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EduardoSaenzdeCabezon_2014X-_数学恒久远_
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| Imagine you're in a bar, or a club, and you start talking, and after a while, the question comes up, "So, what do you do for work?" |
[00:13] |
| And since you think your job is interesting, you say, "I'm a mathematician ." (Laughter) |
[00:24] |
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mathematician:n.数学家;善作数字计算的人;
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| And inevitably , during that conversation one of these two phrases come up: |
[00:31] |
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inevitably:adv.不可避免地;必然地;
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| A) "I was terrible at math, but it wasn't my fault. |
[00:37] |
| It's because the teacher was awful." (Laughter) |
[00:41] |
| Or B) "But what is math really for?" |
[00:44] |
| (Laughter) |
[00:47] |
| I'll now address Case B. |
[00:48] |
| (Laughter) |
[00:50] |
| When someone asks you what math is for, they're not asking you about applications of mathematical science. |
[00:52] |
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mathematical:adj.数学的,数学上的;精确的;
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| They're asking you, why did I have to study that bullshit I never used in my life again? (Laughter) |
[01:00] |
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bullshit:v.胡说,哄骗;n.胡说;
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| That's what they're actually asking. |
[01:05] |
| So when mathematicians are asked what math is for, they tend to fall into two groups: 54.51 percent of mathematicians will assume an attacking position, and 44.77 percent of mathematicians will take a defensive position. |
[01:07] |
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mathematicians:n.[数]数学家(mathematician的复数形式); assume:v.承担;假定;采取;呈现; defensive:n.辩护;守势;adj.防御的;保护的;保卫的;戒备的;
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| There's a strange 0.8 percent, among which I include myself. |
[01:25] |
| Who are the ones that attack? |
[01:29] |
| The attacking ones are mathematicians who would tell you this question makes no sense, because mathematics have a meaning all their own -- a beautiful edifice with its own logic -- and that there's no point in constantly searching for all possible applications. |
[01:31] |
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mathematics:n.数学;数学运算; edifice:n.大厦;大建筑物; logic:n.逻辑;逻辑学;逻辑性;adj.逻辑的; constantly:adv.不断地;时常地;
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| What's the use of poetry ? What's the use of love? |
[01:45] |
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poetry:n.诗;诗意,诗情;诗歌艺术;
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| What's the use of life itself? What kind of question is that? |
[01:47] |
| (Laughter) |
[01:50] |
| Hardy , for instance , was a model of this type of attack. |
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Hardy:adj.坚强的;勇敢的;能吃苦耐劳的;鲁莽的;n.强壮的人;耐寒植物;方柄凿; instance:n.实例;情况;建议;v.举...为例;
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| And those who stand in defense tell you, "Even if you don't realize it, friend, math is behind everything." |
[01:56] |
| (Laughter) |
[02:03] |
| Those guys, they always bring up bridges and computers. |
[02:04] |
| '"If you don't know math, your bridge will collapse ." |
[02:10] |
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collapse:vi.倒塌;瓦解;暴跌;vt.使倒塌,使崩溃;使萎陷;折叠;n.倒塌;失败;衰竭;
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| (Laughter) |
[02:12] |
| It's true, computers are all about math. |
[02:14] |
| And now these guys have also started saying that behind information security and credit cards are prime numbers. |
[02:17] |
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prime:adj.主要的; v.极好地; n.初期; v.使准备好;
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| These are the answers your math teacher would give you if you asked him. |
[02:25] |
| He's one of the defensive ones. |
[02:29] |
| Okay, but who's right then? |
[02:31] |
| Those who say that math doesn't need to have a purpose, or those who say that math is behind everything we do? |
[02:33] |
| Actually, both are right. |
[02:38] |
| But remember I told you |
[02:40] |
| I belong to that strange 0.8 percent claiming something else? |
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claiming:v.声称;要求给予;理应获得;(claim的现在分词)
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| So, go ahead, ask me what math is for. |
[02:45] |
| Audience: What is math for? |
[02:48] |
| Eduardo Sáenz de Cabezón: Okay, 76.34 percent of you asked the question, 23.41 percent didn't say anything, and the 0.8 percent -- |
[02:51] |
| I'm not sure what those guys are doing. |
[03:00] |
| Well, to my dear 76.31 percent -- it's true that math doesn't need to serve a purpose, it's true that it's a beautiful structure , a logical one, probably one of the greatest collective efforts ever achieved in human history. |
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structure:n.结构;构造;建筑物;vt.组织;构成;建造; logical:adj.合逻辑的,合理的;逻辑学的; collective:adj.集体的;共同的;集合的;集体主义的;n.集团;集合体;集合名词;
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| But it's also true that there, where scientists and technicians are looking for mathematical theories that allow them to advance, they're within the structure of math, which permeates everything. |
[03:19] |
