Quantum-Nerve Theory With References

Quantum-Nerve Theory
Abbreviation  :  QNT

TANAKA Akio

Part 0

Cicerone to QNT

Macro Time and Micro Time  2013

For WITTGENSTEIN Ludwig  Position of Language  2005 - 2014

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

 2017

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 even at the time of tea.I consent that geometry is the queen of mathematics. I also remember the saying of Roger Penrose, "We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics."

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.

5.
What now I say as language universals is energy ,distance, dimension and so forth.
Brief comments on the three themes are time to time mentioned through my milestones to the upper steps for the research.

6.
The hardest theme has been in energy all through the research. But Perelman has opened the narrow and steep lane to the aim by physics-mixture mathematics approach,  especially thermodynamics-based means. It was a surprise which way was seemed to be the very hard way or despaired way at my present ability.
  

References

0.

1. Manuscript of Quantum Theory for language
2. On Time Property Inherent in Characters

1.

1. The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 
2. Quantum Theory for Language
3. Property of Quantum
4. Quantification of Quantum
5. Homology Generation of Language
6. Homology Structure of Word

2.

1. Presupposition on Natural Language
2. Macro Time and Micro Time
3. Sayama Assumption on Language   
4. True-false problem of the Crete The example of what language has structure

3.

1. For me geometry is the only one expression to describe the universal language containing the time which is also one of the meanings
2. Mathematics and sculpture
3. Roger Penrose. Understanding the laws of the universe
4. Description 

4.

1. Geometrization Note 1 - Note 2
2. Hyperbolic language Connection of Words

5.

1. Road to language Universals
2. At least three elements for language universals 
3. Mathematical description for three elements of language universals

5-2

1. The days when I was thinking on Energy Distance Theory 
2. Energy Distance Theory Note 1 Energy and Distance
3. Floer Homology Language ​ ​Note 1 ​ Potential of Language

5-3

1. Papers on language dimension  In chronological order

5-4

1. Distance Theory Algebraically Supplemented / Brane Simplified Model 
2. Distance Theory Algebraically Supplemented / Brane Simplified Model / Distance 

6.

1. Interpretation on Perelman's work, Ricci flow and Geometrization conjecture by KOBAYASHI Ryoichi 
2. Work of Perelman 
3. The books on Grisha Perelman
4. Perelman's Approach 1
5. Perelman's Approach 2

This paper is unfinished.

Tokyo

8 November - 13 November 2017

Geometrization language

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Part  1

Making nerve's mathematical model

What is signal? The existence that generates language

Preface, Preparation, Preparation 2, References, Main Issue 1-5,  Anticipation - FAQ

and Comment
Contents Edition

21 November 2018 - 24 April 2019

TANAKA  Akio

Sekinan Library

Tokyo

Original Title 

What is signal? A mathematical model of nerve  ​

For father and mother

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Quantum-Nerve Theory

Part 2

Physical mathematics from quantum group

0

Inspiration The Time of Quantum 2008

1

Quantum Theory for Language 2004

Place where Quantum of language Exists 2004
Frame-Quantum Theory 2005

Frame-Quantum-Time Theory 2005

Quantum Warp Theory Warp 2005

Quantum Linguistics Solidity and Flexibility 2006

Quantum Language Substantiality of Language 2006

2

1.Clifford Algebra Note 1 From Super Space to Quantization 2008

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

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

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

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

6. Simplicial Space Language  Composition of Word 2013

3

1. Floer Homology Language 2009

2. Homology Structure of Word 2009

3. Quantization of Language 2009

4. Discreteness of Language 2009

5. Proto Arithmetic Geometry Language 2009

6.Language, Word, Distance, Meaning and Meaning Minimum 2009

4

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

Read more: https://srfl-paper.webnode.com/news/quantum-nerve-theory-2019/

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Part 3 
Basic Paper

Kac-Moody Lie Algebra

Note 2

Quantum Group

TANAKA Akio

1

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

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

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

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

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

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

Vector space over K     A

Bilinear product over K     A×A → A

When A is ring, it is called associative algebra.

8

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

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 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

Read more: https://srfl-lab.webnode.com/products/kac-moody-lie-algebra-note-2-quantum-group/

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References

Manuscript of Quantum Theory for Language  2013

​Language between Sergej Karcevskij and string theory, one century's trace  2016

Ideogram Paper  2003-2018
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

Overview Paper  2013-2017

 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  2017

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Tokyo
14 October 2019
SRFL Paper