What is signal? Total Edition 21 November 2018-23 April 2019
What is signal?
The existence that generates language
TANAKA Akio
SRFL Paper
Tokyo
21 November - 23 April 2019
Original Title
What is signal? A mathematical model of nerve
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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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
- At least three elements for language universals 2015
- Preparation for the energy of language 2015
- Papers for Language Dimension In chronological order 2015
- Three conjectures for dimension, synthesis and reversion with root and supplement 2014
- Arithmetic Geometry Language 2014
- Potential of Language / Floer Homology Language 2009
- Homology structure of Word / Floer Homology Language 2009
- Amplitude of meaning minimum / Complex Manifold Deformation Theory 2008
- Time of Word / Complex Manifold Deformation Theory 2008
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Preparation
Distance
1.
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
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]
[Definition added / November 3, 2008]
Definition 10, the part of
Tokyo March 3, 2007
Tokyo November 3, 2008 Added
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2.
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
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3.
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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4.
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.
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。
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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
5.
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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6.
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
1.
Word Synthesized is the word that is synthesized meanings in a word by arithmetic or algebraic geometrical method.
For detailed refer to the next.
2.
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.
The details of Word Indexed will be shown the papers after this.
3.
Meanings contained in Word Indexed is deeply related with quantization and discreteness.
Refer to the next.
4.
All the basis of Word Indexed is generated at the next.
Reference
Theory 2003-2016 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://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.
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The Days of Decipherment
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.
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Ideogram Paper 2005-2018
1. Ideogram 2005
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
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7.
Quantum group 2
In 2008 I wrote on Quantum group at studying Kac-Moody-Lie Algebra.
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Note 2
Quantum Group
1
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
2
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.
3
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.
4
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.
5
n-dimensional Euclid space Rn
Linear independent vector v1, …, vn
Lattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )
Lattice of h hZ
6
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
7
Vector space over K A
Bilinear product over K A×A → A
When A is ring, it is called associative algebra.
8
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
8
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
Refer to the next.
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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
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. #3
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
Postscript
[Referential note November 9, 2007]
________________________________
Mirror Theory For the Structure of Prayer Dedicated to the Memory of CHINO Eiichi Tokyo June 5, 2004
________________________________
[Referential note February 9, 2008]
† Concept
Refer to the next.
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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. #3
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.
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8.
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
9.
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.
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The comparison between 2003 and 2017
From Chinese character's 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
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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
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
[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.
11.
Symmetry 2
Symmetry seems to be related with two elements of language universals, distance and time.
Refer to the next.
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Distance Theory Algebraically Supplemented
Brane Simplified Model
1
Bend
TANAKA Akio
1
Language is expressed by< a pair of quanta> that consists of
2
Quantum and anti-quantum have reverse direction.
3
Quantum and anti-quantum are in the shape of strings that are separated parallel longitude L apart.
4
Quantum and anti-quantum are in <AdS5 ( 5-dimensional anti-deSitter ) space>.
5
Left side of quantum and anti-quantum is on
6
Quantum starts from ra in AdS5 space and returns rb in AdS5 space.
ra and rb are equal longitude from D3 brane.
7
8
At the paper Spacetime Symmetry and Escalator Brane in Escalator Language Theory, language goes from ra to rz and in reverse movement to rb.
9
At the paper Actual Language and Imaginary Language,
10
We see real language that is upper side of rz-rz’. Imaginary language is hidden under side of rz-rz’ in our life.
11
At the paper Mirror Language, imaginary language is mirror language of real language.
12
Distance of language is regarded as the longitude from ra ( or rb ) to D3 brane in AdS5 space.
[Reference]
Tokyo October 17, 2007
Sekinan Research Field of Language
www.sekinan.org
...............................................................
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/
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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
2
Distance
Direct Succession of Distance Theory
TANAKA Akio
1
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
2
Using
Distance is defined in
According to
3
Distance in
Now “from <y = –πR> to <y = 0>” is called
Values of
4
In
5
Word has distance at
6
Now distance at
[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
4.5.1 Mirror Language
4.5.2 Mirror Theory
[ATT3] Enlarged Distance Theory
[ATT4] Opened Time and Closed Time
Tokyo October 26, 2007
Sekinan Research Field of Language
www.sekinan.org
........................................................................................
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
1
Distance theory is an extension of Quantum Theory for Language.
2
Distance theory is an extension of strength rule in Quantum Theory for Language.
3
Distance theory is considered for the purpose of the guarantee to language.
4
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.
5
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.
6
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.
7
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.
8
A significant element gets a signification from the real world.
A periodical element gets a time from the real world.
9
An indicator gets a meaning and a period from elements.
10
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.
11
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.
12
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.
13
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.
14
Indicators make meaning and connection rule in a quantum, both are derived from significant and periodical elements in an indicator.
15
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.
16
Connection rule is decided by periodical elements in indicators.
Details are indicated in Quantum Theory for Language.
17
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.
18
Multiplication generally occurs by the addition of signification in an indicator.
But multiplication in meaning of a quantum sometimes occurs without any addition oneself.
19
Multiplication in a quantum without addition occurs by situational transition in the language world.
20
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.
21
A quantum of language itself becomes
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.
22
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]
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/
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13.
Distance 2
Hoph algebra
The upper section 12.'s algebraic defined distance is also related with Hoph algebra.
Refer to the next.
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Distance Theory Algebraically Supplemented
Brane Simplified Model
3
S3 and Hoph Map
TANAKA Akio
1
From RS model,
Refer to the next.
2
3
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.
4
Now
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.
Point of S3 is marked by ( x’a, y’a , x’b, y’b ) .
On S3, refer to the next.
5
6
Tokyo November 12, 2007
Sekinan Research Field of Language
www.sekinan.org
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14
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
4
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
5
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.
13 Minimum model of Symmetry Flow Language is testified by tetrahedron being led from polyhedron’s triangulation.
Tokyo May 17, 2007
Symmetry Flow Language
6
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
Refer to the following paper.
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.
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
Symmetry Flow Language 2
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.
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.
8 Replaced two moduli in Calabi-Yau manifold K is called reflection Calabi-Yau manifold K~.
Refer to the following paper.
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.
Tokyo May 23, 2007
Sekinan Research Field of Language
.............................................................................................................
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.
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.
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
-----------------------------------------------------------
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
Read more: https://srfl-paper.webnode.com/
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
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
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
1 Word contains time inside.
Refer to the following paper.
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.
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.
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
Language and Spacetime Time Flow in Word For KOHARI Akihiro and His Time
1
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
2
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).
3
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’
4
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)
5
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)
6
Here set {φt(x) | t∈R } is presented. The set is called orbit.
7
In word, meaning is expressed by flow and time is expressed by orbit.
Tokyo May 3, 2007
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What is signal? A mathematical model of nerve Preparation 1-15
is over
29 December 2018
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--------------------------------------------------------------------------------------------------------------------------------
Preparation 2
Energy
1.
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
*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)
(iii)
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
|
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
2
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
23 January - 26 January 2018
Tokyo
1.
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.
2.
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.
3.
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.
4.
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.
5.
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.
6.
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.
7.
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.
8.
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.
9.
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)
Distance Theory 2005
Generation Theorem 2008
Generation of Word 2008
(2)
Functional Analysis 2008
Complex Manifold Deformation Theory 2008-2009
(3)
The Time of Quantum 2008
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
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.
3
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
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.
- Potential of Language / Floer Homology Language / 16 June 2009
- Homology structure of Word / Floer Homology Language / Tokyo June 16, 2009
- Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008
- Time of Word / Complex Manifold Deformation Theory / 23 December 2008
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
1
(Definition)
(Gromov-Witten potential)
2
(Theorem)
(Witten-Dijkggraaf-Verlinde-Verlinde equation)
3
(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.
4
(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 at
Tokyo June 16, 2009
Sekinan Research Field of language
....................................................................
4
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
1.
2.
------------------------------------------------
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.
1
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.
2
(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 .
ampBσRD2uCσe(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
-------------------------------------------------------------
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.
1
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 = f
2
Monge-Ampère equation
(Equation 1)
Use continuity method
(Equation 1-2)
Kähler form w' = w + f
Ric(w') = tw' + (1-t)w'
δ>0
I = { }
3 is differential over t.
Ding's functional Fw
4
(Lemma)
There exists constant that is unrelated with t.
When utis the solution of equation 1-2, the next is satisfied.
Fw(ut)C
5
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.
1
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
2
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
3
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
On Time Property Inherent in Characters
#2
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.
6
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
Conjecture
Language is understandable.
[View]
0
(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 .
1
(Harmonic map)
Arbitrary variation of { }
2
(Section of )
3
(Levi-Civita connection)
Levi-Civita connection of (M, g) and (N, h)
[Impression]
1
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.
2
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
-------------------------------------------------------------
7
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.
----------------------------------------------------------
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
8
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.
------------------------------------------------------------------
The Days of Decipherment
31/07/2016 14:46
The Days of Decipherment
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
References 2
References 3
- Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
- Half Farewell to the Linguistic Circle of Prague and Sergej Karcevskij
- Sergej Karcevskij, Soul of Language
- Gift from Sergej Karcevskij
- Follower of Sergej Karcevskij
- For KARCEVSKIJ Sergej
- Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique"
References 4
Tokyo
30 July 2016
----------------------------------------------------------------------------------------
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
1
(Definition)
(Gromov-Witten potential)
2
(Theorem)
(Witten-Dijkggraaf-Verlinde-Verlinde equation)
3
(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.
4
(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.
-------------------------------------------------------------------------------------------------------------------------------
What is signal?
The existence that generates language
Preparation 2 1-8
is over
15 January 2019
-------------------------------------------------------------------------------------------------------------------------------
References
Reference is cited from the papers written at SekinanLibrary and SRFL
by TANAKA Akio
at Tokyo from 2003.
...............................................................................................................
Contents
0
Manuscript of Quantum Theory for Language with Preface, Note and Note 2 2003-2018
1
Language, amalgamation of mathematics and physics
2
Language and I
Language and Philosophy
How is the time alive in Language?
