## [2011-Oct-15] Fun Science Teaching!

Blame Quintushalls for this.

Moderator: Kimra

### [2011-Oct-15] Fun Science Teaching!

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.
patrickthomson

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### Re: [2011-Oct-15] Fun Science Teaching!

Another big assumption here: that water exiting a person enters a worldwide, well-mixed water cycle from which drinking water is drawn. For most of the water out there, that's a reasonable assumption. For the water we drink, it may or may not be, depending on where you live. In some areas, drinking water comes primarily from aquifers, which can have very slow mixing rates with the rest of the world's water. Suppose you're drinking a glass of tap water in Nebraska. It probably just came out of the Ogallala aquifer. Most of the water in the aquifer has been sitting right there for a lot longer than 1200 years. Very few French testicle atoms, if any.

The other assumption that could use some examination... I interpreted the comic as suggesting that the dude on the left was ingesting atoms that had in fact been a constitutive part of the testicles, rather than atoms that were simply in the blood that flowed through them. There does seem to be a worthwhile distinction between atoms involved in moving oxygen & whatnot around the body, and atoms involved in producing sperm & testosterone. The later would presumably be much rarer in the world's water supply.
aspidoscelis

### Re: [2011-Oct-15] Fun Science Teaching!

I think we're pretty safe of the likelihood of drinking Charlemagne's balls.
Quintushalls

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### Re: [2011-Oct-15] Fun Science Teaching!

I don't know science but I know an atom cannot contain another atom so the odds are zero. (Check Spelling in the challenge)
danilosierrac

### Re: [2011-Oct-15] Fun Science Teaching!

I'm pretty sure the chances are zero because Charlemagne is currently asleep in the mountain Untersberg for a time when his kingdom needs him the most so he can rise again and save us all. I mean, I'm pretty sure that's basic history there.
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### Re: [2011-Oct-15] Fun Science Teaching!

Holy crap, where was he when the Nazis occupied France?
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Eisbreaker
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### Re: [2011-Oct-15] Fun Science Teaching!

Eisbreaker wrote:Holy crap, where was he when the Nazis occupied France?

Charlemagne has a different sense of morality than most.

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### Re: [2011-Oct-15] Fun Science Teaching!

Well he was King of what's now modern day Germany and France. Maybe he was conflicted?
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### Re: [2011-Oct-15] Fun Science Teaching!

Don't forget that the human body constantly replaces cells at an average of once per seven years or something to that effect. If Charlemagne had a completely different set of testicles every seven years, you effectively have to multiply the number of cells that were once a part of them by 10 or so.
nanamin

### Re: [2011-Oct-15] Fun Science Teaching!

It's not the same rate for all of the cells in the body, though. And telomeres don't replicate.

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### Re: [2011-Oct-15] Fun Science Teaching!

Eisbreaker wrote:Holy crap, where was he when the Nazis occupied France?

Charlemagne has a different sense of morality than most.

Does that mean he was ubermensch?
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