Sekinan Data: What is signal? The existence that generates language The 1st Edition 21 November

What is signal?

The existence that generates language

TANAKA Akio

SRFL Paper

Tokyo

21 November - 15 January 2019

Original Title

What is signal? A mathematical model of nerve

Preparation 1-15

For father and mother

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Preface

This short paper would finally write on signal through the relation between language and nerve, for which

using mathematical method at the way.

This paper's one of kernels is energy which is naturally accepted at the side of verve, but at the side of

language, it may be not accepted widely till now.

In this paper, I probably do not refer to the language's energy, that has been written several times in the

papers before.

If necessary refer to the next essays.

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The days when I was thinking on Energy Distance Theory 2008

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.

Read more: https://geometrization-language.webnode.com/news/the-days-when-i-was-thinking-on-energy-

distance-theory/?

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Also refer to the next.

Energy of language 2015

1.At least three elements for language universals 2015

2.Preparation for the energy of language 2015

3.Papers for Language Dimension In chronological order 2015

4.Three conjectures for dimension, synthesis and reversion with root and supplement 2014

5.Arithmetic Geometry Language 2014

Preparation for the energy of language 2015

1.Potential of Language / Floer Homology Language 2009

2.Homology structure of Word / Floer Homology Language 2009

3.Amplitude of meaning minimum / Complex Manifold Deformation Theory 2008

4.Time of Word / Complex Manifold Deformation Theory 2008

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Preparation

Distance

Language

Next definition for language shows my simple image to language and energy.

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Language and Spacetime

Language

Definition for the Child who Lost the World

TANAKA Akio

0 The world spreads around the human being.

1 Language divides the world.

2 Language connects the world.

3 Language bends the world.

4 Language stretches the world.

5 Language shrinks the world.

6 Language extinguishes the world.

7 Language creates the world.

8 Language gives despair.

9 Language gives hope.

10 Language is pasting on spacetime with energy.

Postscript

[Referential note / November 29, 2007]

For Authentication of Solidity

[Definition added / November 3, 2008]

Definition 10, the part of is newly added.

Tokyo March 3, 2007

Tokyo November 3, 2008 Added

Read more: https://srfl-lab.webnode.com/news/language-definition-for-the-child-who-lost-the-world/

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Human sense

On language and human sense, I ever wrote simply at the next paper.

Macro Time and Micro time

TANAKA Akio

24 July 2013

atbankofdam

1. Through natural language, in human being, occurred the electrical signal by eye or ear. These complex

situations are beyond this paper’s limits.

2. Language is a physical object as signal and its transmission. At this circumstances, language must be

recognised to be the existence that has finite time.

3. An apple on the desk gradually becomes rotten by passing the time very after the crop in the orchard. #0

4. Like an apple, language has passing physical time in oneself.

5. Language is metamorphosed by the time progressing. #1

6. Language includes the outer world from human being to universe. At this declaration, I recall Blaise

Pascal’s Pensées. XXXIII. PROOFS OF JESUS CHRIST 308 The infinite distance between body and mind

symbolizes the infinitely more infinite distance between mind and charity, for charity is

supernatural.(Translated by A.J. Krailsheimer, 1966) #2

7. Language’s time goes freely from the present to the future or the present to the past. #3

8. Language symbolises the time from finiteness to infinity. #4

9. Human being recognises this vast language world perfectly. #5

References

#0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan

Research Field of Language

#1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos

#2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966.

#3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory /

December 16, 2006 / Sekinan Research Field of Language

#4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos

#5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos

Source: https://atbankofdam.wiki.zoho.com/Macro-Time-and-Micro-Time.html

To be continued.

Author.

Read more: https://srfl-lab.webnode.com/news/macro-time-and-micro-time/

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Signal

Signal Goes to meaning.

Traffic signal shows Go, Attention and Stop to people by three colour lights

Morse code sends a message by short and long signals.

Signal has structure that resembles language.

Morse code can regards as a written language.

What is signal's peculiarity?

It depends on signal's generation that has simple on-off phenomenon.

This phenomenon combines with the other on-off phenomena and become complex structure that has

meaning like language.

Signal seems a primordial form of language.

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Nerve

Is nerve signal?

I have any knowledge on physiological nerve.

So at this paper I prepare a mathematical model of nerve comparative with signals.

At mathematical model, on-off system is not simply fit with the expression of mathematical space.

Here on-off system is arranged for more simple form.

I ever wrote a paper below.

Manuscript of Quantum Theory for Language 2003

The paper is a very intuitive one but there are some hints on signal.

Now I need one chapter for my new trial paper.

The chapter is " 6. Basic principle of quantum theory"

The original text is the following.

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６　量子理論の基本原理

　量子理論は、伝統的には実辞とされる陽性量子が1階層で進行することが基本である。したがってある種の

量子群すなわち文において、陰性量子が冒頭に立つときには、その前に陽性量子または量子群が省略された

と考えることができる。

陰性量子が陽性量子の進行方向に変化を与えて、新しい階層に移行させることは、陰性量子が受けている被

圧迫エネルギーによるとしたが、より正確には、以下のように説明できる。

一般に断定の虚辞とされる「也」は、その実辞としての意味は現代においては不分明であり、陽性量子とし

てはほぼ消滅したと考えることができる。その代わりに陰性量子としての虚辞機能が台頭して現在に至る

が、その機能を細分すれば、断定、主題提示、呼びかけ、詠嘆、疑問、反語等の極めて多様である。

たとえば、「回也不愚」（『論語』為政篇）においては、「回」という人物が、（階層が変わり）孔子の心

中において、（また階層が変わり）否定される存在であり、（さらに階層が変わり）「おろかものの類」が

提示される。」

「階層が変わる」ということは、「回」という人物が、「也」と出現によって実在の人物から、孔子の心中

における考察対象へと変換されたことを意味し、さらにその考察対象が「不」によって抹消されることを意

味し、さらに新しく「愚」という概念が登場することを意味する。

すなわち陰性量子は、陽性量子が有する言語世界への直接的な意味を行うのではなく、実辞としてはもはや

空白となった自らの領域へ、陽性量子を導くjことによって、一種の真空無重力の状態を現前させ、その方位

を転換することであると仮定する。その転換に必要とされるエネルギーは、領域が受けている被圧迫のエネ

ルギーから生ずるものと仮定する。　

Read more: https://srfl-lab.webnode.com/products/manuscript-of-quantum-theory-for-language-with-preface-

note-and-note-2-2003-2018/

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At this chapter, the most important concept is positive quantum and negative quantum.

Negative quantum changed to positive quantum by energy.

At the linear space, quantum changes positive to negative and also negative to positive.

By this model, on-off phenomena are mapped at the linear space's quanta's situation.

In the models, quantum is led from V.G.Drinfel'd and M.Jinbo's Quantum group originated in 1985.

Reference

JIMBO Michio. Quantum group and Yang-Baxter equation. Maruzen Shuppan. Tokyo. 2012

Method

Manuscript of Quantum Theory for Language written in spring 2003 was roughly designed at a days I was in

hospital by pneumonia half a month in October 2002, when I always saw the river and the mountains west

end of Tokyo. I was the very reviewing life time for my research work.

My poor study was restricted in a narrow field of Chinese classical linguistics mainly developed in the late

Qing dynasty the latter half of the 19th century,represented by DUAN Yucai, WANG Niansun, WANG Yingzhi,

my favourite WANG Guowei and so forth.

So I determined that my approach to language was only in it and it was the most intimate for me at that time

and probably herein after considering my tiny accumulation of study.

Next essay shortly showed the situation in 2002.

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1970s' dream, writing clear description on language universals by mathematics

From The Days of Ideogram

4. Time property in characters

In Autumn 2002 I got pneumonia and was hospitalized about 2 weeks, where I thought of 1970s' dream,

writing clear description on language universals by mathematics. The theme was as hard as ever. So, at the

bed I thought the basis of language from the side of Chinese character’s classical approach which had vast

heritage till Qing dynasty. I directed my attention to the character's figure which had compound meanings

containing time elements continuing from Yin dynasty's hieroglyphic characters left on bones and tortoise

carapaces some 2400 years ago. I thought that Chinese characters had containing time and its structure

could be written by geometric approach once I had abandoned for difficulty. After leaving hospital, I wrote a

paper titled On Time Property Inherent in Characters*3-1.

Read more: https://srfl-paper.webnode.com/news/the-days-of-ideogram/‌‌

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Quantum group

I think that language's foundation is in word.

Recently I started the new approach to word that has more simply at form and more wide-range-covered at

usage.

Trial paper is the next.

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Quantum Group Language

Word Indexed and Word Synthesized

TANAKA Akio

Word Synthesized is the word that is synthesized meanings in a word by arithmetic or algebraic geometrical

method.

For detailed refer to the next.

Arithmetic Geometry Language 2013

Algebraic Geometry Language 2014

Word Indexed is the word that has index in a word, by which meanings are separated in a word at waiting

situation. In a word meanings are combined by algebraic axioms and theorems starting from group theory.

Word Indexed seems to be more simply structure than Word Synthesized.

Word indexed basis is at the below.

Kac-Moody Lie Algebra Note 1 Kac-Moody Lie Algebra 2008

Kac-Moody Lie Algebra Note 2 Quantum Group 2008

The details of Word Indexed will be shown the papers after this.

Meanings contained in Word Indexed is deeply related with quantization and discreteness.

Refer to the next.

Floer Homology Language Note 7 Quantization of Language 2009

Floer Homology Language Note 8 Discreteness of Language 2009

All the basis of Word Indexed is generated at the next.

Manuscript of Quantum Theory for Language 2003

Reference

Kac-Moody Lie Algebra 2008

Theory 2003-2016 2018

Genealogical Tree of Sekinan's Paper 7th Edition 2015-2018

This paper is unfinished.

Read more: https://srfl-lab.webnode.com/news/quantum-group-language-word-indexed-and-word-

synthesized/

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Chinese belongs to the isolated language.

In Chinese one character has one meaning and becomes a word in classical usage. Modern Chinese has

many words that contain two or over two characters for one meaning, but basically almost all the characters

have still classical one-character-one-meaning usage at the root of language.

Shuowenjezi Zhu written by DUAN Yucai typically shows some 2,000 year history of characters and their

meanings.

Modern Chinese precisely said by Hanyu is one language of the over 50 languages officially recognized at the

research, and I only know several language's grammars by the field work by linguists.

National Minority Languages in China 2004

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National Minority Languages in China

Zhongguo Shaoshu Minzu Yuyan Jianzhi Congshu

Minzu Chubanshe

1 Buyi yu jianzhi YU Cuirong edited 1980

2 Dongbu yugu yu jianzhi ZHAONA Situ edited 1981

3 Dulong yu jianzhi SUN Hongkai edited 1982

4 Donsiang yu jianzhi LIU Zhaoxiong edted 1981

5 Gelaoyu jianzhi HE Jiashan edited 1983

6 Maonan yu jianzhi LIANG MIin edited 1980

7 Menggu yu jianzhi DAO Bu edited 1983

8 Li yu jianzhi OUYANG Jueya ZHENG Taiqing edited 1980

9 Pumi yu jianzhi LU Shaozun edited 1983

10 Qiang yu jianzhi SUN Hongkai edited 1981

11 Mulao yu jianzhi WANG Jin ZHENG Guoqiao edited 1980

12 Tai yu jianzhi YU Cuirong LUO Meizhen edited 1980

13 Tuzu yu jainzhi ZHAONA Situ edited 1981

14 Wa yu jianzhi Zhou Zhizhi YAN Qixiang edited 1984

15 Yaozu yuyan jianzhi MAO Zongwu MENG Chaoji ZHENG Zongze edited 1982

Guojia minwei minzu wenti 5 zhong congshu zhi 1

Zhongguo Shaoshu Minzu Yuyan Jianzhi Congshu

Minzu Chubanshe

16 Achang yu jianzhi DAI Qingxia SUI Zhichao edited 1985

17 Bulang yu jianzhi LI Daoyong NIE Xiizhen QIU Efeng edited 1986

18 Chaoxian yu jianzhi XUAN Dewu JIN Xiangyuan ZHAO Xi edited 1985

19 Cuonamen yu jianzhi LU Shaozun edited 1986

20 Deang yu jianzhi CHEN Xiangmu WANG Jingliu LEI Yongliang edited 1986

21 Elunchun yu jianzhi HU Zengyi edited 1986

22 Ewenke yu jianzhi HU Zengyi CHAO Ke edited 1986

23 Gaoshanzu yuyan jianzhi (Ameisi yu) HE Rufen ZENG Siqi TIAn Zhongshan LIN Dengxian edited

1986

24 Gaoshanzu yuyan jianzhi (Bunen yu) HE Rufen ZENG Siqi LI Wensu LIN Qingchun edited 1986

25 Gaoshanzu yuyan jianzhi (Peiwan yu) CHEN Kang MA rongsheng edited 1986

26 Heni yu jianzhi LI Yongsui WANG Ersong edited 1986

27 Hesake yu jianzhi GENG Shimin LI Zengxiang edited 1985

28 Heze yu jianzhi AN Jun edited 1986

29 Jing yu jianzhi OUYANG Jueya CHENG Fang YU Cuirong edited 1984

30 Jinuo yu jianzhi GAI Xingzhi edited 1986

31 Keerkezi yu jianzhi HU Shenhua edited 1986

32 Lahu yu jianzhi CHANG Hongen mainly edited

33 Lisu yu jianzhi CHU Lin MU Yuzhang GAI Xingzhi edited 1986

34 Luoba zu yuyian jianzhi (Bengni-Bogaer yu) OUYANG Jueya edited 1985

35 Naxi yu jianzhi HE Jiren JIANG Zhu yi edited 1985

36 Nu zu yuyan jianzhi (Nuban yu) SUN Hongkai LIU Lu edited 1986

37 Cangluo menba yu jianzhi ZHANG Jichuan edited 1986

38 Sala yu LIN Lianyu edited 1985

39 She yu jianzhi MAO zongwu MENG Chaoji edited 1986

40 Xibu yugu yu jianzhi CHEN Zongzhen LEI Xuanchun edited 1985

41 Tajike yu jianzhi GAO erjiang edited 1985

42Tayaer yu jianzhi CHEN Zongzhen YI Liqian edited 1986

43 Tujia yu jianzhi TIAN Desheng HE Tianzhen deng edited 1986

44 Weiwuer yu ZHAO Xiangru SHU Zhining edited 1985

45 Wuzubieke yu jianzhi CHENG Shiliang ABUTURE Heman edited 1987

46 Xibo yu jianzhi LI Shulan ZHONG Qian edited 1986

47 Yi yu jianzhi CHEN Shilin BIAN Shiming LI Xiuqing dited 1985

TOKYO

December 31, 2004

Sekinan Research Field of Language

Read more: https://srfl-collection.webnode.com/news/national-minority-languages-in-china/

Read more: https://geometrization-language.webnode.com/news/national-minority-languages-in-china/

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Xixiayu is a very interesting for me resembling the Hanyu and in the late 20th century the language was

deciphered by Japanese linguist NISHIDA Tatsuo.

