bran987
New member
Before I go on, take a really deep breath. Seriously. Go ahead.
Now, what do you think the chances are that you just inhaled a
molecule that Caesar exhaled on his dying breath? Surprisingly
it's better than 99%. Here's the logic. We can safely assume
that after 2,000 years, all the molecules that Caesar actually
exhaled are evenly distributed throughout the atmosphere. If
there are N molecules of air in the world and Caesar exhaled
X of them, then the probability that any molecule you just
inhaled is from Caesar is X/N. The probability that none of
the molecules you just inhaled are from Caesar is 1-X/N.
Using the multiplicative function, if you inhale three
molecules, the chance that none are his are [1-X/N]^3. In fact,
if you inhale Y molecules, the chance that none are from Caesar
are [1-X/N]^Y. Which means the probability of you inhaling at
least one molecule Caesar exhaled is 1-[1-X/N]^Y. X and Y
are about 1/30th of a mole, or 2.2x10^22 and N is roughly 10^44
molecules, so the probability works out to over 99%! On a
molecular level, we really are all part of each other.
?
Now, what do you think the chances are that you just inhaled a
molecule that Caesar exhaled on his dying breath? Surprisingly
it's better than 99%. Here's the logic. We can safely assume
that after 2,000 years, all the molecules that Caesar actually
exhaled are evenly distributed throughout the atmosphere. If
there are N molecules of air in the world and Caesar exhaled
X of them, then the probability that any molecule you just
inhaled is from Caesar is X/N. The probability that none of
the molecules you just inhaled are from Caesar is 1-X/N.
Using the multiplicative function, if you inhale three
molecules, the chance that none are his are [1-X/N]^3. In fact,
if you inhale Y molecules, the chance that none are from Caesar
are [1-X/N]^Y. Which means the probability of you inhaling at
least one molecule Caesar exhaled is 1-[1-X/N]^Y. X and Y
are about 1/30th of a mole, or 2.2x10^22 and N is roughly 10^44
molecules, so the probability works out to over 99%! On a
molecular level, we really are all part of each other.
?

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