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MargaretWertheim_2009-_珊瑚（和编织）的美丽数学_
I'm here today, as June said, to talk about a project that my twin sister and I have been doing for the past three and half years. 我今天在此,就如琼所说, 要讲述一个我和同胞姐姐 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。
crocheting:n.钩编;钩编技术;钩编工艺;v.钩编(crochet的ing形式); coral:n.珊瑚;珊瑚虫;adj.珊瑚的;珊瑚色的;
And it's a project that we've actually been now joined by hundreds of people around the world who are doing it with us. Indeed thousands of people have actually been involved in this project, in many of its different aspects . 实际上,现在已经有成百上千,来自世界各地的人们 加入到我们的行列中, 他们和我们一起工作,事实上, 成千上万的人们,已经通过各种各样的方式 参与到这个项目中。
involved:adj.有关的; v.涉及; (involve的过去式和过去分词) aspects:n.方面;相位;面貌(aspect的复数);
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。
continents:n.[地理]大陆,大洲(continent复数);
Its roots go into the fields of mathematics , marine biology , feminine handicraft and environmental activism . 它的基础涉及数学, 海洋生物学,女性手工艺品 和环保主义。
mathematics:n.数学;数学运算; marine:adj.海的;海产的;海生的;海船的;n.(尤指美国或英国皇家)海军陆战队士兵; biology:n.(一个地区全部的)生物;生物学; feminine:adj.女性的;妇女(似)的;阴性的;娇柔的; handicraft:n.手工艺;手工艺品; activism:n.行动主义;激进主义;
It's true. 是这样的。
It's also a project that in a very beautiful way, the development of this has actually paralleled the evolution of life on earth, which is a particularly lovely thing to be saying right here in February 2009 -- which, as one of our previous speakers told us, is the 200th anniversary of the birth of Charles Darwin. 这同时也是一个 十分美妙的项目, 因为项目在进行的同时 也与地球生命进化的脉络并行, 这是个很可爱的话题, 2009年2月, 就如之前有位演讲者所说, 是查尔斯·达尔文的 200周年诞辰。
paralleled:adj.并行的,平行的; evolution:n.演变;进化;发展;渐进; particularly:adv.特别地,独特地;详细地,具体地;明确地,细致地; previous:adj.以前的;早先的;过早的;adv.在先;在…以前;
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 some pictures of what this thing looks like. 但首先请我给你们 展示一些这些东西的图片。
Just to give you an idea of scale , that installation there is about six feet across. 为使你们对大小有个概念, 那个作品大概6英尺宽,
scale:n.规模;比例;鳞;刻度;天平;数值范围;v.衡量;攀登;剥落;生水垢; installation:n.安装;设施;设置;安装的设备(或机器);
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。
images:n.印象;声誉;形象;画像;雕像;(image的第三人称单数和复数)
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。
involves:v.包含;需要;牵涉;牵连;影响;(使)参加,加入(involve的第三人称单数)
And indeed there are now thousands and thousands of models that people have contributed all over the world as part of this. 事实上,类似这样的模型,现在已经有数千件, 都来自世界各地人们的捐献。
contributed:v.捐献,捐赠(尤指款或物); (contribute的过去式和过去分词)
The totality of this project involves tens of thousands of hours of human labor -- 99 percent of it done by women. 整个项目 包含了成千上万个小时 的人力劳动—— 99%是有妇女完成的。
totality:n.[天]全食;全体;总数;
On the right hand side, that bit there is part of an installation that is about 12 feet long. 在右手边,那是一个大约12英尺长 的作品的一部分。
My sister and I started this project in 2005 because in that year, at least in the science press, there was a lot of talk about global warming , and the effect that global warming was having on coral reefs. 我和姐姐在2005年开始了这个项目, 因为那一年,至少在科学出版上, 出现了很多有关全球变暖的讨论, 而全球变暖将对珊瑚礁产生影响。
