Willful Ignorance: The Mismeasure of Uncertainty

CHAPTER 11 THE LOTTERY IN SCIENCE

The core idea underlying mathematical probability is that it is often useful to regard a particular aspect of the world as a metaphorical lottery. This expedient of regarding observed variability as if it has resulted from a lottery has provided many practical benefits. However, it can be a serious mistake to forget that this metaphor is not real. In reality, there exist actual generating processes that exhibit varying degrees of regularity. At one extreme, there are processes that are for all practical and completely deterministic purposes, such as Newton's laws of motion. At the other extreme are the subatomic phenomena described by quantum mechanics, which appear to be completely random.

Most of applied science deals with processes situated somewhere between these extremes. So, strictly speaking, the lottery model does not apply. In general, something akin to Peirce's “would-be” or Popper's propensities might be a more valid conception. However, the lottery model implicit in additive mathematical probability has come to dominate our thinking. We attempt to separate neatly the presumed regular causes from the presumed random “error.” Beginning with Galton and Pearson, our statistical theory has been built upon the idea that all “unexplained” variability must be treated as essentially random.

This assumption may seem innocuous, but in fact has had profound consequences. It has led us in many contexts to conceive (and treat) individuals as ...