Dimension Decrease Conjecture

Dimension Decrease Conjecture

TANAKA Akio

1 Dimension conjecture of word
23/09/2013 23:04
Word has dimension. New addition of meaning to word makes dimension of word decrease.
Basis
Pull back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional  meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

2 SAITO Shuji, SATO Kanetomo
24/09/2013 10:14S
SAITO Shuji, SATO Kanetomo. Algebraic Cycle and Etal Cohomology. 2012.

3 Pull-back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

4 Y. Nesterenko, A. Suslin
23/09/2013 15:30
Y. Nesterenko, A. Suslin.
Homology of the general linear group over a local ring, and Milnor’s K-theory. Math. 1990.

5 Higher Chow ring
23/09/2013 15:21
Double graded Abel group becomes double graded ring by defined intersection product.
Its product become commutative at one degree and become noncommutative at the another degree.

6 W.Fulton
23/09/2013 11:01
W. Fulton. Intersection Theory, 2nd ed. 1988.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

7 V. Vodoedsky
22/09/2013 20:09V.
V. Vodoedsky
On motivic cohomology with Z/2-coefficients. Math.98. 2003.
On motivic cohomology with Z/l-coefficients. Ann. of Math.

8 Map that norm residue map induces
22/09/2013 20:03
When k is field and n is commutative integer, map that norm residue map induces is bijection.

Paper for Dimension

Paper for Dimension


1. Dimension Decrease Conjecture
2. Conjecture for synthesis of meaning in word
3. Reversion Conjecture Revised 
    Proto 3. Conjecture for reversion of language

Tokyo

14 June 2015

Sekinan Paper

Sekinan Paper

Sekinan Paper

Tokyo

1 June 2015 arranged

Study result of Sekinan Library from 1986, SRFL from 2003 and Zoho from 2008

Sekinan Paper is the paper site of Sekinan Library and SRFL Sekinan Research Field of Language.
Sekinan Library was founded at Tachikawa, Tokyo in 1986 for the study of language. 
In 2003 for the special study site of language universals, SRFL Sekinan Research Field of Language was added at Hakuba, Nagano.  

Hydrangea

June 2015

At least three elements for language universals

At least three elements for language universals

TANAKA Akio

Supposition 1:
Three elements for language universals

For language universals, now I suppose at least three elements being  based from mathematical description.

Three elements for language universals are energy, dimension and distance.

The most fundamental element is energy. By this energy, all the movements and changes occur in language.
vide: 

• Edward Sapir, Language, 1921
• Substantiallity

All the languages are located at a certain dimension in space. By this dimension, confusions in language are averted.
vide:

• True-false problem of the Crete

In language, all the movements and changes inevitably make distance occurred. By this distance, important phases of language are clearly defined.
vide:

• Distance Theory 

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Supposition 2:
Mathematical description for three elements of language universals

Energy, dimension and distance can be describe by mathematical writing.

Energy in language is now preparatory description til now.
vide:

• Energy of Language / Stochastic Meaning Theory
• Energy and Distance / Energy Distance Theory
• Energy and Functional / Energy Distance Theory
• Potential of Language / Floer Homology Language

For dimension, definite results are presented being aided by arithmetic geometry.
vide:

• Three Conjectures for Dimension, synthesis and Reversion with Root and Supplement

For distance, its vast and vagueness of the concept can not be grasped up. But related papers of mine are probably the most in number.
vide:

• Distance / Direct Succession of Distance Theory / Distance Theory Algebraically Supplemented
• Distance of Word / Complex Manifold Deformation Theory

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This paper is not finished.