global warming:n.全球(气候)变暖;地球大气层变暖;
Corals are very delicate organisms . 珊瑚是非常脆弱的生物。
Corals:n.[无脊椎]珊瑚(coral的复数); delicate:adj.精致的,微妙的,脆弱的,熟练的,柔和的; organisms:n.[生物]生物体(organism的复数);[生物]有机体;
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。
devastated:adj.不安的,混乱的,震惊的; v.彻底破坏; (devastate的过去分词和过去式)
It causes these vast bleaching events that are the first signs of corals of being sick. 这也导致了这些大规模的白化现象, 而这正是珊瑚生病的第一个征兆。
bleaching:v.(使)变白,漂白,晒白,退色(bleach的现在分词)
And if the bleaching doesn't go away, if the temperatures don't go down, reefs start to die. 如果白化不能够消失, 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 , particularly in coral reefs all over the world. 在大堡礁已经有许多这样的情形出现, 全世界的珊瑚礁也同样如此。
A great deal of:大量; Barrier Reef:n.堡礁(近海岸的珊瑚礁);
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。
invocation:n.祈祷;符咒;[法律](法院对另案的)文件调取;(法权的)行使; bleached:adj.漂白的;v.(使)变白,漂白,退色(bleach的过去分词和过去式)
We have a new organization together called The Institute For Figuring, which is a little organization we started to promote , to do projects about aesthetic and poetic dimensions of science and mathematics. 我们还一起成立了一个新的组织,称作计算研究所, 这是个小组织,目的是 促进并从事有关 表现科学和数学中美学和诗意方面的项目。
organization:n.组织;机构;体制;团体; Institute:v.开始(调查);制定;创立;提起(诉讼);n.学会,协会;学院; promote:v.促进;推动;促销;提升;晋升; aesthetic:adj.美的;美学的;审美的,具有审美趣味的; poetic:adj.诗的,诗歌的;诗意的;诗人的;n.诗学,诗论; dimensions:n.规模,大小;
And I went and put a little announcement up on our site , asking for people to join us in this enterprise. 在我们的网站上我做了个小小的声明, 希望人们加入到这项事业中。
site:n.地点;位置;场所;v.设置;为…选址;
To our surprise, one of the first people who called was the Andy Warhol Museum. 出乎我们意料,首先打电话过来的 竟是安迪·沃霍尔博物馆。
And they said they were having an exhibition about artists' response to global warming, and they'd like our coral reef to be part of it. 他们说要举办一个有关 艺术家们对全球变暖作何反应的展览, 并希望我们的珊瑚礁能成为其中一部分。
response:n.响应;反应;回答;
I laughed and said, "Well we've only just started it, you can have a little bit of it." 我笑了,说:“我们才刚刚开始, 你们可以拿一小部分去。”
So in 2007 we had an exhibition, a small exhibition of this crochet reef. 因此2007年我们就办了个展览, 一次这种编织珊瑚的小展览。
And then some people in Chicago came along and they said, "In late 2007, the theme of the Chicago Humanities Festival is global warming. And we've got this 3,000 square foot gallery and we want you to fill it with your reef." 然后有些从芝加哥过来参观的人就说, “2007年底,芝加哥人文艺术节的主题就是全球变暖, 我们有3000平方英尺的展厅, 希望你们用珊瑚礁来填满它。”
Humanities:n.人文学科(humanity的复数); gallery:n.画廊;走廊;旁听席;地道;v.在…修建走廊;挖地道;
And I, naively by this stage, said, "Oh, yes. Sure." 而我,天真得很,说,“噢,好的,没问题。”
naively:adv.无邪地;天真烂漫地;
Now I say "naively" because actually my profession is as a science writer. 我说“天真”其实是因为 我的职业是科学作家。
profession:n.行业,职业;业内人士;同行;
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。
cultural:adj.与文化有关的;文化的;与艺术、文学、音乐等有关的;
