The book’s central debate involves competing epistemologies — in this case, a philosophy that supports scientific decision-making. The seemingly obvious idea is the brainchild of Thomas Bayes, an 18th-century renegade priest and amateur mathematician. “Bayes’s rule’’ seems banal in its simplicity. “[B]y updating our initial belief about something,’’ McGrayne writes, “with objective new information, we get a new and improved belief.’’ Isn’t this how everyone negotiates the world? But the implications for scientific inquiry were staggering, and have remained contentious until the beginning of our 21st century. Why? Notice that the rule commences with belief. Starting from informed belief — hunches, guesses, intuition — Bayes, or actually his more sophisticated successors, devised formal ways of measuring whether additional information added or detracted from the probability that one’s initial notion was true.
Bayes’s theoretical, epistemological opponent is “frequentism.’’ For frequentists, belief means nothing; objectivity and validity occur only through repeated observation of a replicable phenomenon until enough data is amassed for a meaningful sample. The theoretical structure of frequentist statistics presumes that something that has never happened in the past can never happen in the future. This distorts reality. As McGrayne shows, for frequentists, statistically speaking, airplanes couldn’t collide in mid-air. Until, of course, they do, at which point it’s a bit late to calculate the probability of error or determine an actuarial table.
