A Theory Of Nothingness

The Fifth Element

2011-08-19T16:48:00.006+10:00

Vajra cross

Map the four variables of the ideal gas law to the categories of the universe;

((P,V),(N,T)) --->
(((Energy,Momentum),(Time,Space)),((Mass,Charge),(Gravity,Boson)))

Where;

Charge = (Electric,Weak,Color)
Boson = (Light,Weak,Gluon)

Rearrange the categories to expose an implied symmetry;

(((Energy,Time),(Mass,Gravity)),((Momentum,Space),(Charge,Boson)))

Compare it to the categories of life;

(Tissue,Organ) =
(((Muscle,Neural),(Connective,Epithelial)),((Isense,Osense),(Iaction,Oaction)))

Where;

Organ = (Head,Body) = (Sense,Action)

Isense = Inner-sense = ((Pain,Pleasure),(Temperature,Pressure),(Rhythm,Harmony))
Osense = Outer-sense = ((Touch,Balance),(Taste,Smell),(Hear,See))

Iaction = Inner-action = ((Lungs,Kidneys),(Stomach,Penis-Vagina),(Heart,Brain))
Oaction = Outer-action = ((Arms,Legs),(Head,Torso-Tail),(Feet,Hands))

Rearrange the categories of life and compare it to the ideal gas and the universe;

((P,V),(N,T))
(((Energy,Momentum),(Time,Space)),((Mass,Charge),(Gravity,Boson)))
(((Muscle,Isense),(Neural,Osense)),((Connective,Iaction),(Epithelial,Oaction)))

Why does the ideal gas law underlie both classifications?

Perhaps because the primordial soup of life can be approximated as a gas of chemicals dissolved in water. The same argument must apply to the universe. Since Dark Matter can be considered as a quantum liquid, the fifth categories for the universe and life are implied;

(Higgs,DarkMatter)
(Biochemical,Water)

The fifth element in the case of the ideal gas must be the Boltzmann constant;

P*V = k*N*T

Thus the overall symmetry is that of the Vajra cross;

((P,V),{k},(N,T))
(((Energy,Momentum),(Time,Space)),{Higgs,DarkMatter},((Mass,Charge),(Gravity,Boson)))
(((Muscle,Isense),(Neural,Osense)),{Biochemical,Water},((Connective,Iaction),(Epithelial,Oaction)))

64 Aspects of the Universe

2011-07-21T14:59:00.000+10:00

The ideal gas law;

P*V = k*N*T

k; Bolzmann constant.
P; Pressure
V; Volume
N; Number of particles
T; Temperature

Map the four thermodynamic variables to physical categories;

(Energy,Momentum)
(Time,Space)
(Mass,Charge)
(Gravity,Boson)

The symmetries reflect each other;

((P,V),(N,T))
(((Energy,Momentum),(Time,Space)),((Mass,Charge),(Gravity,Boson)))

The choice of the physical categories is also supported by the common (1,3) symmetry;

Momentum; (Px,Py,Pz)
Space; (x,y,z)
Charge; (Electric,Weak,Color)
Boson; (Light,Weak,Gluon)

Mass and Energy are scalars, Time and Gravity are vectors.

The eight physical categories are fully meshed; each is related to the other seven, although the indicated relationships are the strongest. Thus an 8*8 matrix is needed to contain all relationships.

Thirteen Aspects of Mathematics

2011-04-11T14:47:00.001+10:00

My previous post "64 Aspects of Mathematics" assumed 8 elementary theories and predicted higher order theories through a non-commutative multiplication of the octet by itself.

This post is a speculation on the resemblance of the octet to the major scale of the 12 tone equally tempered music. The octet classification has some imperfections that may be addressed better in a stack of 13 (12+1).

The major scale has a modular symmetry when the octave of the root is appended (2C gives a feeling of completion);

(((C,D),(E,F)),((G,A),(B,2C)))

This symmetry can be heard easily by trained ears. The Stern-Brocot Tree easily explains this modularity. Modular Group, SL(2,C), is mentioned in many papers dealing with the music theory.

The equal tempered music is a marriage of two symmetries; the modular group and the logarithm. The cycle of fifths almost meets the octaves in 7 octaves;

((3/2)^12)/2^7 = 1.0136

This is the miracle that makes the equal temperament possible. I think this is not an accident.

The 13 tone stack is;

C,#C,D,#D,E,F,#F,G,#G,A,#A,B,2C

The mathematics octet can similarly be expanded by filling in the missing theories;

Set
-Logic
Analysis
-DifferentialG ... ?
Geometry
Algebra
-Combinatorics ... ?
Probability ... QM
-StochasticP ... QFT
Statistics ... SM
-Inference ... Td
Computation ... SR
Information ... GR

Logic for #C and so on. The most interesting part of this comparison is the relationship of the first to the last;

(Set,Information) ... (C,2C)

Obviously there is a very simple relationship between C and 2C. Is there such a thing for the Set and the Information Theories? There are some studies on this subject. A notable one is by Gregory J. Chaitin, "Gödel's Theorem and Information";

http://www.cs.auckland.ac.nz/~chaitin/georgia.html

I have come across a few studies (proofs?) of Riemann's Hypothesis via the concept of entropy. But as far as I know these are not taken to be the last word yet.

When the experiment part is compared to a classification of physics, IT corresponds to General Relativity. Perhaps this is why the Black Holes have a simple entropy equation. The Modular Group and General Relativity relationship is also all over the net.

The Thermodynamics (Td) and Special Relativity (SR) neighborhood is also interesting;

http://arxiv.org/abs/0712.3793
"On the Relationship between Thermodynamics and Special Relativity"

64 Aspects of Mathematics

2011-03-25T13:22:00.000+11:00

This is an attempt to classify mathematics in an 8*8 matrix. Most items below can be found in the Internet, eg search for Algebraic Geometry or Geometric Algebra. The ones not found are predicted by the matrix. All 8 items are theories in themselves, eg Information Theory or Theory of Computation. When it repeats like Analysis-Analysis, it stands for Elementary Analysis. The model demonstrates the non-commutativity of mathematical classification.

The model also predicts the 3rd and higher iteration theories, like Algebra-Geometry-Analysis. Thus, while Mathematics unites, it also diverges, reminding its paradoxical nature.

1.1. LogicSet-LogicSet

1.2. Analysis-LogicSet

1.3. Algebra-LogicSet

1.4. Geometry-LogicSet

1.5. Probability-LogicSet

1.6. Statistics-LogicSet

1.7. Computation-LogicSet

1.8. Information-LogicSet

2.1. LogicSet-Analysis

2.2. Analysis-Analysis

2.3. Algebra-Analysis

2.4. Geometry-Analysis

2.5. Probability-Analysis

2.6. Statistics-Analysis

2.7. Computation-Analysis

2.8. Information-Analysis

3.1. LogicSet-Algebra

3.2. Analysis-Algebra

3.3. Algebra-Algebra

3.4. Geometry-Algebra

3.5. Probability-Algebra

3.6. Statistics-Algebra

3.7. Computation-Algebra

3.8. Information-Algebra

4.1. LogicSet-Geometry

4.2. Analysis-Geometry

4.3. Algebra-Geometry

4.4. Geometry-Geometry

4.5. Probability-Geometry

4.6. Statistics-Geometry

4.7. Computation-Geometry

4.8. Information-Geometry

5.1. LogicSet-Probability

5.2. Analysis-Probability

5.3. Algebra-Probability

5.4. Geometry-Probability

5.5. Probability-Probability

5.6. Statistics-Probability

5.7. Computation-Probability

5.8. Information-Probability

6.1. LogicSet-Statistics

6.2. Analysis-Statistics

6.3. Algebra-Statistics

6.4. Geometry-Statistics

6.5. Probability-Statistics

6.6. Statistics-Statistics

6.7. Computation-Statistics

6.8. Information-Statistics

7.1. LogicSet-Computation

7.2. Analysis-Computation

7.3. Algebra-Computation

7.4. Geometry-Computation

7.5. Probability-Computation

7.6. Statistics-Computation

7.7. Computation-Computation

7.8. Information-Computation

8.1. LogicSet-Information

8.2. Analysis-Information

8.3. Algebra-Information

8.4. Geometry-Information

8.5. Probability-Information

8.6. Statistics-Information

8.7. Computation-Information

8.8. Information-Information

Eight aspects of mathematics

2011-03-18T19:51:00.003+11:00

Mathematics can be classified in 4 dualities;

Logic/Set-Theory, Analysis

Algebra, Geometry

Probability, Statistics

Computation, Information

Logic and Set Theory are considered to be the foundations. Information stands for Information Theory. Computation is not the computer science, it is the theory of computation.

The symmetry is modular like that of the major scale;

( ((c,d),(e,f)), ((g,a),(b,2c)) )

This symmetry also applies to my previous post, Eight Aspects of Economy.

Curiously enough, the second quartet of the universe classification is missing;

Frame, Celestial

Quantum, Material

As I suggested in a previous post, the 2nd quartet must be the 4 levels of a multiverse theory;

Level-1, Level-2

Level-3, Level-4

The endpoints of the major scale is an octave apart, (c,2c), when completed with 2c. I wonder of there is such a thing in the mathematics and the universe categories.

Eight aspects of economy

2010-06-21T12:38:00.002+10:00

Economy is determined by the methods of production and consumption. It determines the other aspects of societies, as much as it is determined by them. The simplest form of economy is gathering and hunting, and it seems to form a duality;

(Gathering,Hunting)

since hunter gathers the gatherer. Grazers, which are essentially gatherers, are usually accompanied by hunters. Although hunters can not exist without grazers, grazers are in turn shaped by hunters.

A similar duality exists for the next stage of economy;

(Farming,Industrial)

Farming is a tool intensive occupation, more than that of gathering and hunting. Industrial production is a step ahead of farming in that, it is a machine intensive occupation. Machines are tools of tools; they bring together many tools and operate them according to flowcharts. This is also reflected in their utilization in production lines.

The next natural stage of economy is also a duality;

(Information,Intelligence)

We have recently entered the information economy. As it matures, it paves the way for its partner; artificial intelligence. AI systems are already here and evolving with the intensive use of the systems of information.

What is the next stage, if there will be such a thing? Intelligence is strongly linked to psychology, which is the foundation of our spirituality. By implication, there seems to be another duality as the last stage of the evolution of economy;

(Spiritual,Artistic)

In fact all four dualities already exist in many forms, but only one is dominant at any time. Currently we are transiting from the industrial to the information economy. One can only wonder what kind goodies will evolve after the AI economy matures and paves the way to the next stage.

Sound and spectrum of prime/log(prime)

2010-02-03T17:17:00.000+11:00

Self similarity of z/log(z)

2010-01-14T16:28:00.015+11:00

I made the following pics by temporally iterating 3 spatial iterations;

z/log(z)
(z/log(z)) / log(z/log(z))
[(z/log(z)) / log(z/log(z))] / log[(z/log(z)) / log(z/log(z))]

The temporal iteration number is 170. Bailout is 40. The 4th pic is a close-up of the 3rd. They came about after a Google group discussion.

The 3 pictures similarity is amazing I thought. Just like the temporal iteration increasing resolution, the spatial iteration seems to do the same. I think there is a strong link here to the prime numbers, whose distribution is known to be self similar. Apart from the known fact that the primes are semi uniformly distributed in x/log(x), they seem to obey the H-fractal in their further patterns.

Another very interesting point here is that the both temporal and spatial iterations limit to 'e' at the outer region of the shape;

...(z/log(z)) / log(z/log(z))... -> e

demonstrating the binary structure of 'e'.

The tip of the last amplified to the limit of my pc. Note the slight angle. Numbers seem to prefer a side, as far as this function is concerned. This may be due to the accumulation of errors. If not, then this is also very interesting.

The semi-stable points. What is the link to the zeros of the Riemann's Zeta function?

"I will put chaos into fourteen lines"

2009-07-07T15:52:00.000+10:00

This is an update to my previous post "Complementarity of life and universe". The title is from the poem by Edna St. Vincent Millay. In my model there are 15 lines if infinity is included.

0-. (Infinity)

0. ((Individual,Population),(Universe,Multiverse))

0.0. (Biochemical,Tissue,Organ)
0.1. (Populational,Relational,Philosophical)
0.2. ((Frame,Quantum),(Material,Celestial))
0.3. ((Level-1,Level-2),(Level-3,Level-4)) ... (*)

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

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

0.1.0. ((Individual,Family),(Tribe,Species))
0.1.1. ((Interaction,Economics),(Technology,Communications))
0.1.2. ((Politics,Ethics),(Sciences,Philosophy))

0.2.0. (Gravity-Dark-Energy,Higgs,Space-Time)
0.2.1. (Boson,Lepton,Quark)
0.2.2. (Gas,Liquid,Solid)
0.2.3. (Planet,Star,Black-Hole)

0.3.0. Regions beyond our cosmic horizon.
0.3.1. Other post-inflation bubbles.
0.3.2. The many worlds of quantum physics.
0.3.3. Other mathematical structures.

Previously in the post "The song of being in measure 4/3" I added two more levels after multiverse. After changing the symmetry of the universe from 3/4 to 4/3, it agreed with the multiverse classification, removing the need for two more levels.

Some of the further branching is in my previous posts.

Complementarity of life and universe

2009-02-18T12:04:00.005+11:00

The Universe has 12 aspects arranged in measure 4/3;

(((Gravity/Dark-Energy,Higgs,Time-Space),(Boson,Lepton,Quark)),
((Gas,Liquid,Solid),(Planet,Star,Black-Hole)))

Life has 12 aspects arranged in complementary measure 3/4;

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

The outer shape of the Universe has four-fold symmetry;

((Quantum-gravity,Quantum-mechanics),(Statistical-mechanics,General-Relativity))
((GHT,BLQ),(GLS,PSB))

The outer shape of life has three-fold symmetry;

(Biochemical,Tissue,Organ)

,,,

Previously I included Plasma to GLS, and Gas-Dust-Meteor-Comet to PSB triplets to make them quartets. But later I realized that the GLS triplet already stands for the lower level matter. Similarly I excluded Higgs from the particle triplet BLQ and made a new triplet GHT, including Dark-Energy.

The (GHT,BLQ) duality compares to the 12 senses quite well;

(GHT,BLQ) => (Inner-sense,Outer-sense) =

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

They can be compared in many ways since the senses and fields are modular and self similar. The following correspondences are noteworthy;

Time-Space ... (Rhythm,Harmony) ... (Hear,See)
Higgs ... (Temperature,Pressure)
Gravity/DE ... (Pain,Pleasure) ... (Touch,Balance)

Similarly the (GLS,PSB) duality compares to the 12 actions;

(GLS,PSB) => (Inner-action,Outer-action) =

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

Why 3 colors?

