Willful Ignorance: The Mismeasure of Uncertainty

CHAPTER 8 BABEL

Mathematical probability as we know it arose somewhat fortuitously. It gradually supplanted a much older and more ambiguous sense of probability that had prevailed for many centuries. This new mathematical probability grew directly out of the mathematics of games of chance, and was thus not possible until, in the mid-1650s, a critical mass of mathematical talent happened to be focused, albeit momentarily, on such games. It was then not until the 1680s that Jacob Bernoulli first conceived of probability as being calibrated on a scale between zero and one, and 1718 before another lone genius, Abraham de Moivre, defined probability as a fraction of chances.

This classical definition of probability was still not firmly established until Pierre-Simon Laplace promoted its broader appreciation and application in the late 1700s. By around 1800, this version of probability had become the “obvious” way to think about uncertainty. When an outcome (or conclusion) was uncertain, it was as if the result was chosen by chance, as by a lottery or similar random mechanism. That is, we could regard the outcome as being determined by a metaphorical lottery. The laws of nature would of course determine the outcome, but our limited knowledge about the underlying causal processes would place us in the position of a spectator who observes a game of chance. So, Laplace could assert famously that probability is the measure of our ignorance. By this, he meant that probability is the means ...