TED-我们真的可以预测爱情吗？

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《我们真的可以预测爱情吗？》

https://v.qq.com/txp/iframe/player.html?vid=v01576m5yr9&width=500&height=375&auto=0

演说者：Hannah Fry

中英演讲稿

00:12

Today I want to talk to you about the mathematics of love. Now, I think that we can all agree that mathematicians are famously excellent at finding love.(Laughter)

00:23

But it's not just because of our dashing personalities, superior conversational skills and excellent pencil cases. It's also because we've actually done an awful lot of work into the maths of how to find the perfect partner.

00:38

Now, in my favorite paper on the subject, which is entitled, "Why I Don't Have a Girlfriend" 

00:45

Peter Backus tries to rate his chances of finding love. Now, Peter's not a very greedy man. Of all of the available women in the UK, all Peter's looking for is somebody who lives near him, somebody in the right age range, somebody with a university degree, somebody he's likely to get on well with, somebody who's likely to be attractive, somebody who's likely to find him attractive.

01:11

And comes up with an estimate of 26 women in the whole of the UK.

01:17

It's not looking very good, is it Peter? Now, just to put that into perspective, that's about 400 times fewer than the best estimates of how many intelligent extraterrestrial life forms there are. And it also gives Peter a 1 in 285,000 chance of bumping into any one of these special ladies on a given night out. I'd like to think that's why mathematicians don't really bother going on nights out anymore.

01:43

The thing is that I personally don't subscribe to such a pessimistic view. Because I know, just as well as all of you do, that love doesn't really work like that. Human emotion isn't neatly ordered and rational and easily predictable. But I also know that that doesn't mean that mathematics hasn't got something that it can offer us, because, love, as with most of life, is full of patterns and mathematics is, ultimately, all about the study of patterns. Patterns from predicting the weather to the fluctuations in the stock market, to the movement of the planets or the growth of cities. And if we're being honest, none of those things are exactly neatly ordered and easily predictable, either. Because I believe that mathematics is so powerful that it has the potential to offer us a new way of looking at almost anything. Even something as mysterious as love. And so, to try to persuade you of how totally amazing, excellent and relevant mathematics is, I want to give you my top three mathematically verifiable tips for love.

02:52

OK, so Top Tip #1: How to win at online dating. So my favorite online dating website is OkCupid, not least because it was started by a group of mathematicians. Now, because they're mathematicians, they have been collecting data on everybody who uses their site for almost a decade. And they've been trying to search for patterns in the way that we talk about ourselves and the way that we interact with each other on an online dating website. And they've come up with some seriously interesting findings. But my particular favorite is that it turns out that on an online dating website, how attractive you are does not dictate how popular you are, and actually, having people think that you're ugly can work to your advantage.

03:40

Let me show you how this works. In a thankfully voluntary section of OkCupid, you are allowed to rate how attractive you think people are on a scale between one and five. Now, if we compare this score, the average score, to how many messages a selection of people receive, you can begin to get a sense of how attractiveness links to popularity on an online dating website.

04:04

This is the graph the OkCupid guys have come up with. And the important thing to notice is that it's not totally true that the more attractive you are, the more messages you get. But the question arises then of what is it about people up here who are so much more popular than people down here, even though they have the same score of attractiveness? And the reason why is that it's not just straightforward looks that are important. So let me try to illustrate their findings with an example. So if you take someone like Portia de Rossi, for example, everybody agrees that Portia de Rossi is a very beautiful woman. Nobody thinks that she's ugly, but she's not a supermodel, either. If you compare Portia de Rossi to someone like Sarah Jessica Parker, now, a lot of people, myself included, I should say, think that Sarah Jessica Parker is seriously fabulous and possibly one of the most beautiful creatures to have ever have walked on the face of the Earth. But some other people, i.e., most of the Internet ...

05:08

seem to think that she looks a bit like a horse.Now, I think that if you ask people how attractive they thought Jessica Parker or Portia de Rossi were, and you ask them to give them a score between one and five I reckon that they'd average out to have roughly the same score. But the way that people would vote would be very different. So Portia's scores would all be clustered around the four because everybody agrees that she's very beautiful, whereas Sarah Jessica Parker completely divides opinion. There'd be a huge spread in her scores. And actually it's this spread that counts. It's this spread that makes you more popular on an online Internet dating website. So what that means then is that if some people think that you're attractive, you're actually better off having some other people think that you're a massive minger. That's much better than everybody just thinking that you're the cute girl next door.

