Clippings

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.