I've written books about the history of space, the history of physics and religion, and I write articles for people like the New York Times, and the L.A. Times. 我已经写过有关太空历史、 物理学和宗教历史的书, 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。
proposition:n.提议;待处理的问题;任务;(美国)法律修正议案;见解;命题;v.向...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 because Christine is a professor at one of 她几乎大发雷霆, 因为她在洛杉矶最主要的艺术学院,
L.A.'s major art colleges, CalArts, and she knew exactly what it meant to fill a 3,000 square foot gallery. 加州艺术学院里当教授, 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。
overdrive:v.驱使过度;虐待;工作过度;n.超速档;[机]超速传动;
And to cut a long story short, eight months later we did fill the Chicago Cultural Center's 3,000 square foot gallery. 长话短说,八个月之后, 我们真的把芝加哥文化中心3000平方英尺 的展厅填满了。
By this stage the project had taken on a viral dimension of its own, which got completely beyond us. 通过这次展示,我们的项目 出现了“病毒式传播”的效应, 完全出乎我们的想象。
viral:adj.滤过性毒菌引起的;滤过性毒菌的;
The people in Chicago decided that as well as exhibiting our reefs, what they wanted to do was have the local people there make a reef. 芝加哥的人们决定, 在我们的珊瑚礁展览的同时,他们也希望 当地的人们也能造一个珊瑚礁出来。
as well as:也;和…一样;不但…而且; exhibiting:v.展览;展出;表现,显示,显出;(exhibit的现在分词)
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,
techniques:n.技巧;技艺;工艺;技术;(technique的复数) workshops:n.工作坊,[工业]车间;研习会,讲习班(workshop的复数形式);
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。
exhibited:adj.展出的;v.展出;表现出(exhibit的过去分词);
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 in New York, and in London, and in Los Angeles. 我们受邀前往纽约、 伦敦和洛杉矶 进行同样的工作。
In each of these cities, the local citizens, hundreds and hundreds of them, have made reefs. 在每一个城市,当地居民, 成百上千的人们都来制作珊瑚礁。
And more and more people get involved in this, most of whom we've never met. 而且越来越多的人们参与进来, 大部分都是新鲜的面孔。
So the whole thing has sort of morphed into this organic , ever evolving creature , that's actually gone way beyond Christine and I. 所以整个事情似乎渐渐演变成 这种有机的、不断进化的生物, 实际上已经远远超出我和克里斯汀的想象。
morphed:在屏幕上变换图像(morph的过去式和过去分词); organic:adj.有机的;不使用化肥的;绿色的;有机物的;n.分子有机体; evolving:v.(使)逐渐形成,逐渐演变;进化形成;(evolve的现在分词) creature:n.生物;动物;(具有某种特征的)人;
Now some of you are sitting here thinking, "What planet are these people on? 现在在座的一些人会想, “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 two concepts that go together. 羊毛织物和湿漉漉的东西 根本就是风马牛不相及的两个东西。
wetness:n.湿润;下雨;
Why not chisel a coral reef out of marble ? 为什么不用大理石来雕刻珊瑚礁？
chisel:vt.雕,刻;凿;欺骗;vi.雕,刻;凿;欺骗;n.凿子; marble:n.大理石;大理石制品;弹珠;adj.大理石的;冷酷无情的;
Cast it in bronze ." 或者是用青铜来浇铸？”
bronze:n.青铜; adj.青铜色的; vt.镀青铜于; vi.变成青铜色,被晒黑;
But it turns out there is a very good reason why we are crocheting it because many organisms in coral reefs have a very particular kind of structure . 但事实上我们为什么编织它 的原因很合理, 因为许多珊瑚礁生物 的形状结构都很特别。
structure:n.结构;构造;建筑物;vt.组织;构成;建造;
The frilly crinolated forms that you see in corals, and kelps , and sponges , and nudibranchs , is a form of geometry known as hyperbolic geometry. 你们在珊瑚、海带、海绵和海兔等生物上看到 的镶褶边的形状, 实际上是一种称为双曲线的几何形状。