3
Egyptian Hieroglyph Exhibition
4
The days when I was thinking on Energy Distance Theory
Thanks to physics through which I ever dreamt in my future
Glitter of youth through philosophy and mathematics in 1970s
5
6
Genealogical Tree of Sekinan's Paper 7th Edition
-------------------------------------------------------------------------------------------
Selected Texts
0
Manuscript of Quantum Theory for Language
Preface
以下に示す「言語の量子理論」は、英文で書かれたQuantum Theory for Language の草稿となるもので、２００３年３月に長野県白馬の白馬アルプスホテルで書かれたものである。発表するのは今回が初めてである。いままで発表しなかったのは、この草稿がまったく資料のないホテルの部屋できわめて短時間のうちに書かれたものであり、そのためその内容が非常に直感的で、通常の論考とは異なる、私にとってはかなり先鋭的なものであったためである。しかも論考は途中で終わり未完のままである。２００３年１２月に或るシンポジウムで発表するためにこの草稿をもとに書き上げたQuantum Theory for Languageでは、論考の趣旨はほぼ一貫しながらもその表現をより穏やかなものにした記憶がいまもはっきりと残っている。しかし現在この草稿を読み返してみると、私が２００３年当時気にした直感性や先鋭さは、やはり私の言語論の本質に深く根ざしたものであり、ほぼ十年におよぶ言語に関する数学的な記述を経て振り返ると、私が今なお書き残しているもっとも重要ないくつかの主題は、ほぼこの草稿に記されたものであることを私はあらためて確認するに至っている。言語の量子化、量子の出現と消滅、量子の接合と階層、量子集合体、量子群の進行と階層、陽性量子と陰性量子、量子の意味とエネルギー。いずれも私にとって、依然として未知であり魅惑的であり続ける。今後私はふたたびこの草稿の位置にもどり、あらためてみずからの思考を紡いてゆくことになるであろう。老年の今となっては、本質は形態に先行し、もっとも表現したいものを、私にとってそれにもっともふさわしい方法で記述してゆくこととなるであろう。いくばくかの時間がなお残されているのであればだが。二十歳のころ恩師が教えてくれた句は今もそのまま生きている。いざゆかん雪見にころぶところまで。
２０１５年３月２３日、東京にて記す。
Tokyo
23 March 2015
-----------------------------------------------------------------------------------------------
言語の量子理論
０ はじめに
中国における主要な言語である漢語には２０００年を超える記載言語すなわち文字言語の歴史がある。
中国古典を代表する『論語』は、現代に残された文字資料であるが、同時に同書編纂当時の口頭言語を強く含んでいるとされる。（吉川幸次郎 １９６７年）
ここでは、おもに『論語』の文例によりながら、記載言語（文言）と口頭言語（白話）の両面にかかわる、言語の分析を試みる。
１ 言語の量子化
言語類型論で孤立語に分類される漢語、いわゆる中国語は、原理的には一つの音節が一つの意味と一つの文字すなわち漢字を持つ。
音節が連続して新しい意味を形成することはあるが、それぞれの音節は常に本来の独立した意味と文字を改変することなく所持することによって、漢語の内在する言語規則基本的にはほとんど改変することなく、長い歴史時代を通して保持してきた。
漢語の文法的機能が、発音や文字の外形的変化を一切行わなず、一語一語の配列すなわち語順によって、形成されるとするが、その語順すなわち統語法の内在原理は、いまだ十分な解明をみたとはいえない。
ここでは文言と白話をともに含むとされる『論語』を漢語の言語モデルついて採用し、主に文字論的な接近によって、漢語に内在する言語法則ひいては一般的な言語に内在する言語構造を分析しようとするものである。
漢語の統語法については、伝統的に実辞と虚辞の２分類によってなされてきた。実辞は実質的な意味を所有するのに対し、虚辞は実辞が所有する意味を補完するために用いられるとされる。
たとえば、『論語』巻頭の一節、「学而時習之、不亦説乎」（文例１）にあっては、一般的には「学」「時」「習」「之」「説」が実辞であり、「而」「不」「乎」が虚辞である。
ここで、一つの意味を所有する漢字一字を、一意味単位を有する言語量子とし、言語の最小単位と仮定する。
伝統的に実辞とされてきたものは、言語量子として通常、一単位の陽性量子を有するとする。虚辞とされてきたものは、通常、一単位の陰性量子を有するとする。一陽性量子をℓ＋、一陰性量子をℓ－と表記することとする。
一陽性量子は、運動推進エネルギーを有し、量子を前方に移動させようとする力を持つ。一陰性量子は、運動吸収エネルギーを有し、量子の運動を吸収し停止あるいは変更させる力を持つ。一陽性量子は、一陰性量子に接合することによって、自らの運動を停止あるいは変更させる。
文例１「学而時習之、不亦説乎」によれば、「学」は「而」によって、その運動を変更され、「説」は「不」「亦」および「乎」によって、その運動を変更され最終的に停止されている。
陽性量子の運動エネルギーは、通常、常時進行性であり、陰性量子に接合するまで、その運動を停止しない。
陰性量子の運動吸収エネルギーは、通常、「一時停止」「方向変更」「停止」等の機能を有する。
文例１によれば、「而」は「一時停止」、「不」「亦」は「方向変更」であり、「乎」は「停止」として機能している。
まとめるならば、量子は意味とエネルギーを有する言語の最小単位である。
２ 量子の出現と消滅
量子は、新しい意味が言語世界へと出現要請されることによって、出現する。要請は言語世界への新しい意味の付加が必要とされたときになされるものである。言語における発話と文字との関係は、発話の先行が一般的であるが、漢語のように、一つの音節が一つの意味を有する言語においては、後出する文字は、発話行為とともに想像上の形態として要請されていたと仮定することも可能であろう。すなわち一つの意味が一つの具体的な識別形態を要請しているのである。この行為は人間の営為として自然なものである。
言語量子は、言語世界への新しい意味を付加するために、出現する。量子が有するエネルギーは、その新しい意味を言語世界に付加するためのものであり、新しい意味と不可分に結合したものである。
量子は、その意味が言語世界に不要となったときに消滅する。文例１において「不」は本来は「花のめしべの子房」を意味したが、その実辞としての意味は早くに消滅に、「打ち消し」を意味する虚辞としたのみ、言語世界に機能してきた。
この「不」で示されたように、実辞と虚辞は漢語において、明瞭に区別されたものではなく、相互の乗り入れや変換が不断に行われてきた。すなわち、上述したように、量子は、当初、言語世界への新しい意味付与のために出現したものである。
当初は陽性量子であった実辞は、言語世界への意味付与の役割を終えるとともに、その運動エネルギーも消滅する。しかし他の量子の運動エネルギーによって、言語世界が構成され改変された痕跡は、他の量子から運動あるいは圧迫を受け続け、運動を受容する量子として、負のエネルギーを付与されて、言語世界に存続することがあると仮定する。こうして陰性量子が出現する。
出現した陰性量子は負のエネルギーを有するため、陽性量子のエネルギーを吸収し、その運動を停止または変更させることとなる。
３ 量子の接合と階層
二つ以上の量子は、互いに接合することによって、新しい構造体を形成する。
文例１「学而時習之、不亦説乎」によれば、量子の接合は以下のようになる。
＜ ℓ＋ ℓ－ ℓ+ ℓ+ ℓ+ ℓ－ ℓ－ ℓ+ ℓ－＞
ここで、陽性量子は、次の量子まで意味を移動させる。陰性量子は、前の量子の運動エネルギーを吸収し、停止または変更させる。
「而」と「乎」が陰性量子として、構造体すなわち文を「停止」させる機能を働かせていることは明瞭であるが、「不」と「亦」の二つの陰性量子は、量子の運動の「変更」として機能していると仮定する。
伝統的な文法によれば、「不」と「亦」は「説」の意味を補完するとされるが、この量子理論では、後ろの量子は前の量子のエネルギーを受け止めるため、従来の説明では処理できない。
ここで「変更」とは、前の量子の運動の方向を変えさせることである。こうして一つの陽性量子は、その運動が別の軌道に移されることとなる。すなわち、陽性量子はある一つの軌道上で運動をおこなうが、ある種の「変更」陰性量子はその軌道を別の軌道に移し、新しい意味構造体を創出する。
その軌道は、モデル的には、数階建ての高層建築が想定される。「学んで時に之を習う」という階から、他の異なった階へと移動させる。
ここで「不」は「学んで時に之を習う」ことを否定する階へ移し、「亦」はこの「学んで時に之を習う」ことを新しい可能性の階へと移動させる。「乎」はこの状況に疑問を投げかける階へと移動させる。
この一連の状況をモデル化して図示する。
学
↓而習之
↓不
↓亦説
↓乎
『論語』の有名な一節、「有朋自遠方来」（文例は以下のように図示される。
有朋
↓自遠方来
４ 量子と量子集合体の符号化
量子は初め陽性として出現し、その消滅によって陰性を生じる。陰性量子は陽性量子の群にあっては、無意味であるために非圧迫量子であり、陽性量子としてかつて獲得した意味空間をいわば不断に圧縮され続ける状態にある。こうしてポンプで押し出されるようなエネルギーが陰性量子に蓄えられ、陽性量子の軌道を変更して異なる階層へ移動させることとなると仮定する。
したがって、この量子理論によれば、漢語のすべての漢字、すなわち意味とエネルギーを有する量子は、次のように符号化することができる。
量子 / /
意味 ℓ
陽性エネルギー →
陰性エネルギー ↓
文例１の「学而時習之、不亦説乎」の符号化は以下のようになる。
/ℓ→/
/ℓ↓/ /ℓ→/ /ℓ→/ /ℓ→/
/ℓ↓/
/ℓ↓/ /ℓ→/
/ℓ↓/
ここで/ℓ→/を数字の１で、/ℓ↓/を数字の０で表すと、「学而時習之、不亦説乎」は１０１１１００１０と数字化できる。
したがって文例１の「学而時習之、不亦説乎」は［進行５，階層４］の言語量子の構造体であるということができる。これを［move５，class 4］と表記する。
文例２の「有朋自遠方来」は
有朋
↓自遠方来
であるから、
/ℓ→/ /ℓ→/
/ℓ↓/ /ℓ→/ /ℓ→/ /ℓ→/
と符号化され、さらに、
１１０１１１
と数字化される。その構造は［move５，class１］である。
もう一例『論語』から文例をとる。
「三年無改於父之道、可謂孝矣」（文例３）
/ℓ→/ /ℓ→/ /ℓ→/ /ℓ→/
/ℓ↓/ /ℓ→/
/ℓ↓/ /ℓ→/
/ℓ↓/ / ℓ→/ /ℓ→/
/ℓ↓/
１１１１０１０１０１１０ ［move 8，class５］
５ 量子群における進行と階層
量子群である文における、一階層における進行度数を見る。
文例1では、4分の５で0.8度数。文例2では、1分の５で５度数。文例3では５分の８で1.6度数となる。
ここで、一階層進行度数がどのような指標となるかを考察する。
進行度数1とは、文言にあっては、実辞１に対して虚辞１の割合であり、1階層に１意味が存在する最も明瞭な文と考えることができる。
したがって進行度数が1以上となると、1階層に2つ以上の意味が存在することなり、一つの意味を細かく規定してより微細な意味を提示することとなる。
これとは逆に進行度数が1未満となると、1階層において、一つの意味を提示することがなく、2階層以上によって初めて意味の完結をみることとなり、一つの意味の周囲に補足的な意味内容が付加されることによってより構成的な意味が成立することとなる。
文例1は0.8度数であり、補足的意味が付加された文である。文例2は5度数であり、微細な意味が規定された文である。文例3は1.6度数であり、ほぼ標準的かやや微細な規定が加わった文である。
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。
７ 陰性量子の意味
陰性量子が有する意味は、上述した「也」の意味分類でも明瞭なように、陽性量子の意味よりはるかに精妙な場合が多い。これらの意味はどのようにして出現したと考えることができるか。
陰性量子が実辞としての機能を消滅させ、一種の真空領域を有していると仮定したが、ここにひとたび断定という意味が成立すると、この「也」に前から接合する陽性量子の意味によって、その真空領域は一定の反応を示すようになる。たとえば「回」のような人名が前に接合すると、「也」は断定的な意味機能の一変容である主題提示として機能することとなる。
８ 陰性量子のエネルギー
陽性量子のエネルギーは、新しい意味を言語世界に付加するために与えられたものであることは、すでに「２ 量子の出現と消滅」において記述したが、ここでは陰性量子が有するエネルギーについて詳述する。
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Note
22 December 2017
This manuscript was written at a hotel of Hakuba, Nagano, Japan in March 2003, where my family stayed for hot spring and ski. In autumn 2002, I thought of relationship between time and characters inspired by WANG Guowei's paper written on old Chinese character's studies, one of which he declared that character heng 亙 was imaged from a ship coming and going the banks. This character contained the notation of the continuous time of ship operation between the banks.
But if character contain the time going, character seemed to have any existence of inherent energy in it.
Note 2
29 June 2018
Definition of quantum in this manuscript was intuitive while in my mind there was rather precise image that was not able to write by mathematical approach in the days of 2003.
Now the situation has been changed drastically through the development of quantum group. Particularly from the Drinfeld's speech at the international mathematician conference in 1984.
I wrote a simple trial paper on quantum group in 2008.
Kac-Moody Lie Algebra Note 2 Quantum Group 2008
Papers related to the pre-thought on quantum group is seen at SRFL Lab.
SRFL Lab's Preparatory paper
Inherent energy in language has been become a little updated after writing in 2003.
Now arranged at the next.
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Energy
Tokyo
20 June 2018
Sekinan Zoho
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1-1
Under the Dim Light
TANAKA Akio
I frequently talked with CHINO Eiichi at the coffee shop near the station we used to get on. The shop was at the second floor and the steps upstairs always sounded squeaking. Under the dim light the topics of conversation was on language or linguistics after all. He was already a university professor but I was a poor research student. But he was always showing me the general tenderness.
The subject he gave me was impressive and useful for me, in which the most important is the history of The Linguistic Circle of Prague and the excellent pioneers of language study. He had of course the unique approach to the study but I had never any conspicuous one except boundless interest on the study.
In his wide and precious telling for me I gradually determined my course to proceed. It was the making of basic and radical foundation on natural language by searching the structure of language through simple and clear description. For keeping this difficult aim I had a decision that there was only way to use mathematics that I had abandoned at the past for its hardness.
In my age 20s, I had read Ludwig Wittgenstein and Nicolas Bourbaki in concentrating. I did not clearly understand Wittgenstein's approach. But I borrowed his writing style that was simple and clear. So my early work’s descriptions were nearly at him. But I decided that I never adopted strongly-intuitive thinking.
I always considered mathematical basis or analogy. My aim was the independence from the intuitive description. Keeping on this course, there was seen the mathematical basis that I must adopt the model in which language universals are clearly described. I entered to the mathematical description of study that was confirmed premises of my way.
Tokyo
1 August 2012
Sekinan Research Field of Language
About
Table
Read more: https://srfl-essay.webnode.com/news/under-the-dim-light1/
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1-2
Language, amalgamation of mathematics and physics
TANAKA Akio
2 April 2013
Language will become the urgent agenda of this century. Language will be recognised as the amalgamation of mathematics and physics. Because language is a mathematically designed physical transmission system in human being. This transmission is finite and compact within a human body but infinite and eternal connected with the outer worlds in the universe.
[References]
Relation between mathematics and physics Operad Meaning Theory. From Cell to Operad. 24 March 2013. ifbetruezoho
finite and compact Simplicial Space language. Composition of Word. 20 January 2013. ifbetruezoho
Infinite and eternal Infinite Loop Space language. Word as Infinite Loop Space. 6 December 2012. sekinanmodel
Tsugaike Highlands, Nagano. 30 August 2011
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2-1
Language and I
TANAKA Akio
Sekinan Library has researched on language from 1986 and successively at SRFL from 2003.
Papers and essays that have been written at Sekinan Library and SRFL Sekinan Research Field of Language
are shown and searched at SRFL Essay and SRFL Paper.
Sekinan Library's main theme is now at language universals that has been a hard target and researched since 1920s at Linguistic Circle of Prague, but the theme had been always put aside from the centre of the study.
In Japan. on Prague School CHINO Eiichi probably first introduced systematically through his direct study experience at Prague between 1958 and 1964.
I first met with him in 1969 at Tokyo, from whom received Russian language lesson at the beginner's small class.
And after some 10 years I again met him in 1979 at his lecture on structural linguistics, to which I listen till till March 1986 when I get apart from the university.
In 1986 I also started to study my own object on language, in which the main theme was language universals by mathematical description, surging from Nicolas Bourbaki, that were already applied to wide and deep approach even at human studies at that time.
For me algebraic geometry was the great aid to deepen the theme, to which from 1920s many researchers have recognised one of the most important but hard to operate with clear description at the field of philology.
In 2003 I narrowly wrote up the trial paper on language's characters, at that time not for total language, but I got the steady way to approach the hard target of language's basis mainly on meaning, through which I faintly could see the final target, language universals.
