Numbers Make the World Go...er...Spherical?
Stephen Wolfram's A New Kind of Science is one of those books which, when it comes out, you wonder if you haven't just seen the publication of a document (or, this case, a TOME) which might not be one of the revolutionary documents which a historian of science from the 22nd century would refer to as the paradigm shift. You wonder and you heft the damn thing, and then your wee brain tilts. The book -- which I checked out of my public library when it first came out and looked at for three weeks like it was a medium-sized dog which might bite -- is written so that a lug nut like myself can understand the material. Sure...
In the meantime, I'll entertain myself with sites like What's Special About This Number?" which start off a little slower. The definitions of the various "specialness" of the numbers all point to http://mathworld.wolfram.com. It's kind of an easy way into number soup. And don't get distracted like I did on the fact that there are no magic tours available to the knight on the chessboard.
The computational puzzle -- which had been unsolved for 150 years -- postulates the possibility that a Knight (you know, the "horse" in chess) could tour the chessboard through its unique "L" shaped move in such a way that it touches each square of the 8 by 8 board only once. After 61.40 CPU days, a program written by J. C. Meyrignac has determined that such a "tour" is impossible. You can check his work if you like. The piece of software also generated output showing 140 distinct semi-magic tours.