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One of the theories on why more innovations (heliocentrism, discovery of the New World, etc.) happended in Europe instead of China (which is where astronomy, navigation, etc. were far more advanced) is that in China, there was lot more centralization. If you went to the Emperor and couldn't convince him that the earth was round, you were done. In Europe you could shop your idea around to a bunch of Kings and Queens until someone liked your idea.

Success in science and innovation isn't driven by efficiency. It's driven by diversity.  You want to have a lot of little groups trying out crazy ideas.

To understand this, it helpful to understand Moivre's equation, which he described in the article, “The Most Dangerous Equation.” I summarize it below.

Let’s say you wanted to figure out what causes kidney cancer. A reasonable question to ask might be, “which counties in the U.S. have the highest rates of kidney cancer?”

The answer is that rural, sparsely populated counties have the highest rates. You might think that perhaps this was due to pesticides, or lack of access to healthcare, or some other factor related to the rural lifestyle.

However, if you were to ask which counties have the lowest rates, you would find that rural, sparsely populated counties also have the lowest rates. In fact, the counties are often adjacent. See below. The red counties have the highest rates of kidney cancer, and the teal counties the lowest.

What’s going on?

Well, when you have only a few people in the county, the likelihood that there will be very high or low rates, due simply to chance, is high. For example, if there were only 2 people in the county and 1 person got cancer, that would be 50%. If 0 out 2 got cancer, it would be 0%.

This is why the best (and the worst) hospitals in the country or the best (and the worst) places to live often are small hospitals and small towns. And why the best (and the worst) science is done by small groups or individual scientists. Statistically, the smaller the sample size, the greater the likelihood of seeing an outlier.

This phenomenon was discovered by de Moivre, and made famous by Wainer’s.

The point is, as a group group gets larger and larger, innovation regresses more and more toward the mean. This is OK if you're working on a weakest link problem (where what you're doing is to prevent mistakes) but in endeavors like sciences, which is a strongest link problem (where what matters are the few huge breakthroughs), you want to make each group as small as possible.

I go into more detail in my post,