Sekinan Table: February 2023

Sunday 12 February 2023

What facts does Three Conjectures for Dimension, Synthesis and Reversion show us?

vide: Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement

TANAKA Akio

1.
True-false problem of the Crete gives us the infinite circulation of true-false value.
This fact indicates us the existence of deep structure or hierarchy in language.
The Crete's true-false is solved by the perspective from 2-dimension to 3-dimension on structure in language world.

2.
Language has long history as the system of etymology. Apparently language has gradually added the new meaning on the old established meaning in word. At this point new meaning is synthesised to the old meaning. At synthesis word mathematically reduces its dimension to the lower one. As the result time in word relatively occurred in the new word and inevitably connected with dimension.

3.
Where and how does word exists in the world?
The distance from a certain point is absolutely demanded for measuring or observing for knowing the word's place.Reversion is a result for measuring or observing from a point.

4.
For precise description of dimension, synthesis and reversion mathematical tools are definitely needed and for more simple describing algebraic method is the most useful to approach for me and in order to easy-seeing and clear intuition geometrical approach is always inevitable to searching. I am greatly thanks to relevant mathematicians researching against severe problems still now for contemporary times.

Kodaira, Tokyo
20 November 2014
SILessay

Time in Word

TANAKA Akio

Time inherent in word has been one of the most fantastic theme for me for a long period. WANG Guowei’s paper was strongly hinted to the theme towards first writing a trial paper on it. Roman Jakobson was also gave me the basic notion related with the theme. Still now the problem has not solved as the starting point. But being aided by mathematical method and description, learning on it has become more attractive in these days.

Trial paper: On Time Property Inherent in Characters
Basic notion: From Cell to Manifold
Mathematical description: Dimension Decrease Conjecture

Tokyo
24 October 2013
SIL
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[Note]
When I wrote this essay, "Time in Word" in the autumn of 2013, the relation between time and dimension cannot be thought clearly but now in 2014 I distinctly think that the relation exists at the situation of synthesis of the new meaning on the old meaning. The four papers of Arithmetic Geometry Language written between 4 September 2013 and 9 September 2013 are indicating the affinity with time and dimension. Now I show the compact paper in the four, titled " Synthesis Meaning and Transition of Dimension".

Synthesis of Meaning and Transition of Dimension, 6 September 2014

Four papers of Arithmetic Geometry Language are the following.

Arithmetic Geometry Language (Abbreviated AGL)

Dimension of Language (AGL1)
Synthesis of Meaning and Transition of Dimension (AGL 2)
Birth of Word, Synthesis of Meaning and Dimension of New Word (AGL 3)
Dimension Conjecture at synthesis of Meaning (AGL 4)

Tokyo
17 November 2014
SIL
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[Note 2]
The relation between time and dimension is now arranged at the following paper.

Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement / 19 November 2014

The overview of time in language is now shown at the following paper.

How is the time alive in language?

On WANG Guowei and Roman Jakobson, refer to the next.

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[Note 3]
Essay "Pleasure of Mathematics" includes time notion related with Brownian motion.

Pleasure of Mathematics / 15 December 2014

Tokyo
3 December 2014
15 December 2014, Note 3 added
SIL

The Time of Language. Ode to The Early Bourbaki To Grothendieck

The Time of Language

Ode to The Early Bourbaki To Grothendieck

TANAKA Akio

In early 1970s, I had think of language from the side of mathematics, that level of mine is very low and primitive, moreover I never had any talent to mathematics.
But my eager to trying the approach was going to overcme hard barriers before me. So the route had really facscinated my mind for long time.
At that time I had read Chinese classics almost every day. WANG Guowei*, DUAN Yucai and WANG Yingzhi. They were giants on Chinese language historically and modernly.
On the other hand I had thought of language generally, not defined by Chinese.
But in front of the vast world of language, I had stood still lonely, not taking any method for approaching.
Mathematics was the only gleam of hope in the wasteland.
I never took the route of ordinary linguistics.
I really dreamed a dream that time.
There exists set theory before me.
Probably there was the influence of Bourbaki**, that several translations to Japanese, shared from Tokyo Tosho Publisher, were on the desk of mine.
My talent and endeavor were so low, so I had not any results at that time.
My desire was deep but my hand was so shallow.
The time passed by.
In 1979 the meeting again with CHINO Eiichi*** made me the chance to learn on language, the object was clear and direct.
Language universals by mathematics became the never-ending goal of the study hereafter.
Sergej Karcevskij**** gave me the courage to the reseach.
All the way to investigation were taught from CHINO, who was the genuine teacher on language.
In mathematics I took the route from geometry, especially by projection.
Now I stand at algebraic geometry.
Grothendieck is in the northernmost at the end of Bourbaki.
SAITO Takeshi said at the essay on Grothendieck***** that the object of mathematics for Bourbaki was the set of being attached by construction and the object of mathematics for Grothendieck was the object of category representing the presentable functor.
The time has come for describing****** on langauge by mathematics despite my poor ability.
Sincere thanks for the pioneers letting us make the fascinating route of modern mathematics.

