### 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

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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

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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.

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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