The Days of Decipherment 2017

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The Days of Decipherment

TANAKA Akio

On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition A JOURNEY TO THE

IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth

days, so to say, the days of decipherment.

1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and

literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from

Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told at

Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered

the Linear B.

In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered by NISHIDA Tatsuo (1928-

2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki

narabini Seikago bunpou no kenkyuu in 1962.

In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team

developed largely.

In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the

Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the

Qing dynasty and I read them almost every day containing the comparison with the western linguistic results.

The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and

so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin were the most important for

me.

In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I

thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda,

Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was

too much difficult to read on. From the days the long and winding road began to mathematics and its

applicable study for language universals.

At the exhibition of ancient Greece I confirmed in particular that the stability of language was kept by letters

and characters from the Linear A and Linear B.

These language or character's situation especially of ideogram has become my study's foundation.

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These language or character's situation, especially of ideogram has become my study's foundation.

For ideogram, refer to the next papers.

....................................................................

Ideogram Paper 2005-2018

1. Ideogram 2005

2. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by

The British Museum 2012

3. Essence of Language 2016

4. The Days of Decipherment 2016

5. The Days of Ideogram 2017

6. The Days of Ideogram 2017

7. The comparison between 2003 and 2017

From Chinese character's meaning structure to Homological algebraic model of language universals

2017

8. Letter to Y. Of Broad Language 4th edition 2018

9. Determination of the concept, Broad Language 2018

10. Ars longa　Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum

of Fine Arts, Moscow 2018

Read more: https://geometrization-language.webnode.com/

Read more: https://srfl-lab.webnode.com/products/ideogram-paper-2005-2018/

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Quantum group 2

In 2008 I wrote on Quantum group at studying Kac-Moody-Lie Algebra.

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Kac-Moody Lie Algebra

Note 2

Quantum Group

TANAKA Akio

Base field K

Finite index set I

Square matrix that has elements by integer A = ( aij )i, j ∈ I

Matrix that satisfies the next is called Cartan matrix.

i, j ∈ I

(1) aii = 2

(2) aij ≤ 0 ( i ≠j )

(3) aij = 0 ⇔ aji = 0

Cartan matrix A = (aij)i, j ∈I

Family of positive rational number {di}i∈I

Arbitrary i, j∈I diaij = djaji

A is called symmetrizable.

Finite dimension vector space h

Linearly independent subset of h {hi}i∈I

Dual space of h h*= HomK (h, K )

Linearly independent subset of h* {αi} i∈I

Φ = {h, {hi}i∈I, {αi} i∈I }

Cartan matrix A = {αi(hi)} I, j∈I

Φis called fundamental root data of A that is Cartan matrix.

Symmetrizable Cartan matrix A = (aij)i, j ∈I

Fundamental root data {h, {hi}i∈I, {αi} i∈I }

E = αi ⊂h*

Family of positive rational number {di}i∈I

diaij = djaji

Symmetry bilinear form over E ( , ) : E×E → K ( (αi ,αj ) = diaij )

The form is called standard form.

n-dimensional Euclid space Rn

Linear independent vector v1, …, vn

Lattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )

Lattice of h hZ

From the upperv3, 4 and 5, the next three components are defined.

(Φ, ( , ), hZ )

When the components satisfy the next, they are called integer fundamental root data.

i ∈ I

(1) ∈ Z

(2) αi ( hz ) ⊂ Z

(3) ti := hi ∈ hz

Vector space over K A

Bilinear product over K A×A → A

When A is ring, it is called associative algebra.

Integer m

t similarity of m [m]t

[m]t = tm-t-m / t- t-1

Integer m, n m≧n≧0

Binomial coefficient (mn)

t similarity of m! [m]t! = [m]t! [m-1]t!...[1]t

t similarity of (mn) [mn]t = [m]t! / [n]t! [m-n]t!

[m0] = [mm]t = 1

Integer fundamental root data that has Cartan matrix A = ( aij )i, j ∈ I

Ψ = ((h, {hi}i∈I, {αi} i∈I ), ( , ), hz )

Generating set {Kh}h∈hz ∪{Ei, Fi}i∈I

Associative algebra U over K (q), that is defined the next relations, is called quantum group associated with

Ψ.

(1) khkh’ = kh+h’ ( h, h’∈hZ )

(2) k0 = 1

(3) KhEiK-h = qαi(h)Ei ( h∈hZ , i∈I )

(4) KhFiK-h = qαi(h)Fi ( h∈hZ , i∈I )

(5) Ei Fj – FjEi = ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )

(6) p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )

(7) p [1-aijp]qiFi1-aij-pFjFip = 0 ( i , j∈I , i ≠j )

[Note]

Parameter q in K is thinkable in connection with the concept of at the paper Place where Quantum of

Language exists / 27 /.

Refer to the next.

Place where Quantum of Language exists / Tokyo July 18, 2004

Tokyo February 9, 2008

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-lab.webnode.com/news/kac-moody-lie-algebra-note-2-quantum-group/

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In 2004 I wrote the paper named Place where Quantum of Language exists.

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Place where Quantum of Language Exists

TANAKA Akio

1 Quantum of language is the smallest unit of language.

2 Quantum of language moves linearly on the floor of language.

3 Linear movement is the properties of quantum.

4 Floor of language is on the space of language.

5 The space of language is two dimensions.

6 Two dimensions are horizontal and vertical.

7 Horizontal movement makes word, #1

8 Vertical movement makes sentence. #1

9 The space of language is electrical digitized place.

10 Chinese /jiao shi/ means classroom in English.

11 /Jiao/ is a quantum of language.

12 /Shi/ is a quantum of language.

13 /Jiao shi/ is a word.

14 /Jiao/ sends a quantum to /shi/ quantum.

15 /Shi/ quantum receives a quantum from /jiao/ quantum.

16 What sends quantum is called positive.

17 What receives quantum is called negative.

18 Quantum has positive energy in original condition.

19 Quantum changes negative in the situation of quanta set.

20 Quantum change occurs in two situations in general.

21 One situation is what quanta stand side by side on a floor and neighboring quanta connect well. #2

22 The other situation is what quanta change oneself by the non-use of quanta meaning in language

history progress. #2

23 Word has a positive- negative construction.

24 Positive-negative construction occurs on a floor.

25 Sentence has a positive-positive construction.

26 Positive-positive construction occurs on different floors.

27 The latter quantum transfers on a different floor. This transfer is called .†

28 Quantum has electrical energy which flows to the electrical zero level.

29 Electrical zero level is a sentence end where quantum of language ideally accord with the real world.

30 A floor of language is a non-branches electrical circuit.

31 Word is a non-branch circuit.

32 Sentence is a branch circuit.

33 The meaning of word and sentence is a compound system of electrical signals.

#1 Definition of word and sentence can be seen in the paper “Method of Linguistics” and other papers on

the site of Sekinan Research Field of Language /www.sekinan.org/.

#2 Definition of connect well can be seen in the paper of “Quantum Theory for Language Synopsis” and

other papers on the site of SRFL.

#3 Definition of sentence end can be seen in the paper “Mirror Theory”, “Mirror Language” and other

papers on the site of SRFL.

Tokyo July 18, 2004

Sekinan Research Field of Language

www.sekinan.org

Postscript

[Referential note November 9, 2007]

is related with the next papers on the concept.

________________________________

Brane Simplified Model 2 Distance Tokyo October 26, 2007

On Time Property Inherent in Characters Hakuba March 28, 2003

Quantum Theory for language Synopsis Tokyo January 15, 2004

Reversion Theory Tokyo September 27, 2004

Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO Tokyo October 2, 2004

Mirror Theory For the Structure of Prayer Dedicated to the Memory of CHINO Eiichi Tokyo June 5, 2004

Mirror Language Tokyo June 10, 2004

Guarantee of Language For LÉVI-STRAUSS Claude Tokyo June 12, 2004

Actual Language and Imaginary Language To LÉVI-STRAUSS Claude Tokyo September 23, 2004

________________________________

[Referential note February 9, 2008]

† Concept of /27/ is thinkable in connection with q> at the paper Kac-Moody Lie Algebra / Quantum Group /.

Refer to the next.

Kac-Moody Lie Algebra / Quantum Group / February 9, 2008

Read more: https://srfl-lab.webnode.com/news/place-where-quantum-of-language-exists/

.............................................................................................

At this paper, 23-33 is the most important for signal's intuitive image.

23 Word has a positive- negative construction.

24 Positive-negative construction occurs on a floor.

25 Sentence has a positive-positive construction.

26 Positive-positive construction occurs on different floors.

27 The latter quantum transfers on a different floor. This transfer is called .†

28 Quantum has electrical energy which flows to the electrical zero level.

29 Electrical zero level is a sentence end where quantum of language ideally accord with the real world.

30 A floor of language is a non-branches electrical circuit.

31 Word is a non-branch circuit.

32 Sentence is a branch circuit.

33 The meaning of word and sentence is a compound system of electrical signals.

........................................................................................

Quantum group 3

Quantum group is defined by JIMBO Michio as the following.

Definition of quantum group

Generating element: a, b, c, d

Relation: ba = qab, ca = qac

bd = q-1db, cd = q-1dc

bc = cb, ad - q-1bc = da - qbc = 1

Coproduct: Δa Δb a b a b

( ) = ( ) (χ) ( )

Δc Δd c d c d

Δa = a (x）a + b (x) c

JIMBO Michio

Bussei Kenkyu (1992), 57(5): 628-634

Symmetry

Quantum group would be the fundamental concept on symmetry.

JIMBO Michio early wrote at the end of the paper at Bussei Kenkyu 1992.

I ever wrote the symmetry of language several times, which seems to be one of the fundamental elements for

language.

Refer to the recent paper.

............................................................

The comparison between 2003 and 2017

From Chinese character's meaning structure to Homological algebraic model of language universals

Read more: https://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-

characters-meaning-structure-to-homological-algebraic-model-of-language-universals/

...............................................................

At the end of paper 2017, I wrote as the following, where I showed the early intuitive papers related with

symmetry or mirror. This concept has succeeded till now and a little developed a new direction towards

mathematical based concept especially of quantum group.

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 2004

Mirror Language 2004

Read more: https://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-

characters-meaning-structure-to-homological-algebraic-model-of-language-

universals/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=https%3A%2F

%2Fsrfl-paper.webnode.com%2Fnews%2Fthe-comparison-between-2003-and-2017-from-chinese-characters-

meaning-structure-to-homological-algebraic-model-of-language-universals%2F

................................................................

10.

Quantum

Language based on quantum emerged from thinking the simplest model for containing the finite essential

elements of language in summer 2003 at Hakuba, Nagano, Japan at the skirts of Japan Alps. Details are the

next.

Inspiration

The Time of Quantum

TANAKA Akio

In August 2003, I went to Hakuba in Nagano prefecture for the summer vacation with my family. At that time I

had been thinking on the form of language for which I wrote the paper, that connects with time inherent in

characters, in March 2003 also at Hakuba.

At night of August 23 in cottage, I casually saw the advertising paper of electric dictionary. The paper was

brought from the convenience store near the cottage in the evening. The dictionary on the paper was Seiko’s

English-Japanese dictionary that has additionally consultation for Chinese or French language with large

scale. I vaguely considered that after this dictionaries are necessarily taken these multi-lingual way.

