A jar of air
Would you buy a jar of air that supposedly contained molecules breathed by Angelina Jolie or Brad Pitt? Maybe - but would you pay $15,000 for it?! Some enterprising character was selling just that last week - a jar which he’d opened then shut as Jolie and Brad Pitt walked past, possibly (but with no guarantee!) trapping air that they’d breathed inside.
Okay, so this is a ridiculous (but effective…) money making scheme, but one has to wonder - how true was his claim really? This would be a great real-world example of a Fermi problem, named after famous physicist Enrico Fermi. A Fermi problem asks you to estimate something, that you couldn’t intuitively guess at, by making rough but educated guesses about a number of things and putting them together to reach a sensible answer. Examples might be “What is the mass of a fully loaded cement truck?” or “How many blades of grass are in a football field?” or even, “How far would the Earth move if everyone in China jumped at once?”
In this case, I can think of at least two interesting questions - “How many molecules breathed by Jolie and Pitt would likely be in that jar?” and “In any (open!) jar anywhere in the world, how many molecules are likely to have been breathed by Jolie or Pitt some time in their lives?” I haven’t done any guesstimations yet, but I’d expect that both answers are non-zero.
If anyone would like to have a go, a couple of starting points might be to estimate how much air our lungs hold (perhaps by large a single breath can inflate a balloon?), how many breaths we make in a minute/hour/day/year, and how old Angelina and Brad are. Then, estimate how much air there is in the whole world…and so on! Remember that all you’re going for is an order of magnitude estimate - round things to the nearest 100 or 1000 or whatever to keep it simple.
Let me know…
Luke Lea Says:
Actually, I know the answer to this problem from past discussion: the probability is very high (close to 1) that there is at least one molecule of air in our lungs at any given moment which was also, at some point, in the lungs of any other adult living or dead. You, too, can sell those jars with air from: Napoleon, Shakespeare, Jesus, Helen of Troy, etc…..
Les Says:
I think you need to take into acount the movement of the air. As the movement of the air is not truly random, you would need to make some sort of guess at just how old the person has to be before air reaches this side of the world to say you have some of their air. (assuming no travelling of the individual. )
illuminating science » Follow up on air molecules Says:
[…] es
Filed under: General — Joel @ 3:49 pm
If you didn’t read the comments to that post about a guy selling Angelina Jolie’s air, then I highly recommend […]
Josh Says:
It is physically impossible to breathe out the full 5 litres of your lung capacity. If you did, your lungs would collapse and your blood wouldn’t be getting any oxygen and you would suffocate =]
You actually only breathe out about 0.5 l of air during rest (just breathing normally).
Sorry to mess up your calculations!
I’ll have a shot at it (by the way, though I never made the connection myself, Wikipedia reports that such calculations are also called back of the envelope calculations in maths which also kinda made the transition to other areas).
A quick Google gives the average (full) lung capacity as something around 5 litres.
Let’s say you take a breath every 3 seconds (as a rough way to average out breaths you take during your life, including exercising and sleeping).
IMDB says that Angelina Jolie is 30 years (and ten days!) old, and Brad Pitt is about 42 years old. How nice of them to have ages divisible by three
So Angelina has taken (roughly) 300 million breaths during her life. Brad, roughly 400 million.
If each of those are full-lung breaths, and they get celebrity-free air each breath, that’s 1.5 billion liters for Ms Jolie and 2 billion liters for Mr Pitt.
Three-quarters of the atmosphere is contained within 11km from the Earth’s surface (Thanks Wikipedia). For Fermi’s sake, let’s say 10km and that that air is all that’s in consideration. The Earth has a radius of roughly 6000km. So there is 4/3*Pi(6010^3 - 6000^3) which is roughly 4 billion cubic kilometers of air. Which is 4×10^21 liters. Man, that’s a lot.
In the roughest sense, if you collect 100 billion liters of air, one of those will be Brad’s or Angelina’s (or both, cha-ching!). This scales to the molecule level, so out of every 100 billion molecules, one will be celebrity-blessed. This means that one hundred billionth of that jar contained Brad/Angelina molecules. If the jar was (say) a liter, then for a buck fifty you can get about 2.5 billion billion molecules of Brad/Angelina goodness. It sounds like a bargain if you put it like that (and I’ve done my calculations correctly
)
But then in a very rough sense, about that much has also gone through Hitler’s lungs, or maybe Einstein’s, or maybe Osama Bin Laden’s, or maybe Jesus’. So really you’re not going to get exactly the molecules you want, you may get a mixed bag (for better or worse).