Road between Quantum Theory for Language and Generation of Word

Road between Quantum Theory for Language and Generation of Word
 A conclusion for the present on early papers of Sekinan Library

TANAKA Akio

23 January - 25 January 2018

Tokyo

Sekinan Library

1.
I wrote a paper titled Quantum  Theory  for Language in 2004.
This paper was read at the international symposium on Silk Road at Nara, Japan in December 2003.
The encounter with this time's persons and thoughts are written at The Time of Quantum  in September 2008.

2.

This paper's concept was prepared at Hakuba, Nagano, Japan in March 2003.

This concept was jotted down at the hotel of Hakuba so the publication became late till 2015.

The title was named Manuscript of Quantum Theory for Language.

3.

In Autumn 2002 I was hospitalized by pneumonia for two weeks, when I thought to put the linguistic research on old Chinese characters so far in order. The result was arranged as a paper titled On Time Property Inherent in Characters also at Hakuba in March 2003.

4.

Quantum Theory for Language was added proviso, Synopsis, because the paper was thought at that time as a role of a rather long mathematical paper's preface on quantum theory on language.

5.

Time passed by rapidly.

After some preparations of mathematics, I wrote successive papers related with Quantum Theory for Language. von Neumann Algebra was put at the centre of preparation. The days at that time was simply wrote titled as The Days of von Neumann Algebra and The Days between von Neumann Algebra and Complex Manifold Deformation Theory in 2015.

6.

von Neumann Algebra succeeds from 1 to 4. 2's Generation Theorem was written in April 2008. After von Neumann Algebra, Functional Analysis was written. 2's Generation of Word 's result is directly connected to Quantum Theory for Language's mathematical background.

7.

From 2008 I frequently used Zoho site because of easily writing by mathematical equation system. Complex Manifold Deformation Theory was the first result of Zoho. At Floer Homology Language some complementary fruits were gotten for Quantum Theory, Homology Generation of Language in June 2009 and Homology Structure of Word also in June 2009.

8.

Algebraic geometry had been consistently flowing in Quantum Theory.

Recently written Connection between early paper's quantum and recent paper's geometry, November 2017 summarizes the situation at that time concisely.

In July 2017,  The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals was written looking back the days of  quantum.

9.

Quantum Theory's time series representative is the following.

(1)

On Time Property Inherent in Characters 2003

Manuscript of Quantum Theory for Language 2003

Quantum  Theory  for Language 2004

Generation Theorem 2008

Generation of Word 2008

Homology Generation of Language 2009

Homology Structure of Word 2009

(2)

von Neumann Algebra 1-4 2008

Functional Analysis 2008

Complex Manifold Deformation Theory 2008-2009

Floer Homology Language 2009

(3)

The Time of Quantum 2008

The Days of von Neumann Algebra 2015

The Days between von Neumann Algebra and Complex Manifold Deformation Theory2015

Connection between early paper's quantum and recent paper's geometry 2017

The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 2017

10.

Basis of On Time Property Inherent in Characters 2003, Manuscript of Quantum Theory for Language 2003 and Quantum  Theory  for Language 2004 are all led by Qing Dynasty's linguistic (Xiaoxue) tradition, especially from WANG Guowei, whose influence is written at The Time of WANG Guowei in December 2011.

11.
In 1970s in my age 20s, while I read WANG Guowei, also read Ludwig Wittgenstein. 

Quantum Language Theory - A conclusion for the present on early papers of Sekinan Library

Quantum Language Theory 
 A conclusion for the present on early papers of Sekinan Library

TANAKA Akio

23 January - 25 January 2018

Tokyo

Sekinan Library

1.
I wrote a paper titled Quantum  Theory  for Language in 2004.
This paper was read at the international symposium on Silk Road at Nara, Japan in December 2003.
The encounter with this time's persons and thoughts are written at The Time of Quantum  in September 2008.

2.

This paper's concept was prepared at Hakuba, Nagano, Japan in March 2003.
This concept was jotted down at the hotel of Hakuba so the publication became late till 2015.
The title was named Manuscript of Quantum Theory for Language.

3.
In Autumn 2002 I was hospitalized by pneumonia for two weeks, when I thought to put the linguistic research on old Chinese characters so far in order. The result was arranged as a paper titled On Time Property Inherent in Characters also at Hakuba in March 2003.

4.
Quantum Theory for Language was added proviso, Synopsis, because the paper was thought at that time as a role of a rather long mathematical paper's preface on quantum theory on language.