At the time I suddenly realized that the form of language may be spherical style in which language contains

all the information in itself.That was rather satisfied solution for the tough problem of language that I had been

carrying in my life from my twenties.

I wrote the sketch-like paper of the theoretical approach after returning home of Tokyo. The paper was read at

the international symposium of UNESCO opened in winter 2003 at Nara. In the paper, the spherical substance

of language is seemed to be quantum in DELBRUCK’s image-like physical world. After 5 years from the

inspiration at summer of Hakuba, now I consider that spherical essence is manifold in infinite dimensional

world.

Now I also realize that the toughest problem of language is minutely solvable in mathematical approach that

has structurally definable terms.

Tokyo

September 29, 2008

Sekinan Research Field of Language

[January 23, 2012]

The title changed.

The former title is “From Quantum to Manifold”.

[Postscript. January 25,2012]

On quantization of Language.

Refer to the next.

Quantization of Language

Read more: https://srfl-collection.webnode.com/news/inspiration-the-time-of-quantum-2008-2012/

11.

Symmetry 2

Symmetry seems to be related with two elements of language universals, distance and time.

Refer to the next.

Distance Theory Algebraically Supplemented Brane Simplified Model 1 Bend 2007

...............................................................................

Distance Theory Algebraically Supplemented

Brane Simplified Model

Bend

TANAKA Akio

Language is expressed by< a pair of quanta> that consists of and .

Quantum and anti-quantum have reverse direction.

Quantum and anti-quantum are in the shape of strings that are separated parallel longitude L apart.

Quantum and anti-quantum are in <AdS5 ( 5-dimensional anti-deSitter ) space>.

Left side of quantum and anti-quantum is on .

Quantum starts from ra in AdS5 space and returns rb in AdS5 space.

ra and rb are equal longitude from D3 brane.

of D3 brane in AdS5 space gives quantum and anti-quantum bending near r = 0 that is the location of D3

brane.

Quantum’s nearest point to D3 brane is rz.

rz’ is 1/2 of the longitude from ra to rb.

Sketch is below.

At the paper Spacetime Symmetry and Escalator Brane in Escalator Language Theory, language goes from ra

to rz and in reverse movement to rb.

At the paper Actual Language and Imaginary Language, is from ra to rz and is from rz to rb.

We see real language that is upper side of rz-rz’. Imaginary language is hidden under side of rz-rz’ in our life.

At the paper Mirror Language, imaginary language is mirror language of real language.

Distance of language is regarded as the longitude from ra ( or rb ) to D3 brane in AdS5 space.

[Reference]

Escalator Language Theory / 2 Turning Point of Time / Tokyo December 22, 2006

Tokyo October 17, 2007

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-

simplified-model-continuation-of-escalator-language-theory-1-bend-2007/

...............................................................

In 2006 I wrote Escalator Language series.

Paper, Turning Point of Time is a intuitive paper for the three papers of Distance Theory Algebraically

Supplemented 2007.

........................................................................

Escalator Language Theory

Turning Point of Time

For SINGER Isaac Bashevis, WHEN SHLEMIEL WENT TO WARSAW AND OTHER STORIES

TANAKA Akio

1 Time has symmetry.

2 Time consists of the two, real time and imaginary time.

3 Real time is appeared time.

4 Imaginary time is hidden time.

5 Time is recognized by square.

Unit of real time is expressed by t2 = 1.

Unit of imaginary time is expressed by t2 = -1.

6 Real time makes future.

Imaginary time makes past.

Present is expressed by t2 = 0.

7 Time is on escalator belt.

8 Escalator belt has one Turing point of time.

9 Turning point of time is expressed by t2 + x2 + y2 + z2 = r2. Here r is radius of turning point.

10 Turning point of time is smooth and continuously differentiable.

11 Escalator belt has not self-intersection.

12 When time passes, real time and imaginary time are counted.

Real time is visible. Imaginary time is invisible.

13 The belt is in bulky space.

14 Real time is at real number’s coordinate in the space.

Imaginary time is at imaginary number’s coordinate in the space.

15 Real time and imaginary time is symmetrical for coordinate axis.

Tokyo December 22, 2006

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-collection.webnode.com/news/escalator-language-theory-turning-point-of-time-2006/

.......................................................................................

12.

Distance

Distance is one of the most important elements of my language model of language universals. For this

element algebraic approach seems to be clearer description to the model. Refer to the next paper.

Distance Theory Algebraically Supplemented

Brane Simplified Model

Distance

2007

......................................................................................

Distance Theory Algebraically Supplemented

Brane Simplified Model Escalator Language Theory>

Distance

Direct Succession of Distance Theory

TANAKA Akio

Metric model of 5-dimensional spacetime is expressed below from Randall and Sundrum (1999).

ds2 = e2U(y)ηmndxmdxn + dy2

Branes exist at y = 0 and y = d.

Our world is regarded as brane y = 0.

U(y) is called .

Using of circle ( radius R )’s identification, y is expressed by that scales from 0 to ±πR.

Distance is defined in .

According to , of is measured in bulk spacetime of 5 dimensional Anti-deSitter space.

Distance in is expressed from <y = –πR> to <y = 0> and from <y = 0> to <y = +πR>.

Now “from <y = –πR> to <y = 0>” is called and “from <y = 0> to <y = +πR>” is called .

Values of are same at and .

In (abbreviation; DTAS), word is regarded by ’s value.

Word has distance at and .

Now distance at is called distance of and distance at is called distance of .

[References]

2.1.3 Distance Theory

2.1.4 Reversion Theory

2.2.1 Prague Theory

2.3 Warp Theory

2.4 Time Theory

4.3.1 Guarantee of Language

4.3.2 Place where Quantum of Language Exists

4.3.3 Actual Language and Imaginary Language

4.5.1 Mirror Language

4.5.2 Mirror Theory

[AT11] Distance and Time Language Multi-Time Conjecture 3 5th Time for KARCEVSKIJ

[ATT3] Enlarged Distance Theory

[ATT4] Opened Time and Closed Time

1 Deep Fissure between Word and Sentence

2 From Cut and Glue Dimension to Krull Dimension 8th For KARCEVSKIJ Sergej

Tokyo October 26, 2007

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-

simplified-model-2-distance-direct-succession-of-distance-theory-2007/

........................................................................................

Before algebraic approach for distance, I early wrote the more intuitive paper for distance, its name is

Distance Theory in 2004.

Refer to the next.

Distance Theory 2004

........................................................................................

Distance Theory

TANAKA Akio

Distance theory is an extension of Quantum Theory for Language.

Distance theory is an extension of strength rule in Quantum Theory for Language.

Distance theory is considered for the purpose of the guarantee to language.

What quanta of language propel to the end of the sentence is for the purpose of the guarantee to language, in

which quanta of language finally unite the real world in the end of propelling.

The guarantee to the inherent signification of indicator in quantum of language is quantified by the distance

which starts from the real world to the quantum of language.

A quantum consists of indicators.

An indicator has a signification and a period inherently.

The structure of quantum is indicated in Quantum Theory for Language.

An inherent signification is an element in a quantum.

An inherent time is an element in a quantum.

There are two types of elements, significant and periodical.

Element is defined.

A significant element gets a signification from the real world.

A periodical element gets a time from the real world.

An indicator gets a meaning and a period from elements.

An element emerges from the real world to the language world.

An indicator gets power from the elements in the language world.

A quantum moves in the language world by the power of indicators.

An element emerges to the language world, because each element has immanent perceptible area which

works upon visual sensation and auditory sensation of the human beings.

An indicator gets energy in the language world, because each indicator has a tendency which will approach

and finally coincide with the real world.

This continuous tendency guarantees the trust in language for the human beings.

A quantum moves in the language world toward the real world.

A quantum is not guaranteed in the situation of cessation.

A quantum is guaranteed by the connection to the real world.

Therefore a quantum propels to the real world.

Indicators make meaning and connection rule in a quantum, both are derived from significant and periodical

elements in an indicator.

Meaning is guaranteed by the tendency of coincidence with the real world.

Guarantee of the meaning is reduced by the remoteness of distance from the real world.

Connection rule is decided by periodical elements in indicators.

Details are indicated in Quantum Theory for Language.

Signification in an indicator and meaning in a quantum once emerged are occasionally transformed or

expanded in the language world.

This alteration is called multiplication.

Multiplication is defined.

Multiplication generally occurs by the addition of signification in an indicator.

But multiplication in meaning of a quantum sometimes occurs without any addition oneself.

Multiplication in a quantum without addition occurs by situational transition in the language world.

Situational transition in a quantum is caused by difference of distance from the real world.

Difference of distance at a quantum is a proceeding of abstract thinking in human beings.

A quantum of language itself becomes in the language world.

Word is defined.

Therefore each word has a distance toward the real world.

A distance immanent in a word does not emerge itself.

Distance emerges in the linear situation of words gathering.

This situation is called .

Sentence is defined.

Therefore sentence is an emergence of distance in words gathering.

Words form a line, thereafter one arrangement is determined.

Sentence is realized in our world.

In Chinese language, /lai/ come has a larger distance than /liao/completion.

Words are arranged from the end of a sentence, according to the own- possessing- distance.

Therefore /lai le/ having come is realized.

Tokyo

May 5, 2004

For the memory of Kusatsu Shiranesan March 30, 2004

Sekinan Research Field of Language

Postscript

[Referential note / October 14, 2007]

early work.>

On Time Property Inherent in Characters Hakuba March 28, 2003

Quantum Theory for Language Synopsis Tokyo January 15, 2004

Reversion Theory Tokyo September 27, 2004

Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO Tokyo October 2, 2004

Mirror Theory For the Structure of Prayer Dedicated to the Memory of CHINO Eiichi Tokyo June 5, 2004

Mirror Language Tokyo June 10, 2004

Guarantee of Language For LÉVI-STRAUSS Claude Tokyo June 12, 2004

Actual Language and Imaginary Language To LÉVI-STRAUSS Claude Tokyo September 23, 2004

[Referential note / December 25, 2007]

Algebraic Linguistics / From September 11, 2007

Distance Theory Algebraically Supplemented / From October 4, 2007

Noncommutative Distance Theory / From November 30. 2007

[Referential note / July 7, 2008]

For KARCEVSKIJ Sergej

Invitation by Theme-Time / Data first arranged at Tokyo January 6, 2008

Invitation by Theme-Distance / Data first arranged at Tokyo February 20, 2008

Holomorphic Meaning Theory / From Tokyo June 15, 2008

Stochastic Meaning Theory / From Tokyo June 22, 2008

[Referential note / December 7, 2008]

Distance of Word / Tokyo November 30, 2008 / sekinan.wiki.zoho.com

Reflection of Word / Tokyo December 7, 2008 / sekinan.wiki.zoho.com

Mirror Theory Group / Tokyo December 9, 2008

[Referential note / December 22, 2008]

Cell Theory / From Cell to Manifold / Tokyo June 2, 2007

Stochastic Meaning Theory 3 / Place of Meaning / Tokyo July 11, 2008

Stochastic Meaning Theory 2 / Period of Meaning / Tokyo June 27, 2008

Warp Theory

Quantum Warp Theory / Warp

Warp Theory Group

Quantum Warp Theory Group

Amplitude of Meaning Minimum / sekinan.wiki.zoho.com

Complex Manifold Deformation Theory / sekinan.wiki.zoho.com

[Referential note / December 23, 2008]

Time of Word / sekinan.wiki.zoho.com

[Referential note / January 1, 2009]

Orbit of Word / sekinan.wiki.zoho.com

[Referential note / January 31, 2009]

Word Problem of Word-hyperbolic Group / sekinan.wiki.zoho.com

Read more: https://geometrization-language.webnode.com/products/distance-theory/

Read more: https://srfl-collection.webnode.com/news/distance-theory-2004/

................................................................................

13.

Distance 2

Hoph algebra

The upper section 12.'s algebraic defined distance is also related with Hoph algebra.

Refer to the next.

Distance Theory Algebraically Supplemented

Brane Simplified Model

S3 and Hoph Map

......................................................................

Distance Theory Algebraically Supplemented

Brane Simplified Model

S3 and Hoph Map

TANAKA Akio

From RS model, and are abstracted.

Refer to the next.

Distance Theory Algebraically Supplemented / 2 Distance / Tokyo October 26, 2007

s from to at and are both seemed as circle S1.

3-dimensional sphere S3 = { ( x1, y1, x2, y2 ) | x12 + x22 + y12 + y22 = 1 }

Point of S3 ( x1, y1, x2, y2 )

( x1, y1 ) ≠ ( 0, 0 ) π ( x1, y1, x2, y2 ) = ( x2 + i y2 ) / ( x1 + i y1 ) ∈ C

( x1, y1 ) = ( 0, 0 ) π ( x1, y1, x2, y2 ) = ∞

Hopf map π : S3 → Riemann Sphere, C ∪ {∞}

Inverse image of a point p π -1 (p) is S1.

Hoph map is fiber bundle that derived from fiber S1.

On fiber bundle, refer to the next.

Symmetry Flow Language / Leaf of Language / Tokyo May 11, 2007

Now at is identificated as S1.

