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I saw on the web:

La probabilité que vous buviez un verre d'eau qui contient une molécule d'eau qui est également passée à travers un dinosaure est de quasiment 100%.

This translates to:

The probability that the glass of water you are drinking contains a water molecule that a dinosaur also drank is virtually 100%

Is this true ?

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    This may sound impressive, but in fact it vastly understates the reality. The classic image is that in every breath of air that you take, there are some molecules exhaled by Caesar as he spoke his last words. This is far more impressive, since it's one specific breath. Similarly if we picked one specific dinosaur named Fred, taking his first sip of water in the morning after waking up on his 10th birthday, we would also be getting some molecules recycled from that sip. – Ben Crowell Sep 6 '14 at 23:42
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    By the way, I strongly recommend the XKCD What-If series for education on how to usefully think about big numbers and make reasonable ballpark estimates. I think he may have addressed this question there, but if not it'll still show you how one approaches such problems. – keshlam Sep 7 '14 at 19:54
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Yes, this is true – though it's in principle a bit problematic to talk about individual water molecules.

Disregarding molecules for a moment: almost all water on earth has been drunk by dinosaurs at some point. To quote from Randall Munroe's "What If" blog

Dinosaurs, as a taxonomic group, have been around for 230 million years, but their heyday was the mid-to-late Jurassic period. In this period, there were probably around 5 trillion kilograms of dinosaur alive at any given time.[11] (...)

If we assume Jurassic dinosaur water requirements were similar to mammal ones,[13] then this suggests dinosaurs drank something like 1022 or 1023 liters of water during the Mesozoic era—more than the total volume of the oceans (1021 liters).

The average "residence time" of water in the oceans—the amount of time a water molecule spends there before moving into another part of the water cycle—is about 3,000 years,[14] and no part of the water cycle traps water for more than a few hundred thousand years. This means we can assume that, over timescales of millions of years, Earth's water is thoroughly mixed—and dinosaurs had plenty of time to drink it all many times over.

This means that while the chances are that most of the water in your soda has never been in another soda, almost all of it has been drunk by at least one dinosaur.

To target your particular question in that light: the probability of any given water molecule to have been in a dinosaur is quite high, let's say more than 1/10. The probability of no such molecule in a glass of water is then less than (9/10)1023, which is < 10-1010: essentially impossible.

However, as eBusiness remarks, water molecules are subject to self-ionisation. Individual molecules can't really be considered stable. If the half-life is anything short of millenia (and apparently it's no longer than a day), this means no water molecules have survived as such from cretaceous till now, which would render the answer of your question as no.

Even if you consider "the same molecule" as "the same oxygen ion plus protons" then the answer remains no: the question would then be, if you recombine 1021+23 water molecules from their atom components, how many will get back with their original partners? The answer is, none (for pairings of two atoms the expected value would be something small, for three the increase in possible failure combinations make it neglectable).

This caveat doesn't apply if you consider a hydroxid ion as "continued existence" of water molecule, which I'd find quite reasonable since only a proton is lost – all electrons are kept with the oxygen, so the process is basically just like handing on electrons in a metal, where we also still speak of individual atoms that stay the same.

Anyway, it's a bit weird to reason about "continuity" of individual atoms or molecules at all, since quantum mechanics has it that indistinguishable things in a mixed state are the same thing, so once you can't spatially separate the molecules they don't really exist as separate entities anymore.


[11]Jerzy Trammer, Differences in global biomass and energy use between dinosaurs and mammals, Acta Geologica Polonia, Vol. 61 (2011), No. 2, pp. 125–132

[13]Animal weights and their food and water requirements

[14]K. L. Schulz, Water in the Biosphere

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    Wow ! Thanks a lot for this detailed answer ! This is an amazing fact ! – Trevör Sep 6 '14 at 14:22
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    Actually, was it molecules or atoms ? – Trevör Sep 6 '14 at 14:27
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    ... hang on, that last bit was nonsense: as Steven P said water molecules are decomposed: in photosynthesis. Which makes this question rather more interesting... – leftaroundabout Sep 6 '14 at 14:52
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    I've always been bogged down by these kind of statements. How can you say that a molecule belonged to X, since all exact molecules are indistinguishable? I guess there is some kind of classical approximation where you can track an specific particle, but I've never seen a rigorous proof. – jinawee Sep 6 '14 at 15:55
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    @leftaroundabout Actually, for swapping around the atoms of water, photosynthesis is dwarfed by self-ionization. If I understood all the numbers correctly, water molecules effectively have a half-life of ~5 seconds in pure form at room temperature. – aaaaaaaaaaaa Sep 7 '14 at 8:34

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protected by Sklivvz Sep 6 '14 at 17:32

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