Annals Of Mathematics : Transcendental Pickle Slicing

Behold the Heinz Omnihedron.

It's a two dimensional map of one of the strangest and most complex entities in mathematics. Unveiled at MIT today. It represents a 'Lie group' called E8 that  manifests the symmetry of an object boasting as many dimensions as Heinz has varieties.

The mandala-like shadow of its creation shown here took  77 hours on a supercomputer number crunching a  453,060 X 453,060 matrix containing more than 205 billion entries.

The finished product is a 'symmetry operator'  of use to theoretical physicists trying to construct  grand unified theories. A Lie group is a collection of mathematical descriptors that help to illustrate the symmetry of a smooth object,  describing, for example, all the mathematical operations that can be performed on a sphere without changing its appearance. The number of  suchstraightforward Lie groups is infinite, but five 'exceptional groups' also exist, and of them, E8 has defied  complete definition since its discovery in 1887.

What's weirder than weird about it is that while it describes the symmetries of a particular 57-dimensional object , it has 248 dimensions itself. That's one spicy polyhedron.

Comments

[Russell]

Here's a primer approved by Garrett Lisi, the author of the paper in question :
http://science.slashdot.org/comments.pl?sid=362251&cid=21373411

[Health News]

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