*WANG Guowei
Encounter in life / A Letter /2005
Influenced paper / On Time Property Inherent in Characters / 2003 , Quantum Theory for Language / 2004
**Bourbaki
SAITO Takeshi. Bourbaki, Mathematics Seminar, vol.41 no.4 487. Nihonhyoronsya, Tokyo, 2002.
***CHINO Eiicji
First met in 1969, again in 1979. Fortuitous Meeting
****Sergej Karcevskij
Note on Karcevskij's theme. Note for KARCEVSKIJ Sergej's "Dudualisme asymetrique du signe linguistique"
*****Grothendieck
SAITO Takeshi. Grothendieck, Mathematics Seminar, vol.49 no.5 584. Nihonhyoronsya, Tokyo, 2010.
******describing
Note on Grothendieck's theorem. Vector Bundle Model

Tokyo
January 10, 2012
Sekinan Research Field of Language

The days when I was thinking on Energy Distance Theory

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

TANAKA Akio

1.
Around 2008, I was thinking on 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

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
Sekinan Essay

The Days of von Neumann Algebra

The cited papers' texts are shown at Blogger site, SRFL News.

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.

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von Neumann Algebra

Assistant Site : sekinanlogos
TANAKA Akio

On Infinity of Language
1 von Neumann Algebra 1
2 von Neumann Algebra 2
3 von Neumann Algebra 3
4 von Neumann Algebra 4

References

1 Algebraic Linguistics
2 Distance Theory Algebraically Supplemented
3 Noncommutative Distance Theory
4 Clifford Algebra
5 Kac-Moody Lie Algebra
6 Operator Algebra.

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2.
The papers of von Neumann Algebra and References are the next.

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von Neumann Algebra

1 1 Measure
2 Tensor Product
3 Compact Operator

von Neumann Algebra 2

1 Generation Theorem

von Neumann Algebra 3

1 Properly Infinite
2 Purely Infinite

von Neumann Algebra 4

1 Tomita's Fundamental Theorem
2 Borchers' Theorem

Algebraic Linguistics

<Being grateful to the mathematical pioneers>On language universals, group theory is considered to be hopeful by its conciseness of expression. Especially the way from commutative ring to scheme theory is helpful to resolve the problems a step or two.
1 Linguistic Premise
2 Linguistic Note
3 Linguistic Conjecture
4 Linguistic Focus
5 Linguistic Result

Distance Theory Algebraically Supplemented

Algebraic Note
1 Ring
2 Polydisk <Bridge between Ring and Brane>
3 Homology Group
4 Algebraic cycle
Preparatory Consideration
1 Distance
2 Space <9th For KARCEVSKIJ Sergej>
3 PointBrane
Simplified Model
1 Bend
2 Distance <Direct Succession of Distance Theory>
3 S3 and Hoph Map

Noncommutative Distance Theory

Note
1 Groupoid
2 C*-Algebra
3 Point Space
4 Atiyah’s Axiomatic System
5 Kontsevich Invariant[References]
Conjecture and Result
1 Sentence versus Word
2 Deep Fissure between Word and Sentence

Clifford Algebra

Note
1 From Super Space to Quantization
2 Anti-automorphism
3 Anti-self-dual Form
4 Dirac Operator
5 TOMONAGA's Super Multi-time Theory
6 Periodicity
7 Creation Operator and Annihilation Operator
Conjecture
1 Meaning Product

Kac-Moody Lie Algebra

Note
1 Kac-Moody Lie Algebra
2 Quantum Group
Conjecture
1 Finiteness in Infinity on Language

Operator Algebra

Note
1 Differential Operator and Symbol
3 Self-adjoint and Symmetry
4 Frame Operator
Conjecture
1 Order of Word
2 Grammar
3 Recognition
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3.
After writing von Neumann Algebra 1 - 4, I successively wrote the next.

