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does this imply that the universe somehow rewards structures that engender 'compressibility' (coarse graining)? it does seem like our brains subjectively enjoy identifying it, to the point of over-optimization in the form of phenomena like pareidolia

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The universe doesn’t “reward” it so much as it’s just a consequence of random events. For example, if you flip a coin many times, you’ll see long sequences of heads. From the central limit theorem it follows that sufficiently many random events will form a normal distribution, which exhibits clustering phenomenon. Take a look at a Galton board in action.

That's ignoring anything related to actual life we observe and Gaussian distributed data does not have to exhibit clustering either. (But it allows that.)

About the only thing that is naturally uniform so far within bounds is large scale homogeneity and isotropy of universe. Which is an unsolved mystery potentially involving dark matter.

I would argue if it didn't do clustering then there was some sort of pattern/bias at play that caused it.

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