Aesthetic flow

People enjoy looking at things that have symmetry and order – but not too much. Beauty requires an interplay between pattern and chaos. I touched briefly upon this in my October 10 post about a misguided use of computer software to “beautify” the human face by making its features more regular (and therefore more bland).

But I wonder, as I look at a snowflake, or a leaf or sunset or candle flame, or in fact, the face of someone I find lovely to behold, are there principles at work here? Just as Mihaly Csíkszentmihályi spoke of humans being happiest when in a state of “flow” in which things are neither too easy (ie: boring) nor too difficult (ie: frustrating), perhaps there is an equivalent state of aesthetic flow, in which the things we perceive are neither too regular/symmetric nor too chaotic/asymmetric.

There is plentiful evidence that people respond positively to artful assymmetry within a symmetric structure. The genius of great composers from Bach to the Beatles is clearly entwined with their ability to surprise us, to bring a melody or harmonic progression to some wholy unexpected place, while somehow making it all sound right.

Case in point: the second Beatles song that Paul McCartney ever wrote was “I’ll Follow the Sun” (the first was “When I’m Sixty Four” – he composed both songs when he was only sixteen). By the third note of the melody – the flattened E atop an F7 chord (at the word “you’ll” in the lyric “One day you’ll look”) – he has already broken the rules. Right off the bat the melody jumps clean out of the key of C to god only knows where. But he then uses the momentum from that crazily asymmetric choice to launch a lovely and unforgettable tune that ends up sounding not just right but inevitable.

It’s one of those moments that heralds a new kid on the block, a fresh new talent, like Bobby Fischer at the tender age of thirteen sacrificing his queen in his famous game against Donald Byrne – and thereby ensuring a stunning upset victory. That game was outstandingly beautiful because it was outstandingly unexpected, in addition to being brilliant.

On a much more humble scale, I embedded controlled chaos in one of the first computer graphic objects I ever synthesized – a marble vase. I was drawn to the sense of capturing a raging storm within the placid curved surface of a classically sculpted form, and I developed a whole set of techniques that would allow me to express such controlled chaos:


I wonder whether there is any way to calibrate this relationship – to find some formal measure of chaos versus symmetry in any given situation, and then use that ratio to predict a rough measure of potential beauty?

3 Responses to “Aesthetic flow”

  1. Jon says:

    Johann, Mihaly, Paul, Bobby – funny how often references in discussions of beauty are male… Here’s two more, then: Remko Scha and Rens Bod wrote a good paper on “Computational Esthetics” in ’91 which discusses several mathematical models similar to what you describe:

    Also, according to Kant (oh golly, another one), beauty is an ideal that exceeds reason – which suggests that using algorithms to try to measure beauty is a bit like trying to measure a sound using your eyes. You may see the smoke but will miss the bang.

  2. troy says:

    Jon, I miss the bang already…

  3. admin says:

    Jon, I’m not nearly that ambitious. I was not suggesting that we discover the recipe, merely the presence of the right ingredients, in the proper proportions. It’s more of a negative test: As the proportions of chaos and order move away from a certain ideal region, the probability of an aesthetically beautiful result drops off.

    Interestingly, the computational aesthetics you cite based on Birkhoff or even Leeuwenberg are concerned primarily with elegant/minimal expression of symmetries. They don’t really touch on chaos as a component of beauty. So there’s a relationship there, but I think we’re looking in a somewhat different direction.

    Or as Duke Ellington might have said: “It don’t mean a thang if it ain’t got that bang…”

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