06:00

Now, I think this begins to make a bit more sense when you think in terms of the people who are sending these messages. So let's say that you think somebody's attractive, but you suspect that other people won't necessarily be that interested. That means there's less competition for you and it's an extra incentive for you to get in touch. Whereas compare that to if you think somebody is attractive but you suspect that everybody is going to think they're attractive. Well, why would you bother humiliating yourself, let's be honest? But here's where the really interesting part comes. Because when people choose the pictures that they use on an online dating website, they often try to minimize the things that they think some people will find unattractive. The classic example is people who are, perhaps, a little bit overweight deliberately choosing a very cropped photo,

06:47

or bald men, for example, deliberately choosing pictures where they're wearing hats. But actually this is the opposite of what you should do if you want to be successful. You should really, instead, play up to whatever it is that makes you different, even if you think that some people will find it unattractive. Because the people who fancy you are just going to fancy you anyway, and the unimportant losers who don't, well, they only play up to your advantage.

07:12

OK, Top Tip #2: How to pick the perfect partner. So let's imagine then that you're a roaring success on the dating scene. But the question arises of how do you then convert that success into longer-term happiness, and in particular, how do you decide when is the right time to settle down? Now generally, it's not advisable to just cash in and marry the first person who comes along and shows you any interest at all. But, equally, you don't really want to leave it too long if you want to maximize your chance of long-term happiness. As my favorite author, Jane Austen, puts it, "An unmarried woman of seven and twenty can never hope to feel or inspire affection again."

07:56

Thanks a lot, Jane. What do you know about love?So the question is then, how do you know when is the right time to settle down, given all the people that you can date in your lifetime? Thankfully, there's a rather delicious bit of mathematics that we can use to help us out here, called optimal stopping theory. So let's imagine, then, that you start dating when you're 15 and ideally, you'd like to be married by the time that you're 35. And there's a number of people that you could potentially date across your lifetime, and they'll be at varying levels of goodness. Now the rules are that once you cash in and get married, you can't look ahead to see what you could have had, and equally, you can't go back and change your mind. In my experience at least, I find that typically people don't much like being recalled years after being passed up for somebody else, or that's just me.

08:45

So the math says then that what you should do in the first 37 percent of your dating window, you should just reject everybody as serious marriage potential.

08:57

And then, you should pick the next person that comes along that is better than everybody that you've seen before. So here's the example. Now if you do this, it can be mathematically proven, in fact, that this is the best possible way of maximizing your chances of finding the perfect partner. Now unfortunately, I have to tell you that this method does come with some risks. For instance, imagine if your perfect partner appeared during your first 37 percent. Now, unfortunately, you'd have to reject them.

09:34

Now, if you're following the maths, I'm afraid no one else comes along that's better than anyone you've seen before, so you have to go on rejecting everyone and die alone.

09:46

Probably surrounded by cats ...nibbling at your remains.

09:51

OK, another risk is, let's imagine, instead, that the first people that you dated in your first 37 percent are just incredibly dull, boring, terrible people. That's OK, because you're in your rejection phase, so that's fine, you can reject them. But then imagine the next person to come along is just marginally less boring, dull and terrible ...

10:14

than everybody that you've seen before. Now, if you are following the maths, I'm afraid you have to marry them ...

10:21

and end up in a relationship which is, frankly, suboptimal. Sorry about that. But I do think that there's an opportunity here for Hallmark to cash in on and really cater for this market. A Valentine's Day card like this.

10:33

"My darling husband, you are marginally less terrible than the first 37 percent of people I dated."

10:40

It's actually more romantic than I normally manage.

10:45

OK, so this method doesn't give you a 100 percent success rate, but there's no other possible strategy that can do any better. And actually, in the wild, there are certain types of fish which follow and employ this exact strategy. So they reject every possible suitor that turns up in the first 37 percent of the mating season, and then they pick the next fish that comes along after that window that's, I don't know, bigger and burlier than all of the fish that they've seen before. I also think that subconsciously, humans, we do sort of do this anyway. We give ourselves a little bit of time to play the field, get a feel for the marketplace or whatever when we're young. And then we only start looking seriously at potential marriage candidates once we hit our mid-to-late 20s. I think this is conclusive proof, if ever it were needed, that everybody's brains are prewired to be just a little bit mathematical.

