2012 : WHAT IS YOUR FAVORITE DEEP, ELEGANT, OR BEAUTIFUL EXPLANATION?

The Limits Of Intuition

We sometimes tend to think that ideas and feelings arising from our intuitions are intrinsically superior to those achieved by reason and logic. Intuition—the 'gut'—becomes deified as the Noble Savage of the mind, fearlessly cutting through the pedantry of reason. Artists, working from intuition much of the time, are especially prone to this belief. A couple of experiences have made me more sceptical.

The first is a question that Wittgenstein used to pose to his students. It goes like this: you have a ribbon which you want to tie round the centre of the Earth (let's assume it to be a perfect sphere). Unfortunately you've tied the ribbon a bit too loose: it's a meter too long. The question is this: if you could distribute the resulting slack—the extra meter—evenly round the planet so the ribbon hovered just above the surface, how far above the surface would it be?

Most people's intuitions lead them to an answer in the region of a minute fraction of a millimeter. The actual answer is almost 16 cms. In my experience only two sorts of people intuitively get close to this: mathematicians and dressmakers. I still find it rather astonishing: in fact when I heard it as an art student I spent most of one evening calculating and recalculating it because my intuition was screaming incredulity. 

Not many years later, at the Exploratorium in San Francisco, I had another shock-to-the-intuition. I saw for the first time a computer demonstration of John Conway's Life. For those of you who don't know it, it's a simple grid with dots that are acted on according to an equally simple, and totally deterministic, set of rules. The rules decide which dots will live, die or be born in the next step. There are no tricks, no creative stuff, just the rules. The whole system is so transparent that there should be no surprises at all, but in fact there are plenty: the complexity and 'organic-ness' of the evolution of the dot-patterns completely beggars prediction. You change the position of one dot at the start, and the whole story turns out wildly differently. You tweak one of the rules a tiny bit, and there's an explosion of growth or instant armageddon. You just have no (intuitive) way of guessing which it's going to be.

These two examples elegantly demonstrate the following to me:

a) 'Deterministic' doesn't mean 'predictable', 
b) we aren't good at intuiting the interaction of simple rules with initial conditions (and the bigger point here is that the human brain may be intrinsically limited in its ability to intuit certain things—like quantum physics and probability, for example), and 
c) intuition is not a quasi-mystical voice from outside ourselves speaking through us, but a sort of quick-and-dirty processing of our prior experience (which is why dressmakers get it when the rest of us don't). That processing tool sometimes produces incredibly impressive results at astonishing speed, but it's worth reminding ourselves now and again that it can also be totally wrong.