On Mathematical Beauty in Physics

Why would a sense of beauty be related to natural truth? Well, say that everyone is born with a randomly assigned set of aesthetic preferences. The people whose aesthetic preferences just so happen to align with a theory that's about to be discovered will be more likely to guess at it in advance, and they will have lots of career success once experiments confirm those guesses. This selects after the fact for people whose aesthetic preferences are luckily aligned with future discoveries. Anyone who prefers the aesthetics of bad theories over good ones will either waste their time or switch to a different field, and nobody will care what they thought was beautiful at the time.

In the end, when it comes time to vote on which theories are beautiful, the theorists who thought that the best theories were beautiful will say "I always thought it was beautiful," and everyone will listen to them because their randomly assigned bias towards the good theories would have led them to respected positions. The ones who always disliked the good theories will not be around, or will have a less respected voice.

That's my theory for how the word "beauty" gets preferentially assigned to good (as in true) theories. One implication of this theory would be that even though claims of beauty tend to align with known-true theories, they aren't useful for telling in advance which theories are going to be true: the people whose preferences have randomly attached them to the bad theories today won't be silenced until the experiments come out.

It also suggests that ugly theories are more likely to be overlooked. Since the profession selects for people who gravitate to a certain type of theory (what they call beautiful), there might be ugly-but-true theories waiting to be discovered.

> as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen

There is a fair bit of mysticism that gets bandied about along these lines--and I can certainly see why a mathematical platonist might marvel at the spooky correspondence between beautiful mathematics and to-be-discovered physical theories.

But if you can let go of the platonism, then I think a rather straightforward explanation emerges:

A mathematician is one who explores and names the various ways that a human mind can stretch and fold. I guess it's kind of like yoga. The ways of folding that best reflect whatever it is that makes the human mind, well, human--those ones we call beautiful. Nature is the only thing not of human construction that we fold our minds to fit (you might call this process 'perception')--but we are still only able to fold in human-like ways.

So the mathematician catalogs the ways we can see, and the physicist catalogs the things we do see. It doesn't strike me as especially spooky that the physicist finds things that correspond nicely to the mathematician's list.

I think it’s mostly a case of the drunk looking for his keys under the lamp post because that’s where the light is.

We have no idea how much there is to know about reality. We do know how to describe some parts with mathematics, but who knows how much there is out there which is not possible to describe with mathematics.

We may just be discovering infinitesimally small part ls of reality which math happens to describe well.

“The artist, the musical composer, the architect, the scientist all feel a fundamental need to discover and create something new that is whole and total, harmonious and beautiful.”

“Having seen that the perception of harmony and totality need not be a purely private kind of judgement, one can now understand in a new light the fact that the really great scientists have, without exception, all seen in the structural process of nature a vast harmony of order of indescribable beauty… Indeed, every great scientific theory was in reality founded on such perception of some very general and fundamental feature of the harmony of nature’s order. Such perceptions, when expressed systematically and formally, are called “laws of nature.”

-- David Bohm, On Creativity