天才的公交车票理论
天才的公交车票理论
2019年11月
每个人都知道,要做伟大的工作,你需要天赋和决心。但还有一个不太为人理解的第三种成分:对特定话题的痴迷兴趣。
为了解释这一点,我需要冒犯某群人的声誉,我选择公交车票收藏者。有人收集旧公交车票。像许多收藏家一样,他们对所收集物品的细节有着痴迷的兴趣。他们能够记住不同类型公交车票之间的区别,这对我们其他人来说很难记住。因为我们不够在乎。花这么多时间思考旧公交车票有什么意义?
这引出了这种痴迷的第二特征:没有意义。公交车票收藏者的爱是无私的。他们这样做不是为了给我们留下印象,也不是为了让自己富有,而是为了它本身。
当你观察那些做过伟大工作的人的生活时,你会看到一个一致的模式。他们往往从对某个东西的公交车票收藏者式的痴迷开始,这对他们同时代的大多数人来说似乎毫无意义。达尔文关于贝格尔号航行的书籍最显著的特征之一是他对自然史的兴趣深度。他的好奇心似乎无穷无尽。拉马努金也是如此,他一小时一小时地坐在石板上计算级数会发生什么。
认为他们是在为后来的发现”奠定基础”是错误的。这个隐喻中有太多的意图。像公交车票收藏者一样,他们这样做是因为他们喜欢。
但拉马努金和公交车票收藏者有区别。级数很重要,公交车票不重要。
如果我用一句话概括天才的秘诀,可能就是这样:对重要的事情有无私的痴迷。
我不是忘记了其他两种成分吗?比你可能想的少。对某个话题的痴迷兴趣既是能力的代理,也是决心的替代品。除非你有足够的数学才能,否则你不会觉得级数有趣。当你对某事痴迷时,你不需要那么多决心:当好奇心拉着你时,你不需要那么努力地推动自己。
痴迷兴趣甚至会给你带来好运,在某种程度上任何事情都可以。正如巴斯德所说,机会眷顾有准备的头脑,如果说痴迷的头脑有一个特点的话,那就是它是有准备的。
这种痴迷的无私性是其最重要的特征。不仅因为它是真诚的过滤器,而且因为它帮助你发现新想法。
导致新想法的路径往往看起来没有希望。如果它们看起来有希望,其他人早就已经探索过了。那些做伟大工作的人如何发现这些被他人忽视的路径?流行的说法是他们只是有更好的视野:因为他们如此有才华,他们看到别人错过的路径。但如果你观察伟大发现是如何做出的,事情并非如此。达尔文并不比其他人更关注个别物种,因为他看到这会导致伟大的发现,而他们没有。他只是对这类事情真的、真的感兴趣。
达尔文无法关闭这种兴趣。拉马努金也是如此。他们没有发现那些隐藏的路径是因为它们看起来有希望,而是因为他们情不自禁。正是这让他们能够遵循那些仅仅有野心的人会忽视的路径。
什么理性的人会决定写伟大小说的方式是先花几年创造一个虚构的精灵语,像托尔金那样,或者访问英国西南部的每个家庭,像特罗洛普那样?没有人,包括托尔金和特罗洛普。
公交车票理论类似于卡莱尔对天才的著名定义:承受痛苦的无限能力。但有两个区别。公交车票理论明确指出,这种无限承受痛苦能力的来源不是无限的勤奋,正如卡莱尔似乎意味的那样,而是收藏家拥有的那种无限兴趣。它还添加了一个重要的限定:对重要事情承受痛苦的无限能力。
那么什么重要?你永远无法确定。正因为没有人能预先知道哪些路径有希望,你才能通过做你感兴趣的工作来发现新想法。
但你可以使用一些启发式方法来猜测某种痴迷是否可能是重要的。例如,如果你在创造东西,而不仅仅是消费别人创造的东西,它就更有希望。如果你感兴趣的东西很困难,特别是如果它对其他人来说比对你更困难,那就更有希望。而有才华的人的痴迷更可能有希望。当有才华的人对随机事情感兴趣时,它们并不是真正随机的。
