Wednesday, 30 December 2015

Perspective


Perspective 
TANAKA Akio 
     
 
Perspective 1 
Symplectic Approach
1
Language universal is regarded as a type of invariant.
2
Gromov-Witten invariant is only determined by symplectic manifold.
3
Gromov-Witten invariant is  invariant by continuous deformation of symplectic structure.
4
Gromov-Witten invariant is regarded as a language universal.
5
Language consists of words.
6
Word model is given by symplectic manifold.
Manifold    M
2 differential form     w
dw = 0
wn ≠ 0
Symplectic manifold     (Mw)
7
(Darboux)
Word consist of a point, its neighborhood and differential homeomorphim that is from the 
neighborhood to Cn.
PointpM
Neighborhood     Up     
Differential homeomorphism     φ : Up→ Cn
φ*ww
w= Σdxidyi
(Complex coordinate     zi = xi + yi )
8
Word model is also given by spherical object.
9
Sentence model is given by exact sequence of chain complex.
[References]
Basic papers for the themes are seen at Sekinan Linguistic Field.
Recent papers are seen at sekinanlogos.
 
To be continued 
Tokyo February 19, 2009 
Sekinan Research Field of language 

Tuesday, 29 December 2015

​Symplectic Language Theory Conjecture 1 Structure of Meaning​


​Symplectic Language Theory
 


TANAKA Akio  

Conjecture 1 
Structure of Meaning


[Conjecture]​
1​
Meaning has structure.​
(Perspective 1)​
2​
Structure's basis is given by symplectic manifold.​
(LMT Note 1)​
3​
Meaning has symmetry.​
(SLT Note 3)​
4​
Symmetry is given by homological mirror symmetry.​
(SLT Note 3)​
5​
Meaning has meaning minimum.​
(SLT Note 1)​
6​
Meaning minimum is given by Riemann surface's element.​
(SLT Note1)
7​
Meaning is given by group of Riemann surface's elements.​
(SLT Note 2)​
8​
Meaning is variable by time.​
(SLT Note 3)​
9​
Time is given by differential equation's variable.​
(SLT Note 3)​
10​
Language has mirror language.​
(SLT Note 3 SLT Note 4)​
11​
Language's basis is given by Calabi-Yau manifold.​
(SLT Note 4)​
12​
Mirror language's basis is given by isotopy class of symplectic submanifold.​
(SLT Note4)​

[Complement]​
1​
Homology mirror symmetry is also given by the next.​
Complex manifold     M♦​
Structure sheaf of M♦   OM♦​
Category of all the continuous OM♦'s module     Coh(M♦)​
Symplectic manifold     M​
Lagrangian submanifold of M     L​
Floer homology     HF(L1, L2)​
Morphism set from L1 to L2     Lag (M)​
(Conjecture)​
Derived category of Coh(M♦) and derived category Lag (M) is isomorphic.​
2​
(Language symmetry by Floer homology mirror symmetry conjecture)
Language is given by Coh(M♦).​
Mirror language is given by Lag (M).​

To be continued 
Tokyo March 10, 2009 
Sekinan Research Field of language 

Back to sekinanlogos Home 

Language Universal Models


Curriculum Vitae
Curriculum Vitae

Language Universal Models
1. Repeated Integral Model
1.1 Hyperbolic volume / Volume of Language
1.2 Hyperbolic space / Hyperbolic Space Language
2. Minimal Model
2.1 Free group / Notes for KARVESKIJ Sergej, "Dusualisme asymétrique du signe linguistique"  
2.2 Fundamental group / Description of Language
2.3 de Rham complex / Structure of Word
2.4 de Rham complex on spherical surface / Condition of Meaning
3. Knot Theory Model
3.1 Hida deformation space / Loop Time f Character
4. Jones-Witten Theory Model
4.1 Witten invariant / Symmetry of Language
5. Moduli Model
5.1 Projective algebraic manifold / Completion of Language
5.2 Projective algebraic manifold / Meaning Minimum of Language
6. Arithmetic Geometry Model
6.1 Riemann-Roch Formula / Language, Word, Distance, Meaning and Meaning Minimum
7. Projective Space Model
7.1 Grothendieck theorem / Vector Bundle Model
8. Diophantine Approximation Model
8.1 Faltings theorom / Finiteness of Words
8.2 Noguchi, Winkelmann theorem / Dimension of Word

