What does Bayes Theorem look like? I do not mean what does the formula—
—look like; these days, every statistician knows that. I mean, how can we visualize the cognitive content of the theorem? What picture can we appeal to with the hope that any person curious about the theorem may look at it, and, after a bit of study say, “Why, that is clear—I can indeed see what is happening!”
Francis Galton could produce just such a picture; in fact, he built and operated a machine in 1877 that performs that calculation. But, despite having published the picture in Nature and the Proceedings of the Royal Institution of Great Britain, he never referred to it again—and no reader seems to have appreciated what it could accomplish until recently.