Two points a ( xa, ya ), b (xb, yb ) at Gauss plane is objected to Riemann sphere.

At Riemann Sphere, two points a, b is marked by a’ ( x’a, y’a ), b’ (x’b, y’b ) .

On Riemann sphere, refer to the next.

Symmetry Flow Language / Simplex, Simplicial Complex and polyhedron / Tokyo May 17, 2007

Symmetry Flow Language / Meaning Variation and Time Shift in word as Homotogy / Tokyo May 17, 2007

Point of S3 is marked by ( x’a, y’a , x’b, y’b ) .

On S3, refer to the next.

Symmetry Flow Language 2 / Time Shift of Meaning in Moduli Space / Tokyo May 23, 2007

at is also marked on S3.

and are algebraically considered by S3.

Tokyo November 12, 2007

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-

simplified-model-3-s3-and-hoph-map-2007/

...............................................................................

Symmetry 3

On symmetry I wrote Symmetry Flow Language and Symmetry Flow language 2 in 2007.

Contents are the next.

Symmetry Flow Language

On Symmetry of Language and Time

1 Premise for Symmetry Flow in Language

2 Riemannian Metric, Flow and Entropy

3 Leaf of Language

Pourparlers>

4 Homology on Language

5 Simplex, Simplicial Complex and Polyhedron

6 Meaning Variation and Time Shift in Word As Homotopy

Symmetry Flow Language 2

On Symmetry of Language and Time 2

1 Boundary, Deformation and Torus as Language

2 Time Shift of Meaning in Moduli Space

...........................................................................

Related with Hoph algebra, next papers are referential.

Symmetry Flow Language

5 Simplex, Simplicial Complex and Polyhedron

6 Meaning Variation and Time Shift in Word As Homotopy

Symmetry Flow Language 2

2 Time Shift of Meaning in Moduli Space

Texts are the next.

..........................................................................

Symmetry Flow Language

Simplex, Simplicial Complex and Polyhedron

TANAKA Akio

1 Language is given by homology group in topological space.

Homology group is given by module’s chain complex.

{Ck}k=0n, {∂k } k=1n

Ck is module.

∂k: Ck → Ck—1 is homomorphism.

∂k-1o∂k = 0 It is meant that set’s boundary’s boundary becomes null set.

2 Meaning is divided by boundary.

3 Word is given by simplex.

4 Simplex has m+1 vertex and m-dimension. It is called m-simplex.

5 Simplex has orientation that is given by permutation.

6 Orientation gives sentence to vector that consists of words.

7 Vector’s element is given by simplex’s vertex.

8 Sentence is given by simplicial complex.

9 Language is given by polyhedron that consists of union of all simplexes.

10 Polyhedron has triangulation.

11 Sphere’s triangulation is given tetrahedron by homeomorphism.

12 Riemann sphere obtains information from Gauss plane.

Refer to the following papers’ group.

Aurora Theory

Aurora Time Theory

13 Minimum model of Symmetry Flow Language is testified by tetrahedron being led from polyhedron’s

triangulation.

Tokyo May 17, 2007

Sekinan Research Field of Language

Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-simplex-simplicial-complex-

and-polyhedron/

Symmetry Flow Language

Meaning Variation and Time Shift in Word as Homotopy

For WANG Guowei and KARCEVSKIJ Sergej

TANAKA Akio

1< Meaning> in word is given by homotopy.

2< Time> in word is given by continuous map of homotopy.

3 Time is expressed by t of path α(t).

4 In path from x0 to x1 of closed interval [0, 1] , α(0) is called initial point and α(1) is called terminal point.

5< Time shift> in word given by interval of path

5 When path has α(0)= α(1) = x0, it is called loop. In this case, initial point is called base point.

6 Initial point or base point makes

in word.

7< Meaning variation> is generated from of path α(t).

Refer to the following paper.

On Time Property Inherent in Characters Hakuba March 28, 2003

8 Loop has group’s structure that is called fundamental group.

9 In homotopy, 3 laws are secured. (1) Reflection law (2) Symmetry law (3)transition law

10 Laws in homotopy secures construction of word’s meaning.

11 Loop’s equivalence class makes homotopy class.

12 Homotopy class [α] and [β] has product. [α] * [β] = [α * β]

13 Product makes in word.

14 Now 2-dimensional square I2 is presented. Continuous map α to space X is given by the following.

α : I2 →X

α is called 2-loop that expresses dimensional extension of loop concept.

15 2-dimensional sphere is 2-loop.

16 Riemann sphere has information from Gauss plane.

Refer to the following papers’ group.

Aurora Theory

Aurora Time Theory

17 Meaning variation and concomitant time shift in Symmetry Flow Language are testified by 2-loop sphere.

Tokyo May 17, 2007

Sekinan Research Field of Language

Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-meaning-variation-and-time-

shift-in-word-as-homotopy-for-wang-guowei-and-karcevskij-sergej/

Symmetry Flow Language 2

Time Shift of Meaning in Moduli Space

7th for KARCEVSKIJ Sergej

TANAKA Akio

1 Word has variation of meaning in accordance with time shift in space.

Refer to the following papers.

Language and Spacetime Structure of Word Tokyo April 6, 2007

Language and Spacetime Description of Meaning Tokyo April 16, 2007

Language and Spacetime Shift of Time Tokyo April 20, 2007

Symmetry Flow Language Meaning Variation and Time Shift in Word as Homotopy Tokyo May 17,

2007

2 Space that is deformed successively is described by parameter that is called moduli.

3 Set M consists of all of moduli.

4 Moduli space M (M) is presented for variation of word’s meaning.

5 Parameter t is presented for time shift of meaning in word.

6 Calabi-Yau manifold K has two moduli that are deformation of complex structure and Kähler manifold.

Moduli have symmetry that is called Mirror symmetry.

7 K’s Ricci tensor is the following.

Rij¯ = 0 i is regular coordinate. j¯ is non-regular coordinate.

Refer to the following paper.

Language and Spacetime Construction of Spacetime Especially on Transformation with Boundary

for Dimensions Tokyo April 24, 2007

8 Replaced two moduli in Calabi-Yau manifold K is called reflection Calabi-Yau manifold K~.

Refer to the following paper.

Mirror Language Tokyo June 10, 2006

9 In K, Kähler manifold, n-dimensional toric manifold Pn is presented.

Complex torus of Kähler’s form ω described by polar coordinates is the following.

ω = ∑i dzi ∧ dz⁻i = ∑i d|zi|2 ∧ dθi

P1 with line bundle’s direct sum becomes resolved conifold.

10 Conifold’s toric graph has line segment that has the longitude | z1 |2+ | z2 |2 = r. r is parameter of conifold.

11 Parameter r becomes parameter t that is described as complex.

12 Resolved conifold that has parameter t = 0 and is deformed becomes deformed conifold that has S3.

13 Parameter t of deformed conifold S3 means time of word’s meaning variation in language.

14 Deformed conifold S3 means word in language.

15 P1× P1 becomes square that is connected by world sheets.

16 P1× P1 means sentence in language.

Refer to the following paper.

Cube Theory Structure of Cube Tokyo March 25, 2006

Cube Theory Cube Word Hakuba April 1, 2006

Tokyo May 23, 2007

Sekinan Research Field of Language

Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-2-time-shift-of-meaning-in-

moduli-space-7th-for-karcevskij-sergej/

.............................................................................................................

15.

Derived category　Time conjecture of language

At language universals, distance and time are the kernel concepts for my language models.

Measure of distance is deeply related with time which is transcendental unit still now.

Category theory is probably very useful for the relation between distance and time.

For these concepts, I ever wrote several trial papers. Refer to the next one.

Language and Spacetime

Shift of Time

From SAPIR Edward to KAWAMATA Yujiro

TANAKA Akio

1 Language is expressed as structure of spacetime.

2 Spacetime is expressed as manifold.

3 Affine algebraic variety is selected for description of spacetime.

Algebraic variety is pasted together from affine algebraic variety.

Affine algebraic variety is irreducible affine algebraic set.

Affine algebraic set is the set that consists of common zero point of finite polynominal

Polynominal is in n-dimensional complex affine space.

4 Now n-dimensional projective space P n is presented.

C n+1 \ {O} / ~

O is the coordinate’s origin of complex affine space.

~ is mathematical equivalence on elements of set.

5 Projective space P n is covered by n+1 affine space.

6 Now abelian category and derived category are presented.

Abelian category and algebraic variety is placed together.

Derived category is abelian category’s coherent sheaf’s complex that is composition of successive

arrows becomes 0.

7 From derived category, distinguished triangle is presented.

8 Here time conjecture of language is presented.

(1)Distinguished triangle makes the model for shift of time on language.

(2)Time on language is closed, successive and circular in word.

Circulation is worked between starting point and ending point of word.

The origin of shift of time is derived from the following.

On Time Property Inherent in Characters Hakuba March 28, 2003

The concept of time in language is taught from the following.

SAPIR Edward LANGUAGE An Introduction to the Study of Speech Harcout, Brace & Co. Inc

Special thanks to KAWAMATA Yujiro for the mathematical approach on language research, especially from

the following.

KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1, January 2006

Tokyo April 20, 2007

Sekinan Research Field of Language

www.sekinan.org

Read more: https://srfl-collection.webnode.com/news/language-and-spacetime-shift-of-time-from-sapir-

edward-to-kawamata-yujiro-2007/

Read more: https://srfl-collection.webnode.com/news/what-is-signal-a-mathematical-model-of-nerve-22-

december-2018/

-----------------------------------------------------------

At this paper, now I extract the next phrases.

Derived category is abelian category’s coherent sheaf’s complex that is composition of successive

arrows becomes 0.

7 From derived category, distinguished triangle is presented.

8 Here time conjecture of language is presented.

(1)Distinguished triangle makes the model for shift of time on language.

(2)Time on language is closed, successive and circular in word.

Circulation is worked between starting point and ending point of word.

Paper group, Language and Spacetime is especially focused at time in space.

Every paper of Language and Spacetime, Symmetry Flow Language and Symmetry Flow Language 2

can be seen at the at the site, SRFL Paper Top pager's right column's Paper 2003-2007 .

Paper 2003-2007

Symmetry Flow Language 2 Time Shift of Meaning in Moduli Space 7th for

KARCEVSKIJ Sergej

Symmetry Flow Language 2 Boundary, Deformation and Torus as Language

Symmetry Flow Language 2 Contents

Symmetry Flow Language Meaning Variation and Time Shift in Word as

Homotopy For WANG Guowei and KARCEVSKIJ Sergej

Symmetry Flow Language Simplex, Simplicial Complex and Polyhedron

Symmetry Flow Language Homology on Language

Symmetry Flow Language Riemannian Metric, Flow and Entropy

Symmetry Flow Language Premise for Symmetry Flow in Language

Symmetry Flow Language Contents

Language and Spacetime Time Flow in Word For KOHARI Akihiro and His

Time

Language and Spacetime Stability of Language

Language and Spacetime Construction of Spacetime Especially on

Transformation with Boundary for Dimensions

Language and Spacetime Shift of Time From SAPIR Edward to KAWAMATA

Yujiro

Language and Spacetime Description of Meaning 6th Time For KARCEVSKIJ

Sergej

Language and Spacetime Generation of Sentence For WANG Guowei and

CELAN Paul

Language and Spacetime Structure of Word From KARCEVSKIJ to

MACLANE

Language and Spacetime Word Containing Time and 4 Dimensional Sphere

Dedicated to MAC LANE Saunders

Language and Spacetime Language Definition for the Child who Lost the

World

Language and Spacetime Contents

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Language and Spacetime Contents

Language and Spacetime

Relation between Language and Time

1 Language Definition for the Child who Lost the World

2 Word Containing Time and 4 Dimensional Sphere

3 Structure of Word

4 Generation of Sentence

5 Description of Meaning

<6th Time for KARCEVSKIJ Sergej>

6 Shift of Time

7 Construction of Spacetime

Especially on Transformation with boundary for Dimensions

8 Stability of Language

9 Time Flow in Word

Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-contents/

Papers at Time and Spacetime, next two papers are also important to time concepts for me.

Especially No.2 paper is dedicated to Mac Lane for his Category Theory's work.

No.9 Paper is dedicated Kohari Akihiko and his days for his early death at unhappy accident in 1970s.

2 Word Containing Time and 4 Dimensional Sphere

9 Time Flow in Word

Two papers text are the next.

Language and Spacetime Word Containing Time and 4

Dimensional Sphere Dedicated to MAC LANE Saunders

Language and Spacetime

Word Containing Time and 4 Dimensional Sphere

Dedicated to MAC LANE Saunders

TANAKA Akio

1 Word contains time inside.

Refer to the following paper.

On Time Property Inherent in Characters 1 Generation in Characters Hakuba March 28, 2003

2 Word has construction that is expressed by category.

On category, refer to Categories for the Working Mathematicians by Saunders Mac Lane, 1998 Springer-

Verlag New York, LLC.

3 Time has starting point and ending point in word.

4 Meaning has starting point and ending point in word.

5 Generally word shifts meaning from starting point to ending point by time.

Refer to the following paper.

