

which got completely beyond us.

完全出乎我们的想象。

The people in Chicago decided

芝加哥的人们决定，

that as well as exhibiting our reefs, what they wanted to do

在我们的珊瑚礁展览的同时，他们也希望

was have the local people there make a reef.

当地的人们也能造一个珊瑚礁出来。

So we went and taught the techniques. We did workshops and lectures.

所以我们就去教授技术。我们开培训班，开讲座，

And the people in Chicago made a reef of their own.

芝加哥人就做出了自己的珊瑚礁，

And it was exhibited alongside ours.

并在我们的展品旁展览。

There were hundreds of people involved in that.

成百上千的人参与其中。

We got invited to do the whole thing

我们受邀前往纽约、

in New York, and in London,

伦敦和洛杉矶

and in Los Angeles.

进行同样的工作。

In each of these cities, the local citizens,

在每一个城市，当地居民，

hundreds and hundreds of them, have made a reef.

成百上千的人们都来制作珊瑚礁。

And more and more people get involved in this,

而且越来越多的人们参与进来，

most of whom we've never met.

大部分都是新鲜的面孔。

So the whole thing has sort of morphed

所以整个事情似乎渐渐演变成

into this organic, ever-evolving creature,

这种有机的、不断进化的生物，

that's actually gone way beyond Christine and I.

实际上已经远远超出我和克里斯汀的想象。

Now some of you are sitting here thinking,

现在在座的一些人会想，

"What planet are these people on?

“这些人到底是从哪里来的？

Why on earth are you crocheting a reef?

你到底为什么要编织一个珊瑚礁？

Woolenness and wetness aren't exactly

羊毛织物和湿漉漉的东西

two concepts that go together.

根本就是风马牛不相及的两个东西。

Why not chisel a coral reef out of marble?

为什么不用大理石来雕刻珊瑚礁？

Cast it in bronze."

或者是用青铜来浇铸？”

But it turns out there is a very good reason

但事实上我们为什么编织它

why we are crocheting it

的原因很合理，

because many organisms in coral reefs

因为许多珊瑚礁生物

have a very particular kind of structure.

的形状结构都很特别。

The frilly crenulated forms that you see

你们在珊瑚、海带、海绵和海兔等生物上看到

in corals, and kelps, and sponges and nudibranchs,

的镶褶边的形状，

is a form of geometry known as hyperbolic geometry.

实际上是一种称为双曲线的几何形状。

And the only way that mathematicians know

而数学家们所知的

how to model this structure

模拟这种结构的唯一方法，

is with crochet. It happens to be a fact.

就是要靠编织。事实也刚好是这样。

It's almost impossible to model this structure any other way,

几乎没有别的方法来模拟这种形状。

and it's almost impossible to do it on computers.

在电脑上也几乎不可能做出来。

So what is this hyperbolic geometry

那么珊瑚和海蛞蝓到底

that corals and sea slugs embody?

展示了什么样的双曲线几何呢？

The next few minutes is, we're all going to get raised up

接下来几分钟，我们要向

to the level of a sea slug.

海蛞蝓的水平看齐。

(Laughter)

（笑声）

This sort of geometry revolutionized mathematics

在19世纪这种几何形状第一次被发现的时候，

when it was first discovered in the 19th century.

它就引起了数学的革命。

But not until 1997 did mathematicians actually understand

但直到1997年，数学家们才真正知道

how they could model it.

怎么去模拟它。

In 1997 a mathematician

1997年，康奈尔大学的数学家

at Cornell, Daina Taimina,

Daina Taimina，

made the discovery that this structure

发现可以用编织和钩针

could actually be done in knitting and crochet.

来表现这种结构。

The first one she did was knitting.

她的第一个作品是用针织法做的。

But you get too many stitches on the needle. So she quickly realized

但这种方法会使针上面的缝线过多。因此她很快意识到，

crochet was the better thing.

