Todays "Link of the Day" is about the old competition of naming the biggest number one can imagine:
You have fifteen seconds. Using standard math notation, English words, or both, name a single whole number—not an infinity—on a blank index card. Be precise enough for any reasonable modern mathematician to determine exactly what number you’ve named, by consulting only your card and, if necessary, the published literature.
The follwing discussion starts by gowing from Addition to Multiplication to Exponentiation etc. Then in introduces the concept of Turing machines and computability. Finally it show that there are non-computable functions which grow even faster.
This page should be readable and enjoyable for mathematicias nad non-mathematicians alike.