Caesar's last breath

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We are told that we breathe in one or more molecules of Caesar's last breath with each lungfull. I was told this when I was at school and didn't believe it but have have taken a while to come up with a way of showing it to be false. i may be wide of the mark but here goes...

If we take the date of Caesar's death as the time it takes for the breath (10 to the 22 molecules) to spread out evenly it follows that we are breathing in a molecule from every breath of his life, as well as every breath of every person alive at the time, as well as every breath of every person who has lived before him, as well as every breath of every air breathing being with a lung capacity equal to, or larger, than a human's.

15 breaths per minute for 70 years is about 500 million per person. Say there were 10 million people in the world at the time makes 10 to the 15 breaths. Say that there have been at least that population of the above mentioned organisms since they first appeared 200 million years ago makes it up to 10 to the 24 which means we can't get that many molecules into our lungs at once.

Not including, on the minus side, re-breathing, but on the plus side, molecules taken out of the system by plants etc.

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Coming to think of it I reckon I'm doing alright on the 'air breathing organisms' front 'cause I suddenly thought of all the domestic animals through the ages. I reckon 10 mil of them is well conservative. That might even make up for the fact they don't live 'til 70.

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Never mind your sheep, what about the wild ones? What about the wildebeest? That's got to be another handful of noughts. I reckon we're almost there. MY lungs aren't THAT big.

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Does it still count as Ceasar's last breath if the oxygen has been combined with carbon by burning, rebreathing, etc., and inhaled as carbon dioxide? Same question for nitrogen that has become fixed in the soil. Gotta keep up with those variables, ya know? Or do you?

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Fair point. I don't know. I was under the impression that Fermi (for it was he) was on about the ACTUAL molecules, 'cause that's the maths he used. He (apparently) says that each lung full has 10 to the 22 molecules in it, and the Earth's atmosphere has 10 to the 44 molecules in it (roughly speaking). This then gives a 1 : 10 to the 22 chance of any one molecule breathed in by oneself being one of big nose's, which, when we recall that we breath in 10 to the 22 molecules, leaves us with a chance of 1. The way I see it if you want to muck about with numbers you need to set your rules out first, and he made no mention of combustion, oxidation etc so they are better left out of the picture. As far as I am concerned he made the statement and I, using the logic previously described, am saying it is bs.

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If an outcome has a 1:10^22 chance of occurring, and it's given 10^22 opportunities, the probability is NOT 1 that it will occur.

Given Fermi's numbers, the probability of it not occurring with each breath is 1/e.

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Right oh. So does that mean it is true or not? about breathing in a molecule of Caesar's last breath?

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Just using Fermi's numbers and ignoring all of the (probably valid) issues raised in the other posts, it is unlikely that you would go very long without breathing in a molecule of Caesar's last breath.

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Well well. What do you know? Thanks for that.

What do you reckon?, evey third breath takes one in?

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rogers point is valid. You have to look at it as a mass balance , not a poetic exercise. lets take an analog. Approximately 700 billion tons of CO2 are produced by all forms of repiration and power plants etc each year. The entire planet has a potential CO2 uptake that fixes CO2 in approximately the same amount. So Co2 in 44BC may, or may not be precipitated as carbonate chunks or frozen in the deep ocean, or sucked under by convection (so therefore unavailable as respiratory fluid)
Oxygen has the same Pchem dynamic on our planet and theres even an amount that skids off in space.
So, forget the total number of ions , wed have to look at the "engine" of respiration for the entire planet to see whether those molecules would be "in play" realistically.

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Thanks for that farmerman. From what you have suggested it seems that as time goes on there is less and less chance of breathing one of His molecules in again as they are increasingly being taken out of the system. With regard to the actual last breath the amount left would be sliding down an exponential? I still prefer the how many breaths have there been altogether argument.

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What about re-release?
But the molecules being pulled out of the system are being replace with formally removed molecules being reintroduced. You could assume that there is an equilibrium established where the molecules removed and the molecules re-introduced balance out.