钩针编织是更好的方法。

But what she was doing was actually making a model

但她所做的，其实是一个模型，

of a mathematical structure, that many mathematicians

一个数学结构的模型，而许多数学家

had thought it was actually impossible to model.

都认为这种结构是无法模拟的。

And indeed they thought that anything like this structure

事实上他们认为像这种结构的东西

was impossible per se.

本身是不存在的。

Some of the best mathematicians spent hundreds of years

一些最好的数学家花费了数百年时间，

trying to prove that this structure was impossible.

试图证明这种结构不可能存在。

So what is this impossible hyperbolic structure?

那么这种不可能的双曲结构是什么呢？

Before hyperbolic geometry, mathematicians knew

在双曲几何出现之前，数学家已经知道了

about two kinds of space:

两种空间，

Euclidean space, and spherical space.

欧几里得空间和球面空间。

And they have different properties.

它们的特性不同。

Mathematicians like to characterize things by being formalist.

数学家们喜欢用形式主义的方式来定义事物。

You all have a sense of what a flat space is, Euclidean space is.

你们都会有平面空间，也就是欧几里得空间的概念。

But mathematicians formalize this in a particular way.

但数学家们用一种特别的方式来定义它。

And what they do is, they do it through the concept

他们是通过平行线的概念

of parallel lines.

来解释的。

So here we have a line and a point outside the line.

这里我们有一条直线和直线外的一点，

And Euclid said, "How can I define parallel lines?

欧几里得说，“我怎么定义平行线呢？

I ask the question, how many lines can I draw through

问，经过这一点我可以画多少条直线，

the point but never meet the original line?"

且这些直线不与原直线相交？”

And you all know the answer. Does someone want to shout it out?

你们都知道答案。有谁想大声喊出来的？

One. Great. Okay.

一条，没错。好的。

That's our definition of a parallel line.

这就是我们对平行线的定义。

It's a definition really of Euclidean space.

它是欧几里得空间真正的定义。

But there is another possibility that you all know of:

但还有另一种可能性，你们都知道

spherical space.

球面空间，

Think of the surface of a sphere --

想象一个球体的表面，

just like a beach ball, the surface of the Earth.

如沙滩球，地球表面。

I have a straight line on my spherical surface.

在这个球面上有一条直线，

And I have a point outside the line. How many straight lines

在直线外有一个点，那么过这个点，我可以在

can I draw through the point

球面上画多少条直线

but never meet the original line?

而不与原直线相交呢？

What do we mean to talk about

我们所说的弯曲表面上的

a straight line on a curved surface?

直线是怎么回事呢？

Now mathematicians have answered that question.

现在数学家们已经回答了这个问题。

They've understood there is a generalized concept

他们对直线有个总体上的共识，

of straightness, it's called a geodesic.

这被称为测地线。

And on the surface of a sphere,

而在球体表面，

a straight line is the biggest possible circle you can draw.

直线就是你所能画出的最大的圆圈。

So it's like the equator or the lines of longitude.

就像赤道或经线。

So we ask the question again,

因此我们再问一下，

"How many straight lines can I draw through the point,

“经过这一点，我们能够画出多少条直线

but never meet the original line?"

而不与原来的直线相交？”

Does someone want to guess?

有谁想来猜一猜？

Zero. Very good.

零。非常好。

Now mathematicians thought that was the only alternative.

数学家们认为这只是其中一个答案。

It's a bit suspicious isn't it? There is two answers to the question so far,

有点蹊跷是吧？目前这个问题有两个答案，

Zero and one.

零和一。

Two answers? There may possibly be a third alternative.

两个答案？还可能有第三个答案。

To a mathematician if there are two answers,

对一个数学家来说，如果有两个答案，

and the first two are zero and one,

分别是0和1，

there is another number that immediately suggests itself

那另一个作为第三个答案的数字

as the third alternative.

