23/04/2019 19:33
From Autor;
More accurasy, please refer to the original paper.
URL is the next.
https://srfl-theory.webnode.com/news/what-is-signal-total-edition-21-november-2018-23-april-2019/
What is signal?
The existence that generates language
TANAKA Akio
Tokyo
21 November - 23 April 2019
Original Title What is signal? A mathematical model of nerve For father and mother -----------------------------------------------------------------------------------------------------------------------------
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. ---------------------------------------------------------------------------------------------------------------------------- The days when I was thinking on Energy Distance Theory 2008 Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished. Read more: https://geometrization-language.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory/? ---------------------------------------------------------------------------------------------------------------------------- Also refer to the next.
Energy of language 2015
Preparation for the energy of language 2015
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1. Language Next definition for language shows my simple image to language and energy. ................................................................................................. Language and Spacetime Language Definition for the Child who Lost the World TANAKA Akio 0 The world spreads around the human being.1 Language divides the world.2 Language connects the world.3 Language bends the world.4 Language stretches the world.5 Language shrinks the world.6 Language extinguishes the world.7 Language creates the world.8 Language gives despair.9 Language gives hope.10 Language is pasting on spacetime with energy. Postscript[Referential note / November 29, 2007]For Authentication of Solidity [Definition added / November 3, 2008]Definition 10, the part of is newly added. Tokyo March 3, 2007Tokyo November 3, 2008 Added Read more: https://srfl-lab.webnode.com/news/language-definition-for-the-child-who-lost-the-world/ ..........................................................................
2. Human sense On language and human sense, I ever wrote simply at the next paper. Macro Time and Micro time TANAKA Akio24 July 2013atbankofdam 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. #04. Like an apple, language has passing physical time in oneself.5. Language is metamorphosed by the time progressing. #16. 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) #27. Language’s time goes freely from the present to the future or the present to the past. #38. Language symbolises the time from finiteness to infinity. #49. 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.htmlTo be continued. Author. Read more: https://srfl-lab.webnode.com/news/macro-time-and-micro-time/ ...........................................................................
3. Signal Signal Goes to meaning.Traffic signal shows Go, Attention and Stop to people by three colour lightsMorse 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. ..................................................................................
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. Manuscript of Quantum Theory for Language 2003 The paper is a very intuitive one but there are some hints on signal.Now I need one chapter for my new trial paper.The chapter is " 6. Basic principle of quantum theory"The original text is the following. .................................................................................
６ 量子理論の基本原理 量子理論は、伝統的には実辞とされる陽性量子が1階層で進行することが基本である。したがってある種の量子群すなわち文において、陰性量子が冒頭に立つときには、その前に陽性量子または量子群が省略されたと考えることができる。陰性量子が陽性量子の進行方向に変化を与えて、新しい階層に移行させることは、陰性量子が受けている被圧迫エネルギーによるとしたが、より正確には、以下のように説明できる。一般に断定の虚辞とされる「也」は、その実辞としての意味は現代においては不分明であり、陽性量子としてはほぼ消滅したと考えることができる。その代わりに陰性量子としての虚辞機能が台頭して現在に至るが、その機能を細分すれば、断定、主題提示、呼びかけ、詠嘆、疑問、反語等の極めて多様である。たとえば、「回也不愚」（『論語』為政篇）においては、「回」という人物が、（階層が変わり）孔子の心中において、（また階層が変わり）否定される存在であり、（さらに階層が変わり）「おろかものの類」が提示される。」「階層が変わる」ということは、「回」という人物が、「也」と出現によって実在の人物から、孔子の心中における考察対象へと変換されたことを意味し、さらにその考察対象が「不」によって抹消されることを意味し、さらに新しく「愚」という概念が登場することを意味する。すなわち陰性量子は、陽性量子が有する言語世界への直接的な意味を行うのではなく、実辞としてはもはや空白となった自らの領域へ、陽性量子を導くjことによって、一種の真空無重力の状態を現前させ、その方位を転換することであると仮定する。その転換に必要とされるエネルギーは、領域が受けている被圧迫のエネルギーから生ずるものと仮定する。 Read more: https://srfl-lab.webnode.com/products/manuscript-of-quantum-theory-for-language-with-preface-note-and-note-2-2003-2018/ ...................................................................................... 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. ReferenceJIMBO 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 inhospital 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. ............................................................................ 1970s' dream, writing clear description on language universals by mathematics From The Days of Ideogram 4. Time property in charactersIn 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/ .............................................................................
