Looking for a quote about problem solving
February 15, 2022 5:50 PM   Subscribe

I have a memory of a quote that I think was attributed to Dirac that goes something like this: "To solve a problem, divide it into two parts: a simple part and a small part. If you're clever, you'll be able to solve the simple part. And if you're lucky, the small part will turn out to be really small." Help me track it down?

It might have been Feynman telling a story about Dirac, or I might be wrong about Dirac altogether. Thank you!!
posted by cider to Science & Nature (5 answers total) 6 users marked this as a favorite
 
I didn't find exactly what you're looking for, but I found two perfectly good quotes from Feynman lectures on dividing things up:
When we solve a quantum-mechanical problem, what we really do is divide the universe into two parts—the system in which we are interested and the rest of the universe. We then usually act as if the system in which we are interested comprised the entire universe (from Statistical mechanics; a set of lectures, Chapter 2: Density Matrices page 39)
Also Feynman:
A poet once said, “The whole universe is in a glass of wine.” We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the earth’s rocks, and in its composition we see the secrets of the universe’s age, and the evolution of stars. What strange array of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization: all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts—physics, biology, geology, astronomy, psychology, and so on—remember that nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure: drink it and forget it all!
(from The Feynman Lectures on Physics, Volume I, The Relation of Physics to Other Sciences)
Meanwhile,
[Dirac] divided the difficulties of quantum mechanics into two classes, those of the first class and those of the second. The second-class difficulties were essentially the infinities of relativistic quantum field theory. Dirac was very disturbed by these, and was not impressed by the 'renormalisation' procedures by which they are circumvented. Dirac tried hard to eliminate these second-class difficulties, and urged others to do likewise. The first-class difficulties concerned the role of the 'observer', 'measurement', and so on. Dirac thought that these problems were not ripe for solution, and should be left for later. He expected developments in the theory which would make these problems look quite different. It would be a waste of effort to worry overmuch about them now, especially since we get along very well in practice without solving them. (John S. Bell, "Against 'measurement'", Physics World (August 1990) via wikiquote)
posted by the antecedent of that pronoun at 6:19 PM on February 15, 2022 [8 favorites]


That sounds VERY MUCH like something that might have been said about strategies for finding integrals. It almost rings a bell for me.

I’m not having any luck on Google, but if that rings a bell for you too maybe it can help guide your searches.
posted by mekily at 9:57 PM on February 15, 2022


I think it may possibly be an intuitive explanation of integration by parts or a related technique.
posted by mekily at 10:09 PM on February 15, 2022 [1 favorite]


This sounds like it's about approximations in physics to me. Here's an equation made up of two parts, find the part you can solve and figure out some conditions where the part you can't solve "goes to zero." (Is very small relative to the rest )
posted by Lady Li at 6:13 AM on February 16, 2022 [1 favorite]


If there's a pithy saying on the sciences, it's probably Feynman :) But I'll add my $0.02 for George Polya, whose "How to Solve It" and other writings are pervaded with the same spirit as your quote describes.
posted by adekllny at 6:23 AM on February 16, 2022


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