Home site SRFL renewed / 30 September 2014

This blog's home site, SRFL Sekinan Research Field of Language has renewed today.
SRFL shows some phases on language,especially on language universals and their surroundings.
SRFL was established at Hakuba, Nagano in 2003 and in the next year removed to Tokyo.

SRFL Sekinan Research Field of Language

From the garden

Distance of Word / 28 September 2014

Distance of Word

TANAKA Akio

0.
Distance is one of the most important concepts of mathematics. I have gradually approach to it after ambiguous intuitive classical linguistic work.

1. From Distance to Pseudo-Kobayashi Distance / 5 February 2012

1.
Distance is one of the most fundamental concepts of language universals in my part.
It was first thought at the paper, Distance Theory in 2004. Successively several intuitive papers were written in the same year.

1. Distance Theory / 5 May 2004
2. Reversion Theory / 27 September 2004
3. Warp Theory / 24 October 2004
4. Prague Theory 3 / 28 January 2005

2.
Distance is described by the physic expression using brane model.

1. Distance Theory Algebraically Supplemented / Brane Simplified Model / Distance / 26 October 2007

3. 

Mathematical description was first done at the paper, Distance of Word in 2008.

1. Distance of Word / Complex Manifold Deformation Theory / 9 December 2008

4.

Distance is a highly root concept of mathematics for which geometry searches the clear description for further development.

1. Supersymmetric Harmonic Oscillator / Floer Homology Language / 6 May 2009  

<To be continued> 

Tokyo

28 September 2014

Sekinan Research Field of Language

Wellspring / 28 November 2008

Wellspring

TANAKA Akio

1
I read two geniuses in my twenties at early 1970s.
WANG Guowei and WITTGENSTEIN Ludwig.
WANG's Guantangjilin and WITTGENSTEIN's TRACTATUS LOGICO-PHILOSOPHICUS.
I have continued thinking and writing by own-recognized WITTGENSTEIN's TLP's style throughout till now.
2
Linguistic themes are almost all depended on WANG's papers. Yin buci-zhong suojian xian-gong xian-wang kao ( Juan 9 Shilin 1) overwhelmed me by profound considerations and  citations from Chinese vast classic texts.Wang-Heng ( Juan 9 Shilin 1) is the origin of  my early concept that consists of infinite cyclicmeaning minimum  inherent in characters.On Time Property Inherent in Characters and Prague Theory are early embodiment of the concept.
3
On meaning of language, CHINO Eiichi taught me its fascination and hardship mainly throughout the works of Linguistic Circle of Prague.
KARCEVSKIJ Sergej showed me the most fascinating approach to the meaning's flexibility in word.
4
From Orient, WANG Yinzhi lead me the meaning of word  especially by analysis of functional words in Chinese classics.Jingzhuan shici is a compilation of his analysis by which I tried the concept of
positive and negative on the generation of word. The result is shown by early workQuantification of Quantum, from which the concepts of actual language and imaginary language are emerged. Early work of showing the concepts are Guarantee of Language, Mirror Language and Reversion Theory and the like.
5
ZHANG Bingling is the another peak of China.Wenshi is the work I have tried to get understanding over and over again from my youth. My paper is tried as Energy of Language and Brown Motion as Language. Two papers are targeted to the energy inherent in language.
6
Simple chronological table is shown at Theory Dictionary Time.

Tokyo 

November 28, 2008 

Sekinan Research Field of Language

Flow of Language / Heritage of WANG Guowei and Edward Sapir / 26 September 2014

TANAKA Akio

Description form succeeds Ludwig Wittgenstein.
Description / 15 August 2013

1. Wellspring / 28 November 2008
2. For WITTGENSTEIN Revised / Position of Language / 10 December 2005 - 2 August 2014
3. The Time of Wittgenstein /20 January 2012
4. Citation from Ludwig Wittgenstein / 7 February 2012
5. THE ROAD TO REALITY A Complete Guide to the Laws of the Universe, 2005 by Roger Penrose / 25 October 2012

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

0.Progress so far

1. The First Paper on Inherent Time in Word / 26 July 2014
2. 40 years passed from I read WANG Guowei / 16 November 2013
3. Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013 / With References

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

1. Language is substance.

1. Substantiality Dedicated to SAPIR Edward / 27 February 2005
2. Macro Time and Micro Time / 24 July 2013

2. Language has structure.

1. True-false problem of the Crete, The example of What language has structure / 22 July 2013
2. Homology Structure of Word / Floer Homology Language / 16 June 2009

3. Language has dimension.

1. Parts and Whole / 1 September 2013
2. Dimension of Language / 9 September 2013
3. Disposition of Language / 12 September 2014 / With supplement

4. Language has energy.

1. Energy of Language / For ZHANG Taiyan and Wenshi 1908 / Stochastic Meaning Theory / 24 July 2008
2. Potential of Language / Floer Homology Language / 29 April 2009

5. Language has flow.

1. Time Flow in Word / For KOHARI Akihiro and His Time / Language and Spacetime / 3 May 2007

6. Language has time.

1. On Time Property Inherent in Characters / 28 March 2003

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

Note

N1. 

At this paper, the most important theme is "5. Language has flow." For this theme, clear and mathematical description must be proposed for the further research's development. Its premise  by mathematical basic description is shown at
2.2 Homology Structure of Word / Floer Homology Language / 16 June 2009

4.2 Potential of Language / Floer Homology Language / 29 April 2009 

N2.
The intuitive concept of flow of language was prepared by WANG Guowei's Guantangjilin and Edward Sapir's Language for my study.
For WANG Guowei / A Letter / 11 March 2003 
Edward Sapir's Language, 1921 / 5 September 2014  

N3.
Mathematical approach will be done by geometry that is the most  image-able for me. Many thanks to the contemporary mathematicians for their radical works.

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

This paper is still continued.

Tokyo
26 September 2014
SRFL Sekinan Research Field of Language

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

Symplectic Language Theory 

TANAKA Akio 

     

​

 

Note 2 

Gromov-Witten Invariantational Curve​

​

​

[Invariant]​

(Gromov-Witten)​

​

​

​

​

​

​

​

​

 

[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