但你永远无法确定。事实上,这里有一个有趣的想法,如果它是真的,也相当令人不安:可能要做伟大的工作,你还必须浪费大量时间。
在许多不同领域,回报与风险成正比。如果这个规则在这里成立,那么找到导致真正伟大工作的路径的方法就是愿意在那些结果证明完全没有希望的事情上花费大量精力。
我不确定这是否是真的。一方面,只要你努力做有趣的事情,似乎很难浪费时间。你所做的很多事情最终都是有用的。但另一方面,风险与回报关系的规则如此强大,以至于它似乎在风险发生的任何地方都成立。至少牛顿的案例表明,风险/回报规则在这里成立。他以一个特定的痴迷而闻名,这个痴迷结果证明是前所未有的成果:用数学描述世界。但他还有另外两个痴迷,炼金术和神学,似乎完全是浪费时间。他最终净 ahead。他对我们现在称为物理学的赌注如此成功,以至于超过了其他两个的补偿。但其他两个是否必要,从这个意义上说他必须承担大风险才能做出如此大的发现?我不知道。
这是一个更令人不安的想法:一个人可能会做出所有错误的赌注?这可能经常发生。但我们不知道频率,因为这些人没有出名。
不仅仅是遵循某个路径的回报难以预测。它们随时间变化很大。1830年是对自然史痴迷的好时机。如果达尔文出生在1709年而不是1809年,我们可能永远不会听说过他。
面对这种不确定性,一个人能做什么?一个解决方案是对冲你的赌注,在这种情况下,这意味着遵循明显有希望的路径,而不是你自己的私人痴迷。但就像任何对冲一样,当你降低风险时,你也在降低回报。如果你放弃做你喜欢的工作,而遵循一些更传统雄心勃勃的路径,你可能会错过一些你本来会发现的美妙事情。这也一定经常发生,可能甚至比那些赌注都失败的天才更频繁。
另一个解决方案是让自己对许多不同的事情感兴趣。如果你基于哪个似乎迄今为止有效而在同样真实的兴趣之间切换,你不会降低你的上限。但这里也有危险:如果你工作在太多不同的项目上,你可能无法足够深入地进入其中任何一个。
公交车票理论的一个有趣之处是,它可能有助于解释为什么不同类型的人在不同类型的工作中表现出色。兴趣的分布比能力不均匀得多。如果做伟大工作只需要天赋,而天赋是均匀分布的,你必须发明复杂的理论来解释我们在各个领域中实际做伟大工作的人中看到的偏斜分布。但可能大部分偏斜有一个更简单的解释:不同的人对不同的东西感兴趣。
公交车票理论也解释了为什么人们有了孩子后不太可能做伟大的工作。在这里,兴趣不仅要与外部障碍竞争,还要与另一个兴趣竞争,而这个兴趣对大多数人来说是极其强大的。有了孩子后更难找到工作时间,但这是容易的部分。真正的变化是你不想了。
但公交车票理论最令人兴奋的含义是,它提出了鼓励伟大工作的方法。如果天才的秘诀只是天赋加努力,我们能做的就是希望我们有大量能力,并尽可能努力地工作。但如果兴趣是天才的关键成分,我们可能能够通过培养兴趣来培养天才。
例如,对非常有野心的人来说,公交车票理论表明,做伟大工作的方式是放松一点。不要咬牙切齿地勤奋追求所有同龄人都同意的最有希望的研究路线,也许你应该尝试只是为了好玩而做一些事情。如果你被困住了,那可能是突破的方向。
我一直喜欢汉明的著名双管问题:你领域中最重要的问题是什么,你为什么没有在其中之一上工作?这是一个很好的让自己震惊的方式。但它可能有点过度拟合。问自己可能至少同样有用:如果你能休假一年去做一件可能不重要但会非常有趣的事情,那会是什么?
