Thursday, 22 May 2025

​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
Sekinan Essay

The Days of von Neumann Algebra

 The Days of von Neumann Algebra 


The cited papers' texts are shown at Blogger site, SRFL News.

TANAKA Akio

1.
My study's turning point from intuitive essay to mathematical writing was at the days of learning von Neumann Algebra, that was written by four parts from von Neumann Algebra 1 to von Neumann Algebra 4. The days are about between 2006 and 2008, when I was thinking about switching over from intuitive to algebraic writing. The remarkable results of writing these papers were what the relation between infinity and finiteness in language was first able to clearly describe. Two papers of von Neumann 2, Property Infinite and Purely Infinite, were the trial to the hard theme of infinity in language.
The contents' titles are the following.

..............................................................................................................................

  • von Neumann Algebra 
Assistant Site : sekinanlogos
TANAKA Akio

On Infinity of Language
1 von Neumann Algebra 1
2 von Neumann Algebra 2
3 von Neumann Algebra 3
4 von Neumann Algebra 4


  • References
1 Algebraic Linguistics 
2 Distance Theory Algebraically Supplemented
3 Noncommutative Distance Theory
4 Clifford Algebra

5 Kac-Moody Lie Algebra
6 Operator Algebra
.


.................................................................................................................................

2.
The papers of von Neumann Algebra and References are the next.

..................................................................................................................................

  • von Neumann Algebra 

1 1 Measure
2 Tensor Product
3 Compact Operator


  • von Neumann Algebra 2

1 Generation Theorem

  • von Neumann Algebra 3

1 Properly Infinite
2 Purely Infinite


  • von Neumann Algebra 4
1  Tomita's Fundamental Theorem
2 Borchers' Theorem


  • Algebraic Linguistics
<Being grateful to the mathematical pioneers>On language universals, group theory is considered to be hopeful by its conciseness of expression. Especially the way from commutative ring to scheme theory is helpful to resolve the problems a step or two.
1 Linguistic Premise
2 Linguistic Note
3 Linguistic Conjecture
4 Linguistic Focus
5 Linguistic Result 


  • Distance Theory Algebraically Supplemented
Algebraic Note
1 Ring
2 Polydisk <Bridge between Ring and Brane>
3 Homology Group
4 Algebraic cycle
Preparatory Consideration
1 Distance
2 Space <9th For KARCEVSKIJ Sergej>
3 PointBrane 
Simplified Model
1 Bend
2 Distance <Direct Succession of Distance Theory>
3 S3 and Hoph Map 


  • Noncommutative Distance Theory
Note
1 Groupoid
2 C*-Algebra
3 Point Space
4 Atiyah’s Axiomatic System
5 Kontsevich Invariant[References]
Conjecture and Result
1 Sentence versus Word 
2 Deep Fissure between Word and Sentence


  • Clifford Algebra
Note
1 From Super Space to Quantization
2 Anti-automorphism
3 Anti-self-dual Form
4 Dirac Operator
5 TOMONAGA's Super Multi-time Theory
6 Periodicity
7 Creation Operator and Annihilation Operator
Conjecture
1 Meaning Product 


  • Kac-Moody Lie Algebra 
Note
1 Kac-Moody Lie Algebra
2 Quantum Group

Conjecture
1 Finiteness in Infinity on Language


  • Operator Algebra 
Note
1 Differential Operator and Symbol
3 Self-adjoint and Symmetry
4 Frame Operator

Conjecture
1 Order of Word
2 Grammar
3 Recognition

....................................................................................................................................


3.
After writing von Neumann Algebra 1 - 4,  I successively wrote the next.


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


Especially Stochastic Meaning Theory clearly showed me the relationship between mathematics and physics, for example Brownian motion in language. After this theory I really entered the algebraic geometrical writing by Complex manifold deformation Theory. The papers are shown at Zoho site's sekinanlogos.

....................................................................................................................................

