Gromov-Witten Invariantational Curve​ / Symplectic Language Theory / 27 February 2009

Symplectic Language Theory 

TANAKA Akio 

     

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Note 2 

Gromov-Witten Invariantational Curve​

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[Invariant]​

(Gromov-Witten)​

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[Note] 

 

1  

g, m     Integer that are not less than 0 

βH2(M;Z) 

Riemann surface of genus g     ∑ 

Number of element of ∑     m 

Group of elements of ∑    

Pseudo regular map     ,  

Pair    ((∑, β), φ) 

 

2 

All the isomorphism class of ((∑, β), φ)       

 

Gromov-Witten invariant     Virtual fundamental class of  

 

 

[Impression] 

1 

Language is given by . 

2 

Word is given by ((∑, β), φ). 

3 

Word's meaning is given by . 

4 

Meaning unit is given by pi     (1<i<m) 

5 

Connection rule of word is given by φ. 

 

 

[References] 

#1 Dirac Operator 

#2 TOMONAGA'S Super Multi-time Theory​

 

​

 

 

To be continued 

Tokyo February 27, 2009  

Sekinan Research Field of language 

Potential of Language / Floer Homology Language / 29 April 2009

Floer Homology Language

TANAKA Akio

Note1
Potential of Language



¶ Prerequisite conditions
Note 6 Homology structure of Word

1
(Definition)
(Gromov-Witten potential)


2
(Theorem)
(Witten-Dijkggraaf-Verlinde-Verlinde equation)



3
(Theorem)
(Structure of Frobenius manifold)
Symplectic manifold     (M, wM)
Poincaré duality     < . , . >
Product     <V1°V2, V3> = V1V2V3( )
(M, wM) has structure of Frobenius manifold over convergent domain of Gromov-Witten potential.

4
(Theorem)
Mk,β (Q1, ..., Qk) = 

N(β) expresses Gromov-Witten potential.



[Image]
When Mk,β (Q1, ..., Qk) is identified with language, language has potential N(β).

   

[Reference]

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

First designed on <energy of language> at
Tokyo April 29, 2009
Newly planned on further visibility at
Tokyo June 16, 2009

Sekinan Research Field of language

For WANG Guowei / A Letter / 11 March 2003

For WANG Guowei 


TANAKA Akio

A Letter

I met with his book at Kanda in winter early 1970s.
He has be alive in my mind since then.
He historically lived in China at setting-sun, the Qing dynasty.

In those days at Kanda 70s. 
I had been wandering alone like a rhino.
To which I had the most familiar feeling.

But at where, I was not alone for him.
WANG Guowei.
Oh the book Guantangjilin.
It is the very name that I had taken along with my youth.

I met him at Kanda in winter in my age early twenties, 1970s.
There for ever
Bright and ease.
With cold windy rain of dear old Tokyo.



Tokyo 
March 11, 2005
February 18, 2007 Revised
September 25, 2014 Revised
Sekinan Research Field of Language

[Reference added, 25 September 2014]

On Time Property Inherent in Characters / March 28, 2003

Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013 / With References

Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague 

TANAKA Akio

I have thought on language through the rich results of the linguistic Circle of Prague and its important member Sergej Karcevskij. But now my recent thinking has inclined towards algebraic or arithmetic geometrical method and description.

Probably it is the time of half farewell to those milestones which led me to the standing place here with rather sufficient results in my ability. Great thanks to all that always encouraged me for hard and vague target on language especially meaning and its surroundings. And also to CHINO Eiichi with love and respect who taught me all the bases of language study.

For recent results see the following papers group named AGL Arithmetic Geometry Language and related essays.

Papers
AGL Arithmetic Geometry Language 

• Dimension of Language (AGL 1)
• Synthesis of Meaning and Transition of Dimension (AGL 2)
• Birth of Word, Synthesis of Meaning and Dimension of New Word (AGL 3)
• Dimension Conjecture at Synthesis of Meaning (AGL 4)

Essays

• Parts and Whole
• Edward Sapir's Language, 1921
• Macro Time and Micro Time
• Meaning Minimum 
• Disposition of Language

Tokyo
23 October 2013
24 September 2014, references added
Sekinan Research Field of Language

Uniformity of Written Language For SAUSSURE Ferdinand / 18 December 2004

Uniformity of Written Language

For SAUSSURE Ferdinand

TANAKA Akio

1. Language allows us to be approached from various aspects.

2. For the aim of unconditional reproduction of language, firm and uniform state of language is demanded.

3. Uniformity of language is the premise of Quantum Theory for Language.

4. The theory abstracts particular states of language activity.

5. Written language is treated equally to spoken language on the theory because of the standpoint of     uniformity.

6. Written language is nearer to the ideal situation of language on the theoretical approach.

7. The theory is aimed for the automatic generation of language in any situation of necessity.

8. The automatic generated language is expressed on the form of new written language.

9. The new written language is different from the real written language. (Supplement)

This reproductive new language is called to NL.

