Superlinear Returns

October 2023 One of the most important things I didn't understand about the world when I was a child is the degree to which the returns for performance are superlinear.

2023 年 10 月 当我还是个孩子的时候，我对这个世界不了解的最重要的事情之一就是绩效回报的超线性程度。

Teachers and coaches implicitly told us the returns were linear.

老师和教练含蓄地告诉我们，回报是线性的。

"You get out," I heard a thousand times, "what you put in." They meant well, but this is rarely true.

“你把什么放进去，”我听过一千遍了，“你就拿出什么。”他们的本意是好的，但事实却很少如此。

If your product is only half as good as your competitor's, you don't get half as many customers.

如果您的产品只有竞争对手的一半，那么您就不会获得竞争对手的一半数量。

You get no customers, and you go out of business.

你没有顾客，你就倒闭了。

It's obviously true that the returns for performance are superlinear in business.

显然，商业中的绩效回报是超线性的。

Some think this is a flaw of capitalism, and that if we changed the rules it would stop being true.

一些人认为这是资本主义的缺陷，如果我们改变规则，它就不再是真实的。

But superlinear returns for performance are a feature of the world, not an artifact of rules we've invented.

但超线性绩效回报是世界的一个特征，而不是我们发明的规则的产物。

We see the same pattern in fame, power, military victories, knowledge, and even benefit to humanity.

我们在名誉、权力、军事胜利、知识甚至人类利益方面都看到了同样的模式。

In all

总共

of these, the rich get richer.

其中，富者愈富。

[ 1 ] You can't understand the world without understanding the concept of superlinear returns.

[1] 如果不理解超线性回报的概念，你就无法理解世界。

And if you're ambitious you definitely should, because this will be the wave you surf on.

如果你雄心勃勃，你绝对应该这样做，因为这将是你冲浪的浪潮。

It may seem as if there are a lot of different situations with superlinear returns, but as far as I can tell they reduce to two fundamental causes: exponential growth and thresholds.

似乎有很多不同的情况具有超线性回报，但据我所知，它们归结为两个基本原因：指数增长和阈值。

The most obvious case of superlinear returns is when you're working

超线性回报最明显的情况是当你工作时

on something that grows exponentially.

在呈指数级增长的事物上。

For example, growing bacterial cultures.

例如，培养细菌培养物。

When they grow at all, they grow exponentially.

当它们真正成长时，它们会呈指数级增长。

But they're tricky to grow.

但它们的生长很困难。

Which means the difference in outcome between someone who's adept at it and someone who's not is very great.

这意味着擅长与不擅长的人之间的结果差异非常大。

Startups can also grow exponentially, and we see the same pattern there.

初创公司也可以呈指数级增长，我们也看到了同样的模式。

Some manage to achieve high growth rates.

有些成功实现了高增长率。

Most don't.

大多数人没有。

And as a result you get qualitatively different outcomes: the companies

结果，你得到了性质不同的结果：公司

with high growth rates tend to become immensely valuable, while the ones with lower growth rates may not even survive.

增长率高的企业往往会变得非常有价值，而增长率较低的企业甚至可能无法生存。

Y Combinator encourages founders to focus on growth rate rather than absolute numbers.

Y Combinator 鼓励创始人关注增长率而不是绝对数字。

It prevents them from being discouraged early on, when the absolute numbers are still low.

当绝对数字仍然很低时，这可以防止他们在早期就灰心丧气。

It also helps them decide what to focus on: you can use growth rate as a compass to tell you how to evolve the company.

它还可以帮助他们决定关注什么：您可以使用增长率作为指南针来告诉您如何发展公司。

But the main advantage is that

但主要优点是

by focusing on growth rate you tend to get something that grows exponentially.

通过关注增长率，你往往会得到指数级增长的东西。

YC doesn't explicitly tell founders that with growth rate "you get out what you put in," but it's not far from the truth.

YC 并没有明确告诉创始人，随着增长率的增长，“你投入什么，就会得到什么”，但这与事实相差不远。

And if growth rate were proportional to performance, then the reward for performance p over time t would be proportional to p t .

如果增长率与绩效成正比，那么随着时间 t 的绩效 p 的奖励将与 p t 成正比。

Even after decades of thinking about this, I find that sentence startling.

即使经过几十年的思考，我仍然觉得这句话令人震惊。

Whenever how well you do depends on how well you've done, you'll get exponential growth.

每当你做得有多好取决于你做得有多好时，你就会得到指数级的增长。

But neither our DNA nor our customs prepare us for it.

但我们的 DNA 和习俗都没有为此做好准备。

No one finds exponential growth natural; every child is surprised, the first time they hear it, by the story of the man who asks the king for a single grain of rice the first day and double the amount each successive day.

没有人认为指数增长是理所当然的；每个孩子第一次听到这个故事时都会感到惊讶，这个故事是这样的：一个人第一天向国王要一粒米，之后的每一天都会加倍。

What we don't understand naturally we develop customs to deal with,

我们不理解的事情自然会发展出习惯来处理，

but we don't have many customs about exponential growth either, because there have been so few instances of it in human history.

但我们也没有太多关于指数增长的习俗，因为人类历史上这样的例子太少了。

In principle herding should have been one: the more animals you had, the more offspring they'd have.

原则上，放牧应该是这样一种：你拥有的动物越多，它们的后代就越多。

But in practice grazing land was the limiting factor, and there was no plan for growing that exponentially.

但实际上，牧场是限制因素，而且没有计划以指数级增长。

Or more precisely, no generally applicable plan.

或者更准确地说，没有普遍适用的计划。

There was a way

有一个办法

to grow one's territory exponentially: by conquest.

以指数方式扩大领土：通过征服。

The more territory you control, the more powerful your army becomes, and the easier it is to conquer new territory.

你控制的领土越多，你的军队就越强大，也就越容易征服新的领土。

This is why history is full of empires.

这就是为什么历史上充满了帝国。

But so few people created or ran empires that their experiences didn't affect customs very much.

但创建或经营帝国的人太少了，他们的经历并没有对习俗产生太大影响。

The emperor was a remote and terrifying figure, not a source of lessons one could use in one's own life.

皇帝是一个遥远而可怕的人物，不是一个人可以在自己的生活中使用的教训来源。

The most common case of exponential growth in preindustrial times was probably scholarship.

前工业时代指数增长最常见的例子可能是学术。

The more you know, the easier it is to learn new things.

你知道的越多，学习新事物就越容易。

The result, then as now, was that some people were startlingly more knowledgeable than the rest about certain topics.

结果是，无论当时还是现在，有些人对某些话题的了解比其他人要多得多。

But this didn't affect customs much either.

但这也没有对海关产生太大影响。

Although empires of ideas can overlap and there can thus be far more emperors, in preindustrial times this type of empire had little practical effect.

尽管思想帝国可以重叠，从而可以有更多的皇帝，但在前工业时代，这种类型的帝国几乎没有实际作用。