Functional Analysis
Reversion Analysis Theory
Holomorphic Meaning Theory
Stochastic Meaning Theory

Especially Stochastic Meaning Theory clearly showed me the relationship between mathematics and physics, for example Brownian motion in language. After this theory I really entered the algebraic geometrical writing by Complex manifold deformation Theory. The papers are shown at Zoho site's sekinanlogos.

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sekinanlogos

Complex Manifold Deformation Theory

Distance of Word
Reflection of Word
Uniqueness of Word
Amplitude of Meaning Minimum
Time of Word
Orbit of Word
Understandability of Language

Topological Group Language Theory

Boundary of Words

Symplectic Language Theory

Symplectic Topological Existence Theorem
Gromov-Witten Invariantational Curve
Mirror Symmetry Conjecture on Rational Curve
Isomorphism of Map Sequence
Homological Mirror Symmetry Conjecture by KONTSEVICH
Structure of Meaning

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

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4.
The learning from von Neumann Algebra 1 ended for a while at Floer Homology Language, where I first got trial papers on language's quantisation or discreteness. The next step was a little apart from von Neumann algebra or one more development of algebra viz. arithmetic geometry.

# Here ends the paper.

Tokyo
3 December 2015
SILessay

The days between von Neumann Algebra and Complex Manifold Deformation Theory

# Applied papers with this essay are reprinted at SRFL News.

TANAKA Akio

von Neumann Algebra was written from 3 April 2008 to 2 May 2008. And Complex Manifold Deformation Theory was written from 30 November 2008 to 9 January 2009. In the days between the two theories I wrote the following 4 paper groups.

Functional Analysis
Reversion Analysis Theory
Holomorphic Meaning Theory
Stochastic Meaning Theory

These days were the preparatory time for regularised writing by algebraic geometry at Zoho site. But they were relatively precious days for thinking about the reshuffling mathematics and physics related with language. Especially Stochastic Meaning Theory was a milestone for mathematical approaching to physical phenomenon of language.Stochastic Meaning Theory's titles are the next.

Stochastic Meaning Theory

On the other hand, I really realised that mathematical writing of natural phenomenon, for example natural language, inevitably needed clear routes by mathematics that was represented by function analysis approach. Functional Analysis and Reversion Analysis Theory were the trial papers aiming for new ground, especially the comparison of finiteness and infinity in generation of words and sentences.

Functional Analysis 1

Note
1. Baire's Category Theorem
2. Equality and Inequality
3. Space
4. Functional
Conjecture
1. Finiteness of Vocabulary
2. Distance at Hypersurface

Functional Analysis 2

Note
1. Pre-Hilbert Space and Hilbert Space
2. Orthogonal Decomposition
Conjecture
1. Generation of Word

Reversion Analysis Theory

1. Reversion Analysis Theory
2. Reversion Analysis Theory 2

But at that time I could not decide the main field of mathematics for applying to language study. Moreover I never thought about language models parting from natural language and constructing the new field for thinking about language universals.
After these preparation of algebra that was started from Premise of Algebraic Linguistics 1 -1 at 11 September 2007, I barely reached to the entrance of algebraic geometry's use for language and making the language models. It was Complex Manifold Deformation Theory which began to write at 30 November 2008 titling Distance of Word, one of my main themes for language universals from the very starting of language study. Thus my study first focused to making language models of algebraic geometry using complex manifold.

Complex Manifold Deformation Theory

# Here ends the paper.

Tokyo
6 January 2015
SILessay

Thanks to physics about which I ever dreamt in my future

Thanks to physics about which I ever dreamt in my future

TANAKA Akio

In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse wideness at the university, from where returning the clear descriptive situation represented by physics needed long and winding road for me. Now in my mind probably language and physics or mathematics are happily live together constructing the world's one main frame. I wonder why I took so much time to reach here. Long time ago, at least Pascal's days, philosophy and mathematics were both sides of shield for solving the world's hard problems. It is very appropriate that the fact is solved from every fields not being partitioned any artificial walls. Philosophy may be solved by mathematics and mathematics may opened by physical phenomenon. Now they all became common sense. Only I reached here delaying rather late. I am now situated in tranquil field. Thanks to so many pioneers, especially in mathematics. Also to physics about which I ever dreamt in my future.

