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.

Monday, October 27, 2008

The eightfold way of existence

A Tantric Yantra.

There are 4 tissue and 4 organ types in biology;


The symmetry is like the modular group. There are 4 groups and 12 types of Connective tissue;

(Loose,Dense,Cartilage,Other) =

There are 6 inner and 6 outer senses;


Senses have organs inside and outside the brain. The inner senses are more distributed over the body for their outer organs, yet more centralised in the brain. They make up the core of the brain. There are 6 inner and 6 outer organ groups of the body;


The Head reflects the torso in the organ symmetry. Tissue types also differentiate into their own trees.


It seems each sense and action repeat the outer 6/8 pattern to expand their own category trees. For example See has eightfold outer symmetry;


There are in fact 4 eyes; 2 inner, 2 outer. The inner eyes are expert systems to decode and interpret the signal from the outer eyes. They can also operate semi-independently such as visualising. The retina of the eye has triplet symmetry.


Culture obeys the same symmetry;


There are 12 types of Interaction;


Interactions can also be listed in 4 groups of 3, exposing the conjugate symmetry;


There are 6 Sciences;








There are 12 Notes in equal tempered music.







Like the organs of an organism, the astronomical objects are places of transformation. An accumulation of rocks in space become spherical under Gravity after a critical mass. Therefore Planet and Moon represent a phase change from low level space debris. Similarly there is a phase change from Star to Black-Hole. The phases of matter also come in a quartet;


There are 6 leptons and 6 quarks;


There are 3 known Bosons;


The remaining categories (Time,Gravity,Space) must be due to Higgs which is theorised to weigh mass. They seem to match the Boson triplet;


It can also be written in 3 dualities to expose the partner symmetry;


Time is defined by Light. Space has the triplet symmetry like Strong. The implied (Gravity,Weak) duality is interesting, since the energy released by fission is in fact a transformation of mass to light. Maybe Weak holds the key to Gravity.

If compared to biology, Higgs matches the Connective tissue which differentiates into things like Blood and Bone. This makes sense since Higgs is the ultimate stem cell.

Wednesday, May 28, 2008

Thirteen senses and Da Vinci's The Last Supper

The senses can be classified in an ordered stack of length 13;


Because of the complex relationships between the senses, the stack includes many symmetries.

The strongest symmetry is unity. They are all related to each other as they grow and evolve from a root sense. I call this sense Nothingness which is an identity and measurement protocol. It is the ground state of consciousness which is generally used to mean an overall sense of being.

The second strongest symmetry is duality. They all come in dualities, except the root sense. The general symmetry is of the form (Content,Container). Smell forms the background space for Taste. Without Smell, Taste weakens a lot. Similarly Hear is the background space for See. See uses more complicated but the same type of mathematics (FFT).

Are (Rhythm,Harmony) senses? Everything in the body is a clock with a special Rhythm, but Heart and Basal-Ganglia specialize on Rhythm. So it is a sense but hidden like the Balance sense. Harmony is the overall sense between and within the senses. (Rhythm,Harmony) are due to the self-referential or self-similar aspect of the senses.

The 6 strongest dualities have an overall duality that demonstrates the symmetry that simulates a four dimensional hyper space-time;


The corresponding shape is Tesseract.

There are also two dual-duality symmetries;



I think all these symmetries form around some kind of number simulation protocol. It seems to be a category calculator with base 13.


Vision obeys the same symmetry;


(Grey) ... Balance
(Bright,Dark) ... Brightness
(White,Black) ... Contrast
(Rhythm,Harmony) ... Texture
(Yellow,Purple) ... Color


Since Nothingness sits at the center and is neutral, many modules can attach themselves through their centers. This is demonstrated by two stacks of culture;



Politics and Interaction are the Nothingness of their categories, as the 10 elements of the Interaction stack are the fundamental methods of control in Politics.


Fields also obey the 13-symmetry, if 5 new fields are introduced;


This time (hopefully the last time) I rearranged the locations of (Time,Space) in line with the senses (Rhythm,Harmony) locations, since there must be deeper fields that contain (Time,Space).

