Understanding Gaussians

Gaussian, Gaussian, Gaussian. Important to understand Gaussians, but also to recognize how profoundly non-Gaussian, in particular multimodal, the world is. And to build systems that navigate and optimize over such distributions.

(Not complaining about this article, which is illuminating).

A particularly interesting case is Maxwell-Boltzmann distributions of the speeds of molecules in a gas in a 3D space. Even though the individual velocities of gas molecules along the x, y and z directions do follow Gaussian distributions, the distributions of scalar speeds do not (since the speed is obtained from the velocities by a non-linear transformation), resulting in a long tail of high velocities, and a median value less than the mean value.

Incidentally human expertise and ability seems to follow the Maxwell-Boltzmann model far more than the Gaussian 'bell curve' model - there's a long tail of exceptional capabilities.

There was an opportunity when heights of soldiers were discussed. Gaussians have infinite extent, but soldier heights must be positive.

Good example