Clippings

It’s been estimated that, because of the exponential growth of the world’s population, between 10 and 20 percent of all the human beings who have ever lived are alive now. If this is so, does this mean that there isn’t enough statistical evidence to conclusively reject the hypothesis of immortality?

First, take a deep breath. Assume Shakespeare’s account is accurate and Julius Caesar gasped “You too, Brutus” before breathing his last. What are the chances you just inhaled a molecule which Caesar exhaled in his dying breath? The surprising answer is that, with probability better than 99 percent, you did just inhale such a molecule.

For those who don’t believe me: I’m assuming that after more than two thousand years the exhaled molecules are uniformly spread about the world and the vast majority are still free in the atmosphere. Given these reasonably valid assumptions, the problem of determining the relevant probability is straightforward. If there are N molecules of air in the world and Caesar exhaled A of them, them the probability that any given molecule you inhale is from Caesar is A/N. The probability that any given molecule you inhale is not from Caesar is thus 1 − A/N. …if you inhale B molecules, the probability that none of them is from Caesar is approximately (1 − A/N)^B. Hence, the probability of the complementary event, of your inhaling at least one of his exhaled molecules, is 1 − (1 − A/N)^B. A, B (each about 1/30th of a mole, or 2.2 × 10²²), and N (about 10⁴⁴ molecules) are such that this probability is more than .99.

Why is it, incidentally, if all the 3,838,380 ways of choosing six numbers out of forty are equally likely, that a lottery ticket with the numbers 2 13 17 20 29 36 is for most people much preferable to one with the numbers 1 2 3 4 5 6? This is, I think, a fairly deep question.