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

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