What is signal? The existence that generates language Preface-Quantum Group language 2 march 2019 Revised

 

What is signal? 

The existence that generates language

TANAKA Akio

ENSILA

Tokyo

9 February 2019 -  2 March 2019

 

Original Title

What is signal? A mathematical model of nerve
0

Preparation 1-15

For father and mother 

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What is signal?
Preface, Preparation and Preparation 2 Completed

21 November 2018 - 15 January 2019

Zoho Edition
Blogger Edition

PDF Edition

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References

Reference is cited from the papers written at SekinanLibrary and SRFL
by TANAKA Akio
at Tokyo from 2003.

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Contents

0

Manuscript of Quantum Theory for Language with Preface, Note and Note 2 2003-2018

1

Under the Dim Light

Language, amalgamation of mathematics and physics

2

Language and I
Language and Philosophy

How is the time alive in Language?

3

Egyptian Hieroglyph Exhibition

Essence of Language

Ars longa 

4

The days when I was thinking on Energy Distance Theory 
Thanks to physics through which I ever dreamt in my future
Glitter of youth through philosophy and mathematics in 1970s  

5

Ideogram

Letter

The Days and The Time

Prague

Pioneer

Linear B

6

Genealogical Tree of Sekinan's Paper 7th Edition

7
What is letter?

References
Over

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SRFL Paper

Tokyo

27 February 2019

       

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What is signal?
Preface, Preparation and Preparation 2 Completed

21 November 2018 - 15 January 2019

Zoho Edition
Blogger Edition

PDF Edition

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

 

References

Reference is cited from the papers written at SekinanLibrary and SRFL
28 February 2019

Zoho Edition

Webnode Edition

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Main Issue
1

Quantum Group Language

Main Issue is written titled as Quantum group language abbreviated to QGL.

1 March 2019

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1

QGL Preparation Paper

Term Paper

​Ideogram Paper Enlarged Edition

Theme Paper

Sekinan View Paper

Book Paper 2016

Concept Paper 2018

Ideogram Paper 2005-2018

Time Paper 2013-2014

From Hodge diamond of mirror symmetry by KONTSEVICH to mirror language

Preparatory Paper 2 for Quantum Group Theory

Quantum space through Poisson manifold's deformation quantization by Kontsevich

​Ideogram Approach

Pre-history for Quantum Group Language

Language, Amalgamation of Mathematics and Physics

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2

General Preparation Paper

Preparatory paper

1. Kac-Moody Lie Algebra Note 2 Quantum Group 2008

2. Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH​ 2009

3. Floer Homology Language Note 7 Quantization of Language​ 2009

4. Floer Homology Language Note 8 Discreteness of Language​ 2009

5. Simplicial Space Language  Composition of Word 2013

Preparatory Paper 2 

1.Floer Homology Language
     2.  Homology Structure of Word
3. Proto Arithmetic Geometry Language   
      4.Language, Word, Distance, Meaning and Meaning Minimum

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Basic paper

1. Manuscript of Quantum Theory for Language Note added 2003

2. Quantum Theory for Language 2004

3. Quantum Theory for Language   

Theoretical Summarization and Problem in Future 2004

4. Noncommutative Distance Theory  Note 2  C*-Algebra 2007 

5. Kac-Moody Lie Algebra 2008 

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​Ideogram Paper

1. On Time Property Inherent in Characters 2003

2. Ideogram 2005

3. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012

4. ONO Shinobu and Bernhard Karlgren 2015

5. Essence of Language 2016

6. The Days of Decipherment 2016

7. ​The Days of Ideogram 2017

8. The Days of Ideogram Note added Edition 2017

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

10. Time and Shape of Language from How is the time alive in language 2017

11. Connection between early paper's quantum and recent paper's geometry 7th edition 2017

12. Letter to Y. Of the century of language 2018

13.  Letter to Y. Of Broad Language 4th edition 2018

14. Determination of the concept, Broad Language 2018

15. Ars longa　Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018

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Overview Paper

1. In the 21st century, language will definitely become one of the most important themes and targets of mathematics for us all 2016