5.
Time passed by rapidly.
After some preparations of mathematics, I wrote successive papers related with Quantum Theory for Language. von Neumann Algebra was put at the centre of preparation. The days at that time was simply wrote titled as The Days of von Neumann Algebra and The Days between von Neumann Algebra and Complex Manifold Deformation Theory in 2015.

6.
von Neumann Algebra succeeds from 1 to 4. 2's Generation Theorem was written in April 2008. After von Neumann Algebra, Functional Analysis was written. 2's Generation of Word 's result is directly connected to Quantum Theory for Language's mathematical background.

7.
From 2008 I frequently used Zoho site because of easily writing by mathematical equation system. Complex Manifold Deformation Theory was the first result of Zoho. At Floer Homology Language some complementary fruits were gotten for Quantum Theory, Homology Generation of Language in June 2009 and Homology Structure of Word also in June 2009.

8.
Algebraic geometry had been consistently flowing in Quantum Theory.
Recently written Connection between early paper's quantum and recent paper's geometry, November 2017 summarizes the situation at that time concisely.
In July 2017,  The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals was written looking back the days of  quantum.

9.
Quantum Theory's time series representative is the following.
(1)
On Time Property Inherent in Characters 2003
Manuscript of Quantum Theory for Language 2003
Quantum  Theory  for Language 2004
Generation Theorem 2008
Generation of Word 2008
Homology Generation of Language 2009
Homology Structure of Word 2009
(2)
von Neumann Algebra 1-4 2008
Functional Analysis 2008
Complex Manifold Deformation Theory 2008-2009
Floer Homology Language 2009
(3)
The Time of Quantum 2008
The Days of von Neumann Algebra 2015
The Days between von Neumann Algebra and Complex Manifold Deformation Theory 2015
Connection between early paper's quantum and recent paper's geometry 2017
The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 2017


# This paper is unfinished.

The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals

The comparison between 2003 and 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 
 
TANAKA Akio
 
1. Between 2003 and 2017
In 2003 I wrote a paper that showed meaning's inner structure of Chinese characters.
The paper was based on Chinese character's old form, Jaguwen, Chinese inscriptions on animal bones and tortoise carapaces that was first found at Henan-sheng, China in 1999. I wrote the paper mainly depending on WANG Guowei's work. My paper is the following.

On Time Property Inherent in Characters. 28 March 2003 

 
In this 2017 I wrote a related paper with the 2003's paper, which mainly focused on ideogram's general purpose property from hieroglyph to LATEX symbols. My paper is the next.
 
The Days of Ideogram. 20 April 2017


2. From philology to algebra
The 2003 paper is on the continuation of Qing Dynasty's classical philologists in China.
The 2017 paper is on the extension of Category theory's homological approach.



3. From intuitive to definitive
The 2003 is not openly used mathematical approach, as a result  writing style is considerably intuitive.
The 2017 is also intuitive, but in its base, more sufficient mathematical data in the 17 year study result. The most recent work is Derived Category Theory. The theory is at the next.


Derived Category Language


Now the  upper two papers, the 2003 and the 2017 and their related papers are seen at Sekinan Paper and Sekinan Theory.


Sekinan Paper
Sekinan Theory


4. Starting place
The new theory is now being prepared for more mathematical-descriptive expression titled Homology Language.Starting place is at the following papers.

Karcevskij conjecture 1928 and Kawamata conjecture 2002
​Language stability and triangulated category


5. Gist of  Homology Language
 The fundamental essences are the next.
(1)
Set is defined as Universe which can avoid set theory's contradiction.
(2)
Set is considered as Category which can get back to all the concepts to Object and Morphism.
(3)
Topological space is considered as Homology which can get back all the work to algebra.
(4)
Language model is considered as Sheaf which can past functions to the more big function.
(5)
Language can take Contractible which can describe free concepts as meaning.  
 
 
6. Aim of Homology Language
(1)
Language will get near to finite generative a little alike natural language.
Fundamental work was done at the next from set theory but not definitive as universe. 
 
von Neumann Algebra 2 Note Generation Theorem
 
(2)
Category theory seems to be a one-step-up stage to write on language from the days of Maclane Saunders. Refer to the next.
 Topological Semantics. Torus Chain. For MAC LANE Saunders
Language and Spacetime. Word Containing Time and 4 Dimensional Sphere. Dedicated to MAC LANE Saunders
Language and Spacetime. Structure of Word. From KARCEVSKIJ to MACLANE
For MAC LANE Saunders. Categorical Approach toward Language
 
(3) Homological approach
In 2009 I wrote a trial papers titled Floer Homology Language. Still now the papers are important for my study.

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


In Floer Homology Language, the next two papers will become the guidepost for new theory Homology Language. 

