On Wed, 21 Mar 2007, Peter St. John wrote:
Times have sure changed; with Wiles and Fermat's Last Theorm in newspapers
for over a year, then "A Beautiful Mind" from Hollywood; it's almost not
surprising that the solution of a difficult math problem is mentioned at
CNN.com.
The Exceptional Lie Group E8 computation just got done (some info at
http://www.aimath.org/E8/computerdetails.html about the details of the
computation itself). Reference to the system SAGE is a bit ambiguous; it's
the name of a symbolic mathematics package and apparently also a 16-node
system at the same University of Washington. Natually I was curious about
the computer, but ironically, it seems that while they can handle a matrix
with half a million rows and colums each (and each entry is a polynomial of
degree up to 22, with 7 digit coeficients), their departmental web server
can't handle the load of all of CNN's readership browsing at once :-)
The group E8 itself, together with some explanation of the recent news, is
in wiki, http://en.wikipedia.org/wiki/E8_%28mathematics%29
Dr Brown might explain better than I could how sometimes the best way to
understand a thing is to break it down into simple groups of symmetries.
Don't you be puttin' that off on me now. I get off of that particular
bus somewhere around the SU(N) stop, with rare excursions over into
point groups on the other side of the tracks. Unitary, yes.
Orthogonal, why not. SL(2,C) even. Strictly UNexceptional.
Apparently, one of the funky things about E8 is that the "easiest way to
understand it" is itself.
Yeah, and like I have a brain that can manage ~500,000x500,000
complicated polynomial objects. Thanks, I think... but not.
rgb
Peter
--
Robert G. Brown http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567 Fax: 919-660-2525 email:[EMAIL PROTECTED]
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