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A very basic estimate to answer this question is to calculate how much air you breath in and out with each breath, and then compare that to the amount of air we could breathe in the atmosphere.

The diameter of the earth is about 13000 km. Let's assume that atmospheric pressure is 1 ATM from sea level to 1 km in altitude. Calculate the volume in this slice of atmosphere (ID = 13000 km, OD = 13001 km). Humans breathe in about 500 mL of air per breath. Compare these two numbers for your basic estimate.

Of course this is not really right. CO2 that Shakespeare breathed out is probably part of a tree or stuck at the bottom of the ocean, but that's no fun to calculate.

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Q: Is it likely that when a person takes a breath they are inhaling the atoms of Shakespeare's last breath?
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