Pioneers for language study from Sekinan Paper

Sekinan Paper

Essay
vide: SILessay

Sergej Karcevskij
Sergej Karcevskij, Soul of Language
Gift from Sergej Karcevskij
Follower of Sergej Karcevskij
For KARCEVSKIJ Sergej

Linguistic Circle of Prague
Linguistic Circle of Prague
Half Farewell to Linguistic Circle of Prague with References
Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"　with Note

WANG Guowei
40 years passed from I read WANG Guowei 
The Complete Works of WANG Guowei

Ludwig Wittgenstein
For WITTGENSTEIN Ludwig Revised

John von Neumann
The Days of von Neumann Algebra 
The days between von Neumann Algebra and Complex Manifold Deformation Theory

Sekinan Table for main papers of SRFL opened

Blogger Sekinan Table has opened for the main papers written at SRFL for research of language universals by mathematical tools.

New Blogger site

Sekinan Table

Tokyo 23 

23 April 2015

Sekinan Study

Quantization of Language, References added

sekinanlogoshome 

Floer Homology Language 

TANAKA Akio 

    

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Note7 

Quantization of Language​

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Theorem​

1​

(Barannikov, Kontsevich 1998)​

<.,.>, ° defines structure of Frobenius manifold at neighborhood of H's origin.​

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2​

(Kontsevich 2003)​

There exists φk : EkΠ2(Γ(M;Ω(M))) → Π2CD(A, A), k = 2, ... .​

 is L∞ map.​

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Explanation​

1​

(Local coordinates of Poisson structure)​

{f, g} ​

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2​

(Map)​

{.,.} : C∞ × C∞  →C∞​

The map  has next conditions.​

(i)   {.,.} is R bilinear,{f, g} = - {g, f}.​

(ii)  Jacobi law is satisfied.​

(iii) {f, gh} = g{f, h} + h{f, g}​

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3​

(Gerstenharber bracket)​​

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4

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5​

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6

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7​

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8​

(  )​

Manifold     M= R2n​

Coordinates     p, q​

Differential form     w = dqidpi​

Subset of C∞( R2n )        A​

Element of A       F    ​

Differential operator of R2n      D(F)

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D({F, G}) ≡ [D({F}, D({G}]​

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[Image 1]​

Quantization of language is defined by theorem (Kontsevich 2003).​

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[Image 2]​

Complex unit  is seemed to be essential for mirror symmetry of language by explanation 

8.​

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[References] 

Quantum Theory for language / Synopsis / Tokyo January 15, 2004​

Mirror Theory / Tokyo June 5, 2004​

For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005​

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Tokyo ​

June 24, 2009​ 

Sekinan Research Field of Language​

Citation from Ludwig Wittgenstein

Citation from Ludwig Wittgenstein
TRACTATUS LOGICO-PHILOSOPHICUS Translated by C. K. Ogden
Dover edition

Text is lined up according to the order of citation at the essay, The Time of Wittgenstein 
by TANAKA Akio
                                    
6.521
The solution of the problem of life is seen in the vanishing of this problem.
 (Is not this the reason why men to whom after long doubting the sense of life became clear, could not then say wherein this sense consisted?)

6.432
 How the world is, is completely indifferent for what is higher. God does not reveal himself in the world.

6.35
Although the spots in our picture are geometrical figures, geometry can evidently nothing about their actual form and position. But the network is purely geometrical, and all its properties can be given a priori.
 Laws, like the law of causation, etc., treat of the network and not of what the network describes.

6.54
 My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.)
 He must surmount these propositions; then he sees the world rightly.

PUBLISHER'S NOTE by DOVER PUBLICATIONS. INC.
This translation of the German work that originally appeared in Ostwald'sAmalen der Natur-philosophie, final number (1921), was carefully revised by the author himself. In addition, the philosopher and mathematician Frank P. Ramsay assisted C. K. Ogden with the translation.                                                               


Tokyo
February 7, 2012                                  
Sekinan research Field of Language

The Time of Wittgenstein

TANAKA Akio                           

There surely exists the time of Wittgenstein for me.
That time about in my 30s, in the middle of 1970s.
One may aware of the kernel of the problem after almost all the hardships were gone and the problem is going under pursuing in the daily work for oneself, as Wittgenstein wrote at 6.521 in TRACTATUS LOGICO-PHILOSOPHICUS. 

Wittgenstein wrote on language immanently at least in TRACTATUS.
He also said in TRACTATUS 6.432 that how world exists  does not care from the higher dimensions.
I also wanted to write on language from the immanent side in language.
But I had not any pursuing method for writing on language at that time, only remaining set theory typically presented by Bourbaki that some translations were surely on my desk.

