Discussion:
strings, codes and phonemes
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A***@gmail.com
2006-10-18 16:49:01 UTC
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I am sure most of you have noticed how convenient the English keyboard
becomes when using it to label 26 and 10 dimensional spaces: there is
26 alphabetical characters, and 10 numerical ones.

I feel ready to discard the ten numerical chars as mere coincidence,
but I am not so sure about the alphabetical. Let me to tell you why:
the dimensions of the bosonic string are related to the 24 dimensional
Leech lattice and its 25+1 dimensional companion (of signature
25-1=24-0). On the other hand, the 24 dimensional unimodular lattices,
particularly Leech's, are useful in coding theory, because they build
the densest packings we know. Golay's codes and a whole of
error-correcting industry come from these lattices, and it is only for
a small miss that it can not be claimed that error correction is a
byproduct of string theory... Conway's pals come there before, using
their own branch of unorthodox mathematics.

Now I wonder if the existence of Golay codes or Leech packagings has
been speculated to appear in natural recognition system (say, our
neural networks processing sound) or used to justify the survival of
our alphabetical notation system (3300 years old!). Far fetched, but it
could explain the coincidence on the basis of a common mathematical
structure.

Alejandro
A***@gmail.com
2006-11-26 06:30:30 UTC
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Post by A***@gmail.com
byproduct of string theory... Conway's pals come there before, using
their own branch of unorthodox mathematics.
Sorry I have been misleading here; from an answer to my post in the
physics forums interface, it seems that the mention of Conway
mistakenly addressed the game of Life. No, Conway's pals does not refer
to celular automata nor to the game of Life, nor to "winning ways for
your mathematical plays". It refers to a serious book from Conway on
lattices and codes and subsequent work by Borcherds on the fake monster
algebra.

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