Statistics-Physics question

Chatting with a co-worker today, we joked about not wanting to breathe the same air as a particular porcine supervisor. Which led to this set of questions.

  1. Say Jones and Typhoid Bob were in a plane (or other relatively small “closed” system). Can Jones reduce the chance of breathing Bob’s cooties ? (Put another way, does the probability of sharing molecules, as it were, increase faster with the size of the cabin or the length of the flight ?)

  2. What about in a very large closed system, say, a convention center ?

  3. What about “open” systems, say, Bermuda ?

O le mea a tamaali’i fa’asala, a o le mea a tufanua fa’alumaina.

Well I’m going to generalize here, and ignore circulation or filtering with outside air, such as in an airplane. Also neglecting the degraded contagiousness of cooties over time in air at temperature.

Germs, cooties, particles, whatever are assumed to immediately be dispersed evenly throughout a gas in most basic physics problems. This obvioulsly isn’t the way it works, but it does happen very quickly, and after a few minutes it doesn’t matter if your right next to the guy or in seat 37E. The concentration is the variable, that is only dependant on volume, not on distance away from the source. So in a closed system, if the volume of the chamber increases the concentration of the cooties decreases cubicly.

If you are in a open system, like a beach it can be assumed that the cooties are immediately dispersed to infinitesmally small concentrations, except in very close proximity.

A thing to add in the airplane situation, again as long as the cooties don’t degrade and the air isn’t circulated or filtered. Assuming the person expells cooties at a constant rate, the concentration will increase at a constant rate over time. So length of the plane (volume) and length of flight both effect contagiousness. Proximity to subject has no real effect.

In real life the planes air is filtered and exchanged with fresh air constantly, so depending on the efficiency of this system the length of flight is no longer important.

Lets answer your questions systematically:

1)The probability of sharing molecules increases linearly with time. It increases cubically as the volume of the aircraft decreases.

2)Given our assumptions, a large convention center offers a 3rd order decrease in probability relative to the aircraft’s volume.

3)Open systems can be assumed to have a infinately small probability of molecule exchange.

You have a molecule in your body that was probably in Jesus.

By the sheer number of molecule in each breath, each breath you take has molecules from the last breath of Jesus, Einstein, Ghandi, and everyone else whose ever lived.

Dogs love cheese

Thanks, Omniscient. The OP was along those lines (I had written “closed”, etc… in quotes to suggest skipping things like air exchange etc…), to answer the [silly & facetious] question of whether we should choose distance over time when considering occasions to come into contact with management (3 days on Kauai or 4 days on bigger Oahu ? DC-10 or 757 to the mainland ? etc…)

I was somehow trying to figure how the dispersal would figure into it (chaotic motion of the air ?) as opposed to the at-equilibrium assumption of even-distribution, but for the purposes of the admittedly weak humor involved, that’s too much math, and gets suspiciously close to the “1,000,000 Chinese jumping off chairs” style of question.

But now, this ?

That seems, statistically, pretty suspicious (even putting aside trees, combustion engines, gamma rays and whatnot)

I agree that Mr Thin Skin’s assertion is suspicious. While there are lots of molecules in each breath, there are even more lots (sorry!) of molecules in the atmosphere. And, of course, they don’t even have to be in the atmosphere anymore.

Besides, I think it’s pretty unlikely that many of Jesus’s molecules still exist. But I guess that most of his atoms do, and maybe you’re lucky enough to breathe one of those.

Well, of course I read that somewhere. I just can’t remember where. Let me try some numbers on you.

Radius of Earth: 6336 km
Depth of Atmosphere: 20 km (just a guess)
Normal breathing volume of MY lungs: 2 l
liters per mole (at STP): 22.4 l/M
molecules per mole: 6.02E23


molecules/breath: 5.375E22
volume atmosphere: 1.01E22 l
volume atmosphere (in breaths): 5.06E21 B

So assuming that 2005 years is sufficient for equal distribution, there’s on the order of 10 molecules from some 2 l batch in a 2 l batch today.

This is chancy at best.

I don’t know how reactive atmospheric nitrogen is; I don’t know what is the turnover of molecules in the atmosphere; I really don’t know the number of moles of air molecules in the atmosphere; but I do remember reading this once :slight_smile:


At least my final number was greater that 1.

Jorge, did you read what Cecil said about toilet plumes? Yes, when you visit the bathroom, you are throughly breathing your supervisors ummm, whatever he puts in the toilet. Assuming he actually uses the bathroom. With this fantastic information, you can amaze your coworkers.