也就呼之欲出了。

Does anyone want to guess what it is?

有谁想来猜一下是什么？

Infinity. You all got it right. Exactly.

无穷多。你们都对了，没错。

There is, there's a third alternative.

有第三个答案。

This is what it looks like.

这就是那个答案。

There's a straight line, and there is an infinite number of lines

这里有条直线，然后有无数多的直线

that go through the point and never meet the original line.

能经过这点而不与原直线相交。

This is the drawing.

画起来就是这样。

This nearly drove mathematicians bonkers

这几乎使数学家们发疯，

because, like you, they're sitting there feeling bamboozled.

因为，像你们一样，他们也是坐在那里感觉受到欺骗。

Thinking, how can that be? You're cheating. The lines are curved.

想想，这怎么做到的？你在骗人，这些线是曲线。

But that's only because I'm projecting it onto a

但之所以如此只是因为我是在

flat surface.

平面上展示它。

Mathematicians for several hundred years

数百年来，数学家们为此

had to really struggle with this.

真的付出了太多了。

How could they see this?

他们怎么看到这个的？

What did it mean to actually have a physical model

在实际中用物理模型来表现它

that looked like this?

意味着什么？

It's a bit like this: imagine that we'd only ever encountered Euclidean space.

有点像这样：想象我们只看见过欧几里得空间，

Then our mathematicians come along

然后数学家们走过来，

and said, "There's this thing called a sphere,

说，“这种东西叫做球体，

and the lines come together at the north and south pole."

它上面的线在南极和北极汇合。”

But you don't know what a sphere looks like.

但你不知道球体看起来是什么样的。

And someone that comes along and says, "Look here's a ball."

然后有人过来说，“看那有个球。”

And you go, "Ah! I can see it. I can feel it.

你走过去，“啊！我能看到它，我能感觉它。

I can touch it. I can play with it."

我们触摸它。它还能用来玩。”

And that's exactly what happened

而这正是1997年，

when Daina Taimina

当Daina Taimina展示出

in 1997, showed that you could crochet models

可以用编织模型来模拟双曲空间

in hyperbolic space.

时的情景。

Here is this diagram in crochetness.

这里是钩针编织的一个图示。

I've stitched Euclid's parallel postulate on to the surface.

我已经把欧几里得平行共设缝到了上面。

And the lines look curved.

这些线看起来是弯的。

But look, I can prove to you that they're straight

但请看，我向你们证明它们其实是直的，

because I can take any one of these lines,

因为我可以随便拿起一条线，

and I can fold along it.

然后顺着线折叠起来。

And it's a straight line.

这是条直线。

So here, in wool,

因此，这些毛线，

through a domestic feminine art,

通过一种居家女性的艺术形式，

is the proof that the most famous postulate

证明了数学史上最著名的假设

in mathematics is wrong.

原来是错的。

(Applause)

（掌声）

And you can stitch all sorts of mathematical

你可以把各种各样的数学定理

theorems onto these surfaces.

都缝在这些上面。

The discovery of hyperbolic space ushered in the field of mathematics

双曲空间的发现导致了数学领域中

that is called non-Euclidean geometry.

非欧几何学的出现。

And this is actually the field of mathematics

正是这一数学的新领域

that underlies general relativity

构成了广义相对论的基础

and is actually ultimately going to show us

并将最终向我们揭示

about the shape of the universe.

宇宙的形状。

So there is this direct line

因此在女性手工艺和

between feminine handicraft,

欧几里得以及广义相对论之间

Euclid and general relativity.

有直接的联系。

Now, I said that mathematicians thought that this was impossible.

好的，我说过数学家们曾认为这是不可能的。

Here's two creatures who've never heard of Euclid's parallel postulate --

这是两种从未听过欧几里得平行公设的生物，

didn't know it was impossible to violate,

它们并不知道这条不能违背的定理，

and they're simply getting on with it.

