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..the ultimate solution, which took 77 hours to run on a U.S. supercomputer called Sage...was "a very important advance" in physics, for it could be used to test a key theory about the fundamental symmetries in nature. Among the mooted symmetries it may help unravel is the structure of the cosmos, created by the Big Bang some 13.7 billion years ago, and basic particles themselves, said Hermann Nicolai, director of the Albert Einstein Institute in Potsdam, Germany.
The E8 root system consists of 240 vectors in an 8-dimensional space -
vectors are the vertices (or corners) of an 8-dimensional object called
the Gosset polytope 421. In the 1960s, Peter McMullen drew by hand a
2-dimensional representation of the Gosset polytope 421
- this is a computer generated version of that drawing.
vectors are the vertices (or corners) of an 8-dimensional object called
the Gosset polytope 421. In the 1960s, Peter McMullen drew by hand a
2-dimensional representation of the Gosset polytope 421
- this is a computer generated version of that drawing.
Image: John Stembridge/American Institute of Mathematics
The 18-member research team, called Atlas, included mathematicians from France's universities of Poitiers and Lyon. A paper presenting the research results was tabled on Monday; it was entitled "The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness". String & M-theorists rejoice!
Links
Cosmos Magazine
Asymptotia
Wikipedia Article
AIM Math
BBC