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. ................................................................................
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.Arithmetic Geometry Language 2013Algebraic Geometry Language 2014 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.Kac-Moody Lie Algebra Note 1 Kac-Moody Lie Algebra 2008Kac-Moody Lie Algebra Note 2 Quantum Group 2008The 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.Floer Homology Language Note 7 Quantization of Language 2009Floer Homology Language Note 8 Discreteness of Language 2009 4.All the basis of Word Indexed is generated at the next.Manuscript of Quantum Theory for Language 2003 ReferenceKac-Moody Lie Algebra 2008Theory 2003-2016 2018Genealogical Tree of Sekinan's Paper 7th Edition 2015-2018 This paper is unfinished. Read more: https://srfl-lab.webnode.com/news/quantum-group-language-word-indexed-and-word-synthesized/ ....................................................................................... 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.
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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 198310 Qiang yu jianzhi SUN Hongkai edited 198111 Mulao yu jianzhi WANG Jin ZHENG Guoqiao edited 198012 Tai yu jianzhi YU Cuirong LUO Meizhen edited 198013 Tuzu yu jainzhi ZHAONA Situ edited 198114 Wa yu jianzhi Zhou Zhizhi YAN Qixiang edited 198415 Yaozu yuyan jianzhi MAO Zongwu MENG Chaoji ZHENG Zongze edited 1982 Guojia minwei minzu wenti 5 zhong congshu zhi 1Zhongguo Shaoshu Minzu Yuyan Jianzhi CongshuMinzu Chubanshe 16 Achang yu jianzhi DAI Qingxia SUI Zhichao edited 198517 Bulang yu jianzhi LI Daoyong NIE Xiizhen QIU Efeng edited 198618 Chaoxian yu jianzhi XUAN Dewu JIN Xiangyuan ZHAO Xi edited 198519 Cuonamen yu jianzhi LU Shaozun edited 198620 Deang yu jianzhi CHEN Xiangmu WANG Jingliu LEI Yongliang edited 198621 Elunchun yu jianzhi HU Zengyi edited 198622 Ewenke yu jianzhi HU Zengyi CHAO Ke edited 198623 Gaoshanzu yuyan jianzhi (Ameisi yu) HE Rufen ZENG Siqi TIAn Zhongshan LIN Dengxian edited 198624 Gaoshanzu yuyan jianzhi (Bunen yu) HE Rufen ZENG Siqi LI Wensu LIN Qingchun edited 198625 Gaoshanzu yuyan jianzhi (Peiwan yu) CHEN Kang MA rongsheng edited 198626 Heni yu jianzhi LI Yongsui WANG Ersong edited 198627 Hesake yu jianzhi GENG Shimin LI Zengxiang edited 198528 Heze yu jianzhi AN Jun edited 198629 Jing yu jianzhi OUYANG Jueya CHENG Fang YU Cuirong edited 198430 Jinuo yu jianzhi GAI Xingzhi edited 198631 Keerkezi yu jianzhi HU Shenhua edited 198632 Lahu yu jianzhi CHANG Hongen mainly edited33 Lisu yu jianzhi CHU Lin MU Yuzhang GAI Xingzhi edited 198634 Luoba zu yuyian jianzhi (Bengni-Bogaer yu) OUYANG Jueya edited 198535 Naxi yu jianzhi HE Jiren JIANG Zhu yi edited 1985 36 Nu zu yuyan jianzhi (Nuban yu) SUN Hongkai LIU Lu edited 198637 Cangluo menba yu jianzhi ZHANG Jichuan edited 198638 Sala yu LIN Lianyu edited 198539 She yu jianzhi MAO zongwu MENG Chaoji edited 198640 Xibu yugu yu jianzhi CHEN Zongzhen LEI Xuanchun edited 198541 Tajike yu jianzhi GAO erjiang edited 198542Tayaer yu jianzhi CHEN Zongzhen YI Liqian edited 198643 Tujia yu jianzhi TIAN Desheng HE Tianzhen deng edited 198644 Weiwuer yu ZHAO Xiangru SHU Zhining edited 198545 Wuzubieke yu jianzhi CHENG Shiliang ABUTURE Heman edited 198746 Xibo yu jianzhi LI Shulan ZHONG Qian edited 198647 Yi yu jianzhi CHEN Shilin BIAN Shiming LI Xiuqing dited 1985 TOKYODecember 31, 2004Sekinan Research Field of Language Read more: https://srfl-collection.webnode.com/news/national-minority-languages-in-china/ Read more: https://geometrization-language.webnode.com/news/national-minority-languages-in-china/ ........................................................ Xixiayu is a very interesting for me resembling the Hanyu and in the late 20th century the language was deciphered by Japanese linguist NISHIDA Tatsuo. The Days of Decipherment 2017 ..................................................................... The Days of Decipherment TANAKA Akio On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition A JOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth days, so to say, the days of decipherment. 