Apendix
Bibliography

Tokyo
December 2011 - January 2012
sekinanlum

Monday, 28 December 2015

For WITTGENSTEIN Ludwig Revised

For WITTGENSTEIN Ludwig Revised
Position of Language

TANAKA Akio
       
             
1  Quantization 1  is a cliff for consideration of language.
2 Mathematical interpretation of quantized language is now a first step to the theoretical ascent.
3 If there is not mathematics, next conjectures are impossible.
(i) Difference between word and sentence--- Commutative and noncommutative ring 
(ii) Continuation from word to sentence--- Tomita’s fundamental theorem 
(iii) Word’s finiteness and sentence’s infinity--- Property infinite  and  purely infinite 
(iv) Cyclic  structure of word’s meaning--- Infinite cyclic group 
4  Meaning minimum 2 ,  mirror language 3  and  mirror symmetry 4  are inevitable approach to the study of language especially for  language universals 5 .
5 Symplectic Language Theory, Floer Homology Language and Arithmetic Geometry Language are adopted as the model theory   for natural language in the recent.
6 Hereinafter the model theory will be entered to the new concept .  The Model  of Language Universals     will be shown by the description of mathematics .

[References]
0 .  WITTGENSTEIN Ludwig
Theory Dictionary Writing
Theory Dictionary Person
Aim for Frame-Quantum Theory
1 .  Quantized Language
Quantization of Language /Floer Homology Language
2 .  Meaning minimum
Structure of Meaning / Symplectic Language Theory
3 .  Mirror language
Mirror Symmetry on Rational Curve / Symplectic Language Theory
4 .  Mirror symmetry
Homology Mirror Symmetry Conjecture by KONTSEVICH / Symplectic Language Theory
5 .  Language universals
Generating Function / Symplectic Language Theory
6. Models of  Language Universals
Language Universal Models 

Tokyo December 10, 2005
Tokyo November 27, 2008 Revised
Tokyo March 24, 2009 Revised
Tokyo June 27, 2009 Revised
Tokyo February 28, 2011 Revised

Tokyo August 3, 2012 Revised
Tokyo December 8, 2014 Reprinted
SIL

Mirror Theory

Mirror Theory

For the Structure of Prayer
Dedicated to the memory of CHINO Eiichi

TANAKA Akio


1
Language is afar distant from the real world.
2
There is a certain distance between language and the real world.
3
Language is guaranteed to be reliable for the human being
4
Language continuously aims at uniting the real world.
5
The distance from the real world to language is going to be shortened.
6
The end of a sentence is a situation in which language and the real world are united into one or shortened distance to the utmost.
7
Prayer is the act of going beyond the real world by language.
8
Language is usually going to unite the real world.
The real world is a standstill point for language.
In prayer the real world is not a standstill point but a passing point.
Language has a force of uniting or going near the real world.
Language of prayer has an excess force going beyond the real world.
This excess force comes from pray that maintains the distance that exists from language to the real world.
It is a memory.
It is a continuous effort of thinking about never existing in the real world.
9
Beyond the real world language is no more guaranteed by the real world.
This situation is guaranteed by the distance from language to the real world.
This distance is a mirror of real distance.
This distance is called mirror distance.
Mirror distance is defined.
Mirror distance is the central concept of Mirror Theory.
Mirror theory is a trial for exceeding the real world.
We can think of prayer from the linguistic ground.
10
Mirror theory is an extension of  <Distance theory>.

