Yer Better Constants
I know, two quotations in a row from the same person who isn't even Bill Moyers, but there is a reason, mostly that I've been going through some of the archives at Slate and having an enjoyable time. For the last little while I've been looking at "Do The Math" articles by Jordan Ellenberg, whither the previous entry as well as this one.
The previous one was curious; this one made me laugh. It startled Isaac so much that I had to read it to him, although I'm not sure he really saw the humor. Anyway, this is from Ellenberg's analysis of when one should buy a Powerball ticket; my guffawing was in response to the part I've marked in bold face. It's the bit about "the better constants" that seemed the real knee-slapper to me.
First of all, it was pretty clear somebody was going to win. There's a nice rule of thumb for working out questions like this. Suppose there's an event whose probability is 1 in X, where X is a really big number. And suppose you have Y chances for this event to happen. Then the chance the event will happen is just about 1 – e-Y/X; here e is a famous mathematical constant whose value is about 2.718. The unexpected entrance here of e, the base of the natural logarithms, is one of life's happy mysteries; the better constants, like e and pi, appear in all kinds of contexts having no connection whatever with logarithms or with the circumferences of circles.
[Jordan Ellenberg, "Is Powerball a Mug's Game? It all depends on when you play—and what value you put on a dollar." Slate, 31 August 2001.]