Chaitin's "How Real are Real Numbers?"

Chaitin's a bright guy and worth reading.
Unfortunately, this (http://arxiv.org/pdf/math.HO/0411418) paper is merely a rehash of what he (and other people) have said already.

If you're familiar with:
the distinction between countable and uncountable sets,
Cantor's diagonalization argument that the set of reals is uncountable,
the fact that the set of nameable numbers is countable,
and that the halting problem is unsolvable,
then I don't recommend that you read this paper.

If you don't want to read the paper,
here's my version:

Pat pointed to something on the screen and asked Dana "Is that a real number?"
Dana said "Um" and pointed to something on the desk and said "Is that a hunk of metal?"
Pat said "Well, yes. But I see your point- it's also a fork."
Dana said "You can imagine a physical object where the best description of it is 'hunk of metal'. However, a real number inside a computer is never a plain vanilla real number. There's always a more appropriate description."
"In fact it's a rational number between 0 and 1 represented as a rho-shaped linked list of bits."