Red-Blooded Risk: The Secret History of Wall Street

Principle VI: Superposition

The traditional analysis of randomness had one embarrassing weakness until the early 1900s. No one could demonstrate that randomness existed. A coin flipped in the air obeys the laws of physics; it seems random only because it's complicated to compute whether it will land heads or tails. We may not know what the top card on a deck is, but that doesn't make it random. If randomness was just ignorance, as some people argued, then it should obey the rules of psychology, not the rules of mathematics. To avoid bringing subjectivity into the calculation, other people invented elaborate constructs of randomness that frequently led to contradictions.

About a century ago, physicists discovered that something like true randomness existed on a microscopic scale. Unfortunately, it did not behave at all the way a coin flip did. If I hide a ball under a cup, you may not know where it is, but it is under one and only one cup. However, a subatomic particle acts as if it's under all the cups at once, until you lift one. (This is a gross simplification, but sufficient to understand the risk model, just not enough to understand the physics.) This phenomenon is called superposition, and it allows outcomes that are impossible if the particle remained in any single fixed location. For example, with superposition you could pick up all the cups one at a time without finding the ball, even if you know the ball is always under a cup.

There is an important macroscopic analogy. ...