2. Operad Meaning Theory From Cell to Operad Revised Edition 2013

3. Connection between early paper's quantum and recent paper's geometry 7th edition 2017

4. Karcevskij conjecture 1928 and Kawamata conjecture 2002 / I briefly wrote about the conjecture 2017

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

6.  Mathematical description for three elements of language universals 2017 

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Concept Paper

1. Letter to Y. Of the century of language 2018

2. Letter to Y. Of Broad Language 4th Edition 2018

3.  Determination of the concept, Broad Language 2018

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Archive of Paper

1. Genealogical Tree of Sekinan's Paper 7th Edition 2018
2. Zoho paper by year 2016

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Read more: https://srfl-lab.webnode.com/

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3

Selected Paper

(1)

Kac-Moody Lie Algebra

Note 2

Quantum Group

TANAKA Akio

1 <Cartan matrix>

Base field     K

Finite index set     I

Square matrix that has elements by integer     A = ( a_ij )_{i, j ∈ I}

Matrix that satisfies the next is called Cartan matrix.

i, j ∈ I

(1) a_ii = 2

(2) a_ij ≤ 0  ( i ≠j )

(3) a_ij = 0 ⇔ a_ji = 0

2 <Symmetrizable>

Cartan matrix     A = (a_ij)_i, j ∈I

Family of positive rational number    {d_i}_i∈I

Arbitrary i, j∈I    d_ia_ij = d_ja_ji

A is called symmetrizable.

3 <Fundamental root data>

Finite dimension vector space     h

Linearly independent subset of h     {h_i}_i∈I

Dual space of h     h*= Hom_K (h, K )

Linearly independent subset of h*     {α_i} _i∈I

Φ = {h, {h_i}_i∈I, {α_i} _i∈I }

Cartan matrix A = {α_i(h_i)} _{I, j∈I}

Φis called fundamental root data of A that is Cartan matrix.

4 <Standard form>

Symmetrizable Cartan matrix    A = (a_ij)_i, j ∈I

Fundamental root data     {h, {h_i}_i∈I, {α_i} _i∈I }

E = α_i ⊂h*

Family of positive rational number     {d_i}_i∈I

d_ia_ij = d_ja_ji

Symmetry bilinear form over E     ( , ) : E×E → K     ( (α_i ,α_j ) = d_ia_ij )

The form is called standard form.

5 <Lattice>

n-dimensional Euclid space    Rⁿ

Linear independent vector     v₁, …, v_n

Lattice of Rⁿ     m₁v₁+ … +m_nv_n     ( m₁, …, m_n ∈ Z )

Lattice of h     h_Z

6 <Integer fundamental root data>

From the upperv3, 4 and 5, the next three components are defined.

(Φ, ( , ), h_Z )

When the components satisfy the next, they are called integer fundamental root data.

 i ∈ I

(1)  ∈ Z

(2) α_i ( h_z ) ⊂ Z

(3) t_i :=  h_i ∈ h_z

7 <Associative algebra>

Vector space over K     A

Bilinear product over K     A×A → A

When A is ring, it is called associative algebra.

8 <Similarity>

Integer     m

t similarity of m    [m]_t

[m]_t = t^m-t^-m / t- t^-1

Integer   m, n   m≧n≧0

Binomial coefficient     (^m_n)

t similarity of m!     [m]_t! = [m]_t! [m-1]_t!...[1]_t

t similarity of (^m_n)    [^m_n]_t = [m]_t! / [n]_t! [m-n]_t!

[^m₀] = [^m_m]_t = 1

8 <Quantum group>

Integer fundamental root data that has Cartan matrix A = ( a_ij )_{i, j ∈ I}

      Ψ = ((h, {h_i}_i∈I, {α_i} _i∈I ), ( , ), h_z )

Generating set     {K^h}_h∈hz ∪{E_i, F_i}_i∈I

Associative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.

(1) k^hk^h’ = k^h+h’     ( h, h’∈h_Z )

(2) k⁰ = 1

(3) K^hE_iK^-h = q^αi(h)E_i    ( h∈h_Z , i∈I )

(4) K^hF_iK^-h = q^αi(h)F_i   ( h∈h_Z , i∈I )

(5) E_i F_j – F_jE_i = _ij  K_i - K_i^-1 / q_i – q_i^-1     ( i , j∈I )

(6) ^p [^1-aij_p]_qiE_i^1-aij-pE_jE_i^p = 0     ( i , j∈I , i ≠j )

(7) ^p [^1-aij_p]_qiF_i^1-aij-pF_jF_i^p = 0     ( i , j∈I , i ≠j )

[Note]

Parameter q in K is thinkable in connection with the concept of <jump> at the paper Place where Quantum of Language exists / 27 /.

