A Beautiful Explanation For Why The Human Mind May Seem To Have An Elegant Explanation Even If It Doesn't
On reading "The Origin of Species" Erasmus Darwin wrote to his brother Charles in 1859: "The a priori reasoning is so entirely satisfactory to me that if the facts won't fit in, why so much the worse for the facts." Some of the facts—such as Kelvin's calculation of the age of the Earth—looked awkard for Darwin's theory at the time. But the theory of natural selection was too beautiful to be wrong. The brother was sure the troublesome facts would have to change. And so they did.
But it doesn't always work that way. Elegance can be misleading. Consider a simple mathematical example. Given the sequence 2, 4, 6, 8, what rule would you guess is operating to generate the series? There are several theoretically possible answers. One would be the simple rule: take the previous number, x, and compute x + 2. But equally valid for these data would be the much more complicated rule, take the previous number, x, and compute
-1/44 xexp3 + 3/11 xexp2 + 34/11
For the sequence as given so far, the first rule is clearly the more elegant. And if someone, let's call her Tracey, were to maintain that, since both rules both work equally well, she was going to make a personal choice of the second, we would surely think she was being deliberately contrarian and anti-elegant. Tracey Emin not Michelangelo.
But suppose now Tracey were to say: "I bet if we look a little further we shall find I was right all along." And suppose, when we do look further, we find to our surprise that the next number in the sequence is not 10, but 8.91 and the next after that not 12 but 8.67, i.e. the sequence we actually discover goes 2, 4, 6, 8, 8.91, 8.67. Then what had previously seemed the better rule would no longer fit the facts at all. Yet—surprise, surprise—the second rule would still fit nicely. In this case we should be forced to concede that Tracey's anti-elegance had won the day.
How often does the real world tease us by seeming to be simpler than it really is? A famous case is Francis Crick's 1959 theory of how DNA passes on instructions for protein synthesis using a "comma free code". As Crick wrote many years later "Naturally [we] were excited by the idea of a comma-free code. It seemed so pretty, almost elegant. You fed in the magic numbers 4 (the 4 bases) and 3 (the triplet) and out come the magic number 20, the number of amino acids." But alas this lovely theory could not be squared with experimental facts. The truth was altogether less elegant.
A tease? I'm not of course suggesting that Nature was deliberately stringing Crick along. As Einstein said, God is subtle but he is not malicious. In this case the failure of the most elegant explanation to be the true one is presumably just a matter of bad luck. And, assuming this doesn't happen often, perhaps in general we can still expect truth and beauty to go together (as no doubt many of the other answers to this Edge Question will prove).
However I believe there is one class of cases where the elegance of an untrue theory may not be luck at all; where indeed complex phenomena have actually been designed to masquerade as simple ones—or at any rate to masquerade as such to human beings. And such cases will arise just when, in the course of evolution, it has been to the the biological advantage of humans to see certain things in a particularly simple way. The designer of the pseudo-elegant explananda has not been God, but natural selection.
Here is my favorite example. Individual humans appear to other humans to be controlled by the remarkable structures we call "Minds". But the surprising and wonderful thing is that human "minds" are quite easy for others to read. We've all been doing it since we were babies, using the "folk theory" known to psychologists as "Theory of Mind" (or sometimes as "belief desire psychology"). Theory of Mind is simple and elegant, and can be understood by a two-year old. There's no question it provides a highly effective way of explaining the way people behave. And this skill at mind-reading has been essential to human survival in social groups. Yet the fact is Theory of Mind could never have worked so well unless natural selection had shaped human brains to be able to read—and to be readable by—one another in this way. Which is where the explanatory sleight of hand comes in. For, as an explanation of how the brain works, Theory of Mind just doesn't add up. It's a purpose-built over-simplified deep, elegant myth. (A myth whose inadequacy may not become apparent perhaps until those "extra numbers" are added by madness or by brain damage—contingencies which selection has not allowed for).
I find this explanation of the elegance of Theory of Mind beautiful.