Tuesday, July 6, 2010

Beauty in Scientific Theories

by Richard Crews
I want to start by acknowledging that "beauty" is a hard word--a hard concept--to define. Surely there is a subjective aspect. (I am reminded of my dear friend Lorenzo in Texas--one of the brightest and most smooth-sailing-through-a-complex-life sociopaths I have ever met--who had a particular affinity for very fat women; I find them ugly and unhealthy looking. He finally married one who was perhaps 5 foot 2 and 300 pounds. He even had a couple of kids with her--both of whom were born addicted to cocaine, and both of whom were taken away from an obviously unhealthy home by Social Services by the time they were a couple of months old. But I digress.)

In conjunction with its subjectivity, the "Aunt Tilly Principle" certainly applies: "beauty" (like my Aunt Tilly) is hard to "define" but easy to recognize.

Not only does "beauty" mean different things to different people, but there are even severe variations between the lexicons of standardized usages. In this regard, for example, one might be surprised to find the word "beauty" associated with "science" and suspect that in science "beauty" does not mean the same thing it means in architecture, poetry, or music.

Given those caveats, in the words of the great historian Will Durant who said (in the introduction to The Lessons of History that only a fool would attempt to summarize the eleven huge volumes of his [and his wife Ariel's] The Story of Civilization in 100 pages), "I proceed."

"Beauty" is defined as the quality that gives pleasure to the mind or senses and is associated with such properties as harmony of form or color, excellence of artistry, truthfulness, and originality. Beauty is a quality or feature that is most effective, gratifying, or telling.

Another word that sometimes subs for "beauty" in trying to capture the illusive aesthetics of scientific theory is "elegance." "Elegance" is defined as refinement, grace, and beauty in movement, appearance, or manners; tasteful opulence in form, decoration, or presentation.

Now to the question, where does beauty come into scientific theory? Let me begin with a startling quotation by Paul Dirac, a Nobel-Prize-winning physicist who was central to the development of quantum mechanics. "I might tell you the story I heard from Schrodinger of how, when he first got the idea for this equation [the famous and seminal Schrodinger Wave Equation], he immediately applied it to the behavior of the electron in the hydrogen atom, and then he got results that did not agree with experiment.... That, of course, was a great disappointment to Schrodinger, and it caused him to abandon the work for some months.... I think there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment."

Karl Popper, philosopher of science, defined four criteria for a theory to be scientifically "strong": it must be parsimonious, falsifiable, and have explanatory and predictive utility. The last three of these are not hard to understand. "Explanatory utility": the theory must be useful in explaining past observations. "Predictive utility": it must be useful in predicting the results of experiments or observations yet to be made. "Falsifiable": there must be ways of testing it and, if it is wrong, proving that it is wrong. (This is the main reason that the "theories" of creationism or "intelligent design" are not scientific: they can never be proved wrong--whatever observations appear, they are just there because God did it that way. And as you can readily see, creationism and ID also have no predictive utility.)

But the fourth criterion, parsimoniousness, is a puzzler. Essentially it says that for a theory to be scientifically strong, it should be short and sweet. The quintessential example of this is Einstein's equation relating mass and energy: E equals M C-squared (the energy bound up in a physical object is equal to its mass multiplied by the square of the speed of light).

It is an interesting reflection on the functioning of the human mind--its struggles and frustrations, its satisfactions and triumphs--that the more complicated and convoluted a theory is--the more it lacks elegance and beauty--the harder it is for it to hold its head up in the halls of science.