Why are Normal Distributions Normal?

We seem to be surrounded by bell curves—curves more formally known as normal distributions, or Gaussian distributions. All manner of things appear to be distributed normally: people’s heights, sizes of snowflakes, errors in measurements, lifetimes of lightbulbs, IQ scores, weights of loaves of bread, and so on. I argue that the standard explanation for why such quantities are normally distributed, which one sees throughout the sciences, is often false. The standard explanation invokes the Central Limit Theorem, and I argue that in many cases the conditions of the theorem are not satisfied, not even approximately. I then suggest an alternative explanatory schema for why a given quantity is normally distributed. “Everyone believes in it: experimentalists believing that it is a mathematical theorem, mathematicians believing that it is an empirical fact.” — Henri Poincaré.1