He describes coming to Shannon's office one day with a new research idea full of "bells and whistles." For Shannon, though, bells and whistles were just a distraction and he proceeded to take the problem apart piece by piece. At a certain point, I was getting upset, because I saw this neat research problem of mine had become almost trivial.
As Gallager said: "He looked at it, sort of puzzled, and said, 'Well, do you really need this assumption? But at a certain point, with all these pieces stripped out, we both saw how to solve it.
He kept his own counsel, and he wasn't given to waxing philosophical on the creative process or the nature of genius. In a cache of unpublished papers deep in an online archive, we found Shannon's attempt at an answer.
It's the typed text of a March 20th, 1952, lecture to his colleagues at Bell Labs on the topic of "Creative Thinking." And it turned out to represent a tantalizingly rare window into the mind of a scientific genius — a step-by-step breakdown of Shannon's method for formulating and solving problems.
' And I said, well, I suppose we could look at the problem without that assumption. And then he said, again, 'Do you need this other assumption? And then we gradually put all these little assumptions back in and then, suddenly, we saw the solution to the whole problem.
And that was just the way he worked." It's a useful lesson, even for those of us not grappling with high-level mathematics.
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Stripping away everything inessential was just what helped Shannon get to the essence of information.
No matter the problem, Shannon said, "cut it down to size." Shannon admitted that this process could file a problem down to almost nothing, but that was precisely the point: "You may have simplified it to a point that it doesn't even resemble the problem that you started with; but very often if you can solve this simple problem, you can add refinements to the solution of this until you get back to the solution of the one you started with." Bob Gallager, a Shannon graduate student who went on to become a leading information theorist himself, saw this process of radical simplification in action.