2009-01-28T10:16:00.003+11:00

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

2009-01-25T12:06:00.003+11:00

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

2009-01-23T13:03:00.003+11:00

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

2008-10-27T14:45:00.013+11:00

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

2008-05-28T15:35:00.002+10:00

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

2008-05-21T14:25:00.005+10:00

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

2008-05-09T23:03:00.003+10:00

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

2008-02-23T19:46:00.004+11:00

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

2008-01-31T12:33:00.001+11:00

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

2008-01-20T00:40:00.000+11:00

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

2007-10-10T15:13:00.000+10:00

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

2007-10-05T15:01:00.000+10:00

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

2007-06-20T10:45:00.000+10:00

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

2007-06-02T11:48:00.000+10:00

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

2007-05-29T16:54:00.000+10:00

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

2007-04-27T19:47:00.000+10:00

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

2007-03-27T12:28:00.000+10:00

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?

2007-03-09T16:14:00.000+11:00

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?

2007-02-28T09:28:00.000+11:00

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

2007-02-14T19:15:00.000+11:00

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.

To continue...

The need to touch down

2007-02-10T13:05:00.000+11:00

One day I was watching a panaromic rain scene on TV. I observed that some lightnings were followed by sudden bursts of rain. I thought, overly excited localities were dumping the extra energy in the lateral electrical dimension when ionisation potential was reached. This caused a sudden cooling down in the locality, leading to precipitation.

Then I thought, it must had been like this when the universe was first starting out it's evolution. The lightnings were it's 5 fields in some succession, and matter was it's rain. It was it's creative moment. This process is called Spontaneous Symmetry Breaking in physics. Rising on two legs was a creative moment of evolution for humans. Excess symmetry was dumped by freeing the hands. The creative moment works similarly for brains. When we mull over a problem long enough, we get a sudden flash out of the blue and realise a point. We get a touch down. Creative moments can be the sources of most intense pleasures. They are the purest orgasms of our minds.

In our more and more materialised world, we seek quick and definite solutions to our more and more intricate problems. We have come to expect rewarding sex through little tablets. We seek creativity through magic mushrooms and marijuana. We expect happiness in a short and expensive "romantic" getaway. But we soon realise that there is a prize for every quick fix.

When boredom arrives at the door of our inner selves, most ppl take up arms against it. Some drink, some smoke, some inject. Some go for a quick wank. Some abuse themselves. Drown themselves in work, in slavery for some arse hole corporation. Some abuse others and become soldiers and killing machines. We seek external solutions to an essentially inner problem. We try and scare it away. Mask it out. Drown it in alcohol. How can we like boredom? It is not a good feeling. If we can address it with a quick and easy solution, why not do it?

Boredom can also be a prelude to a creative moment. If you allow yourself to be bored for long enough, sometimes a sustainable and pleasurable solution comes out of the blue. After a while you may realize that boredom is a good thing. It heralds inner tension. Like weather before lightning and rain. If you ride it long enough, you finally get a flash inside. You may go for a long walk to nurse it. Take a pencil and paper and write it down. Draw or paint it. Tell a friend. Make it. After a while you seek boredom. You know it is good for you.

Long drowned boredom digs into our soul and covers itself. Makes a knot inside. It creates a tension. The space inside loses a part of it's coherence. Makes us biassed unconsciously. We become the knot that we tied and forgotten. If you keep ignoring your boredom, it finally makes an ensemble of knots inside and finally the person becomes a nut case. An alcoholic. A junkie. A freak. A derelict.

Sometimes you have no choice but ignore yourself. You may be poor. You may not be able to satisfy your most basic needs. You may be forced to bury your innermost desires for survival. You may have unhappy parents. Abusive parents. You may fall for wrong company. You may fall in love with the wrong girl. Sometimes it is just bad luck. You may be born in the wrong country to wrong parents.

Too many of us carry the inner knots to the grave and die unhappy. And maybe spend an eternity trying to find ourselves, life after life. Is the truth within? Is it my own self? Who am I? Just an elaborate concoction of chemicals, or something much deeper?

The uncertainty principle and the quantity trinity

2007-01-23T20:18:00.000+11:00

DxDp >= h/4pi
{0,1,Infinity}

I have made few cases of the Quantity Trinity already. Like {cell,being,species} and {star,galaxy,universe}. I will call it QT. It seems to be the strongest symmetry of the universe. How is it related to the Uncertainty Principle?

QT is in fact the duality of {0,I} mediated by {1}. In large populations, the smallest is related to the largest. I think nature achieves this through renormalisation. It also comes up with finite quantities to approximate 0 and I.

UP is a statement of measurement of uncertainty in coupled dualities like position and momentum. Momentum is derived from position. More accuracy for one means less for the other. But upto a limit. Beyond that limit, neither can be measured. As if they balance around the mediator of the coupling; Planck's constant divided by 4pi. Like 1 mediates 0 and I.

Is Global Village just around the corner?

2007-01-23T08:05:00.000+11:00

Last year was the year of the bloggers. They have penetrated the mainstream media and shattered the corporate stronghold on the global consciousness. YouTube has started a revolution in online video, giving rise to a huge video database, growing bigger everyday and promising infinite potential. Internet is empowering the consumer, reshaping the economy. The doom and gloom of few years before is getting replaced by a wonderful optimism.

It is strange that this should be happening just at a time when the world desperately needed a new direction. Internet has not been around long and it has followed a fairly predictable path until now. It's unifying potential was predicted by many. But how can you predict something like the blogging? YouTube? The intensity of the change is amazing. It has weakened the war-mongers and their sponsors. Many corporations are already shifting alliances. But the threats are still strong. Specially the looming climate disaster.

It seems the global unification was in the cards from the beginning. Like the evolution of the natural brain, computers are getting interconnected at many levels, providing instant communication for humans at many levels and forming a progressively unifying meta-brain to support the forming global consciosness. Like a miracle.

9 aspects of reality

2007-01-19T17:43:00.000+11:00

{0, 1, infinity}

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

I don't know if the words correspond to the symbols but Budh Yantra is ancient and sacred.

I put time in the first position, since it is local. At the base of everything there is time. This is a surprise for me. I have been assuming space to be more fundamental. But when you think about it, everything is a little clock. Everything is an oscillating bundle of energy. Universe is a clock fractal. Being is right in the middle. Everything balance around being. It sits in the middle of a complexity ladder of 9 steps in our universe. Time is the simplest of all and is the origin of all evolution. Being starts as a little bundle of time and climbs the ladder. When it reached the 9 levels of complexity, after a long evolution, it reaches the level of our universe to create beings like us.

Sri Yantra has nine circuits and three elevations apparently.

Cell, being, species

2007-01-15T19:57:00.000+11:00

This symmetry reflects to what degree nature follows the number triplet, {0,1,Infinity}. {star,galaxy,universe} triplet shows the power of this symmetry at the grandest scale we know. It is interesting that galaxy should correspond to being.

{0,1,I} is quantity, {-,0,+} is quality aspect. {-,0,+} corresponds to {female,child,male} symmetry. Galaxies fall into few types like elliptical, spiral, irregular. I would say {+} corresponds to {elliptical} and {male} since it has a simpler symmetry. This needs further thinking.

The reprogrammability of the center, or the mainstream, is clearly seen in each of {cell,being,species}. Cell has DNA to control the rest, being has brain, species has the marginals to reprogram, or easily capture, the mainstream. Species also fall into {herbivores,carnivores} duality reflecting {+,-}. How is reprogrammability reflected in {star,galaxy,universe} triplet? Star transforms matter in it's core. Galaxy transforms matter at a deeper level in it's core, a black hole. What is the center of the universe? Dark matter/energy? Is it easily capturable and reprogrammable?

There is also the lateral aspect; complex numbers, i^2=-1. With complex numbers we get rotating things since it's symmetry is U(1), or the symmetry of circle and square together.

Capturability of the mainstream

2007-01-15T12:28:00.000+11:00

Why is it that the human mainstream is so easy to capture?

In Cronulla race riots in Australia recently, a large number of youth were captured by a few well organised extreme racists. Since the Iraq invasion and the subsequent bombing in Bali, racial harmony suffered greatly. Racist Anglos were ready to be captured it seemed (most Anglos are decent good people I must add). Many of them were drunken and wrapped in Australian flags. They displayed a disgraceful scene, chasing and beating any dark skinned person who happened to be there, including women. The police chief later explained it as crowds being "captured". The oragnisers of the event would have been happy with the results, but I am sure they were not too happy with being seen as a mob of drunken losers.

Didn't Hitler capture an entire nation? He took so many of them to the grave. It seemed capturing humans was as easy as capturing sheep, maybe easier. Hitler was not alone of course. The Europian aristoctarcy and corporations were desperate to counter the Soviet revolution. They supported despots all over Europe to suppress local revolutions. Franco did not reach the efficiency of Hitler, but he also killed a lot of people. Mussolini was of the same kind. They keep showing docos on how bad were the dictators, but they never mention the fact that they were the ones behind the curtain. Later Hitler went rogue, as they do, and became an embarrasment. But Franco stayed a darling until the end.

Neo-cons also tried to capture the American mainstream and succeeded to a great degree. If they were successful in the invasion and holding of Iraq, we would have quite a different world order now. It was amazing to watch how easily they did it to the Americans. Few low life religious preachers were enough to mesmerise a large section of the society. As happened before in Europe, we all know who was behind the curtain. Greedy and ignorant corporate bully. The story of US is still unfolding. Democrats are putting a show but not too effective. Most democrats are also sponsored puppets.

Humans are easy to capture in all scales, from one person to large crowds. You just use slightly different methods. Controlling the media helps greatly. Internet must be quite a nuisance to these bastards. Falling in love is a consensual capture, supported by chemistry. Finding friends also falls into capturing. In the end it comes to reprogrammability. The mainstream provides a programmable power base for the marginal elements. It is a good representation of the concept of nothingness. It slumbers in the center to provide stability with it's size and power. We should study and understand this fact about ourselves and bring it to attention, if we want a peaceful future.

Rigpa

2007-01-07T10:45:00.000+11:00

The nature of everything is open, empty and naked like the sky,
Luminous emptiness, without center or circumference: the pure, naked Rigpa dawns.

(Tibetan book of the dead)

This self-originated Clear Light, which from the very beginning was never born,
Is the child of Rigpa, which is itself without any parents--how amazing!
This self-originated wisdom has not been created by anyone--how amazing!
It has never experienced birth and has nothing in it that could cause it to die--how amazing!
Although it is evidently visible, yet there is no one there who sees it--how amazing!
Although it has wandered through Samsara, no harm has come to it--how amazing!
Although it has seen Buddhahood itself, no good has come to it--how amazing!
Although it exists in everyone everywhere, it has gone unrecognised--how amazing!
And yet you go on hoping to attain some other fruit than this elsewhere--how amazing!
Even though it is the thing that is most essentially yours, you seek for it elsewhere--how amazing!

(Padmasambhava)

Taken from the book "The Tibetan book of living and dying" by Sogyal Rinpoche. Ran into it yesterday. Seems pretty good. Rigpa, or Ground Luminousity or Clear Light is the place dead go, it says. It is not the known physical light.

I thought it is also like a description of the Higgs field which is supposed to underlie everything, including space-time and light. It is not yet directly observed and predicted to be a "scalar" field. Light is a vector field, as it has two polarised electrical and magnetic fields. A scalar field is like money. It has a value but not a commodity itself. Pure numbers are defined to be scalars. They are just numbers and do not represent any specific thing. Therefore numbers are idealisations. Like numbers are at the base of mathematics and science, Higgs field is at the base of everything we know. Similarly, according to Buddhism, life has Rigpa as the base, where spirits reside. When a spirit takes on life, it is bonded to it until death. Lately I saw a doco on ABC about near death experiences. Apparently there are serious scientists who say that Higgs field may allow impressions on it by life.

With the recent confirmations of dark energy and matter, space-time seems not as empty as it looks. In fact they constitute most of the observable mass, something like 95%.

Bach's seal

2006-12-28T18:21:00.000+11:00

Isn't it gorgeous? It has few aspects that I wanted to share with the cyber space.

Mainly it is a representation of mediated duality. Two sides reflect each other and they also merge in the middle to make the mediator. Like (-1,0,+1) and (black,grey,white). Bach is giving the second most outstanding aspect of existence, mediated duality. Unity is the first aspect.

The crown on the mediator has the numbers 4, 5 and 7 coded in a symmetry like Menorah's, the Jewish candle holder icon. There are 5 dashes and 7 knobs on the crown. The center and side knobs are specially capped, leaving 4 not capped. Is Bach giving a clue here about how to link two different symmetries? 4 is also visible in the mediator's inner square divided into 4. 5 is the number of senses, with 4 of them {taste,smell,hear,see} being mediated by {touch}. Thus Bach also gives the third aspect, mediated dual-duality. The reflected JSB on both sides also reveal mediated dualities each, S being the mediator of J and B. The universe is also built on 5 forces, {strong,weak,higgs,light,gravity}. Complex numbers have the same mediated dual-duality symmetry, (-1,+1,0,-i,+i). And as we know, complex numbers are closed.

The symmetry that Bach mastered is the symmetry of music, life and the universe. All music obey the same symmetry, but Bach knew what he was doing, not only feel. What a man. He united the western music with his 48 preludes and fugues. 48=2*24, 4!=24. When the symmetry of the universe is ever found, it may confirm Bach. Bach united music and I think also showed the way forward for science. He heard the sound of unification in his heart and mind in balance, a testament to power of good music. In doing so, he also showed the way for happiness; balance of mind and heart. It is a miracle that he ever existed.

(The seal is from Wikipedia)

Sex and time

2006-12-06T15:52:00.000+11:00

The family tree of a person is like a cone fractal infinitely expanding into past. A person in the past has both sides of the cone until the present. Special relativity defines a light cone for every locality. Sexual reproduction forms the backbone of life's space-time. Every sexual encounter that result in fertilisation forms a node in life's matrix. From this node a being emerges and goes on to make own nodes in the matrix. The distance travelled from one node to the next has a statistical spread. There would be an average speed of gene transmission into the future in this matrix, like speed of light. When looked overall, it looks like a time-cone.

Sexual dynamics may be a clue to quantum mechanics of space-time. What else for life to imitate, apart from space-time itself? Time, light and gravity are intimately linked. Light is like male, gravity like female. Light brings life to matter. Life make space by feeding and doing the chores of life. The locality defined by a life transmits itself through sex to other nodes.

Living make space, fucking make time.

Balance

2006-11-26T09:17:00.001+11:00

{Balance}

Balance is the middle touch and the core of being. It defines one's location in time and space. Balance in space seems to have more priority over balance in time. Evolution clearly displays the importance of territory. In physics, location (geometry) forms the backbone.

For example, hurricane takes it's vortex shape when a highly excited unstable locality brakes symmetry by collapsing and channeling energy in one angular direction. This direction is determined by the rotation of the earth. Spontaneous symmetry breaking is the mechanism used to make balance and define locality.