11:39

OK, so that was Top Tip #2. Now, Top Tip #3: How to avoid divorce. OK, so let's imagine then that you picked your perfect partner and you're settling into a lifelong relationship with them. Now, I like to think that everybody would ideally like to avoid divorce, apart from, I don't know, Piers Morgan's wife, maybe?

12:02

But it's a sad fact of modern life that one in two marriages in the States ends in divorce, with the rest of the world not being far behind. Now, you can be forgiven, perhaps for thinking that the arguments that precede a marital breakup are not an ideal candidate for mathematical investigation. For one thing, it's very hard to know what you should be measuring or what you should be quantifying. But this didn't stop a psychologist, John Gottman, who did exactly that. Gottman observed hundreds of couples having a conversation and recorded, well, everything you can think of. So he recorded what was said in the conversation, he recorded their skin conductivity, he recorded their facial expressions, their heart rates, their blood pressure, basically everything apart from whether or not the wife was actually always right, which incidentally she totally is. But what Gottman and his team found was that one of the most important predictors for whether or not a couple is going to get divorced was how positive or negative each partner was being in the conversation.

13:11

Now, couples that were very low-risk scored a lot more positive points on Gottman's scale than negative. Whereas bad relationships, by which I mean, probably going to get divorced, they found themselves getting into a spiral of negativity. Now just by using these very simple ideas, Gottman and his group were able to predict whether a given couple was going to get divorced with a 90 percent accuracy. But it wasn't until he teamed up with a mathematician, James Murray, that they really started to understand what causes these negativity spirals and how they occur. And the results that they found, I think, are just incredibly impressively simple and interesting. So these equations predict how the wife or husband is going to respond in their next turn of the conversation, how positive or negative they're going to be. And these equations depend on the mood of the person when they're on their own, the mood of the person when they're with their partner, but most importantly, they depend on how much the husband and wife influence one another.

14:14

Now, I think it's important to point out at this stage, that these exact equations have also been shown to be perfectly able at describing what happens between two countries in an arms race.

14:30

So that an arguing couple spiraling into negativity and teetering on the brink of divorce is actually mathematically equivalent to the beginning of a nuclear war.

14:43

But the really important term in this equation is the influence that people have on one another, and in particular, something called "the negativity threshold." Now, the negativity threshold, you can think of as how annoying the husband can be before the wife starts to get really pissed off, and vice versa. Now, I always thought that good marriages were about compromise and understanding and allowing the person to have the space to be themselves. So I would have thought that perhaps the most successful relationships were ones where there was a really high negativity threshold. Where couples let things go and only brought things up if they really were a big deal. But actually, the mathematics and subsequent findings by the team have shown the exact opposite is true. The best couples, or the most successful couples, are the ones with a really low negativity threshold. These are the couples that don't let anything go unnoticed and allow each other some room to complain. These are the couples that are continually trying to repair their own relationship, that have a much more positive outlook on their marriage. Couples that don't let things go and couples that don't let trivial things end up being a really big deal.

15:56

Now of course, it takes a bit more than just a low negativity threshold and not compromising to have a successful relationship. But I think that it's quite interesting to know that there is really mathematical evidence to say that you should never let the sun go down on your anger.

16:14

So those are my top three tips of how maths can help you with love and relationships. But I hope, that aside from their use as tips, they also give you a little bit of insight into the power of mathematics. Because for me, equations and symbols aren't just a thing. They're a voice that speaks out about the incredible richness of nature and the startling simplicity in the patterns that twist and turn and warp and evolve all around us, from how the world works to how we behave. So I hope that perhaps, for just a couple of you, a little bit of insight into the mathematics of love can persuade you to have a little bit more love for mathematics.Thank you.