Tokyo
26 June 2017
Sekinan Library
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3-1
Egyptian Hieroglyph Exhibition
Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012
TANAKA Akio
The British Museum has exhibited The ancient Egypt at Tokyo, titled Journey through the Afterlife Ancient Egyptian Book of the Dead.
The exhibition is excellent, especially total length 37 meters' Greenfield Papyrus is the highlight of the exhibit.
I feel over again that the letters on the papyrus is almost everlasting and my usual thought that the letters are superior than the spoken language which is thought important by Ferdinand Saussure.
Of course I have respected Saussure so much and have read COURS DE LINGUISTIQUE GENERALE time to time.
But the Occidental linguistics has not enough tradition on the ideogram as usual at Chinese characters.
Japan has also succeeded the Chinese tradition and culture. So we have much felt the importance on characters and letters.
Each ideogram has its unique molding technique and coinage ability.
I have very satisfied with the hieroglyph's figures comparison to Chinese characters.
Also refer to the next.
Tokyo
12 September 2012
Sekinan Research Field of Language
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3-2
Essence of Language
Seeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum
TANAKA Akio
20 July 2016 I went to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE being opened at Tokyo National Museum, Ueno,Tokyo.
At the exhibition I first saw 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
40. Clay bar
41. Clay tablet
77. Linear B bar and tablet
About the two Linear I knew the brief information from the book, THE DECIPHERMENT OF LINEAR B by John Chadwick, Cambridge University Press, 1960.
From the exhibition I also knew still now not to decipher the Linear A.
My simple impression is the next.
If the stability of language exist in the structure, the essence of language is appeared at the letters and characters. So I think. The core of this view contains the view for structure of language, which I would be able to write clearly using mathematics.
For more details, refer to the reference 2.
References
A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE [Exhibition Catalogue]. Tokyo National Museum et al. 2016.
THE DECIPHERMENT OF LINEAR B by John Chadwick, Cambridge University Press, 1960.
Reference 2
Perspective for Derived Category Language.Stability of Language
Reference 3
Derived Category Language, 23 July 2016 Edition
Tokyo
27 July 2016
SekinanLibrary
Read more: https://srfl-paper.webnode.com/news/the-essence-of-language/
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3-3
Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow
TANAKA Akio
On 25 May 2018 I went to Tokyo Metropolitan Museum, Ueno, Tokyo to see the exhibition titled French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow.
I have frequently see the modern French paintings represented by the Post-impressionists at the National Western Art Museum,Ueno. But the impression after seeing was pretty different.
The paintings are ranged widely from the 17th to 20th century.
I felt that the The Russian eyes were effected to collect the paintings. For example, Arcadia and the relevant concepts of it were not so popular in Japan but at Russian collectors paid enough attention to them like the Europeans.
One of the most fantastic works for me was Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb). Floating smoke, Cloudy sky, Two horses and people chatting or coming and going.
At the moment to see the painting I recalled the famous quotation, Vita brevis, ars longa.
The painting was drawn in 1885, over 130 years ago. But all the landscapes were vivid like the present and probably in future.
Tokyo
27 May 2018
Sekinan Zoho
The catalogue of the exhibition
French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow
[Note]
6 June 2018
Time and Eternity
When I saw Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb), I felt a fresh awareness of time, which was probably came from the vivid smoke floating in the air or the road partly glistered by the rain immediately before. This landscape was filled with time feeling which was coming on and stopped and was going to the future till now. All paintings may contain such a feeling on time. Now I faced a large canvas of Luir, I freshly got the greatness of painting which has a moment and eternity from the 2 dimensional space.
Does this greatness is only in my mind and not out in the outer world? Do I only feel the eternity in my mind? Almost maybe so, but partly maybe not. Time is real and time feeling floating in the panting is also real. Where is the difference between the two ? Time is direct and time in the painting is in direct, which floats via my eyes and mind. The painting gives me the start of time floating. In that case, what is the painting's giving moment? The moment is made from form and colour on the canvas. Thus, direct time has no tool for going on and indirect time has tools, now canvas, paints and brushes. Direct time and indirect time both enters in my body especially in my mind. The two times both floats in my body. I cannot analyse direct time. But indirect time can be analysed using several methods, form analysis, colour analysis and so forth. Language's letter, character and voice also maybe contain moments for making indirect time. Luigi Loir's Smoke on the Paris Circuit Line ( Paris Suburb) gave reconfirmation of a fresh awareness of indirect time's existence.
[Note 2]
6 June 2018
Research of indirect time
TANAKA Akio
For the research of indirect time now the several tools are prepared for at mine.
Mains are the next.
Overview of the importance and application in the new future is given at the letter to Y., 2018.
This letter is written in Japanese, now not has English version.
Letter to Y. Of Broad language 4th Edition 5 February 2018
For details of research two sites are presented now at SRFL site.
One is from geometrization conjecture started from W.P. Thurston and succeeded by G. Perelman.
The other is from quantum group started from V. G. Drinfel'd.
The two sites are connected through ideogram.
Sekinan Zoho has the invitation to it.
SRFL collection has general relevant information for the present research.
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4-1
The days when I was thinking on Energy Distance Theory
01/02/2016 13:24
q.v. Energy and Distance in Language / 31 August 2008
TANAKA Akio
1.
Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.
2.
In another approach of my study on language universals, Edward Sapir's Language, 1921 was one of my favourite books between 1970s and early 1980s. In his book, the most fantastic concept for me was Drift, that indicated the vast movement of language system itself. I ever gave brief account on it.
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Edward Sapir's Language, 1921 showed me the dynamism of language proposing the concept, drift.
Drift shows us the macro phase of natural language and I was hinted by Sapir's this concept and proposed the micro phase of natural language. The paper "Quantum Theory for Language" is my first total proposal paper describing the natural language's model.
Reference
Substatiality Dedicated SAPIR Edward / 27 February 2005
Tokyo
5 September 2014
Sekinan Research Field of Language
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3.
My language study started from the reading of Old China's Qing dynasty's huge linguistic inheritance, "Xiaoxue", in English Small Study , that is contrary to the name, the most basic and difficult study of classical texts of old China. I particularly loved the books written by WANG Guowei and WANG Yinzhi and DUAN Yucai.
The main book list to which I referred in those days between the age 20s and 40s are shown at the next.
I was especially enchanted with WANG Guowei's work, whose selected papers' title wasGuantangjilin. For him I wrote a short essay as below.
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TANAKA Akio
Guantangjilin is the selection of works by WANG Guowei, which contains vast area of history, literature and linguistics. Some people say that his works are a thousand-year peak from the Song era’s philosopher SHU Xi. I bought his book at Haifeng shudian, Kanda, Tokyo in my mid 20s. The date of colophon is February 1973, publisher is Zhonghua shuju Xianggang fenju.
Probably I bought it in 1973 or 1974. In those days I frequently went Haifeng shudian bookshop for buying Chinese classics, mainly Qing Dynasty’s linguistic works that is called ” Xiaoxue”, Small study at China. Guantangjilin is a very difficult book to understand by my poor study result.
His study era is from Yin Dynasty to Qing Dynasty some 2,500 years of Chinese literary history. At his vast works I was especially charmed in Qing Dynasty’s ancient Chinese hieroglyphic characters, Jiaguwenzi by Chinese. After 40 years, in 2003 I wrote a small paper on language universals through this ancient Chinese hieroglyphic characters at the view point of written language.
The title is On Time Property inherent in Characters. From at that time 10 years passed by. Now I am still learning on language universals but its style is far apart from the days 2003 or 1973. Ambiguity of approach by traditional linguistics is not for my part. I dare challenge to a new frontier of description for language study using mathematics or algebraic geometry.
Refer to the next.
Tokyo
16 November 2013
Sekinan Research Field of Language
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4.
After all,Energy Distance Theory ended in the half-finished situation. But now I am still eager to write and develop the papers on energy and distance. The road is long and winding as ever. I am always accustomed to delay and stagnate. Some rays of light is emitting in the small study room of mine.
Tokyo
19 December 2014
Sekinan Essay
Read more: https://srfl-theory.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory1/
Read more: https://geometrization-language.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory/
Read more: https://srfl-collection.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory1/
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4-2
Thanks to physics through which I ever dreamt in my future
TANAKA Akio
In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I had longed for studying physics in the future. But I selected language's diverse and wide field at the university, from where returning to the clear description like mathematics needed long and winding road for me.
Now in my mind language and physics/mathematics are happily living together for constructing the world's main frame. I wonder why I took so much time to reach here.
Long time ago, at least the days I was strongly influenced by Pascal , philosophy and mathematics were both sides of areas for solving the world's hard problems. It is appropriate that the problems should be solved using all the tools from all the areas, should not be partitioned any artificial walls.
From now on, philosophy so far may be partially solved by mathematics and mathematics might open to the door of complex phenomena in the world never being written clearly. Now they are surely solved one by one by the researchers and we feel the solutions like those are becoming common sense now.
Probably only I reached here being delayed. But at last I am now situated in a tranquil field. Thanks so many pioneers who had cultivated difficult problems to the easier states for applying to the different fields. Especially to mathematicians. Also to physicians through whose worlds I ever dreamt in my future.
References:
Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013
Language, Amalgamation of Mathematics and Physics / 15 April 2014
Tokyo
24 April 2016
SRFL Note
11 December 2017 Text partially revised
Geometrization Language
Read more: https://srflnote.webnode.com/news/thanks-to-physics-through-which-i-ever-dreamt-in-my-future/
.......................................................................................................................
4-3
Glitter of youth through philosophy and mathematics in 1970s
In 1970s at Tokyo or in age 20s, there surely exists glitter of youth in my life, now I remember.
In those days, in Japan many fabulous magazines were successively published. Episteme,Toshi（City）、Chugoku（China) and the likes. Especially I loved reading Episteme which had printed many philosophical or philological articles as the form of special issues concentrated important philosopher, thinker and writer. The chief editor of Episteme was NAKANO Mikitaka（1943-2007), probably one of the best editors in the latter half of the 20th century in Japan. The most impressive number was Ludwig Wittgenstein（1889-1951）, probably in 1977. Also influenced from the issue of Kurt Gödel（1906-1978）who gave me the possibility of set theory and its application.
In my life, Wittgenstein gave the big influence for thinking and writing style, never entering or approaching his essential philosophical themes.After millennium year when I started the regular writing on language universals, my writing style was at first rather resembling in his Tractatus Logico-Philosophicus. My paper written in 2003, Quantum Theory for Language shows a very imitative style to him. This tendency kept on for some time till I changed to adopt algebraic method for clearer description to the themes.
1970s was a relatively calm time after those university’s revolution in the late 1960s in which I was also compellingly rolled in. In those days I time to time had wandered between library and old book shops seraching my life-time true themes cowardly avoiding the turmoils of university and towns. Blaise Pascal（1623-1662）’s Pansees was my favourite one. One day at Kanda’s Taiwan Chinese book shop Haifeng Shudian, I bought WANG Guowei（1877-1927）’s Guantangjilin that clearly opened the new frontier for classical Chinese philology along mainly streamed by Small Study, traditional restrict linguistics in China. Influenced WANG Guowei I trlally wrote a paper titled On Time Property Inherent in Characters, 2003 by which I began the later start of language study.
In 1970s, I had cherished a dream in which I wanted to use mathematical description and get the essential of language. But I had not any ability to proceed the study for it while I read at random mathematical books. One day I found and bought the amount Nicolas Bourbaki（1935-）’s text books at old book shop in Kanda, Tokyo. They were hard to continue reading for my talent in those days. After all, the books were put aside the desk. The only remaining in my mind was adoration to Bourbaki and their brilliant achievement. My return to Bourbaki was long after in 1990s when I again tried the pursuit of language having a clear vision to study language universals according to the Linguistic Circle of Prague, especially aiming to resolve the supposition presented by Sergej Karcevskij（1884-1955).
Turning round the past days, my way was always narrow and winding. But it has been kept till now not breaking off in any situations. The way was almost always glittering in my youth days in spite of under the cloudy skies. Probably I have walked happily till now being assisted by many people especially at the field of language, mathematics and the relevant studies.
At random now I remember the dear names, but from whom I never cannot hear their voices. HASEGAWA Hiroshi, CHEN Donghai both Chinese language, KAJIMURA Hideki, CHO Shokichi both Korean language, Natary Muravijowa Russian language, ONO Shinobu Chinese literature, MIIYAZAKI Kenzo, FURUTA Hiromu, KONDO Tadayoshi all three Japanese literature, ANDO Tsuguo French poem, SAEKI Shoichi Haiku, IKEDA Hiroshi Japanese classical drama, SAITO Kohei sculpture, YAMAGISHI Tokuhei bibliography, NISHI Junzo Chinese philosophy, KAWASAKI Tsuneyuki Buddhism, CHINO Eiichi Russian language, the Linguistic Circle of Prague. At last dear friend of high school days KANEKO Yutaka mathematics and our youth.
Tokyo
6 March 2015
24 March 2018 Text revised and link added
........................................................................................................................
5-1
Ideogram Paper Enlarged Edition
1. On Time Property Inherent in Characters 2003
2. Ideogram 2005
4. ONO Shinobu and Bernhard Karlgren 2015
5. Essence of Language 2016
6. The Days of Decipherment 2016
7. The Days of Ideogram 2017
8. The Days of Ideogram Note added Edition 2017
9. The comparison between 2003 and 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
10. Time and Shape of Language from How is the time alive in language 2017
11. Connection between early paper's quantum and recent paper's geometry 7th edition 2017
12. Letter to Y. Of the century of language 2018
13. Letter to Y. Of Broad Language 4th edition 2018
14. Determination of the concept, Broad Language 2018
.............................................................................................................