 
  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     
 
  1. Boundary of Words
 
  1. Symplectic Topological Existence Theorem 
  2. Gromov-Witten Invariantational Curve
  3. Mirror Symmetry Conjecture on Rational Curve   ​ 
  4. Isomorphism of Map Sequence  
  5. Homological Mirror Symmetry Conjecture by KONTSEVICH 
  6. Structure of Meaning
 
  1. Potential of Language       
  2. Supersymmetric Harmonic Oscillator 
  3. Grothendieck Group   ​ 
  4. Reversibility of language
  5. Homology Generation of Language 
  6. Homology Structure of word 
  7. Quantization of Language
.....................................................................................................................................

4.
The learning from von Neumann Algebra 1 ended for a while at Floer Homology Language,  where I first got trial papers on language's quantisation or discreteness. The next step was a little apart from von Neumann algebra or one more development of algebra viz. arithmetic geometry.


# Here ends the paper.

Tokyo
3 December 2015
Sekinan Essay

Glitter of youth through philosophy and mathematics in 1970s

 

Glitter of youth through philosophy and mathematics in 1970s

TANAKA Akio

In 1970s or in my age 20s there surely exists glitter of youth in my life, now I remember.
In those days, in Japan many fabulous magazines were successively published. Episteme,Toshi(City)、Chugoku(China) and the likes. Especially I loved reading Episteme which had printed many philosophical or philological articles as the form of special issues concentrated important philosopher, thinker and writer. The chief editor of Episteme was NAKANO Mikitaka(1943-2007), probably one of the best editors in the latter half of the 20th century in Japan.  The most impressive number was Ludwig Wittgenstein(1889-1951), probably in 1977. Also influenced from the issue of Kurt Godel(1906-1978)who gave me the possibility of set theory.

In my life, Wittgenstein gave the big influence for thinking and writing style, never entering or approaching his essential philosophical themes.After millennium year when I started the regular writing on language universals, my writing style was resembling in his Tractatus Logico-Philosophicus. My paper written in 2003, Quantum Theory for Language shows a very imitative style to him. This tendency kept on for some time till I changed to adopt algebraic method for more clear description to the themes.

1970s was a relatively calm times after those university's revolution in the late 1960s in which I also compellingly rolled in. In those days I almost had been wandering between library and old book shops aiming my life-time true themes cowardly avoiding the turmoils of university and towns. Blaise Pascal(1623-1662)'s Pansees was my favourite one. One day at Kanda's Taiwan chinese book shop Kaifu Shoten, I bought WANG Guowei(1877-1927)'s Guantangjilin that opened the new frontier for classical Chinese philology mainly streamed by "Small Study", traditional exegetics in China. Influenced WANG Guowei I wrote a paper titled On Time Property Inherent in Characters, 2003 by which I began the latter start of language study.

In 1970s, I had cherished a dream in which I wanted to use mathematical description and get the essential of language. But I had not any ability to proceed the study for it while I read at random several mathematical books. One day I found and bought the amount Nicolas Bourbaki(1935-)'s text books at old book shop in Kanda, Tokyo. They were hard to keep reading for my talent in those days. After all, the books were put aside the desk. The remaining in my mind was adoration to Bourbaki and their brilliant achievement. My return to Bourbaki was long after in 1990s when I again tried the pursuit of language having a clear vision to study language universals according to the Linguistic Circle of Prague, especially aiming to resolve the supposition presented by Sergej Karcevskij(1884-1955).

Turning round the past days, my way was always narrow and winding road. But it keeps till now not breaking off in any situations. The way was finely glittering in my youth days despite under the cloudy sky. Probably I have kept happily walking till now being assisted by many people especially at the field of language, mathematics and relevant studies.