今天我想要和大家谈谈 关于爱情的数学。 我想大家都同意 数学家在寻找真爱上特别在行。 但那并不只是因为我们 精力充沛的性格， 超凡的对话技巧， 和极好的笔盒。 也是因为我们真的 花了许多时间精力在数学上， 计算如何找到完美的伴侣。

00:38

现在，在此学科中我最爱的论文，名为 “为什么我没有女友” （笑声） Peter Backus 试着 计算他寻得真爱的机会。 现在，Peter 不是一个非常贪心的人。 在英国所有适宜的女性对象中， Peter 所看的， 就只是那个住在他附近的对象， 某个处于适宜的年龄阶段， 某个拥有大学文凭， 某个他很有可能相处地不错的对象， 某个有魅力的女子， 以及某个认为他也富有魅力的对象。 （笑声） 结果他估计在全英国 大概有 26 位此类女性。 这看来很不妙，不是吗，Peter？ 我们好好思考一下这件事， 在无数聪明外星生命形式存在的情况下， 那是少于 400 倍数的估计呀。 那也给了 Peter 一个 在某晚遇见一个特别的女子 28 万 5 千之 1 的机会。 我宁愿想着那就是为什么数学家 不再怎么想晚上出去约会了。

01:42

重点是，我个人其实并不同意 这种悲观的看法。 因为我知道，如同你们所有所知道的， 爱情并不是这样发生的。 人类的情感不是那样地秩序井然、 干净利落、逻辑清晰，以及容易预测。 但我也知道那并不意谓着 数学无法提供帮助， 因为爱情，如同生命中多数的事物一般， 充斥着许多规律， 而数学，最终，就是那讲求规律的学说。 从预测天候，到 预测股票市场的开高走低， 到星球的运转，或都市的发展。 如果我们对自己诚实的话， 上述那些东西，没有一个是 井然有序以及容易预测的。 因为我相信，数学的力量非常强大， 以至于它让我们得以以新方法 重新看待任何事物。 就算是和爱情一般神秘的东西也是。 为了试着说服你们 数学的神妙用处， 我想要给大家三个最重要的 在数学上可以验证的爱情秘诀。

02:51

好，首先最重要的秘技一： 如何赢得线上交友的机会。 我最爱的线上交友网站是 OkCupid （网站名：好吧，丘比特）， 这并不仅仅因为这网站 是由一群数学家所架设的。 因为他们是数学家， 他们已经搜集了 近乎这十年来所有 他们网站使用者的资料。 他们试着寻找 我们在线上 谈论自己的方式的模式， 以及我们和他人互动的模式。 他们发现了一些重要的有趣结果。 但我特别喜欢的结果之一是 在线上交友网站上 你的魅力程度并无法 预测你的受欢迎程度， 事实上，让人们觉得你很丑 可以让你拥有优势。 让我向各位展示这是怎么一回事。 在 OkCupid 的一个志愿栏目中， 你可以评价人们的魅力值， 从 1 到 5 。 现在，如果我们比较这个分数， 平均分数， 有多少人收到信息， 你就可以开始理解 在一个线上约会网站上 魅力指数与受欢迎程度有关。

04:03

这是 OkCupid 得到的图表。 一件重要的值得注意的事是 并不是越有魅力的人， 收到的信息越多。 问题是，为什么上面的这些人 比下面这些人要受欢迎得多， 即便他们都有相同的魅力值？ 原因是，并不是直观的外貌是重要的。 让我来谈谈他们的发现， 以一个案例说明。 如果你拿 Portia de Rossi 为例， 每个人都同意 Portia de Rossi 是个非常美丽的女人， 没有人觉得她丑，但她也不是超模。 如果你拿某个人，比如 Sarah Jessica Parker （译者注：欲望都市女主角）来和她比较 许多人，包括我自己，我应该会说， Sarah Jessica Parker 魅力极为出众， 有可能是地表上 最美丽的物种之一。 但许多其他人，比如，大多数的网友 似乎都认为她看起来像马。（笑声） 如果你问人们他们觉得自己有多美， Sarah Jessica Parker 或 Portia de Rossi 你要他们给自己打分，从 1 到 5， 我猜他们也会大约给一个 和大家都差不多的数字。 但是人们投票的方式各自不同。 因此 Portia 的分数会聚集在 4 分左右， 因为所有人都同意，她非常美丽， 然而人们对 Sarah Jessica Parker 却有截然不同的意见。 她的分差悬殊很大。 然而，事实上，就是那分差别具意义， 那差异让你 在交友网站上受欢迎。 所以那意味着 如果有些人认为你别具魅力， 你最好有其他人认为 你很丑。 那远优于所有人认为 你是邻家的可爱女孩。

