Why 3 colors?

Light has 2 degrees of freedom;

(frequency,amplitude) ---> (color,intensity)

All colors saturate to white in high intensity and to black in low, thus defining the evolutionary boundary. Color helps navigation in demanding environments like tree tops and expands in the gray middle range as it evolves. It works as an indexing agent for space, therefore there are 3 colors.

If fast navigation in a 3D environment is an evolutionary selection factor for the species, then they would die off if there were no possibility of extending the gray vision. But this possibility exists since there are 2 degrees of freedom of light.

The vision of 3 primary colors creates a 3D color matrix of the observed scene and maps it to the gray vision of intensity. This creates a 3D addressing mechanism and defines an improved indexing and addressing of the field. Senses are defined by their dedicated organs, like hardware peripherals of computers. Dedicated organs are needed for faster detection.

Gray on/near gray is still gray, but two different colors with the same grayness (intensity) stand out when near each other, and produce a different color when overlap due to two eyes. This improves the stereographic vision. Otherwise you need to swing your head side to side to improve the depth of the field. This is well observed in many animals, and it is a security risk and a time waster.

"Why do dogs have none?"

Assuming that the dogs have no color vision, it would be because they do not need to navigate in a 3D environment.

"Why do some humans with eyes just like yours, still not see any color
or only 2."

All genetic traits have a statistical distribution. Most humans have good color vision.

...

PS; The above is an extract from an exchange at sci.philosophy;

http://groups.google.com.au/group/alt.philosophy/browse_frm/thread/ccddf056eaf7e793?hl=en#

The song of being in measure 4/3

1. (Biochemical,Tissue,Organ)
2. (Populational,Relational,Philosophical)
3. (Quantal,Matter,Celestial)
4. (Multiverse,Omniverse,Divinity?)

The measure 4/3 inverts to 3/4 as it branches further;

1.1. ((Amino-acid,Protein),(Nucleotide,Nucleic-acid))
1.2. ((Connective,Epithelial),(Muscle,Neural))
1.3. ((Inner-action,Outer-action),(Inner-sense,Outer-sense))

2.1. ((Individual,Family),(Tribe,Species))
2.2. ((Interaction,Economics),(Technology,Communications))
2.3. ((Politics,Ethics),(Sciences,Philosophy))

3.1. ((Higgs,Boson),(Lepton,Quark))
3.2. ((Plasma,Gas),(Liquid,Solid))
3.3. ((Gas-Dust-Meteor-Comet,Planet-Moon),(Star,Black-Hole))

The rest is the arena of speculation, but there is enough of it to qualify for a pretty serious MIT paper about the Multiverse. The symmetry suggests further 2 categories. One of them already has a name; Omniverse. About the other, I have no idea. Divinity?

4.1. ((Level-1,Level-2),(Level-3,Level-4)) ... (*)
4.2. ?
4.3. ?

(*) http://space.mit.edu/home/tegmark/multiverse.pdf

Some of the details of the further branching are in my previous posts. There is enough evidence to suggest that the 3rd level belongs to the numbers 3, 6 and 12 for the detailing. The categories add upto 48 at the second level, reminding Bach's 48 preludes and fugues and plenty of references from the ancient cultures. The prelude that I love most, that of BWV-998, has the measure 4/3. My second favorite, BWV-999, has the measure 3/4. Both lute preludes. There you go.

Duet of life and universe in measure 3/4

This is an update to my previous post "The eightfold way of existence". I expanded the biology and universe sections and excluded the sections on culture, language, music and mathematics.

There are 4 biochemicals, 4 tissue and 4 organ types in biology;

(((Amino-acid,Protein),(Nucleotide,Nucleic-acid)),
((Connective,Epithelial),(Muscle,Neural)),
((Inner-action,Outer-action),(Inner-sense,Outer-sense)))

The symmetry of each quartet is like the modular group. I have excluded the chemicals like carbohydrates, lipids and ions from the biochemicals. Although there is not a clear cut boundary between the ordinary chemicals and biochemicals, these clearly define a good quartet. Like nucleotides are parts of nucleic acids, amino acids are parts of proteins, and both nucleotides and amino acids also have other functions. There are 12 amino acids. There are 4 groups and 12 types of Connective tissue;

(Loose,Dense,Cartilage,Other) =
((Areolar,Adipose,Reticular),(Regular,Irregular,Elastic),
(Hyaline,Fibrocartilage,Elastic),(Bone,Blood,Lymphatics))

There are 6 inner and 6 outer senses;

(((Pain,Pleasure),(Temperature,Pressure),(Rhythm,Harmony)),
((Touch,Balance),(See,Hear),(Taste,Smell)))

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;

(((Feeding,Reproductive),(Lungs,Kidneys),(Heart,Brain)),
((Hands,Feet),(Arms,Legs),(Torso-Tail,Head)))

The Head reflects the torso in the organ symmetry.