Homology Generation of Language
Homology Structure of Word


(4) Symplectic algebra
Symplectic algebra is one of the most fantastic fields of the contemporary mathematics.
I also ever wrote simple invitational papers for applying to language universals.
The papers are next.

Symplectic Language Theory
     |
     Symplectic Topological Existence Theorem     
     Gromov-Witten Invariant     
     Mirror Symmetry Conjecture on Rational Curve     
     Isomorphism of Map Sequence     
     Generating Function  
     Homological Mirror  Conjecture by KONTSEVICH
     Structure of Meaning
     On Structure

In the papers, The next contains the update result of homological approach.

Homological Mirror Symmetry Conjecture by KONTSEVICH


(5) Bridge to resolve
Relationship between symplectic geometry and derived category shows the realization of clearer description on  language.universals Because for my part, Symplectic Language Theory and Floer Homology Language seems to be the nearest way to resolve the hardship of natural language's inner structure.
The details are the next.
 Additional meaning and embedding

 
(6) Symmetry
The concept called symmetry is very important to describe the complex situation of natural language.
Symmetry contains undifferentiated factors in itself, for example mirror, distance,ant-world and so forth.
I ever tried to cultivate this fantastic field to resolve the hardship on language universals one more step up. 
My trying paper is the following.

Mirror Theory
Mirror Language

 
 ..............................................................................................................
 
This paper in unfinished.
 
 
Tokyo
6 July - 9 July 2017
Sekinan Library

Read more: http://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-characters-meaning-structure-to-homological-algebraic-model-of-language-universals/

Connection between early paper's quantum and recent paper's geometry

Connection between early paper's quantum and recent paper's geometry

 

TANAKA Akio

0.
Autumn in 2002, I entered hospital by contracting pneumonia, at where I thought that learning on Chinese characters heretofore seemed to be able to used for the model of language universals. Spring 2003 at Hakuba, Nagano I wrote a trial paper titled On Time Property Inherent in Characters, that was focused on the time inherent in characters using the Chinese written language appeared in typical philological text of the Five Classics of Confucianism. After all, this paper led me the long road to try solving language universals in language.

1.
On language universals my early papers are frequently concentrated in quantum's situation applied from theoretical physics. But at recent papers quantum's themes are almost disappear at least from the surface of theoretical progress.
This notable difference  is occurred through language's whereabouts, that is generally called space at scientific field. One of my important quest has been  at this whereabouts description.
Physical space is very hard to describe clearly by my ability. Probably I have not been able to understand physical space for using and observing the situation of language models. On the contrary mathematical spaces are very clear by using minimum axioms and theorems.

2.
Another quest is occurred from natural language's quality.
Natural language consists of physical elements - voice and hearing, writing and seeing. But what being carried by upper elements are going over physical world - thought, remembrance, feeling and so forth. I ever wrote these situation using a sample that is a changing apple passing in the time.
This quest is paraphrased in concrete - physics and abstract - mathematics.

3.
Geometry is a field of mathematics, which I select because of being easily visualised thinking for my approach to the language problems. Geometry hands out intuitive ideas to me not using any formulas for example at the time of tea.

4.
At the geometry field, now I am charmed to W. T. Thurston's geometrization concept, that opens 3-dimensional manifold to hyperbolic geometry's model. This model will probably hint me the new landscape for language models, that will show us more exhaustive language universal theory.

References
0.
On Time Property Inherent in Characters
1.
Quantum Theory for Language
Homology Generation of Language
Homology Structure of Word
2.
Presupposition on Natural Language
3.

For me geometry is the only one expression to describe the universal language containing the time which is also one of the meanings
Mathematics and sculpture
4.
Perelman's Approach 1
Perelman's Approach 2
Geometrization Note 1 - Note 2

This paper is unfinished.

Tokyo
8 November 2017
Geometrization language

Read more: https://geometrization-language.webnode.com/products/connection-between-early-papers-quantum-and-recent-papers-geometry/

The Time of Quantum

The Time of Quantum 
Inspiration   

TANAKA Akio

In August  2003, I went to Hakuba in Nagano prefecture for the summer vacation with my family.  At that time I had been thinking on the form of language for which I wrote the paper,  that connects with time inherent in characters, in March 2003 also at Hakuba.

At night of August 23 in cottage, I casually saw the advertising paper of electric dictionary.  The paper was brought from the convenience store near  the cottage in the evening. The dictionary  on the paper was Seiko’s English-Japanese dictionary that has additionally consultation for Chinese or French language with large scale. I vaguely considered that after this dictionaries are necessarily taken these multi-lingual way.