1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told at Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered the Linear B. In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered by NISHIDA Tatsuo (1928-2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki narabini Seikago bunpou no kenkyuu in 1962.In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team developed largely. In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the Qing dynasty and I read them almost every day containing the comparison with the western linguistic results. The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin were the most important for me. In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda, Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was too much difficult to read on. From the days the long and winding road began to mathematics and its applicable study for language universals. At the exhibition of ancient Greece I confirmed in particular that the stability of language was kept by letters and characters from the Linear A and Linear B. These language or character's situation especially of ideogram has become my study's foundation. ..................................................................... These language or character's situation, especially of ideogram has become my study's foundation.For ideogram, refer to the next papers. .................................................................... Ideogram Paper 2005-20181. Ideogram 20052. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 20123. Essence of Language 20164. The Days of Decipherment 20165. The Days of Ideogram 20176. The Days of Ideogram 20177. The comparison between 2003 and 2017From Chinese character's meaning structure to Homological algebraic model of language universals2017 8. Letter to Y. Of Broad Language 4th edition 20189. Determination of the concept, Broad Language 201810.Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018 Read more: https://geometrization-language.webnode.com/ Read more: https://srfl-lab.webnode.com/products/ideogram-paper-2005-2018/ ................................................................... 7.Quantum group 2 In 2008 I wrote on Quantum group at studying Kac-Moody-Lie Algebra. ..................................................................... Kac-Moody Lie AlgebraNote 2Quantum GroupTANAKA Akio 1Base field KFinite index set ISquare matrix that has elements by integer A = ( aij )i, j∈ IMatrix that satisfies the next is called Cartan matrix.i, j ∈ I(1) aii = 2(2) aij ≤ 0 ( i ≠j )(3) aij = 0 ⇔ aji = 02Cartan matrix A = (aij)i, j ∈IFamily of positive rational number {di}i∈IArbitrary i, j∈I diaij = djajiA is called symmetrizable.3Finite dimension vector space hLinearly independent subset of h {hi}i∈IDual space of h h*= HomK (h, K )Linearly independent subset of h* {αi} i∈IΦ = {h, {hi}i∈I, {αi} i∈I }Cartan matrix A = {αi(hi)} I, j∈IΦis called fundamental root data of A that is Cartan matrix.4Symmetrizable Cartan matrix A = (aij)i, j ∈IFundamental root data {h, {hi}i∈I, {αi} i∈I }E = αi ⊂h*Family of positive rational number {di}i∈Idiaij = djajiSymmetry bilinear form over E ( , ) : E×E → K ( (αi ,αj ) = diaij )The form is called standard form.5n-dimensional Euclid space RnLinear independent vector v1, …, vnLattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )Lattice of h hZ6From 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 ∈ hz7Vector space over K ABilinear product over K A×A → AWhen A is ring, it is called associative algebra.8Integer mt similarity of m [m]t[m]t = tm-t-m / t- t-1Integer m, n m≧n≧0Binomial coefficient (mn)t similarity of m! [m]t! = [m]t! [m-1]t!...[1]tt similarity of (mn) [mn]t = [m]t! / [n]t! [m-n]t![m0] = [mm]t = 18Integer 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∈IAssociative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.