,,,

Universe obeys the same symmetry;

(((Higgs,Boson),(Lepton,Quark)),
((Plasma,Gas),(Liquid,Solid)),
((Gas-Dust-Meteor-Comet,Planet-Moon),(Star,Black-Hole)))

The boson-fermion quartet match the 4 biochemical groups. The 4 phases of matter match the 4 tissue types of biology. 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.

There are 6 leptons and 6 quarks;

(((Electron,E-Neutrino),(Muon,M-Neutrino),(Tau,T-Neutrino)),
((Up,Down),(Strange,Charm),(Bottom,Top)))

They also have their anti-particles. There are 3 known Bosons;

(Light,Weak,Strong)

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

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

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

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

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.

...

The symmetry match between life and universe demonstrates the modularity and self similarity of the universe. It may even show the inseparability of consciousness and matter, since life evolves from the depths of matter and there is no clear boundary between them. All life forms have their own cultures with a matching spectrum to human's, like language, music, tool using and so on, however dilute. Their elements add up to 12+12 = 24, a magic number. The duet they have been singing is still being created and its measure is 3/4, a very popular measure in human music.

The eightfold way of existence

A Tantric Yantra.

















There are 4 tissue and 4 organ types in biology;

(((Connective,Epithelial),(Muscle,Neural)),
((Inner-sense,Outer-sense),(Inner-action,Outer-action)))

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

(Loose,Dense,Cartilage,Other) =
((Areolar,Adipose,Reticular),(Regular,Irregular,Elastic),
(Hyaline,Fibrocartilage,Elastic),(Bone,Blood,Lymphatics))

There are 6 inner and 6 outer senses;

(((Pain,Pleasure),(Temperature,Pressure),(Rhythm,Harmony)),
((Touch,Balance),(See,Hear),(Taste,Smell)))

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;

(((Stomach-Liver,Vagina-Penis),(Lungs,Kidneys),(Heart,Brain)),
((Hands,Feet),(Arms,Legs),(Torso-Tail,Head)))

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;

(((Left,Right),(Inner-Eye,Eye)),
((Open-Close,Rotate),(Focus,AntiFocus)))

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;

(((Interaction,Economics),(Logistics,Communications)),
((Politics,Ethics),(Sciences,Philosophy)))

There are 12 types of Interaction;

(((Chaos,Order),(Predation,Union),(Competition,Cooperation)),
((Feeding,Reproduction),(Maintenance,Extermination),(Production,Consumption)))

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

(((Chaos,Predation,Competition),(Order,Union,Cooperation)),
((Feeding,Maintenance,Production),(Reproduction,Extermination,Consumption)))

There are 6 Sciences;

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

...

Language;

(((Sound,Syllable),(Word,Sentence)),
((Conjunctive,Conditional),(Adjective-Noun,Adverb-Verb)))

...

Music;

(((Note,Interval),(Measure,Theme)),
((Tempo,Rhythm),(Melody,Harmony)))

There are 12 Notes in equal tempered music.

...

Mathematics;

(((Number,Operation),(Function,Equation)),
((Logic/Set-Theory,Analysis),(Algebra,Geometry)))

...

Universe;

(((Higgs,Boson),(Lepton,Quark)),
((Gas-Dust-Meteor-Comet,Planet-Moon),(Star,Black-Hole)))

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;

((Plasma,Gas),(Liquid,Solid))

There are 6 leptons and 6 quarks;

(((Electron,E-Neutrino),(Muon,M-Neutrino),(Tau,T-Neutrino)),
((Up,Down),(Strange,Charm),(Bottom,Top)))

There are 3 known Bosons;

(Light,Weak,Strong)

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

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

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

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

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.

Thirteen senses and Da Vinci's The Last Supper

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

(Pain,(Temperature,(Rhythm,(Touch,(See,(Taste,
(Nothingness),
Smell),Hear),Balance),Harmony),Pressure),Pleasure)

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;

(((Pain,Pleasure),(Temperature,Pressure),(Rhythm,Harmony)),
(Nothingness),
((Touch,Balance),(See,Hear),(Taste,Smell)))

The corresponding shape is Tesseract.

There are also two dual-duality symmetries;

(((Pain,Temperature,Rhythm),(Touch,See,Taste)),
(Nothingness),
((Smell,Hear,Balance),(Harmony,Pressure,Pleasure)))

(((Pain,Temperature,Rhythm),(Harmony,Pressure,Pleasure)),
(Nothingness),
((Touch,See,Taste),(Smell,Hear,Balance)))

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;

(Bright,(White,(Rhythm,(Yellow,(Blue,(Red,(Grey),Green),Orange),Purple),Harmony),Black),Dark)

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

...

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;

(Anarchy,(War,(History,(Communications,(Logistics,(Economics,
(Politics),
Ethics),Science),Aesthetics),Tradition),Peace),Dictatorship)

(Chaos,(Predation,(Adaptation,(Competition,(Production,(Reproduction,
(Interaction),
Extermination),Consumption),Cooperation),Ritual),Union),Order)

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;

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

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;

(((Natural,Integer),(Rational,Irrational),(Real,Complex)),
(Equation)
((Probability,Statistics),(Exponential,Logarithm),(Derivative,Integral)))

They also have some sequential symmetry;

(Derivative,(Exponential,(Probability,(Real,(Natural,(Rational,
(Equation),
Irrational),Integer),Complex),Statistics),Logarithm),Integral)

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.

