Friday, March 09, 2007

Drinking sweet holy Jesus

Shelley at scienceblogs has a post about bottled holy water. This reminds me of the after-dinner back-of-the-napkin calculation that my dad showed me as a kid, in order to demonstrate the size of a mole. The calculation is this:

Determine how many molecules of Jesus are in the glasses on the dinner table.

Assume the following:
That Jesus was a person who actually existed, that he died about 2000 years ago, and that the molecules of his body still exist on Earth.

If you believe in the literal ascension of Jesus to a heaven that is not chemically mixed with the Earth’s atmosphere, that’s fine too; keep following the math and I’ll get back to your point of view at the end.

Please also assume that Jesus weighed 65 kilograms (143 pounds), and that 60% of his body weight was water. This is not an unreasonable bodyweight for that time period, and it makes the math easy.

At present, we are only concerned with the water molecules in Jesus. How many are there? This is determined by dividing the total mass of water by the formula weight, then multiplying by Avogadro’s number.

65kg *0.6 water content = 39 kg of water
39 kg = 39000 g water
39000g / 18 g per mol = 2167 moles water.
2167 moles * 6.022e23 molecules per mole = 1.3e27 total molecules of H2O in Jesus.

So, where is this water?

Assuming that he evaporated during ascension, or was buried in a tomb that allowed evaporation or groundwater flow, then it is likely that Jesus’ water has found its way to the ocean. The ocean has a mixing time of approximately 1000 years, so since Jesus died almost 2000 years ago, it is a reasonable assumption that the water molecules of his body have been homogenously diluted by the entire volume of all the world’s oceans.

What is that volume? According to various sources, it is approximately 1.3 billion cubic kilometers. Because a cubic kilometer is a trillion liters, the total volume of the oceans is 1.3e21 liters.

So, to determine the Jesus dilution factor, we divide the total number of Jesus molecules by the total volume of the oceans.

1.3e27 molecules / 1.3e21 liters = 1e6 molecules per liter.

Each liter of ocean water (and rain water, and tap water, and wine) contains a million molecules of Jesus.

In other words, when multiplied by Avogadro’s number, Jesus is bigger than all the world's oceans- by six orders of magnitude.

For the information of any Satanists who wish to avoid drinking Jesus, I should point out that there are a few sources of water that are isolated from the hydrological cycle for timescales longer that the Reign of our Lord. Fossil aquifers such as the Ogallala or the Great Artesian Basin contain groundwater that fell as rain tens of thousands of years ago, well before Jesus’ time. The Greenland and Antarctic ice sheets sequester ice for hundreds of thousands of years, so only the top layer will contain molecules of Jesus. And fossil fuels, which have been preserved in the sedimentary record for tens to hundreds of millions of years, can be burned to produce CO2 and water vapor, which will be devoid of Jesus’ water molecules.

So what does this mean?

First of all, transubstantiation is moot. The wine already contains a million molecules per liter that derive from Jesus’ blood via the hydrologic cycle. So no further change is necessary. In fact, a miracle is only necessary if, as mentioned above, you believe that Jesus’ body literally disappeared from the Earth during ascension. And even then, the math will still get you.

Because even if a liter of water- or communion wine- doesn’t contain a million molecules of Jesus, it does contain an equal number of molecules of Judas*. And Pontius Pilate*. And of every other scoundrel, heathen, and prehistoric caveman ever to walk the face of the planet. So you’ll probably be needing that miracle you pray for.

The oceans may seem large. People may seem like insignificant specks on the surface of this pale blue dot. But Avogadro’s number is big enough to make up the difference and more. 6.022x10 23 is a very big number.

* This assumes that Judas and Pilate had the same stature and body mass index as Jesus, and that neither of them bodily ascended to heaven upon their demise. I think these are safe assumptions.


Lab Lemming said...

According to our carbon 14 guy, the mixing time of the oceans is around 2500 years, not 1000. So for the next five centuries, this will be a hypothetical situation. Until then, the concentrations calculated here should be a minimum, as the deep ocean will be undersaturated in molecules from religious/historical figures.

David Penington said...

Cute post. Thanks.
But... don't plants metabolise water during photosynthesis? If so, the water molecules will be split up and then reconstituted over time. Are there any back of the envelope calculations of how much water goes through this process, and how this compares to the ocean volume ?

Yami McMoots said...

And what about splitting into H+/OH- for acid/base whooserwhatsits?

You could do the calculation for individual atoms instead, but then you hit deep philosophical questions of identity - if you get hit by a cosmic ray and turn into C-14, are you still the same carbon atom you always were? What if you used to be oxygen, and now you're beryllium?

I propose sensitivity trainings so that crystal structures can accomodate more of their trans-elemental members' needs, rather than passively allowing them to diffuse out of the system. It'd make exposure dating so much easier.

Lab Lemming said...

I actually have no idea what the dissociation / recombination rate for seawater is. But it should be fairly easy to figure out, given a gas mass spec and a bucket of mixed H2O and D2O.

And 14C is formed by an n, p reaction with 14N, so the last time it was a stable C isotope was during its formation in the heart of a long-dead star.

David Penington said...

I can partly answer the H+/OH- question:
pH = -log(concentration of H3O+ ions)
log base 10, concentration in Mole/Litre (modified for 'activity'), so in neutral water (Ph 7) 0.1 micromole per litre is H3O+, and a litre of water is about 55 mole.
Wikipedia says seawater is slightly alkaline (pH 7.5 to 8.4) so about one molecule in 10^9 is disassociated into H3O+, and I guess about one in 10^7 is OH-.
I don't know how long they stay split up. I imagine the OH- ions tend to steal hydrogen from neighbouring H2O, resulting in a bit of an atomic shuffle.

Stephen Fretwell said...

Now we need to consider all the entanglement issues that have long been related to communion, as well as the observer effect of modern physics. After all, Jesus did insist that we "remember" Him as we ate and drank. So, in one form or another, probably entangled sub-atomic particles of Him are handy as we eat and drink, and as we observe them, (remember Him) we might be entangling the particles already existing in our bodies, and so be "touched" by His presence.

Easy enough experiment to run. Take a problem you want to see "touched," sip some wine while remembering Him, and see whether or not, like the woman with an issue of blood who consciously touched the hem of His robe, it gets fixed.