One Hundred Interesting Mathematical Calculations, Number 7: Archive Entry From Brad DeLong's Webjournal
One Hundred Interesting Mathematical Calculations, Number 7 One Hundred Interesting Mathematical Calculations, Number 7: Julius Caesar's Last Breath What's the chance that the breath you just inhaled contains at least one air molecule that was in Julius Caesar's last breath--the one in which he said (according to Shakespeare) " Et tu Brute ? Then die Caesar"? Assume that the more than two thousand years that have passed have been enough time for all the molecules in Caesar's last breath to mix evenly in the atmosphere, and that only a trivial amount of the molecules have leaked out into the oceans or the ground. Assume further that there are about 10 44 molecules of air, and about 2 x 10 22 molecules in each breath--yours or Caesar's. That gives a chance of 2 x 10 22 /10 44 = 2x 10 -22 that any one particular molecule you breathe in came from Caesar's last breath. [1-2x10 -22 ] [2x10^22] How to evaluate this? [e [-2x10^(-22)] ] [2x10^(22)] From John Allen Paulos's Innumeracy .