I think the original argument is faulty because the molecules are reused. It doesn't matter about the organisms alive before or after since they were reusing the air. I think the correct formula would be

1 - (1 - (Ceaser Molecules)*(Equilibrium percentage)/(Total Air Molecules))^(Your breath molecule count)

Where Equilibrium percentage is the fraction of air that is breathable at any time and total air molecules is what is available to breathe world-wide.

Remembering that (1 - small number)^large number = e^(-small number*large number) and if you assume that you and Ceaser have roughly the same lung capacity then you get

1 - e^(-(Ceaser)^2(Equilibrium percentage)/(Total) )

If (Ceaser^2*Equilibrium percentage)/(Total molecules in Air) > 5, give it to your teacher. If not, you have an argument. I don't know the total molecules in air, but that 10^22 squared looks pretty scary.

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That was great in that I must really print it out and get a pencil to draw some pictures. I'm not convinced about the 'if molecules are taken out of the system they will be going back in' argument. I mean, it is true what you say, but then we get into geological time (oxygen becoming part of iron oxide and getting buried, carbon dioxide getting used by plants, becoming wood, and getting buried). Also, even if it DOES get back into the atmosphere it is unlikely to be the SAME molecule.

I agree on the rebreathing front, but I would hesitate to suggest that all the lungfuls taken over the years have been the same lungfuls.

Going back to the original argument, and this has all been very instructive, that there is enough of the original molecules to have one per lungful if they were distributed around the world, does it not mean that if it can be demonstrated that there have been more breaths taken by the animals previously mentioned (all of which have an equal chance of being breathed in) then we simply cannot accomodate that many molecules in our lungs.

Coming to think of it maybe the difference is the amount rebreathed.

Oh Bugger, back to the drawing board....

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engineer. This is great. I suggest we set up a theoretical experiment, similar to a Lincoln Index for Oxygen. We could trace the oxygen by tagging a fixed ratio of atmosphere that is taken in , within a fixed atmospheric system. Then , say, using a duck (Gus has a surfeit of ducks). Then we do an uptake/energy balance and follow the respiration (what percent is metabolized and used in Blood and biomass , as opposed to just respiration)
Then that which is exhaled is free to become part of the atmosphere wherein, a certain percentage of hydroxyl or oxygen ions are used in oxidation, methanagenic reactions, adsorption etc.
All we need is a duck and a tank and some land.

This would be the mass balance to end all mass balances

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Why use a duck? A duck floats, and what else floats? Wood. That's what. Since they're basically the same thing, you could just put a chunk of wood inside and save yourself the trouble of finding a duck. You're obviously not wise in the ways of science.[/thinly-veiled-monty-python-reference]

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engineer. The number of molecules in the atmosphere is put at 10^44. That is the scary number.

You would need a duck AND some wood, connected to a tree (the wood, not the duck).

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That fills in the answer

Quote:

The number of molecules in the atmosphere is put at 10^44

Well then, that answers the question. If all the Ceaser molecules are available, then Ceaser^2/Total Air = 1. You need 5 to say that you are likely breathing a Ceaser molecule every time. It's fair to say that you are breathing some molecules Ceaser breathed during his death, but not his final breath.

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Excellent. Thank you. As I suspected. When you say 'during his death' and using the number 5 can we say that we are breathing in one molecule from any one of his last 5 breaths? breath, breath, breath, et tu brutus, ugh.

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Numbers got to be correct
Let's just hope that one of the numbers is not off by an order of magnitude. Not knowing your 10^44 molecules in air number, I tried to calculate it myself and got 4*10^42. If that were correct, it would mean that we are getting several Ceaser molecules with each breath. Based on this level of uncertaincy, please don't track down your former teacher for a confrontation.

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Numbers from
http://paulburney.com/thoughts/caesars_breath.html
and
http://www.vendian.org/envelope/dir2/breath.html
and
http://www.hk-phy.org/articles/caesar/caesar_e.html
and
http://wine1.sb.fsu.edu/chm1045/notes/Gases/Density/Gases05.htm
there are others.

No conFRONTation intended, I'm going to creep up from behind.

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Caesar's last breath

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