Thursday 31 January 2019

Karcevskij conjecture 1928 and Kawamata conjecture 2002 / 2016

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:

Tale / Print by LI Koh / 27 January 2012

Reference:

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

Reference 2:

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

References 3:

References 4:

Reference 5:

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.

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

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, complexed 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]

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]

[Reference 3]

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

[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

The days when I was thinking of Energy Distance Theory 2014

The days when I was thinking of Energy Distance Theory

q.v. Energy and Distance in Language / 31 August 2008

TANAKA Akio

1.
Around 2008, I was thinking of energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.

Energy Distance Theory

Note
1 Energy and Distance
2 Heat and Diffusion
3 Energy and Functional
4 Finsler Manifold and Distance

Conjecture
1 Word and Meaning Minimum
2 Geometry of Word

2.
In another approach of my study on language universals, Edward Sapir's Language, 1921 was one of my favourite books between 1970s and early 1980s. In his book, the most fantastic concept for me was Drift, that indicated the vast movement of language system itself. I ever gave brief account on it.

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Edward Sapir's Language, 1921

Edward Sapir's Language, 1921 showed me the dynamism of language proposing the concept, drift.
Drift shows us the macro phase of natural language and I was hinted by Sapir's this concept and proposed the micro phase of natural language. The paper "Quantum Theory for Language" is my first total proposal paper describing the natural language's model.

Reference
Substatiality Dedicated SAPIR Edward / 27 February 2005

Tokyo
5 September 2014
Sekinan Research Field of Language

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3.
My language study started from the reading of Old China's Qing dynasty's huge linguistic inheritance, "Xiaoxue", in English Small Study , that is contrary to the name, the most basic and difficult study of classical texts of old China. I particularly loved the books written by WANG Guowei and WANG Yinzhi and DUAN Yucai.
The main book list to which I referred in those days between the age 20s and 40s are shown at the next.

Library 10 General Index, SRFL Sekinan Research Field of Language

Especially I was enchanted with WANG Guowei's work, whose selected papers' title wasGuantangjilin. For him I wrote a short essay as below.

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40 years passed from I read WANG Guowei / 16 November 2013

TANAKA Akio

Guantangjilin is the selection of works by WANG Guowei, which contents contains vast area of history, literature and linguistics. Some people say that his works is a thousand-year peak from Song era’s philosopher SHU Xi. I bought his book at Haifeng shudian, Kanda, Tokyo in my mid 20s. The date of colophon is February 1973, publisher is Zhonghua shuju Xianggang fenju.

Probably I bought it in 1973 or 1974. In those days I frequently went Haifeng shudian bookshop for buying Chinese classics, mainly Qing Dynasty’s linguistic works that is called ” Xiaoxue”, Small study at China. Guantangjilin is a very difficult book to understand by my poor study result.

His study era is from Yin Dynasty to Qing Dynasty some 2,500 years of Chinese literary history. At his vast works I was especially charmed in Qing Dynasty’s ancient Chinese hieroglyphic characters, Jiaguwenzi by Chinese. After 40 years, in 2003 I wrote a small paper on language universals through this ancient Chinese hieroglyphic characters at the view point of written language.

The title is On Time Property inherent in Characters. From at that time 10 years passed by. Now I am still learning on language universals but its style is far apart from the days 2003 or 1973. Ambiguity of approach by traditional linguistics is not for my part. I dare challenge to a new frontier of description for language study using mathematics or algebraic geometry.

Refer to the next.

Tokyo 16 November 2013
Sekinan Research Field of Language

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4.
After all,Energy Distance Theory ended in the half-finished situation. But now I still eager to write and develop the papers on energy and distance. The road is long and winding as ever. I always accustomed to delay and stagnate. Some rays of light is emitting in the small study room of mine.

Tokyo
19 December 2014
SIL

Murayama Dam, Sayama Hills, Tokyo

11 May 2017

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

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

TANAKA Akio

1. Between 2003 and 2017
In 2003 I wrote a paper that showed meaning's inner structure of Chinese characters.
The paper was based on Chinese character's old form, Jaguwen, Chinese inscriptions on animal bones and tortoise carapaces that was first found at Henan-sheng, China in 1999. I wrote the paper mainly depending on WANG Guowei's work. My paper is the following.