{OuterTouch, Balance, InnerTouch}

Balance uses inner and outer touch as its agents, when it evolves and differenciates more. Outer touch is the known touch, the screened interaction. Inner touch happens when allowed energy focus in the center. Brain performs the balancing function between these two touches. It mediates by correlating the inner to the outer.

Like reflection and refraction of light at a boundary. The boundary is closed for a being and the allowed energy makes patterns inside, creating an image of the outside. Energy comes in two modes; acoustic and electromagnetic or light. Acoustic energy gives an instant overview of the mechanics of the locality, if it is processed by an algorithm like FFT. Light energy is directional and provides 2D information. Acoustics is like gravity, globally felt. The inner brain develops ways to detect this dual energy pattern. Inner hearing and inner vision would evolve first. And then organs would evolve as the brain grows and differenciates.

{{Taste, Touch, Smell}, Balance, {Hear, InnerTouch, See}}

Then a similar splitting happens for both touch and inner touch, as the organism gets more complex and finds it's fundamental dual duality shape of the outer look. {Taste, See} and {Smell, Hear} correspondence demonstrates the level of correlation. See and Taste form the inner or local, while Smell and Hear form the outer territory. Dogs use smell and hear as the agents for defining outer territory.

Taste --> {Mouth, Stomach, Anus}
Smell --> {Nose, Lungs ? }
Hear --> {LeftEar, InnerEar, RightEar}
See --> {LeftEye, InnerEye, RightEye}

Then each sense splits to create it's organs. When organs split, they leave the boson of the relationship in the center as the mediator. InnerEar combines two sides to make a stereo image like model of the sound-scape outside. Duality in hearing gives depth, like also in seeing. I am not so sure about the nose-lung connection, in comparision to mouth-stomach. Maybe nose took dual role of mouth and anus at the same time, since it is only air.

{{Strong, Space, Weak}, Higgs, {Gravity, Time, Light}}

The energy expressed by gravity balances that of light. This is known but not integrated into physics properly yet. Potential/kinetic duality of energy comes from this. I suspect a similar thing is happening with {Strong, Weak}. {Light, Weak} and {Gravity, Strong} correlate strongly. The 3*2 symmetry of space is closely related to 3/2 symmetry of Strong. Higgs forms the background field which supports everything. Space is inner touch, time is outer touch.

Light --> {+ECharge, Light, -ECharge}
Strong --> {3 Color Charges, 3 Color Gluons}
Weak --> {W+, Z0, W-}

Then each field splits similarly to form an expanding tree, forming own charges. Strong seems to be like Taste. It branches deeper. Taste has mouth, stomach, anus, liver?, intestines...

Being, music and universe

2006-11-12T13:47:00.000+11:00

ATON-M6 classification thus meets a serious challenge from a modular group like symmetry, {{a,b},{c,d}}, which is also in line with the new multifactorials and Zeta function formulation.

================================

==================================

Time/Space takes the center stage
as Not-Doing/Not-Being.

=================================

A typical cycle of action;
{Feed,Feel,Think,Judge}
displays the 4/4 measure of being
as also done by musical conductors.
Christians do the same sign.

===================================

Do/Be expanded to reveal
a model of nothingness or slumber.
My kind of model this one.

Mirror Set, rev-2

2006-11-12T09:58:00.000+11:00

After discovering the multifactorials, or Barnes G-functions, a revision is necessary since G-functions are more general. Mirror Set maps pairs of naturals to rationals;

Where m,n are natural, G(m,n)=m!n is multifactorial of m to depth n. Revising and broadening Mirror Set previously defined as M(m)=M(m,2). This form is more general and combines G-functions and Zeta function. It has a ying-yang look and variables do not commute, G(m,n)=/G(n,m). Here are some small values;

M(1,1-4) = (1, 1/2, 1/3, 1/4)
M(2,1-4) = (2, 1/2, 2/9, 1/8)
M(3,1-4) = (6, 3/2, 8/9, 3/4)
M(4,1-4) = (24, 18, 4^4/3, 6^4)

Previously I took M(3,2) as the center. Now M(2,2) =2/4=1/2 takes the center, standing for time/space. {2,2/9}={light,gravity}, why 2/9 for gravity? (3/2,1/2}={strong,weak} is reasonable.

Applying continuity by setting m-->z and summing gives a harmonically weighed G-function. For G=1 it is the Zeta function;

Assuming continuity holds, G may be generalised to a function of 2 complex variables;

Where z!w stands for the multifactorial to depth w, G(z,w). The form of M seems to imply the extension of G but it remains to be seen if it can be made continuous. I think G works like a local correlation function.

Thus naturals take the center stage of ATON, instead of sets. Maybe not surprising. Don't they (mathematicians) consider number theory as the purest?

Multifactorials

2006-11-11T13:55:00.000+11:00

Lately I found, to my great surprise, that ATON Exponential Set is in fact already defined in the number domain as the second multifactorial, also called Barnes G-function;

G2(z+1)=Gamma(z)*G2(z)
G2(1)=1
Gamma(z+1)=z*Gamma(z)

Higher multifactorials follow. To see how it works, expand 3 to depth 6;

G0(3) = 3 = 3*2^0
G1(3)=3.2.1.1 = 6 = 3*2^1
G2(3)=(3.2.1.1).(2.1.1).(1.1).(1) = 12 = 3*2^2
G3(3)=[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)] = 24 = 3*2^3

G4(3)={[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]} = 48 = 3*2^4

G5(3)={{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.

.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}} = 96 = 3*2^5

G6(3)={{{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.

.{{{[(1)]}}} = 192 = 3*2^6

Therefore Gn(3)=3*2^n.

Instead of multiplying, one could add the expanded elements (with no apparent benefits);

GS0(3)=3
GS1(3)=7
GS2(3)=14
GS3(3)=25
GS4(3)=41
GS5(3)=63
GS6(3)=92

4. The religion of knowledge

2006-11-06T14:22:00.000+11:00

Krishna:
This deathless Yoga, this deep union,
I taught Vivaswata, the Lord of Light;
Vivaswata to Manu gave it; he
To Ikshwaku; so passed it down the line
Of all my royal Rishis...

Vivaswata is the Sun. This chapter is about light. Knowledge is trapped light or action. Computer memory is a self referring transistors circuit that can trap action (flip-flops). 4ness of the chapter is also meaningful. There are 4 main players in the light theory of Maxwell's,
{{electrical charge, current (moving charge)}, {electrical field, magnetic field}}
2+2=2*2=2^2=4
4 has a very special symmetry. Complex numbers display the light symmetry in a more compact form;
{0,{i,-i,1,-1}}
a+i*b=Sqrt(a^2+b^2)*e^(i*Arctan(b/a))
It is known as U(1) symmetry in Group Theory. In ATON, it is M1. Tetrahedron is the corresponding shape in ATON.

Krishna:
Manifold the renewals of my birth
Have been, Arjuna! and of thy births too!
But mine I know, and thine thou knowest not,
...
Who knows the truth touching my births on earth
And my divine work, when he quits the flesh
Puts on its load no more, falls no more down
To earthly birth: to Me he comes, dear Prince!
...
Now to the lower Gods. I say to thee
Here have they their reward. But I am He
Made the Four Castes, and proportioned them a place
After their qualities and gifts.
...
Needs must one rightly meditate those three---
Doing,---not doing,---and undoing. Here
Thorny and dark the path is! He who sees
How action may be rest, rest action---he
Is wisest 'mid his kind; he hath the truth!
He doeth well, acting or resting. Freed
In all his works from prickings of desire,
Burned clean in act by the white fire of truth,
The wise call that man wise; and such an one,
Renouncing fruit of deeds, always content,
Always self-satisfying...

{Doing, not doing, undoing} triplet stands out. "Self-satisfying" relates to the self referring autonomy of light. Self referral is is clearly visible in the 4 Maxwell's eqns in vacuum reflecting 4 degrees of freedom. Two relate to charges, and two relate to each other.

"Renouncing fruit of deeds" also mathces light. Light travels lossless, reflecting conservation of energy.

The sacrifice is Brahm, the ghee and grain
Are Brahm, the fire is Brahm, the flesh it eats
Is Brahm, unto Brahm attaineth he
Who, in such officem meditates on Brahm.

Everything is made of light, or energy. This seems to refer to E=mc^2. Relativity also seems to be here.

...Knowing Truth, thy heart no more
Will ache with error, for the Truth shall show
All things subdued to thee, as thou to Me.

The importance of the knowledge of energy conservation and mutability. We know this one.

Here is a tetrahedron model from the web;

Here is another one;

Tarot card-4 is Emperor. Light can be considered as a masculine quality, since energy brings matter to life. Sun is masculine, earth is feminine. 4ness is pretty obvious by the throne. Two*two rams would be electric, magnetic fields and charge, current. Metal shoes may indicate the undestroyability of light, or energy. Scepter is a circle-cross design demonstrating U(1) symmetry. The eagle on his left shoulder is another reference to light. He seems to be holding a mirror in his left hand.

3. Virtue in work

2006-11-05T15:00:00.001+11:00

Arjuna:
If meditation be a nobler thing
Than action, wherefore, then, great Kesava!
Dost thou impel me to this dreadful fight?

Krishna:
I told thee, blameless Lord! there be two paths
Shown to this world; two schools of wisdom. First
The Sankhya's, which doth save in way of works
Prescribed by reason; next, the Yog, which bids
Attain by meditation, spiritually:
Yet these are one!
...
He who sits
Suppressing all the instruments of flesh,
Plays the inept and guilty hypocrite:
But he who, with strong body serving mind,
Gives up his mortal powers to worthy work,
Not seeking gain, Arjuna! such an one
Is honorable. Do thine allotted task!
...
Govern thy heart! Constrain th' entangled sense!
Resist the false, soft sinfulness which saps
Knowledge and judgement! Yea, the world is strong,
But what discerns it is stronger, and the mind
Strongest; and high o'er all the ruling Soul.

The Principle of Least Action of classical mechanics seems to be related;

Action S is minimised by variational method, reflecting seeking no gain from work. This point is similar to definition of line in geometry. The shortest path between two points is a line. Here the two points are the limits of the integral, t1 and t2. This chapter defines action.

{sense, mind, soul} triplet stands out. x(t) seems to correspond to sense, since it is the base of action. Then mind is L, and soul is the variational minimisation or balancing.

There is also quantum mechanical equivalent of PLA.

Tarot card-3 is Empress. 12 stars on the crown match SE3=3!2!1!0!=12. Feminine and earthly are together here. The strength of the symmetry of 3 is expressed. Virtue in work is related to feminine productivity.

2. The book of doctrines

2006-11-02T19:54:00.000+11:00

Never the spirit was born, the spirit shall cease to be
never
Never was time it was not; End and Beginning are
dreams!
Birthless and deathless and changeless remaineth the spirit
for ever;
Death hath not touched it at all, dead though the house of
it seems!

Definition of nothingness.
0+0=0
0*0=0

Nay, but as one layeth
His worn-out robes away,
And, taking new ones, sayeth,
"These will I wear to-day!"
So putteth by the spirit
Lightly its garb of flesh,
And passeth to inherit
A residence afresh.

0+x=x
1*x=x

Wonderful, wistful, to contemplate!
Difficult, doubtful, to speak upon!
Strange and great for toung to relate,
Mystical hearing for everyone!
Nor wotteth man this, what a marvel it is,
When seeing, saying, and hearing are done!

{seeing,saying,hearing} is a mediated duality. Saying is the mediator.

And like the ocean, day by day receiving
Floods from all lands, which never overflows;
Its boundary-line not leaping, and not leaving,
Fed by the rivers, but unswelled by those;---

So is the perfect one! to his soul's ocean
The world of sense pours streams of witchery,
They leave him as they find, without commotion,
Taking their tribute, but remaining sea.

Definition of everythingness.
Infinity+Infinity=Infinity
Infinity*Infinity=Infinity

Spirit as a mediated duality is introduced. {0,1,infinity}. It is nothing and everything at the same time. {seeing, saying, hearing} triplet stands out.

Tarot card-2 ia also about mediated duality. {do, not-do, undo} triplet is implied by the pillars. Night seems to be conquered, by the position of the crescent. Chaos is over. Wise order has arrived. Tora stands out. Cross as duality.

1. The distress of Arjuna

2006-11-02T19:53:00.000+11:00

Arjuna;
Better I deem it, if my kinsmen strike,
To face them weaponless, and bare my breast
To shaft and spear, then answer blow with blow.

So speaking, in the face of of those two hosts,
Arjuna sank upon his chariot-seat,
And let fall bow and arrows, sick at heart.

In the beginning there was nothing and everything at the same time (anon)

Arjuna is distressed before a battle. Storm before sunshine. Definition of chaos before the order arrives in chapter-2. Chaos as the unifier. This is the piece of clay before shaping.

Fool. The inexperience of Arjuna matches 0. The togetherness of 0 and 1 reflects the duality of {nothing, everything}.

Magician heralds solution to Arjuna's distress. It is all one. Arjuna is not alone. Infinity sign reflects life and God. Four Tarot suits on the table; sword, stick, cup, 5-star. These are his tools of the trade. As he points out, he makes the whole thing. The wand in the right hand is curious, maybe reflecting earth-sky symmetry. A snake curls on his waist, indicating his cyclic nature. Stick is measure, sword is shaping operator, 5-star is geometry, cup for containing and balancing.

Here is a Babylonian or Mesopotomian match,

When on high the heaven had not been named,
Firm ground below had not been called by name,
When primordial Apsu, their begetter,
And Mummu-Tiamat, she who bore them all,
Their waters mingled as a single body,
No reed hut had sprung forth, no marshland had appeared,
None of the gods had been brought into being,
And none bore a name, and no destinies determined--
Then it was that the gods were formed in the midst of heaven.
Lahmu and Lahamu were brought forth, by name they were called. (10)

Apsu, the god of fresh water, and his wife Mummu-Tiamat, the goddess of the sea; nothing-everything. Lahmu and Lahamu must be the next stage.

Jewish-Christian myth has the same {nothing, everything} mix;

Genesis
1:1 In the beginning God created the heavens and the earth.
1:2Now the earth was formless and empty. Darkness was on the surface of the deep. God’s Spirit was hovering over the surface of the waters.

Bhagavadgita: A theory of being?

2006-11-01T19:07:00.000+11:00

Lately I ran into Bhagavadgita (Lord's song) at the wonderful Theosophical Shop in the city. Books, other stuff and people there are very nice. A more interesting aspect of religion as a social expression of spirituality, rather than the greedy and ignorant moronity of some mainstream religions. The good force is stronger in Australia. I have been looking for a good ancient book of wisdom. Many of them are spoiled over time. But B seems very nice indeed! Religion was more interesting in the ancient times, when it was unified with science. How they achieved such wisdom is a mystery. My guess is, we are the remnants of an alien colony. Maybe this is a good way of keeping the galactic/universal genetic stock in good shape. The theory of the universe would spoil the natural evolution. That could be why they don't leave any technology. Just good advice.

