by pat » Mon Sep 25, 2006 2:54 am
Yes, Tony Smith's web pages are incredibly disjointed. He leaves out a great deal of context. I had hopes at one point that I would be able to gather enough knowledge to have the context. But, I would be back at the "database of every possible image" scenario where I might have the context, but I would also have 10 trillion other contexts and no idea which one we was working from.
One of his pages declares: "There are 28 diffeomorphic structures on S<sup>7</sup>. This is because one is prime, two is prime, three is prime, but four is not prime."
Someday, I hope to find enough information to agree with that statement. That, I might be able to sniff out the correct context for. Most of the rest of the contexts are needles in haystacks (and one doesn't even know which haystack). Incidentally, the one is prime, two is prime, three is prime, but four is not prime is also, according to Tony, responsible for the fact that there are only four real division algebras (R, C, H, and O). This may be a stepping stone to the S<sup>7</sup> thing. I'm not sure yet.