# Frank Morgan's Math Chat

September 2, 1999

### HUMANITY'S LIFE SPAN

OLD CHALLENGE. Estimate the life span of the human race.

ANSWER. Al Zimmermann says with 80% confidence that we have between 100,000 and 10 million years to go. Perhaps another million years is the best guess. (By comparison, the dinosaurs reigned for over 100 million years.)

Zimmermann assumes that the human race is a million years old and that as a random observer he can be 80% confident of being in the middle 80%, past the initial 10% and before the final 10%. If just before the final 10%, we'd have about 100,000 years to go. If just after the initial 10%, we'd have 10 million years to go.

Zimmermann is using the approach of the celebrated Princeton astrophysicist J. Richard Gott III, as described for example in the New Yorker of July 12. Gott has applied the same reasoning to predict successfully the lifetime of Broadway plays and musicals. For any activity, a good general rule is that with 80% confidence, the remaining time is somewhere between 1/10 and 10 times the current age. For example, the current computer era, in which computers have played the dominant innovative role for say 20 years, will probably continue another 2-200 years, with another 20 years a good guess.

Joe Shipman points out that for the life span of the human race, we should really assume that the number of people to come is about the same as the number of people so far, instead of that the time to come is about the same as the time so far. Perhaps human survival will be much briefer at very large population levels or much longer at very small population levels.