Some time or other boredom may occupy your mind. Today that happened to me. So I began to think (always a dangerous thing) about breathing. Yep, breathing. At the same time my bored mind drifted to James Madison, probably due to reading, "James Madison and the Struggle for the Bill of Rights." So, I wondered about Madison and tried to calculate the possibility that the same molecules that Madison breathed, or at least a couple of them, may now be inside my lungs. Is this possible to calculate? Hmmm. Let's think about this. First one must accept the fact that the Earth's atmosphere contains the same molecules that it did during Madison's lifetime. That is a fact, since everything on the Earth is recycled, even the air. Next, one would have to know how much air there actually is. This is not easy to do, but it can in fact be done. The volume of the Earth is 4 pi r squared. That's about 200 million square miles. The atmosphere is not so easy since it thins out as you go up. But through a little searching I found that the volume of the atmosphere in liters is 5,000,000,000,000,000,000,000 or 5 times 10 to the 21st power. If the capacity of a lung is one liter, then the amount of atmosphere in your lungs is 1/5,000,000,000,000,000,000,000. Now, how many molecules are in that amount of atmosphere? One liter of gas contains 27,000,000,000,000,000,000,000 molecules. So it would be 27,000,000,000,000,000,000,000/5,000,000,000,000,000,000,000 or 5.4. So one Madison breath would be 1/5,000,000,000,000,000,000,000 of the atmosphere. On an average there is the possibility of breathing in 5.4 molecules that Madison breathed out.
Aren't you happy to know this? I am.
See what your mind can do when you are bored.