Set theory was enough fascinating at the time, but it did not give me any relative and constructive situations on language or widely on the world. It was isolated and non-relative for writing on language. I wanted the bond of the world.

Now I have geometry for which the world can be bonded enough tightly. In 1970s I was never aware of the existence of geometry by myself, probably not being influenced from Wittgenstein's 6.35 in TRACTATUS, Geometry absolutely tell nothing on how the figure is and where the figure situated.
So I had remain silently in the days not being able to write on the theme, the basic essence of language. Then I never knew the object on language, language universals that was taught from CHINO Eiichi later in 1980s. CHINO showed me the paper of Sergej Karcevskij, Du dualisme asymétrique du  singe linguistique. The theme determined my remain life hereafter. CHINO was the true teacher of my study.

Wittgenstein wrote at the last 6.54 of TRACTATUS that his some propositions must be abandoned. I began to go through the wood of hard theme of language universals by mathematics especially using geometry. About what can be told to, I never must be silent. 

Reference
Citation from Ludwig Wittgenstein

                                                              Tokyo
                                                  January 20, 2012
                                   Sekinan Research Field of Language

Description

TANAKA Akio

For language study, its theoretical  description is a very important role for understandability and clarity of the paper. Till my age 30s , I had never been satisfied with my way to study and write. Philosophical and philological methods have been felt somewhere ambiguous and unreliable to proceed sensitive research of language.

My great turn occurred at the relearning of mathematics, especially geometrical algebra. In the past 1970s, I was also one of the many influenced students from Bourbaki, that was the brightest star in the universe of minute and rigorous road to the destination. But my poor way was always unevenness and wide deep fog was surrounded in the vast field in front of mine. What at last I  arrived at the gate of confirmed style was the beginning of the 21st century. At that time I wrote several trial papers related with language universals but still never had been satisfied for their ambiguity and intensive styles. My next crux came at my study of new wave of algebraic geometry, complex manifold deformation at 2008. Its result became some papers named Complex Manifold Deformation Theory. This was the very fresh and clear way to study language for me.

• Complex Manifold Deformation Theory

Conjecture A
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
Conjecture B
1.  Map between Words
2.  Understandability of Language

• Papers at Zoho 2008-2013

Tokyo
15 August 2013
Sekinan Research Field of Language

Homological Mirror Symmetry Conjecture by KONTSEVICH​

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sekinanlogoshome 

 

Symplectic Language Theory 

TANAKA Akio 

     

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Note6 

Homological Mirror Symmetry Conjecture by KONTSEVICH​

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1​

R       Commutative ring over C​

C       R module that has degree​

(ΠC)k = Ck+1​

BC     Free coassociative coalgebra​

EC     Free coassociative cocommutative coalgebra​

BkΠC  BΠC that has k number tensor product​

EkΠC  EΠC that has k number tensor product​

mk : BkΠC → ΠC​

lk   : EkΠC → ΠC​

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2                         Coderivative​

A∞-algebra             = 0 at (BΠC, mk) (k>0)​

Weak A∞-algebra     = 0 at (BΠC, mk) (k≥0)​

L∞-algebra             = 0 at (EΠC, mk) (k>0) ​

Weak L∞-algebra     = 0 at (EΠC,  mk) (k≥0) ​

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3 ​

M(C)                     Complex structure's moduli space over compact manifold c     ​

Unobstructed         Weak A∞-algebra that satisfies M(C)     ​

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4 ​

M       Symplectic manifold​

M†   

          Complex manifold that is mirror of M​

L        Lagrangian submanifold of M that Weak A∞-algebra  is unobstructed            ​

FL      Object of M†  's analitic coherent sheaf's category​

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(Conjecture)​

For L there exists FL. FL's infinite small transformation's moduli space is coefficient to 

M(L).  ​

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5​

[b]     Element of M(L)​

[b] defines A∞-algebra.​

[b] defines chain complex's boundary map m1b​

Cohomologyy of m1 b is called Floer cohomology.​

Floer cohomology is expressed by HF((L, b), (L, b)) ​

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6 (Impression)​

Word is seemed as L.​

For L there exist language FL and M(L).​

Mirror theory on language is supposed by the existence of FL and M(L).​

<References>​

Mirror Theory papers in early stage of Sekinan Linguistic Field​

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To be continued 

Tokyo April 26, 2009 

Sekinan Research Field of language 

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