frilly:adj.镶褶边的;多饰边的; kelps:n.海带;海草;巨藻;(kelp的复数) sponges:n.[无脊椎]海绵(sponge的复数形式); v.用海绵擦拭,吸收掉,抹掉(sponge的第三人称单数形式); nudibranchs:n.裸鳃亚目动物;裸鳃类动物(nudibranch的变形); geometry:n.几何学;几何结构; hyperbolic:adj.双曲线的;夸张的;
And the only way that mathematicians know how to model this structure, is with crochet. It happens to be a fact. 而数学家们所知的 模拟这种结构的唯一方法, 就是要靠编织。事实也刚好是这样。
mathematicians:n.[数]数学家(mathematician的复数形式);
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 that corals and sea slugs embody ? 那么珊瑚和海蛞蝓到底 展示了什么样的双曲线几何呢？
slugs:n.[无脊椎]蛞蝓; v.猛击; embody:v.具体表现,体现,代表(思想或品质);包括;
The next few minutes is, we're all going to get raised up to the level of a sea slug. 接下来几分钟,我们要向 海蛞蝓的水平看齐。
(Laughter) （笑声）
This sort of geometry revolutionized mathematics when it was first discovered in the 19th century. 在19世纪这种几何形状第一次被发现的时候, 它就引起了数学的革命。
revolutionized:adj.革命化的;被彻底改革的;v.彻底改革(revolutionize的过去式);
But not until 1997 did mathematicians actually understand how they could model it. 但直到1997年,数学家们才真正知道 怎么去模拟它。
In 1997 a mathematician at Cornell, Daina Taimina, made the discovery that this structure could actually be done in knitting and crochet. 1997年,康奈尔大学的数学家 Daina Taimina, 发现可以用编织和钩针 来表现这种结构。
knitting:n.针织;编织物;[外科]骨愈合;v.编织;皱眉(knit的ing形式);
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 crochet was the better thing. 但这种方法会使针上面的缝线过多。因此她很快意识到, 钩针编织是更好的方法。
stitches:n.(缝纫的)一针; v.缝; (stitch的第三人称单数和复数) needle:n.针;针头;指针;缝针;v.穿过;刺激;拿针缝;拿针穿;
But what she was doing was actually making a model of a mathematical structure, that many mathematicians had thought it was actually impossible to model. 但她所做的,其实是一个模型, 一个数学结构的模型,而许多数学家 都认为这种结构是无法模拟的。
mathematical:adj.数学的,数学上的;精确的;
Indeed they thought that anything like this structure was impossible per se . 事实上他们认为像这种结构的东西 本身是不存在的。
per se:adv.本身;本质上;
Some of the best mathematicians spent hundreds of years trying to prove that this structure was impossible. 一些最好的数学家花费了数百年时间, 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 about two kinds of space, 在双曲几何出现之前,数学家已经知道了 两种空间,
Euclidean space and spherical space. 欧几里得空间和球面空间。
spherical:adj.球形的,球面的;天体的;
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。
characterize:v.描述;是…的特征;以…为典型;使…具有特点(或最引人注目的特征); formalist:n.拘泥形式的人;形式主义者;adj.形式主义的;
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。
formalize:vt.使形式化;使正式;拘泥礼仪;vi.拘泥于形式;
And what they do is, they do it through the concept of parallel lines. 他们是通过平行线的概念 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,
Euclid said, "How can I define parallel lines? 欧几里得说,“我怎么定义平行线呢？
Euclid:n.欧几里得;欧几里德几何学; define:v.定义;使明确;规定;
I ask the question, how many lines can I draw through the point but never meet the original line?" 问,经过这一点我可以画多少条直线, 且这些直线不与原直线相交？”
original:n.原件;原作;原物;原型;adj.原始的;最初的;独创的;新颖的;
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. Right. 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。
definition:n.定义;清晰度;(尤指词典里的词或短语的)释义;解释;
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 -- spherical space. 但还有另一种可能性,你们都知道 球面空间,