On Time Property Inherent in Characters 2 Function of Characters Hakuba March 28, 2003

6 Primitive word does not shift time and stays in the same point.

7 In category, the names of language are called by following terms.

Meaning is called object.

Shift is called arrow.

Starting point is called domain or source.

Ending point is called codomain or target.

No shift or stay is called identity.

Arrow can be composed. The composed arrow is called composite.

In category two axioms are presupposed.

One is associativity.

The other is unit law.

These terms are all complied with above quoted Mac Lane.

8 Word with starting point is expressed on Gauss plane.

9 Word with ending point is also expressed on Gauss plane.

10 Shift time from starting point to ending point is expressed by coordinates’ transference.

11 Here Riemann sphere is putted with having the same origin to Gauss plane.

12 Word with starting point is projected toward the North Pole of Riemann sphere.

13 Word with starting point has coordinates ws (xs ys, zs) on Riemann sphere’s surface.

Refer to the following paper.

Aurora and Riemann Sphere Tokyo October 2 – October 3, 2006

Aurora Plane Tokyo October 14, 2006

Word, phrase and Sentence Tokyo October 25, 2006

14 Word with ending point has also coordinates we (xe, ye, ze) on Riemann sphere.

15 Here 4 dimensional sphere is putted with having the same origin to Riemann sphere.

16 A indefinite strait line determined by coordinates ws and coordinates we makes coordinates wt (xt, yt, zt, tt)

on 4 dimensional sphere’s surface.

17 Coordinates wt on 4 dimensional sphere’s surface is uniquely reflected in word with starting point and word

with ending point.

18 Word containing time is uniquely expressed on 4 dimensional sphere’s surface.

Tokyo April 5, 2007

Sekinan Research Field of Language

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dimensional-sphere-dedicated-to-mac-lane-saunders/

Language and Spacetime Time Flow in Word For

KOHARI Akihiro and His Time

Language and Spacetime

Time Flow in Word

For KOHARI Akihiro and His Time

TANAKA Akio

Word is expressed by phase space in the situation on dynamical system.

Phase space M has a point x.

Continuous time t is expressed by group R that consists of real number.

Homomorphism φt(x)expresses the system.

φs+t(x) =φs (φt(x)), φ0 (x) = x

In thermodynamics, equilibrium is presented.

Equilibrium situation is expressed by (U, V, n).

U is energy in the system. V is volume. n is material.

Here new equilibrium is expressed by (U’, V’, n).

Now a category is presented.

(U, V, n) →f (U’, V’, n)

f is function of entropy.

Here (U, v, n) is expressed by P. (U’, V’, n) is expressed by P’.

The situation of equilibrium is expressed by the following.

f : P → P’

The situation of equilibrium is rewritten by phase space.

Each situation of equilibrium is expressed by a point x.

After time t, point x and x’ is presented by the following.

φ : φs(x) →φs+t(x)

Now equilibrium system is expressed by {φt} that is called flow.

Here phase space M can take tangent vector X.

Point x has tangent vector Xx = dφt(x)/dtt=0

The flow has solution as equation φt(x)/dt = Xφt(x)

Here set {φt(x) | t∈R } is presented. The set is called orbit.

In word, meaning is expressed by flow and time is expressed by orbit.

Tokyo May 3, 2007

Sekinan Research Field of Language

Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-time-flow-in-word-for-kohari-

akihiro-and-his-time/

-------------------------------------------------------------------------------------------------------------------------------

What is signal? A mathematical model of nerve Preparation 1-15

is over

29 December 2018

-------------------------------------------------------------------------------------------------------------------------------

SRFL Paper

Tokyo

29 December 2018

--------------------------------------------------------------------------------------------------------------------------------

Preparation 2

Energy

Generation

From where language is born?

Signal generates language as the Morse code generates letters and language.

But language does not generate signal code because language has not electric energy.

It maybe that signal is the root of language.Truly or not?

What is signal?

What is generation?

I once wrote a trial paper, Generation Theorem in 2008.

Text is the below.

.....................................................................................................

von Neumann Algebra 2

Note

Generation Theorem

TANAKA Akio

[Main Theorem]

Commutative von Neumann Algebra N is generated by only one self-adjoint operator.

[Proof outline]

N is generated by countable {An}.

An = *An

Spectrum deconstruction An = ∫1-1 λdEλ(n)

C*algebra that is generated by set { Eλ(n) ; λ∈Q∩[-1, 1], n∈N} A

A’’ = N

A is commutative.

I∈A

Existence of compact Hausdorff space Ω = Sp(A )

A = C(Ω)

Element corresponded with f∈C(Ω) A∈A

N is generated by A.

[Index of Terms]

|A|Ⅲ7-5

|| . ||Ⅱ2-2

||x||Ⅱ2-2

<x, y>Ⅱ2-1

*algebraⅡ3-4

*homomorphismⅡ3-4

*isomorphismⅡ3-4

*subalgebraⅡ3-4

adjoint spaceⅠ12

algebraⅠ8

axiom of infinityⅠ1-8

axiom of power setⅠ1-4

axiom of regularityⅠ1-10

axiom of separationⅠ1-6

axiom of sumⅠ1-5

B ( H )Ⅱ3-3

Banach algebraⅡ2-6

Banach spaceⅡ2-3

Banach* algebraⅡ2-6

Banach-Alaoglu theoremⅡ5

basis of neighbor hoodsⅠ4

bicommutantⅡ6-2

bijectiveⅡ7-1

binary relationⅡ7-2

boundedⅡ3-3

bounded linear operatorⅡ3-3

bounded linear operator, B ( H )Ⅱ3-3

C* algebraⅡ2-8

cardinal numberⅡ7-3

cardinality, |A|Ⅱ7-5

characterⅡ3-6

character space (spectrum space), Sp( )Ⅱ3-6

closed setⅠ2-2

commutantⅡ6-2

compactⅠ3-2

complementⅠ1-3

completeⅡ2-3

countable setⅡ7-6

countable infinite setⅡ7-6

coveringⅠ3-1

commutantⅡ6-2

D ( )Ⅱ3-2

denseⅠ9

dom( )Ⅱ3-2

domain, D ( ), dom( )Ⅱ3-2

empty setⅠ1-9

equal distance operatorⅡ4-1

equipotentⅢ7-1

faithfulⅡ3-4

Gerfand representationⅡ3-7

Gerfand-Naimark theoremⅡ4

HⅡ3-1

Hausdorff spaceⅠ5

Hilbert spaceⅡ3-1

homomorphismⅡ3-4

idempotent elementⅡ9-1

identity elementⅡ9-1

identity operatorⅡ6-1

injectiveⅢ7-1

inner productⅡ2-1

inner spaceⅠ6

involution*Ⅰ10

linear functionalⅡ5-2

linear operatorⅡ3-2

linear spaceⅠ6

linear topological spaceⅠ11

locally compactⅠ3-2

locally vertexⅠ11

NⅢ3-8

N1Ⅲ3-8

neighborhoodⅠ4

normⅡ2-2

normⅡ3-3

norm algebraⅡ5

norm spaceⅡ2-2

normalⅡ2-4

normalⅡ3-4

open coveringⅠ3-2

open setⅠ2-2

operatorⅡ3-2

ordinal numberⅡ7-3

productⅠ8

product setⅡ7-2

r( )Ⅱ2

R ( )Ⅱ3-2

ran( )Ⅱ3-2

range, R ( ), ran( )Ⅱ3-2

reflectiveⅠ12

relationⅢ7-2

representationⅡ3-5

ringⅠ7

Schwarz’s inequalityⅡ2-2

self-adjointⅡ3-4

separableⅡ7-7

setⅠ7

spectrum radius r( )Ⅱ2

Stone-Weierstrass theoremⅡ1

subalgebraⅠ8

subcoveringⅠ3-1

subringⅠ7

subsetⅠ1-3

subspaceⅠ2-3

subtopological spaceⅠ2-3

surjectiveⅢ7-1

system of neighborhoodsⅠ4

τs topologyⅡ7-9

τw topologyⅡ7-9

the second adjoint spaceⅠ12

topological spaceⅠ2-2

topologyⅠ2-1

total order in strict senseⅡ7-3

ultra-weak topologyⅢ6-4

unit sphereⅡ5-1

unitaryⅡ3-4

vertex setⅡ3-3

von Neumann algebraⅡ6-3

weak topologyⅡ5-3

weak * topologyⅡ5-3

zero elementⅡ9-1

[Explanation of indispensable theorems for main theorem]

ⅠPreparation

<0 Formula>

0-1 Quantifier

(i) Logic quantifier ┐ ⋀ ⋁ → ∀ ∃

(ii) Equality quantifier =

(iii) Variant term quantifier

(iiii) Bracket [ ]

(v) Constant term quantifier

(vi) Functional quantifier

(vii) Predicate quantifier

(viii) Bracket ( )

(viiii) Comma ,

0-2 Term defined by induction

0-3 Formula defined by induction

<1 Set>

1-1 Axiom of extensionality ∀x∀y[∀z∈x↔z∈y]→x=y.

1-2 Set a, b

1-3 a is subset of b. ∀x[x∈a→x∈b].Notation is a⊂b. b-a = {x∈b ; x∉a} is complement of a.

1-4 Axiom of power set ∀x∃y∀z[z∈y↔z⊂x]. Notation is P (a).

1-5 Axiom of sum ∀x∃y∀z[z∈y↔∃w[z∈w∧w∈x]]. Notation is ∪a.

1-6 Axiom of separation x, t= (t1, …, tn), formula φ(x, t) ∀x∀t∃y∀z[z∈y↔z∈x∧φ(x, t)].

1-7 Proposition of intersection {x∈a ; x∈b} = {x∈b; x∈a} is set by axiom of separation. Notation is a∩b.

1-8 Axiom of infinity ∃x[0∈x∧∀y[y∈x→y∪{y}∈x]].

1-9 Proposition of empty set Existence of set a is permitted by axiom of infinity. {x∈a; x≠x} is set and has

not element. Notation of empty set is 0 or Ø.

1-10 Axiom of regularity ∀x[x≠0→∃y[y∈x∧y∩x=0].

<2 Topology>

2-1

Set X

Subset of power set P(X) T

T that satisfies next conditions is called topology.

(i) Family of X’s subset that is not empty set <Ai; i∈I>, Ai∈T→∪i∈I Ai is belonged to T.

(ii) A, B ∈T→ A∩B∈T

(iii) Ø∈T, X∈T.

2-2

Set having T, (X, T), is called topological space, abbreviated to X, being logically not confused.

Element of T is called open set.

Complement of Element of T is called closed set.

2-3

Topological space (X, T)

Subset of X Y

S ={A∩Y ; A∈T}

Subtopological space (Y, S)

Topological space is abbreviated to subspace.

<3 Compact>

3-1

Set X

Subset of X Y

Family of X’s subset that is not empty set U = <Ui; i∈I>

U is covering of Y. ∪U = ∪i∈I ⊃Y

Subfamily of U 　　V = <Ui; i∈J > (J⊂I)

V is subcovering of U.

3-2

Topological space X

Elements of U Open set of X

U is called open covering of Y.

When finite subcovering is selected from arbitrary open covering of X, X is called compact.

When topological space has neighborhood that is compact at arbitrary point, it is called locally compact.

<4 Neighborhood>

Topological space X

Point of X a

Subset of X A

Open set B

a∈B⊂A

A is called neighborhood of a.

All of point a’s neighborhoods is called system of neighborhoods.

System of neighborhoods of point a V(a)

Subset of V(a) U

Element of U B

Arbitrary element of V(a) A

When B⊂A, U is called basis of neighborhoods of point a.

<5 Hausdorff space>

Topological space X that satisfies next condition is called Hausdorff space.

Distinct points of X a, b

Neighborhood of a U

Neighborhood of b V

U∩V = Ø

<6 Linear space>

Compact Hausdorff space Ω

Linear space that is consisted of all complex valued continuous functions over Ω C(Ω)

When Ω is locally compact, all complex valued continuous functions over Ω, that is 0 at infinite point is

expressed by C0(Ω).

<7 Ring>

Set R

When R is module on addition and has associative law and distributive law on product, R is called ring.

When ring in which subset S is not φ satisfies next condition, S is called subring.

a, b∈S

ab∈S

<8 Algebra>

C(Ω) and C0(Ω) satisfy the condition of algebra at product between points.

Subspace A ⊂C(Ω) or A ⊂C0(Ω)

When A is subring, A is called subalgebra.

<9 Dense>

Topological space X

Subset of X Y

Arbitrary open set that is not Ø in X A

When A∩Y≠Ø, Y is dense in X.

<10 Involution>

Involution * over algebra A over C is map * that satisfies next condition.

Map * : A∈A ↦ A*∈A

Arbitrary A, B∈A, λ∈C

(i) (A*)* = A

(ii) (A+B)* = A*+B*

(iii) (λA)* =λ-A*

(iiii) (AB)* = B*A*

<11 Linear topological space>

Number field K

Linear space over K X

When X satisfies next condition, X is called linear topological space.

(i) X is topological space

(ii) Next maps are continuous.

(x, y)∈X×X ↦ x+y∈X

(λ, x)∈K×X ↦λx∈X

Basis of neighborhoods of X’ zero element 0 V

When V⊂V is vertex set, X is called locally vertex.

