[Beowulf] The recently solved Lie Group problem E8

Peter St. John peter.st.john at gmail.com
Thu Mar 22 07:13:09 PDT 2007

Well to me that's the point. My brain is too small for 500Kx500K matrices
over a ring of 22 degree polynomials, too. So we throw a 16-node computer at
it and crush it under the hobnailed jack-boots of Higher Mathematics.
I wish I know more about the SAGE (machine) that hosts the SAGE (software)
that was used for this, but apparently washington.edu's web server can't
handle the CNN exposure as well as their number cruncher can crunch numbers.
They are still down.

On 3/22/07, Robert G. Brown <rgb at phy.duke.edu> wrote:
> 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:rgb at phy.duke.edu
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