Eleven senses

Moroccan tile.
















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

(Pain,(Temperature,(Touch,(See,(Taste,(Nothingness),Smell),Hear),Balance),Pressure),Pleasure)

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;

(((Nothingness),(Pain,Pleasure),(Temperature,Pressure)),
((Touch,Balance),(See,Hear),(Taste,Smell)))

The corresponding shape is Tesseract.

...

Colors also obey the same symmetry;

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

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
(Blue,Orange)
(Red,Green)

...

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;

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

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

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
(Production,Consumption)
(Reproduction,Extermination)

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;

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

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)))

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.

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;

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

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;

(Gas-Dust,Meteor-Comet,Moon,Planet,Star,Black-Hole-Galaxy,Universe)
(Atmosphere,Sea,Crust,Core,Rotation,Spin,Magnetic-Shield)

(Higgs,Light,Weak,Strong,Space-Time,Gravity,Dark-Energy)
(Yellow,Blue,Red,Grey,Green,Orange,Purple)

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;

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

(D,F,A,C,E,G,B)

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;

(D,(F,(A,(C),E),G),B)

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

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.

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.

A classification of life and universe

The universe starts from a fuzzy state;

0. {universe}

and it remains essentially fuzzy while building structures. Then it polarizes into a mediated duality;

1. {sense,{field}}

The transition {} --> {,{}} has two implied directions of evolution;

{,{}} = [,[]] + [,[]]*[[],] + [[],]

Where the format is loosely stated, but it is somewhat like the Clifford algebra. It is undecidable whether 'sense' leads to 'field' or vice-versa. Like the chicken-egg dilemma. The fuzzy parent state transforms to [,[]]*[[],], and becomes the mediator of the duality. Like a tossed coin settling on it's rim, or having sexually fuzzy offspring.

The mediated duality form is observable in many areas;

. {mathematics} --> {operator,{number}}
. {quantum mechanics} --> {observer,{observed}}
. {music} --> {listener,{performer}}

Then, iterate again to get offspring functionality;

1. {sense,{field}}

2. {exclusive,{inclusive}, {space-time-gravity*-light, {weak-strong}} }

Where 'exclusive' stands for 'observe-move' or soft interaction, and 'inclusive' for 'reproduce-feed' or hard interaction. '*' stands for the field-antifield pair.

The combination 'space-time-gravity*-light' is non-intrusive or soft interaction, while 'weak-strong' is hard.

In mathematics;

1. {operator,{number}}
2. {additive,{multiplicative}, {0,{1}} }

'additive' is not intrusive like 'observe-move', yet 'multiplicative' is intrusive like 'feed-reproduce'. '0' and '1' are are the identity elements of the operators.

Therefore, 'field' seems to correspond to 'higgs'. The scalar field and it's associated operators are at the foundation of all systems. Like numbers for mathematics, money for economy.

Then, iterate until 6;

2-0. {exclusive,{inclusive}}
3-0. {observe,{move}, {reproduce,{feed}} }

2-1. {space-time-gravity*-light, {weak-strong}}
3-1. {space-time,{gravity*-light}, {weak,{strong}} }

;;;

3-0-0. {observe,{move}}
4-0. {analyze-hear,{imagine-see}, {sustain-propel,{navigate-manipulate}} }

3-0-1. {reproduce,{feed}}
4-1. {non-sexual,{sexual}, {taste*,{smell*}} }

,,,

3-1-0. {space-time,{gravity*-light}}
4-2. {space,{time}, {gravity*,{light}} }

3-1-1. {weak,{strong}}
4-3. {neutral-weak,{charged-weak}, {strong,{residual-strong}} }

The symmetry of 'weak' seems to be the symmetry of reproduction. Taste-strong correspondence is reasonable. Residual-strong refers to the force between nucleons.

;;;

4-0-0. {analyze-hear,{imagine-see}}
5-0. {analyze,{hear}, {imagine,{see}} }

4-0-1. {maintain-propel,{navigate-manipulate}}
5-1. {maintain,{propel}, {navigate,{manipulate}} }

,,,

4-1-0. {non-sexual,{sexual}}
5-2. {self-repr,{shared-repr}, {female,{male}} }

4-1-1. {taste*,{smell*}}
5-3. {taste,{untaste}, {smell,{unsmell}} }

...

4-2-0. {space,{time}}
5-4. {along-space,{lateral-space}, {along-time,{lateral-time}} }

4-2-1. {gravity*,{light}}
5-5. {gravity,{antigravity}, {electric,{magnetic}} }

,,,

4-3-0. {neutral-weak,{charged-weak}}
5-6. {organism-cell,{dna-molecule}, {star-planet,{moon-comet}} }

===> There seems to be a problem here with 'neutral-weak' to life mapping. Star-weak mapping seems to be OK. Still thinking about this.