依旧继续着简单的生活。

They've been doing it for hundreds of millions of years.

亿万年来，它们一直保持这样的形态。

I once asked the mathematicians why it was

我曾问过数学家它为什么会这样，

that mathematicians thought this structure was impossible

而数学家们认为这种结构是不可能的，

when sea slugs have been doing it since the Silurian age.

即使海蛞蝓从志留纪开始就一直是这样。

Their answer was interesting.

他们的答案很有趣。

They said, "Well I guess there aren't that many mathematicians

他们说，“呃，我猜也没有多少数学家

sitting around looking at sea slugs."

会坐下来观察海蛞蝓。”

And that's true. But it also goes deeper than that.

这是真的。但这背后还有更多东西。

It also says a whole lot of things

它能告诉我们很多，

about what mathematicians thought mathematics was,

数学家们对数学是什么、

what they thought it could and couldn't do,

数学能做到和不能做到的

what they thought it could and couldn't represent.

数学能表达和不能表达出来的等的思考。

Even mathematicians, who in some sense

甚至数学家，他们在某种程度上

are the freest of all thinkers,

是最自由的思想者，

literally couldn't see

不仅不能确实看到

not only the sea slugs around them,

身边的海蛞蝓，

but the lettuce on their plate --

也看不到盘子里的生菜叶，

because lettuces, and all those curly vegetables,

因为生菜叶，还有所有有褶的蔬菜，

they also are embodiments of hyperbolic geometry.

它们都能体现出双曲几何。

And so in some sense they literally,

某种程度上他们确实，

they had such a symbolic view of mathematics,

他们对数学有种符号化的观点，

they couldn't actually see what was going on

他们看不到面前的生菜叶

on the lettuce in front of them.

到底体现了什么。

It turns out that the natural world is full of hyperbolic wonders.

而事实上自然界到处都有双曲线的奇观。

And so, too, we've discovered

同样，我们已经发现

that there is an infinite taxonomy

编织出来的双曲线型生物

of crochet hyperbolic creatures.

也有无穷无尽的种类。

We started out, Chrissy and I and our contributors,

我们着手开始，克丽希和我，还有我们的志愿者，

doing the simple mathematically perfect models.

从简单的，数学上完美的模型开始做。

But we found that when we deviated from the specific

但我们发现，当我们偏离了那一整套

setness of the mathematical code

特定的数学准则，

that underlies it -- the simple algorithm

以简单的运算法则为基础的数学准则，

crochet three, increase one --

钩针编织三次，放一次针。

when we deviated from that and made embellishments to the code,

当我们偏离了这些准则并对它做了一些修饰之后，

the models immediately started to look more natural.

模型立刻变得更加自然起来。

And all of our contributors, who are an amazing

而且我们的志愿者们，他们来自世界各地，

collection of people around the world,

非常出色的一群人，

do their own embellishments.

他们用自己的方式进行修饰。

As it were, we have this ever-evolving,

由此，我们拥有了一棵不断演化

crochet taxonomic tree of life.

的编织分类学生命之树。

Just as the morphology

就好比地球上的生命

and the complexity of life on earth is never ending,

从未停止在形态学和复杂性上的进化，

little embellishments and complexifications

对DNA编码稍微的

in the DNA code

修饰和复杂化，

lead to new things like giraffes, or orchids --

就导致了像长颈鹿或兰花这样的新物种出现。

so too, do little embellishments in the crochet code

同样的，对钩针编织法则一点点的修饰

lead to new and wondrous creatures

就能导致在编织生命进化树上

in the evolutionary tree of crochet life.

新的，更完美的生物的出现。

So this project really has

所以这一项目真正地

taken on this inner organic life of its own.

具有它本身内在的有机的生命力。

There is the totality of all the people who have come to it.

这里是所有参加这个项目的人的总数。

And their individual visions,

还有他们的个人观点，

and their engagement with this mathematical mode.