[Reference]
Theory Map / Map 1 / Quantum Theory for Language

Tokyo June 5, 2004
Sekinan Research Field of Language

[Referential note June 5, 2009]
Reversibility of Language / Floer Homology Language Note 4 / Tokyo June, 2009

Quantum Theory for Language

Quantum Theory for Language

Synopsis

Revised and Noted from Prototheory Paper   On Time Property Inherent in Characters


TANAKA Akio

1
The object of this theory is isolating languages. #1
2
The Chinese language is adopted for the model of isolating languages. #2
3
In this theory the Chinese character is regarded as the Chinese language.
Therefore this theory is the theory for written language. #3  
4
The Chinese character is the basis of this theory.
5
The Chinese character is the quantum of language. #4
Quantum is defined.
The quantum of language is the smallest unit of language.
The quantum of language has the force.
This force propels oneself to the next quantum.
Force is defined.
6
The quantum consists of indicators. #5
7
The indicator is the shape abstracted from the real world.
Indicator is defined.
The indicator has the signification and the period inherently.
8
The inherent signification of the indicator is produced from the work of the real world.
Inherent signification is defined.
The inherent period of the indicator is produced from the time of the real world.
Inherent period is defined.
9
The quantum consists of one or more than one indicators.
10
The quantum has the inherent meaning and the inherent time that is produced from one or more than one indicators. #6
11
The inherent meaning of the quantum is produced from the indicator or the combination of the indicators.
Inherent meaning is defined.
12
The inherent time of the quantum is produced from the indicator or the combination of the indicators.
Inherent time is defined.
13
The period of indicator has the start point and the end point.
The length of two points is called the period zone.
Period zone is defined.
The time of quantum have the start point and the end point.
The length of two points is called the time zone.
Time zone is defined.
14
The time zone of the quantum decides the state of the connection of the two quanta.
This state of the connection is called <time principle of quantum>.#7
15
The front quantum that has the short time zone can connect the rear quantum that has the long time zone.
This qualification is called <connection rule>.
This situation of connection is called word.
Word is defined.
16
The front quantum that has the long time zone cannot connect the rear quantum that has the short time zone.
This qualification is called <separation rule>.
This situation of separation is called sentence.
Sentence is defined.
17
Language has the gathering of words.
This gathering is called territory.
Territory is defined.
18
Language has the gathering of sentences.
This gathering is called province.
Province is defined.
19
The quantum appears for the purpose of adding the new value of the territory. #8
The value can spread the recognition of the human being.
This value is called harvest.
Harvest is defined.
20
Quantum propels oneself to the next quantum on a line.
This line is called orbit.
Orbit is defined.
21
Quanta propel on an orbit by the force of quanta.
The force of the quantum is produced from the indicator.
The indicator is the shape abstracted from the real world.
Therefore the indicator constantly approach to the real world.
This approach makes the force of quantum.
The force is placed in this theory.
The quantum connects real world by the force of approach.
This connection guarantees the existence of the quantum.
The quantum makes the word.
The quanta make the word.
The word is guaranteed.
The quanta make the sentence.
The sentence is guaranteed.
The quanta make the language.
The language is guaranteed.
22
A sentence needs an orbit.
Another sentence needs another obit.
Two sentences cannot propel on the same orbit.
This qualification is called <propelling rule>.
23
A sentence becomes at rest when a quantum approaches the most nearly to the real world.
The force of the quantum disappears because of no use of approaching to the real world.
This phenomenon is called standstill.
Standstill is defined.
Standstill phenomenon is concerned with the prayer of belief in human being.
Because the prayer is the act of constantly approach to the real world of religion.
Standstill phenomenon is a subject for the anthropology of religion. #9
24
The orbit is linear.
Next orbit is under the former orbit in this theory.
The quantum of next orbit is located just below the quantum of the former orbit.
For example from Chinese, / Wo shuo de shi jiade. /In English, What I say is a lie.
By the combination rule, the separation rule and propelling rule, this Chinese is showed below.
     Wo
shuo
             de
               shi jia
                    de.
This showing of the orbits is called orbit table. #10
Orbit table is defined.
The quanta on the same orbit is called phrase.
Phrase is defined.
In the orbit table, the place of the each orbit is called the layer.
Layer is defined.
25
In upper orbit table, the orbit of /shuo/, say, and /shi jia/, is a lie, is located in another layer.
The orbit of /shuo/ is guaranteed.
The orbit of /shi jia/ is also guaranteed.
26
The orbit of /shuo/ and the orbit of /shi jia/ are different.
Two orbits belong to another place of the language. 
Language is made from orbits on which quanta are located.
27
/Wo shuo de shi jia de. / becomes contradiction in the current recognition of language.
But in this theory /shuo/ and /jiade/ are located another orbit.
Therefore contradiction is avoided.
Two orbits are equally guaranteed.
But the quantum of /shuo/ is farther than the quanta of /shi jia/ from the standstill.
/shi jia/ is nearer to the real world than /shuo/.
In the linear obit, nearer quantum to the standstill is stronger to the real world.
This is called <strength rule>.
Strength is a quantity of distance, from one quantum to the real world.
Strength is defined.
28
/Wo shuo de shi jia de. / is recognized below.
“The world is a lie. One place in this world I tell someone something.”
There is no contradiction here.

