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, May 09, 2008

Five dimensions of culture

Although not very obvious, colors have a binary tree like symmetry;

(((White,Yellow),(Blue,Red)),Grey,((Green,Orange),(Purple,Black)))

Yellow is somewhat closest to White. If the primary colors had perfect symmetry, they should all have equal distance to White. This is a clue to how color vision evolves in a binary tree of depth 3; 2^3=8. At the third level, some of the binary symmetry is broken to get the triplet symmetry;

(White,(Yellow,Blue,Red),Grey,(Green,Orange,Purple),Black)

The (White,Grey,Black) triplet rotates vertical to others to make the intensity or scalar dimension. I think the primary reason for this is that knots (therefore stable structures) can only be made in 3 dimensions. Chaos can happen in 3 (or more?) dimensions, but this must be related to the knot restriction.

The strongest symmetry determines the 4 color dimensions;

(White,(Yellow,(Blue,(Red,(Grey),Green),Orange),Purple),Black)

(White,Black)
(Yellow,Purple)
(Blue,Orange)
(Red,Green)

...

Culture can be classified in two stacks, and they also display the color symmetry;

(((War,Communications),(Logistics,Economics)),
Politics,
((Ethics,Science),(Aesthetics,Peace)))

(((Predation,Competition),(Production,Reproduction)),
Interaction,
((Extermination,Consumption),(Cooperation,Union)))

There are 4 obvious dimensions of culture;

(War,Peace)
(Communications,Aesthetics)
(Logistics,Science)
(Economics,Ethics)

and 4 dimensions of drivers;

(Predation,Union)
(Competition,Cooperation)
(Production,Consumption)
(Reproduction,Extermination)

The fifth dimension comes from the mediation between the Politics and Interaction (Quality and Quantity) stacks. It seems the mediating element is Government, reminding the (Memory,Consciousness,Intelligence) triplet of life. Other elements of the Politics stack also come in stack form, producing a self similar fractal. Therefore the fifth dimension is self reference.

Similarly colors also have Quantity control elements like Contrast and Brightness, but I am still thinking about them.

...

The fields can be classified in a similar stack;

(((Time,Light),(Weak,Strong)),Higgs,((Black-Hole,Dark-Energy),(Gravity,Space)))

With a different order than my previous posts. This time I put Space-Time at the outer edge, and Higgs in the middle. Higgs has to be the mediating agent since it is a scalar field. It has 4 dimensions;

(Time,Space)
(Light,Gravity)
(Weak,Dark-Energy)
(Strong,Black-Hole)

They compare well with the drivers of culture. I am still thinking about the self referential aspect of the universe. It also seems to be a stack fractal that opens up like origami.

...

Senses obey the same symmetry if Time, Space and Intensity are considered as senses;

(((Time,Touch),(See,Taste)),Intensity,((Smell,Hear),(Balance,Space)))

Senses of Space/Time are really always there, in sleep or not, but taken for granted. My cat knows almost the exact time to wake me up. The regulation of sleep, which is one of the most fundamental functions of the body, implies an intimate knowledge of time. The heart and Basal Ganglia are central to organ coordination in the body and the head.

The sense of Intensity is also taken for granted. All senses come with Intensity.

Balance is a sense since it has dedicated organs coupled to the ears.

...

There are 14 real number axioms;

Addition axioms;

x+0 = x, zero element, stability
x+y = 0, negation, balance
x+y = y+x, commutativity
(x+y)+z = x+(y+z), associativity

Multiplication axioms;

1*x = x, unit element, stability
x*y = 1, inversion, balance
x*y = y*x, commutativity
(x*y)*z = x*(y*z), associativity

x*(y+z) = x*y + x*z, distributivity

Order axioms;

If x =< y, then x + z =< y + z, stability
If 0 =< x, 0 =< y, then 0 =< x*y, balance
If x =< y, y =< x, then x = y, commutativity
If x =< y, y =< z, then x =< z, associativity

And the Least Upper Bound axiom.

There are 4 obvious dimensions;

((stability,balance),(commutativity,associativity))

and they also compare well to the drivers of culture. The fifth dimension seems to be the mediation between the (Addition,Order,Multiplication) triplet. Distributivity sticks out of the model at the moment.

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