Refer to the next.

Place where Quantum of Language exists / Tokyo July 18, 2004

Tokyo February 9, 2008

Sekinan Research Field of Language

www.sekinan.org

(2)

Symplectic Language Theory 

TANAKA Akio 

     

​

Note 6 

Homological Mirror Symmetry Conjecture by KONTSEVICH​

​

​

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​

​

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) ​

 ​

3 ​

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

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

​

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​

​

(Conjecture)​

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

M(L).  ​

​

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)) ​

​

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).​

​

Mirror Theory papers in early stage of Sekinan Linguistic Field​

​ 

To be continued 

Tokyo April 26, 2009 

Sekinan Research Field of language 

Read more: https://srfl-lab.webnode.com/products/symplectic-language-theory-note-6-homological-mirror-symmetry-conjecture-by-kontsevich/

(3)

Home Site: ifbetrue

Autor: TANAKA Akio

Theme: Language Universals

Method: Homotopy Theory

Title: Homotopy Language

Paper 1: Simplicial Space Language

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Simplicial Space Language

Composition of Word

TANAKA Akio

20 January 2013

ifbetrue

1. 

 is topological space.

 is simplicial space.

 is represented by geometric realization of   as the next.

2.

 is topological space.

 is singular simplex.

 is free Abelian group generated by set .

 .

 is singular chain complex of  and has strongly convergence spectral sequence called Atiyah-Hirzebruch spectral sequence.

3.

Interpretation.

Word  is given by geometric realization of simplicial space  .

Meaning unit in word is given by free Abel group .

(Paper end)

Read more: https://srfl-lab.webnode.com/products/simplicial-space-language/mutative-distance-theory-note-2-c-algebra/

(4)

Karcevskij conjecture 1928 and Kawamata conjecture 2002

TANAKA Akio

Sergej Karcevskij declared a conjecture for language's asymmetric structure on the TCLP of the Linguistic Circle of Prague in 1928. I briefly wrote about the conjecture as the following.

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Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"

From Print 2012, Chapter 18

Non-symmetry. It was the very theme that I repeatedly talked on with C. Prague in 1920s. Karcevskij's paper "Du dualisme asymetrique du signe linguistique" that appeared in the magazine TCLP.  Absolutely contradicted coexistence between flexibility and solidity, which language keeps on maintaining, by which language continues existing as language.  Still now there will exist the everlasting dual contradiction in language. Why can language stay in such solid and such flexible condition like that. Karcevskij proposed the duality that is seemed to be almost absolute contradiction. Sergej Karcevskij's best of papers, for whom C called as the only genius in his last years' book Janua Linguisticae reserata 1994.

Source: 

1. Tale / Print by LI Koh / 27 January 2012  

Reference:

1. Fortuitous Meeting, What CHINO Eiichi Taught Me in the Class of Linguistics / 5 December 2004 

Reference 2:

1. Linguistic Circle of Prague / 13 July 2012 - 19 July 2012

References 3:

1. Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / 8 September 2011
2. Condition of Meaning / 11 September 2011

References 4:

1. Dimension of Language / 4 September 2013
2. Synthesis of Meaning and Transition of Dimension / 6 September 2013

Reference 5:

1. Reversion Conjecture Revised / 1 May 2014 - 20 May 20

[Note, 2 October 2014]
In this Tale, Print 2012, C is CHINO Eiichi who was the very teacher in my life, taught me almost all the heritage of modern linguistics. I first met him in 1969 at university's his Russian class as a student knowing nothing on language study.

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

Tokyo
23 February 2015
SIL
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This asymmetric duality of linguistic sign presented by Karcevskij has become the prime mover for my study from the latter half of the 20th century being led by my teacher CHINO Eiichi.
But the theme was very hard even to find a clue. The turning point visited after I again learnt mathematics especially algebraic geometry in 1980s. 
In 2009 I successively wrote  the trial papers of the theme assisted by several results of contemporary mathematics. The papers are the following.

