Willful Ignorance: The Mismeasure of Uncertainty

CHAPTER 6 A DEFECT OF CHARACTER

Before 1700, probability had a somewhat nebulous connotation, referring to a qualitative degree of certainty based on evidence, argument, and authority. In this broad sense, probability described the partial knowledge humans could obtain, in contrast with God's perfect understanding. In John Locke's famous phrase, probability expressed a kind of twilight knowledge suitable “to that state of mediocrity and probationership he has been pleased to place us in here.”¹ For us, because of our limited capacities, the world can appear confusing and uncertain.

Jacob Bernoulli was the first great thinker to attempt a quantitative formulation of this uncertainty. This quantification depended on drawing an analogy between our uncertainty in the moral, political, and economic spheres on the one hand and the randomness in games of chance on the other. In many practical situations, the outcomes are completely unpredictable except to the extent that previous experience provides some rough indication of their propensity to occur. In effect, therefore, life can be regarded as just like a lottery in which there exists an unknown proportion of winning tickets. In these situations, the probability of a particular outcome could be conceived of as the proportion of “fertile” or “favorable” chances in this lottery of life.

This formal equivalence provided a way to calculate the hidden ratio of chances. However, Jacob never took the further step of identifying the fraction ...