Tokyo
27 February 2015
SIL

Manuscript of Quantum Theory for Language

Manuscript of Quantum Theory for Language

TANAKA Akio

Tokyo 6 June 2015
Sekinan Study

以下に示す「言語の量子理論」は、英文で書かれたQuantum Theory for Language の草稿となるもので、２００３年３月に長野県白馬の白馬アルプスホテルで書かれたものである。発表するのは今回が初めてである。いままで発表しなかったのは、この草稿がまったく資料のないホテルの部屋できわめて短時間のうちに書かれたものであり、そのためその内容が非常に直感的で、通常の論考とは異なる、私にとってはかなり先鋭的なものであったためである。しかも論考は途中で終わり未完のままである。２００３年１２月に或るシンポジウムで発表するためにこの草稿をもとに書き上げたQuantum Theory for Languageでは、論考の趣旨はほぼ一貫しながらもその表現をより穏やかなものにした記憶がいまもはっきりと残っている。しかし現在この草稿を読み返してみると、私が２００３年当時気にした直感性や先鋭さは、やはり私の言語論の本質に深く根ざしたものであり、ほぼ十年におよぶ言語に関する数学的な記述を経て振り返ると、私が今なお書き残しているもっとも重要ないくつかの主題は、ほぼこの草稿に記されたものであることを私はあらためて確認するに至っている。言語の量子化、量子の出現と消滅、量子の接合と階層、量子集合体、量子群の進行と階層、陽性量子と陰性量子、量子の意味とエネルギー。いずれも私にとって、依然として未知であり魅惑的であり続ける。今後私はふたたびこの草稿の位置にもどり、あらためてみずからの思考を紡いてゆくことになるであろう。老年の今となっては、本質は形態に先行し、もっとも表現したいものを、私にとってそれにもっともふさわしい方法で記述してゆくこととなるであろう。いくばくかの時間がなお残されているのであればだが。二十歳のころ恩師が教えてくれた句は今もそのまま生きている。いざゆかん雪見にころぶところまで。
２０１５年３月２３日、東京にて記す。
..................................................................................................................................

言語の量子理論

２００３年３月
長野県白馬にて執筆

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Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"

Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"

TANAKA Akio

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:

• Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / 8 September 2011
• Condition of Meaning / 11 September 2011

References 4:

• Dimension of Language / 4 September 2013
• Synthesis of Meaning and Transition of Dimension / 6 September 2013

Reference 5:

• Reversion Conjecture Revised / 1 May 2014 - 20 May 2014

[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

5 June 2015

Sekinan Study

Quantum space through Poisson manifold's deformation quantization by Kontsevich

Quantum space through Poisson manifold's deformation quantization by Kontsevich

TANAKA Akio

From Print 2012, Chapter 18

対称性。それはかつてＣと繰り返し話した内容だ。１９２０年代のプラハ。雑誌TCLPに載ったカルツェフスキイの論文、「言語記号の非対称的二重性」。言語が保持し続けるところの、それによって言語が言語であり続けるところの、絶対的に矛盾する柔構造と硬構造の共存。言語において二重に内在し続けるだろう永遠の矛盾。言語がかくも柔軟でかくも堅固でいられるのはなぜか、そのほとんど絶対的に矛盾するかともおもわれる二重性をカルツェフスキイは提示した。Ｃがその最後の本の中でただ一人天才と称した言語学者、セルゲイ・カルツェフスキイが残した白眉の論考。

なぜこの共存が可能なのか、この二重性に対する整合的な理解は今もなお、たぶん提出されていない。これに比して世界の量子化quantizationについては着実な進展があった。

深谷によれば、コンツェヴィッチは１９９７年の論文で形式性予想を提示し、２００３年の論文に至って、みずからその予想を証明した。「ポアッソン多様体の変形量子化」。深谷は彼の本の中でその証明の概略をｎＲの場合に限って述べている。証明の全容は計り知れない。量子による空間、それももう夢ではないかもしれない。

Source: Tale / Print by LI Koh / 27 January 2012

Reference:
Quantization of Language / 24 June 2009

Komaba Park, Tokyo in midafternoon

3 July 2014

Tokyo

4 June 2015

Sekinan Library