Monday, March 19, 2007

Flatland and the 248 dimensions of time

In the 19th century two dimensional world of Flatland the hero infers the existence of dimensions beyond those of his god-like 3 dimensional correspondent. He would be willing to image a 248 dimensional creature:
Is this the fabric of the universe? | Science News | Connected | Telegraph

Mathematicians have successfully scaled their equivalent of Mount Everest. Today they unveil the answer to a problem that, if written out in tiny print, would cover an area the size of Manhattan.

At the most basic level, the calculation is an arcane investigation of symmetry – in this case of an object that is 57 dimensional...

... What makes this group of symmetries so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8. I find it rather extraordinary that of all the symmetries that mathematician’s have discovered, it is this exotic exceptional object that Nature has used to build the fabric of the universe...

... Today’s feat rests on the drive by mathematicians to study symmetries in higher dimensions. E8 is the symmetries of a geometric object that is 57-dimensional. E8 itself is 248-dimensional...

....The ways that E8 manifests itself as a symmetry group are called representations. The goal is to describe all the possible representations of E8. These representations are extremely complicated, but mathematicians describe them in terms of basic building blocks. The new result is a complete list of these building blocks for the representations of E8, and a precise description of the relations between them, all encoded in a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in all, each a mathematical expression called a polynomial.

..."This is an impressive achievement," said Hermann Nicolai, Director of the Albert Einstein Institute in Potsdam, Germany. "While mathematicians have known for a long time about the beauty and the uniqueness of E8, we physicists have come to appreciate its exceptional role only more recently - yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner...
I'd love to hear an explanation of how E8 might relate to non-local action and the seemingly bizarre nature of time. Are meaning-free instantaneous communications between entangled photons instances of higher dimensional structures protruding into 4 space? Is there really only one dimension of time, or is it simply that meaning can't exist in the others?

Oh, and did those last two sentences of mine make any sense at all?

It's a thin line between being an amateur commentator on math and physics and being a complete loon! :-)

Update: Another article explained that E8 has merely 57 dimensions, but 248 symmetric rotations. Whatever that means. Mathematics left the scope of mere mortals well over a hundred years ago, it's not surprising that non-specialists should struggle with this announcement.

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