4-3-1. {strong,{residual-strong}}
5-7. {black-hole/galaxy,{neutron-star/white-dwarf}, {hadron-lepton,{neutron-proton}} }

Male/female and star-planet/moon-comet correspondence rings a mythological bell.

;;;

5-0-0. {analyze,{hear}}
6-0. {specialize,{generalize}, {left-hear,{right-hear}} }

Analyzing is dual and performed by the two halves of the brain. While one side concentrates on detail, the other side concentrates on the context. This gives a clue to how we hear as well. The {bass,{treble}} duality of music corresponds to this.

5-0-1. {imagine,{see}}
6-1. {plan,{aim}, {left-see,{right-see}} }

Imagining is also dual, but lateral to analyzing and in the forward-backward direction. The frontal cortex does the long term planning ('aim' above). This gives a clue to how we see as well.

,,,

5-1-0. {maintain,{propel}}
6-2. {sustain,{break}, {propel-forward,{propel-backward}} }

Breaking is a part of maintaining, like sustaining.

5-1-1. {navigate,{manipulate}}
6-3. {left-turn,{right-turn},{make,{unmake}}

Navigation seems to be more than just left and right turn, but in general this is the case. Cars have just a steering wheel for navigation.

Manipulation is essentially an upmarket type of navigation involving choices along the way.

,,,

5-2-0. {self-repr,{shared-repr}}
6-4. {undifferentiated,{hermaphrodite}, {host,{guest}} }

5-2-1. {female,{male}}
6-5. {feminine-female,{masculine-female}, {masculine-male,{feminine-male}} }

,,,

5-3-0. {taste,{untaste}}
6-6. {eat,{drink}, {defecate,{urinate}} }

At the 6th step, sense becomes organ related.

5-3-1. {smell,{unsmell}}
6-7. {breathe-in,{breathe-out},{impregnated,{impregnate}}

Nose and sexual organs are closely related.

---

5-4-0. {along-space,{lateral-space}}
6-8. {forward,{backward}, {left,{right}} }

Space is essentially one complex dimension. Complex numbers are closed, and they have one along and one lateral dimension; {1,i}. There is only one space dimension between two objects. The surface of the earth can be viewed as a complex plane. There seems to be 3 perfect dimensions of space, but this is never the case, since there is always gravity distortion. Space can not exist without gravity. I think the apparent threeness of space is related to it's content; matter.

5-4-1. {along-time,{lateral-time}}
6-9. {forward,{backward}, {left,{right}} }

This point is also surprising for me, like the previous one on space, although it is well known that time is complex. Time travel is predicted here.

,,,

5-5-0. {gravity,{antigravity}}
6-10. {+gravity,{-gravity}, {+antigravity,{-antigravity}} }

Gravity is a polarized field like electric field. Anti-gravity is predicted here and it maps to magnetic field below, to give a clue about it's character. It seems anti-gravity can be produced by electric currents.

5-5-1. {electric,{magnetic}}
6-11. {+electric,{-electric}, {+magnetic,{-magnetic}} }

The poles of magnetic field do not exist separately, but electric field's do.

,,,

5-6-0. {organism-cell,{dna-molecule}}
6-12. {organism,{cell}, {dna,{molecule}} }

===> There seems to be a problem here with 'neutral-weak' to life mapping. Star-weak mapping seems to be OK. Still thinking about this.

5-6-1. {star-planet,{moon-comet}}
6-13. {star,{planet}, {moon,{comet}} }

5-7-0. {hadron-lepton,{neutron-proton}}
6-14. {hadron,{lepton}, {neutron,{proton}} }

5-7-1. {black-hole/galaxy,{neutron-star/white-dwarf}}
6-15. {black-hole,{galaxy}, {neutron-star,{white-dwarf}} }

***

Senses and fields expand into two parallel binary trees complementing each other. The numbers involved correlate strongly with mythology.

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

They add up to 2*(1+2+3+4+5+6) = 42 (The answer maybe 42 after all!). The tree expands into 64 distinct categories at the outer edge. Reminding I-Ching and the Jewish mythology about creation. Many more interesting numbers can be extracted from the tree, depending on how it is looked at.

Complex numbers, modular group and Mobius transformation are closely related.

A link to computers is also made. Electronic computing is based on binary trees. The universe seems to be a boolean computer at the overall category calculation level.

13 senses

I have proposed that measure and balance are complementary senses mediated by their corresponding touch sense. The balance sense is out of the way and and it's two organs are hidden in the middle ear. For this reason it is usually not regarded as a sense. I have not been able to figure out the organ for the measure sense. I proposed that it is somehow related to the central clock in the brain. But what is this clock and where is it?

I concluded that the organ of the measure sense is in fact the body itself. We touch the universe with our bodies while measuring and balancing. Without measure and touch one can not balance. In fact both measure and balance senses are types of touch evolved from their root touch sense. Like {see,touch,hear} and {smell,touch,taste}. Touch is a generic sense, the scalar field of the senses.

