Saturday, 22 October 2016

If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.

Duality of Language. Derived Category Language

Duality of Language

TANAKA Akio

1. Model
Calabi-Yau 3-folds.

2. Theorem
R. Pandharipande and R.P. Thomas.
Pandharipande-Thomas Theorem (1998).
K. Behrend.
Behrent contructable function (2009).

Y. Toda.
Generating functions of stable pair invariants via wall-crossing in derived categories in algebraic geometry. (2008)
Curve-counting theories via stable objects (2010).
T. Bridgeland.
Hall algebras and curve-counting invariants (2011).
D. Joyce and Y.Song.
A theory of generalized Donaldson-Thomas invariants. (2012)

3. Definition
Generalized DT invariants. ( Joyce and Song. 2012)

4. Isomorphism
Isomorphism is induced in the defined moduli spaces.

5. Duality and mirror
If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.

Reference
Rensetsuso no Doraiken ni kakawaru shomondai. TODA Yukinobu. 2016. Sugaku shobo. Tokyo.

Reference 2
Derived Category Language, 25 May 2016 Edition.

Reference 3.
Actual Language and Imaginary Language. To LÉVI-STRAUSS Claude.

Reference 4.
Symplectic Language Theory Note 3 Mirror Symmetry Conjecture on Rational Curve.
Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH.

Reference 5.
Main papers of Sekinan Library.
SRFL Paper.

Paper ends.
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This paper is unfinished.

Tokyo
22 July 2016
Sekinan Library

Thursday, 13 October 2016

The Days of von Neumann Algebra

TANAKA Akio

1.
My study's turning point from intuitive essay to mathematical writing was at the days of learning von Neumann Algebra, that was written by four parts from von Neumann Algebra 1 to von Neumann Algebra 4. The days are about between 2006 and 2008, when I was thinking about switching over from intuitive to algebraic writing. The remarkable results of writing these papers were what the relation between infinity and finiteness in language was first able to clearly describe. Two papers of von Neumann 2, Property Infinite and Purely Infinite, were the trial to the hard theme of infinity in language.
The contents' titles are the following.

Monday, 10 October 2016

Preface of Language between Sergej Karcevskij and string theory, one century's trace. SRFL paper

Preface

When I started Sekinan Library at Tachikawa, Tokyo on 1 April 1986, I was 38 years old, after I left the seven year post-graduate study at university at March.

At first I thought that ideogram would become the main study target for several years as the preparatory work for language universals ever being taught from CHINO Eiichi related with Linguistic Circle of Prague in 1920s. But ideogram being typical by Chinese characters is very hard to write down by the clear description using mathematical approach. several years passed by grope for adequate approach to ideogram's meaning structure.

In May 2003 I happened to see the application of paper on the Silk Road area's history and culture. I determined to entry this chance by writing a clear and understandable approach to the meaning of vast and vague world of ancient written Chinese's grammatical structure. In summer that year I wrote over the paper, Quantum Theory for Language that was aimed complex grammar inherent in Chinese characters itself. The paper was presented at the literature section of symposium opened at Nara, Japan in December 2003. At this symposium I met many foreign researchers especially from East Europe and East-central Asia whose mother languages were of course diverse but all headed for the Silk Road's history and culture. At that time I determined that my primary way to convey was for them who might not be interest in my tiny study.

I put small laboratory for language study especially aiming for language universals from the point of view at using ideogram, so to say characters, in the daily life now in Japan. European alphabets had already lost ideogram's function. The study of Linear B sent me the complicated situation of ancient Greece and its surrounding areas. My small lab was named Sekinan Research Field of Language. Its location was Hakuba, Nagano, Japan where I completed the proto-paper of symposium's presentation, that was titled On Time Property Inherent in Characters.

In March 2003 I stayed at Hakuba and wrote a short manuscript for universal grammatical structure. Now I later named Manuscript of Quantum Theory for Language. It was unfinished paper because of the not having the efficient accumulation continuing the clear description to the others attracted in language. Still now I have walked on the way to the hard target of the study on language or language universals.

Note 1

Note 2

Note 3

Note 4

TANAKA Akio

August, 2016