moments are important theoretically because they provide an alternative way to fully and uniquely specify a probability distribution, a fact that is intuitive if you understand how moment’s quantify a distribution’s location, spread, and shape

However, there’s a third way to think about the first moment, and it’s the one that I think is most useful for understanding moments generally: the first moment tells us how far away from the origin the center of mass is. I like this interpretation because it is analogous to a moment arm in mechanics, which is the length of an arm between an axis o... See more

The glow in the centre of the k-space image represents the lower spatial frequencies, which contains the bulk of the image contrast information. As we move away from this central glow, the finer details and edges, representing the higher spatial frequencies

The Fisher information matrix is simply the Hessian of KL divergence at the point where two distributions are equal.

Differential geometry is all about constructing things which are independent of the representation

Only the future can tell. But we need to mend our ways. Otherwise, nihilism will win and we will deconstruct ourselves into oblivion. Maybe this is will be the million dollar question of the next century. What do we do, when we do not have to do anything?