5-2
Letter
1. Letter to O. again. 2 January 2018
vide: At the campus of university Abstract from The letter to O. again
2. Letter to Y. Toward geometrization of language 8 January 2018
3. Letter to Y. Of Broad Language 4th Edition . 5 February 2018
4. Letter to the library Short autobiography between 1969 and 1986. 19 May 2018
vide: At the lawn terrace before library
Tokyo
14 June 2018
Sekinan Zoho
.............................................................................................................
5-3
The Days and The Time
The days between von Neumann Algebra and Complex Manifold Deformation Theory
Language between Sergej Karcevskij and string theory, one century's trace
Quantum Language between Quantum Theory for Language 2004 and Generation of Word 2008
Tokyo
13 August 2018 Arranged
SRFL Lab
Read more: https://srfl-lab.webnode.com/news/the-days-and-the-time/
...........................................................................................................
5-4
Prague
Tokyo
2 August 2016
30 May 2018 Revised
Sekinan Zoho
Read more: https://srfl-collection.webnode.com/news/prague/
............................................................................................
5-5
Pioneer
Bourbaki, Nicolas
The Time of Language, Ode to The Early Bourbaki To Grothendieck
Bourbaki' ELEMENTS DE MATHEMATIUE Troisieme edition, 1964
Karlgren, Bernhard
ONO Shinobu and Bernhard Karlgren
Karcevskij, Sergej
Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
Half Farewell to the Linguistic Circle of Prague and Sergej Karcevskij
Sergej Karcevskij, Soul of Language
Gift from Sergej Karcevskij
Follower of Sergej Karcevskij
For KARCEVSKIJ Sergej
Jakobson, Roman
Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
Sapir, Edward
Edward Sapir, Language, 1921
Substantiality
Saussure, Ferdinand de
Uniformity For SAUSSURE Ferdinand
WANG Guowei
The Time of WANG Guowei
40 years passed from I read WANG Guowei
von Neumann
The days of von Neumann Algebra
The days between von Neumann Algebra and Complex Manifold Deformation Theory
Wittgenstein, Ludwig
The Time of Wittgenstein
For WITTGENSTEIN Ludwig Revised with Symplectic Language Theory and Floer Homology Language
Read more: https://srfl-paper.webnode.com/products/pioneer-of-language-study-at-gist/
Tokyo
2 August 2016
Sekinan Zoho
Read more: https://srfl-collection.webnode.com/news/pioneer/
...................................................................................................
5-6
Linear B
From seeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum, Ueno, Tokyo. 2017
Essence of Language
The Days of Decipherment
Reference
Derived Category Language
Read more: https://srfl-collection.webnode.com/news/linear-b/
.....................................................................................................
7
What is letter?
TANAKA Akio
23 February 2019
ENSILA
1
Provisional definition of Letter, word and sentence.
Letter is immutable.
Letter has an indication.
Letter connects other letters.
Letters are finite.
Connected letters have a new indication, which is called word.
Word connects other words.
Words are infinite.
Connected words have a new indication, which is called sentence.
Sentences are infinite.
2
Letter is assumed to be generated from signal.
Provisional definition of signal.
Signal is immutable.
Signal has energy.
Signal has an indication.
Signal connects other signals.
References
1
What is signal?
Preface, Preparation and Preparation 2 Completed
21 November 2018 - 15 January 2019
2
How the language has been sought for ? 1-8
Read more: https://srfl-paper.webnode.com/news/what-is-letter-23-february-2019/
......................................................................................................
Tokyo
27 February 2019
.............................................................................................................
1
Quantum Group Language
1 March 2019
Language, Amalgamation of Mathematics and Physics
2
1. Kac-Moody Lie Algebra Note 2 Quantum Group 2008
2. Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH 2009
1.Floer Homology Language
2. Homology Structure of Word
3. Proto Arithmetic Geometry Language
4.Language, Word, Distance, Meaning and Meaning Minimum
1. Manuscript of Quantum Theory for Language Note added 2003
2. Quantum Theory for Language 2004
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
2. Operad Meaning Theory From Cell to Operad Revised Edition 2013
3. Connection between early paper's quantum and recent paper's geometry 7th edition 2017
4. Karcevskij conjecture 1928 and Kawamata conjecture 2002 / I briefly wrote about the conjecture 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 2017
αi ⊂h*
∈ Z hi ∈ hz
ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )
p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )p [1-aijp]qiFi1-aij-pFjFip = 0 ( i , j∈I , i ≠j )
Coderivative
= 0 at (BΠC, mk) (k>0)
= 0 at (BΠC, mk) (k≥0)
= 0 at (EΠC, mk) (k>0) 
= 0 at (EΠC, mk) (k≥0) 
Read more: https://srfl-lab.webnode.com/products/symplectic-language-theory-note-6-homological-mirror-symmetry-conjecture-by-kontsevich/
is topological space.
is simplicial space.
is represented by geometric realization of 
as the next.
is topological space.
is singular simplex.
is free Abelian group generated by set 
.
.
is singular chain complex of 
and has strongly convergence spectral sequence called Atiyah-Hirzebruch spectral sequence.
is given by geometric realization of simplicial space 
.
.Sergej Karcevskij declared a conjecture for language's asymmetric structure on the TCLP of the Linguistic Circle of Prague in 1928. I briefly wrote about the conjecture as the following.
......................................................................................................................................
Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"
From Print 2012, Chapter 18
Non-symmetry. It was the very theme that I repeatedly talked on with C. Prague in 1920s. Karcevskij's paper "Du dualisme asymetrique du signe linguistique" that appeared in the magazine TCLP. Absolutely contradicted coexistence between flexibility and solidity, which language keeps on maintaining, by which language continues existing as language. Still now there will exist the everlasting dual contradiction in language. Why can language stay in such solid and such flexible condition like that. Karcevskij proposed the duality that is seemed to be almost absolute contradiction. Sergej Karcevskij's best of papers, for whom C called as the only genius in his last years' book Janua Linguisticae reserata 1994.
Source:
- Tale / Print by LI Koh / 27 January 2012
Reference:
- Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / 8 September 2011
- Condition of Meaning / 11 September 2011
- Dimension of Language / 4 September 2013
- Synthesis of Meaning and Transition of Dimension / 6 September 2013
[Note, 2 October 2014]
In this Tale, Print 2012, C is CHINO Eiichi who was the very teacher in my life, taught me almost all the heritage of modern linguistics. I first met him in 1969 at university's his Russian class as a student knowing nothing on language study.
Tokyo
23 February 2015
SIL
.....................................................................................................................................
But the theme was very hard even to find a clue. The turning point visited after I again learnt mathematics especially algebraic geometry in 1980s.
In 2009 I successively wrote the trial papers of the theme assisted by several results of contemporary mathematics. The papers are the following.
..................................................................................................................................
- Notes for KARCEVSKIJ Sergej, "Du Dualisme asymétrique du signe linguistique"
- Description of Language
- Structure of Word
- Condition of Meaning
Category theoretic mirror symmetry conjecture
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
.....................................................................................................................................
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complex image of symplectic geometry's some theorems will become clearer.
References
Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009
.
.- TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, Derived category of coherent sheaf and birational geometry, page 148, Conjecture 6.43.
- Bridge across mathematics and physics
- Kontsevich's conjecture Category theoretic mirror symmetry conjecture
Bridge across mathematics and physics / Revised
(5)
In the 21st century, language will definitely become one of the most important themes and targets of mathematics for us all
Boundary:
Why is boundary necessary in language?
Description
THE ROAD TO REALITY A Complete Guide to the Laws of the Universe
Dimension
Language and Dimension
Distance
Distance of Word
Geometry
Arithmetic Geometry Language
Meaning
Meaning Minimum
Space
Quantization of Language
Structure
Homology Structure of Word
True and False
The True-false problem of the Crete
Read more: https://srfl-lab.webnode.com/products/in-the-21st-century-language-will-definitely-become-one-of-the-most-important-theme-and-target-of-mathematics-for-us-all/
......................................................................................................................
Contents
Read more: https://srfl-theory.webnode.com/news/derived-category-language-23-july-2016-edition/
Bridge across mathematics and physics / Revised
Category theoretic mirror symmetry conjecture
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
-----------------------------------------------------------------------------------------------------------------------
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
References
Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009
Tokyo
10 May 2016
SRFL Theory
Read more: https://srfl-theory.webnode.com/news/kontsevichs-conjecture-category-theoretic-mirror-symmetry-conjecture/
19 May 2016
SRFL Theory
Derived Category Language 1 |
Fukaya category is
Fuk(X, ω).
General symplectic manifold is
.3.
is 
.Conjecture
and 
Sergej Karcevskij declared a conjecture for language's asymmetric structure on the TCLP of the Linguistic Circle of Prague in 1928. I briefly wrote about the conjecture as the following.
.....................................................................................................................................
Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique"
From Print 2012, Chapter 18
Non-symmetry. It was the very theme that I repeatedly talked on with C. Prague in 1920s. Karcevskij's paper "Du dualisme asymetrique du signe linguistique" that appeared in the magazine TCLP. Absolutely contradicted coexistence between flexibility and solidity, which language keeps on maintaining, by which language continues existing as language. Still now there will exist the everlasting dual contradiction in language. Why can language stay in such solid and such flexible condition like that. Karcevskij proposed the duality that is seemed to be almost absolute contradiction. Sergej Karcevskij's best of papers, for whom C called as the only genius in his last years' book Janua Linguisticae reserata 1994.
Source:
- Tale / Print by LI Koh / 27 January 2012
Reference:
- Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / 8 September 2011
- Condition of Meaning / 11 September 2011
- Dimension of Language / 4 September 2013
- Synthesis of Meaning and Transition of Dimension / 6 September 2013
[Note, 2 October 2014]
In this Tale, Print 2012, C is CHINO Eiichi who was the very teacher in my life, taught me almost all the heritage of modern linguistics. I first met him in 1969 at university's his Russian class as a student knowing nothing on language study.
Tokyo
23 February 2015
SIL
....................................................................................................................................
This asymmetric duality of linguistic sign presented by Karcevskij has become the prime mover for my study from the latter half of the 20th century being led by my teacher CHINO Eiichi.
But the theme was very hard even to find a clue. The turning point visited after I again learnt mathematics especially algebraic geometry in 1980s.
In 2009 I successively wrote the trial papers of the theme assisted by several results of contemporary mathematics. The papers are the following.
......................................................................................................................................
Sekinan Research Field of Language
Category theoretic mirror symmetry conjecture
When there exists mirror relation between X1 and X2, derived category of X1's coherent sheaf and derived Fukaya category defined from X2's symplectic structure become equivalence.
M. Kontsevich. Homological algebra of mirror symmetry, Vol. 1 of Proceedings of ICM. 1995.
-----------------------------------------------------------------------------------------------------------------------
[Note by TANAKA Akio]
In the near future, symplectic geometry may be written by derived category. If so, complexed image of symplectic geometry's some theorems will become clearer.
References
Mirror Symmetry Conjecture on Rational Curve / Symplectic Language Theory / 27 February 2009
Tokyo
10 May 2016
SRFL Theory
............................................................................................................................................
In the TODA's book, I received the great hint on Karcevskij's conjecture for language's hard problem.
The hint exists at Kawamata conjecture presented in 2002. The details are the following.
............................................................................................................................................
Derived Category Language 2
..- TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, Derived category of coherent sheaf and birational geometry, page 148, Conjecture 6.43.
- Bridge across mathematics and physics
- Kontsevich's conjecture Category theoretic mirror symmetry conjecture
For TODA's book, refer to the next my short essay.
...........................................................................................................................................
Bridge across mathematics and physics / Revised
19 May 2016
SRFL Theory
Read more: https://srfl-theory.webnode.com/news/karcevskij-conjecture-1928-and-kawamata-conjecture-2002/
Additional meaning and embedding
1.Derived category
Fuk(X, ω).
General symplectic manifold is
.3.
is .Conjecture
and 2.Embedding
Derived Category Language 2
.3.Stable and mobile
TANAKA Akio
September 11, 2011
*(Sn)
, 
. .All rights reserved.
© 2011 by The Sekinan Research Field of Language
4.Additional meaning
[x1, x2, ..., xn]
Cn f (a1, a2, ..., an) = 0, 
a }
Cn | f (a1, a2, ..., an) ≠ 0}
, O)
Rf
.
)-1U) )-1U), X→Y )
is surjection, t is isomorphism overclosed partial set defined by p= Ker 
.
p 
is injection 
is dominant. that is given by natural injection is isomorphism over open set, is called open immersion.
satisfies next conditions is called algebraic variety.
I, intersection 
is open partial set of 
.
that defines surjective homomorphism is expressed by 
.
of closed embedding defined by is called diagonal.
is called glue of A and B by C.
Spm R, Spm T 
Spm S
, next is equivalent.
is generated by R and S.
is called R value point of X. is called set of R value point of X, expressed by X(R).
X(S), 
is function from ring category over k to category of set.
over ring R {
}
} has functional morphism.
satisfies the next conditions, X is called coarse moduli. : 
.
,
is existent uniquely.
k, 
(k') is always bijection.
is functor to group's category is called algebraic group.
are commutative for 
.
for A.
{
}
.
is called closed map when 
is closed set image 
becomes closed set.
is closed map for arbitrary manifold Y.
is closed map.All rights reserved.
© 2011 by The Sekinan Research Field of Language
5.
Note
- From symplectic geometry to Fukaya category.
- From Fukaya category to derived category.
