Claude Shannon on Problem-Solving

Thursday, March 22, 2018

Over at Business Insider is a thought-provoking piece on how Claude Shannon, the father of Information Theory, attacked problems. We are all quite fortunate in this regard, because the introverted Midwesterner was hardly the Cal Newport of his era: He explained his process ... once, in a 1952 lecture for his colleagues at Bell Labs. The authors found this lecture in Shannon's archives and have been kind enough to pass his advice on. Rob Goodman and Jimmy Soni list and summarize the highlights of the process before pointing to the entire lecture. I found the first bit of advice, below, to be Feynmaneqsue:

Claude Shannon (Image via Wikipedia)
Step one, Shannon said, you should approach a problem -- any problem -- 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."

Shannon's information theory, for instance, began with a colossal simplification: It treated every source of information, from a TV broadcast to a gene, as fundamentally the same. All of the information that they send can be measured in the same unit -- the bit -- and they can all be studied as instances of the same basic process of encoding, transmitting, and decoding. 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." ...
The full list of techniques -- I'm not sure I'd call them "steps" -- is:
  1. Simplify. Simplify. Simplify.
  2. Fill your 'mental matrix' with solutions to similar problems.
  3. Approach the problem from many different angles.
  4. Break a big problem down into small pieces.
  5. Solve the problem 'backwards.'
  6. If you've solved the problem, extend that solution out as far as it will go.
Shannon's work was seminal not just to my thesis topic back in grad school, but to my entire field, so I have no trouble seeing the value of hearing out Shannon. But for anyone who doubts he may have something to say, consider the following:
At each stage, he found bridges between fields that had no prior connection. For his PhD dissertation, he applied algebra to the science of genetics and produced publishable work within a year, despite having no background as a biologist or geneticist. His years of work on symbolic logic and electrical engineering provided him with a wealth of portable concepts that shed new light on the field.
Whatever you need to tackle, I think Shannon's advice is worth considering.

-- CAV

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