Shannon left little behind in the way of memoir, and the closest he ever came to autobiography was a talk he delivered in a Bell Labs auditorium in the same year that Theseus made its public debut. Fittingly, the talk revealed nothing of his background or his private life, but it was the kind of autobiography that mattered to him: a window into the workings of his brain. Ostensibly a lecture on “Creative Thinking,” it turned out to be a tantalizingly brief tutorial on the appearance of the world from the eyes of a Shannon-level genius.
In one sense, the world seen through such eyes looks starkly unequal. “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.” He was not, he quickly added, claiming membership for himself in the mental aristocracy—he was talking about history’s limited supply of Newtons and Einsteins. Of course, he was also lecturing a roomful of America’s most gifted scientists on the prerequisites of genius, so one imagines that his humility only extended so far. In any case, once the prerequisites of talent and training had been satisfied, a third quality was still missing—something without which the world would have its full share of competent engineers but would lack even one real innovator.
It was here, naturally, that Shannon was at his fuzziest. It is a quality of “motivation . . . some kind of desire to find out the answer, the desire to find out what makes things tick.” For Shannon, this was a requirement: “If you don’t have that, you may have all the training and intelligence in the world, [but] you don’t have the questions and you won’t just find the answers.” Yet he himself was unable to nail down its source. As he put it, “It is a matter of temperament probably; that is, a matter of probably early training, early childhood experiences.” Finally, at a loss for exactly what to call it, he settled on curiosity. “I just won’t go any deeper into it than that.”
But then the great insights don’t spring from curiosity alone, but from dissatisfaction—not the depressive kind of dissatisfaction (of which, he did not say, he had experienced his fair share), but rather a “constructive dissatisfaction,” or “a slight irritation when things don’t look quite right.” It was, at least, a refreshingly unsentimental picture of genius: a genius is simply someone who is usefully irritated.
And finally: the genius must delight in finding solutions. It must have seemed to Shannon that though many around him were of equal intellect, not everyone derived equal joy from the application of intellect. For his part, “I get a big bang out of proving a theorem. If I’ve been trying to prove a mathematical theorem for a week or so and I finally get the solution, I get a big bang out of it. And I get a big kick out of seeing a clever way of doing some engineering problem, a clever design for a circuit which uses a very small amount of equipment and gets apparently a great deal of result out of it.” For Shannon, there was no substitute for the “pleasure in seeing net results.”
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? Here Shannon was more concrete: he proposed six strategies, and the fluency with which he walked his audience through them—drawing P’s for “problems” and S’s for “solutions” on the chalkboard behind him for emphasis—suggests that these were all well-trodden paths in his mind.
You might, he said, start by simplifying: “Almost every problem that you come across is befuddled with all kinds of extraneous data of one sort or another; and if you can bring this problem down into the main issues, you can see more clearly what you’re trying to do.” Of course, simplification is an art form in itself: it requires a knack for excising everything from a problem except what makes it interesting, a nose for the distinction between accident and essence worthy of a scholastic philosopher. 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.
Failing this difficult work of simplifying, or supplementing it, you might attempt step two: 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. Call it ingenious incrementalism—or, as Shannon put it, “It seems to be much easier to make two small jumps than the one big jump in any kind of mental thinking.”
If you cannot simplify or solve via similarities, 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.” Avoid “ruts of mental thinking.” In other words, don’t become trapped by the sunk cost, the work you’ve already put in. There’s a reason, after all, why “someone who is quite green to a problem” will sometimes solve it on their first attempt: they are unconstrained by the biases that build up over time.
Fourth, 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. “Many proofs in mathematics have been actually found by extremely roundabout processes,” Shannon pointed out. “A man starts to prove this theorem and he finds that he wanders all over the map. He starts off and proves a good many results which don’t seem to be leading anywhere and then eventually ends up by the back door on the solution of the given problem.” Fifth, 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. Finally, once you’ve found your S, by one of these methods or by any other, take time to see how far it will stretch. The math that holds true on the smallest levels often, it turns out, holds true on the largest. “The typical mathematical theory is developed . . . to prove a very isolated, special result, [a] particular theorem. Someone always will come along and start generalizing it.” So why not do it yourself?
In each of these methods, it’s difficult to miss the echoes of Shannon’s own work: the great simplification that turned computer relays into a shorthand for the language of logic, or the great generalization that identified the rules underlying every system of communication. Yet it is one thing to put these modes of thinking into words—and something else entirely to live inside them. Shannon seemed to recognize as much: “I think that good research workers apply these things unconsciously; that is, they do these things automatically.” He went on to express his rationalist faith that any researcher would benefit from naming the tools, from making the unconscious conscious. But if it were really that simple, then why is it that “a very small percentage of the population produces the greatest proportion of the important ideas”? If there was any tension in the auditorium when he concluded—and invited the audience up to the front to examine a new gadget he’d been tinkering on—it was between Shannon the reluctant company man and Shannon the solitary wonder. The latter was as elusive as ever.
There is a famous paper on the philosophy of mind called “What Is It Like to Be a Bat?” The answer, roughly, is that we have no idea. What was it like to be Claude Shannon?