Re: Conway sequence and octonions
- From: Proginoskes <CCHeckman@xxxxxxxxx>
- Date: Sun, 01 Jul 2007 04:50:51 -0000
On Jun 30, 5:40 am, john11 <john.chonv...@xxxxxxxxx> wrote:
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,
No, it isn't. It's related to 1x=x. "22" is two 2's, and "2" is one
two.
[...]
The sequence can be seen as a language with a parsing, but the
reveverse algorithm halts on odd length strings.
Exercise: Find all even strings for which the reverse algorithm
(eventually) halts on an odd length string.
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 G?del's proof.
Not immediately.
[...]
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.
???
--- Christopher Heckman
.
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