Think of the surface of a sphere -- just like a beach ball , the surface of the Earth. 想象一个球体的表面, 如沙滩球,地球表面。
sphere:n.球;领域;球体;球形;v.使成球形;包围;把…放在球内;使处于天体之间; beach ball:n.沙滩球;
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 can I draw through the point but never meet the original line? 在直线外有一个点,那么过这个点,我可以在 球面上画多少条直线 而不与原直线相交呢？
What do we mean to talk about a straight line on a curved surface? 我们所说的弯曲表面上的 直线是怎么回事呢？
curved:adj.呈弯曲状的; v.(使)沿曲线运动;
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 of straightness . It's called a geodesic . 他们对直线有个总体上的共识, 这被称为测地线。
generalized:adj.广义的,普遍的; v.推广(generalize的过去分词); straightness:n.[机]平直度;率直;笔直; geodesic:adj.测地线的;
And on the surface of a sphere, a straight line is the biggest possible circle you can draw. 而在球体表面, 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。
longitude:n.[地理]经度;经线;
So we ask the question again, "How many straight lines can I draw through the point, but never meet the original line?" 因此我们再问一下, “经过这一点,我们能够画出多少条直线 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。
alternative:adj.供选择的;选择性的;交替的;n.二中择一;供替代的选择;
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,
suspicious:adj.可疑的;怀疑的;多疑的;
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, and the first two are zero and one, there is another number that immediately suggests itself, as the third alternative. 对一个数学家来说,如果有两个答案, 分别是0和1, 那另一个作为第三个答案的数字 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。
Infinity:n.无穷;无限大;无限距;
There is a third alternative. 有第三个答案。
This is what it looks like. 这就是那个答案。
It has a straight line, and there is an infinite number of lines that go through the point and never meet the original line. 这里有条直线,然后有无数多的直线 能经过这点而不与原直线相交。
infinite:adj.无限的,无穷的; n.无限;
This is the drawing. 画起来就是这样。
This nearly drove mathematicians bonkers because, like you, they're sitting there feeling bamboozled . 这几乎使数学家们发疯, 因为,像你们一样,他们也是坐在那里感觉受到欺骗。
bonkers:adj.疯狂的;精神不正常的; bamboozled:vt.迷惑;愚弄(bamboozle过去式);
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 flat surface. 但之所以如此只是因为我是在 平面上展示它。
Mathematicians for several hundred years had to really struggle with this. 数百年来,数学家们为此 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 that looked like this? 在实际中用物理模型来表现它 意味着什么？
physical:adj.[物]物理的;身体的;物质的;符合自然法则的;n.体格检查;
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,
encountered:v.遭遇,遇到;偶然碰到;意外地遇见;(encounter的过去分词和过去式)
Then our mathematicians come along and said, "There's this thing called a sphere, and the lines come together at the north and south pole ." 然后数学家们走过来, 说,“这种东西叫做球体, 它上面的线在南极和北极汇合。”
south pole:n.南极;
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。”
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 when Daina Taimina in 1997, showed that you could crochet models in hyperbolic space. 而这正是1997年, 当Daina Taimina展示出 可以用编织模型来模拟双曲空间 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。