A good connection to quantum mechanics is made as well. Quantum mechanics studies scattering of quanta. Basically it studies touch. I have already attempted a mapping of senses and organs to fields and charges. Thus this study of the senses is an attempt to figure out the universe by comparing it to life. A top-down look at or a short cut to unification. The string theory has already proposed ten dimensions, corresponding to my ten senses.

When a dynamical system goes through the process of quantization, it has to keep it's balance. An organism is made of cells and higher quanta (organs) while it balances itself. Without balance, it can not execute it's other senses and survive. Strangely enough, the balance sense couples to hearing, like space couples to gravity. I think {measure,balance} coupling corresponds to {space,time} coupling, suggesting that space and time are fields. The organs of the balance sense are three liquid filled hairy (inside) and coupled rings for each ear. Thus balance maps to space, and measure maps to time.

The heart is the organ of the measure sense, and the whole body is the organ of the mediating touch sense. It provides the essential rhythm for the brain and the body. The brain's (and the body's) clock is the heart. The definition of 'second' comes from the heart's rhythm.

Senses and organs are not stand-alone things; they interact. I find the {balance,hearing} coupling most interesting, like {space,gravity} coupling. There is a duct between the nose and the eyes, mapping to the {weak,light} coupling.

The following format exposes the importance of {measure,balance} coupling;

{measure,{see,{taste,{touch},smell},hear},balance}

They are foundation of existence, like space-time. Both are hidden. Of course the real foundation is the touch sense, like the Higgs field. Previously I proposed that {taste,smell} were the foundation. I am still somewhat undecided on this point, but I prefer the {measure,balance} coupling as the base.

Another interesting point is the {mouth,stomach,anus} coupling. I think there is connection to the black holes here. Black holes couple to space-time strongly, like {mouth,stomach,anus} making a hole right through the body. Life is essentially a filtering process from the feeding angle. Nose couples to mouth, and genitals couple to anus. There seems to be a strong link between the nose and the genitals. It seems that while the nose was differentiating from the mouth, genitals differentiated from the anus. Reproduction and feeding come from the same base. Is that why many humans (and animals!) like anal and oral sex I wonder?

Are there senses corresponding to the genitals? Which fields do they map to? Maybe there are 12 senses. What are the two complementary senses of sex? Penetrating and being penetrated? I will call them 'pen' and 'vag' for the moment. The organs are obvious; penis and vagina and their attached organs. If they are all listed together in a suitable format exposing their hierarchy;

{measure,{see,{taste,{pen,{touch},vag},smell},hear},balance}

or all 12 of them with their corresponding mediating touch senses;

{{measure,touch,balance},
{see,touch,hear},
{taste,touch,smell},
{pen,touch,vag}}

With the all inclusive nothingness {}, they are 13. That strange prime number with lots of ancient historical reference. 13 and 20 make the foundation of the Mayan calendar. I wonder where 20 comes from?

Senses and organs, fields and charges

The parallels between life and the universe has been suspected for a long time. After all, we are a subset of the universe and also situated in the middle of it, as also proposed by my recent 'Ten Aspects of Reality (TAR)' posting. Cliff Pickover's Reality Carnival occasionally prints the following;

'If we wish to understand the nature of reality, we have an inner hidden advantage: we are ourselves a little portion of the universe and so carry the answer within us.' - Jacques Boivin

I have come across to this concept for a while now, but not seen any explicit comparison. Since my recent TAR, I have been thinking about this a bit more. Previously I posted '7 Senses' but the fields were not right.

TAR suggests that there are ten senses;

{{measure,touch,balance},
{taste,touch,smell},
{see,touch,hear}}

Together with the all inclusive nothingness {}, they are ten. Each triplet is mediated by it's own type of touch sense. In a sense, they differentiate or evolve from this root sense. They touch each other by this sense in the brain. The three touch senses are mediated by the touch sense mediating the {taste,smell} duality. The feeding related touch sense is the origin of all senses.

There are 5 known fields;

{{strong,weak},{higgs},{light,gravity}}

Higgs is not observed yet and theorized to be a scalar field. Each field has it's own charges. Light has (+,-) charges, Gravity has mass, Strong has the color charges, and Weak has the (W+,W-) charges.

Similarly senses have their own organs. Vision has eyes, hearing has ears, taste has mouth, and smell has nose. They are all mediated by the root senses in the brain. Clearly the brain mediates all senses. I propose that there is a root sense doing all this mediation. Consider the following mapping;

{see,hear} ---> {light,gravity} ---> {star,universe}
{taste,smell} ---> {strong,weak} ---> {cell,species}
{measure,balance} ---> {?,?} ---> {time,space}

The last column is from TAR.