- Kawamata conjecture at derived category.
- Smooth objective algebraic manifolds satisfies birational map.
- Fully faithful embedding exists between two manifolds.
Extract of Zoho papers at Sekinan Library.
More details refer to Sekinan Zoho.
- [2012]
- [2011]
Stable and Unstable of Language
- [2009]
Floer Homology Language
..- TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016.Chapter 6, derived category of coherent sheaf and birational geometry page 148 Conjecture 6.43.
- Bridge across mathematics and physics
- Kontsevich's conjecture Category theoretic mirror symmetry conjecture
Read more: https://srfl-theory.webnode.com/news/derived-category-language-2-kawamata-conjecture/
Language stability and triangulated category
Language's stability presented by Sergej Karcevskij in 1928.
Bridgeland's stability seems to hint for Karcevskij's stability.
This paper is unfinished.
Tokyo
23 May 2016
SRFL Theory
Read more: https://srfl-theory.webnode.com/news/language-stability-and-triangulated-category/
Language stability and triangulated category
Language's stability presented by Sergej Karcevskij in 1928.
Bridgeland's stability seems to hint for Karcevskij's stability.
is bounded kernel of t-structure.
gives stability condition on A .2.
[Paper on Karcevskij conjecture by TANAKA Akio 2011]
TANAKA Akio
September 11, 2011
*(Sn), . .[Paper on description of language by TANAKA Akio 2011]
TANAKA Akio
September 9, 2011
generates £ ( 
)
is identified as the partial space of £( 
) that quadrastic Lie bracket of 
generates.
) that Im η generates a 
becomes isomorphic with holonoly Lie algebra completion 
.
of M's fundamental group.All rights reserved.
© 2011 by The Sekinan Research Field of Language
25 May 2016
SRFL Theory
Read more: https://srfl-theory.webnode.com/news/derived-category-language-3/
9
Perspective for Derived Category Language. Stability of Language.
TANAKA Akio
1. Model
Derived Category Language.
2. Base
Manifold.
3.Main method
Stability conditions.
4. Theorem
R. Pandharipande and R.P. Thomas. Pandharipande-Thomas Theorem (1998).
K. Behrend. Behrent contructable function (2009).
Y. Toda. Curve-counting theories via stable objects (2010).
T. Bridgeland. Hall algebras and curve-counting invariants (2011).
5. Definition
Mu limit semi-stable object.
6. Space
Mu limit semi-stable object's moduli space.
7. Stability of Language
In the space(6.) language keeps stability as the set of derived duality.
8. Essence of Language
Duality is the essence of language.
Refer to the next.
Derived Category Language, 25 May 2016 Edition.
Actual Language and Imaginary Language. To LÉVI-STRAUSS Claude.
This paper is unfinished.
Tokyo
19 July 2016
Sekinan Library
Read more: https://srfl-paper.webnode.com/news/perspective-for-derived-category-language-stability-of-language/
10
Calabi-Yau 3-folds.
2. Theorem
R. Pandharipande and R.P. Thomas.
Pandharipande-Thomas Theorem (1998).
K. Behrend.
Behrent contructable function (2009).
Y. Toda.
Generating functions of stable pair invariants via wall-crossing in derived categories in algebraic geometry. (2008)
Curve-counting theories via stable objects (2010).
T. Bridgeland.
Hall algebras and curve-counting invariants (2011).
D. Joyce and Y.Song.
A theory of generalized Donaldson-Thomas invariants. (2012)
3. Definition
Generalized DT invariants. ( Joyce and Song. 2012)
4. Isomorphism
Isomorphism is induced in the defined moduli spaces.
5. Duality and mirror
If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.
Reference
Rensetsuso no Doraiken ni kakawaru shomondai. TODA Yukinobu. 2016. Sugaku shobo. Tokyo.
Reference 2
Derived Category Language, 25 May 2016 Edition.
Reference 3.
Actual Language and Imaginary Language. To LÉVI-STRAUSS Claude.
Reference 4.
Symplectic Language Theory Note 3 Mirror Symmetry Conjecture on Rational Curve.
Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH.
Reference 5.
Main papers of Sekinan Library.
SRFL Paper.
Paper ends.
------------------------------------------------------------------------------------------------------
This paper is unfinished.
Tokyo
22 July 2016
Sekinan Library
Issue Paper 2
Over
Tokyo
3 March 2019
ENSILA
...............................................................................
Main Issue 4
Space and Boundary
Contents
- Why is boundary necessary in language?
- Boundary of Words
- Frame-Sentence Language Boundary
- Language and Spacetime
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
6 Shift of Time
7 Construction of Spacetime specially on Transformation with boundary for Dimensions
8 Stability of Language
9 Time Flow in Word
..................................................................................................................
Text 1
Why is boundary necessary in language?
I have thought of language as a physic existence that has inevitably boundary to the outer world.
My question is simple and primitive. I ever wrote about the change of language - If there be change, there are exactly the situations before change and after change. Just where does changing substance exist? In the essay, rotten apple was used as the symbol of changing language.
..................................................................................................................................
Presupposition on Natural Language
TANAKA Akio
1.
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a home-maker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
Reference
For WITTGENSTEIN Ludwig / Position of Language / 10 December 2005-3 August 2012
Tokyo
22 August 2012
Sekinan Research Field of Language
..................................................................................................................................
2.
Language&s substantiality has been considered since I returned to the mathematical approach for learn language universals from the utterly beginning. In 2005 I wrote a tiny trial paper on the substantiality of language for thinking the study course hereafter.
.....................................................................................................................................
In 2013, I again wrote on the substantiality of language at the new level containing the determinate essence of language, dimension and time. The title is Macro Time and Micro Time. In this paper I thought that dimension is the essential factor of meaning, especially containing Infinitive meaning.
....................................................................................................................................
Macro Time and Micro Time
24 July 2013
atbankofdam
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 circumstanstances, langauge 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.
(Poincaré duality)
For oriented compact n-dimension topological manifold M ,
biliear form
is exact,
and 
become dual space each other.♦
Word := M Boundary of language := p Dual language :=
and Language := 
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.
Distance Theory
Mirror Theory
Guarantee of Language
25 May 2012
Sekinan Research Field of Language
5.
Relation between boundary and synthesis in language is utterly unknown field for me. Study has just started from the entrance position. Recent results are the next.
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Synthesis Conjecture
Conjecture for synthesis of meaning in word
TANAKA Akio
Synthesis
1 Conjecture for synthesis of meaning in word
29/09/2013 19:25
For synthesis of meaning in word, Conjecture: Condition for synthesis of meaning in word i s proposed by cohomological expression.
2 Conjecture: Condition for synthesis of meaning in word
29/09/2013 18:38
On condition for synthesis of meaning in word, at conjecture is proposed by the next result of etale cohomology.
Result
——————————————————-
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A”
A and A’ have enough many injective objects.
If F transfers A’ s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
——————————————————–
Conjecture
Preparation
Word is shown by R . This word is called old word .
Base meaning in word is shown by F .
Word that has base meaning is shown by RF .
Additional meaning to word is shown by G .
Word that has additional meaning is shown by RG . This word is called intermediate word .
Word that has base meaning and additional meaning is shown by R ( G O F ). This word is called new word .
Conjecture
For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology.
3 Canonical natural equivalence
29/09/2013 18:08
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A”
A and A’ have enough many injective objects.
If F transfers A ‘s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
Source: Conjecture for synthesis of meaning in word / sekinanlatest 2013
Tokyo
1 May 2014
Sekinan Research Field of Language
6.
Three Conjectures containing Synthesis Conjecture are shown at the next.These conjectures are the latest result of language universals at SRFL Sekinan Research Field of Language.
Read more: https://srfl-theory.webnode.com/news/why-is-boundary-necessary-in-language/
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Text 2
Boundary of Words
X } 
X } S ∞ ( X ) 
min{( x | z)x 0 , ( y | z ) x 0 }- δ 
, δ -hyperbolic space is abbreviatedly called hyperbolic. 
max{ d ( x, z ) + d ( y, w ), d ( x, w ) + d ( y, z ) } +2 δ 
[0, λ ] 
X is expressed by 
. 
xyz = 
is called geodesic triangle. 
X }.
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Text 3
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Text 4-1
Definition for the Child who Lost the World
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.
Tokyo November 3, 2008 Added
[Referential note / November 29, 2007]
For Authentication of Solidity
[Definition added / November 3, 2008]
Definition 10, the part of
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Text 4-9
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Text 4-8
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Text 4-7
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Text 4-6
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Text 4-5
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Text 4-4
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Text 4-3
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Text 4-2
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Main Issue 5
Time and ideogram
Contents
- On Time Property Inherent in Characters
- Aurora Theory Distance and Time
5th Time for KARCEVSKIJ Aurora Theory
From Gauss Plane to AuroraDictoron Quantum and Trace [AT1]
Dictoron and Aurora
＜Language is aurora dancing above us.> [AT2]Aurora and Curvature [AT3]
Dictoron as Language quantum [AT4]
Aurora and Riemann Sphere [AT5]
Dictoron, Time and Symmetry
＜Language Multi-Time Conjecture> [AT6]Limitation of Meaning [AT7]
Aurora Plane [AT8]
Dictoron and Time [AT9]
Word, Phrase and Sentence
＜Language Multi-Time Conjecture 2> [AT10]Distance and Time
＜Language Multi-Time Conjecture 3> 5th Time for KARCEVSKIJ [AT11]Why Human Time Flows Fast and Slow on Occasion
[IL1]
Read more: https://srfl-paper.webnode.com/products/aurora-theory-contents/Aurora Time Theory
From Gauss Plane to Aurora 2Time on Aurora [ATT1]
Imaginary Time and Imaginary Space From HAWKING Stephen [ATT2]
Enlarged Distance Theory [ATT3]
Opened Time and Closed Time For WANG Guowei
Opened Time and Closed Time Revised For WANG Guowei and DELBRÜCK Max [ATT4-2]
Read more: https://srfl-paper.webnode.com/products/aurora-time-theory-contents/
Ideogram Paper
- Ideogram 2005
- Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012
- Macro Time and Micro Time 2013
- Essence of Language 2016
- The Days of Decipherment 2016
- The Days of Ideogram 2017
- The Days of Ideogram 2017
- The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 2017
- Letter to Y. Toward geometrization of language 2018
- Letter to Y. Of Broad Language 4th edition 2018
- Determination of the concept, Broad Language 2018
- Ars longa Seeing Masterpieces o f French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018
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Text 1
Here I will try to consider on the generation and the function of characters that have been used in Chinese which is classified to isolating language in linguistic typology.
Concerning the early forms of characters, we can verify them by the ancient inscriptions on bone and tortoiseshell that were discovered at /Yinxu/ and so forth. At the first stage that is usually classified to five on the inscriptions, they already displayed the inceptive completion, from where it is very difficult to speculate the beginning shapes of characters. On vocabulary and syntax, inscriptions displayed the almost same inceptive completion. Here what is inceptive completion is meant that comprehension or speculation is practicable by the usage of modern Chinese. Therefore the generation and the function of characters are subsidiary after the inscriptions. On the situation of forming the inscriptions namely explanation to decipher inscriptions, many researches are accumulated. Here, in these researches, I proceed with consideration claiming the works of after 1990 in main.
1 Generation of characters
When we see the inscription of character /yu/ that means bringing up in English, it is impossible to doubt that this inscription shows the situation of childbirth time by woman. In this inscription the situation of childbirth is shown by three stages. First there is a figure in which woman is going to give birth to a baby crossing both arms at the front of her chest. She takes a bent-forward posture, sticks her buttocks out and bend her knees gently. Second the situation of what the waters break is shown by the signs similar to dotted lines. Third at central or under part of the waters, a new born baby is shown in the shape of baby’s head inverted. Through three factors illustrated in the inscription, character /yu/ is clearly expressed the situation of childbirth time and the immediately after the birth time.
When we see the inscription of character /yan/ that means language or speak in English, the form of the inscription is simplified or transformed considerably at the first stage of classification on inscriptions. So the explanation to decipher inscriptions is developed variously. Here I will show one interpretation including the result of Chinese archeology in recent years. A form of character /yan/ is able to see the three parts that are upper, middle and under. According to the result of Chinese archeology, the upper part is regarded as the tongue’s point of a bronze bell used at meeting in /Yin/ period. The central part of character /yan/ is the body of a tongue. The under part of character /yan/ is regarded to be the outside of a bell. In /Yin/ period, at the time to let the meeting begin, the bronze-like bell was ringed loudly to let the people connected to know. When the meeting was opened, the bell was inferred to put up side down on a table. That is to say, the main body of a bell is inferred to be putted up side down and the tongue of a bell is inferred to be putted upward on the form of bell’s setting. This setting of a bell is shaped regarded to become the character’s form of inscription of on bone and tortoiseshell. According to this interpretation of the inscription, /yan/ can be said to show the situation of post-notification of a meeting in /Yin/ period.
Therefore the figuration of the reversed bell was regarded to become the inscription of character /yan/.
When we see the inscription of character /geng/ that means to cross in English, we comprehend that the inscription shows the two parallel lines in which a bow pattern is included. WANG Guowei†0 regarded that this inscription is as same as the character /heng/ that means permanent or lasting in English. Now I follow his interpretation. He wrote in his paper that two up-and-down lines are both banks of a river and inner bow shaped figure is a ship which goes and returns between the banks†1. According to this interpretation, /geng/ or /heng/ shows the operations of crossing a river, that operations are permanently repeated in an identical space†1.
From the inscriptions of three characters of /yu/, /yan/ and /geng/, now we can induce or infer the following.
