Fortuitous Meeting

What CHINO Eiichi Taught Me in the Class of Linguistics 

TANAKA Akio

CHINO taught me the core of linguistics in the class of structural linguistics.
The most remarkable thing is what he explained the paper of KARCEVSKIJ to us.
The title is “Du dualisme asymétrique du signe linguistique”. It became a miracle of my life.

 I summarize the essence of the paper from one of CHINO’s most major book,Gengogaku eno hirakareta tobira, Janua linguarum reserata in Latin. Language has the dualism.
One is firm structure. The other is flexible variability.

This is a very revelation in the roaming of study.
At first I selected the firmness of language for my research target.
It overlapped with the research of Chinese characters.
Thought of KARCEVSKIJ fructified the quantum of language.
The theory I reached is Quantum Theory for Language.
The starting point of the theory was given from CHINO.
I deeply appreciate him for teaching me almost all the things on language. 

CHINO Eiich died March 19, 2002.
At age 70.

Tokyo 

December 5, 2004
July 16, 2014 Added

Sekinan Research Field of Language

The days between von Neumann Algebra and Complex Manifold Deformation Theory

vide:  Applied papers with this essay are reprinted at SRFL News' January 2015 blogs.

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

• Period of Meaning

• Period of Meaning 2 

• Place of Meaning 

• Energy of Language 

• 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. Space4. 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

• Distance of Word

• Reflection of Word 

• Uniqueness of Word

• Amplitude of Meaning Minimum  

• Time of Word

• Orbit of Word 

• Understandability of Language 

# Here ends the paper.

Tokyo

6 January 2015

SIL

The Days of von Neumann Algebra 

viz. The cited papers' texts are shown at the blog site SRFL News' January 2015 blogs.

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 

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 Algebra5 Kac-Moody Lie Algebra6 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 Focus5 Linguistic Result 

Distance Theory Algebraically Supplemented

Algebraic Note1 Ring2 Polydisk <Bridge between Ring and Brane>3 Homology Group4 Algebraic cycle

Preparatory Consideration1 Distance2 Space <9th For KARCEVSKIJ Sergej>3 Point

Brane Simplified Model1 Bend2 Distance <Direct Succession of Distance Theory>3 S3 and Hoph Map 

Noncommutative Distance Theory

Note1 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 Grammar3 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

• Distance of Word

• Reflec bsp;of Word 

• Uniqueness of Word

• Amplitude of Meaning Minimum  

• Time of Word

• Orbit of Word 

• Understandability of Language     

• Topological Group Language Theory

• Boundary of Words

Symplectic Language

• Symplectic Topological Existence Theorem 

• Gromov-Witten Invariantational Curve

• Mirror Symmetry Conjecture on Rational Curve   ​ 

• Isomorphism of Map Sequence  

• Homological Mirror Symmetry Conjecture by KONTSEVICH 

• Structure of Meaning

Floer Homology Language

• Potential of Language       

• Supersymmetric Harmonic Oscillator 

• Grothendieck Group   ​ 

• Reversibility of language

• Homology Generation of Language 

• Homology Structure of word 

• Quantization of Language

• Discreteness 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.## The cited papers' texts are also shown at this site.

vide: The days between von Neumann Algebra and Complex Manifold Deformation Theory

Tokyo

3 December 2015

SIL

Roman Jakobson References added

TANAKA Akio     
                               
THE SOUND SHAPE OF LANGUAGE by Roman Jakobson & Linda Waugh, 1979 is one of put-aside-desk book for the study. The authors wrote the Preface to The Japanese Edition, 1980 that the primary concern was the basic opposition between form and meaning, furthermore there were definite difference and intimate bonding between these two essential phenomena.
For turning to myself, I had already determined the main target on meaning, and sound had been put aside, while Jakobson's book  was still referred time to time. It  was a great teacher for me, and   probably from now on.

References

1. Cell Theory Continuation of Quantum Theory for Language / From Cell to Manifold For LEIBNIZ and JAKOBSON / Tokyo June 2, 2007
2. Meaning minimum / On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi

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

Tokyo
16 July 2012
Sekinan Research Field of Language

3 December 2014 Revised
SIL

Reference added
5 March 2016
SRFL Paper

Read more: https://srfl-collection.webnode.com/news/roman-jakobson-references-added/

On Structure
​Symplectic Language Theory

TANAKA Akio
    
Dialogue 1
On Structure
For HORI Tatsuo, Footprints on the snow, 1946


Why do you think that language has structure?
_We have true-false problem since Greece had logic on language, Crete man tells himself a liar. The situation suggests that if language has structure and we see the structure's whole, there is no more problem in the upper funny but radical story.

