Mathematics 102

A Gamesworth

Excerpted from Platt's The Art of Creative Thinking.

I would like to suggest the convenience of having a rough unit of analytical reasoning so that we can talk more or less quantitatively about how much thinking is involved in this job or that. I think a good unit would be the amount of reasoning involved in a forty-move game of chess or a hard end-game problem, or a fairly hard (for you) crossword puzzle; that is, half an hour to an hour of problem-solving. This might be called "one gamesworth" of reasoning, to give it an obvious name. It is a useful unit because we are all acquainted with such problems and have a feeling for their difficulty easily distinguished from ten-minute problems on the one hand and from three-hour problems on the other. I also think the sequence of mental operations is fairly typical of formal thinking on complex problems, a mixture of memory, rules of procedure, deductions, analogies, inductions, evaluations and insight, all leading to an elegant and novel solution with the loose ends tied up. Also we shall see that it is a natural unit, measuring roughly the amount of reasoning most of us can do at one sitting.

Many of us do crossword puzzles every day, but I think that few do a gamesworth of serious reasoning every day. Sherlock Holmes lived for nothing else, but most people, even creative artists and scientists, are creatures of habit and only think occasionally. This is unfortunate. Our highest powers lie unfocused. ... If, one day, a hundred million adult Americans all gave one gamesworth of thought to their work, the world would tremble and mankind would never be the same again.

... when Newton was asked "how he had made discoveries in astonomy surpassing those of all his predecessors," Newton replied, "By always thinking about them."
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Actually, I believe that the time need not be very long, that no one really spends a whole working day every day in the kind of intense analysis I am talking about.
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Probably the brain, like the rest of our physiology, is designed for maximum power output in short bursts only. ... Patience and interest flag. In some sense the brain is indeed tired. I suggest that in concentrated analytical thought, one or two gamesworth every day would be about the maximum for most of us. This much actual thought--a couple of crossword puzzles' worth--is not so distressing, is it? This principle is often neglected in the long hours and numerous courses of our schools.
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Who knows what immortal little result you are but two hours away from: Have you done--or revised--your page of thought today?
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I conclude that a page or a gameworth or two of thought every day is about the maximum; and yet this amount is possible for everyone and even easy. We all confess it, in our enjoyment of the daily crossword puzzle. Real thinking is brief and it is fun. ... The daily intellectual tortoise can pass many a high-speed brain that only operates when fancy strikes.

The effort itself changes a person's outlook for the better. A gamesworth of thought takes so little time that a man who has done his hour of reasoning and has had even one idea--even a small one and still buried in the notebook--feels a sense of success and freedom for the rest of the day, or night.
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This pleasure and confidence is seductive, and makes it easy to go on with such a program--one of the motivational feedbacks.