First, Inscriptions which are original shapes of characters, in some cases, have a proceeding time in characters themselves. That is to say, as for character /yu/, that means the time of childbirth, from beginning to end. As for character /yan/, that means the time of meeting, from announcement to being open. As for character /heng/, that means the proceeding time of crossing the river by ferry.
Second, on the inscriptions, several aspects of the various phenomena which occur on the proceeding time in characters are sometimes shown by the images or implications. As for character /yu/, remarkable aspects’ figures are bending mother’s body, amniotic fluid and new born baby†2. As for character /yan/, the one remarkable is the bell which is set in the upside down condition, which means the announcement of meeting which was already opened a few minutes ago. The other remarkable is the same bell which is set on the table in the upside down condition, which means the meeting is now going†3. As for character /heng/, remarkable aspects are both banks and a ferry boat.
Third, on the inscriptions, several aspects, which are shown by the remarkable figures, transmit the messages. As for character /yu/, babybirth from mother’s body, the situation of birth time and new baby appeared in this world are transmitted simultaneously by the one character /yu/. As for character /yan/, transmitting is announcement of meeting, opening of meeting and contents of being discussed by the meeting. As for character /heng/, work of crossing the river, reach the opposite bank of the river and repetitions of these works, namely, constancy are transmitted for the information.
Therefore from the induction or inference on the generation of character’s meaning above mentioned, the following function of characters is led for us.
2 Function of characters
First, the time-proceeding aspect being inhered in every character has the strong tendency toward the most distinctive information of the real world. As for character /yu/, while woman is giving birth to a baby, the most distinctive information is the figure of mother’s body bending, and after birth, the existence of a new baby becomes the most distinctive information†2. The various grammatical functions of one character are generated from the time proceeding and successive phenomena of distinctive aspects in the real world.
As for character /yu/, at the birth time, verbal aspect of giving birth is emphasized, but after birth nounal aspect of a new born baby oneself is emphasized. As for character /yan/, before the meeting verbal aspect of telling the opening is the most important thing, but while being opened or after the meeting the nounal aspect of speaking content of the meeting is the most valuable thing†3.
Second, when two or over two characters are connected, every character wants to emphasizes selecting one distinctive aspect inherent in oneself, and want to connect to the other character or characters. Because if two or over two aspects is transmitted, there will appear the non-clearness in the information. As for character /yu/, connection with character /sheng/ (which means grow in English), namely /sheng yu/, in this situation /yu/ means give birth to in English. Connection with /cai/ (which means a person of talent in English), namely /yu cai/, in this situation /yu/ means educate in English. That is to say, character /yu/ has two phases of meanings. One is concerned with the situation of child-birth of mother’s body. The other is concerned with the situation of a person that is already growing.
Third, every character has several aspects of inherent time inclination. When there is a connection of two characters, each character has the choosing operation from the several meanings in the character. Two or over two characters generate a new meaning complex by the operations of choosing the most precedent meaning in the each. This complex can maintain the new clearness of information on the connection of characters which have many branches of meanings in total.
For example, from above mentioned characters /yu/, /yan/ and /heng/, when two characters /heng/ and /yan/ are connected to one word /heng yan/, /heng/ chooses the meaning constant in English and /yan/ chooses the meaning utterance in English. New meaning complex is the expression by the stable person. This /heng yan/ appears in the Chinese classic Mengzi by the complex meaning.
Then, when every individual character does selectivity of aspects, what functions does work in the characters? On the other hand, when two or over two characters connect by the choosing the most precedent meaning respectively, what functions does work out of the characters?
3 Self selectivity of function on character
Now I examine the situation of what two or over two characters connect and generate the new aspect complex. For instance, I adopt above mentioned characters connection word /heng yan/.
In the first place, /yan heng/, which is a reverse disposition of /heng yan/, is examined. This characters disposition is not notified as the one word generally in the Chinese. This characters set is usually recognized as a sentence. The meaning is <The utterance is eternal.> in English. That is to say, this characters set does not generate new aspect complex and two aspects of every individual character form in a line. Why this divergence, namely generating word or sentence, occurs in the characters disposition?
Here I infer that< time property inherent in characters> is worked. Detailed inference is mentioned below.
On
†1
†2
†3
[Postscript July 11. 2008]
- Solid Trace Theory / Solid Trace / Tokyo April 19, 2006
- For Authentication of Solidity / Tokyo November 6, 2005
[Postscript December 23, 2008]
- Energy Distance Theory / Conjecture 2 / Geometry of Word / Tokyo November 23, 2008
- Complex Manifold Deformation Theory / Conjecture 5 / Time of Word / sekinan.wiki.zoho.com
[Postscript July 30, 2014]
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Text 2
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Text 3
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Text 4
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Text 5
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Text 6
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Text 7
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Text 8
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Text 9
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Text 10
March 4, 2005
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Text 11
TANAKA Akio
The British Museum has exhibited The ancient Egypt at Tokyo, titled Journey through the Afterlife Ancient Egyptian Book of the Dead.
The exhibition is excellent, especially total length 37 meters' Greenfield Papyrus is the highlight of the exhibit.
I feel over again that the letters on the papyrus is almost everlasting and my usual thought that the letters are superior than the spoken language which is thought important by Ferdinand Saussure.
Of course I have respected Saussure so much and have read COURS DE LINGUISTIQUE GENERALE time to time.
But the Occidental linguistics has not enough tradition on the ideogram as usual at Chinese characters.
Japan has also succeeded the Chinese tradition and culture. So we have much felt the importance on characters and letters.
Each ideogram has its unique molding technique and coinage ability.
I have very satisfied with hieroglyph's figures comparison to Chinese characters.
Also refer to the next.
Tokyo
12 September 2012
Sekinan Research Field of Language
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Text 12
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.
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
References 2
References 3
- Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
- Half Farewell to the Linguistic Circle of Prague and Sergej Karcevskij
- Sergej Karcevskij, Soul of Language
- Gift from Sergej Karcevskij
- Follower of Sergej Karcevskij
- For KARCEVSKIJ Sergej
- Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique"
References 4
References 5
- The Time of Language, Ode to The Early Bourbaki To Grothendieck
- Bourbaki' ELEMENTS DE MATHEMATIUE Troisieme edition, 1964
Tokyo
30 July 2016
Sekinan Library
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Text 13
Ideogram from hieroglyph to LATEX Symbol List
TANAKA Akio
Sekinan Library
Mark * in the text shows Reference number.
1. Ideogram
Ideogram has long history.
In the early paper I ever simply defined ideogram*0-1.
I also wrote relative papers on ideogram from the viewpoint of Chinese characters*3-1, 3-2, 3-3.
Especially Manuscript of Quantum Theory for Language 2003 is a starting root of my research on language universals*3-2.
The history of ideogram continues from Egyptian hieroglyph to Chinese character and now adds LATEX Symbol List*6-1.
The 21st century will necessarily become the century of ideogram.
The reasons are below.
- Ideogram can contain rich information in small space.
- Ideogram can show information at a glance.
- Ideogram can sustain information stably in long time*1-7.
- Ideogram has fertile capability to superb diversity of languages*8-5.
2. Set theory
Probably in summer 1977, I was designing for a paper on the sentence in language. The central part of the paper was connection between words or sentence, in which the logic of language would be shown using the set theory as a simplified model of true and false. I was strongly influenced from Kurt Godel, Gaishi Takeuchi and Bourbaki*1-1. But this design was abandoned for my lack of mathematical basis keeping on.
3. Qing dynasty's linguistics
In 1980s and 1990s I was lost in learning Chinese classical character theory, Xiaoxue, especially Qing dynasty for ideogram's fundamental property*2-1. At this period I did not write any paper on language. I solely read WANG Guowei*1-2, WANG Yinzhi, DUAN Yucai and Qing dynasty's linguists.
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 a 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.
5. Quantum elements
In 2003 staying at Hakuba, Nagano, I wrote a rial paper on language universals from the viewpoint of physics. This was remained manuscript till now. The title was Manuscript of Quantum Theory for Language*3-2 for the time being. Because in summer 2003 I wrote the first paper on language universals from physics titles as Quantum Theory for Language*3-3 which was read at a conference held in winter 2003 of Nara Japan.
6. Finite generative
Language probably begins from finite elements and generates.*3-6, 3-7 its world responding to outer world. I learned the concept of finite generative from von Neumann Algebra*4-1 at around 2006 and 2007.
7. Structure and dimension
Language probably has structure, which details are unknown now for me. But several phenomena hints me the existence of structure containing dimension. Its example is shown at the Crete's lie, on which I wrote a tiny paper titled as True-false problem of the Crete*3-8 in 2013.
More details on mathematical approach to dimension is shown at Algebraic Geometry Language*4-2.
8. Immanent time
Chinese character has immanent time in figure *3-1, 3-4. On the theme I wrote several papers between 2003 and 2005. Main papers related with the theme are seen in Early Paper and Early Paper 2*5-1, 5-2.
For the immanent time, I wrote a mathematical paper titles as Word as Infinite Loop Space*3-9.
In comparison with Chinese character, hieroglyph is very fantastic object on ideogram. For more details, hieroglyph is more complex for describing the concept using two functions, logogram expressing things' meaning and phonogram expressing words' pronunciation*0-2, 8-3.
Besides hieroglyph has also definitive element which is put at the end of the word. This element is very similar to Chinese character's meaning element which is called Pang 旁 in Chinese*8-3.
But even for learning hieroglyph's basis, I have not enough time now. I only like to see the relative events on hieroglyph at time to time . The exhibition held at Mori Arts Gallery in 2012, Tokyo titled as The British Museum ANCIENT EGYPTIAN BOOK OF THE DEAD JOURNEY THROUGH THE AFTERLIFE *8-2 was very fantastic, in which The Greenfield Papyrus was overwhelming.
9. Disposition, distance, flow and boundary
For thinking of language, I have been interested in four elements, disposition, distance flow and boundary*3-10,11,12, 13, which seem to become the basis of language.
especially at researching ideogram, disposition is fundamental to construct grammar.
10. Energy, dimension and distance
For more further research language , now I suppose at least three elements being based from mathematical description, which are energy, dimension and distance*3-14.
11. Mapping and category
Ideogram now has an important part in computer age. Image confirmation is very popular at internet banking system, which can contain vast information in one image, so password decoding is more difficult than phonogram or Arabic numerals.
Generally ideogram has vast information to the others using comparatively easy way.
This ideograms situation resembles mapping at category theory in mathematics. For this point I wrote rough sketch to apply category theory to language theory. Sketch name is Derived Category Language 2016*4-3.
Appendix
Sekinan Library's publicised papers are shown at SRFL Paper*7-1.
Theoretical development on language universals are shown at Genealogical Tree of Sekinan's Paper Sixth Edition*6-2.
Related words and concepts on language universals are shown at Appendix / Language between Sergej Karcevskij and string theory, one century's trace The 30th Anniversary of Sekinan Library Memorial Essay*6-1.
Relative themes on language universals at Sekinan Library are seen at Twitter Sekinan Library’s Moments*7-3.
References
Sekinan Library
Author
TANAKA Akio
0
1
- The Time of Language
- The Time of WANG Guowei
- The Time of Wittgenstein
- The Time of Quantum
- The Days of Distance
- The days when I was thinking on Energy Distance Theory
- The Days of Decipherment
- The days of von Neumann Algebra
- The days between von Neumann Algebra and Complex Manifold Deformation Theory
- Language between Sergej Karcevskij and string theory, one century's trace
2
- 40 years passed from I read WANG Guowei
- For WITTGENSTEIN Ludwig Revised with Symplectic Language Theory and Floer Homology Language
- Language between Sergej Karcevskij and string theory, one century's trace Preface
- Karcevskij conjecture 1928 and Kawamata conjecture 2002
3
- On Time Property Inherent in Characters
- Manuscript of Quantum Theory for Language
- Quantum Theory for language
- Prague Theory
- Distance Theory
- von Neumann Algebra 2 Note Generation Theorem
- von Neumann Algebra 3 Note 1 Properly Infinite
- True-false problem of the Crete
- Word as Infinite Loop Space
- Disposition of Language
- Distance of Word
- Flow of language
- Boundary of language
- At least three elements for language universals
4
5
6
- Appendix / Language between Sergej Karcevskij and string theory, one century's trace The 30th Anniversary of Sekinan Library Memorial Essay
- Genealogical Tree of Sekinan's Paper Sixth Edition
7
Outer sites and publication
8
- The Comprehensive LATEX Symbol List Scot Pakin 19 January 2017.
- The exhibition catalogue of The British Museum ANCIENT EGYPTIAN BOOK OF THE DEAD JOURNEY THROUGH THE AFTERLIFE. Asahi Shinbun.
- Steven Snape. Decoding the stone. George Weidenfield and Nicolson Ltd. 1997.
- John Chadwick. THE DECIPHERMENT OF LINEAR B. Cambridge University Press. 1958.
- The exhibition catalogue of A JOURNEY TO THE IMMORTALS : TREASURES OF ANCIENT GREECE. Asahi Shinbun et al. 2016.
- Unicode® Technical Report #51 UNICODE EMOJI.