6 strongest dualities simulate a hyper Space-Time;

(((A1,A2),(B1,B2),(Time,Space))), (Higgs), ((Light,Gravity),(Weak,W*),(Strong,Black-Hole)))


Mathematics falls into two broad categories, numbers and operators;


They also have some sequential symmetry;


Comparing gives some hints about the predicted fields;

(Derivative,Integral) --> (A1,A2)
(Exponential,Logarithm) --> (B1,B2)
(Probability,Statistics) --> (Time,Space)

(Real,Complex) --> (Gravity,Light)
(Natural,Integer) --> (W*,Weak)
(Rational,Irrational) --> (Strong,Black-Hole)

There seems to be good correspondence. Rational-Strong correspondence is good since Strong is based on the Rationals (1/3,2/3). Integer-Weak is also good since Weak has three bosons; (W-,Z,W+). Light's symmetry is Complex.


Da Vinci's The Last Supper has many symmetries that correlate strongly with the 13 senses.

(Nothingness) ... (Christ)

(Pain,Temperature,Rhythm) ... (Bartholomew,James,Andrew)
(Touch,See,Taste) ... (Peter,Judas,John)

(Smell,Hear,Balance) ... (James,Thomas,Philip)
(Harmony,Pressure,Pleasure) ... (Matthew,Jude,Simon)

Christ is demonstrating a triangle with the hands forming the base. The right hand is making a grabbing action on the table, while the left is open. This seems to represent the (Content,Container) duality. While this shows the duality of his self, it also points to the overall duality at the table. He wears red on the right, and blue on the left as a further illustration of this duality.

Bartholomew and Simon (Pain and Pleasure) sit at either ends of the table, thus setting the extreme boundaries. Peter leans over Judas to talk to John, indicating Touch-Taste relationship, while holding a knife pointed back towards Bartholomew indicating his nature.

Judas (See) is looking at Christ to synchronise the bread grabbing, while holding a bag of goodies, symbolising the excessive dominance of vision. Judas betrays Christ since we usually believe what we see, not what we can not see.

Thomas (Hear) leans over James (Smell) to listen to Christ. James (Smell) looks appalled, by what is happening, since he is getting a rough deal. Philip (Balance) is leaning over while standing in front of a corner.

John (Taste) looks young, feminine and tasty.

There are windows behind Christ, James and Thomas, indicating their airy character (Nothingness,Smell,Hear).

The room has few related symmetries coded. The three windows show the fundamental mediated duality symmetry. Four openings at either side show the 4-symmetry. 36 (6*6) pattern on the ceiling show the (6+1+6) symmetry of 13.

How come da Vinci knew this to so much detail? Much seem to come from the so called sacred geometry and science, but his knowledge seems so advanced.

Wednesday, May 21, 2008

Eleven senses

Moroccan tile.

The senses can be classified in an ordered stack of length 11;


Where the strongest symmetry is shown. Nothingness is the ground state of Consciousness. When there is nothing to sense, it senses itself. The senses are converted, by their organs, to a common electrical code before they are sent to the brain through Thalamus which is the switching organ at the center of the brain. Consciousness is centered at Thalamus it seems.

The 6 strongest dualities (Nothingness is a duality in itself) have an overall duality that demonstrates the symmetry that simulates a four dimensional hyper space-time;


The corresponding shape is Tesseract.


Colors also obey the same symmetry;


All colors saturate to White at higher Brightness, and to Black at lower. Brightness (Bright,Dark) is the enveloping element of Vision. Therefore it completes the symmetry of colors;

(Grey) ... Stability
(Bright,Dark) ... Brightness
(White,Black) ... Contrast
(Yellow,Purple) ... Color


Since Nothingness sits at the center and is neutral, many modules can attach themselves through their centers. This is demonstrated by two stacks of culture;



Politics and Interaction are the Nothingness of their categories, as the 10 elements of the Interaction stack are the fundamental methods of control in Politics. They compare to colors;

(Interaction) ... Stability
(Chaos,Order) ... Brightness
(Predation,Union) ... Contrast
(Competition,Cooperation) ... Color

In a stable system, (Chaos,Order) and (Predation,Union) dimensions rotate vertical to the color dimensions to make 3 dimensional structures with the other 3 dimensions curled-up and finely distributed over them.


