number theory

 In sff.net, jerry said “i figure there will be at least one similar [Doomsday] event per century with say a 1% chance of destroying humanity, so with my simple calculations our expected lifetime is 100*100 = 10,000 years.”


I must be a compulsive teacher or something. If there’s a 1% chance of humanity destroying itself in any given century, then the probability that humanity will not destroy itself in n centuries is (0.99)^n -- so for a hundred centuries it’s 0.99 to the hundredth power, which is about 36.6%.

But it seems to me (if I may be allowed an optimistic moment) that if we do survive the first century after the development of doomsday weapons, then that bespeaks a maturity that may reduce the probability of destroying humanity in succeeding years, and centuries.

Something to think about as memorial day approaches.

Joe