At the time I suddenly  realized that the form of language may be spherical style in which language contains all the information in itself.That was rather satisfied solution for the tough problem of language that I had been carrying in my life from my twenties.

I wrote the sketch-like paper of the theoretical approach after returning home of Tokyo. The paper was read at the international symposium of UNESCO opened in winter 2003 at Nara. In the paper, the spherical substance of language is seemed to be quantum in DELBRUCK’s image-like physical world. After 5 years from the inspiration at summer of Hakuba,  now I consider that spherical essence is manifold in infinite dimensional world.

Now I also realize that the toughest problem of language is minutely solvable in mathematical approach that has structurally definable terms.

Tokyo
September 29, 2008
Sekinan Research Field of Language 

[January 23, 2012]
The title changed.
The former title is “From Quantum to Manifold”.
[Postscript. January 25,2012]
On quantization of Language.
Refer to the next.
Quantization of Language 

Read more: https://geometrization-language.webnode.com/products/inspiration-the-time-of-quantum/

Floer Homology Language Note 6 Homology Structure of Word​

 

​​

 

Floer Homology Language 

TANAKA Akio 

     

​

 

Note 6 

 

Homology Structure of Word​

​

​

§ 1​

1​

Compact manifold in small diameter      M​

Inner product space     h (M)​

Map      h (M) 

k→  h (M)     ​

2​

A model and B model by Witten, E.​

A model     M as symplectic structure​

B model     M as complex structure  ​

3​

(A model)​

(Definition)​

H kA (M) = H k(M;C)​

​

H *A (M) = 

H kA (M) ​

Inner product <. , .>A     <u, v>A = 

     ( 

 ; cup product)​

mA, 02(u, v) = 

​

4​

(Theorem)​

( H *A (M), mA, 02, <. , .>A ) is Frobenius algebra.​

5​

Oriented  2-dimensional manifold with genus g     Σg​

6​

J (Σg) = {JΣg | Smooth complex structure over Σg }​

Integer over 0     k​

Different k-number points over Σg     z1, ..., zk     (Gathered points are expressed by 

. )​

Diff (Σg, 

) = {ψ : Σg → Σg | ψ(

) = 

, ψ is differential homeomorphism. }​

Quotient space      M g,k = J (Σg) / Diff (Σg, 

) ​

Rieman surface of genus g with k marked points     (Σ, 

) ​

(Σ, 

) 

M g,k ​

Autmorphism group     Aut (Σ, 

) = { ψ : Σ → Σ | ψ is biregular.ψ(

) = 

}​

Compactification of  M g,k      CM g,k ​

​

§2​

１​

Symplectic manifold    M​

Differential 2-form over M     wM​

Well-formed almost complex structure with wM     JM​

β

H2(M; Z)​

 (

is pseudoholomorphic.)​

(Σ,

, φ) 

​

2​

[(Σ,

, φ)] 

​

Evaluation map     ev[(Σ,

, φ)]=

​

3​

Forgetting map    fg : 

​

​

Enlarged Forgetting map    fg : 

​

3​

(Definition)​

(Gromov-Witten invariant)​

(ev, fg)*

​

Gromov-Witten invariant is expressed by GWg,k(M, wM; β)​

4​

(Theorem)​

Sumset  

  is compact.​

5​

(Associative law)​

(Theorem)

​

​

​

[Image]​

Meaning minimum of word is identified with 

.​

Word is identified with 

​

Commutativity of meaning minimums in word guaranteed by theorem of associative law. ​

​

​

[References]​

Homology on Language / Symmetry Flow Language / Tokyo May 15, 2007​

From Cell to Manifold / Cell Theory / Tokyo June 2, 2007​

Deep Fissure between Word and Sentence / Algebraic Linguistics / Linguistic Result / Tokyo 

September 10, 2007​

Reversion Analysis Theory / Tokyo June 8, 2008​

Reversion Analysis Theory 2 / Tokyo June 12, 2008​

Holomorphic Meaning Theory 10th for KARCEVSKIJ Sergej / Tokyo June 15, 2008​

Holomorphic Meaning Theory 11th for KARCEVSKIJ Sergej / Tokyo June 19, 2008​

Word and Meaning minimum / Energy Distance Theory / Conjecture 1 / Tokyo September 

22, 2008​

Geometry of Word / Energy Distance Theory /  Conjecture2 / Tokyo November 23, 2008​

Amplitude of meaning minimum / Complex Manifold Deformation Theory / Conjecture A4 / 

Tokyo December 17, 2008​

​

​

​

​

Tokyo June 16, 2009​

Sekinan Research Field of Language​

​

​