On Time Property Inherent in Characters. 28 March 2003

In this 2017 I wrote a related paper with the 2003's paper, which mainly focused on ideogram's general purpose property from hieroglyph to LATEX symbols. My paper is the next.

The Days of Ideogram. 20 April 2017

2. From philology to algebra
The 2003 paper is on the continuation of Qing Dynasty's classical philologists in China.
The 2017 paper is on the extension of Category theory's homological approach.

3. From intuitive to definitive
The 2003 is not openly used mathematical approach, as a result writing style is considerably intuitive.
The 2017 is also intuitive, but in its base, more sufficient mathematical data in the 17 year study result. The most recent work is Derived Category Theory. The theory is at the next.

Derived Category Language

Now the upper two papers, the 2003 and the 2017 and their related papers are seen at Sekinan Paper and Sekinan Theory.

Sekinan Paper
Sekinan Theory

4. Starting place
The new theory is now being prepared for more mathematical-descriptive expression titled Homology Language.Starting place is at the following papers.

Karcevskij conjecture 1928 and Kawamata conjecture 2002
Language stability and triangulated category

5. Gist of Homology Language
The fundamental essences are the next.
(1)
Set is defined as Universe which can avoid set theory's contradiction.
(2)
Set is considered as Category which can get back to all the concepts to Object and Morphism.
(3)
Topological space is considered as Homology which can get back all the work to algebra.
(4)
Language model is considered as Sheaf which can past functions to the more big function.
(5)
Language can take Contractible which can describe free concepts as meaning.

6. Aim of Homology Language
(1)
Language will get near to finite generative a little alike natural language.
Fundamental work was done at the next from set theory but not definitive as universe.

von Neumann Algebra 2 Note Generation Theorem

(2)
Category theory seems to be a one-step-up stage to write on language from the days of Maclane Saunders. Refer to the next.
Topological Semantics. Torus Chain. For MAC LANE Saunders
Language and Spacetime. Word Containing Time and 4 Dimensional Sphere. Dedicated to MAC LANE Saunders
Language and Spacetime. Structure of Word. From KARCEVSKIJ to MACLANE
For MAC LANE Saunders. Categorical Approach toward Language

(3) Homological approach
In 2009 I wrote a trial papers titled Floer Homology Language. Still now the papers are important for my study.

Floer Homology Language
|
Potential of Language
Supersymmetric Harmonic Oscillator
Grothendieck Group
Reversibility of Language
Homology Generation of Language
Homology Structure of Word
Quantization of Language
Discreteness of Language

In Floer Homology Language, the next two papers will become the guidepost for new theory Homology Language.

Homology Generation of Language
Homology Structure of Word

(4) Symplectic algebra
Symplectic algebra is one of the most fantastic fields of the contemporary mathematics.
I also ever wrote simple invitational papers for applying to language universals.
The papers are next.

Symplectic Language Theory
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Symplectic Topological Existence Theorem
Gromov-Witten Invariant
Mirror Symmetry Conjecture on Rational Curve
Isomorphism of Map Sequence
Generating Function
Homological Mirror Conjecture by KONTSEVICH
Structure of Meaning
On Structure

In the papers, The next contains the update result of homological approach.

Homological Mirror Symmetry Conjecture by KONTSEVICH

(5) Bridge to resolve
Relationship between symplectic geometry and derived category shows the realization of clearer description on language.universals Because for my part, Symplectic Language Theory and Floer Homology Language seems to be the nearest way to resolve the hardship of natural language's inner structure.
The details are the next.
Additional meaning and embedding

(6) Symmetry
The concept called symmetry is very important to describe the complex situation of natural language.
Symmetry contains undifferentiated factors in itself, for example mirror, distance,ant-world and so forth.
I ever tried to cultivate this fantastic field to resolve the hardship on language universals one more step up.
My trying paper is the following.

Mirror Theory
Mirror Language

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This paper in unfinished.

Tokyo
6 July - 9 July 2017
Sekinan Library