公交车票理论还提出了一种避免随着年龄增长而放缓的方法。也许人们随着年龄增长新想法变少的原因不仅仅是因为他们失去了锋芒。也可能是因为一旦你确立地位,你就不能再像年轻时那样不负责任地搞副项目,那时没有人关心你做什么。
解决方案很明显:保持不负责任。但这会很困难,因为你为了防止衰退而承担的看似随机的项目,在外人看来会证明衰退的证据。你自己也不会确定他们是错的。但至少做你想做的工作会更有趣。
我们甚至可以在孩子中培养智力公交车票收集的习惯。教育中的通常计划是从广泛、浅显的关注开始,然后逐渐变得更专业化。但我对我的孩子做了相反的事情。我知道我可以依靠他们的学校来处理广泛、浅显的部分,所以我带他们深入。
当他们对某事感兴趣时,无论多么随机,我都鼓励他们达到荒谬的、公交车票收藏者式的深度。我这样做不是因为公交车票理论。我这样做是因为我想让他们感受到学习的乐趣,他们永远不会对我让他们学习的东西有这种感觉。必须是他们感兴趣的东西。我只是遵循阻力最小的路径;深度是副产品。但如果在试图向他们展示学习乐趣的同时,我最终训练他们深入,那就更好了。
会有任何效果吗?我不知道。但这种不确定性可能是最有趣的一点。关于如何做伟大工作还有很多要学习的。人类文明感觉如此古老,如果我们还没有掌握如此基本的东西,它实际上仍然非常年轻。想到关于发现还有发现要做,这是令人兴奋的。如果那是你感兴趣的那种事情。
注释
[1] 还有其他类型的收集比公交车票更好地说明这一点,但它们也更受欢迎。使用一个较差的例子似乎更好,而不是通过告诉他们他们的爱好不重要来冒犯更多人。
[2] 我有点担心使用”无私”这个词,因为有些人错误地相信它意味着不感兴趣。但任何期望成为天才的人都必须知道这样一个基本词的含义,所以我想他们不妨现在就开始。
[3] 想想天才一定经常被告知,或告诉自己,停止胡闹并负责任而在萌芽中被扼杀。拉马努金的母亲是一个巨大的促成者。想象一下,如果她不是。想象一下,如果他的父母让他出去找工作,而不是坐在家里做数学。
另一方面,任何引用前一段来证明不找工作的人可能是错误的。
[4] 1709年的达尔文在时间上相当于空间上的米兰达芬奇。
[5] “承受痛苦的无限能力”是对卡莱尔所写内容的意译。他在《腓特烈大帝史》中写道的是…它是’天才’的果实(首先意味着承受烦恼的卓越能力)…”由于意译在此时似乎是这个想法的名称,我保留了它。
卡莱尔的《历史》于1858年出版。1785年,埃罗·德·塞谢勒引用布丰说”Le génie n’est qu’une plus grande aptitude à la patience.”(天才只是对耐心更大的适应能力。)
[6] 特罗洛普正在建立邮政路线系统。他自己意识到他追求这个目标的痴迷程度。看着激情如何在一个人身上增长是很有趣的。在这两年里,用乡村邮递员覆盖全国是我人生的雄心。即使是牛顿偶尔也意识到他痴迷的程度。在将pi计算到15位数后,他在给朋友的信中写道:我羞于告诉你我把这些计算进行了多少位数字,当时没有其他事情要做。顺便说一句,拉马努金也是一个强迫性的计算者。正如卡尼格尔在他优秀的传记中所写的那样:一位拉马努金学者,B.M.威尔逊,后来告诉拉马努金对数论的研究通常是”以数值结果表为前提的,通常延伸到我们大多数人会退缩的长度。”
[7] 努力理解自然世界算作创造而不是消费。
牛顿在选择研究神学时在这个区别上绊倒了。他的信念不允许他看到这一点,但追寻自然中的悖论是有成果的,而追寻神圣文本中的悖论则不是。
[8] 人们对某个话题产生兴趣的倾向有多少是天生的?我到目前为止的经验表明答案是:大部分。不同的孩子对不同的事情感兴趣,很难让孩子对他们本来不会感兴趣的事情感兴趣。不是以一种持久的方式。你能为一个话题做的最多的事情是确保它得到公平的展示——例如,向他们明确说明,数学不仅仅是他们在学校做的乏味练习。之后就取决于孩子了。
The Bus Ticket Theory of Genius
November 2019
Everyone knows that to do great work you need both natural ability and determination. But there’s a third ingredient that’s not as well understood: an obsessive interest in a particular topic.
