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.

Thursday, January 31, 2008

Four dimensions of culture

Consider the following classification of culture in two stacks of length 7;

(Interaction,Logistics,Economics,Politics,Ethics,Science,Aesthetics)
(Competition,Production,Reproduction,Politics,Extermination,Consumption,Cooperation)

Politics sits in the middle and mediates 12 elements in two stacks which make a duality. The stacks follow an increasing order of complexity and have 3 symmetries;

(0,(1,(2,(3,(4,(5,(6)))))))
(0,(1,(2,(3),4),5),6)
((0,1,2),3,(4,5,6))

Like the color symmetry;

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

The dualities (Yellow,Purple), (Red,Green), (Blue,Orange) complement each other and combine to give Grey, as the triplets themselves.

The triplet (Interaction,Logistics,Economics) are the primary colors of culture, and (Ethics,Science,Aesthetics) the secondary colors.

...

The softer side of culture have 3 dualities and a singularity;

(Interaction,Aesthetics)
(Logistics,Science)
(Economics,Ethics)
(Politics)

Previously I had Production instead of Interaction which is a better choice as it is the simplest form of collective action. The universe displays beauty at all levels of action, specially life. This is a profound mystery.

Logistics includes things like Communications, Transportation and couples to Science strongly.

Ethics includes things like Law, Religion, Tradition and couples to Economics strongly since Economics is the way of distribution of resources.

The drivers of culture have 3 dualities and a singularity;

(Competition,Cooperation)
(Production,Consumption)
(Reproduction,Extermination)
(Politics)

...

Music has a similar form;

(Beat,Tempo,Meter,Rhythm,Pitch,Melody,Harmony)
(Quiet,Slow,Bass,Rhythm,Treble,Fast,Loud)

The drivers make 3 dualities and a singularity;

(Bass,Treble)
(Slow,Fast)
(Quiet,Loud)
(Rhythm)

The world of vision also has 4 drivers;

(Contrast,Brightness,On/Off,Color)

The (Competition,Cooperation) duality is like Contrast. Competition makes boundaries sharper. (Production,Consumption) is like Brightness. (Reproduction,Extermination) is like On/Off.

...

Geert Hofstede identified 4 dimensions of culture;

Power-Distance
Collectivism-Individualism
Femininity-Masculinity
Uncertainty avoidance

I think there is some similarity.

...

Buddha identified 4 noble truths;

The nature of suffering
The origin of suffering
Cessation of suffering
The way leading to cessation of suffering

I think it matches my list quite a bit;

(Competition,Cooperation)
(Production,Consumption)
(Reproduction,Extermination)
(Politics)

...

There many other entities that obey this 7-stack form;

(Touch,See,Taste,Measure,Smell,Hear,Balance)
(Higgs,Light,Weak,Strong,Space-Time,Gravity,Dark-Energy)
(Mathematics,Physics,Chemistry,Biology,Psychology,Intelligence,Aesthetics)
(Binary,Natural,Integer,Real,Complex,Quaternion,Octonion)
(Beat,Tempo,Meter,Rhythm,Pitch,Melody,Harmony)
(Space,Character,Word,Sentence,Paragraph,Chapter,Book)

Clearly the corresponding shape is hexagon, or the ancient Atman Yantra or David's Star.

Each duality make a dimension mediated by the center, giving 3 dimensions.

Why hexagon and why 3 dimensions? There are some clues. Complex numbers are closed and they define a plane. Plane and a hexagon are closely linked since hexagon can be drawn by a compass only. Knots can only be made in 3 dimensions. Chaos can happen only in 3 (and higher?) dimensions. And what else is there to imitate apart from the strongest symmetry of the universe; space-time.

...

Four dimensionality comes from the fractal and self-similar shape of the stack. Like Politics, the other elements also come in the same shape, for example Science.

Sunday, January 20, 2008

The shape of being

The ancient and mysterious flower of life (taken
from Wikipedia).

In the end, I ended up with this monster as the
symmetry of being. I have found that all
autonomous and living entities obey this
symmetry, though not yet filled out all categories.
It refers to itself to one level, ie each constituting
point reflects the overall shape to one iteration. It
is David's Star fractal. I think somehow it opens
up like origami to produce more complicated
shapes. Note that it already has cube look.







The ancient and mysterious Surya Yantra
(taken from Wikipedia).

Surya means "the supreme light" and regarded to
be the visible form of God. It can easily be
extracted from the flower of life.













An aspect of E8.

E8 is the name of the symmetry that Garrett Lisi
lately suggested to be the symmetry of the
universe.











There are 5 obvious senses of life;

(See,Taste,Touch,Smell,Hear)

While Touch is singular, (See,Hear) and (Taste,Smell) come in dualities. Touch is a generic sense and it's main organ is the skin. The remaining 4 senses can also be considered as specialized types of touch. After all, according to Quantum Mechanics, everything is a scattering event. Skin is made of a type of nerve cell, like the organs of the other senses.

After singularity, duality is the most common aspect of life. They tend to evolve from a common ancestor, like (black,grey,white). Taste and Smell differentiated with the separation of the corresponding organs mouth and nose, due to the separation of breathing and eating. I suspect a corresponding separation of anus from genitals.

Similarly See and Hear couple to each other, although this is not as obvious as (Taste,Smell). The underlying mathematics of See and Hear are the same, See being a more involved version of Hear. This can easily be seen when they are compared to the mathematics of Video and Audio.

I think both (See,Hear) and (Taste,Smell) separations evolve in parallel. They constitute the 4 pillars of senses, like the 4 pillars of the body; arms and legs. There seems to be a link here to the bifurcation concept of the Logistic Map and Mandelbrot Set. Bifurcation happens when two opposing trends, like demand and supply of economics, come together in one event that feeds back to itself. There is also a link to the complex numbers; {+1,-1,0,+i,-i}, when the cartesian representation is considered.