stitched:v.缝;缝补;缝合(伤口);(stitch的过去分词和过去式) postulate:vt.假定;要求;视…为理所当然;n.基本条件;假定;
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 because I can take any one of these lines, and I can fold along it. 但请看,我向你们证明它们其实是直的, 因为我可以随便拿起一条线, 然后顺着线折叠起来。
fold:v.折叠;包;可叠平(以便贮存或携带);裹;n.褶;褶层;折叠部分;褶痕;
It's a straight line. 这是条直线。
So here, in wool , through a domestic feminine art, is the proof that the most famous postulate in mathematics is wrong. 因此,这些毛线, 通过一种居家女性的艺术形式, 证明了数学史上最著名的假设 原来是错的。
wool:n.毛;毛线;毛料;毛织物; domestic:n.佣人;家佣;家庭纠纷;家庭矛盾;adj.本国的;国内的;家用的;家庭的; proof:n.证据;证实;adj.能抵御;可防护;
(Applause) （掌声）
You can stitch all sorts of mathematical theorems onto these surfaces. 你可以把各种各样的数学定理 都缝在这些上面。
theorems:[数]定理;
The discovery of hyperbolic space ushered in the field of mathematics that is called non-Euclidean geometry. 双曲空间的发现导致了数学领域中 非欧几何学的出现。
ushered:n.引座员,带位员; vt.引导,招待; vi.作招待员; in the field of:在…方面,在…领域;
This is actually the field of mathematics that underlies general relativity and is actually ultimately going to show us about the shape of the universe. 正是这一数学的新领域 构成了广义相对论的基础 并将最终向我们揭示 宇宙的形状。
underlies:vt.成为…的基础;位于…之下; relativity:n.相对论;相关性;相对性; ultimately:adv.最终;最后;归根结底;终究;
So there is this direct line between feminine handicraft, 因此在女性手工艺和 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 -- didn't know it was impossible to violate , and they're simply getting on with it. 这是两种从未听过欧几里得平行公设的生物, 它们并不知道这条不能违背的定理, 依旧继续着简单的生活。
creatures:n.生物;动物;(具有某种特征的)人(creature的复数) violate:v.违反,违背(法律、协议等);侵犯(隐私等);亵渎;
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 that mathematicians thought this structure was impossible when sea slugs have been doing it since the Silurian age. 我曾问过数学家它为什么会这样, 而数学家们认为这种结构是不可能的, 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 sitting around looking at sea slugs." 他们说,“呃,我猜也没有多少数学家 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 about what mathematicians thought mathematics was. 它能告诉我们很多, 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。
represent:v.代表;表现;描绘;回忆;再赠送;
Even mathematicians, who in some sense are the freest of all thinkers, literally couldn't see not only the sea slugs around them, but the lettuce on their plate because lettuces, and all those curly vegetables, they also are embodiments of hyperbolic geometry. 甚至数学家,他们在某种程度上 是最自由的思想者, 不仅不能确实看到 身边的海蛞蝓, 也看不到盘子里的生菜叶, 因为生菜叶,还有所有有褶的蔬菜, 它们都能体现出双曲几何。
literally:adv.按字面:字面上:确实地: embodiments:n.体现;化身(embodiment的复数);
In some sense they literally -- they had such a symbolic view of mathematics -- they couldn't actually see what was going on on the lettuce in front of them. 某种程度上他们确实, 他们对数学有种符号化的观点, 他们看不到面前的生菜叶 到底体现了什么。
symbolic:adj.象征的;符号的;使用符号的;
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 that there is an infinite taxonomy of crochet hyperbolic creatures. 同样,我们已经发现 编织出来的双曲线型生物 也有无穷无尽的种类。
taxonomy:n.分类学;分类法;
We started out, Chrissy and I and our contributors , doing the simple mathematically perfect models. 我们着手开始,克丽希和我,还有我们的志愿者, 从简单的,数学上完美的模型开始做。