Well, not really good advice overall. Lately, "vinayak" brought a troubling aspect of Gita to my attention;
https://www2.blogger.com/comment.g?blogID=26992738&postID=114653421935749885
Which I have been aware of. I thought I commented on it already, maybe deleted. Anyway, Krishna, in chapter-2, encourages Arjuna to kill. Not very good. I thought maybe the book is modified by the ruling classes of the past to suit their own ends. They have done it to many sacred books already. It could be that all sacred books are written by the ruling classes. They have access to talented and greedy minds. But you never know. Some things in these books are too good.

Could it be read in another angle like a theory of being? A theory of the universe? Chapters are; (I am using E.Arnold's translation, I hope I don't infringe any copyrights here)

1. The distress of Arjuna
Nothing-everything duality as a chaotic unity with no mediator.
2. The book of doctrines
Unity as mediated duality.
3. Virtue in work
The principle of least action.
4. The religion of knowledge
Light. Knowledge.
5. Religion by renouncing fruit of works
6. Religion by self-restraint
7. Religion by discernment
8. Religion by devotion to the one supreme God
The unifier, like the exponential function.
9. Religion by the kingly knowledge and the kingly mystery
Certainty and uncertainty.
10. Religion by the heavenly perfections
Geometry.
11. The manifesting of the one and manifold
Algebra.
12. The religion of faith
Prediction.
13. Religion by seperation of matter and spirit
Time and frequency domains. Seperation of executive and juduciary.
14. Religion by seperation from the qualities
Balance.
15. Religion by attaining the supreme
16. The seperateness of the divine and undivine
Like 13.
17. Religion by the threefold kinds of faith
Space.
18. Religion by deliverence and renunciation
Time. Free will. Self determination.

Note the number of chapters: 18 = 4!3!2!1!0! / 2^4 = 288/16 = SM4 . 18 is also the magic number of the periodic table.

I will keep filling this summary as I read more. Then I may open up seperate posts for each chapter if more detail comes out. Tarot seems to be strongly related, as a surprise.

Future >= Present/Past

2006-10-26T16:57:00.000+10:00

The uncertainty principle (by Heisenberg) is expressed by a dual duality in physics,
D={{P,M},{T,E}} = {{Position,Momentum},{Time,Energy}}
It states that the uncertainty in the measurement of "coupled" entities is always larger than a cetain limit, Planck's constant divided by 4pi. Momentum is also a function of position, and energy is also a function of time.

It is a statement of prediction. It predicts that nothing can be measured beyond a certain limit, with the available means of D. It applies to every measurement process, therefore to everything. For example, measurement of pitch in sound is optimised by balancing accuracy (the length of the buffer (window)) with timeliness. Speech recognition and synthesis is an event that has to happen in real time. Therefore parameters like pitch are measured in flight. Longer windows give more accurate measurement of pitch, but the location is lost. Shorter window locates the pitch better but misses length for accuracy of intensity. Therefore an optimum buffer length is used.

Note the black hole form in the action divided onto a spherical surface. 4pi is the amount of solid angle around a point in 3D space.

Since it is a statement of prediction, it suits quantum mechanical language well. QM's language is probability. It has an involved derivation but I will go through it, since it is so important...

Complex Normal Distribution

2006-10-24T23:06:00.000+10:00

I called it CND but I haven't seen it defined. I just put complex variables in ND;

z=(1/c1*sqrt(2*pi))*e^((-1/2)*((z-c0)/c1)^2)

Where c1 and c0 are standard variation and mean. In the following c1 is the free parameter. A surprise here is that Mandel and Julia are similar in large scale. Although ND has that property of looking similar after a frequency transformation.

As before, restricting expansion also limits domain. I think I made a mistake with the expansion of CND. Fractal Explorer's Exp(z) does not give Taylor's expansion to a number. The expansion is not so trivial to calculate. Too many terms. I will keep the "expanded to 6" ones until I correct them. Currently I am trying to learn some Java.

Mandel
e^x expanded to 6
Sitting Buddha, hmm

Julia
e^x expanded to 6
c1=(1.01,-1.11)
Doesn't it look like infinity sign?
Unfortunately the above Mandel
is not at the same c1, Mandel is below

Mandel
e^x to 6

Mandel
bailout=49

Mandel
bailout=324

Julia
bailout= 25

Mandel
bailout=25

Julia
bailout= 361

Mandel
bailout=361

Mandel
c0 free

Mandel
c0=(0,-1)
e^x expanded to 6
Mandel as mouth

Performance and nothingness

2006-10-24T19:50:00.000+10:00

Performance of a difficult piece needs higher concentration and relaxation at the same time. Regardless of what piece. Musical piece, sexual piece academic piece. A paradox. How can you relax and concentrate at the same time? How can you create on demand? Even a purely mechanical performance needs a lot of juice. The key it seems is passion with wisdom. Passion knows the destination, wisdom knows the way. The destination is beauty, the way is nothingness. Like drops making an ocean.

Playing guitar needs a lot of concentration and relaxation at the same time. To learn a difficult piece, the fastest way is to play as slow and light as possible. A paradox. As Abel Carlevaro states clearly in his guitar method, you gotta give your full attention to balance from the start. Balance is achieved fastest by building it from little. So to learn you decrease tempo and power as much as possible but keep good balance and control. The {position, amplitude} duality of Delta Function is here as {tempo, power}. After all, learning is locating. Slowing down is as difficult as playing faster. You have to hold notes longer with your left hand, but the real difficulty is to remember. It is easier to remember when you play in a relaxed tempo which happens to be the natural tempo of the piece. The brain likes different speeds for different things. Intensity or power is also difficult to reduce. You have to play your right hand really close to the strings, which is really hard. So it is as hard to play slow and light as fast and powerful. But to learn, or to teach the piece to your brain, you have to slow down. Like learning a language.

Performing for musicality is similar. If you don't relax you can't bring the beauty out. Improvisation must be the real test for any musician. Improvisation, or creating on the go, is the way to go. The way is nothingness.

In the end everything is mediation, or compromise, or balance. It is difficult to play powerful and fast or light and slow at the same time. So you find a middle way that suits you best. But you keep pushing the difficult limits to keep your domain nice and roomy. Build strength around your comfort zone, and extend your comfort zone to meet your difficulties.

e^((z^2+c1)/c2), expanded to 6

2006-10-24T09:51:00.000+10:00

Expanded the exponential to power 6, like M6. Bailout does not expand the domain in this case. The set looks similar from either of c1 and c2, which is interesting. Limiting the expansion of e^x to 6 seems to restrict the domain. A bit like the top of the pyramid flying off in the Egyptian mythology. Hunab Ku also seems to imply that ying-yang part is seperate.

Expansion to 6 is faulty. I found that expansion of ND is not easy. It has too many terms and difficult to calculate. I am trying to shift to Java at the moment.

Mandel
c2=(1.36,-0.66)

Julia
(0.5,0.5)
c2=(1.36,-0.66)

What do you reckon?

Mandel
c1=(0.26,-0.35)

Julia
(0.5,0.05)
c1=(0.26,-0.35)

I always wondered what those points were inside.

Smiling Buddhabrot

2006-10-23T18:42:00.000+10:00

e^((z^2+c1)/c2)
c1=(-3.17,0.02)
bailout=25

How about that?

Hahaha

e^((z^2+c1)/c2)

2006-10-23T16:18:00.000+10:00

c1=(2.05,-2.01), max-iter=194, bailout=25,100,1024,10000

I like this form because it looks like the normal distibution. It also has a similar form to Mirror Set, as exponential for given H-fractal of z^2+c form. Totally unexpected looks though. Look at the smiling Buddha Mandel!

I made this with Fractal Explorer which is free. The diameter increase in both Mandel and Julia (which are contained in circles) corresponds to the bailout. Thus the domain is half the complex plane which is weird.

Check out the amazing similarity to Mayan icons.

Mandel
bailout=25

Julia
bailout=25

Etznab

Hunab Ku

Mandel
bailout=100

Julia
bailout=100

Mandel
bailout=1024

Julia
bailout=1024

Mandel
bailout=10000

Julia
bailout=10000

Another Julia
bailout=25

Julia up close

Bronze age
Gold

M0

2006-10-19T07:30:00.000+10:00

In the beginning there was nothing and everything at the same time. (anon)

M0=,/,
SM0=0!/0^0={1/1,1/0}
0^0 is double valued, {0,1}. A special case of x^y. From x it looks like 0, from y like 1. We are forced to consider two variables {x,y} since exponential is hierarchical. exp(y*ln(x)) is the dual of x^y, reflecting the duality 0^0={0,1}. M0 has either 1 state or infinite states at the same time. If you want fireworks it seems you gotta measure zero.

The duality of measurement (or counting) is exposed here. Combinatorial for given exponential. Measurement is relative to a base which is the normal case. The norm is exponential in the universe. Everything is expressed as compared to a base which is always quantised. 0^0 expression is attempting to take 0 as base and this creates problem. This will be resolved by transforming to M0+ and taking a boolean base, 2^0. The nominator is factorial since it measures complexity of the meta structure on top of base.

A state is needed to express just a point. But this state is only needed in retrospect to M0+=E0/H0 to explain H0={}. M0 reflects the identity element. In fact (,/,) reflects the concept of nothingness better. Something really insignificant compared to itself. Then Higgs is M0 since (,/,) looks more like a self interacting scalar or dust field. No dimensions and infinite dimensions live together here. A bit like the impulse function, or rather Dirac Delta Function;

Like we had to consider x^y form when looking at 0^0, here we have a duality, {position, intensity}. In fact Delta Function is the algebraic definition of a point;

It can be defined in any space, the simplest being one dimensional.

Although it looks thorny, it is possible to deal with it analytically and an essential part of dynamical system analysis. In electrical process control, a system is defined by it's impulse response. It seems ATON has landed on it's analytical bottom. This is the place to dwell for a while and maybe look at some quantum mechanics.

There is also the discrete equivalent of DF, Kronecker Delta Function with similar properties to DF;

KDF behaves like DF in definition of position;

I always thought Tarot cards looked strange. Look at the card-1 of the "major arcana" of the magician. Can you see the Delta function?

M3 (take-2)

2006-10-18T18:27:00.000+10:00

M3=E3/H3={,{},{,{}}}/{,{,{,{}}}} is the form that shapes all the rest since it has the overall symmetry of SM3=12/8=3/2. 3/2 is the symmetry that makes quarks/gluons and equal tempered tuning in music. I used call it Bion but given up on that. It is made by translating M2 by half and rotating by pi/4 in each of the 6 faces. And then completed the 3 manifested cubes giving M3 an outer shape like one of Escher's works.

It has 3 distinct aspects;

M2

2006-10-18T18:09:00.000+10:00

M2=E2/H2={,{}}/{,{,{}}} comes directly from M1, without using an intermediate form like M1.5. M2 is a tetrahedron reflected onto itself. 12 sticks on 8 points form a cube by it's diagonals. M2 corresponds to weak force and also to quaternion symmetry. It has 4 distinct aspects;

M1

2006-10-18T14:30:00.000+10:00

M1=E1/H1={}/{,{}} stands for tetrahedron which is the symmetry of light and many other things. It has 3 distinct faces, all require some kind of collapsing. E1 stands for electric charge and H1 stands for light. So it has the same charge/field form. 4 independent equations of Maxwell's is based on tetrahedron symmetry.

M0.5

2006-10-18T12:25:00.000+10:00

The next form triangle is obtained by a simple transformation of a stick by rotating it around one of it's points. M0.5 is between M0=,/{} and M1={}/{,{}};
M0.5={}/{}
It first updates it's charge or nominator to become M0.5, and then it's field or denominator to become M1. Thus it follows a zigzag. To become M0=,/{}, it must come from M0-=,/,

Triangle has two other views, both are lines;

These views are equivalent since sameness is not allowed, {,}={}. Triangle is the middle form between stick and tetrahedron which corresponds to M1. To make 2 to 4 you go through 3. Charge (,) makes own field ({}), and then field makes next charge; electric charge {+,-}. This implies that Higgs is a bipolar field {0,1}. {0,1} mutates to {+,-} by reflecting 1 accross 0 and making -1.

M0.5 reflects integers, if M0 reflects natural numbers.

M0.5 is the point where mirror symmetry is used.

M0+

2006-10-18T10:42:00.000+10:00

M0+=,/{}
SM0+=0!/2^0=1/1=1

M0 is a very stressed state. Like a tossed hyper coin. Quantisation is the answer to resolve this stress;
dx*dp >= h/4*pi
h/4*pi is the smallest action possible in the universe. Note the black hole format, the 3D solid angle 4*pi. Out of this quantisation comes M0+=,/{}. Condensation of the dust field into small droplets creates a reaction like springs between nodes.

To get rid of the infinity, substitute 0 => 2 where it counts and break the symmetry;
0^0 => 2^0
SM0+=0!/2^0=1/1=1
This substitution reflects a dual polarisation of the dust field into a field of line segments. Boolean is the minimum space.

MSet is a quotient set. It takes 2^n as it's norm. M0+ has 2 aspects. The point aspect and the line segment (or stick) aspect. It has only one possible state at a time. Either point or stick. The collapse of wave function in quantum mechanics is based on this reasoning. If you look at it to see the point, you can't see the stick.

M0+ corresponds to Boolean algebra, {0,1}. Boolean is the minimum space.

In color, {black,white}.

In sex, {male,female}.

M6

2006-10-13T15:45:00.000+10:00

A visualisation of M6 with smallest element M4.5 simplified for speed and many inner lines missing. 20 M5.5 make M6. They are tiled into a 3^3 cube by leaving the center and the 6 centers of the faces empty, 27-6-1=20. The relative finality of M6 is apparent from the completion of square and hexagon, both have good 2D tiling. MSet continues to produce interesting numbers after M6 but the ones that I checked all have 20 as a factor. Therefore the 20-cube is the final form. It just keeps getting finer and finer in detail after M6. This implies that our universe is the smallest possible. From here on it goes on and on until infinity. Our universe it seems is just a small speck in the final 20-cube.

Following are 2D aspects with no perspective;

Flower of life;

Following makes an attempt to compare Sri Yantra to M6 with M5 simplified to a tetrahedron. It seems it is there but I have not got the angles right yet.

Although I have no religious motives in ATON, the visuals have striking resemblance to some religious symbols. David's Star, the cross of M4.5, and finally the cubic shape of M6 like Mohammed's tomb;

In ancient Persia, a "talent" of gold was equal to 388800 grains. 388800 is the state quotient of M6. It seems some ancients knew the symmetry of the universe. Are we remnants of some ancient alien colony? Why was the technical knowledge not passed on?

M5.5

2006-10-13T05:54:00.000+10:00

A visualisation of M 5.5 with M4 simplified to speed up computing. 18 M5 make M5.5. It is a 3^3 cube with corners and center missing, 27-8-1=18. Since M5 is a tetrahedron, it is alternated to tile the box.