(1) khkh’ = kh+h’ ( h, h’∈hZ )(2) k0 = 1(3) KhEiK-h = qαi(h)Ei ( h∈hZ , i∈I )(4) KhFiK-h = qαi(h)Fi ( h∈hZ , i∈I )(5) Ei Fj – FjEi = ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )(6) p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )(7) p [1-aijp]qiFi1-aij-pFjFip = 0 ( i , j∈I , i ≠j ) [Note]Parameter q in K is thinkable in connection with the concept of at the paper Place where Quantum of Language exists / 27 /.Refer to the next.Place where Quantum of Language exists / Tokyo July 18, 2004Tokyo February 9, 2008Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-lab.webnode.com/news/kac-moody-lie-algebra-note-2-quantum-group/ ........................................................................................ In 2004 I wrote the paper named Place where Quantum of Language exists. ........................................................................................ Place where Quantum of Language Exists TANAKA Akio 1 Quantum of language is the smallest unit of language.2 Quantum of language moves linearly on the floor of language.3 Linear movement is the properties of quantum.4 Floor of language is on the space of language.5 The space of language is two dimensions.6 Two dimensions are horizontal and vertical.7 Horizontal movement makes word, #18 Vertical movement makes sentence. #19 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. #222 The other situation is what quanta change oneself by the non-use of quanta meaning in language history progress. #223 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. #330 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, 2004Sekinan Research Field of Languagewww.sekinan.orgPostscript [Referential note November 9, 2007] is related with the next papers on the concept. ________________________________ <Distance Theory Algebraically Supplemented> Brane Simplified Model 2 Distance Tokyo October 26, 2007<Quantum Theory for Language>On Time Property Inherent in Characters Hakuba March 28, 2003Quantum Theory for language Synopsis Tokyo January 15, 2004Reversion Theory Tokyo September 27, 2004Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO Tokyo October 2, 2004Mirror Theory For the Structure of Prayer Dedicated to the Memory of CHINO Eiichi Tokyo June 5, 2004Mirror Language Tokyo June 10, 2004Guarantee of Language For LÉVI-STRAUSS Claude Tokyo June 12, 2004Actual Language and Imaginary Language To LÉVI-STRAUSS Claude Tokyo September 23, 2004 ________________________________ [Referential note February 9, 2008]† Concept of /27/ is thinkable in connection with q> at the paper Kac-Moody Lie Algebra / Quantum Group /.Refer to the next.Kac-Moody Lie Algebra / Quantum Group / February 9, 2008 Read more: https://srfl-lab.webnode.com/news/place-where-quantum-of-language-exists/ ............................................................................................. At this paper, 23-33 is the most important for signal's intuitive image. 23 Word has a positive- negative construction.24 Positive-negative construction occurs on a floor.25 Sentence has a positive-positive construction.26 Positive-positive construction occurs on different floors.27 The latter quantum transfers on a different floor. This transfer is called .†28 Quantum has electrical energy which flows to the electrical zero level.29 Electrical zero level is a sentence end where quantum of language ideally accord with the real world. #330 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. ........................................................................................ 8.Quantum group 3 Quantum group is defined by JIMBO Michio as the following. Definition of quantum group Generating element: a, b, c, dRelation: ba = qab, ca = qac bd = q-1db, cd = q-1dc bc = cb, ad - q-1bc = da - qbc = 1Coproduct: 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. ............................................................ The comparison between 2003 and 2017From Chinese character's meaning structure to Homological algebraic model of language universals Read more: https://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-characters-meaning-structure-to-homological-algebraic-model-of-language-universals/ ...............................................................At the end of paper 2017, I wrote as the following, where I showed the early intuitive papers related with symmetry or mirror. This concept has succeeded till now and a little developed a new direction towards mathematical based concept especially of quantum group. The concept called symmetry is very important to describe the complex situation of natural language.Symmetry contains undifferentiated factors in itself, for example mirror, distance,ant-world and so forth.I ever tried to cultivate this fantastic field to resolve the hardship on language universals one more step up.My trying paper is the following.Mirror Theory 2004Mirror Language 2004 Read more: https://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-characters-meaning-structure-to-homological-algebraic-model-of-language-universals/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=https%3A%2F%2Fsrfl-paper.webnode.com%2Fnews%2Fthe-comparison-between-2003-and-2017-from-chinese-characters-meaning-structure-to-homological-algebraic-model-of-language-universals%2F ................................................................ 10.Quantum Language based on quantum emerged from thinking the simplest model for containing the finite essential elements of language in summer 2003 at Hakuba, Nagano, Japan at the skirts of Japan Alps. Details are the next. Inspiration The Time of QuantumTANAKA Akio In August 2003, I went to Hakuba in Nagano prefecture for the summer vacation with my family. At that time I had been thinking on the form of language for which I wrote the paper, that connects with time inherent in characters, in March 2003 also at Hakuba. At night of August 23 in cottage, I casually saw the advertising paper of electric dictionary. The paper was brought from the convenience store near the cottage in the evening. The dictionary on the paper was Seiko’s English-Japanese dictionary that has additionally consultation for Chinese or French language with large scale. I vaguely considered that after this dictionaries are necessarily taken these multi-lingual way. At the time I suddenly realized that the form of language may be spherical style in which language contains all the information in itself.That was rather satisfied solution for the tough problem of language that I had been carrying in my life from my twenties. I wrote the sketch-like paper of the theoretical approach after returning home of Tokyo. The paper was read at the international symposium of UNESCO opened in winter 2003 at Nara. In the paper, the spherical substance of language is seemed to be quantum in DELBRUCK’s image-like physical world. After 5 years from the inspiration at summer of Hakuba, now I consider that spherical essence is manifold in infinite dimensional world. Now I also realize that the toughest problem of language is minutely solvable in mathematical approach that has structurally definable terms. TokyoSeptember 29, 2008Sekinan Research Field of Language [January 23, 2012]The title changed.The former title is “From Quantum to Manifold”.[Postscript. January 25,2012]On quantization of Language.Refer to the next.Quantization of Language Read more: https://srfl-collection.webnode.com/news/inspiration-the-time-of-quantum-2008-2012/11.Symmetry 2 Symmetry seems to be related with two elements of language universals, distance and time.Refer to the next.Distance Theory Algebraically Supplemented Brane Simplified Model 1 Bend 2007 ............................................................................... Distance Theory Algebraically SupplementedBrane Simplified Model 1BendTANAKA Akio 1Language is expressed by< a pair of quanta> that consists of and .2Quantum and anti-quantum have reverse direction.3Quantum and anti-quantum are in the shape of strings that are separated parallel longitude L apart.4Quantum and anti-quantum are in <AdS5 ( 5-dimensional anti-deSitter ) space>.5Left side of quantum and anti-quantum is on .6Quantum starts from ra in AdS5 space and returns rb in AdS5 space.ra and rb are equal longitude from D3 brane.7of D3 brane in AdS5 space gives quantum and anti-quantum bending near r = 0 that is the location of D3 brane.Quantum’s nearest point to D3 brane is rz.rz’ is 1/2 of the longitude from ra to rb.Sketch is below. 