Ummm

[dukeblack]

Okay. I realise that the module Statistical Physics and Entropy is about making assumptions and working with statistics, but I think our most recent assessed question is taking the piss. Here, I quote:

Make a fully reasoned order of magnitude estimate of the number of molecules from Julius Caesar's last breath which were also present in your

Comments

[livingarmchair]

It's an interesting question. Caesar's last breath would have entered the atmosphere and over the years the molecules would have been spread evenly around the Earth's atmosphere due to various forces of nature. Therefore, there's a good chance that you're breathing in at least one molecule from caesar's last breath... I suppose you're last breath will contain x molecules, so there's a good chance that you'll have one of caesar's in it...

Won't it be something like x molecules in caesar's last breath. Y molecules in the atmosphere...

Then if your breath is z (Which is close to x, so call it x) you get (x^2) /(Y)... as something... It's been so long (16 years?) since I last did anything like this!!!

Fuck knows what I'm talking about!!!!!

[dukeblack]

Well, 16 years or not there's nothing wrong with your reasoning! That's pretty much the logic I have used.

The only difference being that I haven't chosen to include my own lung capacity at the end. I've simply left it as the number of molecules he exhaled compared to the number of molecules in the whole atmosphere. Otherwise I would probably have to start dealing with permutations and I think I would end up with some scary numbers.

[livingarmchair]

And here you go, freshly googled:

http://www.j-bradford-delong.net/movable_type/archives/001392.html

The chance is apparently 98.8%.

My probability calculation was completely wrong... You have to look at every molecule and multiply the probabilities for each molecule together as they're unconnected events (Don't you have to use binomial theorem if the events are connected?) It's been 20 years since I did probabilities! God knows why e comes into it. I can't even remember why you use that sucker anymore!

My brain hurts at the moment. I've just been researching time travel and quantum phsyics/multiverse stuff for a short story... Which isn't really about time travel or quantum phsyics, but that stuff provides a nice McGuffin for me to play with.

And I'm listening to Tangerine Dream as well.

[dukeblack]

98%? Whut? *scratches head*

They have made the same assumptions I did (that in 2000 years the molecules distribute themselve across the whole atmosphere; no molecules absorbed by organisms or water etc.). However, as you inhale molecules, with each molecule slipping down the windpipe, you're altering the odds. Hence why I thought of permutations (choosing some number of objects/outcomes from the total available). Hmmm. I need sleep before I think this one through again.

What I've ended up with is the probability per molecule. Ugh. Dang. Sleep.

[livingarmchair]

There's no odds in that calculation - he's calculated the probability that a molecule of air is from Caesar and then multiplied it up (It's all coming back to me now...)

There's an equal chance of each molecule being from ceasar...

[dukeblack]

Yes, but his method - to calculate the opposite, when the molecule does not come from Caesar - in the form (1 - x) would tend towards one (1) as we multiply out each probability. I'm going to investigate the approximation using e and see how that is validated.

[dukeblack]

Yes, precisely. This is one of the unrealistic assumptions I had to make before beginning the calculation: that all the molecules JC breathed out in that last breath are still in the atmosphere and are available for me to breathe in. It is pretty much nonsensical really. It's more an exercise of stating assumption and getting a reasonable estimate.

My answer came to 2 molecules. 2 molecules that JC breathed out, I breathed in with pretty much every breath. Utter rot!

[dukeblack]

On second thoughts I'm not sure I would have to deal with permutations. I shall ponder that when I've had some sleep!