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

Read more: http://srfl-paper.webnode.com/news/duality-of-language-derived-category-language/

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The Days of Distance

The Days of Distance
From Distance to Pseudo-Kobayashi-Distance
​
TANAKA Akio 
​                                  
In 2004 I wrote the paper titled "Distance Theory". The paper handled the structure of sentence, using the classic written Chinese for its simplicity of form that has not any transformation at word. In Chinese, word namely character does not change anymore. Nevertheless grammatical functions strictly exist by its sequence of characters. I had been very interesting the style of language that never appears in the European languages. But the study for it was too hard to pursue at my age 20s and 30s by my talent.

In 1979, I met CHINO Eiichi again at the university to where I returned from the work of teaching at senior high school. He taught me the importance of the Linguistic Circle of Prague. We talked with many problems of language study at the campus or coffee shop near the station we usually got on and off. The shop were old and steps were always sounded rattling. The light of the shop were dim and yellowed with age. We were both young, he was late 40s and I was early 30s.


Before these days we already met at the Russian class. The time was 1969, he taught us the language in the tiny classroom. Then he was just after coming back from the long study at Czechoslovakia.


From 1979, he had actively introduced the Linguistic Circle of Prague while studying his own subjects. It was a really happy time for me. He told us at the class of linguistics and told me more frankly at the coffee shop on the various themes related with language. Prague was always at the centre in the conversation.I gradually went on to the narrow theme concerned with language universals. What decisively entered to my mind was Sergej Karcevskij.


If there only be Saussure, I could not determined so smoothly.In my age 30s, 1980s, I had been wandering to and fro at Kanda, the central part Tokyo, where I encountered many Chinese classics at the Chinese book shops. From my familiar language I wanted to research the study on the subject. But  there were no clear road to going ahead.  I had hoped concise and clear description on the theme, if I wish, using mathematics.


In 1960s, in my front, Bourbaki emerged the huge target that was built by the vast from-set-theory-to-topology. At the time's going my level was very low and primitive. I was never able to use such a difficult mathematics.


I spent the lag time in 1970s. reading Chinese classic books at random. The main was Qing dynasty's Xiaoxue (Small Study in Chinese) on Chinese characters classical research.


In 1990s, the target of language study decided to language universals, being led by Sergej Karcevskij for that almost all the information were given from CHINO. At that time mathematics were going on and on to the wide and deep fields covering the humanities, e.g. category, sheaf and discreteness.


In March 2003 I stayed some days at Hakuba, Nagano, where I wrote the proto-paper on language model for the first time, titled " On Time Property Inherent in Characters". It treated the unchanging language, Chinese, as the typical one for its simplicity and familiarity in my life. The paper's main theme was time that is hypothetically inherent in each character in Chinese. The basis of the theory was in the study of WANG Guowei's ancient Chinese inscriptions on bone and tortoiseshell.


In order to possess grammar in unchanging language, there should be the another functions to express grammar or near -grammar. I selected inherent time in each character supposedly.


In August 2003, I again stayed at Hakuba, where I wrote "Quantum Theory for Language". It was the enlarged paper of the March's one. There intuitive long-short times were supposed. There was not any description of mathematics. But important points were presented not using mathematics, I thought. 
The problem was how precisely writing the theory using mathematics.


In 2004 I wrote " Distance Theory" from the viewpoint of clear concept using distance instead of time that was not able to mention enough descriptively. But the theory was also intuitive and philosophical one. I never satisfied the expression. The theory's essentials were distance and connection, that is to say, words connect according by the distance inherent in words.


Succeeding this theory, I tried to write many fields on language making the efficient models for natural language, namely language universals in my mind, being led by Karcevskij.


Hereafter the main target was the mathematical description for many varieties that were almost intuitively remained or noted. Now I use algebraic or arithmetic one for their strict simplicity and beauty.


Recently I wrote in distance from pseudo-Kobayashi-distance that was very fantastic and widely perspective views for me. The paper's title is 'Connection of Words", that is my long winding road from encountering CHINO and Linguistic Circle of Prague.


Grateful thanks to CHINO Eiichi. You wrote "Linguistics of the 21th Century" in  1998,  four years before your death, that there are studies undergoing to be able to understand meaning by combination of several elements. Still now I am your student and probably forever. 


[Reference]
Distance of Language, Historical Review                                                                   
                                                                  

Tokyo 
February 5, 2012  
February 2015, revised       
September 16, 2016, Title. The Days of Distance, added         
Sekinan Research Field of Language              

SRFL Collection

SRFL Collection

SRFL Collection contains papers and essays written at SRFL Sekinan Research Field of Language from 2003 at Tokyo, which succeeds Sekinan Library founded in 1986 at Tokyo.
Main theme is on language universals that has been researched since 1920s, as SRFL, Linguistic Circle of Prague has been always put at the centre of the study.
In Japan. on Prague School CHINO Eiichi probably first introduced systematically through his direct study experience at Prague between 1958 and 1964.
I first met with him in 1969 at Tokyo, from whom received Russian language at beginner's small class.

Read more: http://srfl-collection.webnode.com/

SIL Lab is a portal and search site of Sekinan Library

SIL Lab

SIL Lab is a portal and search site of Sekinan Library,

 that was founded in 1986 at Tokyo for studying 

language universals at first from ideogram 

and after making models using algebraic geometry.

For more details see following SRFL Essay, SRFL Paper 

and SRFL Note written between 2003 and 2016.

Update information is sent from Blog SIL Lab News.
For total overview refer to SRFL Collection. 

Tokyo, 22 March 2016, Sekinan Library