Physicists like to talk about the beauty and elegance of theories, books have been written about the beautiful equations, and the internet, being the internet, offers a selection of various lists that are just a Google search away.Max Tegmark famously believes all math is equally real, but most physicists are pickier. Garrett Lisi may be the most outspoken example who likes to say that the mathematics of reality has to be beautiful. Now Garrett’s idea of beautiful is a large root diagram which may not be everybody’s first choice, but symmetry is a common ingredient to beauty.
Personally, I value interesting over beautiful. Symmetry and order is to art what harmony and repetition is to music – it’s bland in excess. But more importantly, there is no reason why the sense of beauty that humans have developed during evolution should have any relevance for the fundamental laws of nature. Using beauty as guide is even worse than appealing to naturalness. Naturalness, like beauty, is a requirement based on experience, not on logic, but at least naturalness can be quantified while beauty is subjective, and malleable in addition.
Frank Wilczek has an interesting transcript of a talk about “Quantum Beauty” online in which he writes
“The Standard Model is a very powerful, very compact framework. It would be difﬁcult... to exaggerate.. its beauty.”He then goes on to explain why this is an exaggeration. The Standard Model really isn’t all that beautiful as with all these generations and families of particles and let’s not even mention Yukawa couplings. Frank thinks a grand unification would be much more beautiful, especially when supersymmetric:
“If [SUSY’s new particles] exist, and are light enough to do the job, they will be produced and detected at [the] new Large Hadron Collider – a fantastic undertaking at the CERN laboratory, near Geneva, just now coming into operation. There will be a trial by ﬁre. Will the particles SUSY requires reveal themselves? If not, we will have the satisfaction of knowing we have done our job, according to Popper, by producing a falsiﬁable theory and showing that it is false.”Particle physicists who have wasted their time working out SUSY cross-sections don’t seem to be very “satisfied” with the LHC no-show. In fact they seem to be insulted because nature didn’t obey their beauty demands. In a recent cover story for Scientific American Joseph Lykken and Maria Spiropulu wrote:
“It is not an exaggeration to say that most of the world’s particle physicists believe that supersymmetry must be true.”That is another exaggeration of course, a cognitive bias known as the “false-consensus effect”. People tend to think that others share their opinion, but let’s not dwell on the sociological issues this raises. Yes, symmetry and unification has historically been very successful and these are good reasons to try to use it as a guide. But is it sufficient reason for a scientist to believe that it must be true? Is this something a scientist should ever believe?
Somewhere along the line theoretical physicists have mistaken their success in describing the natural world for evidence that they must be able to recognize truth by beauty, that introspection suffices to reveal the laws of nature. It’s not like it’s only particle physicists. Lee Smolin likes to speak about the “ring of truth” that the theory of quantum gravity must have. He hasn’t yet heard that ring. String theorists on the other hand have heard that bell of truth ringing for some decades and, ach, aren’t these Calabi-Yaus oh-so beautiful and these theorems so elegant etc. pp. One ring to rule them all.
But relying on beauty as a guide leads nowhere because understanding changes our perception of beauty. Many people seem to be afraid of science because they believe understanding will diminish their perception of beauty, but in the end understanding most often contributes to beauty. However, there seems to be an uncanny valley of understanding: When you start learning, it first gets messy and confused and ugly, and only after some effort do you come to see the beauty. But spend enough time with something, anything really, and in most cases it will become interesting and eventually you almost always find beauty.
If you don’t know what I mean, watch this classic music critic going off on 12 tone music. [Video embedding didn't work, sorry for the ad.]
Chances are, if you listen to that sufficiently often you’ll stop hearing cacophony and also start thinking of it as “delicate” and “emancipating”. The student who goes on about the beauty of broken supersymmetry with all its 105 parameters and scatter plots went down that very same road.
There are limits to what humans can find beautiful, understanding or not. I have for example a phopia of certain patterns which, if you believe Google, is very common. Much of it is probably due to the appearance of some diseases, parasites, poisonous plants and so on, ie, it clearly has an evolutionary origin. So what if space-time foam looks like a skin disease and quantum gravity is ugly as gooseshit? Do we have any reason to believe that our brains should have developed so as to appreciate the beauty of something none of our ancestors could possibly ever have seen?
The laws of nature that you often find listed among the “most beautiful equations” derive much of their beauty not from structure but from meaning. The laws of black hole thermodynamics would be utterly unremarkable without the physical interpretation. In fact, equations in and by themselves are unremarkable generally – it is only the context, the definition of the quantities that are put in relation by the equation that make an equation valuable. X=Y isn’t just one equation. Unless I tell you what X and Y are, this is every equation.
So, are the laws of nature beautiful? You can bet that whatever law of nature wins a Nobel prize will be called “beautiful” by the next generation of physicists who spend their life studying it. Should we use “beauty” as a requirement to construct a scientific theory? That, I’m afraid, would be too simple to be true.