Aright, so I did some
calculations, and I thought I should repost them here:
This cartoon poses some interesting science questions - specifically, what are the odds that the water you're drinking now was once part of charlemagne (and optionally, napoleon's as well) testicles?
To solve this we need to make some pretty big assumptions:
Firstly, that water doesn't exchange out of the water cycle. There are lots of ways it can do, such as photosynthesis, geothermal subduction, evaporation into space, but over the last 1200 years or so most of the water that was liquid is still liquid. The volume of water in the ocean (which will have been in free circulation) dominates any small terms from locked-up polar ice. Thus, the size of the water cycle is our working pool, which is about 1.25e21 liters, 1.25e24 grams, or 7e46 molecules.
The next big assumption is that a person's daily water output enters the water cycle and the vast majority never returns to them. Of course some molecules will inevitably cycle back, but for the purposes of a simple approximation, a person's daily water cycle commitment will be fully exchanged with the environment. Thus, 2 liters/day * lifespan gives a good estimate of the total volume of water that's been in a person.
Charlemagne: ~70 years * 365.25 * 2 liters/day = ~51,000 liters (fraction = 2.9e-17)
Napoleon: 50 years * 365.25 * 2 liters/day = ~ 36,000 liters (fraction = 4e-17)
The next big assumption concerns the testicles. Between consumption and excretion, every molecule of water (probably) circulates through every organ in the form of blood. The fraction that don't will probably be <5%, which is swamped by our other errors. So every molecule of those 36,000 liters has been in Napoleon's balls.
A glass of water is about 200ml, or 2e25 molecules, so
each glass of water will contain about 580 million molecules of water that have been in Napoleon's balls, and about 800 million molecules that have been in Charlemagne's balls.
Barring any non-random link such as napoleon's alleged thirst for the occult and power leading him to eat parts of the preserved corpse of Charlemagne, some small fraction of Napoleon's water will also have been in Charlemagne. How small? we already worked it out! It's just the two fractions from before.
So, total molecules of water in the world which have been in both men's balls:
2.9e-17 * 4e-17 = 1.16e-33, or about 80 trillion molecules (when multiplied by the total water on earth)
What are the odds that one of those molecules is in a specific glass of water?
a glass of water is 2e25 molecules randomly chosen from the water cycle. When we multiply that by the fraction of double-balled water in the world (1.16e-33) this gives us an expected molecule number much less than 1, specifically 1e-8. You're safe for now!
In fact, the expected number of double-ballers you'll drink in your entire life is only 1.16e-33 (double-balled molecule fraction) * 4e-17 (assuming you live 70 years like Charlemagne, that's the fraction of earth water you'll drink!) * 7e46 (molecules of water in the world), or 0.003.
So, odds are someone you know will drink a molecule of double-french balls somewhere in their life, but it probably won't be you.
Aright, so I did some [url=http://accidentallyinformative.blogspot.com/2011/10/fun-science-water-cycle.html]calculations[/url], and I thought I should repost them here:
This cartoon poses some interesting science questions - specifically, what are the odds that the water you're drinking now was once part of charlemagne (and optionally, napoleon's as well) testicles?
To solve this we need to make some pretty big assumptions:
Firstly, that water doesn't exchange out of the water cycle. There are lots of ways it can do, such as photosynthesis, geothermal subduction, evaporation into space, but over the last 1200 years or so most of the water that was liquid is still liquid. The volume of water in the ocean (which will have been in free circulation) dominates any small terms from locked-up polar ice. Thus, the size of the water cycle is our working pool, which is about 1.25e21 liters, 1.25e24 grams, or 7e46 molecules.
The next big assumption is that a person's daily water output enters the water cycle and the vast majority never returns to them. Of course some molecules will inevitably cycle back, but for the purposes of a simple approximation, a person's daily water cycle commitment will be fully exchanged with the environment. Thus, 2 liters/day * lifespan gives a good estimate of the total volume of water that's been in a person.
Charlemagne: ~70 years * 365.25 * 2 liters/day = ~51,000 liters (fraction = 2.9e-17)
Napoleon: 50 years * 365.25 * 2 liters/day = ~ 36,000 liters (fraction = 4e-17)
The next big assumption concerns the testicles. Between consumption and excretion, every molecule of water (probably) circulates through every organ in the form of blood. The fraction that don't will probably be <5%, which is swamped by our other errors. So every molecule of those 36,000 liters has been in Napoleon's balls.
A glass of water is about 200ml, or 2e25 molecules, so [b][color=#FF0000]each glass of water will contain about 580 million molecules of water that have been in Napoleon's balls, and about 800 million molecules that have been in Charlemagne's balls.[/color][/b]
Barring any non-random link such as napoleon's alleged thirst for the occult and power leading him to eat parts of the preserved corpse of Charlemagne, some small fraction of Napoleon's water will also have been in Charlemagne. How small? we already worked it out! It's just the two fractions from before.
So, total molecules of water in the world which have been in both men's balls:
2.9e-17 * 4e-17 = 1.16e-33, or about 80 trillion molecules (when multiplied by the total water on earth)
What are the odds that one of those molecules is in a specific glass of water?
a glass of water is 2e25 molecules randomly chosen from the water cycle. When we multiply that by the fraction of double-balled water in the world (1.16e-33) this gives us an expected molecule number much less than 1, specifically 1e-8. You're safe for now!
In fact, the expected number of double-ballers you'll drink in your entire life is only 1.16e-33 (double-balled molecule fraction) * 4e-17 (assuming you live 70 years like Charlemagne, that's the fraction of earth water you'll drink!) * 7e46 (molecules of water in the world), or 0.003. [b][color=#FF0000] So, odds are someone you know will drink a molecule of double-french balls somewhere in their life, but it probably won't be you.[/color][/b]