The first line groups {see,light,star} and {hear,gravity,universe}. The fist triplet is reasonable. In the second, {gravity,universe} correspondence is also fine since gravity is the force shaping the outer aspect of the universe. Interesting that hearing gets mapped to gravity. Gravity makes the geometry for light to operate in, and hearing sets the context for vision to operate in. Bats use the this context setting property of sound to navigate. In movies, audio sets the mood, while video coveys information.

The second line groups {taste,strong,cell} and {smell,weak,species}. {taste,strong} relationship is reasonable, since both are short range. It is interesting that {cell} falls in this triplet. It seems cell is all about taste. They have to touch each other to do things. {smell,weak} correspondence also seems reasonable. Weak has a longer range than Strong, like Smell and Taste. Why does Species fall into this triplet?

The third line groups {measure,?,time} and {balance,?,space}. {measure,time} and {balance,space} correspondences are reasonable. The organs of the balance sense are the three liquid filled hairy rings for each inner ear. What is the organ of the measure sense? It is known that the brain is run by clocks. Maybe there is a central clock. What are the fields standing for the question marks? There must be two unknown fields. Thus ATON predicts two new fields and their corresponding charges. Maybe space-time are the charges of these fields. Maybe space-time is a field of the black holes. This seems quite credible since they are the boundaries. Also rings a bell with Hawking's holographic principle.

Moreover, there must be ten fields to reflect the ten senses proposed by TAR. Higgs is like touch; it is a scalar or generic field. Maybe Higgs divides into three.

Nucleon, brain, and black hole

This is a another look at the Ten Aspects of Reality (TAR), which are;

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

With the all inclusive bracket {} nothingness, they are ten.

Recently it occurred to me that the new cosmological models predict ten dimensions. Anyway, this is not the main point here, I just wanted to mention it.

Hawking's entropy formula for a black hole is proportional to the area of the event horizon. This means that nothing gets lost in a black hole and there is a maximum entropy density, which happens to be on a surface. I suppose the area of a black hole is calculated according to the flat space-time much further away from the horizon, since space-time does not exist at the surface itself.

Encouraged by the TAR, I wanted to compare the brain to the black hole. Neurons are distributed on the surface of the brain and all the inner bits are wiring. Whatever happens in the brain, actually happens on the surface. Like a black hole. The difference is that black holes are connected to it's body from the outside, and brains from the inside. Black hole is like the brain of a galaxy. It's body consists of stars, nebula, gas, dust and other stuff. Latest research suggest that the earliest galaxies also had black holes. Brains also form very early in organisms.

Galaxies seem to form a huge collective meta brain, like humans and other organisms form a huge meta brain. Now we are building the internet to take this meta brain to a new level. I think the internet is the first step of humanity in the merging of our minds to the hardware of the universe. This has been suggested before. I think there are types of black holes, as there are types of galaxies. There are two main types; elliptical and spiral. Like organisms; male and female. Galactic society seems to be a reflection of the organic society, but maybe inside out.

Nucleons are made of 3 quarks and 3 gluons. There are two types; proton and neutron. Proton is stable by itself; neutron decays to proton, electron, and neutrino. Proton seems to have infinite life-time. Maybe it has the life-time of the universe. There are also 3 primary and 3 secondary senses of an organism; {{measure,see,taste},{balance,hear,smell}}. Touch is a generic sense and mediates all senses. All senses are types of touch. Brain is made around the senses. Proton seems to be the smallest possible black hole. Well, maybe not a black hole but something closely related. It's constituents are confined. As if it reflects the outer world; space-time. It is also connected to it's body (electrons, photons, and other stuff} from the outside.

It seems the organic brain mediates two types of 'material' brains; {nucleon,brain,black hole}. It exists by sandwiching itself between two reverse brains. And it's form obeys the quantity triplet; {0,1,infinity}. The question is; what is the nothingness that includes the lot?

The following Escher work (from http://www.mcescher.com/) reflects the symmetry of the brain triplet quite well I thought. There are two boundaries, inner and outer, and everything happens in between;

Ten aspects of reality

The seven senses are;

{measure,{see,{taste,{touch},smell},hear},balance}

Measure and balance are not normally regarded in the senses. Balance is achieved in the inner ear's hardware in the form of three liquid filled hairy rings for each ear. Balance seems to qualify to be a sense. Measure is more difficult to judge as a sense. If sciences are also listed in the same manner, measure becomes clearer when it is mapped to mathematics;

{mathematics,{physics,{chemistry,{biology},psychology},intelligence},aesthetics}

Psychology is usually regarded to be a pseudo science. Intelligence is gaining more acceptance amongst cognitive sciences as computing advances. I think psychology will also acquire a respectable place amongst cognitive sciences in due time. Aesthetics includes things like philosophy, art, music, poetry, and not regarded as science. It studies beauty and sometimes uses mathematics as a tool.

This particular ordering of sciences has two aspects that relates to senses. All sciences are based on mathematics and they form a complexity ladder. Biology seems to mediate all sciences in dualities. Psychology couples to -or based on- chemistry, in that it operates in a field of chemicals like hormones. Intelligence couples to physics, in that it uses electricity -or light- in the neuronal circuitry provided by brain. As suggested before, aesthetics somewhat couples to mathematics.

