Red-Blooded Risk: The Secret History of Wall Street

Exponentials and Culture

But we're not going to talk only about play, probability, and money. There will be an entire chapter on exponentials. The mathematical definition of an exponential is something with a rate of growth proportional to its level. The bigger it gets, the faster it grows. These relate to risk for three reasons.

The first reason is that if you examine a sudden, dramatic change, it usually turns out to be an exponential. It was small and growing slowly for a long time, and was unnoticed as a result. Exponentials work both ways: The smaller it is, the more slowly it grows. Once it starts getting big, it grows so fast that it seems to come out of nowhere. By that time it has lost its exponential character, as nothing physical can grow forever. It hits up against some limit. People describe it as a Black Swan, an unanticipated event—in fact, one that was impossible to anticipate—and focus on the sudden growth and spectacular collision with its limit. Anyone serious about risk has to concentrate on the exponential nature instead. Once the thing becomes obvious, it's usually too late either to avoid its danger or to exploit its opportunity. Nonexponentials are much easier to deal with. If they are big or fast growing, you notice them. If they are small or slow growing, they don't cause a lot of problems or offer a lot of opportunities.

The second reason to discuss exponentials goes back to the 1956 discovery by physicist John Kelly that exponentials trump risk. If you ...