Notes from Claude Shannon's talk on where great ideas come from
Why does history have such limited supply of Newtons and Einsteins?
"A very small percentage of the population produces the greatest proportion of the important ideas," Shannon began, gesturing toward a rough graph of the distribution of intelligence. "There are some people if you shoot one idea into the brain, you will get a half an idea out. There are other people who are beyond this point at which they produce two ideas for each idea sent in. Those are the people beyond the knee of the curve."
Prerequisites: talent, training, and curiosity. But then the great insights don’t spring from curiosity alone, but from dissatisfaction — genius is simply someone who is usefully irritated. And finally: the genius must delight in finding solutions.
Presuming that one was blessed with the right blend of talent, training, curiosity, irritation, and joy, how would such a person go about solving an actual mathematical or design problem?
Some strategies:
- First, simplify: excising everything from a problem except what makes it interesting. From the standpoint of Shannon’s information theory, for instance, the difference between a radio and a gene is merely accidental, and yet the difference between a weighted and an unweighted coin carries essential weight.
- Encircle your problem with existing answers to similar questions, and then deduce what it is that the answers have in common — in fact, if you’re a true expert, your mental matrix will be filled with P’s and S’s, a vocabulary of questions already answered.
- try to restate the question: Change the words. Change the viewpoint.... Break loose from certain mental blocks which are holding you in certain ways of looking at a problem.
- Mathematicians have generally found that one of the most powerful ways of changing the viewpoint is through the structural analysis of a problem— that is, through breaking an overwhelming problem into small pieces.
- Problems that can’t be analyzed might still be inverted. If you can’t use your premises to prove your conclusion, just imagine that the conclusion is already true and see what happens — try proving the premises instead.