​The days between von Neumann Algebra and Complex Manifold Deformation Theory

​The days between von Neumann Algebra and Complex Manifold Deformation Theory

Applied papers with this essay are reprinted at SRFL News.

TANAKA Akio

von Neumann Algebra was written from 3 April 2008 to 2 May 2008. And Complex Manifold Deformation Theory was written from 30 November 2008 to 9 January 2009. In the days between the two theories I wrote the following 4 paper groups.

• Functional Analysis 
• Reversion Analysis Theory
• Holomorphic Meaning Theory
• Stochastic Meaning Theory

These days were the preparatory time for regularised writing by algebraic geometry at Zoho site. But they were relatively precious days for thinking about the reshuffling mathematics and physics related with language. Especially Stochastic Meaning Theory was a milestone for mathematical approaching to physical phenomenon of language.Stochastic Meaning Theory's titles are the next.

• Stochastic Meaning Theory

1. Period of Meaning
2. Period of Meaning 2 
3. Place of Meaning 
4. Energy of Language 
5. Language as Brown Motion 

On the other hand, I really realised that mathematical writing of  natural phenomenon, for example natural language, inevitably needed clear routes by mathematics that was represented by function analysis approach. Functional Analysis and Reversion Analysis Theory were the trial papers aiming for new ground, especially the comparison of finiteness and infinity in generation of words and sentences. 

• Functional Analysis 1

Note
1. Baire's Category Theorem
2. Equality and Inequality
3. Space
4. Functional
Conjecture
1. Finiteness of Vocabulary
2. Distance at Hypersurface

• Functional Analysis 2

Note
1. Pre-Hilbert Space and Hilbert Space
2. Orthogonal Decomposition
Conjecture
1. Generation of Word

• Reversion Analysis Theory

1. Reversion Analysis Theory
2. Reversion Analysis Theory 2


But at that time I could not decide the main field of mathematics for applying to language study. Moreover I never thought about language models parting from natural language and constructing the new field for thinking about language universals. 
After these preparation of algebra that was started from Premise of Algebraic Linguistics 1 -1 at 11 September 2007, I barely reached to the entrance of algebraic geometry's use for language and making the language models. It was Complex Manifold Deformation Theory which began to write at 30 November 2008 titling Distance of Word,  one of my main themes for language universals from the very starting of language study. Thus my study first focused to making language models of algebraic geometry using complex manifold.

• Complex Manifold Deformation Theory

1. Distance of Word
2. Reflection of Word 
3. Uniqueness of Word
4. Amplitude of Meaning Minimum  
5. Time of Word
6. Orbit of Word 
7. Understandability of Language 

# Here ends the paper.

Tokyo
6 January 2015
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