Aesthetics is used by most animals, if not by all animals and maybe all life. Aren't the flowers' smell and looks selected by insects? Similarly most plants are selected and shaped by animals. Animals also select and shape themselves. Isn't the sexual selection largely responsible for humanity's success? I think the universe shapes itself through a common sense of aesthetics. Don't many animals have a similar sense of music? My cat likes Bach. I was amazed with a camel's love of music when I saw the film Weeping Camel.

Similarly touch mediates all senses in three mediated dualities, as it is essential for sensing;

{{measure,touch,balance},
{taste,touch,smell},
{see,touch,hear}}

Smell evolves (or diverges) from taste as breathing separates from eating. {see,hear} coupling is not that obvious, but the symmetry involved is the same. It is like the {audio,video} duality in signal processing. The mathematics involved in video is a more complex version of audio. In both cases, dual sensing gives depth of field. {measure,balance} coupling is the hairiest. I think the core of a brain evolves around these two and their mediating touch sense. Measure is the root of all evolution. In quantum mechanics it corresponds to quantization of a field.

It seems the touch sense involved in each case is different, as there are many different types of touch. Touch is a generic sense. It senses temperature, pressure, hardness and so on. Thus we end up with nine senses, to match the nine aspects of reality;

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

As life {cell,organism,species} mediates the universe, eating {taste,touch,smell} mediates life. We also get a clue to the nature of the three kinds of touches mediating senses. Consuming or fusing kind of touch mediates the other two; one soft, the other hard. The quantity triplet {0,1,infinity} determines all four mediated dualities. Three dualities themselves form a mediated duality through their mediators.

With the predicted 'zero' to include the lot, we have the ten aspects of reality. The tenth aspect is the aspectlessness, or rather nothingness. If the Higgs field corresponds to 'zero', what is the corresponding sense?

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?

Time and pressure

Time displays thermodynamic aspects. Consider the triplets;

{Time, Matter, Space}
{Pressure, Temperature, Volume}

The P-T-V triplet are related to each other by the famous equation of ideal gas; PV = NkT, where N is the number of particles, k is the Boltzmann constant.

Time stops at the event horizon of a black hole. The entropy of a black hole is proportional to it's area; S = k(c^3)A / 4G(hb), where c is speed of light, hb is Planck's constant. This equation contains all the goodies. Black holes are the boundaries of space-matter-time, so they must contain it. It also includes the Boltzmann's constant k, and makes the link to thermodynamics pretty explicit. The great surprise of this equation was that the entropy is proportional to the area A. Time slows down in gravity, and eventually stops at the most intense gravity gradient; the even horizon of a black hole.

Gravity works as if space-time is squishing out it's contents towards less pressure, since space-time dilate in gravity. A gravity field is like a 3D hill's surface of a 4D volume (a normal hill's surface is 2D). We feel the squeeze down of gravity by the counter pressure of the earth. Thus space-time is has strong thermodynamic aspects. {Matter, Temperature} correspondence makes sense since matter is equivalent to energy. {Space, Volume} correspondence is obvious. Thus we get {Time, Pressure} correspondence implied. As we well know, pressure cookers shorten the time of cooking. Sounds funny I know, but I think this fact reflects the correspondence quite well, since pressure increases the event density in time.

What exactly is nothingness?

When I started this blog on nothingness (Nn), I had a vague idea of what Nn is, and I still am not totally clear on it, although clearer. I have come to believe that it is a trancendental and relative concept.

I have already given few examples of what it might be; water for taste, air for smell, space-time for matter and so on. I still think these examples are pretty close, but there is still a problem. Water by itself is not taste, although taste evolves out of water. The smallest amount of taste, as compared to water, corresponds to Nn. Therefore Nn is a relative concept like probability;

Nn0 = ,/,

At the limiting case Nn0, both numerator and denominator are equal in quantity. I use numerical concepts since ATON aspires to be based on numbers. It also relates to the word nothingness since it compares almost nothing to almost nothing. Through comparision to itself, "nothing" (N) gets lifted and becomes "nothingness" (Nn). Thus we seem to get a connection to the concept of equivalence class as well. I like to iterate on this later.

A connection to my Mirror Set is also made;

M(m,n) = m!n / n^m

Where m!n is the multifactorial of m to depth n. M(0,0) is undefined, or fuzzy and multivalued, as I imagined Nn to be.

Let me try another example from my cat Rupty. I adopted her when she was very little, maybe a week or two old. After I brought her to my place, the first thing she did was to inspect the room, starting from a wander around the outer perimeter of the room. She did not get out of the room until she was sure where she was, I gathered. After many hours, she started little trips out of the room to inspect the corridor. Every time she would come back running and excited. In this fashion she finished inspecting the house in a day or two. Then she did the backyard, the frontyard and the street in many days to come.