The real language is called to RL.

10. NL is complied with the principles and rules of the theory.

So NL has an identical expression in the same set of quanta of language.

11. RL is converted to NL.

NL is not always converted to RL. 

12. NL is assumed to be used under the difficult condition of language operation,

13. NL is probably useful for the handicapped people on language.

14. Under the proper presentation of a set of quanta of language, NL will be used for the automatic construction of thought of human being ultimately. 

Tokyo December 18, 2004

Sekinan Research Field of Language

[Note, 23 September 2014]

Title changed from Uniformity to Uniformity of Written Language.

[Supplement, 24 September 2014]
"The new writing language" of this paper later became "the language models" that was scripted by the mathematical approach. For more details see the following.

• Language Universal Models / sekinanlum
• SRFLZoho / SRFL Sekinan Research Field of Language

Charles Bally / 9 November 2012

Charles Bally

TANAKA Akio 




                                        

Charles Bally is a successor of Ferdinand de Saussure together with Sergej Karcevskij.
He wrote LINGUISTIQUE GENERALE ET LINGUISTIQUE FRANCAISE 1932-1963 that is a clear basis for my language study till now.
             

Tokyo
9 November 2012
Sekinan Research Field of Language 

[Note, 24 September 2014]

One of the most important concepts of this Bally's book is the comparison between <Dystaxie> and <Polysemie>. This comparison has been combined in my study's one main theme <situation of stable and unstable in one word> supposedly proposed by Sergej Karcevskij's paper,  "Du dualisme asymetrique du signe linguistique". For my approach to this theme see the following as the sample.

• Notes for Sergej Karcevskij / 8 September 2011- 11 September 2011 / sekinanmetria

Homology Generation of Language / Floer Homology Language / 11 June 2009

Floer Homology Language

TANAKA Akio

   

Note5

Homology Generation of Language


1
Isomorphism class of manifold     moduli space
Moduli space     M
2
Compactification of Mg, k       CMg, k         
3
Compact Hausdorff space     Σ
Riemann surface that has finite sum that is not intersected each other     
Continuous map     π :  →Σ
There exists finite set S(Σ) Σ.
π's restriction  is homeomorphism.
 consists of 2 points over 
Structure over Σ is abbreviatedly  called semistable curve.
4
z1, ..., zk is different regular point.     （Σ、) is called k pointed semistable curve.
3
Pointed semistable curve （Σ、) is stable.     Automorphism Aut（Σ、) group is finite group. 
5
Simply-connected and connected compact 1-dimensional simplicial complex       tree
Stable curve that has genus 0       Σ
Tree       ΓΣ       
6
Tree       Γ
Vertex number that each vertex has only one side      k+1
Tree that has k+1 vertexes        TRk+1
Γ TRk+1
Stable curve Σ that is ΓΣ = Γ       CM (Γ)
7
(Theorem, Knudsen-Keel)
Homology group  is generated from fundamental group of CM (Γ).
8
Γ TRm+1
shh : RT k+1 →TRm+1
h0 : {1, 2, 3, 4} →{1, ..., k}
shh0 is expressed by sh.
9
Forgetting map     fg : Mg,k (M,JM;β) →Mg,k

10
There exists next equality at .
         (1)
11
(Theorem, Knudsen-Keel)
 is generated by  .
 is vector space expressed by relation (1).

[Image]
It is seemed to be existential that language is expressed by homology.



[References]

On Time Property Inherent in Characters / Hakuba March 28, 2003
Prague Theory 3 / Tokyo January 28, 2005
Generation Theorem / von Neumann Algebra 2 / Note / Tokyo April 20, 2008
Homological Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory / Note 6 / Tokyo April 26, 2009

Tokyo June 11, 2009

Sekinan Research Field of Language