[T]ake a deep breath. Assume Shakespeare's account is accurate and Julius Caesar gasped "You too, Brutus" before breathing his last. What are the chances you just inhaled a molecule which Caesar exhaled in his dying breath? The surprising answer is that, with probability better than 99%, you did just inhale such a molecule.
For those who don't believe me: I'm assuming that after more than two thousand years the exhaled molecules are universally spread about the world and the vast majority are still free in the atmosphere. Given these reasonably valid assumptions, the problem of determining the relevant probability is straightforward. If there are N molecules of air in the world and Caesar exhaled A of them, then the probability that any given molecule you inhale is from Caesar is A/N. The probability that any given molecule you inhale is not from Caesar is thus 1 - A/N. By the multiplication principle, if you inhale three molecules the probability that none of these three is from Caesar is [1-A/N]3. Similarly, if you inhale B molecules, the probability that none of them is from Caesar is [1-A/N]B. Hence the probability of the complimentary event, of your inhaling at least one of his exhaled molecules, is 1-[1-A/N]B. A, B (each about 1/3oth of a liter, or 2.2 x 1022), and N (about 1044 molecules) are such that this probability is more than .99. It's intriguing that we're all, at least in this minimal sense, eventually part of one another.
The above passage comes from Innumeracy: Mathematical Illiteracy and its Consequences, by John Allen Paulos. I picked it up from the Quincy library yesterday and after only thirty pages, I'm alread confused and amazed. The amount of information Paulos gleans from very simple facts, although not earth shattering is at least amazing. For instance, he claims it takes a mere 367 people to assure that more than one person will have the same birthday. Extremely interesting reading.
And yes, I know I need to update the currently reading section... Maybe I should look into using all consuming instead.
does the model account for gaseous molecules that are converted into biomass by plants and microbes?
i will try to track this book down. it sounds like i would like it. you might also be interested in Carl Sagan's "the demon-haunted world: science as a candle in the dark"
I don't think he takes into account losses in the amount of air exhaled due to chemical reactions of any sort, merely that the vast majority are still floating around. Scientifically, this may or may not be the case.
As for the book, the point is that people don't understand mathematics well enough to make the kind of baseless assumptions that they make. He takes aim at things such as the "hot hand" athletes claim to have occasionally as well as theories such as "I missed the last seven billion times, I'm sure I'll hit this time!". There's a second book after this one that I also picked up, but as I'm currently reading more than one book I've yet to finish this one or the next one.
I've added Sagan's book to my must read list. Thanks for the tip.
thank YOU for the tip. sagan's book describes a similar set of conditions due to the poor scientific education we recieve as part of our high school curricula. i can speak for myself and say that i wish i would have studied mathematics more seriously in high school...but the instruction was not much more inventive than: here are 20 practice problems...do them. instead, i usually made up dirty lyrics to songs and checked out all the hot math babes.
In reading this book on the subway today, Paulos quotes Sagan. I wouldn't have even known who he was talking about if you hadn't said anything.
As for wishing you had learned more math, that's the whole reason I picked up this book in the first place (which, to be honest, although it's interesting, it's not what I was looking for). I was hoping to find something that would expose me to math that I could apply to topics I'm familiar with now... The problem I had, and it sounds like the same one you had, is that math was so boring and I couldn't figure out how it applied to anything. As I've been exposed to more things, I'm finding more and more applications, and now I'm wishing I had paid more attention. Things like Power Laws, vectors, statistics (which I've never taken a single class in), and trig are all things I find uses for now.
Now, those math babes... Where do I find them? They might be able to interest me in math...