8At the paper Spacetime Symmetry and Escalator Brane in Escalator Language Theory, language goes from ra to rz and in reverse movement to rb.9At the paper Actual Language and Imaginary Language, is from ra to rz and is from rz to rb.10We see real language that is upper side of rz-rz’. Imaginary language is hidden under side of rz-rz’ in our life.11At the paper Mirror Language, imaginary language is mirror language of real language.12Distance of language is regarded as the longitude from ra ( or rb ) to D3 brane in AdS5 space. [Reference]Escalator Language Theory / 2 Turning Point of Time / Tokyo December 22, 2006 Tokyo October 17, 2007Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-simplified-model-continuation-of-escalator-language-theory-1-bend-2007/............................................................... In 2006 I wrote Escalator Language series.Paper, Turning Point of Time is a intuitive paper for the three papers of Distance Theory Algebraically Supplemented 2007. ........................................................................ Escalator Language TheoryTurning Point of TimeFor SINGER Isaac Bashevis, WHEN SHLEMIEL WENT TO WARSAW AND OTHER STORIESTANAKA 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, 2006Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-collection.webnode.com/news/escalator-language-theory-turning-point-of-time-2006/ ....................................................................................... 12.Distance Distance is one of the most important elements of my language model of language universals. For this element algebraic approach seems to be clearer description to the model. Refer to the next paper. Distance Theory Algebraically SupplementedBrane Simplified Model 2Distance
2007 ...................................................................................... Distance Theory Algebraically SupplementedBrane Simplified Model Escalator Language Theory>2DistanceDirect Succession of Distance TheoryTANAKA Akio 1Metric model of 5-dimensional spacetime is expressed below from Randall and Sundrum (1999).ds2 = e2U(y)ηmndxmdxn + dy2Branes exist at y = 0 and y = d.Our world is regarded as brane y = 0.U(y) is called .2Using of circle ( radius R )’s identification, y is expressed by that scales from 0 to ±πR. Distance is defined in .According to , of is measured in bulk spacetime of 5 dimensional Anti-deSitter space.3Distance in is expressed from <y = –πR> to <y = 0> and from <y = 0> to <y = +πR>.Now “from <y = –πR> to <y = 0>” is called and “from <y = 0> to <y = +πR>” is called .Values of are same at and .4In (abbreviation; DTAS), word is regarded by ’s value.
5Word has distance at and .6Now distance at is called distance of and distance at is called distance of . [References]<Quantum Theory for Language Map>2.1.3 Distance Theory2.1.4 Reversion Theory2.2.1 Prague Theory2.3 Warp Theory2.4 Time Theory4.3.1 Guarantee of Language4.3.2 Place where Quantum of Language Exists4.3.3 Actual Language and Imaginary Language4.5.1 Mirror Language4.5.2 Mirror Theory<Aurora Theory>[AT11] Distance and Time Language Multi-Time Conjecture 3 5th Time for KARCEVSKIJ<Aurora Time Theory>[ATT3] Enlarged Distance Theory[ATT4] Opened Time and Closed Time<Algebraic Linguistics Linguistic Result>1 Deep Fissure between Word and Sentence2 From Cut and Glue Dimension to Krull Dimension 8th For KARCEVSKIJ SergejTokyo October 26, 2007Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-simplified-model-2-distance-direct-succession-of-distance-theory-2007/ ........................................................................................ Before algebraic approach for distance, I early wrote the more intuitive paper for distance, its name is Distance Theory in 2004.Refer to the next. Distance Theory 2004 ........................................................................................
