What is signal?
The existence that generates language
TANAKA Akio
ENSILA
Tokyo
9 February 2019 - 2 March 2019
ENSILA
Tokyo
9 February 2019 - 2 March 2019
Original Title
What is signal? A mathematical model of nerve
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Preparation 1-15
For father and mother
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References
Reference is cited from the papers written at SekinanLibrary and SRFL
by TANAKA Akio
at Tokyo from 2003.
by TANAKA Akio
at Tokyo from 2003.
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Contents
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1
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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
Thanks to physics through which I ever dreamt in my future
Glitter of youth through philosophy and mathematics in 1970s
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References Over
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Tokyo
27 February 2019
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References
Reference is cited from the papers written at SekinanLibrary and SRFL
28 February 2019
28 February 2019
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Main Issue
Quantum Group Language
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
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
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
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
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Ideogram Paper
2. Ideogram 2005
5. Essence of Language 2016
6. The Days of Decipherment 2016
7. The Days of Ideogram 2017
9. The comparison between 2003 and 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
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Overview Paper
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
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
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Concept Paper
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Archive of Paper
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Selected Paper
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Note 2
Quantum Group
1 <Cartan matrix>
Base field K
Finite index set I
Square matrix that has elements by integer A = ( aij )i, j ∈ I
Matrix that satisfies the next is called Cartan matrix.
i, j ∈ I
(1) aii = 2
(2) aij ≤ 0 ( i ≠j )
(3) aij = 0 ⇔ aji = 0
2 <Symmetrizable>
Cartan matrix A = (aij)i, j ∈I
Family of positive rational number {di}i∈I
Arbitrary i, j∈I diaij = djaji
A is called symmetrizable.
3 <Fundamental root data>
Finite dimension vector space h
Linearly independent subset of h {hi}i∈I
Dual space of h h*= HomK (h, K )
Linearly independent subset of h* {αi} i∈I
Φ = {h, {hi}i∈I, {αi} i∈I }
Cartan matrix A = {αi(hi)} I, j∈I
Φis called fundamental root data of A that is Cartan matrix.
4 <Standard form>
Symmetrizable Cartan matrix A = (aij)i, j ∈I
Fundamental root data {h, {hi}i∈I, {αi} i∈I }
E = 
αi ⊂h*
αi ⊂h*
Family of positive rational number {di}i∈I
diaij = djaji
Symmetry bilinear form over E ( , ) : E×E → K ( (αi ,αj ) = diaij )
The form is called standard form.
5 <Lattice>
n-dimensional Euclid space Rn
Linear independent vector v1, …, vn
Lattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )
Lattice of h hZ
6 <Integer fundamental root data>
From the upperv3, 4 and 5, the next three components are defined.
(Φ, ( , ), hZ )
When the components satisfy the next, they are called integer fundamental root data.
i ∈ I
(1) 
∈ Z
∈ Z
(2) αi ( hz ) ⊂ Z
(3) ti := hi ∈ hz
hi ∈ hz
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 = tm-t-m / t- t-1
Integer m, n m≧n≧0
Binomial coefficient (mn)
t similarity of m! [m]t! = [m]t! [m-1]t!...[1]t
t similarity of (mn) [mn]t = [m]t! / [n]t! [m-n]t!
[m0] = [mm]t = 1
8 <Quantum group>
Integer fundamental root data that has Cartan matrix A = ( aij )i, j ∈ I
Ψ = ((h, {hi}i∈I, {αi} i∈I ), ( , ), hz )
Generating set {Kh}h∈hz ∪{Ei, Fi}i∈I
Associative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.
(1) khkh’ = kh+h’ ( h, h’∈hZ )
(2) k0 = 1
(3) KhEiK-h = qαi(h)Ei ( h∈hZ , i∈I )
(4) KhFiK-h = qαi(h)Fi ( h∈hZ , i∈I )
(5) Ei Fj – FjEi = 
ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )
ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )
(6) 
p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )
p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )
(7) p [1-aijp]qiFi1-aij-pFjFip = 0 ( i , j∈I , i ≠j )
p [1-aijp]qiFi1-aij-pFjFip = 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.
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Symplectic Language Theory![]()
Note 6
Homological Mirror Symmetry Conjecture by KONTSEVICH
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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
Coderivative
A∞-algebra 
= 0 at (BΠC, mk) (k>0)
= 0 at (BΠC, mk) (k>0)
Weak A∞-algebra 
= 0 at (BΠC, mk) (k≥0)
= 0 at (BΠC, mk) (k≥0)
L∞-algebra 
= 0 at (EΠC, mk) (k>0)
= 0 at (EΠC, mk) (k>0)
Weak L∞-algebra 
= 0 at (EΠC, mk) (k≥0)
= 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) 
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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).
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[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).
To be continued
Tokyo April 26, 2009
Read more: https://srfl-lab.webnode.com/products/symplectic-language-theory-note-6-homological-mirror-symmetry-conjecture-by-kontsevich/
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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
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 
.
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/
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Karcevskij conjecture 1928 and Kawamata conjecture 2002 / I briefly wrote about the conjecture
10/11/2017 18:29
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:
Reference:
[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.
Tokyo
23 February 2015
SIL
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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
.
.
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.
......................................................................................................................................
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:
- Tale / Print by LI Koh / 27 January 2012
Reference:
Reference 2:
References 3:
- Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / 8 September 2011
- Condition of Meaning / 11 September 2011
References 4:
- Dimension of Language / 4 September 2013
- Synthesis of Meaning and Transition of Dimension / 6 September 2013
Reference 5:
[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.
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.
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, "Du Dualisme asymétrique du signe linguistique"
- Description of Language
- Structure of Word
- Condition of Meaning
The papers on this site have been published by
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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.
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
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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]
- 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]
- Bridge across mathematics and physics
- Kontsevich's conjecture Category theoretic mirror symmetry conjecture
[Reference 3]
Tokyo
19 May 2016
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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]
[References 2]
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This paper is unfinished.
Tokyo
20 May 2016
Read more: https://srfl-lab.webnode.com/products/karcevskij-conjecture-1928-and-kawamata-conjecture-2002-i-briefly-wrote-about-the-conjecture/
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