"The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12." There are people lauding a

"The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12." There are people lauding and panning Feynman in this thread, but this story illustrates a very important lesson that I've seen a lot of very smart people fail to learn. Whenever you're doing a calculation, especially if you're using a computer or calculator, make an approximate estimate of what the result should be. Don't just assume that whatever method you use will produce a correct answer. A man with an abacus (or computer) is probably going to be faster than someone like Feynman most of the time, but he's also going to make mistakes. Big ones. He might not make them frequently, but mistakes always happen sooner or later. The trick is to catch them when they do happen. That's hard to do if you have absolutely no sense of what the answer should be. If, however, you start from a rough estimate using anything your brain can come up with, as Feynman does in his anecdote, you're a lot less likely to produce a badly wrong answer without realizing it. If this contest had gone on long enough, Feynman would have been beaten badly in several rounds if he messed up a calculation and had to start over. The thing is, Feynman would know when this happened because the outcome wouldn't agree with his initial estimate. The man with the abacus would, eventually, have produced answers off by several orders of magnitude without realizing. Rough estimates are important.