Laplace and Gauss were in mad competition to find a general rule for the pattern of errors for measurements in astronomy. It's around 1800, and the medium of ex

Laplace and Gauss were in mad competition to find a general rule for the pattern of errors for measurements in astronomy. It's around 1800, and the medium of exchange is letters. Laplace has recently shown that the integral of minus t squared, where t goes from minus to plus infinity has a definite answer. Gauss starts a paper, basically says, let's just run with the arithmetic average, the usual mean, as the go-to best estimate, from a big series of measurements of a single thing, each of which has errors, because, yeah, why not. Moments later the guy shows that squaring the errors makes it equivalent to that thing Laplace did, and we now have a general rule. His argument follows by supposing each repeated error due to a specific cause has an expected error of zero, with no particular rule of distribution, but that as the number of specific causes goes to infinity, the Law of large numbers applies (go Euler, fair play). Hence, wiggley wiggley, Laplace's thing. Beautiful piece of work, and resting on Laplace and Euler too, two other heroic oddballs. The best thing is the underlying explanation: Take a nearly-infinite number of different measurements of a thing, each measurement with its own pattern of rubbishness, and the average of those measurement will approach having this distribution. That bit is what makes it so broadly applicable.