Beauty Is Not Truth — It Is an Artifact of Our Brain Size

Keats gets quoted, physicists nod along about elegance, and the identification of beauty with truth passes as one of those deep observations that serious people accept. I think it is a sentimental human proclivity with nothing behind it, and there are two arguments that dispose of it.

The Argument From Brain Size

The four-colour theorem was proved in 1976 with substantial computer assistance. The proof required checking a very large number of configurations, and the full verification runs to something no human will ever read in one sitting.

It is universally regarded as ugly. Mathematicians said so at the time and many still hope for a proof a person could hold in their head.

But ask why it is ugly. The theorem is true. The proof is valid. What exactly is the defect?

The defect is that it does not fit inside a human head. That is the entire complaint. For a machine, a verification of that length poses no difficulty whatever — it is not experienced as unwieldy, because nothing is experiencing it.

So our preference for the compact formula — E = mc² and its relatives — reflects our limited working memory and our need to grasp a result all at once. The correlation between beauty and truth is therefore a fact about the size of our brains, not a fact about truth.

A creature with a much larger working memory would find our elegant equations unremarkable and would experience the four-colour proof as a single graspable object. Its aesthetics would differ from ours, and neither aesthetics would tell it anything about which theorems were true.

The Argument From Symmetry

The second argument is shorter and I find it decisive.

In mathematics, truth and falsehood are perfectly symmetrical. Every true statement becomes false when negated, and every false one becomes true. There is an exact one-to-one correspondence between the set of truths and the set of falsehoods.

Which means: if you knew precisely which statements were false, you would thereby know precisely which were true. The two bodies of information are equivalent. Neither is more informative or more structured than the other.

Now, if beauty tracked truth, this symmetry would be inexplicable. The set of falsehoods is exactly as large, exactly as structured, and stands in exactly the same relation to the set of truths as the truths do to it. Any aesthetic property one has, the other has too, in mirror image.

So the notion that beauty attaches to truth rather than to falsehood is suspect from the start. There is no asymmetry available for it to attach to.

A Related Puzzle

Something I have not worked out and would like to: the relationship between the length of mathematical proofs and the length of musical works, with respect to beauty.

Many people dislike long proofs. Many of the same people dislike Mahler's symphonies. Both complaints have the same shape — it goes on too long, I cannot hold it, it does not resolve when I want it to — and both are treated as aesthetic judgements about the object rather than as reports about the listener's capacity.

If the brain-size argument is right, the two are the same phenomenon. What we call beauty in both domains is substantially a measure of fit between the object and our working memory. That would explain why aesthetic standards vary so much with training: a musician who has internalised the form hears Mahler as coherent, exactly as a topologist who has internalised the machinery finds a long proof natural.

Which suggests that beauty is not a property of objects at all, but a relation between an object and a mind — and that the mind's limits are doing most of the work.