The way she was doing these inspections was seemingly random. She would pick a direction and time out of the blue and inspect it many times until she was confident. The randomness is also displayed in her switching of the sleeping place. One day, out of the blue, she would swithch the place and start sleeping somewhere else she inspected before. This also applied to her other favorite places where she did one of her numbers like having a nap or sitting and watching.

I concluded that her behavior pattern is a fuzzy and random ball, like nothingness. It changed and took shape over time, but the essential fuzziness remained. We humans are also like cats when we are not regulated too much. We like to slumber along in a fuzzy pattern.

Nature abhors gradients?

Lately I ran into this book Into The Cool by Schneider and Sagan. It's on the developing science Non Equilibrium Thermodynamics (NET). It's central theme is the 2nd law of thermodynamics, nicely formulated as "nature abhors gradients". Nature likes to even out differences. Concentrations of heat get dissipated in time. Nature likes disorder. The novelty of the book is that it includes life into the 2nd law. That life is an integral part of the machinery of dissipation of order. The paradox here is that life is a process of building order. While it builds order, it consumes gradients which are larger order.

I am still reading the book, but I could not help commenting on the paradox. It is pretty clear that, while nature abhors gradients, it also loves them. It first builds them, and then rides them. For example, the gradient between the heat of the sun and the cool of the earth is consumed by life. Life builds intermediate structures to even out the temperature gradient. But the sun does not come out of the blue. It rides the gradient of the black hole in the center of the galaxy. And the galaxies are, in turn, processes that ride another invisible gradient, probably a white hole.

Another example is the seperation of the sexes. The male-female gradient is built by gradual evolution, starting from hermaphrodites. And then nature uses this gradient to make offspring.

An analysis of symmetry in BWV-999

This is my second and more detailed look at BWV-999, which is a lone prelude amongst the lute works by Bach. It seems to be the opening piece of all the lute works, which are 4 suites, prelude-fuge-allegro-998 which is a toughie and also very lovely, and a lone fugue which is also from the violine works. Apparently 999 is specifically marked to be for lute, and it also suits the 6 stringed modern guitar perfectly. It is also regarded to be one of the "kleine" keyboard preludes. It would be easy for the keyboard but not so for the guitar, with it's difficult chord changes and fast arpeggio. I will analyse all of it's 83 bars one by one, by looking at it from harmonic, melodic and fractal aspects, as much as I can with my limited musical knowledge. I hope to learn some more music through this analysis, as the piece is a relatively simple one. The main emphasis will be it's fractal structure. I am currently practising 999, 998 and the first suite.





The most outstanding aspect of a musical piece is it's measure, which is 3/4 here. 3/4 is a very special number with mythical, religious and mathematical significance. 999 is a uniform arpeggio piece with 12 sixteenths for each measure. 12 is also a magical number. Bach opens the keyboard prelude and fuges with an arpeggio prelude as well. A bit like a historical reference to the ancient harp. 999 opens with D-minor and closes with A-major.

Like most good musical pieces, it has {bass,mid-range,treble} symmetry. The mid-range is the spine of the piece, and bass and treble reflect each other and dance around it. I will use letters for notes and numbers for octaves, like D and 2D. Here is the first measure coded;
1. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The second measure is the same;
2. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The spine of the piece falls in the even numbers, or the alternate beats, if a measure is numbered from 1-12. All alternate beats are the same except the 4th sixteenth. The odd numbered notes make either side of the spine.

The first beat is the bass, and sets the dominant tone of the measure. It also completes the harmony started in the end of the previous measure. This bass linking is typical of most, if not all, musical pieces, and it comes from the linking of the scales. To see this, consider a 2 octave C-major scale;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a 1 octave scale is played, it sounds complete only after adding the octave higher root (2C here). Thus we get 8 notes in a complete sounding octave, although there are only 7 different notes. When 2 octaves are played, it sounds complete with 15 notes. The middle note 2C both ends the previous octave and also starts the next. Therefore 2C has a dual, or linking, role.

The measure is divided into 3 quarters, each with 4 sixteenths. The 1st and 3rd quarters reflect each other around the mediator 2nd quarter. The 1st quarter(D,2D,2F,2A) is a typical 4 note chord with it's bass and 3 trebles (D minor here). The last 3 notes of the 1st q (2D,2F,2A) are reflected by the 1st and 3rd notes of the 3rd q ((A),2D,(F),2D), and the 1st note of the 1st q ((D),2D,2F,2A), in reverse order, half speed and in the previous octave (2D,2F,2A)-(A,X,F,X,D). The 2nd q acts as a mirror. But the symmetry is slightly distorted by the shifted position of the 1st chord. This creates tension and movement. Thus we get two chords reflecting each other and dancing around a spine, in a slightly imbalanced form. When you consider different tones for the chords in the rest of the piece, you get the fireworks.

The genius of Bach here shows itself in the complexity contained in the simplicity.

A measure is the smallest unit that contains all essential properties of a piece. In this sense, it corresponds to atoms of physics and cells of life. This is such a powerful metaphor. Universe and life are essentially musical forms.



























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