tag:blogger.com,1999:blog-11295132.post114348611465734210..comments2016-12-05T13:41:53.469-08:00Comments on A Neighborhood of Infinity: The Most Amazing and Mysterious Thing in All of MathematicsDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-11295132.post-1143568029130111112006-03-28T09:47:00.000-08:002006-03-28T09:47:00.000-08:00They're closely related. There's the obvious physi...They're closely related. There's the obvious physical interest of 4. There's an algebraic side to 4 coming from the quaternions and this is part of a sequence 1,2,4,8 of division algebras. This all ties up nicely with the physics through representation theory with things like the 'spinorial chessboard'. But there's a topological dimension to this too with the division algebras closely tied to Hopf bundles. The Hopf bundles give rise to many of the interesting phenomena in this table. Notice how the size of the homotopy group is much larger for k one less than a multiple of 4.<BR/><BR/>Deep down, however, I feel that ΞΆ(-1)=-1/12 is a more special number...sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1143531674491438542006-03-27T23:41:00.000-08:002006-03-27T23:41:00.000-08:00I think the number four is a pretty good candidate...I think the number four is a pretty good candidate for the most mysterious thing in all of mathematics.<BR/><BR/>(Specifically, why 4 dimensional things are so bloody weird)David R. MacIverhttp://www.blogger.com/profile/12893796777558636623noreply@blogger.com