Who Were the Sea Peoples?

If you wish to better understand Zeno's worry about the continuum, you could do worse than to consider loops in software. Case 1: You want to loop over 10 records. You write: for i from 1 to 10     process_record() What could be simpler? OK, let's loop over the positive integers, finding the prime numbers: for i from 1 to ∞     check_for_primality() This loop will run forever, but it is a perfectly valid loop. We can even set it up to loop over all integers: j = 0 for i from 0 to ∞     j = j - 1     print i     print j And with only a little more trouble, we could loop over the rational numbers as well. But what if I ask you to loop over the real numbers between, say, 0 and 1? The problem here is much worse than the loop running forever: the loop can't even get started. We could print out "0"... and then what? There is no "next" real number to which we can proceed. And note: the concept of a lim...

Surprisingly, my post on probability theory has generated quite a discussion thread. (And here I thought I saying Ron Paul won't win the GOP nomination was the key to lengthy threads!) In the course of the discussion, I thought of a way to refine my first example to clarify the issues a bit. Instead of an infinitely fine-pointed dart, let's take an ordinary one, and instead of the real number line, we'll just throw it at the wall. Now, I ask you, "Does the exact middle of the head of the dart have some exact x, y coordinates on the grid of that wall, despite the fact that, of course, we could never measure that exact x or that exact y?" If you answer "yes," then I will note that there was a 0% chance that the dart would land at those coordinates, and yet there it is. If you answer "no," you have adopted a respectable philosophical position, denying the physical reality of the continuum. But you have changed subjects on us: you've do...