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, 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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