Quantum-Nerve Theory
Abbreviation : QNT
Part 0
Cicerone to QNT
For WITTGENSTEIN Ludwig Position of Language 2005 - 2014
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.
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
1.
2.
3.
4.
5.
5-2
6.
- The days when I was thinking on Energy Distance Theory
- Energy Distance Theory Note 1 Energy and Distance
- Floer Homology Language Note 1 Potential of Language
5-3
5-4
5-4
- Distance Theory Algebraically Supplemented / Brane Simplified Model
- Distance Theory Algebraically Supplemented / Brane Simplified Model / Distance
6.
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Part 1
Making nerve's mathematical model
21 November 2018 - 24 April 2019
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
2
2. Kac-Moody Lie Algebra Note 2 Quantum Group 2008
3. Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH 2009
3
4
Read more: https://srfl-paper.webnode.com/news/quantum-nerve-theory-2019/
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Part 3
Basic Paper
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 = ( 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
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
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
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
n-dimensional Euclid space Rn
Linear independent vector v1, …, vn
Lattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )
Lattice of h hZ
6
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
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 = 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
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 at the paper Place where Quantum of Language exists / 27 /.
Refer to the next.
Tokyo February 9, 2008
www.sekinan.org
Read more: https://srfl-lab.webnode.com/products/kac-moody-lie-algebra-note-2-quantum-group/
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References
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
Overview Paper 2013-2017
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
From Chinese character's meaning structure to Homological algebraic 2017
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