Wednesday, December 31, 2014

A Fuzzy Boundary with Randomness

Consider straight-forward, atomic level simulations of both a frog and a glass of water of roughly the same mass. The same amount of memory will needed store the position and velocity data (for a Newtonian version) or wave function correlations for both systems - in this sense both contain the same amount of information. But of course almost all of the information that describes the glass of water will be random in nature, while decent fraction of the frog's binary encoding is structured / nonrandom, i.e. nontrivial.

Going back to the cat/dog example it is also the case that real world objects, formed from arrangements of moles of atoms, necessarily have somewhat fuzzy descriptions (e.g. Fuzzy Set). One could decree that the first "true cat" was born 10,003 years ago (the offspring of two admittedly catlike creatures), but attempts at such exact definitions are almost always ambiguous (obviously enough, but one encounters the occasional debate over, say, what the true definition of life is). This type of fuzzy boundary also applies to our frog example, between what would count as structured and nontrivial in the description, and the random remainder (such as the orientations of the water molecules within the cells, etc...). More broadly this provides a pleasing way of viewing the world at large: full of hierarchical patterns (and thus amenable to science), but permeated by a fuzzy boundary with randomness.

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