At random now I remember the dear names from whom I  never cannot hear their voices. HASEGAWA Hiroshi, CHEN Donghai Chinese languageKAJIMURA Hideki, CHO Shokichi Korean languageNatary Muravijowa Russian languageONO Shinobu Chinese literatureMIIYAZAKI Kenzo, FURUTA Hiromu, KONDO Tadayoshi Japanese literatureANDO Tsuguo French poemSAEKI Shoichi HaikuIKEDA Hiroshi Japanese classical dramaSAITO Kohei sculptureYAMAGISHI Tokuhei bibliographyNISHI Junzo Chinese philosophyKAWASAKI Tsuneyuki BuddhismCHINO Eiichi Russian language, the Linguistic Circle of Prague. At last dear friend of high school days KANEKO Yutaka mathematics and our youth.

Tokyo
6 March 2015
Sekinan Library

Affinity between philosophy and mathematics

  Affinity between philosophy and mathematics


TANAKA Akio


Philosophy

  1. For WITTGENSTEIN Ludwig Revised
  2. Glitter of youth through philosophy and mathematics in 1970s
  3. NISHI Junzo, Philosopher of Modern Japan
  4. Intuition and Mathematics,  NISHI Junzo 2

Mathematics

  1. Time in Word
  2. Language and Dimension
  3. The days when I was thinking on Energy Distance Theory
  4. Pleasure of Mathematics 
  5. The days of von Neumann Algebra
  6. The days between von Neumann Algebra and Complex Manifold Deformation Theory

Letter concerned

  1. Letter to Y.  Toward geometrization of language 
  2. Letter to Y. Of Broad Language



Tokyo
9 September 2018
Sekinan Study

Read more:
sqgl.weebly.com/affinity


Read more: https://srfl-paper.webnode.com/news/affinity-between-philosophy-and-mathematics1/

For Wittgenstein Revised / Position of Language

 For Wittgenstein Revised / Position of Language


TANAKA Akio 



    
                         
Quantization1 is a cliff for consideration of language.
2 Mathematical interpretation of quantized language is now a first step to the theoretical ascent.
3 If there is not mathematics, next conjectures are impossible.
(i) Difference between word and sentence---Commutative and noncommutative ring
(ii) Continuation from word to sentence---Tomita’s fundamental theorem
(iii) Word’s finiteness and sentence’s infinity---Property infinite and purely infinite

(iv) Cyclic
 structure of word’s meaning---Infinite cyclic group
Meaning minimum2mirror language3 and mirror symmetry4 are inevitable approach to the study of language especially for language universals5.
5 Symplectic Language Theory, Floer Homology Language and Arithmetic Geometry Language are adopted as the model theory
 for natural language in the recent.
6 Hereinafter the model theory will be entered to the new concept
The Models of Language Universals 6 will be shown by the description of mathematics.

Tokyo December 10, 2005
Tokyo November 27, 2008 Revised
Tokyo March 24, 2009 Revised
Tokyo June 27, 2009 Revised
Tokyo February 28, 2011 Revised
Tokyo August 3, 2012 Revised

Wandering between language and philosophy

 

Wandering between language and philosophy

 

15 Silk Road and 16 Story 2021 Revised 2022

 

15 Silk Road and 16 Story 2021
Revised 2022

 

15.
2003
Silk Road
 

In the fall of 2002, I had pneumonia and was admitted to Ome Municipal General Hospital for about two weeks. Fortunately, the progress after admission was smooth, and after one week, my breathing and physical condition returned to normal, but my doctor was cautious about whether I was exhausted, and it took another week before I was discharged. Looking out the window at the mountains of Okutama, I was keenly aware that I hadn't written anything about the subject of the language I finally found. When I was discharged from the hospital, I was repeatedly checking the words and phrases of the dissertation to be written, thinking that I should give priority to that first and foremost.

The essence of the discussion was gradually coming together. There was something unwavering about the pursuit of what the essence of language was the subject of my dissertation, but considering the depth and vastness of the language itself, I have accumulated myself so far. Based on this, I focused on Chinese characters, and while using Kiyoyo's elaborate linguistics, elementary school, I was aiming for a universal linguistic theory, and from there I was thinking of a direction to approach the language itself.