To explain this point I need to burn my reputation with some group of people, and I’m going to choose bus ticket collectors. There are people who collect old bus tickets. Like many collectors, they have an obsessive interest in the minutiae of what they collect. They can keep track of distinctions between different types of bus tickets that would be hard for the rest of us to remember. Because we don’t care enough. What’s the point of spending so much time thinking about old bus tickets?
Which leads us to the second feature of this kind of obsession: there is no point. A bus ticket collector’s love is disinterested. They’re not doing it to impress us or to make themselves rich, but for its own sake.
When you look at the lives of people who’ve done great work, you see a consistent pattern. They often begin with a bus ticket collector’s obsessive interest in something that would have seemed pointless to most of their contemporaries. One of the most striking features of Darwin’s book about his voyage on the Beagle is the sheer depth of his interest in natural history. His curiosity seems infinite. Ditto for Ramanujan, sitting by the hour working out on his slate what happens to series.
It’s a mistake to think they were “laying the groundwork” for the discoveries they made later. There’s too much intention in that metaphor. Like bus ticket collectors, they were doing it because they liked it.
But there is a difference between Ramanujan and a bus ticket collector. Series matter, and bus tickets don’t.
If I had to put the recipe for genius into one sentence, that might be it: to have a disinterested obsession with something that matters.
Aren’t I forgetting about the other two ingredients? Less than you might think. An obsessive interest in a topic is both a proxy for ability and a substitute for determination. Unless you have sufficient mathematical aptitude, you won’t find series interesting. And when you’re obsessively interested in something, you don’t need as much determination: you don’t need to push yourself as hard when curiosity is pulling you.
An obsessive interest will even bring you luck, to the extent anything can. Chance, as Pasteur said, favors the prepared mind, and if there’s one thing an obsessed mind is, it’s prepared.
The disinterestedness of this kind of obsession is its most important feature. Not just because it’s a filter for earnestness, but because it helps you discover new ideas.
The paths that lead to new ideas tend to look unpromising. If they looked promising, other people would already have explored them. How do the people who do great work discover these paths that others overlook? The popular story is that they simply have better vision: because they’re so talented, they see paths that others miss. But if you look at the way great discoveries are made, that’s not what happens. Darwin didn’t pay closer attention to individual species than other people because he saw that this would lead to great discoveries, and they didn’t. He was just really, really interested in such things.
Darwin couldn’t turn it off. Neither could Ramanujan. They didn’t discover the hidden paths that they did because they seemed promising, but because they couldn’t help it. That’s what allowed them to follow paths that someone who was merely ambitious would have ignored.
What rational person would decide that the way to write great novels was to begin by spending several years creating an imaginary elvish language, like Tolkien, or visiting every household in southwestern Britain, like Trollope? No one, including Tolkien and Trollope.
The bus ticket theory is similar to Carlyle’s famous definition of genius as an infinite capacity for taking pains. But there are two differences. The bus ticket theory makes it clear that the source of this infinite capacity for taking pains is not infinite diligence, as Carlyle seems to have meant, but the sort of infinite interest that collectors have. It also adds an important qualification: an infinite capacity for taking pains about something that matters.
So what matters? You can never be sure. It’s precisely because no one can tell in advance which paths are promising that you can discover new ideas by working on what you’re interested in.