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technicians:n.[劳经]技术员(technician的复数);工作人员; permeates:v.弥漫(permeate的第三人称单数);
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| It's true that we have to go somewhat deeper, to see what's behind science. |
[03:32] |
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somewhat:n.几分;某物;adv.有点;多少;几分;稍微;
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| Science operates on intuition , creativity. |
[03:37] |
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intuition:n.直觉;直觉力;直觉的知识;
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| Math controls intuition and tames creativity. |
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tames:驯服;
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| Almost everyone who hasn't heard this before is surprised when they hear that if you take a 0.1 millimeter thick sheet of paper, the size we normally use, and, if it were big enough, fold it 50 times, its thickness would extend almost the distance from the Earth to the sun. |
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millimeter:n.毫米; sheet:n.薄板;床单;纸张;报纸;v.覆盖;展开;给…铺床单;铺开;adj.片状的; normally:adv.正常地;通常地,一般地; 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; thickness:n.厚度;层;浓度;含混不清; extend:vt.延伸; vi.延伸;
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| Your intuition tells you it's impossible. |
[04:04] |
| Do the math and you'll see it's right. |
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Do the math:盘算一下;
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| That's what math is for. |
[04:09] |
| It's true that science, all types of science, only makes sense because it makes us better understand this beautiful world we live in. |
[04:12] |
| And in doing that, it helps us avoid the pitfalls of this painful world we live in. |
[04:19] |
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pitfalls:n.危险;困难;(尤指)陷阱,隐患;(pitfall的复数) painful:adj.痛苦的;疼痛的;令人不快的;
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| There are sciences that help us in this way quite directly . |
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directly:adv.直接地;立即;马上;正好地;坦率地;conj.一…就;
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| Oncological science, for example. |
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Oncological:肿瘤学的(oncology的形容词形式);
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| And there are others we look at from afar , with envy sometimes, but knowing that we are what supports them. |
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afar:adv.遥远地;在远处; envy:n.嫉妒,妒忌;羡慕;v.嫉妒,妒忌;羡慕;感到妒忌;显示出妒忌;
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| All the basic sciences support them, including math. |
[04:35] |
| All that makes science, science is the rigor of math. |
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rigor:n.严厉;精确;苛刻;僵硬;
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| And that rigor factors in because its results are eternal . |
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factors:n.因素(factor的复数); v.做代理商; eternal:adj.永恒的;不朽的;
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| You probably said or were told at some point that diamonds are forever, right? |
[04:49] |
| That depends on your definition of forever! |
[04:56] |
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definition:n.定义;清晰度;(尤指词典里的词或短语的)释义;解释;
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| A theorem -- that really is forever. |
[04:58] |
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theorem:n.[数]定理;原理;
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| (Laughter) |
[05:00] |
| The Pythagorean theorem is still true even though Pythagoras is dead, I assure you it's true. (Laughter) |
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Pythagorean:adj.毕达哥拉斯的;n.毕达哥拉斯哲学; assure:vt.保证;担保;使确信;弄清楚;
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| Even if the world collapsed the Pythagorean theorem would still be true. |
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collapsed:v.倒塌,坍塌;倒下,昏倒;坐下;(collapse的过去分词和过去式)
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| Wherever any two triangle sides and a good hypotenuse get together |
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triangle:n.三角形;三角形物体;三角铁(打击乐器);三角关系; hypotenuse:n.直角三角形的斜边; get together:聚会
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| (Laughter) |
[05:16] |
| the Pythagorean theorem goes all out. It works like crazy . |
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like crazy:拼命地;发疯似的;
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| (Applause) |
[05:20] |
| Well, we mathematicians devote ourselves to come up with theorems . |
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devote:v.贡献;把…专用于;听任; come up with:提出;想出;赶上; theorems:[数]定理;
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| Eternal truths. |
[05:31] |
| But it isn't always easy to know the difference between an eternal truth, or theorem, and a mere conjecture . |
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mere:adj.仅仅的;只不过的;n.小湖;池塘; conjecture:n.推测;猜想;v.推测;揣摩;;
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| You need proof . |
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proof:n.证据;证实;adj.能抵御;可防护;
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| For example, let's say I have a big, enormous , infinite field. |
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enormous:adj.庞大的,巨大的;凶暴的,极恶的; infinite:adj.无限的,无穷的; n.无限;