7 march 2018
Read more: https://srfl-lab.webnode.com/products/the-days-of-ideogram-ideogram-from-hieroglyph-to-latex-symbol-list/
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Contents
Anticipation
FAQ
Read more: https://srfl-lab.webnode.com/products/what-problems-are-there-on-language-universals/
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Text 1
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a homemaker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
Read more: https://srfl-paper.webnode.com/news/presupposition-on-natural-language/
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Text 2
*1 Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej’s “Du dualisme asymetrique du signe linguistique” / 8 September 2011
*2 Presupposition on Natural Language / 22 August 2012
*3 Time of WANG Guowei / Loop Time of Character / 15 September 2011
*4 Topological Group language Theory / Boundary of Words / 12 February 2012
*5 Notes for KARCEVSKIJ Sergej / Structure of Word / 11 September 2011
*6 Notes for KARCEVSKIJ Sergej / Description of Language / 9 September 2011
Read more: https://srfl-paper.webnode.com/news/sayama-assumption-on-language/
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Text 3
March 12, 2009
Sekinan Research Field of Language
Read more: https://srfl-theory.webnode.com/news/why-do-you-think-that-language-has-structure/
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Text 4
Where is the change's power or energy?
My unripeness to language study has come to the declining years.
Return to physics or mathematics is almost alike to back to youth age, when almost every day solving rudimentary problems for entire interest to unknown world.
In my mind there still are some hard themes to challenge, one of which is energy in language. The theme is originated from Edward Sapir, who presented the concept "drift" in Language, 1921.
It was the macro and intuitive concept that was supposed by his precise thinking and vast field work of America native's language. I think that I would develop the theme from the physics-mathematics field.
- Substantiality, Dedicated to SAPIR Edward / 27 February 2005
- Macro time and Micro Time / 24 July 2013
- Flow of Language / Heritage of WANG Guowei and Edward Sapir / 26 September 2014
- The days when I was thinking on Energy Distance Theory / 19 December 2014
- Energy of Language / Stochastic Meaning Theory 4 / 24 July 2008
- Energy and Distance / Energy Distance Theory / 31 August 2008
- Energy and Functional / Energy Distance Theory /18 October 2008
- Potential of Language / Floer Homology Language / 2009
Tokyo
1 January 2015
SILNote
Read more: https://srfl-theory.webnode.com/news/where-is-the-changes-power-or-energy/
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Text 5
Why is boundary necessary in language?
1.
I have thought of language as a physic existence that has inevitably boundary to the outer world.
My question is simple and primitive. I ever wrote about the change of language - If there be change, there are exactly the situations before change and after change. Just where does changing substance exist? In the essay, rotten apple was used as the symbol of changing language.
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Presupposition on Natural Language
TANAKA Akio
1.
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a home-maker.
An apple is recordable and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.
Reference
For WITTGENSTEIN Ludwig / Position of Language / 10 December 2005-3 August 2012
Tokyo
22 August 2012
Sekinan Research Field of Language
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2.
Language&s substantiality has been considered since I returned to the mathematical approach for learn language universals from the utterly beginning. In 2005 I wrote a tiny trial paper on the substantiality of language for thinking the study course hereafter.
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3.
In 2013, I again wrote on the substantiality of language at the new level containing the determinate essence of language, dimension and time. The title is Macro Time and Micro Time. In this paper I thought that dimension is the essential factor of meaning, especially containing Infinitive meaning.
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Macro Time and Micro Time
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.
(Poincaré duality)
For oriented compact n-dimension topological manifold M ,
bilinear form
is exact,
and become dual space each other.♦
Word := M Boundary of language := p Dual language :=
and Language := Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.
Distance Theory
Mirror Theory
Guarantee of Language
25 May 2012
Sekinan Research Field of Language
5.
Relation between boundary and synthesis in language is utterly unknown field for me. Study has just started from the entrance position. Recent results are the next.
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Synthesis Conjecture
Conjecture for synthesis of meaning in word
TANAKA Akio
Synthesis
1 Conjecture for synthesis of meaning in word
29/09/2013 19:25
For synthesis of meaning in word, Conjecture: Condition for synthesis of meaning in word i s proposed by cohomological expression.
2 Conjecture: Condition for synthesis of meaning in word
29/09/2013 18:38
On condition for synthesis of meaning in word, at conjecture is proposed by the next result of etale cohomology.
Result
——————————————————-
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A”
A and A’ have enough many injective objects.
If F transfers A’ s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
——————————————————–
Conjecture
Preparation
Word is shown by R . This word is called old word .
Base meaning in word is shown by F .
Word that has base meaning is shown by RF .
Additional meaning to word is shown by G .
Word that has additional meaning is shown by RG . This word is called intermediate word .
Word that has base meaning and additional meaning is shown by R ( G O F ). This word is called new word .
Conjecture
For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology.
3 Canonical natural equivalence
29/09/2013 18:08
Canonical natural equivalence
The next two are left exact additional functors.
F : A -> A’
G : A’ -> A”
A and A’ have enough many injective objects.
If F transfers A ‘s injective object to G acyclic object, the next canonical natural equivalence is concluded.
R ( G O F ) =~ RG O RF .
Source: Conjecture for synthesis of meaning in word / sekinanlatest 2013
Tokyo
1 May 2014
Sekinan Research Field of Language
6.
Three Conjectures containing Synthesis Conjecture are shown at the next.These conjectures are the latest result of language universals at SRFL Sekinan Research Field of Language.
21 December 2014
SIL
Read more: https://srfl-theory.webnode.com/news/why-is-boundary-necessary-in-language/
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Text 6
How is the time alive in language?
TANAKA Akio
1.
When one first hear the existence of time in language, he may doubt its certainty. But I have intuitively believe it since I learned the ancient Chinese inscription on bone ad tortoise shell (in Chinese called Jiaguwen). In my early 20s, I met with the book of Chinese modern linguists, WANG Guowei, this belief changed the conviction. His lifework book Guantangjilin is hard to read till now. But some papers in it are always inspires me by his deep and vast insight to character, language and history of ancient China. He also wrote fine criticism on Chinese pre-modern poem Ci.The title is RenjianCihua. The book is one of my favourite books of Chinese literature. People sometimes say that he was the highest genius after Song Dynasty, 1,000 years.In 2003 I wrote a tiny paper hinted by WANG's paper. It was the first paper for me that I directly faced the time inherent in inscription using Jiaguwen's update linguistic results. The title is " On Time Property Inherent in Characters".
2.
In summer 2003, I stayed at Hakuba, Nagano for a while for writing over the paper that was intended to present a symposium at Nara in winter. The paper was taking up the structure of written language that was dealt with the relation between time and grammar. But I did not solve the question on with what shape language exists in the language world. What shape has language and at where space does language exist or float? The theme on space was hard to deal at that time. I only concentrated to the shape in space. At 28 August I was fatigued to think and went for a stroll outside the inn putting up. The place was at the mountain side of the Hakuba Range and there was only one convenience store, where I walked in the shop and saw one advertisement of electric pocket dictionary. I returned having this advert to the inn and read its sentences. At the very time I found the shape of language I sought was sphere that was inherited time in it, also having grammatical functions. The paper's title was named to " Quantum Theory for Language" by the shape of language. This was a really product of clear and fine atmosphere of Hakuba with a distant view of the North Alps of Japan.
3.
From 2004 to 2008 I wrote some papers on inscription and language. But I was not satisfied inwardly for the style of intuitive approach to language. I wanted to write more simple and clear expression. For being realised of my wish, I definitely needed to use mathematical tools. I returned to my 20s days' reading of Bourbaki that was desperately difficult for may ability. I again gradually read mathematical books and journals for seeking useful source of my hope to converting to language study. A certain results that came to my papers with satisfaction was appeared in 2008 by the papers titled Complex Manifold Deformation Theory.
Above all, the first paper in this group, I first defined the concept, distance by complex manifold.
The concept of distance was one of the most important themes on language, so I at early times wrote the intuitive paper, "Distance Theory".
At the fifth paper of Complex Manifold Deformation Theory, I again challenged the hard theme of the time in language, titled to " Time of Word".
4.
The definition of space in which language exists is one hard target for me to write satisfactory. A fixed results came to me at the papers group titles Symplectic Language Theory in 2009.
In the group, a paper focused on mirror phase on language became one peak for my writing.
5.
Related with the shape of language, quantization and discreteness on language was the urgent themes for the further step of studying the total image of language I was pursuing. Floer Homology Language was the one milestone for me to overcome to the next stage.
In this group, the eighth paper was dealt with the quantization and discreteness of language.
6.
What situation does the time in language have? This question exists in my mind at the early days when I wrote the paper "On Time Property Inherent in Characters". The first step to solution was described at the paper " Prague Theory". The group of Prague Theory was written due to dedicate to Prague, The Linguistic Circle of Prague and Sergej Karcevskij with the memory of my teacher CHINO Eiichi.
In this paper, Chinese Character /kun/, that meaning is difficult in English, was used for the eternity of loop time. This loop time was also appeared in the paper " On Time Property Inherent in Characters". But Prague Theory shows more direct and compact by growing tree and its obstructive enclosing fence. This intuitive image was more clearly described at the paper " Word as Infinite Loop Time " at Infinite Loop Space Language in 2012.
In this paper, time in language is clearly connected with dimension of algebraic group saying as the next. Word has dimension that belongs to algebraic K group.
7.
The relation between time and dimension was entered on a new phase at the learning of algebraic geometry, especially of arithmetic geometry. Arithmetic Geometry Language, abbreviated to AGL, was the starting papers for me to arithmetic method.
From these four papers, I concisely extracted the next three conjectures.
At these conjectures, time inherent in language is in the basis of describing dimension, synthesis and reversion. The process of leading to the conjectures is over viewing the next.
- Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement / 19 November 2014
Acknowledgement
Time inherent in language is a fantastic but as hard to pursue for me still now. I would examine this theme further more and more, probably till the end of my research life. Now all the thanks are going to The Linguistic Circle of Prague and especially its member Sergej Karcevskij, with my teacher CHINO Eiichi who taught me their precise information from his long study at Prague in 1960s.
9.
For CHINO Eiichi
9.1 Golden Prague
C also died early, who had taught me Russian and linguistics. He loved
the old city that had the beautiful towers and bridges.
In C's many works there was the essay "The Moon of Carpathians". He wrote
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached "Golden Prague".
Prague, it was his youth itself.
Now I cannot hear his voice telling the various anecdotes on languages,
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as "the genius of linguistics".
- 9 October 2014 -
9.2 Coffee shop named California
If C live, he also may ask me, "What are you researching now?"
And I also will answer him as same as ever.
"I have pursued universals, never done facts, without repenting."
Oh C, if you live, will we also talk on language?
At the table facing each other under the low ceiling of the shop going up the steep stairs.
The name of the shop is California.
For the memory of our daily forgetful life,
its never miserable though poor all over,
I will write down our delight.
- 27 October 2014 -
10.
Ode to Kanda
"I need not more wander the book shop streets." / From Tale, Print, 2012
This tale was written by TANAKA Akio, pen-named LI Koh in autumn 2012 for remembering the poor but brilliant youth time of myself. This is one of my favourite phrases in this tale.
The book shop streets described in the tale is Kanda, Tokyo, which is located in the central Tokyo, where I frequently walked seeking the old Chinese classic books for the study from Oriental way of linguistics. In late 1960s, the streetcars were surely running in the old fashioned streets of Kanda, now perfectly changed to the subway streets.
From Print 2012, Chapter 10
もはや本屋街をさまようことはない。I need not more wander the book shop streets. 対象は私のうちにある。The object exists in my mind. 私はただこの運河をながめていればいい。I would better watch the canal. 遍歴は終わった。Wandering is over now. たぶん永遠にマイスターにはなれないだろうが、みずからの小さな仕事場で、日が落ちるまで作業をすればいい。Perhaps I would not become meister forever. In my narrow working place, I 'd better do my work till sunset. すると仕事場の窓辺を聖者が通って行く。 So out of the window by the working place, the saint passes by. かつてそんなロシアの民話を読んだ。I ever read the Russian folk tale like that.
秋の日ぐれは早い。The Autumn evening is fast. 路面電車のヘッドランプがまぶしいくらいだ。The headlight of streetcar is dazzling. 黄褐色の窓に少ない乗客が照らし出され、古本屋街の方へ消えて行った。In the yellow-lighten window the passengers are picked out by the light. The car disappeared to the book streets. 駅の売店がにぎやかな橙の光に包まれている。The station shop is also lighted up by the yard's busy orange light.
- 40 years passed from I read WANG Guowei / 16 November 2013
- Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique" / Print, 2012
26 November 2014
SIL
Read more: https://srfl-theory.webnode.com/news/how-is-the-time-alive-in-language/
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Text 7
What facts do Three Conjectures for Dimension, Synthesis and Reversion show us?
TANAKA Akio
1.
True-false problem of the Crete gives us the infinite circulation of true-false value.
This fact indicates us the existence of deep structure or hierarchy in language.
The Crete's true-false is solved by the perspective from 2-dimension to 3-dimension on structure in language world.
2.
Language has long history as the system of etymology. Apparently language has gradually added the new meaning on the old established meaning in word. At this point new meaning is synthesised to the old meaning. At synthesis word mathematically reduces its dimension to the lower one. As the result time in word relatively occurred in the new word and inevitably connected with dimension.
3.
Where and how does word exists in the world?
The distance from a certain point is absolutely demanded for measuring or observing for knowing the word's place.Reversion is a result for measuring or observing from a point.
4.
For precise description of dimension, synthesis and reversion mathematical tools are definitely needed and for more simple describing algebraic method is the most useful to approach for me and in order to easy-seeing and clear intuition geometrical approach is always inevitable to searching. I am greatly thanks to relevant mathematicians researching against severe problems still now for contemporary times.
Kodaira, Tokyo
20 November 2014
SIL
Read more: https://srfl-theory.webnode.com/news/what-facts-do-three-conjectures-for-dimension-synthesis-and-reversion-show-us/
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Comment
Here ends the preparatory work for What is signal?, that began from 16 October 2016.
