Skip to content

Comment on The Normal Distribution: A derivation from basic principles [pdf]parent

Comments

Well, I think textbooks often give the maxent justification as well, but probably neither is strictly superior to the other.

Often, where a measurement is perturbed by a litany of physically unlinked disturbances (e.g., antenna noise), the CLT argument is compelling. In a case like antenna or front-end electronics noise, justifying the maxent argument would require buying in to an almost mystical belief by comparison.

Interestingly, the two seem to have a deep connection related to thermodynamics, e.g. http://en.wikipedia.org/wiki/Thermal_fluctuations, where you can see both as expansions of a configuration count up to second order in the exponent.

This is manifest in the detectable remnants of the Big Bang, which are a particular realization of a Gaussian random field that was present due to quantum fluctuations of a primordial system. It's funny to think of the universe as a draw from a random number generator.

AboutSource Built by g1lg1l

Hackerly is an independent reader for Hacker News, built on the public HN API. Not affiliated with Y Combinator.