References:

Tokyo
25 July 2015 Reprint
Sekinan Study

TANAKA Akio

In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse wideness at the university, from where returning the clear descriptive situation represented by physics needed long and winding road for me. Now in my mind probably language and physics or mathematics are happily live together constructing the world's one main frame. I wonder why I took so much time to reach here. Long time ago, at least Pascal's days, philosophy and mathematics were both sides of shield for solving the world's hard problems. It is very appropriate that the fact is solved from every fields not being partitioned any artificial walls. Philosophy may be solved by mathematics and mathematics may opened by physical phenomenon. Now they all became common sense. Only I reached here delaying rather late. I am now situated in tranquil field. Thanks to so many pioneers, especially in mathematics. Also to physics about which I ever dreamt in my future.

References:

Tokyo
25 July 2015 Reprint
Sekinan Study

Tachikawa Youth Days , for SAEKI Shizuto

Tachikawa Youth Days , for SAEKI Shizuto

TANAKA Akio

Tachikawa is the largest city of the west Tokyo area now . I spent high school days at this city. But the scenery at the surrounding of station has changed so big and speedy. My old days' image cannot be seen anywhere around here. At that time I used the south gate, that was rather lonesome and only a few people walked even at the main street after evening.
Now the pedestrian decks have spread in all directions. Near the station vast number bicycles are parked for business persons and students. Surely half a century passed by. It is very natural to be changed in all phases. Old person must see the vigorous long view calmly standing at the deck. The monorail train are passing over the city streets carrying many people that gather and leave the city.
After graduated university I came back to Tachikawa for working job. My dear old coffee shop "Road" is vanished perfectly, where I often talked on our present and future with my best friend and colleague SAEKI Shizuto till closed time when Auld Lang Syne was playing.

Tokyo
11 October 2012
Sekinan Research Field of Language

vide: Henry the Fourth, For SAEKI Shizuto and Shakespeare
8 March 2015 Revised
Sekinan Library

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

Road to Language Universals

Road to Language Universals

TANAKA Akio

Sekinan Research Field of Language was established in 2003 for the study on language universals, that was the core theme since my youth time some 40 years ago in the 1970s. But real start was much later in the late 1980s.

In 1986 I established the Sekinan Library for the base of study at Tachikawa, Tokyo. At that time my main theme was declined to the study of old Chinese character's classical semantics using the traditional study of the form of characters reading Qing Dynasty's WANG Guowei. The study from the direction had not given me so rich results. I at the same time read some mathematical books influenced from Bourbaki that was the big stream in 1970s in Japan. Set theory represented by Gödel was also the favourite at the time.

In 1990s I determined the direction of study only to language universals taught from CHINO Eiichi, one of the modern typical philologists of Japan. He taught me almost all the aspects of European philology that were unknown for me. In the various themes he gave me, the most impressive was the existence of the Linguistic Circle of Prague. Above all Sergej Karcevskij was overwhelmingly deep and moving. But Karcevskij's approach was seemed to be intuitive and far from clear descriptiveness.

I began to learn the theme hinted by Karcevskij while learning Gödel, Bourbaki and Wittgenstein that was also gave me the big influence form the age 20s. I had frequently read Wittgenstein's TRACTATUS. But my base of math was so poor and never became the descriptive use for language's delicate phases. So I again restarted math from geometry that gave the most familiar and clear image for me. My intuitive image and basic math description were seemed to be able offer in nearly millennium days.

In spring 2003 I knew the application paper for the international symposium held by a certain institute. I arranged the short paper for it till early summer and sent it. The paper was happily adopted as one of the language and literature section of the symposium. The paper's title was Quantum Theory for Language. It was again arranged next year 2004 as the title Quantum Theory for Language synopsis.

The establish date of Sekinan Research Field of Language was 23 August 2003, that was the date of completion of proto-conceptive paper of Quantum Theory for Language at the hutte in Hakuba, Nagano. Now the time passed rapidly 10 years. The home site, sekinan, has become full by the papers accumulation. So the new site has become indispensable.

Tokyo
31 December 2012
Sekinan Research Field of Language

[Postscript]
Tokyo
14 July 2015 Added
Sekinan Study

Saturday 11 February 2023

Preparation for the energy of language

TANAKA Akio

The energy of language seems to be one of the most fundamental theme for the further step-up study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory papers written so far.

Tokyo
3 April 2015
Sekinan Library