During the early 1980s, I had the wonderful fortune to spend a great deal of time with Richard Feynman, and our innumerable conversations extended over a very broad range of topics (not always physics!). At that time, I had just finished re-reading his wonderful book, The Character of Physical Law, and wanted to discuss an interesting question with him, not directly addressed by his book:
Why is our sense of beauty and elegance such a useful tool for discriminating between a good theory and a bad theory?
And a related question:
Why are the fundamental laws of the universe self-similar?
Over lunch, I put the questions to him.
"It's goddam useless to discuss these things. It's a waste of time," was Dick's initial response. Dick always had an immediate gut-wrenching approach to philosophical questions. Nevertheless, I persisted, because it certainly was to be admitted that he had a strong intuitive sense of the elegance of fundamental theories, and might be able to provide some insight rather than just philosophizing. It was also true that this notion was a successful guiding principle for many great physicists of the twentieth century including Einstein, Bohr, Dirac, Gell-Mann, etc. Why this was so, was interesting to me.
We spent several hours trying to get at the heart of the problem and, indeed, trying to determine if it was even a true notion rather than some romantic representation of science.
We did agree that it was impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. It wasn't that mathematics was just another language for physicists, it was a tool for reasoning by which you could connect one statement with another. The physicist has meaning to all his phrases. He needs to have a connection of words to the real world.
Certainly, a beautiful theory meant being able to describe it very simply in terms of fundamental mathematical quantities. "Simply" meant compression into a small mathematical expression with tremendous explanatory powers, which required only a finite amount of interpretation. In other words, a huge number of relationships between data are concisely fit into a single statement. Later, Murray Gell-Mann expressed this point well, when he wrote, "The complexity of what you have to learn in order to be able to read the statement of the law is not really very great compared to the apparent complexity of the data that are being summarized by that law. That apparent complexity is partly removed when the law is formed."
Another driving principle was that the laws of the universe are self similar, in that there are connections between two sets of phenomena previously thought to be distinct. There seemed to be a beauty in the inter-relationships fed by perhaps a prejudice that at the bottom of it all was a simple unifying law.
It was easy to find numerous examples from the history of modern science that fit within this framework (Maxwell's equations for electromagnetism, Einstein's general-relativistic equations for gravitation, Dirac's relativistic quantum mechanics, etc.,), but Dick and I were still working away at the fringes of the problem. So far, all we could do was describe the problem, find numerous examples, but we could not answer what provided the feeling for great intuitive guesses.
Perhaps, our love of symmetries and patterns, are an integral part of why would embrace certain theories and not others. For example, for every conservation law, there was a corresponding symmetry, albeit sometimes these symmetries would be broken. But this led us to another question: Is symmetry inherent in nature or is it something we create? When we spoke of symmetries, we were referring to the symmetry of the mathematical laws of physics, not to the symmetry of objects commonly found in nature. We felt that symmetry was inherent in nature, because it was not something that we expected to find in physics. Another psychological prejudice was our love for patterns. The simplicity of the patterns in physics were beautiful. This does not mean simple in action the motion of the planets and of atoms can be very complex, but the basic patterns underneath are simple. This is what is common to all of our fundamental laws.
It should be noted that we could also come up with numerous examples where one's sense of elegance and beauty led to beautiful theories that were wrong. A perfect example of a mathematically elegant theory that turned out to be wrong is Francis Crick's 1957 attempt at working out the genetic coding problem (Codes without Commas). It was also true that there were many examples of physical theories that were pursued on the basis of lovely symmetries and patterns, and that these also turned out to be false. Usually, these were false because of some logical inconsistency or the crude fact that they did not agree with experiment.
The best that Dick and I could come up with was an unscientific response, which is, given our fondness for patterns and symmetry, we have a prejudice — that nature is simple and therefore beautiful.
Since that time, the question has disappeared from my mind, and it is fun thinking about it again, but in doing scientific research, I now have to concern myself with more pragmatic questions.
AL SECKEL is acknowledged as one of the world's leading authorities on illusions. He has given invited lectures on illusions at Caltech, Harvard, MIT, Berkeley, Oxford University, University of Cambridge, UCLA, UCSD, University of Lund, University of Utrecht, and many other fine institutions. Seckel is currently under contract with the Brain and Cognitive Division of the MIT Press to author a comprehensive treatise on illusions, perception, and cognitive science.