05:59

当你们开始思考一下 这些寄送信息的人的话， 这开始变得合理些了。 这么说吧，假设你认为那个人很美， 但你同时猜想其他人并不会 和你有同样的审美观。 那就意味着，你的竞争对手略少， 这就给你增加了额外的动机 去与他/她认识。 与之相对的情况是 你认为某人很有吸引力， 但你猜想所有其他的人 都认为那人很有吸引力， 嗯，让我们面对事实 为什么要自取其辱呢？ 这就是最有趣的部分。 因为当人们去选择他们 在交友网站上使用的照片时， 他们总是试图最小化 其他人认为不吸引人之处的可能性。 最经典的例子是， 那些体重略重的人 故意选择一个 剪裁非常不正的照片， 例如那些秃顶的男士， 故意去选择他们带着帽子的照片。 但你的行为是与你的目标相悖的， 如果你想要在网上交友成功。 你真的应该，去选择 让你看起来与众不同的照片， 即便你认为某些人会对此失去兴趣。 因为那些喜欢你的人 无论如何都会去喜欢你， 而那些不重要的路人 只是渲染你的优势。

07:12

好了，最高秘诀 2 号： 如何选择完美的伴侣。 让我们想象你的约会 精彩成功。 但问题来了 你如何将那成功的约会 转变成长期的快乐，尤其是， 你要如何选择 在哪个时刻安定下来？ 一般来说， 并不建议人们立刻 与第一个出现 对你表达好感的人结婚。 但是，一般来说，如果你想要 最大化你未来数十年幸福婚姻的机会， 你也不愿等待太久。 我最喜欢的作家简·奥斯汀这样说， “一个未婚的 27 岁女子 就别指望再能感受或激发爱情了。” （笑声） 这太严重了，简。 你对爱了解多少呢？

07:59

那么问题来了， 你怎么知道哪个时刻 是该要安定下来的时刻， 毕竟生命中你有很多可能的对象？ 幸好，我们可以运用一点儿数学 来帮助我们计算解决这个问题， 名叫 “最优停止理论”。 那么让我们来想象一下， 你在 15 岁的时候开始交往， 理想状态下，你在 35 岁的时候会结婚。 你的人生中 有很多潜在的约会对象， 他们都有各自的优点。 规则是，你一旦跳进婚姻， 你就不能继续前进寻找 你可能可以有的对象， 你也不能回头来改变你的主意。 我个人的经验看来， 一般人们不希望 在被拒绝又过了多年后被找回来， 也许只有我这样想。

08:45

数学告诉我们 你应该拒绝认为会和 在你人生约会周期 前 37% 时段出现的任何人 有严肃认真的婚姻关系。 （笑声） 接着，你要选择下一个人， 那个比你以前约会对象都好的人。 这里举个例子。 如果你这么做，从数学证明来看 可以认为，事实上 这可能是最好的选择 来最大化你找到完美伴侣的机会。 现在不幸的是，我必须告诉你 这个方法也是有风险的。 比如，想象一下，假设你的完美伴侣 出现在你约会历程的前 37% 那就很不幸了， 你会拒绝他们。 （笑声） 如果你相信数学， 恐怕你不会再找到 比你以往见过更好的对象， 你就会持续拒绝每个人 然后孤独终老。 （笑声） 可能会被猫咪包围 一点点啃食你的遗骸。

09:51

好，另一个风险是， 让我们想象，相反的， 你约会历程前 37% 里第一个对象 极度愚蠢，无聊又很糟糕。 没事，因为你还在拒绝对象的阶段， 没问题， 你可以拒绝他们。 但想象一下，下一个出现的人 只是没那么无聊，愚蠢 比你以前的对象都略好那么一点儿。 如果你遵循数学， 恐怕你要和他们结婚 然后沉浸在一段， 实话说，次优的关系中。 很抱歉。 但我认为，机会还是有的 贺曼公司迎合市场需求 出售这样的情人节贺卡。 （笑声） “我亲爱的丈夫，你没有 我约会历程中前 37% 的男士 那么糟糕。” 这比一般的贺卡浪漫很多。

10:45

这个数学方法不能保证 100% 的成功率， 但也没有更好的策略了。 事实上，在动物界， 某个特定种类的鱼 遵循使用这样的策略。 在交配期，它们拒绝 出现在前 37% 的每个求婚者， 接着它们选择 37% 后出现的下一个 比所见过的鱼 体型更加庞大，更加结实的鱼。 我想作为人类 我们潜意识里也在做同样的选择。 我们给自己更多时间寻找， 在我们年轻的时候 感受婚恋市场。 我们只有在 20 岁年龄段的中后期 才会很真寻找潜在的结婚对象。 我想这证明了， 即使不确定是否需要， 每个人的大脑 都预配了点儿数学能力。