Notes
#1
This theory originates in the concept <drift> of Edward Sapir.
#2
This theory is indebted to the book of Wang Yingzhi, Jingzhuanshici.
#3
Chinese characters are almost the Chinese language itself.
Because Chinese syllabic sounds always request the own images for the memories.
Therefore Chinese characters can also act as the spoken Chinese.
#4
This Concept originates in the paper of Wang Guowei, Yinbucizhong suojian xiangong xianwang kao.
#5
Chinese character /yu/ generally means give birth to in English.
In ancient style of character /jia gu wen/ inscriptions on bones or tortoise shells, it has three indicators, woman bending forward, body fluid at childbirth, new born baby.
Therefore this character has the inherent meaning and time.
In other words, there are three successive categories of meaning and time, pregnancy, birth and support.
The quantum is essentially structural.
#6
This concept originates in the paper of Sergej Karcevskij, “Du dualisme asymetrique du signe linguistique”.
#7
The quantum of language disappears when the meaning of the quantum goes out of use.
For example, Chinese character /bu/ not originally meant a part of flower.
But this notional meaning disappeared early in the Chinese language.
Later instead of this meaning, /bu/ possessed the denial function.
#8
Chinese character /jiao/ means teach in English, containing short time.
Chinese character /shi/ means room in English, containing long time.
Time of existence is longer than time of movement. Therefore /jiao shi/ makes one word. It means classroom.
But /shi jiao/ make one sentence, not one word. It means in the classroom I teach.
So connection and separation of the quanta are the new syntactic principle of the Chinese language.
It is called< time principle of quantum>.
#9
This theory is also a gift to anthropology, which always gives the theory flashes of thinking.
Many thanks for anthropology, especially for the book of Kawada Junzo, Mumoji shakai no rekishi.  
#10
In Chinese traditional syntax, characters have been classified into two groups, /shi ci/ notional words and /xu ci/ functional words.
In this quantum theory, notional words have long time, functional words have short time.
Orbit table is made by the time measuring of this traditional classification.
<Quantum Theory for Language> inherits the linguistic method from /xiaoxue/ small study of the /Qing/ Ching dynasty.


Tokyo 
January 15, 2004
For the memory of Hakuba August 23, 2003
Sekinan Research Field of Language


Postscript
[References / January 21, 2008]
<On the property of quantum>
Clifford Algebra / Note 1 / From Super Space to Quantization / Tokyo January 10, 2008
<On orbit and orbit table>
Clifford Algebra / Note 3 / Anti-self-dual Form / Tokyo January 15, 2008

[References / December 21, 2008]
<Survey at the time>
Quantum Theory for Language / Simplified Review
Brief History of Quantum Theory for language
Log of Quantum Theory for Language / Love and Thanks to the Pioneers
Log of Quantum Theory for Language / On the Themes of SAPIR and KARCEVSKIJ
<Following theory at the time>
Mirror Theory
<A conclusion at the time>
Warp Theory

[Reference / January 1, 2009]
<On meaning and grammar>Orbit of Word / Complex Manifold Deformation Theory / sekinanlogos