Do you mention that language has dimensions in it for preventing the confusion?
_Surely dimension is an important factor of structure. But language is a vast building in which all the logisc and all the feelings are expressible for all the hope of human beings.

Then how the structure is built, do you imagine?
_I ever learned the history of Linguistic Circle of Prague, in which the most important hypothesis is said that language has function. Function is inevitably occurred following after the completion of structure, I think.

Do you say that from the observation of language function is adequately acceptable for structure's surface?
_Yes, I think so.

Then on inner structure of language, what do you think?
_At first, language has meaning. But it was put aside by Prague Linguistic Circle as the hardest problem on language for its ambiguity as MATHESIUS V. gave the famous lecture, Latency of　language phenomena, 1911.  I attracted the theme, language has ambiguity.

Did you go to Prague? 
_No. I only heard on PLC from CHINO Eiichi. He learned linguistics at Prague, from 1958 to 1967. He gave me the basis of linguistics after his returning to Tokyo. I first met him at Tokyo 1969. I learned Russian at that time in the small class. He was young at 37, and I also young too at 21.   

You really respect CHINO.
_I remember him respectfully, but more frequently merrily, for his fantastic conversation to the younger beginner, studying language from various fields, from art to classical languages at the university. 

On language, ambiguity is important?
_Undoubtedly. CHINO gave me the concept of asymmetric dualism of linguistic sign. The paper was written by KARCEVSKIJ Sergej at 1929. Precisely to say, "Du dualisme asymétrique du signe linguistique", Travaux du Cercle Linguistique de Prague 1.

From ambiguity to structure, through what course did you choose?
_I took the road from the minimum unit of meaning that was extracted by WANG Guowei's GUANTANG JILIN, the book was real youth of my life, for which I named <meaning minimum> by reference of JAKOBSON Roman's concept <semantic minimum>. I dearly remember CHINO's warm advice "not to enter such a theme that are firstly treated by WITTGENSTEIN-like person. We are not invited", backing to the railway station from the university, after his lecture on linguistics at early summer twilight. 

<Meaning minimum> is your starting point, I recognized. After that, To where did you go?
_At first, from set theory. I ever learned it mainly from TAKEUCHI Gaishi's papers. Now I yet like his approch to the mathematical object. And I, at that time, also came under the influence of LÉVI-STRAUSS Claude.

That course was productive to you?
_It is a difficult question. For first step of my study, partly yes and mostly no.

Mostly no, for what?
_For me the most important is the relation between <meaning minimum>s. But set theory is not efficient for that direction.

Is relation important?
_Perhaps yes.

Why?
_Back to MATHESIUS's <latency> or KARCEVSKIJ's <asymmetric duality>, there exists relationship between one meaning and another meaning. For me, this relationship is not able to be handled by my set theory's level. But set theory is enough charming for its elemental simplicity.

And where did you go to the next?
_Geometry. It is the most natural and fantastic approach by its freely intuitive methods. 

Intuition is surely familiar. But selection is only done by such reason?
_I have not any other choices at considering my mathematical level then.

Geometry was respondent to your hope?
_Yes, absolutely yes. As people say that geometry is a heimat of mathematics, I really think so.

Geometry is more easily way to approach for you?
_Repeatedly say, I have not any choices at that time. Meeting with geometry, I often wrote various figures containing topological ones, for instance at on the train to the town in which mother is under medical care.

Such drawings can express language's validity?
_Much interesting to express but the themes containing validity of language and so forth are very hard to access.

Why?
_Relationship among language inside is far away beyond my amateurishly imaginary figures.

And after that?
_I came here, at my present mathematical situation as PENROSE Rogersaid in his book THE ROAD TO REALITY, that mathematics is the most highly investigated way for the study of universe. His confidence to mathematics is put up on my home page of Sekinan Research Field of Language.

Where do you stand now?
_Symplectic geometry.

Why do you stand there?
_Also natural for me. And freely thinkable.

Freely thinkable, what imagine by that?
_Mathematics is radically free. Just like a wind at high lands, far-sighted and transparent.

Mmm. Transparent. 
_Yes,perfectly transparent. In contrast with language. Language is always having ambiguity.

Ambiguous language and transparent mathematics.
_That's all.

Many thanks today.
_It's my pleasure. 


Tokyo
12 March 2009
14 December 2015 Revised
​Sekinan Research Field of Language

[References added, 12 January 2016]
 

1. Symplectic Language Theory
2. Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"
3. Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague

SIL Data +1's is a simple overview of Sekinan Library.
 

Preparation for the energy of language

Half Farewell to Sergej Karcevskij and the Linguistic Circle of Prague with References