But there are some heuristics you can use to guess whether an obsession might be one that matters. For example, it’s more promising if you’re creating something, rather than just consuming something someone else creates. It’s more promising if something you’re interested in is difficult, especially if it’s more difficult for other people than it is for you. And the obsessions of talented people are more likely to be promising. When talented people become interested in random things, they’re not truly random.
But you can never be sure. In fact, here’s an interesting idea that’s also rather alarming if it’s true: it may be that to do great work, you also have to waste a lot of time.
In many different areas, reward is proportionate to risk. If that rule holds here, then the way to find paths that lead to truly great work is to be willing to expend a lot of effort on things that turn out to be every bit as unpromising as they seem.
I’m not sure if this is true. On one hand, it seems surprisingly difficult to waste your time so long as you’re working hard on something interesting. So much of what you do ends up being useful. But on the other hand, the rule about the relationship between risk and reward is so powerful that it seems to hold wherever risk occurs. Newton’s case, at least, suggests that the risk/reward rule holds here. He’s famous for one particular obsession of his that turned out to be unprecedentedly fruitful: using math to describe the world. But he had two other obsessions, alchemy and theology, that seem to have been complete wastes of time. He ended up net ahead. His bet on what we now call physics paid off so well that it more than compensated for the other two. But were the other two necessary, in the sense that he had to take big risks to make such big discoveries? I don’t know.
Here’s an even more alarming idea: might one make all bad bets? It probably happens quite often. But we don’t know how often, because these people don’t become famous.
It’s not merely that the returns from following a path are hard to predict. They change dramatically over time. 1830 was a really good time to be obsessively interested in natural history. If Darwin had been born in 1709 instead of 1809, we might never have heard of him.
What can one do in the face of such uncertainty? One solution is to hedge your bets, which in this case means to follow the obviously promising paths instead of your own private obsessions. But as with any hedge, you’re decreasing reward when you decrease risk. If you forgo working on what you like in order to follow some more conventionally ambitious path, you might miss something wonderful that you’d otherwise have discovered. That too must happen all the time, perhaps even more often than the genius whose bets all fail.
The other solution is to let yourself be interested in lots of different things. You don’t decrease your upside if you switch between equally genuine interests based on which seems to be working so far. But there is a danger here too: if you work on too many different projects, you might not get deeply enough into any of them.
One interesting thing about the bus ticket theory is that it may help explain why different types of people excel at different kinds of work. Interest is much more unevenly distributed than ability. If natural ability is all you need to do great work, and natural ability is evenly distributed, you have to invent elaborate theories to explain the skewed distributions we see among those who actually do great work in various fields. But it may be that much of the skew has a simpler explanation: different people are interested in different things.
The bus ticket theory also explains why people are less likely to do great work after they have children. Here interest has to compete not just with external obstacles, but with another interest, and one that for most people is extremely powerful. It’s harder to find time for work after you have kids, but that’s the easy part. The real change is that you don’t want to.
But the most exciting implication of the bus ticket theory is that it suggests ways to encourage great work. If the recipe for genius is simply natural ability plus hard work, all we can do is hope we have a lot of ability, and work as hard as we can. But if interest is a critical ingredient in genius, we may be able, by cultivating interest, to cultivate genius.
For example, for the very ambitious, the bus ticket theory suggests that the way to do great work is to relax a little. Instead of gritting your teeth and diligently pursuing what all your peers agree is the most promising line of research, maybe you should try doing something just for fun. And if you’re stuck, that may be the vector along which to break out.
I’ve always liked Hamming’s famous double-barrelled question: what are the most important problems in your field, and why aren’t you working on one of them? It’s a great way to shake yourself up. But it may be overfitting a bit. It might be at least as useful to ask yourself: if you could take a year off to work on something that probably wouldn’t be important but would be really interesting, what would it be?
The bus ticket theory also suggests a way to avoid slowing down as you get older. Perhaps the reason people have fewer new ideas as they get older is not simply that they’re losing their edge. It may also be because once you become established, you can no longer mess about with irresponsible side projects the way you could when you were young and no one cared what you did.