<12 Adjoint space>

Norm space X

Distance d(x, y) = ||x-y|| (x, y∈X )

X is locally vertex linear topological space.

All of bounded linear functional over X X*

Norm of f ∈X* ||f||

X* is Banach space and is called adjoint space of X.

Adjoint space of X* is Banach space and is called the second adjoint space.

When X = X*, X is called reflective.

ⅡIndispensable theorems for proof

<1 Stone-Weierstrass Theorem>

Compact Hausdorff space Ω

Subalgebra A ⊂C(Ω)

When A ⊂C(Ω) satisfies next condition, A is dense at C(Ω).

(i) A separates points of Ω.

(ii) f∈A →　f－∈A

(iii) 1∈A

Locally compact Hausdorff space Ω

Subalgebra A ⊂C0(Ω)

When A ⊂C0(Ω) satisfies next condition, A is dense at C0(Ω).

(i) A separates points of Ω.

(ii) f∈A → f－∈A

(iii) Arbitrary ω∈A , f∈A , f(ω) ≠0

<2 Norm algebra>

C* algebra A

Arbitrary element of A A

When A is normal, limn→∞||An||1/n = ||A||

limn→∞||An||1/n is called spectrum radius of A. Notation is r(A).

[Note for norm algebra]

<2-1>

Number field K = R or C

Linear space over K X

Arbitrary elements of X x, y

< x, y>∈K satisfies next 3 conditions is called inner product of x and y.

Arbitrary x, y, z∈X, λ∈K

(i) <x, x> ≧0, <x, x> = 0 ⇔x = 0

(ii) <x, y> =

(iii) <x, λy+z> = λ<x, y> + <x, z>

Linear space that has inner product is called inner space.

<2-2>

||x|| = <x, x>1/2

Schwarz’s inequality

Inner space X

|<x, y>|≦||x|| + ||y||

Equality consists of what x and y are linearly dependent.

||・|| defines norm over X by Schwarz’s inequality.

Linear space that has norm || ・|| is called norm space.

<2-3>

Norm space that satisfies next condition is called complete.

un∈X (n = 1, 2,…), limn, m→∞||un – um|| = 0

u∈X limn→∞||un – u|| = 0

Complete norm space is called Banach space.

<2-4>

Topological space X that is Hausdorff space satisfies next condition is called normal.

Closed set of X F, G

Open set of X U, V

F⊂U, G⊂V, U∩V = Ø

<2-5>

When A satisfies next condition, A is norm algebra.

A is norm space.

∀A, B∈A

||AB||≦||A|| ||B||

<2-6>

When A is complete norm algebra on || ・ ||, A is Banach algebra.

<2-7>

When A is Banach algebra that has involution * and || A*|| = ||A|| (∀A∈A), A is Banach * algebra.

<2-8>

When A is Banach * algebra and ||A*A|| = ||A||2(∀A∈A) , A is C*algebra.

<3 Commutative Banach algebra>

Commutative Banach algebra A

Arbitrary A∈A

Character X

|X(A)|≦r(A)≦||A||

[Note for commutative Banach algebra] ( ) is referential section on this paper.

<3-1 Hilbert space>

Hilbert space inner space that is complete on norm ||x|| Notation is H.

<3-2 Linear operator>

Norm space V

Subset of V D

Element of D x

Map T : x → Tx∈V

The map is called operator.

D is called domain of T. Notation is D ( T ) or dom T.

Set A⊂D

Set TA {Tx : x∈A}

TD is called range of T. Notation is R (T) or ran T.

α , β∈C, x, y∈D ( T )

T(αx+βy) = αTx+βTy

T is called linear operator.

<3-3 Bounded linear operator>

Norm space V

Subset of V D

sup{||x|| ; x∈D} < ∞

D is called bounded.

Linear operator from norm space V to norm space V1 T

D ( T ) = V

||Tx||≦γ (x∈V ) γ > 0

T is called bounded linear operator.

||T || := inf {γ : ||Tx||≦γ||x|| (x∈V)} = sup{||Tx|| ; x∈V, ||x||≦1} = sup{; x∈V, x≠0}

||T || is called norm of T.

Hilbert space H ,K

Bounded linear operator from H to K B (H, K )

B ( H ) : = B ( H, H )

Subset K ⊂H

Arbitrary x, y∈K, 0≦λ≦1

λx + (1-λ)y ∈K

K is called vertex set.

<3-4 Homomorphism>

Algebra A that has involution* *algebra

Element of *algebra A∈A

When A = A*, A is called self-adjoint.

When A *A= AA*, A is called normal.

When A A*= 1, A is called unitary.

Subset of A B

B * := B*∈B

When B = B*, B is called self-adjoint set.

Subalgebra of A B

When B is adjoint set, B is called *subalgebra.

Algebra A, B

Linear map : A →B satisfies next condition, π is called homomorphism.

π(AB) = π(A)π(B) (∀A, B∈A )

*algebra A

When π(A*) = π(A)*, π is called *homomorphism.

When ker π := {A∈A ; π(A) =0} is {0},π is called faithful.

Faithful *homomorphism is called *isomorphism.

<3-5 Representation>

*homomorphism π from *algebra to B ( H ) is called representation over Hilbert space H of A .

<3-6 Character>

Homomorphism that is not always 0, from commutative algebra A to C, is called character.

All of characters in commutative Banach algebra A is called character space or spectrum space. Notation

is Sp( A ).

<3-7 Gerfand representation>

Commutative Banach algebra A

Homomorphism ∧: A →C(Sp(A))

∧is called Gerfand representation of commutative Banach algebra A.

<4 Gerfand-Naimark Theorem>

When A is commutative C* algebra, A is equal distance *isomorphism to C(Sp(A)) by Gerfand

representation.

[Note for Gerfand-Naimark Theorem]

<4-1 equal distance operator>

Operator A∈B ( H )

Equal distance operator A ||Ax|| = ||x|| (∀x∈H)

<4-2 Equal distance *isomorphism>

C* algebra A

Homomorphism π

π(AB) = π(A)π(B) (∀A, B∈A )

*homomorphism π(A*) = π(A)*

*isomorphism { π(A) =0} = {0}

<5 Banach-Alaoglu theorem>

When X is norm space, (X*)1 is weak * topology and compact.

[Note for Banach-Alaoglu theorem]

<5-1 Unit sphere>

Unit sphere X1 := {x∈X ; ||x||≦1}

<5-2 Linear functional>

Linear space V

Function that is valued by K f (x)

When f (x) satisfies next condition, f is linear functional over V.

(i) f (x+y) = f (x) +f (y) (x, y∈V)

(ii) f (αx) = αf (x) (α∈K, x∈V)

<5-3 weak * topology>

All of Linear functionals from linear space X to K L(X, K)

When X is norm space, X*⊂L(X, K).

Topology over X , σ(X, X*) is called weak topology over X.

Topology over X*, σ(X*, X) is called weak * topology over X*.

<6 *subalgebra of B ( H )>

When *subalgebra N of B ( H ) is identity operator I∈N , N ”= N is equivalent with τuw-compact.

[Note for *subalgebra of B ( H )]

<6-1 Identity operator>

Norm space V

Arbitrary x∈V

Ix = x

I is called identity operator.

<6-2 Commutant>

Subset of C*algebra B (H) A

Commutant of A A ’

A ’ := {A∈B (H) ; [A, B] := AB – BA = 0, ∀B∈A }

Bicommutant of A A ' ’’ := (A ’)’

A ⊂A ’’

<6-3 von Neumann algebra>

*subalgebra of C*algebra B (H) A

When A satisfies A ’’ = A , A is called von Neumann algebra.

<6-4 Ultra-weak topology>

Sequence of B ( H ) {Aα}

{Aα} is convergent to A∈B ( H )

Topology τ

When α→∞, Aα →τ A

Hilbert space H

Arbitrary {xn}, {yn}⊂H

∑n||xn||2 < ∞

∑n||yn||2 < ∞

|∑n<xn, (Aα- A)yn>| →0

A∈B ( H )

Notation is Aα →uτ A

[ 7 Distance theorem]

For von Neumann algebra N over separable Hilbert space, N1 can put distance on τs and τw topology.

[Note for distance theorem]

<7-1 Equipotent>

Sets A, B

Map f : A → B

All of B’s elements that are expressed by f(a) (a∈A) Image(f)

a , a’∈A

When f(a) = f(a’) →a = a’, f is injective.

When Image(f) = B, f is surjective.

When f is injective and surjective, f is bijective.

When there exists bijective f from A to B, A and B are equipotent.

<7-2 Relation>

Sets A, B

x∈A, y∈B

All of pairs <x, y> between x and y are set that is called product set between a and b.

Subset of product set A×B R

R is called relation.

x∈A, y∈B, <x, y>∈R Expression is xRy.

When A =B, relation R is called binary relation over A.

<7-3 Ordinal number>

Set a

∀x∀y[x∈a∧y∈x→y∈a]

a is called transitive.

x, y∈a

x∈y is binary relation.

When relation < satisfies next condition, < is called total order in strict sense.

∀x∈A∀y∈A[x<y∨x=y∨y<x]

When a satisfies next condition, a is called ordinal number.

(i) a is transitive.

(ii) Binary relation ∈ over a is total order in strict sense.

<7-4 Cardinal number>

Ordinal number α

α that is not equipotent to arbitrary β<α is called cardinal number.

<7-5 Cardinality>

Arbitrary set A is equipotent at least one ordinal number by well-ordering theorem and order isomorphism

theorem.

The smallest ordial number that is equipotent each other is cardinal number that is called cardinality over set

A. Notation is |A|.

When |A| is infinite cardinal number, A is called infinite set.

<7-6 Countable set>

Set that is equipotent to N countable infinite set

Set of which cardinarity is natural number finite set

Addition of countable infinite set and finite set is called countable set.

<7-7 Separable>

Norm space V

When V has dense countable set, V is called separable.

<7-8 N1>

von Neumann algebra N

A∈B ( H )

N1 := {A∈N; ||A||≦1}

<7-9 τs and τw topology>

<7-9-1τs topology>

Hilbert space H

A∈B ( H )

Sequence of B ( H ) {Aα}

{Aα} is convergent to A∈B ( H )

Topology τ

When α→∞, Aα →τ A

|| (Aα- A)x|| →0 ∀x∈H

Notation is Aα →s A

<7-9-2 τw topology>

Hilbert space H

A∈B ( H )

Sequence of B ( H ) {Aα}

{Aα} is convergent to A∈B ( H )

Topology τ

When α→∞, Aα →τ A

|<x, (Aα- A)y>| →0 ∀x, y∈H

Notation is Aα →w A

<8 Countable elements>

von Neumann algebra N over separable Hilbert space is generated by countable elements.

<9 Only one real function>

For compact Hausdorff space Ω,C(Ω) that is generated by countable idempotent elements is

generated by only on real function.

<9-1>

Set that is defined arithmetic・ S

Element of S e

e satisfies a・e = e・a = a is called identity element.

Identity element on addition is called zero element.

Ring’s element that is not zero element and satisfies a2 = a is called idempotent element.

To be continued

Tokyo April 20, 2008

Sekinan Research Field of Language

www.sekinan.org

Generation 2

I also wrote a overview paper on generation in 2018.

Text is the following.

..............................................................................................

Quantum Language

between Quantum Theory for Language 2004 and Generation of Word 2008

adding their days and after

A conclusion for the present on early papers of Sekinan Library

TANAKA Akio

23 January - 26 January 2018

Tokyo

Sekinan Library

I wrote a paper titled Quantum Theory for Language in 2004.

This paper was read at the international symposium on Silk Road at Nara, Japan in December 2003.

The encounter with this time's persons and thoughts are written at The Time of Quantum in September

2008.

This paper's concept was prepared at Hakuba, Nagano, Japan in March 2003.

This concept was jotted down at the hotel of Hakuba so the publication became late till 2015. The title was

named Manuscript of Quantum Theory for Language.

In Autumn 2002 I was hospitalized by pneumonia for two weeks, when I thought to put the linguistic research

on old Chinese characters so far in order. The result was arranged as a paper titled On Time Property

Inherent in Characters also at Hakuba in March 2003.

Quantum Theory for Language was added proviso, Synopsis, because the paper was thought at that time

as a role of a rather long mathematical paper's preface on quantum theory on language.

In 2005 Distance Theory was written as a successive paper of Quantum Theory for Language. In those

days Reversion Theory in September 2004, Prague Theory in October 2004 were successively written.

Time passed by rapidly.

After some preparations of mathematics, I wrote successive papers related with Quantum Theory for

Language. von Neumann Algebra was put at the centre of preparation. The days at that time was simply

wrote titled as The Days of von Neumann Algebra and The Days between von Neumann Algebra and

Complex Manifold Deformation Theory in 2015.

von Neumann Algebra succeeds from 1 to 4. 2's Generation Theorem was written in April 2008. After von

Neumann Algebra, Functional Analysis was written. 2's Generation of Word 's result is directly connected

to Quantum Theory for Language's mathematical background.