When the hidden senses Measure and Balance are also included, there are 7 senses;

(Measure,See,Taste,Touch,Smell,Hear,Balance)

The organ of Measure is the entire body, while the organ of Balance is hidden in the middle ear, in the form of 3 interlocked liquid filled hairy rings. Clearly they also couple to each other to make a duality; (Measure,Balance).

...

There are 4 observed fields of the universe;

(Light,Weak,Strong,Gravity)

Light, Weak and Strong are closely related to each other. Their symmetries reflect this; U(1), SU(2) and SU(3). Basically U(1) is about the transformations one complex variable, SU(2) two complex variables, and SU(3) three complex variables. The Standard Model relates them to each other; U(1)*SU(2)*SU(3). I don't know if SU(3) is understood as much as the other two, but SM is a very successful theory. Gravity has General Relativity, but it is a classical theory, and a quantum theory of gravity does not exist yet.

Light couples to Gravity. The kinetic and potential energy duality comes from this. Gravity makes the stage for Light to operate in. What does Weak couple to? The symmetry of Weak is related to the symmetry of Space-Time. I think it is the symmetry of Quaternions and SL(2,C). Lets consider ST as a field and add it to the list;

(Light,Weak,Strong,Space-Time,Gravity)

Lets compare with senses;

(See,Taste,Touch,Smell,Hear)

Like the Touch sense, Strong sits in the middle. The symmetry of Strong is 3/2. There are 3 quarks and 3 gluons in a nucleon. There are 3 dimensions of a vertebrate body; 2 arms, 2 legs, and torso with head and tail. Strong is the strongest field, and Touch is the strongest sense.

Hear-Gravity correspondence is interesting, considering the Balance-Hear coupling. Like Gravity providing the stage for Light, audio provides the background mood to video in movies.

The symmetry of equal tempered music is also 3/2. When the perfect fifth (3/2 of the root) is taken 12 times it covers 7 octaves.

Could there be also 7 fields? When Higgs and Dark energy are also added;

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

Compare with 7 senses;

(Measure,See,Taste,Touch,Smell,Hear,Balance)

Like (Measure,Balance), (Higgs,Dark-Energy) are also hidden.

Higgs has been predicted but not observed yet. Effects of Dark energy are observed but it is not even predicted properly by a theory yet. Hopefully LHC will shed some light on these fields. This model predicts that Higgs and DE make a duality.

When numbered 0 to 6, the list makes more sense, considering the corresponding symmetries;

(0.Higgs,1.Light,2.Weak,3.Strong,4.Space-Time,5.Gravity,6.Dark-Energy)

...

There are 7 fundamental sciences;

(Mathematics,Physics,Chemistry,Biology,Psychology,Intelligence,Aesthetics)

Biology sits in the middle. Chemistry couples to Psychology, since Psychology uses hormones. Physics couples to Intelligence, as Intelligence uses Light symmetry. Aesthetics couples to Mathematics.

...

Physically significant numbers seem to fit in a 7 stack as well;

(Boolean,Natural,Integer,Real,Complex,Quaternion,Octonion)

Like the fields, numbers make 3 inner and 3 outer layers. Real sits in the middle, (Boolean,Natural,Integer) make the inner, and (Complex,Quaternion,Octonion) make the outer or hyper layers. Like Strong sits in the middle, (Higgs,Light,Weak) make inner structures, and (ST,Gravity,DE) make the outer or hyper structures of reality.

Garrett Lisi lately proposed that E8 is the shape of the universe. Octonions are closely related and 2^6 = 8^2.

...

Music has 7 basic elements;

(Loudness,Tempo,Meter,Rhythm,Pitch,Melody,Harmony)

Rhythm sits in the middle and mediates, as can be observed easily from the practice of music. Rhythm evolves into Pitch since Pitch has color unlike a mono-color signal. When a signal with complex Pitch observed on the oscilloscope, it looks like Rhythm with many peaks of varying amplitude. The list evolves from simple to complex. We get Harmony only when melodies interact. Vertical harmony is in fact Pitch. Therefore Harmony is the highest form in Music, like counterpoint.

Lets compare to the number stack;

(Boolean,Natural,Integer,Real,Complex,Quaternion,Octonion)

Boolean and Loudness match since "1" is loud compared to "0". Natural and Tempo obviously match. Complex and Pitch match since Complex numbers are the natural formalism to study signals. Interesting that Octonions correspond to Harmony, considering the production of a major scale through the Stern Brocot tree at the third level, 2^3 = 8.

...

Courtship mediates 3 dualities;

(Observation,Body-language,Dance,Courtship,Music,Language,Aesthetics)

Music couples to Dance, Language couples to Body-Language to make theatre, and Aesthetics couples to Observation. (Observation,Body-Language,Dance) make the inner world of courtship, and (Music,Language,Aesthetics) make the outer. Aesthetics includes things like poetry, philosophy.

...

Books have 7 layers;

(Space,Character,Word,Sentence,Paragraph,Chapter,Book)

Sentence sits in the middle, with 3 inner layers (Space,Character,Word) and 3 outer hyper layers (Paragraph,Chapter,Book). I think Space also corresponds to things like comma, period.

...

DNA seems to have 7 layers;

(Space?,Base,Codon,Gene,Operon,Chromosome,DNA)

Gene sits in the middle and mediates, as it does the actual work. It seems to have 3 inner and 3 outer layers. This needs more work as it is a new field. I can not figure out what Space is.

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