We do indeed breathe in a considerable number of molecules that once passed through Leonardo’s lungs and, unfortunately, Adolf Hitler’s or anyone else’s for that matter.
The calculation is not too difficult and is as follows.
The total mass of the Earth’s atmosphere is about 5 x 10^21 grams.
If we take air to be a mixture of about four molecules of nitrogen to one of oxygen, the mass of 1 mole of air will be about 28.8 grams. One mole of any substance contains about 6 x 10^23 molecules. So there are about 1.04 x 10^44 molecules in the Earth’s atmosphere.
A single mole of any gas at body temperature and atmospheric pressure has a volume of about 25.4 liters.
The volume of air breathed in or out in the average human breath is about 1 litre. So we can assume that Leonardo da Vinci, in one breath, breathed out about 2.4 x 10^22 molecules.
The average human takes, say, 25 breaths per minute, so during his 67-year lifetime (1452 to 1519) Leonardo would have breathed out about 2.1 X 10^31 molecules. So, about molecule in every 5 x 10^12 molecules in the atmosphere was breathed out by Leonardo da Vinci.
However, because we breathe in about 2.4 x 10^22 molecules with each breath, there is a pretty good chance we breathe in about 4.9 x 10^9 molecules that Leonardo breathed out. In fact, you can also show in a similar way that you probably breathe in about 5 molecules that he breathed out in his dying gasp.
Of course, there are some pretty crude assumptions involved here in order to arrive at the conclusion.
We assume that there has been a good mixing of Leonardo’s molecules with the rest of the atmosphere (quite likely in 500 years), that he didn’t recycle some of his own molecules, and that there is no loss from the atmosphere due to later users, combustion, nitrogen, fixation and so on.
But there is still scope for a considerable loss of molecules without it affecting the main point of the calculation.
By knowing that the number of molecules in the hydrosphere is 5.7 x 10^46 molecules, similar calculations can be made for water.
These show that a mouthful of liquid contains about 18 x 10^6 molecules that passed through Leonardo during his lifetime. So, in addition to breathing in his breath, there is also a pretty good chance of picking up some of Leonardo’s urine in every glass of water that you drink.
The law of conservation of matter ensures that atoms are constantly being recycled in the Universe.
Gravity ensures that most of those on the Earth stay there. Some of the atoms floating around were breathed by da Vinci, although the number of these atoms compared to all those in the Earth’s atmosphere would make them pretty few and far between.
However, considering the length of time in which, say, the dinosaurs inhabited the Earth, you can be pretty sure that every breath you take contains what was once part of one or more of these creatures, and that every apple you eat has many atoms that were once part of an animal, even a human.
Of course all this could have some very worrying implications for vegetarians.
This question provides some food for thought for homeopaths.
There is a very high probability that a cup of water contains a few homeopathic molecules that are effective in countering every illness we may have, and at no cost.