From 2008 I frequently used Zoho site because of easily writing by mathematical equation system. Complex

Manifold Deformation Theory was the first result of Zoho. At Floer Homology Language some

complementary fruits were gotten for Quantum Theory, Homology Generation of Language in June 2009

and Homology Structure of Word also in June 2009.

Algebraic geometry had been consistently flowing in Quantum Theory.

Recently written Connection between early paper's quantum and recent paper's geometry, November

2017 summarizes the situation at that time concisely.

In July 2017, The comparison between 2003 and 2017 From Chinese character's meaning structure to

Homological algebraic model of language universals was written looking back the days of quantum.

10.

Quantum Theory's time series representative is the following.

(1)

On Time Property Inherent in Characters 2003

Manuscript of Quantum Theory for Language 2003

Quantum Theory for Language 2004

Reversion Theory 2004

Prague Theory 2004

Distance Theory 2005

Generation Theorem 2008

Generation of Word 2008

Homology Generation of Language 2009

Homology Structure of Word 2009

(2)

von Neumann Algebra 1-4 2008

Functional Analysis 2008

Complex Manifold Deformation Theory 2008-2009

Floer Homology Language 2009

(3)

The Time of Quantum 2008

The Days of von Neumann Algebra 2015

The Days between von Neumann Algebra and Complex Manifold Deformation Theory2015

Connection between early paper's quantum and recent paper's geometry 2017

The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological

algebraic model of language universals 2017

11.

Basis of On Time Property Inherent in Characters 2003, Manuscript of Quantum Theory for Language 2003

and Quantum Theory for Language 2004 are all led by Qing Dynasty's linguistic (Xiaoxue) tradition,

especially from WANG Guowei, whose influence is written at The Time of WANG Guowei in December 2011.

12.

In 1970s at my age 20s, while I had read WANG Guowei, also read Ludwig Wittgenstein, from whom I

narrowly learnt writing style that was maintained through early papers. On Wittgenstein I wrote The Time of

Wittgenstein in January 2012. Especially written essayFor WITTGENSTEIN Ludwig Position of Language

intermittently wrote from December 2005 to August 2012.

13.

WANG Guowei taught me the micro phase of language and Edward Sapir taught me the macro phase of

language. His book, Language 1921 shows us the conception of language's change system, Drift. I ever

wrote

some essays on him and his book titled Flow of Language in September 2014.

On Edward Sapir I recently wrote a essay titled Edward Sapir gave me a moment to study language

universals together with Sergej Karcevskij in July 2017.

14.

I met again with CHINO Eiichi in 1979, from whom I learnt almost all the contemporary linguistics' basis,

because of my bias to Chinese historical linguistics ( Xioxue) and Japanese classical phonology in characters.

Reunion with CHINO was written at a essay titled Fortuitous Meeting What CHINO Eiichi Taught Me in the

Class of Linguistics in December 2004. Also wrote Under the Dim Light in August 2012, CHINO Eiichi and

Golden Prague in June 2014, Coffee shop named California in February 2015 and Prague in 1920s in April

2016.

15.

CHINO Taught me the existence of Linguistic Circle of Prague and Sergej Karcevskij at Prague in 1920s. I

wrote Linguistic Circle of Prague in July 2012 and also wrote on Karcevskij, Gift from Sergej Karcevskij in

October 2005, Sergej Karcevskij, Soul of Language in November 2012, , Follower of Sergej Karcevskij in

November 2012 Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi in April

2013 and For KARCEVSKIJ Sergej from time to time.

16.

In 1970s, I also learnt mathematics for applying to describe language's minute situation. I had thought that

language had to be written clear understanding form for free and precise verification going over philosophical

insight. When set theory led by Kurt Godel was raised its head to logical basis, I was also deeply charmed by

it. But even if fully using it, language's minute situation seemed to be not enough to write over clearly by my

poor talent. The circumstance was written titled Glitter of youth through philosophy and mathematics in

1970s in March 2015. .

17.

One day when I found and bought Bourbaki's series Japanese-translated editions, which were seemed to be

possibility to apply my aim to describe language's situation. But keeping to read them were not acquired at

that time. So I was engrossed in Chinese classical linguistics achieved in Qing dynasty, typically DUAN Yucai,

WANG Niansun, WANG Yinzhi and so forth. The days were written as The Time of Language Ode to The

Early Bourbaki To Grothendieck.

18.

Algebraic geometry began from von Neumann Algebra. After these days, Zoho time came to me. Its first

result is shown as the title Complex manifold Deformation Theory in 2008. Distance of Word in November

2008 is a mathematical conclusion of Distance Theory in May 2005. Zoho's main papers were seen at the

site Sekinan Zoho.

19.

Distance Theory has some derivations towards physical phases in my thought. Distance Theory Algebraically

Supplemented Brane Simplified Model was written in October-November 2007. Each paper is the following.

Distance Theory Algebraically Supplemented

Brane Simplified Model

Bend

Distance <Direct Succession of Distance Theory>

S3 and Hoph Map

Physics was one of the most fantastic fields in high school days. I ever wrote the days of yearning for physics

and after that. Perhaps Return to Physics in April 2014, Winding road to physics in January 2015, Thanks

to physics about which I ever dreamt in my future in April 2015,

20.

After 2008 at Zoho sites, mathematics based language papers were successively written aiming clearer

definition. Zoho's annual papers are shown at Sekinan Zoho's Zoho by year from 2008 to 2013. While I

continued writing papers, my aim was gradually changed to confirm language's basis through mathematical,

especially algebraic geometrical description by language models a little parting from natural language. The

circumstances behind confirmation was written at Half farewell to Sergej Karcevskij and the Linguistic

Circle of Prague in October 2013 and 40 years passed from I read WANG Guowei in November 2013.

Read more: https://geometrization-language.webnode.com/products/quantum-language-between-quantum-

theory-for-language-2004-and-generation-of-word-2008-adding-their-days-and-after/

Energy

Signal needs energy for dispatching messages to the world by hand power of flag semaphore, hand power

and electricity of Mores code and light and electricity of lighthouse.

Language also needs energy for dispatching by human voice and hand of speaking and writing. But there is

not human energy, there is not language.

Signal's energy is more diverse than language's.

There is energy's diversity at the root of distinction between signal and language.

The question, what is signal is also meant what is energy.

Now I cannot describe accurate explanation to this question clearly.

Little by little it may be able to writing using mathematics hereafter.

Now I would show several trial papers on the relation between language and energy.

Refer to the below.

...................................................................

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.

1.Potential of Language / Floer Homology Language / 16 June 2009

2.Homology structure of Word / Floer Homology Language / Tokyo June 16, 2009

3.Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008

4.Time of Word / Complex Manifold Deformation Theory / 23 December 2008

Tokyo

3 April 2015

Sekinan Library

Read more: https://geometrization-language.webnode.com/news/preparation-for-the-energy-of-

language/

.......................................................................

Floer Homology Language Note 1 Potential of Language

Floer Homology Language

TANAKA Akio

Note 1

Potential of Language

¶ Prerequisite conditions

Note 6 Homology structure of Word

(Definition)

(Gromov-Witten potential)

(Theorem)

(Witten-Dijkggraaf-Verlinde-Verlinde equation)

(Theorem)

(Structure of Frobenius manifold)

Symplectic manifold (M, wM)

Poincaré duality < . , . >

Product <V1°V2, V3> = V1V2V3(

)

(M, wM) has structure of Frobenius manifold over convergent domain of Gromov-Witten

potential.

(Theorem)

Mk,β (Q1, ..., Qk) =

N(β) expresses Gromov-Witten potential.

[Image]

When Mk,β (Q1, ..., Qk) is identified with language, language has potential N(β).

[Reference]

Quantum Theory for language / Synopsis / Tokyo January 15, 2004

First designed on <energy of language> at

Tokyo April 29, 2009

Newly planned on further visibility at

Tokyo June 16, 2009

Sekinan Research Field of language

Read more: https://geometrization-language.webnode.com/news/floer-homology-language-note-1-potential-

of-

language/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=https%3A%2F%

2Fgeometrization-language.webnode.com%2Fnews%2Ffloer-homology-language-note-1-potential-of-

language%2F

....................................................................

Energy 2

Signal and language send message, for which they need energy directly or indirectly.

What exists between message and energy?

I ever wrote several trial papers on this theme.

Here I show the two of them

Amplitude of meaning minimum / Complex Manifold Deformation Theory 2008

Time of Word / Complex Manifold Deformation Theory 2008

------------------------------------------------

Complex Manifold Deformation Theory

Conjecture A

4 Amplitude of Meaning Minimum

TANAKA Akio

Conjecture

Meaning minimum has finite amplitude.

[View*]

*Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains

and vigorous port towns at dawn.

Bounded domain of Rm Ω

C∞ function defined in Ω u, F

u, F satisfy the next equation.

F(D2u) = Ψ

D2u is hessian matrix of u.

F is C∞ function over Rm×m .

Open set that includes range of D2u U

U satisfies the next.

(i) Constant λ, Λ

(ii) F is concave.

(Theorem)

Sphere that has radius 2R in Ω B2R

Sphere that has same center with B2R and has radius σR in Ω BσR

Amplitude of D2u ampD2u

ampBσRD2u = supBσRD2u – infBσRD2u

0<σ<1

C and e are constant that is determined by dimension m and

ampBσRD2u

Cσe(ampBRD2u +

supB2R|D

| +

supB2R |D2

| )

[Impression]

1 Meaning minimum is the smallest meaning unit of word. Refer to the reference #2 and

#2′.

2 If meaning minimum of word is expressed by BσR, it has finite amplitude in adequate

domain.

[References 1 On meaning minimum]

#1 Holomorphic Meaning Theory / 10th for KARCEVSKIJ Sergej

#2 Word and Meaning Minimum

#2′ From Cell to Manifold

#3 Geometry of Word

[References 2 On generation of word]

#4 Growth of Word

#5 Generation Theorem

#6 Deep Fissure between Word and Sentence

#7 Tomita’s Fundamental Theorem

#8 Borchers’ Theorem

#9 Finiteness in Infinity on Language

#10 Properly Infinite

#11 Purely Infinite

[References 3 on distance and mirror on word]

#12 Distance Theory / Tokyo May 5, 2004 / Sekian Linguistic Field

#13 Quantification of Quantum / Tokyo May 29, 2004 / Sekinan Linguistic Field

#14 Mirror Theory / Tokyo June 5, 2004 / Sekinan Linguistic Field

#15 Mirror Language / Tokyo June 10, 2004 / Sekinan Linguistic Field

#16 Reversion Theory / Tokyo September 27, 2004 / Sekinan Linguistic Field

#17 Mirror Theory Group / Tokyo December 9, 2008 / Sekinan Linguistic Field

To be continued

Tokyo December 17, 2008

Sekinan Research Field of language

[References 4 / December 23, 2008 / on time of word]

#18 Time of Word / Tokyo December 23, 2008 / sekinan.wiki.zoho.com

Read more: https://srfl-paper.webnode.com/news/amplitude-of-meaning-minimum/

-------------------------------------------------------------

Complex Manifold Deformation Theory

Conjecture A

5 Time of Word

TANAKA Akio

Conjecture

Word has time.

[View¶]

¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains

and vigorous port towns at dawn.

Kähler manifold X

Kähler form w

A certain constant c

Cohomology class of w 2πc1(X)

c1(X)>0

Kähler metric g

Real C∞ function f

∫X (ef- 1)wn = 0

Ric(w) -w =

Monge-Ampère equation

(Equation 1)

Use continuity method

(Equation 1-2)

Kähler form w' = w +

Ric(w') = tw' + (1-t)w'

δ>0

I = {

}

is differential over t.

Ding's functional Fw

(Lemma)

There exists constant that is unrelated with t.

When utis the solution of equation 1-2, the next is satisfied.

Fw(ut)

Proper of Ding's functional is defined by the next.

Arbitrary constant K

Point sequence of arbitrary P(X, w)K {ui}

(Theorem)

When Fw is proper, there exists Kähler-Einstein metric.

[Impression¶]

¶ Impression is developed from the view.

If word is expressed by u , language is expressed by Fw and comprehension of human

being is expressed by C, what language is totally comprehended by human being is

guaranteed.

Refere to the next paper.

#Guarantee of Language

If language is expressed by being properly generated, distance of language is expressed by

Kähler-Einstein metric and time of language is expressed by t, all the situation of language

is basically expressed by (Equation1-2).

Refer to the next paper.

#Distance Theory

If inherent time of word is expressed by t's [δ, 1], dynamism of meaning minimum is

mathematically formulated by Monge-Ampère equation.

Refer to the next papers.

#1<For inherent time>

On Time Property Inherent in Characters

#2<For meaningminimum>

From Cell to Manifold

#3<For meaning minimum's finiteness>

Amplitude of Meaning Minimum

Tokyo January 1, 2009

Sekinan Research Field of language

Read more: https://srfl-paper.webnode.com/news/complex-manifold-deformation-theory-conjecture-a-5-time-

of-word/

------------------------------------------------------

From upper two papers, Amplitude of Meaning Minimum and Time of Word, I think that energy,

distance, meaning and time are closely related.

Understandability

Meaning is understood in the finite time by human or machine assisted by human.