TANAKA Akio 1Distance theory is an extension of Quantum Theory for Language.2Distance theory is an extension of strength rule in Quantum Theory for Language.3Distance theory is considered for the purpose of the guarantee to language.4What 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.5The 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.6A quantum consists of indicators.An indicator has a signification and a period inherently.The structure of quantum is indicated in Quantum Theory for Language.7An 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.8A significant element gets a signification from the real world.A periodical element gets a time from the real world.9An indicator gets a meaning and a period from elements.10An 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.11An 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.12An 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.13A 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.14Indicators make meaning and connection rule in a quantum, both are derived from significant and periodical elements in an indicator.15Meaning 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.16Connection rule is decided by periodical elements in indicators.Details are indicated in Quantum Theory for Language.17Signification 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.18Multiplication generally occurs by the addition of signification in an indicator.But multiplication in meaning of a quantum sometimes occurs without any addition oneself.19Multiplication in a quantum without addition occurs by situational transition in the language world.20Situational 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.21A quantum of language itself becomes in the language world.
Word is defined.
Therefore each word has a distance toward the real world.
A distance immanent in a word does not emerge itself.
Distance emerges in the linear situation of words gathering.
This situation is called .
Sentence is defined.
Therefore sentence is an emergence of distance in words gathering.
Words form a line, thereafter one arrangement is determined.
Sentence is realized in our world.
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]
early work.>
On Time Property Inherent in Characters Hakuba March 28, 2003
Quantum Theory for Language Synopsis Tokyo January 15, 2004
Reversion Theory Tokyo September 27, 2004
Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO Tokyo October 2, 2004
Mirror Theory For the Structure of Prayer Dedicated to the Memory of CHINO Eiichi Tokyo June 5, 2004
Mirror Language Tokyo June 10, 2004
Guarantee of Language For LÉVI-STRAUSS Claude Tokyo June 12, 2004
Actual Language and Imaginary Language To LÉVI-STRAUSS Claude Tokyo September 23, 2004
[Referential note / December 25, 2007]
Algebraic Linguistics / From September 11, 2007
Distance Theory Algebraically Supplemented / From October 4, 2007
Noncommutative Distance Theory / From November 30. 2007
[Referential note / July 7, 2008]
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
Amplitude of Meaning Minimum / sekinan.wiki.zoho.com
Complex Manifold Deformation Theory / sekinan.wiki.zoho.com
[Referential note / December 23, 2008]
Time of Word / sekinan.wiki.zoho.com
[Referential note / January 1, 2009]
Orbit of Word / sekinan.wiki.zoho.com
[Referential note / January 31, 2009]
Word Problem of Word-hyperbolic Group / sekinan.wiki.zoho.com Read more: https://geometrization-language.webnode.com/products/distance-theory/ Read more: https://srfl-collection.webnode.com/news/distance-theory-2004/ ................................................................................ 13.Distance 2
Hoph algebra The upper section 12.'s algebraic defined distance is also related with Hoph algebra.Refer to the next.Distance Theory Algebraically SupplementedBrane Simplified Model3S3 and Hoph Map ...................................................................... Distance Theory Algebraically SupplementedBrane Simplified Model 3S3 and Hoph MapTANAKA Akio 1From RS model, and are abstracted.Refer to the next.Distance Theory Algebraically Supplemented / 2 Distance / Tokyo October 26, 20072s from to at and are both seemed as circle S1.33-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 + iy1 ) ∈ C( x1, y1 ) = ( 0, 0 ) π ( x1, y1, x2, y2 ) = ∞Hopf map π : S3 → Riemann Sphere, C ∪ {∞} Inverse image of a point p π -1 (p) is S1.Hoph map is fiber bundle that derived from fiber S1.On fiber bundle, refer to the next.Symmetry Flow Language / Leaf of Language / Tokyo May 11, 20074Now at is identificated as S1.Two points a ( xa, ya ), b (xb, yb ) at Gauss plane is objected to Riemann sphere.At Riemann