Durga yantra;

The following is M5.5 with M5 simplified to tetrahedron;

Here are more matches with antiquity. M5.5 corresponds half-way to gravity/mass in ATON. I think M5.5 is like gravity and M6 is like mass.

M5

2006-10-12T20:37:00.000+10:00

A visualisation of M5 with smallest unit M3 simplified to speed up computing. M5 is a tetrahedron with different views. 10 of M4.5 make M5.

Following are 2D aspects with no perspective;

M4.5

2006-10-11T21:18:00.000+10:00

A visualisation of M4.5 which is made of 6 M4 arranged in a 3D cross;

Following are 2D aspects with no perspective;

M4

2006-09-28T18:26:00.000+10:00

A visualisation of M4 which is made of 18 M3. It is a 3^3 cube with corners and center missing, 27-8-1=18.

Following are 2D aspects with no perspective;

A super-imposed Sri Yantra on a non-perspective aspect of M4;

Sixness of gravity

2006-09-21T12:13:00.000+10:00

M6 classifies elementary aspects of the universe into 7 steps;
0 Higgs
1 Light
2 Weak
3 Strong
4 Lepton
5 Time
6 Gravity
As it happens, there are 6 independent equations of the Einstein Field Equations (EFE). Here they are in compacted form;

Higgs as the ultimate stem cell

2006-09-15T08:31:00.000+10:00

Picture taken from http://biochem118.stanford.edu/Stem%20Cell.html.

The ultimate stem cell is the fertilized egg. Many stem cells make an embryo which then settles in the womb and develops following a tree. Embryo obviously is a being capable of feeding off the mother. When the fertilized egg starts multiplying, it forms a clone population with no overall polarisation. Like a piece of clay before it is formed into shape. Clay is formed of small particles but their size is small enough to be neglected.

Higgs is a quantised scalar field. Everything else is a pattern in the Higgs ocean, including light. It would be difficult, if not impossible, to probe into it using it's own patterns. So it looks undifferentiated to us. One needs a finer resolution to analyse it. Maybe the whole universe comes from a single Higgs particle. The ultimate self reference. Then Higgs follows the M6 category ladder to complete it's growth;

0. Higgs
1. Electric-charge/Light
2. Weak-charge/Weak-boson
3. Quark/Gluon
4. Lepton
5. Space/Time
6. Mass/Gravity

The first differentiation in the stem cells happens in {Muscle, Blood, Nerve} mediated duality. This is like {Plus-electric-charge, Light, Minus-electric-charge}. Light carries energy and blood carrries resources. Nerve is a modified muscle cell, and (-) is derived from (+); (-)*(-)=(+). Light has 0 mass, like blood cell floats in blood's base liquid. Action is ordered from nerve to muscle and the tension in muscle is fed back to nerve. In a similar way, electrons flow from (-) to (+), and holes flow from (+) to (-) in semi-conductors. Blood cell is closer to stem cell. Muscle and Nerve cells are specialised cells. Like 0 is a mirror between +1 and -1, Blood cell is a mirror between Muscle and Nerve cells.

{Muscle, Blood, Nerve} mediated duality produces motion to feed. Therefore the next polarisation must be the {Mouth, Stomach, Anus} mediated duality. Like {W+, Z0, W-} seperation of the weak charge and field.

Being as a book

2006-09-13T08:19:00.000+10:00

0. Measure ... Space
1. See ... Letter
2. Taste ... Word
3. Touch ... Sentence
4. Smell ... Paragraph
5. Hear ... Chapter
6. Balance ... Book

Isn't it amazing that an average book is structured in the same 7 step ladder? The optimum of 7 levels of nested subroutines in programming reflects the same fact. Like {Measure, Balance}, {Space, Book} couple to each other. Book provides the space to write. {Letter, Chapter} coupling is demonstrated by the number of letters and chapters being in the same range. We do not like books with hundreds of chapters. 10-20 chapters seems to be the norm. Similarly there are similar numbers of letters in a word and paragraphs in a chapter. Sentence makes irreducable sense. In that way, what binds a sentence is like the strong force.

There is a similar mapping for DNA;

0. Space ... This must be the chemical soup the DNA is immersed in.
1. Letter ... Base
2. Word ... Codon
3. Sentence ... Gene
4. Paragraph ... Operon
5. Chapter ... Chromosome
6. Book ... DNA

Yantra and unification

2006-09-10T11:43:00.000+10:00

2-7-07; Please check my later posts for a more correct classification of the fields.

Yantra of 'supreme self' Atman taken from http://sivasakti.com.

In ATON M6, when action reaches 7 octave stage, it undergoes a transformation and curls up to form a quantum in a double triangle design also called David's Star. This curling is due to the particular symmetry in the sequence {0,1,2,3,4,5,6}. The 3-symmetry at the center forces the outside to the same. This transformation is like spontaneous symmetry breaking. Like clouds do in rain, when a system is over-excited it prefers to settle to a lower entropy by shedding the excess energy. The inside and the outside reflect each other. 3 dualities or 2 triplets (2*3=3*2=6) arranged around a center of 3-symmetry make a quantum. The following yantra shows the red triangle inside the star explicitely, showing that there is 3-symmetry at the center.

It is a duality of two interlaced triangles. {Mathematics, Physics, Chemistry} are 'primary', {Psychology, Intelligence, Aesthetics} are 'secondary' or 'trancendental' sciences. Like colors, {Yellow, Red, Blue} are primary, {Orange, Green, Purple} are 'secondary' or derived colors. Biology is the science that mediates all others. Without life, there can not be science. Biology corresponds to Grey which mediates all colors including the special case of Black and White. Biology is like Probability since it essentially studies mutations. Reproduction in a population is a large stochastic process with tossing of a large coin at every insemination. The success of sexual reproduction mediated duality, {Male, Child, Female}, is a reflection of the strength of {Black, Grey, White}. Therefore the center would polarise into a duality vertical to the plane. This would make the star into a reflected star pyramid. One pole Black and the other White, each expanding towards the rainbow at the equator.

It is also a triplet of dualities. {Mathematics, Aesthetics}, {Physics, Intelligence} and {Chemistry, Psychology}, all mediated by Biology. Aesthetics uses Mathematics, Intelligence uses Physics and Psychology uses Chemistry. This is like {Algebra, Geometry} duality three times. To iterate this a bit more, consider why {See, Hear} are coupled and are similar to {Physics, Intelligence}. See is spatial whle Hear is temporal. Intelligence is temporal since it studies temporal correlations.

The outside enclosure with 4-symmetry is a reflection of the polarisation of the star along the {Mathematics, Biology, Aesthetics} axis.

The other Jewish icon Menorah also has a related symmetry that reveals the sequential aspect more;

How did the ancients know the symmetry of the universe? Maybe a simple and pure investigation of nature reveals it. David's star is also depicted earlier in the ancient Asian Yantras. Menorah seems to belong to the Middle East.

It seems the origin of being is Touch. Then 3 dualities emerge from it like the branches of a tree, the original tree of life. But there is also the other way as implied by the increasing complexity from 0 to 6. These numbers are not just indices, they also show the symmetry. Life promotes life but what was there when there was no life? Maybe there was always life. Maybe there is a way to build a being from scratch, starting by measurement or observation and moving on until building it's partner Balance. The following picture is a part of an old religious painting. Representing the origin of being.

Touch has to be the core of being. Isn't sex an act of touch? Don't electrical charges touch each other through light? Isn't the fundamental bra/ket expression of quantum mechanics an expression of touch? Touch is in fact an act of observation involving at least a duality mediated by the agent of touch, the boson of physics. The boson of touch in sex is the child.

Duality, quantisation and symmetry in BWV-999

2006-08-18T17:02:00.000+10:00

I just love BWV-999, the Dm Prelude to the lute works by Bach. It is relatively simple to get started and there is ample potential to improve. It seems to be written to be played fast. As usual with Bach, it should be played very balanced to make the different parts stand together coherently. Speed and balance in a piece with very difficult chord transitions. A piece for life.

Measure is the most outstanding aspect of a musical piece. BWV-999 has 3/4, with each quarter further divided into 4, giving 12 sixteenths. Bach chooses special numbers with religious and mystical qualities, 2, 3, 4, 12. No surprises here. 2 comes from bass and treble duality.

Measure also happens to be the most outstanding aspect of any physical entity. Life is made of cells. Matter is made of atoms. Light is made of photons.

The first beat of all measures belongs to bass. Although it is the opening shot of the measure, it also closes the previous measure. This linking, or chaining, is very elementary and comes from the scales;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a two octave scale is played, one can hear the dual role of the root C. It is both the ending of the previous and the beginning of the next. This dual property of the root is central to music.

Life also displays this property of ever becoming.

Bass and treble make a 3+3 pattern with bass twice slower. Bass has 2+1 pattern with 2 completing to 3 in the next measure.

Another duality comes from the bass-treble interaction. Chords act as vertical glue to bind bass and treble. The first quartet (D,2D,2F,2A) sets out the dual vertical pattern.
((D,2D),(2F,2A)) and (D,(2D,2F,2A))
The 2+2 pattern arises since D and 2D attract each other, being the same.
The 1+3 pattern is due to bass and treble duality. Treble flock together.

The ambiguity in meaning is what makes the bonding between parts. He then plays with harmony, in the rest of the peace, to explore the interactions between dualities. The quantum, or measure, is the one that carries all these dualities. Reminding the uncertainty principle.

Dual ambiguity gives us depth in our vision and hearing.

There is also a spine of the piece, formed out of 6 alternate 16ths. Bass and treble are bonded to aech other around a spine. When played fast it sounds like a tremelo. As if the whole thing is like a DNA piece, with bass and treble dancing around each other around a spine. Even the numbers of bases match (2+2). We enjoy music because, it seems, the patterns of the mind match that of music.

Measurement and Consciousness

2006-08-03T10:42:00.000+10:00

Consciousness is awareness of being. It comes as a mediated duality;
{nothingness,self,other}
(0,1,infinity}
Whole existence is defined on the concept of being one. Awareness of anything requires the concept of nothingness. It is the canvas. When there is picture on the canvas, it always has two aspects;
{detail,overall}
Eyes have two modes of operation (also less obviously ears);
{focus,anti-focus}
Anti-focus is the way of paying attention to overall aspects.

The dual split in the brain reflects this duality. The 'eye' in the brain makes it's own scenery by analysing and feeling at the same time. Feeling provides the context for analysing. Thinking is based on feeling.

Thinking takes it's symmetry from Space-Time, since ST is the arena of reality;
{temporal,local,spatial}
{analytic,existential,emotional}
{algebra,number theory,geometry}
{melody,rythm,harmony}
Thinking is an act of measurement, or observation, of this duality in the brain, therefore it obeys the law of uncertainty;
dx.dp >= h/4*pi
'dx' for spatial, 'dp' for temporal, h/4*pi for local. The limit of focusing in the brain is neuron. Locality definition, or quantisation, is the prime act of any being.

7 ways of being

2006-07-31T20:23:00.000+10:00

2-7-07; Please check my later posts for a more correct classification of the fields.

Consider the mapping of M6 classification of sciences to aspects of being;

0 Mathematics ... Observe
1 Physics ... Move
2 Chemistry ... Feed
3 Biology ... Sense
4 Psychology ... Feel
5 Intelligence ... Think
6 Aesthetics ... Judge

I took Judge as the practice of Aesthetics. These 7 aspects are obviously present in many animals, including insects. Flowers' look and smell evolve through the selection by insects. Isn't it amazing that we share some appreciation of aesthetics with insects. How about birds? Don't they sing and look amazing? All that through individual and social selection.

The act of eating climbs the same ladder. You first observe and focus on the food. Then move to get it. After that you chew and taste it. Then you feel satisfied. And then you decide whether you like it. Consuming wisely, it seems, is the blueprint to being. Seeing and hearing are forms of eating, but eating light and sound energy.

Measurement, or Observation, is the root of all being. All beings are made of atoms. The atoms of life (as we know it) are cells. The number of cells of a being gives its fundamental measure. The act of observation is the root of Quantum Mechanics, and comes in a mediated duality form, the law of uncertainty;
dx*dp >= hb/2
Position and momentum of an object are mediated by the smallest action possible. Thus the law of observation is the law of uncertainty and of quantisation.

Motion brings change, and change brings evolution.

Feeding brings growth, growth brings survival.

Sensing brings prediction, prediction brings survival. Senses also climb the same ladder. But Measure and Judge are not sensed as obviously. They are trancendental. They form the background nothingness. Like water for taste and air for smell.

0 Mathematics ... Observe ,,, Measure
1 Physics ... Move ,,, See
2 Chemistry ... Feed ,,, Taste
3 Biology ... Sense ... Touch
4 Psychology ... Feel ,,, Smell
5 Intelligence ... Think ,,, Hear
6 Aesthetics ... Judge ,,, Balance

Senses obey the SM3=SE3/SH3=12/8=3/2 symmetry. Therefore there are only 5 obvious senses;
{{Taste,Smell,Touch}, {See,Hear}}
{See,Hear} provide the geometry for {Touch,Taste,Smell} to operate in. Clearly senses are centered around touch. Smell couples to Taste, and Hear couples to See. The strength of Sense comes from it's symmetry, and makes it the core of being.

Why is the science ladder limited to only 7 steps? Why is there an overall direction of evolution towards Aesthetics? Can there be anything higher than beauty? The beauty of the universe has a unity to it. Otherwise how can insects and humans share a similar appreciation of beauty when it comes to flowers?

Universe is a being
Higgs is it's Measure
Light is it's Vision
Weak particles are it's Taste
Quark-Gluons are it's Touch
Leptons are it's Smell
Space-Time is it's Thought
Mass-Gravity is it's Judgement

0 Mathematics ... Observe ,,, Higgs
1 Physics ... Move ,,, Light
2 Chemistry ... Feed ,,, Weak
3 Biology ... Sense ,,, Quark
4 Psychology ... Feel ,,, Lepton
5 Intelligence ... Think ,,, Space-Time
6 Aesthetics ... Judge ,,, Mass-Gravity

The tree of life

2006-07-30T09:10:00.000+10:00

Life evolves into a tree, or a fractal. In fact everything evolves into a tree. The tree may be convoluted and compacted and therefore invisible in many cases. It is clearly visible in most plants.

Life, as we know it, starts out in the primordial chemical soup by building self replicating molecular structures. However it is only pseudo-life before it builds the cell. A cell is a stomack-womb. At the cell level, feeding and sex are intermingled more. The roots of of oral and anal sex go very deep indeed! It's skin is porous and filters food in and excrement out. The cell core is made of DNA and it's related chemicals. It has the accumulated technology to break down food to make construction materials, heat and other functions. The content of the core is active with physical and chemical motion.

In Mirror Set language, an entity is almost nothing when it first starts out it's voyage;
,
It is nothingness.
Zero mediates infinity.
It is the first polarisation, the emergence of locality.
In mathematics it is the emergence of zero;
0
However, for measure to emerge a boundary is needed.
Then it builds a boundary for itself by polarisation and becomes a cell;
{,}
A boundary has to have at least two sides.
In number theory;
{1,0,-1}

In quantum mechanics, an entity can never be localized indefinitely.
dx.dp >= hb/2 ... (where hb is h-bar)
The reason for this is that the smallest possible action is always made of a duality and quantised to a minimum value. It is either {momentum,position} or {time,energy}. hb is very small and indicates that the universe is quantised to an astounding resolution. Therefore no entity can emerge with an absolute value like 0 as claimed above. It has to have dual uncertainty. Macroscopically, the vacuum seems to be empty, but upen deeper measurements it reveals it's uncertainty. Therefore all entities have to emerge as unpolarised duality. Like a tossed coin before collapse. Before collapse (polarisation), it is impossible to predict the outcome. After collapse, it polarises to a certain value. Therefore 0 can not emerge by itself. It has to be accompanied. The first duality to emerge, therefore, is the duality;
{0,1,infinity}
Zero and infinity are mediated by 1. Since one can never have 0 or infinity, they must emerge as;
{almost-zero,one,almost-infinity}
In the beginning, there was nothing and everything at the same time. (anon)
In the beginning there was something, but it was uncertain whether it was very small or very large.

Plants polarise into the mediated dual form {root,stem,branch} in an environment which is polarised with activity in the same direction driven by solar or other heat. Light and gases from above, food from below. Cells align with this environmental polarisation and start branching out in two directions.

Animals also polarise in the resource activity direction by building a tube (stomack). They start out as a cell, multiply to make a group of interdependent cells, and then form into a tube to make the mediated duality of {anus,stomack,mouth}. Reproduction and feeding are intermingled more at the cell level. In multi cellular structures, which are just delivery mechanisms for the reproductive cells, reproduction and feeding seperate.

To continue...

Atom

2006-06-05T21:00:00.000+10:00

All entities are made of a smallest unit, an atom.
Chemical elements are made of atoms.
Carbon based life is based on cells, the atoms of life.
Species are made of individuals.
Galaxies are made of stars.
Universe is made of galaxies.

Atoms are made of a core, a shell and a core-shell relationship.
Cell core is made of genetic material.
Cell shell or skin is made of porous tissue made of proteins that allows bothways filtration.
Cell's inside is a dynamic environment, reflecting it's outer environment, that digests the food eaten, defends against invaders, does maintenance, creates heat and many other tasks.
The know-how is stored in the core, which is in a periodic swirling motion like a beating heart.
This motion is both inwards and outwards so that there is loop.

Like galaxies, all atoms spin in a preferred direction, left or right handed.
This spin creates a moment and allows atoms to line up to make networks.
Higher spins create inner moments.

For contained smooth motion to exist, a minimum of 2 dimensions are required.
The smallest sphere is a circle.
This is demonstrated by the closure of complex numbers by 2 dimensions {+-1, +-i}.
Contained motion defines the entity, e^i*a.
The first motion that emerges is that of communication or exchange.
i*i = -1
Sqrt[-1] = i

In the wild, all populations have predators until the top ones.
Even the top ones have predators in another context.
A relatively contained Predator/Prey relationship oscillates around a mean and defines both species.
Without a predator, a species would not evolve as fast and becomes extinct easily.
Predator eats the weak and the sick and thus refines the genetic pool of the prey.
Thus a good PP relationship defines an entity out of it's base.

7 sciences

2006-05-06T17:00:00.000+10:00

0. Mathematics
1. Physics
2. Chemistry
3. Biology
4. Psychology
5. Intelligence
6. Aesthetics

The above is the M6 classification of sciences. I previously took 6 as Art. Aesthetics is a larger concept than art and also implies philosophy. Biology is at the center and the others couple to each other around it. Psychology uses Chemistry, Intelligence uses Physics (electromagnetics) and Aesthetics uses Mathematics.

Mathematics comes as a mediated duality;
{Algebra, Probability, Geometry}
Physics is also currently dual;
{Quantum Mechanics, Statistical Mechanics, General Relativity}
Statistical Mechanics should unify Physics. Sex unifies around hermaphrodites similarly. Elementary particles unify around high energy (fire). Probability has to be the unifying science. Science is the study of uncertainty. It mediates all science dualities. Chemistry's engine is heat. Bilogy's engine is mutation. Psychology's engine is mood change. Intelligence's engine is statistical analysis. Aesthetics engine is Probability. My cat Rupty is driven by a random behaviour generator. She switches the nest and the territory inspections randomly. Her mind seems to be an arena of fuzzy behavioral balls' dance.

Aesthetics is beyond intelligence, yet it rests on it. Intelligence is not enough to deal with the level of complexity a being faces in nature. One needs a supervisory function to make an educated guess in many situations in life. Intelligence provides the tactical information to this function of strategy. Life needs all sciences applied in combination. Therefore all life forms use all of these faculties in different ways. Each faculty also follows own evolution to make it deeper. More depth means slower response time, therefore only necessary amount of depth evolves. A small proportion of humans acquire Aesthetics as the leading function. Intelligence is a tactical function and acquired by most humans as the leading function. Most animals are controlled by Psychology. Intelligence and Aesthetics are subserviant to it. Psychology can take over temporarily in humans when fast reaction is required. Parts of human mind can be disabled by social dynamics for stability. Humans exhibit bully worshipping like many monkey species. Most humans get programmed early in childhood to disable their higher functions. Religion, sports, shopping, sex fulfill the vacuum created by this disability.

Art in nature

2006-04-25T17:34:00.000+10:00

Some humans are artier than others.
The artiest humans are usually the strangest.
Marginal thinking is just that, marginal.
Most humans prefer to think nothing.
Thinking is painful for them.
They would rather exist in a fantasy land secured for them by the bullies.
The bully worshipping is typical for many monkey species.
When a new bully takes over the clan, he first encounters resistance.
After a while the bully becomes accepted and loved.
The bullies of the society scare the wits of any potential challengers early in life.
Like ants, most of us get programmed in childhood by the politics of power into subserviance.
This happens in many ways at the same time for each individual.
Freedom to create is one's best asset.
The ultimate feeling is that of the creative moment.
Some people are almost impossible to oppress in any society.
They will protect their freedom at any cost.
The most important thing for them is the freedom to create.
Scientists are artists, they just use a different palette.
Musicians and mathematicians are the most blessed and cursed individuals of them all.
Blessed by the creative pleasure, while cursed by the obsession to create.
The creative people are always in the minority for any time or society.

Creativity in animals is rarely acknowledged.
We like to think they have no feelings or thoughts.
Otherwise how can we eat them?
Have you seen the Bowerbird art?
A bird obsessed in blue easthetics.
Bird songs are usually in tune and some very melodic.
Heard male cats singing the cat-sex blues?
I once heard a song lasting minutes.
It was unbelivable, a musically interesting song improvised on the spot by a horny cat!
Seen cats courting?
Birds courting?
Usually animals dance and sometimes sing in courting rituals.
Sexual and social selection may have shaped humans, but it is also very noticable in many animals.
My cat Rupty likes to posture like an equal member of the household.
And she does that with considerable style.
Cats have definite style for every individual.
I also noticed from her growing, that she has creative moments.
She slowed down in playing now but I can still see her having fun moments.
I believe all life have feeling and thought in the full spectrum.

We humans are about to enter the post natural evolution stage, if we survive the coming energy/climate singularity.
Humans most probably will survive anything, we are tough creatures.
If we can find the theory of the universe, then nothing can stop us, except the aliens.
One wonders why there aren't any definite contact.
Hard to believe we are alone in this gigantic universe.
Maybe there is a universal code of ethics about not contacting lower forms of life, until they have to.
We keep listening to e/m radiation from space, but who said they would use that form of communication anyway?
They would have mastered gravity and zero point energy.

Resolution

2006-04-25T09:37:00.000+10:00

Resolution, or the smallest/largest ratio is the first aspect of an entity.
,/{}
Matter is made of atoms.
All plants and animals are made of cells.
All living populations are made of individuals.
The universe is made of galaxies.
Galaxies are made of stars.
In fact the universe is an atom fractal.
TV screen is made of pixels which are made of 3 colors.
The retina of the eye is also made of smallest units.
This fact is known as quantisation in quantum field theory.

Cells differentiate from stem cells to form different tissues.
Embryo is the ultimate stem cell and in it's growth it summarizes the evolution of the it's species.
Ontogeny recapitulates phylogeny. (Ernst Haeckel)
Thus an embryo traces a compacted tree fractal in it's growth.

The smallest unit is like nothingness.
It is made to be taken for granted, yet it makes the entity.
Atoms are nothingness to a cell.
What atoms make the atoms, Higgs?

The universe has an astounding resolution.
We don't even know yet what the smallest part is.
It could be Planck's constant, h.
The smallest/largest ratio is what gives measure to an entity.
Measure is the first thing that enables an entity to exist.
All senses are based on measure, they have degrees.
Measure is not sensed since it is the foundation.
Like water has no taste.
It makes the nothingness for taste.
Air makes the nothingness for smell.
A slave is nothingness in a farm, yet it makes the farm run.
Space/time is like nothingness for matter and energy.

All entities exist in a shell of nothingness.

Why 3 colors?

2006-04-16T16:30:00.000+10:00

There are 3 primary colors;
{yellow,blue,red}
And there are 2 intensity limits;
{black,white}
Perception of color shifts to white in high intensity, to black in low intensity.
3/2 symmetry of color reflects the quark/gluon and space symmetry.
Space has 3 dimensions, each dimension with forward/backward duality.
Quark/gluon symmetry determines the space symmetry,
and space symmetry determines the symmetry of color perception.

Color perception would evolve from intensity (black and white) perception.
With humans, color perception has a full octave spectrum.
Unlike sound, color has only one cycle, infra-red to ultra-violet.
But within one cycle, sound also reflects color.
{C,D,E,F,G,A,B}
can be compared to white and 3 colors;
{White,Yellow,Orange,Red,Purple,Blue,Green}
Black would be silence.
Tree top living would enforce a 3D phase (state) space in the mind.
Moving around in a 3D grid requires an inner simulation of this grid for fast response.
Essentially it is about 3D pattern recognition.
Color identification of each space locality is the result of this inner mapping.
Like the RAM (Random Access Memory) address in computers,
color is a fast indexing mechanism to label space.

Charge and field

2006-04-14T14:59:00.000+10:00

The elementary particles come in two types, charge and field.
Mass is charge, gravity is field.
(+) and (-) electrical charges, light or electric and magnetic fields.
Quarks are color charges, gluons are color fields.

Algebra is like charge, geometry is like field.
Algebra operates in the boundary provided by geometry.

Analytical brain performs algebra, while emotional brain provides geometry.
Although the brain hemispheres tend to specialise to a degree, they can perform both tasks.
Like the elementary particles, brain hemispheres also divide into parts.
The frontal lobes are for higher functions like planning.
The higher functions form a weak field of influence on the brain.
They only control the available free parameters, thus acting like a donkey leading a camel herd.
Mass/Gravity are the higher functions of the universe, forming it's overall shape.

A town is like charge, it's villages are like field.

A cat in the wild holds it's territory by random inspections, thus forming a field of influence.

In ATON, charge is like ESet, field is like HSet.

Lateral of lateral is opposite

2006-04-12T14:34:00.000+10:00

Self of self is self,
opposite of opposite is self,
lateral of lateral is opposite.
Or,
(+)*(+)=(+)
(-)*(-)=(+)
(i)*(i)=(-)
This shows the "sign" aspect of "i".
The 1st one stands for a cycle of modularity 1, the 2nd for 2, and the 3rd for 4.
(+)^n=(+,+,+,+,...)
(-)^n=(+,-,+,-,...)
(i)^n=(+,-,-i,+i,...)
(i)^n shows a circular cycle, i^n=e^(i*n*pi/2), of modularity 4.
Circular rotation comes with the "lateral" concept.
It allows us to go beyond the logic of opposites and introduces us to cycles.
In a rotating system, self becomes lateral first, before it becomes opposite.
According to a point, there are two kinds of motions, along and lateral.
Lateral motion allows a system to change smoothly, without disturbing the distance between the observer and the observed too quickly.
In physics this duality is translational and angular momentum.

In biped walk, the action of the arms is like lateral motion.
It balances the upper body against the (+,-) action of the legs.
On 4 leg walk, where 2 leg one comes from, there are few modes of motion like horse's trot and gallop.
Gallop involves a smoother circular action to go fast.
Running comes naturally to 4 leg movers, 2 leggers like us lost it when we decided to use our front legs exclusively for other purposes.

The lateral motion for electric field is magnetic field.
Light action shows the symmetry of the 4 leg moving.

In electrical engineering time comes with the imaginary or lateral, e^(i*w*t), where 'w' is angular frequency.
I heard in special relativity time is lateral as well.
Time has to be lateral to space since it is not manifested explicitely like 3 space dimensions.
Space dimension, Real numbers, couples laterally to time dimension, i^2=-1.
Space is always one dimensional for motion, and time couples to it laterally.
Translational motion happens on a line, and angular motion happens around a line.
Time makes it possible for space to reflect itself smoothly along a polarised line by having a lateral motion, like a spiral.
Therefore as far as space-time is concerned, together they make 1 complex dimension.
What makes space look 3 dimensional is the 3/2 symmetry of quark/gluon.

SU(2)

2006-04-12T09:40:00.000+10:00

SU(2) is the symmetry of the weak force and has a base of 3 2*2 complex matrices with unit determinant;
((0,1),(1,0))
((0,-i),(i,0))
((1,0),(0,-1))
They all square to the unit matrix;
((1,0),(0,1))
SU(2) is like an extention to complex numbers.

SU(2) compares to E2/H2={,{}}/{,{,{}}} with the state quotient SE2/SH2=2/4=1/2.
Consider the collapsing iteration of H2;
{,{,{}}}
[,{,{}}]+[{,{}},]
[,[,{}]]+[,[{},]]+[[,{}],]+[[,{}],]
The collapse of {} gives only one state [], like +1-1=0.
H2 has a 2*2 form when collapsed, like a 2*2 matrix.
As I noted before, E2=H1={,{}} compares to Complex numbers.
{,{}}
[,{}]+[{},]
Thus E2/H2 is interpreted as "E2 for given H2".

Modular group has also 2*2 form and obeys a condition similar to unit determinant.
((a,b),(c,d)) with ad-bc=1.
DNA has a similar form with 2*2 bases.

Go 7!

2006-04-10T14:14:00.000+10:00

2-7-07; Please check my later posts for a more correct classification of the fields.

I made quite a few lists of 7 atomic objects.

{Mathematics, Physics, Chemistry, Biology, Psychology, Intelligence, Aesthetics}
{Higgs, Atom, Cell, Planet, Star, Galaxy, Universe}
{Higgs, Light, Weak, Strong, Leptons, Time, Gravity}
{Measure, See, Taste, Touch, Smell, Hear, Balance}

It is interesting that all should obey the same number of steps.
Each has it's own nothingness at the first position and it also couples to the last.

7 days a week.
7 is the consciousness age for most children.
7 notes in a diatonic scale.
7 heavens in Islam.
7 days of creation in Judaism.
7 deadly sins.
7 periods in the periodic table.
7 registers of short-term memory in humans (average 7, plus/minus 2).
7 nests of subroutines in optimum programming.
and so on.

Go M6!

Light and complex numbers

2006-04-10T10:43:00.000+10:00

I previously compared C to H2={,{,{}}} and Light to E1/H1={}/{,{}}.
There is a mistake since the symmetry of light is U(1), the circle group, or the complex unit circle, e^(i*x).
Therefore C has to be like H1={,{}} and R like H0={}.
In fact, it works better if {} is interpreted as {-1,0,+1}, reflecting dual nature of {}.
0 is the content and -1, +1 are the boundary.
Boundary determines the content and vice versa;
+1-1=0
Quantum Mechanics has a similar form as Bra and Ket vectors.
Then C is obtained by an iteration on R;
x^2=-1
x={+i,-i}
Like magnetic field is obtained from electric field.
A complex number can be written in two dual formats;
a+i*b=Sqrt(a^2+b^2)*e^(Arctan(b/a))
Reflecting the collapse;
{,{}} -> (,())+((),)

It is interesting to see that C closes so quickly.
The reason for this is that, {,{}} is the last common form to E and H sets.
E0=,
E1={}
E2={,{}}
H0={}
H1={,{}}
E1=H0 and E2=H1.
After that they diverge.

E1/H1={,}/{,{}} reflects electrical-charge/light duality.
Electrical charge comes with (+,-) duality, like integers.
Light comes with two dualities, (+,-) and (electric, magnetic).

E3/H3={,{},{,{}}}/{,{,{,{}}}} reflects strong-charge/strong-field duality.
SE3/SH3=3!2!1!0!/2^3=6*2/8 indicates 2*6 quarks and 8 gluons.

Evolution

2006-04-09T08:31:00.000+10:00

Evolution is the adaptive process that has led to the current situation.
The rate of evolution changes from species to species, time to time and place to place.
It is usual for a species to change to another species in a relatively short time, like a revolution.
This kind of rapid change happens in highly excited localities, through Spontaneous Symmetry Breaking, like lightnings.
When early humans got down from tree tops and stood up, tail lost it's utiliterian balance and other functions (like hiding your privates), and got clipped off in a short time.
Standing up and freeing hands would have happened in a short time as well.
Once the direction is set, previously stored energy builds the momentum for sustained change.
An excited system develops an outward force on it's boundary, like heating water in a closed container.
When a system bursts it's boundary, it settles to lower entropy, therefore a simpler arrangement.
Like many legs of early life forms finally ended up just 2.
The general pattern of evolution is like a river flowing down to ocean through a series of ponds, lakes and fast streams.
First it accumulates and developes inner tension, then it bursts it's boundary and settles to a new form.
This pattern comes right from the beginning of the universe.
All existence imitates this blueprint, M6.
Ontogeny recapitulates phylogeny. (Ernst Haeckel)
M6 is in fact an act of evolution (of form and content) in 7 stages.
The last stage is that of art, or creation.
Humans are very close to that.
A singularity in our culture is fast approaching.
It is hard to tell what happens after that.
We will be able to create life.
Maybe in the end we will find that, a hunter gatherer life style is the most interesting of them all.
And probably we will create simulations to experince that life.
Maybe we are simulations after all.
What is a good simulation?
One that is very hard to figure out.

7 senses

2006-04-08T08:17:00.002+10:00

29-2-2008; Here is what I think currently

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,Measure,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 is my old post.
---------------------------------------------------------------------------------

Menorah, the tree of life.

Consider the mapping of M6 to sciences, ways of being and senses;

0 Mathematics ... Observe ... Measure
1 Physics ... Move ... See
2 Chemistry ... Eat ... Taste
3 Biology ... Sense ... Touch
4 Psychology ... Feel ... Smell
5 Intelligence ... Think ... Hear
6 Aesthetics ... Judge ... Balance

Curl them into the following Yantra, following the symmetry;

Yantra of 'supreme self' Atman taken from http://sivasakti.com.

Touch is the strongest and mediates all senses. Taste/Smell, See/Hear and Measure/Balance reflect each other around Touch, indicating their origin or base. Thus M6 takes the form of 3/2 symmetry of David's star formed of two interlaced triangles, {{Measure, See, Taste}, {Touch}, {Balance, Hear, Smell}}, with Touch at the center.

Only 5 senses are obvious to us, {See,Taste,Touch,Smell,Hear}. The other two at the margins are trancendental and hidden, {Measure,Balance}. We experience them but we don't admit them into the 5 "real" senses. Measure is too simple and Balance is too complicated to sense. We like to take them for granted as background process. Like water for taste and air for smell. Because of it's complexity, Balance is calculated in dedicated tissue in the middle brain.

In case of universe, Higgs is like nothingness to us. It is a scalar field and doesn't easily interact with anything. So it is taken for granted. Gravity is so complicated, things like to observe it on the everage, like weighing, it makes the background geometry and taken as trancendental. It's small but complicated action has made it very difficult to unify with the others. In the M6 comparision, it couples with Higgs, indicating it's small action.

Some ancients seem to be right in claiming that human body and mind are a reflection of the universe. Specially the Tantric wisdom. One wonders what happened in the ancient past.

Science fractal

2006-04-07T14:49:00.000+10:00

Consider the mapping;

SM0=1 ... Higgs ... Higgs ... Mathematics
SM1=1/2 ... Light ... Atom ... Physics
SM2=1/2 ... Weak ... Cell ... Chemistry
SM3=3/2 ... Quarks ... Planet ... Biology
SM4=18 ... Leptons ... Star ... Psychology
SM5=1080 ... Time ... Galaxy ... Intelligence
SM6=12150 ... Gravity ... Universe ... Aesthetics

Biology corresponds to Planet and sits in the middle. Implying that the universe is a biological form, or that all life obeys M6. Also displaying the analytical/emotional split of a brain. Chemistry/Psychology coupling shows that chemicals make the mood, like Star light make Cell. Physics/Intelligence coupling shows that Physics (electricity or light) make Intelligence, since our chemical and biological brain support the electrical action that make Intelligence. Since light speed is needed to go beyond the chemical reaction speeds to make a hyper-structure like brain.
The most interesting is Mathematics/Aesthetics coupling. Aesthetics is beyond intelligence. It is beyond religion, beyond everything, but it needs all of them.

Religion replaces art in broken spirits. Spirits are broken, mostly early in childhood, by power dynamics of society. Spirit of an individual is broken to dominate the person, like breaking horses. But a shepherd is needed to keep the herd, so preachers are invented by the rich and powerful. Revolutionary preachers are eliminated, if not then adopted, like Romans adoptedChristianity and Moors adopted Islam. A monotheistic religion naturally reflects the politics of an empire. This is not to say that there are no spirits. Just replace Art with Spirit. But it belongs to the bearer only. When we learn to go beyond the L&S+B&D+S&M+V&amp;amp;amp;amp;M (The Mudular Group of monkey culture; Love and Sex, Bondage and Discipline, Sadism and Masochism, Violence and Murder) culture of our monkey past, we will know that a spirit is the most valuable entity of a society, and that it should not be broken by the proxies of the bullies.

Spontaneous Symmetry Breaking

2006-04-06T12:03:00.000+10:00

SSB happens when a highly excited system discards some action and settles to lower entropy.

Before a tossed coin hits the ground and collapses to one side, it has full entropy, say 1.
{,{}}
When it collapses it displays a definite side with probability (entropy here) 1/2, since sides are marked. When a sequence of tossings are considered, the state becomes a mixture of two. Like in quantum mechanics.
(,())+((),)
Thus we get a collapse of a duality by SSB. A tossed coin in air represents a highly excited system.

Stopping walk is SSB, like coin tossing. While you are walking, it is an excited system, and freezes upon stopping.

Standing on 2 legs and freeing up hands was SSB in evolution. 4 legs is good if you are always on ground. Spend less energy by discarding the balancing on 2 legs. But if you are also doing things with your hands, like on trees, it becomes a highly excited system that wants to split. Hands are freed up from walking thus reducing the entropy of walking and manipulating.

When a locality of atmosphere becomes highly excited, it discards energy as lightning and reduces entropy. A state of a system has a geometry that defines it's boundary. The action within this geometry is determined by it. Like water in a cup. Bit of shaking makes it to prefer the lower ground. For lightning, the boundary is the ionisation potential. When the e/m energy in the system gets out of hand, it tears the boundary and gets out. Clouds convert some of their kinetic energy into e/m energy. E/m energy is always present in kinetic environments since atoms do not always behave neutral.

When the early universe was an excited cloud in the mother universe, it was tossing it's options around, and decided to make a big spark in 7 phases and made all fields and their associated charges, and settled into a lower entropy.

Yantra

2006-04-05T16:56:00.000+10:00

Mysterious.
What kind of a culture would come up with this?
The triangle design has the symmetry 3/2.
8-petal shape enclosing triangles has 2/4 symmetry, like two squares interlaced.
The way the triangles put in the center looks like M6 symmetry.

Another classic is called Sri Yantra.
Looks like Bion at an angle.
This one has a 16 petal shape as well.
But still has the triangles in squares look.
Did some ancients know the symmetry of the universe?
How can that be?

DNA

2006-04-05T10:08:00.000+10:00

DNA comes with 4 bases in 2 pairs,
((A,T),(G,C))
that make two strands that spiral around each other by using Hydrogen bonds of the pairs.
Thus one strand determines the other.
This makes it very easy to split for cloning.
After the split, the second strands are rebuilt in their own cells.

Complex numbers also come in a similar form,
((-1,+1),(-i,+i))
also forming a rotating cross like DNA bases.
Complex numbers can be represented by two equivalent forms, cartesian and polar,
a+ib=Sqrt(a^2+b^2)*e^(i*arctan(b/a))
where a,b are real.
The unit circle e^(i*a) is isomorphic to U(1), the symmetry group of light.
Light traces a double helix form as it moves in space.

Modular group is also isomorphic to unit circle,
((a,b),(c,d)), ... a*d-b*c=1

All this shows that M2 is a universal set.

SU(3)

2006-04-04T16:42:00.000+10:00

SU(3) is the symmetry of quark and gluon interactions.
It consist of 3*3 complex matrices with determinant 1.
SU(3) is in fact the symmetry of the 3D space.
Quark-Gluon symmetry determines the number of space dimensions.
Not surprising since atoms are balanced around heavy quarks.
In MSet language 3/2 is the number that corresponds to SU(3).
SM3=SE3/SH3=12/8=3/2
3 colors, 2 color/anti-color.
3 dimensions, 2 opposite directions.
3 inter-dependent complex numbers.
12 for the number of quarks, 6 quarks, 6 anti-quarks.
8 for the number of gluons.

Atom fractal

2006-04-03T17:12:00.000+10:00

This chapter is superceded;
http://a-theory-of-nothingness.blogspot.com/2006/11/music-and-universe.html

Consider the mapping of M6;

SM0=1 ... Higgs ... Higgs
SM1=1/2 ... Light ... Atom (+/-)
SM2=1/2 ... Weak ... Cell (Male/Female)
SM3=3/2 ... Quarks ... Planet (Full energy spectrum)
SM4=18 ... Leptons ... Star
SM5=1080 ... Space-Time-like ... Galaxy
SM6=12150 ... Mass-Gravity-like ... Universe

The atom fractal,
{Higgs,Atom,Cell,Planet,Star,Galaxy,Universe}
includes all objects with atomic symmetry.
An atom always has skin, flesh and nucleus.
Planet has atmosphere, biosphere and rocksphere.
This classification puts cell (life) right in there with the great players in cosmology.
There seems to be correspondence between the weak symmetry SU(2) and life.
Life obeys the modular group in many ways.
SU(2) has three irreducable complex 2*2 matrices as it's base.
These matrices all have determinant 1, like the modular group condition ad-bc=1.
Another aspect of this mapping is that it puts planet in the center.
Not surprising in a way since a planet provides the widest spectrum of matter and energy.
The application of 1/2 symmetry to atom (+/-) and to cell (male/female) is also interesting, increasing the strength of the mapping.

Higher numbers are curious.
18; Since a star is in plasma state, leptons are free to roam and express their symmetry.
1080; Maybe the next meltdown happens with Space-Time, in the form of a black hole.
Assuming ST is some kind of a frozen state like an atom.
Then you get a horizon appear, to seperate the hot ST plasma from ST.
12150; Then the next meltdown is with Mass-Gravity.
This would represent a higher class black hole, a universe.
Then the atom fractal starts to look like a black hole fractal.

3 boundaries

2006-04-03T09:27:00.000+10:00

The purest moment is the Creative Moment.
It comes out of nowhere.
Or does it?
"For every action, there is an opposite and equal reaction."
The master said.
What is the intention reacting to?
What caused the big spark that made it rain matter in Big Bang?
What causes the lightning that leads to rain?
CM is like Symmetry Breaking.
SB happens when a highly excited system settles to lower entropy, by discarding the extra action.
Lower entropy brings a new boundary.
Boundary transition happens through SB.

Boundary has two irreducable elements, Inner Boundary and Outer Boundary .
{,}
When two things are the same, there is no need to separate them.
{,}={}
Life has two boundaries.
OB is skin, IB is cell skin.
In fact everything has two boundaries, in any context.
Atoms have leptons as OB, and quarks as IB.
Atmosphere's outer is space, inner is earth.
Birth is IB, death is OB.
Time is IB, space is OB.

What was first, IB or OB?
IB seems to be the first to appear, to be followed by OB in it's due time.
Nature prefers things to start small and grow to make OB.
There is a third boundary that is invisible.
It is the boundary that appears before the first boundary, nothingness.
Simply put, "," can only be written in an empty space.
Disturbance needs something to disturb.
Our universe must also be sitting in some environment that acts like nothingness.

Thus there are three boundary types, inner, middle, outer.
{,}
IB is ",", MB is {}, OB is Infinity.
Thus we go back to the triplet;
{0,1,I}

When a boundary forms, it comes with Surface Tension.
ST forms as the flattening surface forces particles to line-up in a grid made by inter-particle forces.
This grid imposes secondary dynamics within a gradual skin-depth.
ST allows water bugs to navigate the surface by using it like a trampoline.
They can also use ST gradients to climb menisci at the edges.
As the universe cooled, it would also have settled into boundaries with ST.

Sex, mathematics and politics

2006-04-01T07:34:00.000+11:00

Sex evolved from a sexually neutral being;
{male,hermaphrodite,female}
Sexual polarisation is a low entropy solution to many ways of reproductive interactions within a localised and differentiated population.
Many ways of reproduction is still observed in nature, from hermaphrodites to humans.
The success of sexual reproduction comes from the differentiated merging, which opens up a larger territory for the species.

Mathematics has a similar mediated duality;
{algebra,probablity,geometry}
When something is totally unintelligible, like white noise with infinite band-width, there can be no means of analysis.
Therefore probability, as a method, can only arrive after some differentiation in the phase space, like white noise acquiring a spectral shape like Gaussian distribution.
To have probability, one has to have both algebra and geometry to measure it.
In Gaussian, numbers provide geometry and the exponential provides algebra.
Only when total chaos settles, we get mathematics.

Politics also settles into a mediated duality when things are stable;
{socialist,pragmatist,capitalist}
It is amusing to see that these days socialist aint socialist.
Things can never settle down to absolute zero.
Therefore there is always change.
The moment the labor movement became a political commodity, it attracted the attention of the capitalist, to find out ways of manipulation.
Labor is no longer labor, if it ever really was anyway.
Tony Blair can pursue "our way of life" with surprising acceptance from voters.
USA democrats are also practically indistinguishable from the republicans.
This shows that there is a political vacuum emerging fast.
The reason is that capitalists acquired total power, reflecting the exponential increase in global consumption.
But now the order is about to turn into chaos.
It is unavoidable since there are more than one singularities approaching.
There is not enough time or resources for a benign political revolution.
Petrol is running out.
Climate is changing alarmingly fast.
Nasty global epidemics seem to be around the corner.
Water is running out.
Species are dying too fast.
And as an indication what is to come, we got Iraq.
Like cats, humans become violently territorial when resource conflicts arise.

If there is no miracle soon, we are all doomed, most probably within a decade or two.
There is only one miracle left that is possible;
A theory of the universe.

Brain

2006-03-30T16:02:00.000+11:00

All brains come in dual form;
{,{}}
(right,left)=(emotional,analytical)
Sometimes this mapping is flipped;
(right,left)=(analytical,emotional)
Like the split in mathematics;
(Algebra,Geometry)
Algebra for analytical, geometry for emotional.
Like the split in computers;
(Programs,Operating System)
Programs for algebra, OS for geometry.
Emotions set the overall mood by using hormones.
Thus the material base for the dual split is science;
(Physics, Chemistry)
Chemistry sets the geometry for physics (electricity) to operate in.

An M6 brain should unite around M3, like ETT.
M3=E3/H3
SE3/SH3=3!2!1!0!/2^3=12/8=3/2
Would 3/2 symmetry correspond to color perception?
Basically there is only one color to start with;
{gray}
Then it seperates into a mediated duality;
{gray} -> {black,gray,white}
Then white seperates into 3 colors;
{white} -> {yellow,blue,red}
Each color pair also get their own mediation;
{yellow,orange,red}
{yellow,green,blue}
{red,purple,blue}
Thus 3/2 colors, {yellow,red,blue}/{black,white}, define a 3D coordinate system, 3D space.
Each color gets an axis, and {black,white} gives intensity like {-,+}
Like the universe, a brain that perceives 3 colors obeys M3.

Although the color symmetry obeys 3/2, it doesn't necessarily mean light is essential for a brain to evolve.
As ETT shows, sound also obeys the same symmetry.
It seems the brain opens up a seperate 3D phase-space to solve each problem.
3D aspect of hearing is clearly visible in the conic spiral shape of cochlea in ear.
Then there must be other 3/2 modules in the brain to deal with other cognition tasks.
Sense comes in 5 types;
{see,hear,taste,touch,smell}
I think consciousness has to be added in this list.
Even then I think there is one missing, considering M6.
Taste has 3 colors;
{sweet,sour,salty}
With taste intensity we again get 3/2 symmetry.
I regarded 'bitter' as extreme sour.
Touch has 3 colors?
{elastic,stick,inelastic}
Smell comes from taste, therefore obeys the same symmetry.

Vertebrate body

2006-03-29T20:24:00.000+11:00

The most obvious aspect of an animal body is that of mouth-stomach-anus or head-body-tail mediated duality.
Mouth-stomach-anus aspect would be the first to evolve for any living entity.
Life starts with birth and then eating and growth follow.
If you can't eat, you can't grow, very simple.
Eating can be as simple as in and out of a simple tube, like worms suggest.
A particular eating action evolves as a low entropy solution to many types of action that a differentiated population would use.
An eating action would have to controlled from the front since sensors would be there.
The first sense for an animal to experience would be taste.

The second most obvious aspect is left-middle-right mediated duality.
L/R seperation is necessary since most movements would have to be in a plane for a water-land margin living entity.
With head/tail and left/right setup, we are ready to navigate a plane.
A certain type of head/tail, left/right oscillation would be enough to move.
This motion would be the one that splits the first animal brain.
Then we get many appendages appear, as worm evolution shows, and these settle to head/tail, left/right and arms/legs configuration for vertebrates.

These steps map to M0-2;
SM0=1/1=1 ... mouth/anus (head/tail)
SM1=1/2 ... left/right
SM2=2/4 ... arms/legs

To continue.

M3

2006-03-29T16:30:00.000+11:00

Above are 3 visualisations of M3 with no perspective. It is a shape I found while playing with equal length bamboo sticks. Previously I called it Bion. I decided to call it just M3. Now I aso don't divide the outer cubes. It's outer aspect is the 3 interlaced cubes like the Escher's. Inside, it has a cube made of two reflected tetrahedrons. The number of total faces of the outer cubes is 18. The tetrahedrons have 8 triangle faces. Note the resemblance to some ancient Asian yantras, specially Shri Yantra.

I found it when I was admiring the beauty of a tetrahedron made using 6 equal length sticks. Then I rotated it pi/2 and added them to each other making a cube made of two reflected tetrahedrons. This is a cube made by it's diagonals. The diagonals of the cube make two interlaced tetrahedrons. Then I wondered what would happen if I kept this iteration of making a transformation and adding it to the parent shape. I rotated the cube pi/2 and translated it by 1/2 in each of the 6 face directions and added them all to each other. Then I completed the manifested cubes and also divided the cubes to into 8 equal pieces.

There may be more things one can do to Bion with equal length sticks as suggested by M6. There is already a large octahedron inside. I expect all the Plato's polyhedrons to appear in some iteration of Bion. I had enough of playing with sticks, too tedious.
I am thinking about a little program to experiment with Bion. Someday it may happen. It would be wonderful to make a full connection with M6.

In the middle there are two interlaced Tetrahedrons, made by rotating one of them pi/4 and adding. Each T is made of 6 sticks representing the edges. T+T(pi/4) has 2*6=12 sticks. There are 6 crosses making the faces of a cube. There are 8 corners made by the tips of Ts. Thus we got our;
12/8=3/2=E3/H3={,{},{,{}}}/{,{,{,{}}}}
T^2 is a cube made by it's diagonals.

The outer layer of Bion has 3 cubes made by sticks at the edges. There are 3*6=18=SE4/SH4 faces.

Fundamental Theorem of Calculus

2006-03-26T19:40:00.000+11:00

FTC states the existence of the integral;
Integral[f(x)dx,a,b] = F(b)-F(a)
An iteration of FTC gives Taylor's expansion and maps e^z to polynomials;
e^z = Sum[z^n/n!, n=0,...,Infinity]
The weighing factor 1/n! diminishes the higher polynomials and ensures absolute convergence.
It reminds the number of states of ESet;
SEn = n!(n-1)!(n-2)!...1!0!
ESet is derived from iterating a simple operation, like the e^z sum.
Then one would expect the Integral[] definition to be like the ESet operator E.
ESet accumulates its past and determined uniquely by its initial and final states, like Integral[].
ESet seems isomorphic to e^z.

Equal Tempered Tuning

2006-03-26T10:29:00.000+11:00

E0/H0= /{}
SE0/SH0=0!/2^0=1/1=1
The root note, say C.

E1/H1={}/{,{}}
SE1/SH1=1!0!/2^1=1/2
The octave of the root, 2C.

E2/H2={,{}}/{,{,{}}}
SE2/SH2=2!1!0!/2^2=2/4=1/2
The octave of the root, 2C.

E3/H3={,{},{,{}}}/{,{,{,{}}}}
SE3/SH3 = 3!2!1!0!/2^3 = 12/8 = 3/2
3/2 is the frequency ratio of the 5th to it's root, like G/C.
12 is the number of semi-tones in an octave.
(C,#C,D,#D,E,#E,F,G,#G,A,#A,B,C)
The frequency ratio between any two adjacent notes is the 12th root of 2.
When you iterate the same ratio 12 times you reach the octave,
(Root[2,12])^12=2
This homogeneous division gives transposability.
8 is the number of notes in a diatonic scale,
(C,D,E,F,G,A,B,2C)
In fact there are only 7 different notes but only when the 8th is played it gives the ending feeling.
It can be viewed as a HFractal of depth 3;
(((C,D),(E,F)),((G,A),(B,2C)))
Like modular group.
The grouping becomes clearer when the corresponding rational numbers are considered;
(((1,9/8),(5/4,4/3)),((3/2,5/3),(15/8,2)))
G leads the second group on the way forward.
F leads the second group on the way backward.
When two scales are played, the octave 2C leads the second group;
(((C,D),(E,F)),((G,A),(B,(((2C))),2D),(2E,2F)),((2G,2A),(2B,4C)))
The two scales overlap at 2C and become linked.
There is a wonderful modularity in the scales.
This can be heard clearly when one plays the scale (specially over and over again!).

ETT compares the power taking iteration of 5th to 8th and makes them meet at some real number a/b;
(3/2)^a = 2^b
a*log(3/2) = b*log(2)
a/b = log(2)/(log(3)-log(2)) = 1.7095
12/7 = 1.7143 has a very close match.
((3/2)^12)/2^7 = 1.0136
If you take power of 3/2 12 times you get the 7th octave, almost.
If a/b is set exactly to 12/7, then all other ratios have to be adjusted.
12 is the number of semi-tones in an octave, and 7 is the number of octaves it takes for the 5th to make a complete cycle and also the number of notes in CM scale.
Thus harmony is distorted slightly to get transposability.
The miracle of ETT is that harmony and equal tempering meet with a surprisingly small distortion of harmony.
This 7 octave travel of the 5th suggests M6.

I referred to Michael Rubinstein's page for the algebra;
http://www.math.uwaterloo.ca/~mrubinst/index.html

M6 suggests further division of the octave, like some Arabic scales which divide a tone into 9 commas.
12/7 equal tempering seems to correspond to the outer shape of M6, since it is centered around E3/H3.

Mirror Set and the elementary particles

2006-03-26T10:20:00.000+11:00

Now revised;
http://a-theory-of-nothingness.blogspot.com/2006/11/mirror-set-rev-1.html

Mirror Set of order n is the (n+1)*(n+1) matrix quotient set;
Mn=Mnkl=Ek/Hl, (k,l)=0,...,n

M6 seems interesting with the following main diagonal state quotients and proposed mappings to elementary particles;
SE0/SH0=1 ... Higgs?
SE1/SH1=1/2 ... Light
SE2/SH2=1/2 ... Weak
SE3/SH3=3/2 ... Quarks
SE4/SH4=18 ... Leptons
SE5/SH5=1080 ... Space-Time-like?
SE6/SH6=388800 ... Mass-Gravity-like?
The digits of 4,5,6 all add to multiples of 9.
388800/1080=360
1080/18=60
18/3/2=12
3/2/1/2=3
1/2/1/2=1
1/2/1=1/2

3/2 is the symmetry of quarks and equal tempered tuning.
Quarks come in 3 generations and 2 types;
{{u,d},{c,s},{t,b}}
I put 3/2 in the middle and proposed M6 since energy seems to be balanced around quarks. This balancing is achieved by the large mass ratio Mp/Me=1836.
When the state quotient is expressed more explicitely it becomes clearer;
E3/H3={,{},{,{}}}/{,{,{,{}}}}
SE3/SH3=3!2!1!0!/2^3=12/8=3*2*2/2*2*2=3/2
There is 2*2*3 ness (3 generations, 2*2 types) and 2*2*2 ness (3 color/anti-color pairs) at the same time.

18=2*3*3 is the number for leptons.
Leptons also come in 3 generations and 2 types;
{{e,ve},{m,vm},{t,vt}}
18 is pretty obvious in the periodic table, displaying the 18-slot lepton wrapping of the nucleus.
6 is is kinda explained but how about 3*6=18, why does it get multiplied by 3?
Maybe leptons are satisfying the color multiplicity of quarks.

1/2 is degenerate curiously.
The first 1/2 has to be light, electric and magnetic together make one unit.
The second 1/2 then stands for weak, with W+,Z0,W-.
The degeneracy may stand for the realtively easy light-weak unification.

1 must be Higgs which is assumed to be scalar and not detected yet.

I made a guess about what the other two are, 1080 and 388800, space-time-like and mass-gravity-like.
Gravity seems to be a deeper field as black hole theories suggest.
Space-Time stop at the event horizon but Mass-Gravity don't.
Putting quarks in the middle suggests the couplings;
{Higgs,Mass-Gravity}
{Light,Space-Time}
{Weak,Leptons}
Weak-Lepton coupling is observed in the decay of neutron;
n->p+e+ve
Light-Space-Time coupling is pretty obvious.
We define Space-Time with light.
Higgs-Mass-Gravity coupling remains to be seen.

Exponential Set

2006-03-25T14:47:00.000+11:00

This set should be called Factorial Set of order 2, in line with the updated definition of Mirror Set;
http://a-theory-of-nothingness.blogspot.com/2006/11/mirror-set-rev-1.html

E0=,
E1=EE0=E={,}={}
E2=EE1={,{}}={{},}
E3=EE2={,{},{,{}}}
E4=EE3={,{},{,{}},{,{},{,{}}}}
...
En=EE(n-1)

Where E is a reflection operator. It gathers the past under one roof. Although it has multiple content, it also has an overall duality like HSet. ESet looks like e^z since the self similarity in breadth. HSet is self similar in depth, for example H3={,{,{,{}}}}. Self similarity of exponential function is evident from differentiation, (d/dz)e^z=e^z. Taylor's expansion of e^z is an iterated process, like ESet.

The identity (E0=,) is a bit strange but my hand was forced by 0!=1. But it also makes some sense since the seperator is defined first. (E0=) is even stranger.

The number of states;

SE0=0!=1
SE1=1!0!=1
SE2=2!1!0!=2
SE3=3!2!1!0!=12
SE4=4!3!2!1!0!=288
SE5=5!4!3!2!1!0!=34560
SE6=6!5!4!3!2!1!0!=24883200
...
SEn=n!(n-1)!(n-2)!...2!1!0!

Self similarity also shows up in the state calculation. The factorial is calculated to depth 2.

Note the curious 'nineness' of 4-6;

2+8+8=18=2*9
3+4+5+6+0=18=2*9
2+4+8+8+3+2+0+0=27=3*9