Thoughts on Mathematical Definitions of Beauty

Given a set of all music including cacophony what is the expected
number of bits used to describe it most efficiently? This is the
Shannon’s entropy.

Given a piece of music which may be cacophony what is the number of
bits necessary to describe that particular piece of music most
efficiently? This is the Kolmogorov complexity.

I feel musical beauty lies in sequences with the highest Kolmogorov
complexity but lowest Shannon entropy.

I would bet that almost all beauty lies in phenomena with such a
maximal divergence.

But as is the case with all hierarchy of values, there can exist minds
with an inverted hierarchy which value. In other words, there can
exist minds which consider a maximum Shannon entropy and minimum
Kolmogorov complexity as beauty.

I would bet that environmentalists and repetitive club/gym music
lovers would have an inverted hierarchy.

The problem with Kolmogorov complexity is that it is not computable.
It can only be estimated.

I look forward to the day when brain scans will reveal the structures
which estimate Kolmogorov complexity.

P.S. Coffee is an amazing drug.


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