Elegance is more than an aesthetic quality, or some ephemeral sort of uplifting feeling we experience in deeper forms of intuitive understanding. Elegance is formal beauty. And formal beauty as a philosophical principle is one of the most dangerous, subversive ideas humanity has discovered: it is the virtue of theoretical simplicity. Its destructive force is greater than Darwin's algorithm or that of any other single scientific explanation, because it shows us what the depth of an explanation is.
Elegance as theoretical simplicity comes in many different forms. Everybody knows Occam's razor, the ontological principle of parsimony: Entities are not to be multiplied beyond necessity. William of Occam gave us a metaphysical principle for choosing between competing theories: All other things being equal, it is rational to always prefer the theory that makes fewer ontological assumptions about the kinds of entities that really exist (souls, life forces, abstract objects, or an absolute frame of reference like electromagnetic ether). We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances—Isaac Newton formulated this as the First Rule of Reasoning in Philosophy, in his Principia Mathematica. Throw out everything that is explanatorily idle, and then shift the burden of proof to the proponent of a less simple theory. In Albert Einstein's words: The grand aim of all science … is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms.
Of course, in today's technical debates new questions have emerged: Why do metaphysics at all? Isn't it simply the number of free, adjustable parameters in competing hypotheses what we should measure? Is it not syntactic simplicity that captures elegance best, say, the number fundamental abstractions and guiding principles a theory makes use of? Or will the true criterion for elegance ultimately be found in statistics, in selecting the best model for a set of data points while optimally balancing parsimony with the "goodness of fit" of a suitable curve? And, of course, for Occam-style ontological simplicity the BIG question always remains: Why should a parsimonious theory more likely be true? Ultimately, isn't all of this rooted in a deeply hidden belief that God must have created a beautiful universe?
I find it fascinating to see how the original insight has kept its force over the centuries. The very idea of simplicity itself, applied as a metatheoretical principle, has demonstrated great power—the subversive power of reason and reductive explanation. The formal beauty of theoretical simplicity is deadly and creative at the same time. It destroys superfluous assumptions whose falsity we just cannot bring ourselves to believe, whereas truly elegant explanations always give birth to an entirely new way of looking at the world. What I would really like to know is this: Can the fundamental insight—the destructive, creative virtue of simplicity—be transposed from the realm of scientific explanation into culture or onto the level of conscious experience? What kind of formal simplicity would make our culture a deeper, more beautiful culture? And what is an elegant mind?