contributors:n.贡献者;参与者;编著者(contributor的复数形式); mathematically:adv.算术地,数学上地;
But we found that when we deviated from the specific setness of the mathematical code that underlies is the simple algorithm, crochet three, increase one. 但我们发现,当我们偏离了那一整套 特定的数学准则, 以简单的运算法则为基础的数学准则, 钩针编织三次,放一次针。
deviated:v.背离;偏离;违背;(deviate的过去分词和过去式) specific:adj.特殊的,特定的;明确的;详细的;[药]具有特效的;n.特性;细节;特效药;
When we deviated from that and made embellishments to the code, the models immediately started to look more natural. 当我们偏离了这些准则并对它做了一些修饰之后, 模型立刻变得更加自然起来。
embellishments:n.[建]装饰品(embellishment的复数);
And all of our contributors, who are an amazing collection of people around the world, do their own embellishments. 而且我们的志愿者们,他们来自世界各地, 非常出色的一群人, 他们用自己的方式进行修饰。
As it were , we have this ever evolving, crochet taxonomic tree of life. 由此,我们拥有了一棵不断演化 的编织分类学生命之树。
As it were:可以说是,似乎就是;好像; taxonomic:adj.[生物]分类的;[生物]分类学的;
Just as the morphology and the complexity of life on earth is never ending, little embellishments and complexifications in the DNA code, lead to new things like giraffes or orchids . 就好比地球上的生命 从未停止在形态学和复杂性上的进化, 对DNA编码稍微的 修饰和复杂化, 就导致了像长颈鹿或兰花这样的新物种出现。
morphology:n.形态学,形态论;[语]词法,[语]词态学; complexity:n.复杂性;难以理解的局势 orchids:n.[园艺]兰花,淡紫色;称赞(orchid的复数);
So too, little embellishments in the crochet code lead to new and wondrous creatures in the evolutionary tree of crochet life. 同样的,对钩针编织法则一点点的修饰 就能导致在编织生命进化树上 新的,更完美的生物的出现。
wondrous:adj.奇妙的;令人惊奇的;非常的; evolutionary:adj.进化的;发展的;渐进的;
So this project really has taken on this inner organic life of its own. 所以这一项目真正地 具有它本身内在的有机的生命力。
inner:n.内部;射中接近靶心部分的一发;adj.里面的;向内的;内部的;接近中心的;
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 , and their engagement with this mathematical mode. 还有他们的个人观点, 和他们对这一数学模式的理解。
individual:n.个人;有个性的人;adj.单独的;个别的; visions:n.愿景; v.想像; engagement:n.婚约;约会;交战;诺言;n.参与度;
We have these technologies . We use them. 我们有这些技术,我们利用这些技术。
technologies:n.技术;科技(technology的复数);
But why? What is 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？
stake:n.桩,棍子;赌注;火刑;奖金;v.资助,支持;系…于桩上;把…押下打赌;
For Chrissy and I, one of the things that's important here is that these things suggest the importance and value of embodied knowledge. 对于克里希和我来说,这里最重要的事情之一, 就是这些东西表明了 具体表达出知识的重要性和价值。
embodied:v.呈现(embody的过去式及过去分词形式);具体表达;
We live in a society that completely tends to valorize symbolic forms of representation -- algebraic representations , equations , codes. 我们生活在一个 完全趋向于为各种象征性的表述方式 规定价格的社会, 代数式的表述, 等式,编码等等。
valorize:v.(政府)以给予各种补助的形式稳定(维持)(商品)价格; algebraic:adj.[数]代数的;关于代数学的; representations:代表;表现(representation的复数); equations:n.方程式;等式;均等;均势(equation的复数形式);
We live in a society that's obsessed with presenting information in this way, teaching information in this way. 我们生活的社会深深迷恋上 这一种表述信息 和传授信息的方式。
obsessed:v.使痴迷;使迷恋;使着迷;(obsess的过去式和过去分词)