Fields also obey the 11-symmetry, if 3 new fields are introduced;


Previously I used Dark-Energy for ZZZ which is supposed to be the dual of Weak. Now that there are 2 more fields predicted, XXX and YYY, I will use generic names. XXX and YYY seem to be like Energy and Anti-Energy. Maybe all three make up the Dark-Energy.

6 strongest dualities simulate a hyper Space-Time;

(((Higgs),(Time,Space),(XXX,YYY)), ((Light,Gravity),(Weak,ZZZ),(Strong,Black-Hole)))

Friday, May 09, 2008

Five dimensions of culture

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


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;


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;




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



There are 4 obvious dimensions of culture;


and 4 dimensions of drivers;


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;


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;


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;


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;


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.

Saturday, February 23, 2008

Modularity and self reference in life, universe and music

Koch's Star eigenvalues

Consider the following septet of septets in ordered stacks;

a. (Tail,Feet,Legs,Torso,Arms,Hands,Head)
b. (Lungs,Stomach,Vagina,Heart,Penis,Liver,Kidneys)

c. (Body,Eyes,Mouth,Brain,Nose,Ears,Balance-rings)
d. (Spine,Occipital,Cerebellum,Basal-Ganglia,Fore-brain,Temporal,Parietal)

e. (Touch,See,Taste,Sense,Smell,Hear,Balance)
f. (Observe,Move,Feed,Communicate,Feel,Think,Judge)

X. (e,c,a,x,b,d,f)

The septets have dual modularity combining the symmetries of numbers 2 and 3, each mediated by the center;


Defining 3 dimensions in the shape of hexagon, when represented in 2 dimensions. The symmetry of colors and sound harmony. All elements of the septets could be further expanded into sub-septets giving a self reference of depth one, although it may not look too obvious for some of them. Legs-Feet and Arms-Hands display this symmetry more obviously than others. For example the finger-like structures of the eyes and ears are not very obvious, let alone the heart, but I think it can be done.

Organs of the torso come in mediated dualities. As such, Stomach should be considered together with it's (Mouth,Anus) duality. Similarly for Vagina and Penis; Ovaries and Testicles.

The central rhythmic role of Basal-Ganglia is well known. Compared with the other mediators, it fits well. Maybe it should be considered together with Thalamus which has the central switching role connecting the cortex to it's field of senses. Kidney-Lung connection is mentioned in the net and seems reasonable. Stomach-Liver connection is pretty clear. They should be considered with their counterparts; Intestines and Pancreas.

(e,f) are software, (c,d) are middleware, and (a,b) are hardware, if compared to computers. Each sense is first transformed and then transmitted to the brain by specialized connections. 'x' mediates all 6 mediators and I can't quite figure out what it is at the moment.


The following quartet is for the universe;



Where Strong is expanded into it's color charges. Green is for anti-Red and so on. Strong mediates all forces, being the strongest. Space-Time is taken as a field like others and couples to Weak. I think this is reasonable. The second law and time's directionality weaken towards smaller scale.

Gravity-Light coupling is obvious because of the equivalence principle. In fact each duality could stand for it's own principle of equivalence. This remains to be proven. The other dualities may have some hysteresis, unlike Light-Gravity, but it may also have some form of hysteresis under some conditions. This reasoning assumes that each duality come with some kind of balance, like that of supply-demand of economics.

If the life classification is considered, three septets corresponding to 'software' and coordination functions are missing. My guess is that they are related to the Dark Energy. In life, intelligence and awareness weighs the most in some respect, when the success of humans is considered. Not to say that DE is self aware but it is very important in cosmology, as it has the most of the universe's mass, yet it is hidden like Higgs.


Music also comes with septets;



The harmonic space of music expands around the strong notes (C,E,G,B) and their dual counterparts (C,A,F,D). A is backward 3rd, F is backward 5th, and D is backward 7th. C mediates 3 dualities;


giving 3 dimensions. I am still thinking about it's dual.

Thursday, January 31, 2008

Four dimensions of culture

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


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;


Like the color symmetry;


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;


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;



Music has a similar form;


The drivers make 3 dualities and a singularity;


The world of vision also has 4 drivers;


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;

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;



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


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

There are 5 obvious senses of life;


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;


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 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;


Lets compare with senses;


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;


Compare with 7 senses;


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;



There are 7 fundamental sciences;


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;


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;


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 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;


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;


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;


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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