As a result, by the time of discharge, I found that some of the typical forms and meanings of the oracle bone script contained time in those letters, referring to Wang Guowei's papers, etc. Based on this, I considered the direction of the syntactic theory, in which a sentence is formed by concatenating words that include time, as the second article. However, my traditional dream was to set them in a physically verifiable direction rather than in a philosophical direction. My longing for theoretical physics, which has existed within me since high school, was still at the core of my thinking. And now  I was learning the basics of the epic algebraic geometry systematized by the French Bourbaki group Nicolas Bourbaki by the 1960s.

When I was a research student, Sergej Karcevskij's "Asymmetric Duisme asymmetrique du linguistique 1929" by Sergej Karcevskij of the Prague Linguistic Circle of Prague continued to come and go in me. For example, I had just set up a base camp far below this high peak.

Regarding "asymmetric duality of language symbols", I have written a short sentence before, so I will reprint it below.

"Symmetry. It's what I once talked to C in linguistics. Prague in the 1920s. Karzewski's paper in the magazine TCLP," Asymmetric Duplexity of Linguistic Signs. " The coexistence of absolutely contradictory flexible and rigid structures where the language continues to hold, thereby the language remains the language. An eternal contradiction that will continue to be doubly inherent in language. Karzevski presented the duality of why the language can be so flexible and so robust, and that it is almost absolutely inconsistent. A discussion of the white eyebrows left by linguist Sergei Karzevskiy, whom C described as the only genius in his last book. A consistent understanding of this duality as to why this coexistence is possible has probably not yet been submitted. Karzevskiy

's dissertation was a breakthrough that briefly bisected its macroscopic structure of the meaning that was difficult and barely touched in linguistics.

In 2003, I began to put together the above two directions almost in parallel, but spring came without being able to construct the logic of the language that connects the two of vocabulary and syntax. Two children went out for spring skiing in Yuzawa, Niigata prefecture, which has been continued in recent years, because the school was on spring break, and the children and my wife enjoyed skiing according to their respective strengths, but I went to the hotel alone. For the rest, I focused on following the invisible logic for building the word-to-syntactic connection that was absolutely necessary for my dissertation .

As a result, I didn't bring any reference materials, so the day after I arrived in Yuzawa, I wrote with almost no writing, and summarized the principle logic that connects vocabulary and syntax. Was done. This sentence was scribbled and incomplete, so I didn't upload it on the Web even after I finished writing the two articles, but in 2015, when I reread it in detail, I found that this sentence Since I recognized most of the sprout of the subject that I continued to write about my language, I decided to add a short preface and upload  it under the title of Manuscript of Quantum Theory for Language  . ..

Around April, a while after I returned to Tokyo, I opened the Site of the National Institute of Informatics, which I used to see from time to time, and announced that an international symposium on Silk Road would be held in Nara, co-sponsored by the Institute and the Ministry of Education. The call for papers to be published there was posted. Since I had written two dissertations based on the draft I wrote in Yuzawa, I decided to submit the dissertation on syntax as an application paper, and since it was an international symposium, the dissertation should be written in English in principle. Since it was said that it was supposed to be translated into English, I corrected a part to make it more logical and clear, and I was able to apply safely by the submission deadline in May. The paper, entitled Quantum Theory for Language  , regarded language as a physical quantum and the combination formed a sentence.

Although I felt common sense anxiety about treating language as a quantum, I was sensuously convinced of the future prospects in that direction, so I hardly hesitated. Fortunately, this paper was adopted as one of the four oral papers in the linguistics and literature section of the symposium, and I was on December 23 and 24, 2003, at the far right of Nara Todaiji Temple. It will be announced on the 23rd at the symposium held at the public hall. The presenters in this department were a professor at Hokkaido University, a member of the Toyo Bunko, a researcher at a company, and myself.

