Conway sequence and octonions

Hi,

Pr. John H. Conway studied in 1987 the look and say sequence that
starting from 1 describes the former term ie:

1
11
21
1211
111221
312211
13112221



















Still some question might remain open about this object.

First, the first two lines are obviously linked with the idempotence
principle xx=x, that is the base for groups, algebras and rewritten as
x(x-1)=0 boolean binary algebras. Still 00 is not the description of
0. On the other hand, the sequence appears rapidly to be ternary and
not binary.

The sequence can be seen as a language with a parsing, but the
reveverse algorithm halts on odd length strings. In other words, I do
not how a bottom-up parser starting from 11 would decide of the
parsing of the first 1, making it a qbit. Actually, the fact that the
sequence is metamathematic and the fact that this operation can be
seen as a diagonalization makes the link clear with Gödel's proof.

Stephen Wolfram as recently proven that even 1D automaton can be
universal.

Last but not least, the sequence appears quickly to be composed of 8
strings 11 12 13 21 22 23 31 32 that can easily be linked with 000 001
010 011 100 101 110 111 that are the usual encoding of the unit
octonions. Octonions are the base of string theory and can be mapped
to the quarks.

Given this remark, THE QUESTION OF THE UNIVERSE BEEING ACTUALLY CONWAY
SEQUENCE should be examined seriously.

Thank you for reading.

.

Relevant Pages

  • Re: Conway sequence and octonions
    ... octions and string theory and look and say sequence using to model physics... ... seems like fitting an elephant ... ...
    (sci.math)
  • Re: Conway sequence and octonions
    ... The sequence can be seen as a language with a parsing, ... reveverse algorithm halts on odd length strings. ... Find all even strings for which the reverse algorithm ... Octonions are the base of string theory and can be mapped ...
    (sci.math)