Against Beauty II

This blog just recently celebrated its first year anniversary!

In my first post, Against Beauty, I’ve argued that beauty is not likely a good criterion for scientific theories.

It is just telling, that now a year later I came across a quote from one of my heroes – Ludwig Boltzmann:

If you are out to describe the truth, leave elegance to the tailor.

— Ludwig Boltzmann

Incidentally, Lisa Randall talks along similar lines in a recent episode of the On Being podcast:

[…] you can frame things so that they seem more beautiful than they are, or less beautiful than they are. For science to be meaningful, you want to have as few ingredients as possible to make as many predictions as possible with which you can test your ideas. So I think that’s more the sense — I think that’s what people are thinking of. And simplicity, by the way, isn’t always beauty.

While I agree with the beauty part, I’m of different opinion on the ultimate role of simplicity in evaluating scientific theories (understood here as the Kolmogorov-Chaitin complexity of the given model).

As we learn more about the universe we necessarily will have to abandon effective theories that are “human readable”. The world is too complex, to be describable by human-mind-sized models.

For every complex problem there is an answer that is clear, simple, and wrong.

— H. L. Mencken

Beauty and simplicity are often conflated – I’m also not always clear on which one I mean).

My current thinking is that if we consider beauty of a theory to be the ratio of the model’s explanative (predictive) power to its Kolmogorov length, then this will remain a relevant model selection criterion.

But I think, that ultimately we will have to say goodbye to the notion that the Kolmogorov complexity of models is not allowed to cause a stack overflow in human brains.

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