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

How To Have a Good Idea

You don't have to be human to have a good idea. You can even be a fish.

There is a large fish in shallow Micronesian waters that feeds on little fish. The little fish dwell in holes in the mud, but swarm out to feed. The big fish starts to gobble up the little fish, one by one, but they immediately retreat back into their holes, when his meal has barely begun. What to do?

I have put this problem to my classes over the years, and I remember only one student who came up with the big fish's Good Idea. Of course he did it after a little thought, not after millions of years of evolution, but who's counting?

Here is the elegant trick. When the school of little fishes appears, instead of gobbling, he swims low so that his belly rubs over the mud and blocks the escape holes. Then he can dine at leisure.

What do we learn? To have a good idea, stop having a bad one. The trick was to inhibit the easy, obvious but ineffective attempts, permitting a better solution to come to mind. That worked for the big fish, by some mechanism of mutation and natural selection in fish antiquity. Instead of tinkering with the obvious, obsessing about eating faster, taking bigger bites, etc. junk plan A, and plan B comes swimming up. For humans, supposing that the second solution still does not work, block that too, and wait. A third floats into awareness, and so on, until the insoluble is solved, even if the most intuitively obvious premises have to be overridden in the process.

To the novice the Good Idea seems magical, a leap of intellectual lightning. More likely, however, it resulted from an iterative process as outlined above, with enough experience in back to help reject seductive but misleading premises. Thus the extraordinary actually arises step by step out of the ordinary.

Having a good idea is far from rare in the evolution of non-human species. Indeed, many if not most species need to have an idea or trick that works well enough for them to continue to exist. Admittedly, they may not be able to extrapolate its principle from the context in which it emerged, and generalize it as (some) people can, courtesy of their prefrontal cortex.

When the finest minds fail to resolve a classical problem, during decades, or centuries of trying, they were probably trapped by a premise that was so culturally "given", that it did not even occur to them to challenge it, or they did not even notice it at all. But cultural context changes and what seemed totally obvious yesterday becomes dubious at best today or tomorrow. Sooner or later someone who may be no more gifted than his/her predecessors, but is unshackled from some very basic and very incorrect assumption, may hit upon the solution with relative ease.

Alternatively, one can be a fish, wait a million years or two, and see what comes up.