Monday, March 11, 2013
Cloud of randomness
What is the difference between a cat and a dog? These (classes of) entities are truly different - it's not as if the differences are entirely subjective or purely a matter of opinion. And yet, there can be no complete, precise, and unambiguous definition that cleaves the two, as is demonstrated by the fact that they share a common ancestor. The principle holds in general: all emergent structures (those formed out of arrangements of vast numbers of mathematical building blocks) are surrounded by clouds of randomness. For instance, the particular orientations of the water molecules in your brain were completely unimportant during your reading of this paragraph. But this fundamental randomness is also not irrelevant: it is a central component of the engine for generating nontrivial information, i.e. iterative trial and error.