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Comment by nessunodoro | Hacker News Reader

To me the connection between the golden ratio and beauty is tied to iterated function systems, and fractals. I feel like it boils down to efficiency of representation of a larger system. If a complex, balanced system can be represented efficiently by a small number of values, variables, and operations, then it's favored by the universe somehow, and by our mind's eye. It "snaps into place" more easily, it aligns with itself, and therefore our conception of it is also performed with less work, more "naturally."

The golden rectangle and spiral represent this best to me. The whole is found in the parts, infinitely, the further you iterate, like looking down a well and seeing all the way to the bottom. It's gratifying to conceive of more by doing less. I wish I were better with words, but I do feel φ's beauty somehow boils down to efficiency of representation.

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There's an interesting correlation to information theory and compressibility. Someone did an analysis of pop lyrics[1] where they compressed the plaintext using a lossless compression algorithm and determined that (as expected) many pop songs compress very well and are highly redundant. But taken another angle, this could also represent that we as human beings find lyrics which have high degrees of self-similarity with small amounts of variation to be pleasing to the ear, which tracks with what makes pop music (which must be singable and usually danceable to go viral) successful.

[1] https://pudding.cool/2017/05/song-repetition/

"favored by the universe somehow"

With a large enough population, you are going to end up with the same representation (structure of neurons, glial cells etc) in some subset of brains.

As a painter, I am very aware that taste is not as universal as is constantly advertised. Some people like the shades of blue I use and some don't or are indifferent. Why I chose that blue and why they liked that blue is cause we probably share, in some small corner of a trillion brain cells, a small clump of structure that's exactly alike.

And the reason why systems generally default to simpler representations over more complex ones in nature is because the process of evolution is in many ways basically just a very slow random search. Simpler solutions fundamentally are more likely to occur than complex ones. Of course over many iterations of simple changes, an overarching complexity often can seemingly emerge over time.

Also, to be 100% accurate, I should say that technically evolution is a form of a genetic algorithm which is slightly different and more constrained than a pure random search, but it's not that big of a deal with respect to this conversation.

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