Thursday, March 22, 2007

Mapping E8

The AP reports that a group of mathematicians have at last characterized the E8 Lie group. I'm intrigued by the fact that it seems to be in the gray zone between the understandable and the unintelligible.

Jeffrey Adams, the project's leader and a math professor at the University of Maryland, is reported as saying, "To say what precisely it is is something even many mathematicians can't understand." The scale of E8 boggles the mind: all the information about E8 and its representations is 60 gigabytes in size.

For more on E8, see Curiously, the representation on that page is a semi-lattice - cf. my post on Christopher Alexander's application of this mathematical concept to the complexity of cities.

The language used to describe this topic is strikingly physical: "The classical groups A1, A2, A3, ... B1, B2, B3, ... C1, C2, C3, ... and D1, D2, D3, ... rise like gentle rolling hills towards the horizon. Jutting out of this mathematical landscape are the jagged peaks of the exceptional groups G2, F4, E6, E7 and, towering above them all, E8. E8 is an extraordinarily complicated group: it is the symmetries of a particular 57-dimensional object, and E8 itself is 248-dimensional!"

[Thanks to Scott Forbes for alerting me to this result.]

No comments: