12 aspects of being

Anahata

(((Number,Function),(Operation,Equation)),
((Set/Logic,Analysis),(Algebra,Geometry)),
((Probability,Statistics),(Computation,Information)))

(((Economics,Finance),(Trade,Money)),
((Politics,Religion),(Relationship,Emotion)),
((Science,Philosophy),(Technology,Communications)))

(((Nucleotide,Nucleic-Acid),(Amino-Acid,Protein)),
((Muscle,Neural),(Connective,Epithelial)),
((Inner-Sense,Outer-Sense),(Inner-Action,Outer-Action)))

(((Sound,Syllable),(Word,Sentence)),
((Definition,Explanation),(Description,Conclusion)),
((Expression,Conversation),(Meeting, Conference)))

(((Note,Interval),(Measure,Theme)),
((Tempo,Rhythm),(Melody,Harmony)),
((Solo,Duet),(Chamber,Orchestra)))

(((Higgs?,?),(Dark-Matter?,Dark-Energy?)),
((Position,Momentum),(Charge,Field)),
((Matter,Planet),(Star,Black-Hole)))

I have finally come back to 12, after being stuck on 4 for a while. This time though I reckon I found the symmetry I have been after for a long time. It has the numbers 1, 2, 3, 4, 6 included in the overall symmetry, indicating that the classification is in fact a computer. 12 is a very popular number in religion and science. The lists speak for themselves.

The most important outcome is the predictive power of this classification. It places the scalar elements of the universe nicely into the 1st quartet, and predicts an unknown element besides Higgs and the already theorized dark ones. Perhaps Higgs splits into two.

The symmetry has two other less dominant representations;

1. (((,),(,)), ((,),(,)), ((,),(,))) ... 3*4
2. (((,),(,),(,)), ((,),(,),(,))) ... 2*6
3. (((,,),(,,)), ((,,),(,,))) ... 4*3

Following the commutation and association property of multiplication of naturals;

3*4 = 4*3 = 2*6 = 12

Does not seem to have the 6*2 symmetry. It is not surprising that the overall symmetry imitates the small natural numbers, since they are the simplest and purest forms. The pure symmetry of the naturals has to be broken though, to have complexity. 3*4 seems to be the dominant symmetry. I think this is based on the triplet symmetry of numbers;

(0,1,Infinity)

The 3*4 symmetry is in fact 3*2*2 = 3!!, the double factorial of 3. The double factorial has a self reference; it reiterates itself.

An interesting thing that seems to be related to this classification is the Kleiber's Law. It relates the metabolic rate of animals to their masses;

Metabolic Rate ~ m^(3/4)

It's explanation involves the self similarity and the fractal structure of the metabolism.

The Fifth Element

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

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

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

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

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

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.