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| I want to cover it with equal pieces, without leaving any gaps . |
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gaps:n.差异,缺口;缝隙(gap的复数形式);v.裂开;使豁裂(gap的第三人称单数形式);
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| I could use squares, right? |
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| I could use triangles . Not circles, those leave little gaps. |
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triangles:n.[数]三角形,三角型态(triangle的复数形式);
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| Which is the best shape to use? |
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| One that covers the same surface, but has a smaller border. |
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| In the year 300, Pappus of Alexandria said the best is to use hexagons , just like bees do. |
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Alexandria:n.亚历山大港(位于埃及);亚历山大大帝;亚历山大市(美国弗吉尼亚一城市); hexagons:n.[数]六边形;六角钢(hexagon的复数);
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| But he didn't prove it. |
[06:12] |
| The guy said, "Hexagons, great! Let's go with hexagons!" |
[06:13] |
| He didn't prove it, it remained a conjecture. |
[06:16] |
| '"Hexagons!" |
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| And the world, as you know, split into Pappists and anti-Pappists, until 1700 years later when in 1999, Thomas Hales proved that Pappus and the bees were right -- the best shape to use was the hexagon. |
[06:21] |
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split:v.分离;使分离;劈开;离开;分解;n.劈开;裂缝;adj.劈开的;
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| And that became a theorem, the honeycomb theorem, that will be true forever and ever, for longer than any diamond you may have. (Laughter) |
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honeycomb:n.蜂巢,蜂巢状之物; vt.使成蜂巢状; adj.似蜂巢的; vi.变成蜂巢状;
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| But what happens if we go to three dimensions ? |
[06:48] |
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dimensions:n.规模,大小;
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| If I want to fill the space with equal pieces, without leaving any gaps, |
[06:51] |
| I can use cubes , right? |
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cubes:n.[数]立方体,数据库(cube的复数形式); v.使成立方形(cube的第三人称单数形式);
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| Not spheres , those leave little gaps. (Laughter) |
[06:58] |
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spheres:n.[数]球体(sphere的复数); v.把…放在球体内(sphere的第三人称单数形式);
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| What is the best shape to use? |
[07:01] |
| Lord Kelvin , of the famous Kelvin degrees and all, said that the best was to use a truncated octahedron which, as you all know -- |
[07:04] |
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Lord:n.(英国)贵族,大人,大臣;v.使成贵族;作威作福; Kelvin:n.开尔文(英国物理学家,数学家); adj.开氏度的(常作K-); truncated:adj.缩短了的; v.缩短(truncate的过去分词); octahedron:n.八面体;
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| (Laughter) -- is this thing here! |
[07:19] |
| (Applause) |
[07:22] |
| Come on. |
[07:27] |
| Who doesn't have a truncated octahedron at home? (Laughter) |
[07:30] |
| Even a plastic one. |
[07:32] |
| '"Honey, get the truncated octahedron, we're having guests." |
[07:34] |
| Everybody has one! (Laughter) |
[07:36] |
| But Kelvin didn't prove it. |
[07:38] |
| It remained a conjecture -- Kelvin's conjecture. |
[07:40] |
| The world, as you know, then split into Kelvinists and anti-Kelvinists |
[07:44] |
| (Laughter) |
[07:50] |
| until a hundred or so years later, someone found a better structure. |
[07:51] |
| Weaire and Phelan found this little thing over here -- |
[08:02] |
| (Laughter) -- this structure to which they gave the very clever name "the Weaire-??Phelan structure." |
[08:08] |
| (Laughter) |
[08:15] |
| It looks like a strange object, but it isn't so strange, it also exists in nature. |
[08:17] |
| It's very interesting that this structure, because of its geometric properties, was used to build the Aquatics Center for the Beijing Olympic Games . |
[08:22] |
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geometric:adj.几何学的;[数]几何学图形的; Aquatics:n.水上运动; Olympic Games:n.奥林匹克运动会;奥运会;
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| There, Michael Phelps won eight gold medals, and became the best swimmer of all time. |
[08:32] |
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swimmer:n.游泳者;
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| Well, until someone better comes along, right? |
[08:38] |
| As may happen with the Weaire-??Phelan structure. |
[08:42] |
| It's the best until something better shows up. |
[08:45] |
| But be careful, because this one really stands a chance that in a hundred or so years, or even if it's in 1700 years, that someone proves it's the best possible shape for the job. |
[08:47] |
| It will then become a theorem, a truth, forever and ever. |
[09:02] |
| For longer than any diamond. |
[09:07] |
| So, if you want to tell someone that you will love them forever you can give them a diamond. |
[09:10] |
| But if you want to tell them that you'll love them forever and ever, give them a theorem! |
[09:20] |
| (Laughter) |
[09:26] |
| But hang on a minute! |
[09:27] |
| You'll have to prove it, so your love doesn't remain a conjecture. |
[09:30] |
| (Applause) |
[09:36] |