But through this sort of modality , crochet, other plastic forms of play, people can be engaged with the most abstract , high powered, theoretical ideas -- the kinds of ideas that normally you have to go 但通过模型的方式, 如钩针编织,其他塑料形式的展示, 人们能理解那些最抽象的, 高难度的理论化的概念, 也就是那些你通常需要跑到
modality:n.形式,形态;程序;物理疗法;主要的感觉; engaged:adj.已订婚的; v.吸引住; (engage的过去分词和过去式) abstract:n.摘要; adj.抽象的; vt.摘要; vi.做摘要; theoretical:adj.理论的;理论上的;假设的;推理的; normally:adv.正常地;通常地,一般地;
to university departments to study in higher mathematics, which is where I first learned about hyperbolic space. 大学里面才能学到的高等数学, 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 is that what we're trying to do with the Institute for Figuring, and projects like this, we're trying to have kindergarten for grown-ups . 我们已经想到了这一点, 这也是我们想要通过计算研究所来尝试的一个项目, 像这样的项目,我们想要 建一个属于成人的幼儿园。
kindergarten:n.幼儿园; grown-ups:n.成人(grown-up的复数形式);
Kindergarten was actually a very formalized system of education, established by a man named Friedrich Froebel, who was a crystallographer in the 19th century. 幼儿园其实是一种非常形象化 的教育系统, 由19世纪一位名叫福禄贝尔 的检晶科学家创立。
formalized:adj.形式化的; v.使正式; established:adj.已确立的;著名的;v.建立;创立;设立;(establish的过去分词和过去式) crystallographer:n.检晶器;
He believed that the crystal was the model for all kinds of representation. 他认为晶体可以作为 所有表述方式的模型。
He developed a radical alternative system of engaging the smallest children with the most abstract ideas through physical forms of play. 他发展了一套激进另类的系统, 即使最小的孩子也能够通过 寓于物理形式的玩耍 来理解最抽象的概念。
radical:n.自由基;激进分子;游离基;adj.根本的;彻底的;完全的;全新的; engaging:adj.有趣的; v.吸引住(注意力、兴趣); (engage的现在分词)
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。
worthy:adj.值得的; n.杰出人物;
The value of education is something that Froebel championed, through plastic modes of play. 福禄贝尔通过 娱乐的可塑模式 捍卫了教育的价值。
modes:n.模式(mode的复数形式);方法;分辨率;
We live in a society now where we have lots of think tanks, where great minds go to think about the world. 我们现在身处的社会, 有许多的“智库”, 许多优秀的头脑在那里思索世界问题。
They write these great symbolic treatises called books, and papers, and op-ed articles. 他们写下这些伟大的符号化的专著, 也叫书籍,和论文, 还有专栏文章。
treatises:n.论文,论述(treatise的复数形式);政府论(书名); op-ed:n.评论版;
We want to propose , Chrissy and I, through The Institute For Figuring, another alternative way of doing things, which is the play tank. 我们,克里希和我想要提出, 通过计算研究所来提出,另一种做事情的方式, 我们称之为“玩库”。
propose:v.建议;提议;求婚;打算;
The play tank, like the think tank , is a place where people can go and engage with great ideas. 玩库,就像智库, 是一个人们过来 认识那些伟大思想和概念的地方。
think tank:智囊团、思想库;
But what we want to propose, is that the highest levels of abstraction , things like mathematics, computing , logic , et cetera -- all of this can be engaged with, not just through purely cerebral algebraic symbolic methods, but by literally, physically playing with ideas. 但我们想提议的, 是那些最高层次的抽象思维, 如数学,计算,逻辑等等, 所有这些都能够, 不仅仅通过单纯的代数性的, 符号化的方法, 也可以通过文学的,物理上的方法“玩转”概念。
abstraction:n.抽象;出神;心神专注;提取;分离; computing:n.计算;计算机技术;信息处理技术;v.计算;求出;(compute的现在分词) logic:n.逻辑;逻辑学;逻辑性;adj.逻辑的; et cetera:na.以及其他; purely:adv.完全;仅仅; cerebral:adj.大脑的,脑的;
Thank you very much. 非常感谢。
(Applause) （掌声）