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Notes for KARCEVSKIJ Sergej

TANAKA Akio

1. Notes for KARCEVSKIJ Sergej, "Du Dualisme asymétrique du signe linguistique"
2. Description of Language
3. Structure of Word
4. Condition of Meaning

The papers on this site have been published by   

Sekinan Research Field of Language

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Entering in this year 2016, I read TODA Yukinobu's book, Several Problems on Derived Category of Coherent sheaf, Tokyo, 2016. The book shows me the update overview on derived category of coherent sheaf. The essence of my notable points are noted at the following.

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Kontsevich's conjecture
Category theoretic mirror symmetry conjecture

When there exists mirror relation between X1 and X2, derived category of X1's  coherent sheaf  and derived Fukaya category defined from X2's symplectic structure become equivalence.

M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.

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[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complex image of symplectic geometry's some theorems will become clearer.

References
Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009

Homological Mirror Symmetry Conjecture by KONTSEVICH
/ Symplectic Language Theory / 26 April 2009

Quantization of Language / Floer Homology Language / 24 June 2009

Tokyo
10 May 2016
SRFL Theory

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In the TODA's book, I received the great hint on Karcevskij's conjecture for language's hard problem.

The hint exists at Kawamata conjecture presented in 2002. The details are the following.

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Derived Category Language 2

Kawamata Conjecture

Conjecture

is birational map between smooth objective algebraic manifolds.

And

.

At This condition,

there exists next fully faithful embedding.

.

[Reference]

1. TODA Yukinobu. Several problems on derived category of coherent sheaf.  Tokyo, 2016.Chapter 6, Derived category of coherent sheaf and birational geometry, page 148, Conjecture 6.43.

[References 2]

1. Bridge across mathematics and physics
2. Kontsevich's conjecture Category theoretic mirror symmetry conjecture

[Reference 3]

1. Stability of Language / Language and Spacetime

Tokyo

19 May 2016

SRFL Theory

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Kawamata conjecture will hint me the new meaning's entrance in the old meaning at a word. 

Notes for KARCEVSKIJ Sergej that I ever wrote will be newly revised through TODA's fine work over viewing the recent 20 year development on derived category that began by Grothendieck.  

For TODA's book, refer to the next my short essay.

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Bridge across mathematics and physics / Revised

TODA Yukinobu. Several problems on derived category of coherent sheaf.  Tokyo, 2016

TODA Yukinobu's  Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.

Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.

I ever wrote several notes on language related with string theory.  Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on.

[References]

Distance Theory Algebraically Supplemented

1.     Bend     
2.      Distance 
3.      S3 and Hoph Map

[References 2]

Isomorphism of map Sequence / Symplectic Language Theory

Tokyo
19 May 2016
SRFL Theory

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This paper is unfinished.

Tokyo

20 May 2016

SRFL Theory

Read more: https://srfl-theory.webnode.com/news/karcevskij-conjecture-1928-and-kawamata-conjecture-2002/

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(5)

In the 21st century, language will definitely become one of the most important themes and targets of mathematics for us all

TANAKA Akio

The main reasons are the following.
 

1.Language is the most convenient tool for human being.

2.Language has the vast variations in natural language and technical language. 

3.Natural language has speech language, written language and their recorded language, for example books, records, CD and so on.

4.Technical language has many computer languages and their related devices.

5.At natural language, there exists many meanings not to confirm clear definitions, for example finite,infinite, discrete, continuity, universal and super. 

6.Technical language has naturally defines the meanings by its discrete arithmetical basic using of discreteness.

7.Mathematics is probably belonged to natural language, that uses speech and written language by usual conversations and papers or books. 

8.But mathematics can clearly define the meaning through a few axioms and derived theorems. for example boundary, continuity, distance, finite, infinite and space.

9.Mathematics has many strong tools for description, for example mapping, projection and identification.

10.Mathematics has solid structure through long historical verifications from ancient Greece.

 

References
Boundary:
Why is boundary necessary in language? 
Description
THE ROAD TO REALITY A Complete Guide to the Laws of the Universe
Dimension
Language and Dimension
Distance
Distance of Word
Geometry
Arithmetic Geometry Language

Language

Presupposition on Natural Language
Meaning
Meaning Minimum
Space
Quantization of Language
Structure
Homology Structure of Word
True and False
The True-false problem of the Crete
 

 

 

Tokyo

8 February 2016

Geometrization Language

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Main Paper

1

Over

TANAKA Akio

SRFL Paper

Tokyo

2 March 2019