和他们对这一数学模式的理解。

We have these technologies. We use them.

我们有这些技术，我们利用这些技术。

But why? What's at stake here? What does it matter?

但为什么？什么才是利害攸关的？什么才是重要的？

For Chrissy and I, one of the things that's important here

对于克里希和我来说，这里最重要的事情之一，

is that these things suggest

就是这些东西表明了

the importance and value of embodied knowledge.

具体表达出知识的重要性和价值。

We live in a society

我们生活在一个

that completely tends to valorize

完全趋向于为各种象征性的表述方式

symbolic forms of representation --

规定价格的社会，

algebraic representations,

代数式的表述，

equations, codes.

等式，编码等等。

We live in a society that's obsessed

我们生活的社会深深迷恋上

with presenting information in this way,

这一种表述信息

teaching information in this way.

和传授信息的方式。

But through this sort of modality,

但通过模型的方式，

crochet, other plastic forms of play --

如钩针编织，其他塑料形式的展示，

people can be engaged with the most abstract,

人们能理解那些最抽象的，

high-powered, theoretical ideas,

高难度的理论化的概念，

the kinds of ideas that normally you have to go

也就是那些你通常需要跑到

to university departments to study in higher mathematics,

大学里面才能学到的高等数学，

which is where I first learned about hyperbolic space.

其实我也是在那里才第一次学到双曲空间的。

But you can do it through playing with material objects.

但你们可以用实际的物件来做到这些。

One of the ways that we've come to think about this

我们已经想到了这一点，

is that what we're trying to do with the Institute for Figuring

这也是我们想要通过计算研究所来尝试的一个项目，

and projects like this, we're trying to have

像这样的项目，我们想要

kindergarten for grown-ups.

建一个属于成人的幼儿园。

And kindergarten was actually a very formalized

幼儿园其实是一种非常形象化

system of education,

的教育系统，

established by a man named Friedrich Froebel,

由19世纪一位名叫福禄贝尔

who was a crystallographer in the 19th century.

的检晶科学家创立。

He believed that the crystal was the model

他认为晶体可以作为

for all kinds of representation.

所有表述方式的模型。

He developed a radical alternative system

他发展了一套激进另类的系统，

of engaging the smallest children

即使最小的孩子也能够通过

with the most abstract ideas

寓于物理形式的玩耍

through physical forms of play.

来理解最抽象的概念。

And he is worthy of an entire talk on his own right.

他自己本身就值得作一整个演讲了。

The value of education

福禄贝尔通过

is something that Froebel championed,

娱乐的可塑模式

through plastic modes of play.

捍卫了教育的价值。

We live in a society now

我们现在身处的社会，

where we have lots of think tanks,

有许多的“智库”，

where great minds go to think about the world.

许多优秀的头脑在那里思索世界问题。

They write these great symbolic treatises

他们写下这些伟大的符号化的专著，

called books, and papers,

也叫书籍，和论文，

and op-ed articles.

还有专栏文章。

We want to propose, Chrissy and I,

我们，克里希和我想要提出，

through The Institute for Figuring, another alternative way of doing things,

通过计算研究所来提出，另一种做事情的方式，

which is the play tank.

我们称之为“玩库”。

And the play tank, like the think tank,

玩库，就像智库，

is a place where people can go

是一个人们过来

and engage with great ideas.

认识那些伟大思想和概念的地方。

But what we want to propose,

但我们想提议的，

is that the highest levels of abstraction,

是那些最高层次的抽象思维，

things like mathematics, computing, logic, etc. --

如数学，计算，逻辑等等，

all of this can be engaged with,

所有这些都能够，

not just through purely cerebral algebraic

不仅仅通过单纯的代数性的，

symbolic methods,

符号化的方法，

but by literally, physically playing with ideas.

也可以通过文学的，物理上的方法“玩转”概念。

Thank you very much.

非常感谢。

(Applause)

（掌声）