The days between von Neumann Algebra and Complex Manifold Deformation Theory 2015

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
SILessay

The Days of von Neumann Algebra 2015

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.

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

• sekinanlogos

• 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     

• Topological Group Language Theory

1. Boundary of Words

• Symplectic Language Theory

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

• Floer Homology Language

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
SILessay

The Days of Decipherment 2016

The Days of Decipherment

TANAKA Akio

On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth days, so to say, the days of decipherment.

1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told  at Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered the Linear B.

In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered by NISHIDA Tatsuo (1928-2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki narabini Seikago bunpou no kenkyuu in 1962.
In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team developed largely.

In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the Qing dynasty and I read them almost every day containing the comparison with the western linguistic results. The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin  were the most important for me.

In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda, Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was too much difficult to read on. From the days the long and winding road began to mathematics and its applicable study for language universals.

At the exhibition of ancient Greece I confirmed in particular that the stability of language was  kept by letters and characters from the Linear A and Linear B. 

Exhibition Catalogue numbers are the next.
The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.

39. Clay juglet c. 1800 B.C. ~ c. 1700 B.C.
40. Clay bar c. 1700 B.C. ~ c. 1650 B.C.
41. Clay tablet c. 1375 B.C. ~ c. 1350 B.C.
77. Linear B bar and tablet c. the 13th century B.C.

For my part the stability  has been one of the biggest themes on language phenomena since I was taught from CHINO Eiichi through the results of the Linguistic Circle of Prague, especially of Sergej Karcevskij.



​

​​The exhibition catalogue and Chadwick's book Japanese translated edition.
 

 
Reference

1. Essence of Language / SRFL Paper 
2. Derived Category Language, 26 July 2016 Edition

References 2

1. The Time of WANG Guowei
2. 40 years passed from I read WANG Guowei

References 3

1. Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
2. Half Farewell to the Linguistic Circle of Prague and Sergej Karcevskij
3. Sergej Karcevskij, Soul of Language
4. Gift from Sergej Karcevskij
5. Follower of Sergej Karcevskij
6. For KARCEVSKIJ Sergej
7. Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique"

References 4

1. Fortuitous Meeting
2. ​Linguistic Circle of Prague
3. Prague in 1920s
4. Under the dim light

References 5

1. The Time of Language, Ode to The Early Bourbaki To Grothendieck
2. Bourbaki' ELEMENTS DE MATHEMATIUE Troisieme edition, 1964

Tokyo
30 July 2016
Sekinan Library

Read more: http://srfl-paper.webnode.com/news/the-days-of-decipherment/

The days when I was thinking on Energy Distance Theory 2014

The days when I was thinking on Energy Distance Theory

q.v. Energy and Distance in Language / 31 August 2008

TANAKA Akio

1.
Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.

• Energy Distance Theory

1. Energy and Distance 
2. Heat and Diffusion
3. Energy and Functional
4. Finsler Manifold and Distance 
5. Word and Meaning Minimum 
6. Geometry of Word

2.
In another approach of my study on language universals, Edward Sapir's Language, 1921 was one of my favourite books between 1970s and early 1980s. In his book, the most fantastic concept for me was Drift, that indicated the vast movement of language system itself.  I ever gave brief account on it.

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

• Edward Sapir's Language, 1921

Edward Sapir's Language, 1921 showed me the dynamism of language proposing the concept, drift.
Drift shows us the macro phase of natural language and I was hinted by Sapir's this concept and proposed the micro phase of natural language. The paper "Quantum Theory for Language" is my first total proposal paper describing the natural language's model.

Reference
Substatiality Dedicated SAPIR Edward / 27 February 2005

Tokyo
5 September 2014
Sekinan Research Field of Language 
..................................................................................................................................................................................................................................................................................................................

3.
My language study started from the reading of Old China's Qing dynasty's huge linguistic inheritance, "Xiaoxue", in English Small Study , that is contrary to the name, the most basic and difficult study of classical texts of old China. I particularly loved the books written by WANG Guowei and WANG Yinzhi and DUAN Yucai.
The main book list to which I referred in those days between the age 20s and 40s are shown  at the next.

• Library 10 General Index,  SRFL Sekinan Research Field of Language

Especially I was enchanted with WANG Guowei's work, whose selected papers' title wasGuantangjilin. For him I wrote a short essay as below.

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

• 40 years passed from I read WANG Guowei / 16 November 2013

TANAKA Akio

Guantangjilin is the selection of works by WANG Guowei, which contents contains vast area of history, literature and linguistics. Some people say that his works is a thousand-year peak from Song era’s philosopher SHU Xi. I bought his book at Haifeng shudian, Kanda, Tokyo in my mid 20s. The date  of colophon is February 1973, publisher is Zhonghua shuju Xianggang fenju.

Probably I bought it in 1973 or 1974. In those days I frequently went Haifeng shudian bookshop for buying Chinese classics,  mainly Qing Dynasty’s linguistic works that is called ” Xiaoxue”, Small study at China. Guantangjilin is a very difficult book to understand  by my poor study result.

His study era is from Yin Dynasty to Qing Dynasty some 2,500 years of Chinese literary history. At his vast works I was especially charmed in Qing Dynasty’s ancient Chinese hieroglyphic characters, Jiaguwenzi by Chinese. After 40 years, in 2003 I wrote a small paper on language universals through this  ancient Chinese hieroglyphic characters at the view point of written language.