Understandability of meaning is closely related with time.

At this situation I ever wrote a following trial paper titled understandability of language in

2008.

---------------------------------------------------------

Complex Manifold Deformation Theory

Conjecture B

2 Understandability of Language

TANAKA Akio

Conjecture

Language is understandable.

[View]

(Eells-Sampson Theorem)

Compact Riemannian manifolds (M, g), (N, h)

Section curvature of (N, h) everywhere non-positive

Arbitrary C∞ map f : M → N

Equation

Solution of the equation exists at

When there exists

is convergent to harmonic map

and

is free

homotopic with

(Harmonic map)

Arbitrary variation of

{

}

(Section of

)

(Levi-Civita connection)

Levi-Civita connection of (M, g) and (N, h)

[Impression]

From Eells-Sampson Theorem, if language is supposed to be expressed by the equation and

word is supposed to be expressed by

, language is understandable in finite time.The

situation contributes guarantee of language.

In infinite time, Language still can be understood by word's generation system

[References]

For impression, refer to the next.

#1 Finiteness in Infinity of Language / Kac-Moody Lie Algebra / Conjecture 1 / Tokyo February

10, 2008

#2 Properly Infinite / von Neumann Algebra 3 / Note 1 / Tokyo May 1, 2008

#3 Purely Infinite / von Neumann Algebra 3 / Note 2 / Tokyo May 1, 2008

#4 Guarantee of Language / Tokyo June 12, 2004

#5 Generation Theorem /von Neumann Algebra 2 / Note / Tokyo April 20, 2008

Tokyo January 9, 2009

Sekinan Research Field of language

-------------------------------------------------------------

Understandability 2

Understandability of signal and language is dependant on time processing.

Finite time is generally understandable for human or human assisted machine.

In case of infinite time, what situation occur to understandability?

I once think about infinity's details at the next two papers at von Neumann Algebra 3 in 2007.

Properly Infinite / von Neumann Algebra 2008

Purely Infinite / von Neumann Algebra 2008

----------------------------------------------------------

von Neumann Algebra 3

Note 1

Properly Infinite

TANAKA Akio

[Theorem]

On von Neumann algebra N, next are equivalent.

(i) N is properly infinite.

(ii) There exist {En : n∈N}⊂P(N) and En~I, ∑nEn = I.

(iii)There exist E∈P(N) and E~E⊥~I.

[Explanation]

<1 Objection Operator>

<1-1>

Hilbert space H

Linear subspace of H Subspace

Subspace that is closed by norm || ・|| of H Closed subspace

Arbitrary subspace of H K

K⊥: = {x∈H ; <x, y> = 0, ∀y ∈K} Orthogonal complement of K

Subspaces of H K, L

<x, y> = 0 ∀x∈K ∀y∈L It is called that x and y are orthogonal each other.

Notation is K⊥L.

Direct sum K⊕L : = {x+y ; x∈K, y∈L}

<1-2>

x∈H

d = dist(x, K) : = inf{||x-y|| ; y∈K}

z∈K

d = ||x-z||

z : = PKx

PK is called objection operator from H to K.

<1-3>

von Neumann algebra N

All of objection operators that belong to N P (N)

All of unitary operators that belong to N U (N)

<2 Bounded operator>

<2-1>

Hilbert space H, K

Subspace of H D

Map A

A(λx+μy) = λAx+μAy, ∀x, y∈D, ∀λ, μ∈C

A is called linear operator from H to K.

D domain of A Notation is dom A.

Set {Ax ; x∈D} range of A Notation is ran A.

<2-2>

dom A = H

Constant M>0

||Ax|| ≦M||x|| (∀x∈H)

A is called bounded operator from H to K

All of As B(H, K)

H = K

B(H) := B(H, H)

<2-3>

A∈B(H)

A*∈B(H)

<x, Ay> = <A*x, y>

A* is called adjoint operator of A.

A = A*

A is called self-adjoint.

A*A = AA*

A is called normal operator.

A = A* = A2

A is called objection operator.

||Ax|| = ||x|| (∀x∈H)

A is called isometric operator.

A*A = AA* = I ( I is identity operator.)

A is called unitary operator.

Ker A := {x∈H, Ax = 0}

A that is isometric over (Ker A)⊥ is called partial isometric operator.

<2-4>

von Neumann algebra N

Commutant of N N ‘

Center of N Z := N∩N ‘

Z = CI

N is called factor.

E∈P(N)

Central projection E that belongs to Z

All of central projections P(Z)

<2-5>

Projection operator E, F∈P(N)

Partial isometric operator W∈N

F1∈P(N)

F1≦F

E ~ F1

Situation is expressed by E ≺ F.

≺ gives P(N) partial order relation.

<3 Comparison theorem>

<3-1>

[Theorem]

For E, F∈P(N), there exists P∈P(Z) , while EP≺FP and FP⊥≺EP⊥.

<4 Cardinality>

<4-1 Relation>

Sets A, B

x∈A, y∈B

All of pairs <x, y> between x and y are set that is called product set between a

and b.

Subset of product set A×B R

R is called relation.

x∈A, y∈B, <x, y>∈R Expression is xRy.

When A =B, relation R is called binary relation over A.

<4-2 Ordinal number>

Set a

∀x∀y[x∈a∧y∈x→y∈a]

a is called transitive.

x, y∈a

x∈y is binary relation.

When relation < satisfies next condition, < is called total order in strict sense.

∀x∈A∀y∈A[x<y∨x=y∨y<x]

When a satisfies next condition, a is called ordinal number.

(i) a is transitive.

(ii) Binary relation over a is total order in strict sense.

<4-3 Cardinal number>

Ordinal number α

α that is not equipotent to arbitrary β<α is called cardinal number.

<4-4 Cardinality>

Arbitrary set A is equipotent at least one ordinal number by well-ordering

theorem and order isomorphism theorem.

The smallest ordinal number that is equipotent each other is cardinal number

that is called cardinality over set A. Notation is |A|.

When |A| is infinite cardinal number, A is called infinite set.

<4-5 Countable set>

Set that is equipotent to N countable infinite set

Set of which cardinarity is natural number finite set

Addition of countable infinite set and finite set is called countable set.

<4-6 Zermelo’s well-ordering theorem>

If there exist Axiom of Choice, there exists well-ordering over arbitrary set.

<4-7 Order isomorphism theorem>

Arbitrary well-ordered set is order isomorphic to only one ordinal number.

<4-8 Axiom of choice>

∀x∃f [ f ∈Map(x, ∪x)∧∀y[y∈x∧y≠0 → f(y)∈y]]

To be continued

Tokyo May 1, 2008

Sekinan Research Field of Language

www.sekinan.org

--------------------------------------------------------------------------

von Neumann Algebra 3

Note 2

Purely Infinite

TANAKA Akio

[Theorem]

The necessary and sufficient condition for what von Neumann algebra N is

purely infinite ( Ⅲtype) is what semi-finite normal trace that is not 0 does not

exist over N.

[Explanation]

<1 Trace>

<1-1>

Trace over von Neumann algebra N τ : N+ → [0, ∞] 0∞ := 0

τ is the map that has next condition.

(i) τ ( A+B ) =τA +τB, ∀A,B∈N

(ii) τ (λA ) = λτ ( A ) ∀A∈N+, ∀λ∈[0, ∞)

(iii) τ ( A*A ) = τ ( AA* ) ∀A∈N

<1-2>

Trace over von Neumann algebra N τ

(1) τ is faithful. A∈N, τ (A) = 0 → A = 0

(2) τ is normal. Increase net {An} ⊂N+ τ (supα Aα) = supα τ (Aα)

(3) τ is definite. τ (I ) < ∞

(4) τ is semi-definite. When A(≠0)∈N+, there exist B(≠0) ∈N+ while B≦A and

τ (B) ≠0.

To be continued

Tokyo May 1, 2008

Sekinan Research Field of Language

www.sekinan.org

---------------------------------------------------------------------------

On infinity and finiteness in language, I have not total image through mathematical approach.

I ever wrote several papers related with meaning and time in language.

Picked-up applicable papers are the next.

Language, Word, Distance, Meaning and Meaning Minimum / Proto Arithmetic Geometry Language 2009

Loop Time of Character / Time of WANG Guowei 2011

Finiteness of Words / Diophantine Language 2012

Word as Infinite Loop Space / Infinite Loop Space Language 2012

Signal

At this paper, signal is belonged to human world not belonged to outer world or universe.But Signal

itself exists to go abroad to the widely opened worlds or universe.

Understanding signal may be able to possess if there be energy which dispatch to the outer.

Decipherment of the all the signals maybe a dream but the routes to decipher areternally remained by

the very human ourselves.

Refer to the next.

The Days of Decipherment 2016

Basis of the further study on language - Potential 2009-2015

------------------------------------------------------------------

The Days of Decipherment

31/07/2016 14:46

The Days of Decipherment

TANAKA Akio

On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition AJOURNEY TO THE

IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth

days, so to say, the days of decipherment.

1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and

literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from

Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told at

Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered

the Linear B.

In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered byNISHIDA Tatsuo (1928-

2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki

narabini Seikago bunpou no kenkyuu in 1962.

In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team

developed largely.

In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the

Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the

Qing dynasty and I read them almost every day containing the comparison with the western linguistic results.

The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and

so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin were the most important for

me.

In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I

thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda,

Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was

too much difficult to read on. From the days the long and winding road began to mathematics and its

applicable study for language universals.

At the exhibition of ancient Greece I confirmed in particular that the stability of language was kept by letters

and characters from the Linear A and Linear B.

Exhibition Catalogue numbers are the next.

The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.

39. Clay juglet c. 1800 B.C. ~ c. 1700 B.C.

40. Clay bar c. 1700 B.C. ~ c. 1650 B.C.

41. Clay tablet c. 1375 B.C. ~ c. 1350 B.C.

77. Linear B bar and tablet c. the 13th century B.C.

For my part the stability has been one of the biggest themes on language phenomena since I was taught

from CHINO Eiichi through the results of the Linguistic Circle of Prague, especially of Sergej

Karcevskij.

The exhibition catalogue and Chadwick's book Japanese translated edition.

Reference

1.Essence of Language / SRFL Paper

2.Derived Category Language, 26 July 2016 Edition

References 2

1.The Time of WANG Guowei

2.40 years passed from I read WANG Guowei

References 3

1.Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi

2.Half Farewell to the Linguistic Circle of Prague and Sergej Karcevskij

3.Sergej Karcevskij, Soul of Language

4.Gift from Sergej Karcevskij

5.Follower of Sergej Karcevskij

6.For KARCEVSKIJ Sergej

7.Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe

linguistique"

References 4

1.Fortuitous Meeting

2.Linguistic Circle of Prague

3.Prague in 1920s

4.Under the dim light

References 5

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

2.Bourbaki' ELEMENTS DE MATHEMATIUE Troisieme edition, 1964

Tokyo

30 July 2016

Sekinan Library

Read more: https://srfl-paper.webnode.com/news/the-days-of-decipherment/

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Basis of the further study on language – Potential

01/05/2016 18:46

Basis of the further study on language – Potential

Floer Homology Language

TANAKA Akio

Note1

Potential of Language

¶ Prerequisite conditions

Note 6 Homology structure of Word

(Definition)

(Gromov-Witten potential)

(Theorem)

(Witten-Dijkggraaf-Verlinde-Verlinde equation)

(Theorem)

(Structure of Frobenius manifold)

Symplectic manifold (M, wM)

Poincaré duality < . , . >

Product <V1 V2, V3> = V1V2V3(

)

(M, wM) has structure of Frobenius manifold over convergent domain of Gromov-

Witten potential.

(Theorem)

Mk,β (Q1, …, Qk) =

N(β) expresses Gromov-Witten potential.

[Image]

When Mk,β (Q1, …, Qk) is identified with language, language has potential N(β).

[Reference]

Quantum Theory for language / Synopsis / Tokyo January 15, 2004

First designed on

Tokyo April 29, 2009

Newly planned on further visibility

Tokyo June 16, 2009

Sekinan Research Field of Language

[Note, 31 March 2015]

This paper was first designed for energy of language. But at that time, I could not

write

the proper approach from the concept of energy by mathematical process. So I

wrote

the paper through the concept of potential. Probably energy is one of the most

fundamental

factors on language.

In 2003 I wrote Quantum Theory for Language , before which I wrote the

manuscript focusing

the concept of quantum abstracted from the ideogram of classical Chinese written

language.

The last target of manuscript was energy and meaning of quantum that was the

ultimate

unit of language.

Refer to the next.

Manuscript of Quantum Theory for Language. Hakuba, Nagano. March 2003

-------------------------------------------------------------------------------------------------------------------------------

What is signal?

The existence that generates language

Preparation 2 1-8

is over

15 January 2019

-------------------------------------------------------------------------------------------------------------------------------

SRFL Paper

Tokyo

15 January 2019

Monday, 14 February 2022

What is signal? The existence that generates language The 1st Edition 21 November - 15 January 2019

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Monday, 14 February 2022

What is signal? The existence that generates language​ ​The 1st Edition 21 November - 15 January 2019

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What is signal? The existence that generates language The 1st Edition 21 November - 15 January 2019