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The Rule of Three: A/B = C/D
We came across an interesting passage in our former professor Stephen Stigler’s “The Seven Pillars of Statistical Wisdom.”
Charles Darwin had little use for higher mathematics. He summed up his view in 1855 in a letter to his old friend (and second cousin) William Darwin Fox with a statement that Karl Pearson made famous: “I have no faith in anything short of actual measurement and the Rule of Three.” In 1901, Pearson adopted this as the motto for the new journal Biometrika … it was as close to an endorsement of mathematics as Pearson could find in Darwin’s writing.
Darwin was surely right in valuing actual measurement, but his faith in the Rule of Three was msiplaced. The Rule of Three that Darwin cited would have been familiar to every English schoolboy who had studied Euclid’s book 5. It is simply the mathematical proposition that if a/b = c/d, then any three of a, b, c, and d suffice to determine the fourth. For Darwin, this would have served as a handy tool for extrapolation, just as it had for many other before him … In the 1600s, John Graunt and William Petty ahd used such rations to estimate population and economic activity; int he 1700s and early 1800s, so, too, did Pierre Simon Laplace and Adolphe Quetelet.
Neither Darwin nor anyone before him realized what weak analytical support the Rule of Three provides. The rule works well in prorating commercial transactions and for the mathematical problems of Euclid; it fails to work in any interesting scientific question where variation and measurement error present …
1) The rule of three. Who knew it had that name? Could be a good way to get your kids interested in it.
2) The other rule of three we know is in comedy, where it’s pretty darn important.
2) Who knew that Darwin and Pearson had little faith in fancy math? Wonder what they’d make of modern statistical methods.