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.
Teachers and coaches implicitly told us the returns were linear. "You get out," I heard a thousand times, "what you put in." They meant well, but this is rarely true. If your product is only half as good as your competitor's, you don't get half as many customers. You get no customers, and you go out of business.
It's obviously true that the returns for performance are superlinear in business. Some think this is a flaw of capitalism, and that if we changed the rules it would stop being true.
But superlinear returns for performance are a feature of the world, not an artifact of rules we've invented. We see the same pattern in fame, power, military victories, knowledge, and even benefit to humanity. In all of these, the rich get richer. 
You can't understand the world without understanding the concept of superlinear returns. And if you're ambitious you definitely should, because this will be the wave you surf on.
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:
The most obvious case of superlinear returns is when you're working on something that grows exponentially. For example, growing bacterial cultures.
When they grow at all, they grow exponentially. But they're tricky to grow. Which means the difference in outcome between someone who's adept at it and someone who's not is very great.
Startups can also grow exponentially, and we see the same pattern there. Some manage to achieve high growth rates. Most don't.
And as a result you get qualitatively different outcomes: the companies with high growth rates tend to become immensely valuable, while the ones with lower growth rates may not even survive.
Y Combinator encourages founders to focus on growth rate rather than absolute numbers. It prevents them from being discouraged early on, when the absolute numbers are still low.
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. But the main advantage is that by focusing on growth rate you tend to get something that grows exponentially.
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. And if growth rate were proportional to performance, then the reward for performance p over time t would be proportional to pt.
Even after decades of thinking about this, I find that sentence startling.
Whenever how well you do depends on how well you've done, you'll get exponential growth. But neither our DNA nor our customs prepare us for it.
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.
What we don't understand naturally we develop customs to deal with, but we don't have many customs about exponential growth either, because there have been so few instances of it in human history.
In principle herding should have been one: the more animals you had, the more offspring they'd have. But in practice grazing land was the limiting factor, and there was no plan for growing that exponentially.
Or more precisely, no generally applicable plan. There was a way to grow one's territory exponentially: by conquest. The more territory you control, the more powerful your army becomes, and the easier it is to conquer new territory.
This is why history is full of empires. But so few people created or ran empires that their experiences didn't affect customs very much. The emperor was a remote and terrifying figure, not a source of lessons one could use in one's own life.
The most common case of exponential growth in preindustrial times was probably scholarship. The more you know, the easier it is to learn new things.
The result, then as now, was that some people were startlingly more knowledgeable than the rest about certain topics. But this didn't affect customs much either.
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.