The solution to that is obvious: remain irresponsible. It will be hard, though, because the apparently random projects you take up to stave off decline will read to outsiders as evidence of it. And you yourself won’t know for sure that they’re wrong. But it will at least be more fun to work on what you want.
It may even be that we can cultivate a habit of intellectual bus ticket collecting in kids. The usual plan in education is to start with a broad, shallow focus, then gradually become more specialized. But I’ve done the opposite with my kids. I know I can count on their school to handle the broad, shallow part, so I take them deep.
When they get interested in something, however random, I encourage them to go preposterously, bus ticket collectorly, deep. I don’t do this because of the bus ticket theory. I do it because I want them to feel the joy of learning, and they’re never going to feel that about something I’m making them learn. It has to be something they’re interested in. I’m just following the path of least resistance; depth is a byproduct. But if in trying to show them the joy of learning I also end up training them to go deep, so much the better.
Will it have any effect? I have no idea. But that uncertainty may be the most interesting point of all. There is so much more to learn about how to do great work. As old as human civilization feels, it’s really still very young if we haven’t nailed something so basic. It’s exciting to think there are still discoveries to make about discovery. If that’s the sort of thing you’re interested in.
Notes
[1] There are other types of collecting that illustrate this point better than bus tickets, but they’re also more popular. It seemed just as well to use an inferior example rather than offend more people by telling them their hobby doesn’t matter.
[2] I worried a little about using the word “disinterested,” since some people mistakenly believe it means not interested. But anyone who expects to be a genius will have to know the meaning of such a basic word, so I figure they may as well start now.
[3] Think how often genius must have been nipped in the bud by people being told, or telling themselves, to stop messing about and be responsible. Ramanujan’s mother was a huge enabler. Imagine if she hadn’t been. Imagine if his parents had made him go out and get a job instead of sitting around at home doing math.
On the other hand, anyone quoting the preceding paragraph to justify not getting a job is probably mistaken.
[4] 1709 Darwin is to time what the Milanese Leonardo is to space.
[5] “An infinite capacity for taking pains” is a paraphrase of what Carlyle wrote. What he wrote, in his History of Frederick the Great, was ”… it is the fruit of ‘genius’ (which means transcendent capacity of taking trouble, first of all)…” Since the paraphrase seems the name of the idea at this point, I kept it.
Carlyle’s History was published in 1858. In 1785 Hérault de Séchelles quoted Buffon as saying “Le génie n’est qu’une plus grande aptitude à la patience.” (Genius is only a greater aptitude for patience.)
[6] Trollope was establishing the system of postal routes. He himself sensed the obsessiveness with which he pursued this goal. It is amusing to watch how a passion will grow upon a man. During those two years it was the ambition of my life to cover the country with rural letter-carriers. Even Newton occasionally sensed the degree of his obsessiveness. After computing pi to 15 digits, he wrote in a letter to a friend: I am ashamed to tell you to how many figures I carried these computations, having no other business at the time. Incidentally, Ramanujan was also a compulsive calculator. As Kanigel writes in his excellent biography: One Ramanujan scholar, B. M. Wilson, later told how Ramanujan’s research into number theory was often “preceded by a table of numerical results, carried usually to a length from which most of us would shrink.”
[7] Working to understand the natural world counts as creating rather than consuming.
Newton tripped over this distinction when he chose to work on theology. His beliefs did not allow him to see it, but chasing down paradoxes in nature is fruitful in a way that chasing down paradoxes in sacred texts is not.
[8] How much of people’s propensity to become interested in a topic is inborn? My experience so far suggests the answer is: most of it. Different kids get interested in different things, and it’s hard to make a child interested in something they wouldn’t otherwise be. Not in a way that sticks. The most you can do on behalf of a topic is to make sure it gets a fair showing — to make it clear to them, for example, that there’s more to math than the dull drills they do in school. After that it’s up to the child.