ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Friday, August 19, 2011

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)))

Thursday, July 21, 2011

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.

Monday, April 11, 2011

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"

Friday, March 25, 2011

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

Friday, March 18, 2011

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.

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