11:39

好，上述就是最高秘诀 2 号。 现在，最高秘诀 3 号：如何避免离婚。 好的，让我们想象一下 你找到了你的完美对象 你和他/她进入了一生的婚姻关系。 我假设每个人都不希望离婚， 当然，也许除了 Piers Morgan 的太太？ 可是，现代婚姻一个悲伤的事实 就是美国离婚率高达 50%， 世界其他国家也离这个数据不远。 当然，你可以认为 婚姻破裂的原因 不是数学运算理想的数据源。 一方面来说，很难了解到 你该去测量什么 或者是你该去量化什么。 但这并没有阻止心理学家 John Gottman 做这样的研究。 Gottman 观察了数百对夫妇的对谈 尽可能录下来所有信息。 记录了对话的内容， 皮肤的传导性， 面部表情， 心跳，血压， 基本上除了“太太永远是对的” 以外的所有东西， 当然，太太永远是对的。 但是，Gottman 和他的团队发现 最能够准确预测 这对夫妻是否未来会离婚的 是双方在对话过程中 积极还是消极。

13:11

那些离婚风险很低的夫妻 在 Gottman 的测试中得到了 更多正面而不是负面的分数。 相反的，在糟糕的关系中， 我是指那些可能离婚的夫妻， 他们发现自己沉浸在消极的漩涡中。 就用这些非常简单的方法， Gottman 和他的团队能够准确预测 一对夫妻是否会离婚, 准确率高达 90% 但是，直到他与 数学家 James Murray 联手， 他们才真正找出 那些消极漩涡是 如何产生，为什么产生的。 结果是他们发现 我认为不可思议太令人惊叹 的简单而有趣。 这些算式，他们用来预测 妻子或是丈夫是如何去回应 他们下一段对话， 他们的积极或消极程度是多少。 这些算式，取决于 当他们独处时各自的情绪， 当他们和伴侣在一起时候的情绪， 但最重要的是， 取决于丈夫和妻子相互间的影响。

14:13

在这个阶段我认为最重要的是， 这个一模一样的算式 同时也可以完美预测 两个国家是否会开战。 （笑声） 因此一对沉浸于消极情绪 在离婚边缘摇摆的夫妻-- 实际在数学上等同于 即将开始一场核战争。 （笑声）

14:42

事实上，这个算式最重要的部分 是人们给对方带来的影响， 尤其是消极阈值。 消极阈值， 你可以认为它指的是 丈夫讨厌到什么程度 就能惹到妻子真的暴怒， 或者是相反。 我一直认为美好的婚姻 是基于妥协和理解 并且给对方留足独处空间。 我会想，最成功的关系是 当那里有非常高的消极阈值时 夫妻共同选择不去理会这些问题。 只有在非常严重的时候 才会严肃讨论。 事实上，团队得出的 数学运算结果和后续研究成果显示 完全相反的结果。 最完美的夫妻， 最成功的夫妻， 有着很低的消极阈值。 这些夫妻不会忽视矛盾 给对方抱怨的空间。 这些夫妻持续努力 修复他们的关系， 他们对自己的婚姻 有着非常积极的预期。 他们不会忽略矛盾 他们不会让一件件琐碎的小事 堆积成为巨大的问题。

15:56

当然，这不仅仅是 一个低消极阈值 和对成功关系毫不妥协的态度。 但我认为，很有趣的是 真的有数学证据 来证明你永远不该长时间 积攒愤怒，太阳要下山了。 （译者注：这句话出自圣经）

16:14

上述就是我的三条最高秘诀， 有关数学如何让你有 更美好的爱情和关系。 我希望，除了作为爱情秘诀， 它们也展示了数学的力量。 对我来说，算式和符号 不仅仅是一样东西。 它们表达出 自然令人赞叹的丰富性 以及简化 那些我们身边 扭曲，旋转，包围，进化的事物， 从世界是如何运作的， 到人类行为举止。 我希望，也许你们中的一部分人 能够了解一些 爱的数学运算， 能够让你爱数学稍微多一点。 谢谢。 （鼓掌）

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