It seems to me apparent that every time I take a breath, there is a very good chance that some of the nitrogen or oxygen molecules I breath were also inspired by famous historical figures. How may I calculate just what fraction of the total this is, and hence what total I’ve re-breathed so far?
The rough answer would assume constant volume of the atmosphere, perfect mixing in the intervening time, average inhaled volume per breath (->per day ->over lifetime) and my average volume per inspiration.
One could get fancier and adjust for imperfect mixing of exhalations due to CO2 being recycled into plants, absorption of atmospheric gas by plants, oceans, etc, and so on.
This page and this page (.doc file) both discuss calculating whether or not you breathe in molecules of air breathed in by Julius Caesar each time you breathe, and if so, how many.
Both pages agree that you almost certainly constantly breathe in Caesarian air molecules, but seem to differ greatly on the final number: 10,000,000,000 molecules per breath vs. 8. However, the first site is calculating the number of air molecules you breathe in with each lungful that Caesar breathed over the course of his entire lifetime; the second, the number of molecules you inhale that were in Caesar’s dying breath. Site 1 estimates Caesar breathed in about 500,000 liters during his entire lifetime (at a rate of 1 liter an hour over a lifetime of 56 years x 365.25 days/year x 24 hours/day); Site 2 is concerned only with his last breath, which we’ll say took 1 second, or 1/3600 of 1/500,000 of his lifetime, so 8 x 3600 x 500,000 = 14,400,000,000 molecules of air in each of your lungfuls from the entire span of Caesar’s lifetime, which is quite close to the first site’s estimate of 10,000,000,000.
The first site is especially helpful in laying out the details of the estimates, simplifications, and calculations.
I’m astounded. The precise question addressed, right on the net, even with a reprint of the Goscinny-Uderzo cartoon. I can only assume that heard or saw a reference to this problem somewhere and it’s been niggling at my subconcious since.
This thread makes me think of that quote from Hamlet –
“Imperious Caesar, dead and turned to clay,
Might stop a hole to keep the wind away.
O that that earth that kept the world in awe
Should patch a wall t’expel the winter’s flaw!”
This has nothing to do with anything, really. I just like quoting Hamlet…
Of course, there’s probably a website somewhere calculating the probability of that, too.
There’s something that these calculations often seem to overlook; many of the Oxygen, Nitrogen and Carbon atoms that were in free circulation in the atmosphere at the time of Caesar will now be locked away in mineral deposits, peat bogs, living plant material and so on (conversely, there will be many atoms in free circulation now that were locked away at that time).
Both physicist Lawrence Krauss in Atom and mathematician John Allen Paulos in one of his books, Innumeracy, I believe, discuss this and come up with yet other estimates, pointing out just how many assumptions need to go into this argument.
Krauss’ whole book traces how oxygen goes into and out of circulation, so he is aware of the problem that Mangetout brings up, so he has to make one of his assumptions that the oxygen has been freely available in the atmosphere since. Whatta ya gonna do?
An even more glaring error (at least on the first page – I haven’t looked at the Word file) is that it says Caesar breathed 1 m[sup]3[/sup] of “new” air – that is, air molecules he did not previously inhale – per hour. I’m not so sure about this. Caesar very likely inhaled billions of the same molecules over and over again thousands of times. After all, if at every moment, as the article says, “your own lungs contain 10,000,000,000 of the very same molecules that were inhaled by Julius Caesar”, then wouldn’t it stand to reason that the same was true of Caesar himself?
What the solvers of this question have failed to realize is that Julius Caesar was a world class hypochondriac on the level of Howard Hughes…He KNEW that people in the future would be asking questions about the ultimate disposition of his mortal parts, excreta, and molecular associations, so he assiduously guarded all of these. He collected all of his urine, feces, and sweat, not to mention nail and hair cuttings, in various urns and had these sequestered deep in long forgotten caves. He similarly collected his various airy ehalations and erructations in sheep badders and these were similarly sequestered. His body was likewise sequestered with the utmost care to prevent any molecules from straying into contact with posterity of no account, like the OP…who might otherwise develop fat heads from the vicarious association with the Great Caesar…