The title is On Time Property inherent in Characters. From at that time 10 years passed by. Now I am still learning on language universals but its style is far apart from the days 2003 or 1973. Ambiguity of approach by traditional linguistics is not for my part. I dare challenge to a new frontier of description for language study using mathematics or algebraic geometry.

Refer to the next.

• On Time Property Inherent in Characters 2003
• From Distance to Pseudo-Kobayashi-Distance 2012
• Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague 2013

Tokyo 16 November 2013
Sekinan Research Field of Language
............................................................................................................................................................................................................................................................................................................................

4.
After all,Energy Distance Theory ended in the half-finished situation. But now I still eager to write and develop the papers on energy and distance. The road is long and winding as ever. I always accustomed to delay and stagnate. Some rays of light is emitting in the small study room of mine.


Tokyo
19 December 2014
Sekinan Essay

The Days of Distance 2012

​
The Days of Distance
From Distance to Pseudo-Kobayashi-Distance
​
TANAKA Akio 
​                                  
In 2004 I wrote the paper titled "Distance Theory". The paper handled the structure of sentence, using the classic written Chinese for its simplicity of form that has not any transformation at word. In Chinese, word namely character does not change anymore. Nevertheless grammatical functions strictly exist by its sequence of characters. I had been very interesting the style of language that never appears in the European languages. But the study for it was too hard to pursue at my age 20s and 30s by my talent.


In 1979, I met CHINO Eiichi again at the university to where I returned from the work of teaching at senior high school. He taught me the importance of the Linguistic Circle of Prague. We talked with many problems of language study at the campus or coffee shop near the station we usually got on and off. The shop were old and steps were always sounded rattling. The light of the shop were dim and yellowed with age. We were both young, he was late 40s and I was early 30s.


Before these days we already met at the Russian class. The time was 1969, he taught us the language in the tiny classroom. Then he was just after coming back from the long study at Czechoslovakia.


From 1979, he had actively introduced the Linguistic Circle of Prague while studying his own subjects. It was a really happy time for me. He told us at the class of linguistics and told me more frankly at the coffee shop on the various themes related with language. Prague was always at the centre in the conversation.I gradually went on to the narrow theme concerned with language universals. What decisively entered to my mind was Sergej Karcevskij.


If there only be Saussure, I could not determined so smoothly.In my age 30s, 1980s, I had been wandering to and fro at Kanda, the central part Tokyo, where I encountered many Chinese classics at the Chinese book shops. From my familiar language I wanted to research the study on the subject. But  there were no clear road to going ahead.  I had hoped concise and clear description on the theme, if I wish, using mathematics.


In 1960s, in my front, Bourbaki emerged the huge target that was built by the vast from-set-theory-to-topology. At the time's going my level was very low and primitive. I was never able to use such a difficult mathematics.


I spent the lag time in 1970s. reading Chinese classic books at random. The main was Qing dynasty's Xiaoxue (Small Study in Chinese) on Chinese characters classical research.


In 1990s, the target of language study decided to language universals, being led by Sergej Karcevskij for that almost all the information were given from CHINO. At that time mathematics were going on and on to the wide and deep fields covering the humanities, e.g. category, sheaf and discreteness.


In March 2003 I stayed some days at Hakuba, Nagano, where I wrote the proto-paper on language model for the first time, titled " On Time Property Inherent in Characters". It treated the unchanging language, Chinese, as the typical one for its simplicity and familiarity in my life. The paper's main theme was time that is hypothetically inherent in each character in Chinese. The basis of the theory was in the study of WANG Guowei's ancient Chinese inscriptions on bone and tortoiseshell.


In order to possess grammar in unchanging language, there should be the another functions to express grammar or near -grammar. I selected inherent time in each character supposedly.


In August 2003, I again stayed at Hakuba, where I wrote "Quantum Theory for Language". It was the enlarged paper of the March's one. There intuitive long-short times were supposed. There was not any description of mathematics. But important points were presented not using mathematics, I thought. 
The problem was how precisely writing the theory using mathematics.


In 2004 I wrote " Distance Theory" from the viewpoint of clear concept using distance instead of time that was not able to mention enough descriptively. But the theory was also intuitive and philosophical one. I never satisfied the expression. The theory's essentials were distance and connection, that is to say, words connect according by the distance inherent in words.


Succeeding this theory, I tried to write many fields on language making the efficient models for natural language, namely language universals in my mind, being led by Karcevskij.


Hereafter the main target was the mathematical description for many varieties that were almost intuitively remained or noted. Now I use algebraic or arithmetic one for their strict simplicity and beauty.


Recently I wrote in distance from pseudo-Kobayashi-distance that was very fantastic and widely perspective views for me. The paper's title is 'Connection of Words", that is my long winding road from encountering CHINO and Linguistic Circle of Prague.


Grateful thanks to CHINO Eiichi. You wrote "Linguistics of the 21th Century" in  1998,  four years before your death, that there are studies undergoing to be able to understand meaning by combination of several elements. Still now I am your student and probably forever. 


[Reference]
Distance of Language, Historical Review                                                                   
                                                                  

Tokyo 
February 5, 2012  
February 2015, revised       
September 16, 2016, Title. The Days of Distance, added         
Sekinan Research Field of Language                                          
                           

History of SRFL :: SRFL Lab

History of SRFL :: SRFL Lab

History of SRFL :: SRFL Lab

History of SRFL :: SRFL Lab