From now on this paper will be written at the viewpoint of quantum group for the relationship between quantum and signal-language, that has been the most important theme, quantum language since 2003, when I wrote a paper titled, manuscript of Quantum Theory for Language.
refer to the next.
Manuscript of Quantum Theory for Language with Preface, Note and Note 2 2003-2018
以下に示す「言語の量子理論」は、英文で書かれたQuantum Theory for Language の草稿となるもので、２００３年３月に長野県白馬の白馬アルプスホテルで書かれたものである。発表するのは今回が初めてである。いままで発表しなかったのは、この草稿がまったく資料のないホテルの部屋できわめて短時間のうちに書かれたものであり、そのためその内容が非常に直感的で、通常の論考とは異なる、私にとってはかなり先鋭的なものであったためである。しかも論考は途中で終わり未完のままである。２００３年１２月に或るシンポジウムで発表するためにこの草稿をもとに書き上げたQuantum Theory for Languageでは、論考の趣旨はほぼ一貫しながらもその表現をより穏やかなものにした記憶がいまもはっきりと残っている。しかし現在この草稿を読み返してみると、私が２００３年当時気にした直感性や先鋭さは、やはり私の言語論の本質に深く根ざしたものであり、ほぼ十年におよぶ言語に関する数学的な記述を経て振り返ると、私が今なお書き残しているもっとも重要ないくつかの主題は、ほぼこの草稿に記されたものであることを私はあらためて確認するに至っている。言語の量子化、量子の出現と消滅、量子の接合と階層、量子集合体、量子群の進行と階層、陽性量子と陰性量子、量子の意味とエネルギー。いずれも私にとって、依然として未知であり魅惑的であり続ける。今後私はふたたびこの草稿の位置にもどり、あらためてみずからの思考を紡いてゆくことになるであろう。老年の今となっては、本質は形態に先行し、もっとも表現したいものを、私にとってそれにもっともふさわしい方法で記述してゆくこととなるであろう。いくばくかの時間がなお残されているのであればだが。二十歳のころ恩師が教えてくれた句は今もそのまま生きている。いざゆかん雪見にころぶところまで。
２０１５年３月２３日、東京にて記す。
Tokyo
23 March 2015
言語の量子理論
０ はじめに
中国における主要な言語である漢語には２０００年を超える記載言語すなわち文字言語の歴史がある。
中国古典を代表する『論語』は、現代に残された文字資料であるが、同時に同書編纂当時の口頭言語を強く含んでいるとされる。（吉川幸次郎 １９６７年）
ここでは、おもに『論語』の文例によりながら、記載言語（文言）と口頭言語（白話）の両面にかかわる、言語の分析を試みる。
１ 言語の量子化
言語類型論で孤立語に分類される漢語、いわゆる中国語は、原理的には一つの音節が一つの意味と一つの文字すなわち漢字を持つ。
音節が連続して新しい意味を形成することはあるが、それぞれの音節は常に本来の独立した意味と文字を改変することなく所持することによって、漢語の内在する言語規則基本的にはほとんど改変することなく、長い歴史時代を通して保持してきた。
漢語の文法的機能が、発音や文字の外形的変化を一切行わなず、一語一語の配列すなわち語順によって、形成されるとするが、その語順すなわち統語法の内在原理は、いまだ十分な解明をみたとはいえない。
ここでは文言と白話をともに含むとされる『論語』を漢語の言語モデルついて採用し、主に文字論的な接近によって、漢語に内在する言語法則ひいては一般的な言語に内在する言語構造を分析しようとするものである。
漢語の統語法については、伝統的に実辞と虚辞の２分類によってなされてきた。実辞は実質的な意味を所有するのに対し、虚辞は実辞が所有する意味を補完するために用いられるとされる。
たとえば、『論語』巻頭の一節、「学而時習之、不亦説乎」（文例１）にあっては、一般的には「学」「時」「習」「之」「説」が実辞であり、「而」「不」「乎」が虚辞である。
ここで、一つの意味を所有する漢字一字を、一意味単位を有する言語量子とし、言語の最小単位と仮定する。
伝統的に実辞とされてきたものは、言語量子として通常、一単位の陽性量子を有するとする。虚辞とされてきたものは、通常、一単位の陰性量子を有するとする。一陽性量子をℓ＋、一陰性量子をℓ－と表記することとする。
一陽性量子は、運動推進エネルギーを有し、量子を前方に移動させようとする力を持つ。一陰性量子は、運動吸収エネルギーを有し、量子の運動を吸収し停止あるいは変更させる力を持つ。一陽性量子は、一陰性量子に接合することによって、自らの運動を停止あるいは変更させる。
文例１「学而時習之、不亦説乎」によれば、「学」は「而」によって、その運動を変更され、「説」は「不」「亦」および「乎」によって、その運動を変更され最終的に停止されている。
陽性量子の運動エネルギーは、通常、常時進行性であり、陰性量子に接合するまで、その運動を停止しない。
陰性量子の運動吸収エネルギーは、通常、「一時停止」「方向変更」「停止」等の機能を有する。
文例１によれば、「而」は「一時停止」、「不」「亦」は「方向変更」であり、「乎」は「停止」として機能している。
まとめるならば、量子は意味とエネルギーを有する言語の最小単位である。
２ 量子の出現と消滅
量子は、新しい意味が言語世界へと出現要請されることによって、出現する。要請は言語世界への新しい意味の付加が必要とされたときになされるものである。言語における発話と文字との関係は、発話の先行が一般的であるが、漢語のように、一つの音節が一つの意味を有する言語においては、後出する文字は、発話行為とともに想像上の形態として要請されていたと仮定することも可能であろう。すなわち一つの意味が一つの具体的な識別形態を要請しているのである。この行為は人間の営為として自然なものである。
言語量子は、言語世界への新しい意味を付加するために、出現する。量子が有するエネルギーは、その新しい意味を言語世界に付加するためのものであり、新しい意味と不可分に結合したものである。
量子は、その意味が言語世界に不要となったときに消滅する。文例１において「不」は本来は「花のめしべの子房」を意味したが、その実辞としての意味は早くに消滅に、「打ち消し」を意味する虚辞としたのみ、言語世界に機能してきた。
この「不」で示されたように、実辞と虚辞は漢語において、明瞭に区別されたものではなく、相互の乗り入れや変換が不断に行われてきた。すなわち、上述したように、量子は、当初、言語世界への新しい意味付与のために出現したものである。
当初は陽性量子であった実辞は、言語世界への意味付与の役割を終えるとともに、その運動エネルギーも消滅する。しかし他の量子の運動エネルギーによって、言語世界が構成され改変された痕跡は、他の量子から運動あるいは圧迫を受け続け、運動を受容する量子として、負のエネルギーを付与されて、言語世界に存続することがあると仮定する。こうして陰性量子が出現する。
出現した陰性量子は負のエネルギーを有するため、陽性量子のエネルギーを吸収し、その運動を停止または変更させることとなる。
３ 量子の接合と階層
二つ以上の量子は、互いに接合することによって、新しい構造体を形成する。
文例１「学而時習之、不亦説乎」によれば、量子の接合は以下のようになる。
＜ ℓ＋ ℓ－ ℓ+ ℓ+ ℓ+ ℓ－ ℓ－ ℓ+ ℓ－＞
ここで、陽性量子は、次の量子まで意味を移動させる。陰性量子は、前の量子の運動エネルギーを吸収し、停止または変更させる。
「而」と「乎」が陰性量子として、構造体すなわち文を「停止」させる機能を働かせていることは明瞭であるが、「不」と「亦」の二つの陰性量子は、量子の運動の「変更」として機能していると仮定する。
伝統的な文法によれば、「不」と「亦」は「説」の意味を補完するとされるが、この量子理論では、後ろの量子は前の量子のエネルギーを受け止めるため、従来の説明では処理できない。
ここで「変更」とは、前の量子の運動の方向を変えさせることである。こうして一つの陽性量子は、その運動が別の軌道に移されることとなる。すなわち、陽性量子はある一つの軌道上で運動をおこなうが、ある種の「変更」陰性量子はその軌道を別の軌道に移し、新しい意味構造体を創出する。
その軌道は、モデル的には、数階建ての高層建築が想定される。「学んで時に之を習う」という階から、他の異なった階へと移動させる。
ここで「不」は「学んで時に之を習う」ことを否定する階へ移し、「亦」はこの「学んで時に之を習う」ことを新しい可能性の階へと移動させる。「乎」はこの状況に疑問を投げかける階へと移動させる。
この一連の状況をモデル化して図示する。
学
↓而習之
↓不
↓亦説
↓乎
『論語』の有名な一節、「有朋自遠方来」（文例は以下のように図示される。
有朋
↓自遠方来
４ 量子と量子集合体の符号化
量子は初め陽性として出現し、その消滅によって陰性を生じる。陰性量子は陽性量子の群にあっては、無意味であるために非圧迫量子であり、陽性量子としてかつて獲得した意味空間をいわば不断に圧縮され続ける状態にある。こうしてポンプで押し出されるようなエネルギーが陰性量子に蓄えられ、陽性量子の軌道を変更して異なる階層へ移動させることとなると仮定する。
したがって、この量子理論によれば、漢語のすべての漢字、すなわち意味とエネルギーを有する量子は、次のように符号化することができる。
量子 / /
意味 ℓ
陽性エネルギー →
陰性エネルギー ↓
文例１の「学而時習之、不亦説乎」の符号化は以下のようになる。
/ℓ→/
/ℓ↓/ /ℓ→/ /ℓ→/ /ℓ→/
/ℓ↓/
/ℓ↓/ /ℓ→/
/ℓ↓/
ここで/ℓ→/を数字の１で、/ℓ↓/を数字の０で表すと、「学而時習之、不亦説乎」は１０１１１００１０と数字化できる。
したがって文例１の「学而時習之、不亦説乎」は［進行５，階層４］の言語量子の構造体であるということができる。これを［move５，class4］と表記する。
文例２の「有朋自遠方来」は
有朋
↓自遠方来
であるから、
/ℓ→/ /ℓ→/
/ℓ↓/ /ℓ→/ /ℓ→/ /ℓ→/
と符号化され、さらに、
１１０１１１
と数字化される。その構造は［move５，class１］である。
もう一例『論語』から文例をとる。
「三年無改於父之道、可謂孝矣」（文例３）
/ℓ→/ /ℓ→/ /ℓ→/ /ℓ→/
/ℓ↓/ /ℓ→/
/ℓ↓/ /ℓ→/
/ℓ↓/ / ℓ→/ /ℓ→/
/ℓ↓/
１１１１０１０１０１１０ ［move8，class５］
５ 量子群における進行と階層
量子群である文における、一階層における進行度数を見る。
文例1では、4分の５で0.8度数。文例2では、1分の５で５度数。文例3では５分の８で1.6度数となる。
ここで、一階層進行度数がどのような指標となるかを考察する。
進行度数1とは、文言にあっては、実辞１に対して虚辞１の割合であり、1階層に１意味が存在する最も明瞭な文と考えることができる。
したがって進行度数が1以上となると、1階層に2つ以上の意味が存在することなり、一つの意味を細かく規定してより微細な意味を提示することとなる。
これとは逆に進行度数が1未満となると、1階層において、一つの意味を提示することがなく、2階層以上によって初めて意味の完結をみることとなり、一つの意味の周囲に補足的な意味内容が付加されることによってより構成的な意味が成立することとなる。
文例1は0.8度数であり、補足的意味が付加された文である。文例2は5度数であり、微細な意味が規定された文である。文例3は1.6度数であり、ほぼ標準的かやや微細な規定が加わった文である。
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。
７ 陰性量子の意味
陰性量子が有する意味は、上述した「也」の意味分類でも明瞭なように、陽性量子の意味よりはるかに精妙な場合が多い。これらの意味はどのようにして出現したと考えることができるか。
陰性量子が実辞としての機能を消滅させ、一種の真空領域を有していると仮定したが、ここにひとたび断定という意味が成立すると、この「也」に前から接合する陽性量子の意味によって、その真空領域は一定の反応を示すようになる。たとえば「回」のような人名が前に接合すると、「也」は断定的な意味機能の一変容である主題提示として機能することとなる。
８ 陰性量子のエネルギー
陽性量子のエネルギーは、新しい意味を言語世界に付加するために与えられたものであることは、すでに「２ 量子の出現と消滅」において記述したが、ここでは陰性量子が有するエネルギーについて詳述する。
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Note
22 December 2017
This manuscript was written at a hotel of Hakuba, Nagano, Japan in March 2003, where my family stayed for hot spring and ski. In autumn 2002, I thought of relationship between time and characters inspired by WANG Guowei's paper written on old Chinese character's studies, one of which he declared that character heng 亙 was imaged from a ship coming and going the banks. This character contained the notation of the continuous time of ship operation between the banks.
But if character contain the time going, character seemed to have any existence of inherent energy in it.
Note 2
Definition of quantum in this manuscript was intuitive while in my mind there was rather precise image that was not able to write by mathematical approach in the days of 2003.
I wrote the simple trial paper on quantum group in 2008.
Kac-Moody Lie Algebra Note 2 Quantum Group 2008
Papers related on the pre-thought on quantum group is seen at SRFL Lab.
SRFL Lab's Preparatory paper
Now arranged at the next.
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Energy
- Potential of Language 2009
- The days when I was thinking on Energy Distance Theory 2014
- Preparation for the energy of language 2015
Tokyo
20 June 2018
Sekinan Zoho
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Here ends Manuscript of Quantum Theory for Language
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