Thursday, January 05, 2006

Strogatz's "Dangerous Idea" and the Nature of Insight

Disclaimer: My background is in biology and I have no right to comment on mathematics. That said, I will proceed to do so. has once again asked over a hundred prominent scientists and other thinkers a provocative question. This year, the question was, "What is your dangerous idea?".

Steven Strogatz's answer is particularly intriguing. Strogatz, of network and complex systems fame, comments on the use of computers in mathematical proofs, writing "we're able to figure out what's true or false, we're less and less able to understand why". Somehow, to him this means that "insight is becoming impossible". He concludes,
When the End of Insight comes, the nature of explanation in science will change forever. We'll be stuck in an age of authoritarianism, except it'll no longer be coming from politics or religious dogma, but from science itself.
But what is insight and do computers threaten it? Mathematical facts -- theorems -- automatically come with explanations -- proofs. In other sciences, however, facts and the theories that explain them are distinct. Rocks fall. The Galapagos Islands have 14 slightly different finch species. I submit that insight is what it takes to go from these sundry observations to the theories of evolution and gravity.

The first step in science is making observations. Mathematicians have not traditionally been able to do this, at least not as an initial step. Now they can, and the nature of the discipline may approach that of the other sciences. Facts may get ahead of structures of thought and require ex post facto explanations. Is this really a tragedy?

There is one more response to Strogatz' worries. Computers, for all their power, do what they are programmed to do. No computer can test a conjecture that did not originate in a human brain or answer a question that a human did not ask. Surely there's room enough for insight in questioning and conjecturing.