After the oral presentation on the afternoon of the 23rd, I was really relieved. On the afternoon of the 24th of the second day, when I went to the hall, which was the main venue, researchers from various countries gathered and various languages ​​were spoken. Perhaps because of the subject of the symposium, there seemed to be a large number of people attending from Central Asia. Starting with an invited lecture, there were lectures by department, oral presentations, panel presentations, posting of related information, etc. were held throughout the public hall, and it was reported that the total number of participants was close to 400. To me, the venue itself seemed like the end of the modern Silk Road.

Quantum, which is the center of my discussion, is a concept of physics, but it was also very attractive from the viewpoint of mathematics, so it was taken into group theory in mathematics and defined as a quantum group in the 1980s. Proposed by VG Grinfeld.
Hopf algebra and the quantum Yang-Baxter equation. 1985 is the first paper. In the same year, Michio Jimbo of Japan also published a paper A  q -difference analogue of  U (g) and the Yang-Baxter equation. 1985, which bridged physics and mathematics.

It was later in the late 2000s that it became clear to me that it became possible to use quanta strictly in mathematics. My sensory direction to the quantum can thus be used as being completely determined by a strict mathematical definition.

I have further geometrically transformed this quantum, and with the help of the achievements of Perelman and others who introduced the calories of physics into mathematics, I have expanded the language from natural language to signals and further to the energy elements that are the basis of them. Quantum-Nerve Theory, which advances to representation and its application and tries to quantumly transform human nerves to lead to applied science, has almost finished its preparatory consideration from 2018 to 2019, and now We have reached the direction of advancing its mathematical structure algebraically. At the same time, I would like to continue learning important directions such as David Marr's work Vision, which passed away at the age of 35 in 1980, which created the skeleton of neural theory, and  "visual computational theory and brain expression" as a subtitle.

Let's go back to 2004.
In January 2004, the Institute of Informatics sent me a completed manuscript because I would like to publish an oral presentation paper as a booklet, and I received an email saying that the oral presentation manuscript was further corrected and sent. In May, a thick booklet containing papers was delivered to the people concerned. To distinguish it from the conventional manuscript, the title on the booklet is Quantum Theory for Language Synopsis  .

In the year I entered university in 1967, I was thinking of one of my goals as a major direction from Asian to European languages. Half a century later, my first booklet containing a dissertation summarizing my subject was presented from Japan to Central Asia and then to Western Europe. It may have been one of the accumulations of wisdom delivered on the modern Silk Road. Even if my dissertation itself was really small in it. 

Tokyo
7 February 2022 Revised
Sekinan Library



 

16 .
2015 
Story

In the winter of 2012, when I felt that the Paper dissertation on the universality of the Language Universals language, which I had been writing since 2003, had settled down in my own way, at the age of 65, I derived the language from axioms and theorems. However, in some respects, the desire to take a step away from the ruthless world of mathematics and to warmly portray the human beings living there has become stronger, and one youth that includes an autobiographical element. I wanted to portray the possibilities as two people who are both lonely but never isolated.

Her A, the main character, her I, who reunited with her, and the bulbul that hurt her wings were all, in a sense, the alter ego of the author. As an amateur, I can't tell if it's complete as a story, but as I write this story, I'd like to express what I should call salvation while wandering in the days of youth. became.

In their lifetime, they have met many people, received unpredictable support, and faced unexpected farewells, and would have continued their journey to discover their own subject of life. I was one of them.

One will never be able to continue when he is strong. So, there, you might come across something that could be called salvation somewhere without realizing it. It wasn't because it was weak, or because it was weak, and it wasn't asking for it, but in life itself, perhaps inevitably, salvation would have existed as something that would come unknowingly. I was naturally like that one day.

The story begins with the days of autumn when the wind is cold, and ends with a day full of light that makes you feel the loneliness of winter.
I wonder if everyone is the two of the day.

"Winter is coming to them like grace now."

I conclude this story so.