ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Friday, April 27, 2007

Quantity Triplet and Stern-Brocot Tree

How far can the correspondence between numbers and fundamental categories be pushed? The quantity triplet {0,1,infinity} seems to map to the triplets,

{{time,matter,space},
{cell,organism,species},
{star,galaxy,universe}}

as proposed recently in the Nine Aspects of Reality blog.

{time,matter,space} mapping is not that obvious. Locality of time, as established by the relativity theory, points to separateness of it. Quantum gravity theory proposes quantum space-time and thus also points to the locality of time. Space seems to be made of time quanta.

{cell,organism,species} triplet can be used to get some clues about the nature of {time,matter,space}. Cell is the object that determines organism's life-time. Species is the space in which the genetic information move from node to node. Each node is an organism. For sexual reproduction, two nodes get together to spawn another, thus enlarging the gene space. Hermaphrodite nodes spawn two nodes by themselves. Maybe time is more like hermaphrodites, since it is fundamental. The topology of the genetic space-time of a species must reflect that of space-time.

The life triplet also points to other invisible universes, since there are many species of life.

Stern-Brocot Tree is based on {0,1,infinity};












(From http://www.cut-the-knot.org/blue/Stern.shtml)

Cut-the-knot says 'A remarkable thing about Stern-Brocot tree is that it contains all possible non-negative fractions expressed in lowest terms and each exactly once.' The space between {0,1,infinity} is filled by a simple method of mediants.

Can SBT be mapped to fundamental categories?

0. {0/1,1/0} ... Higgs (U(0)?)
1. {1/1} ... Light (U(1))
2. {1/2,2/1} ... Weak (SU(2))
3. {1/3,2/3,3/2,3/1} ... Strong (SU(3))
4. {1/4,2/5,3/5,3/4...} ... Gravity (SU(4)?)

0. Higgs seems to have locality and universality combined. It seems when you reach the zero, you also reach the infinite.

1. 1/1 ... electric / magnetic. For life, this may be the stem cell.

2. 1/2 ... Z0 / {W+,W-}. For life, blood/{muscle,nerve}.

3. 1/3 and 2/3 make sense since they are used in the make-up of nucleons by quarks, and there are 3 color charges.

4. Gravity comes out of a 3+1 dimensional space-time and mass. The 5th item must refer to 'mass'. 1/4 seems to map to mass/space-time. 3/4 seems to map to space/space-time. I don't know much gravity so I can not interpret the rationals 2/5,3/5.

Note the 5ness of the classification list, {0,1,2,3,4}. 5 is related to 9 in a funny way that relates to the 3 triplets;

1+2+3+4+5+6+7+8+9 = 45
45/9=5

If the numbers are grouped into 3 triplets;

{{1,2,3},{4,5,6},{7,8,9}}
{{time,matter,space},{cell,organism,species},{star,galaxy,universe}}

Giving 5 at the position of 'organism', which has 5 senses. Also time gets 1, and space gets 3. Star gets 7; 7 layers of the periodic table? Matter gets 2; electric/magnetic?

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