Arcadian Functor

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Marni D. Sheppeard

Wednesday, July 02, 2008

Carbon Beauty

In a series of posts on the buckyball trinity, Lieven Le Bruyn gives a link to this paper by P. Martin and D. Singerman on the genus 70 buckyball curve. On page 8 they discuss the familiar Fano geometry of seven points and seven lines, described by a 7 dimensional circulant

1110010
0111001
1011100
0101110
0010111
1001011
1100101

This geometry is embedded in the genus 3 Klein surface. The buckyball curve appears as an embedding space for the p=11 analogue, described by an 11 dimensional circulant

10110100011
11011010001
11101101000
01110110100
00111011010
00011101101
10001110110
01000111011
10100011101
11010001110
01101000111

One guesses that this must somehow be associated to the algebra E11, the mathematics of which give the likes of Woit so much confidence that they know more than a lot of very smart string theorists. But in M Theory, we don't care so much about the continuum mathematics, because the physics is actually much simpler than that.

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