Sphere, two points a, b is marked by a’ ( x’a, y’a ), b’ (x’b, y’b ) .On Riemann sphere, refer to the next.Symmetry Flow Language / Simplex, Simplicial Complex and polyhedron / Tokyo May 17, 2007Symmetry Flow Language / Meaning Variation and Time Shift in word as Homotogy / Tokyo May 17, 2007Point of S3 is marked by ( x’a, y’a , x’b, y’b ) .On S3, refer to the next.Symmetry Flow Language 2 / Time Shift of Meaning in Moduli Space / Tokyo May 23, 20075at is also marked on S3.6and are algebraically considered by S3. Tokyo November 12, 2007Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-collection.webnode.com/news/distance-theory-algebraically-supplemented-brane-simplified-model-3-s3-and-hoph-map-2007/ ............................................................................... 14Symmetry 3 On symmetry I wrote Symmetry Flow Language and Symmetry Flow language 2 in 2007.Contents are the next. Symmetry Flow LanguageOn Symmetry of Language and Time
Symmetry Flow Language 2On Symmetry of Language and Time 2
........................................................................... Related with Hoph algebra, next papers are referential. Symmetry Flow Language
Symmetry Flow Language 2
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=1nCk is module.∂k: Ck → Ck—1 is homomorphism.∂k-1o∂k = 0 It is meant that set’s boundary’s boundary becomes null set.2 Meaning is divided by boundary.3 Word is given by simplex.4 Simplex has m+1 vertex and m-dimension. It is called m-simplex.5 Simplex has orientation that is given by permutation.6 Orientation gives sentence to vector that consists of words.7 Vector’s element is given by simplex’s vertex.8 Sentence is given by simplicial complex.9 Language is given by polyhedron that consists of union of all simplexes.10 Polyhedron has triangulation.11 Sphere’s triangulation is given tetrahedron by homeomorphism.12 Riemann sphere obtains information from Gauss plane.Refer to the following papers’ group.Aurora TheoryAurora Time Theory13 Minimum model of Symmetry Flow Language is testified by tetrahedron being led from polyhedron’s triangulation. Tokyo May 17, 2007Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-simplex-simplicial-complex-and-polyhedron/ Symmetry Flow Language 6 Meaning Variation and Time Shift in Word as HomotopyFor 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 path5 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.On Time Property Inherent in Characters Hakuba March 28, 20038 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 law10 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 →Xα is called 2-loop that expresses dimensional extension of loop concept.15 2-dimensional sphere is 2-loop.16 Riemann sphere has information from Gauss plane.Refer to the following papers’ group.Aurora TheoryAurora Time Theory17 Meaning variation and concomitant time shift in Symmetry Flow Language are testified by 2-loop sphere. Tokyo May 17, 2007Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-meaning-variation-and-time-shift-in-word-as-homotopy-for-wang-guowei-and-karcevskij-sergej/ Symmetry Flow Language 2 2 Time Shift of Meaning in Moduli Space7th for KARCEVSKIJ Sergej TANAKA Akio 1 Word has variation of meaning in accordance with time shift in space.Refer to the following papers.Language and Spacetime Structure of Word Tokyo April 6, 2007Language and Spacetime Description of Meaning Tokyo April 16, 2007Language and Spacetime Shift of Time Tokyo April 20, 2007Symmetry Flow Language Meaning Variation and Time Shift in Word as Homotopy Tokyo May 17, 20072 Space that is deformed successively is described by parameter that is called moduli.3 Set M consists of all of moduli.4 Moduli space M (M) is presented for variation of word’s meaning.5 Parameter t is presented for time shift of meaning in word.6 Calabi-Yau manifold K has two moduli that are deformation of complex structure and Kähler manifold. Moduli have symmetry that is called Mirror symmetry.7 K’s Ricci tensor is the following.Rij¯ = 0 i is regular coordinate. j¯ is non-regular coordinate.Refer to the following paper.Language and Spacetime Construction of Spacetime Especially on Transformation with Boundary for Dimensions Tokyo April 24, 20078 Replaced two moduli in Calabi-Yau manifold K is called reflection Calabi-Yau manifold K~.Refer to the following paper.Mirror Language Tokyo June 10, 20069 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 ∧ dθiP1 with line bundle’s direct sum becomes resolved conifold.10 Conifold’s toric graph has line segment that has the longitude | z1 |2+ | z2 |2 = r. r is parameter of conifold.11 Parameter r becomes parameter t that is described as complex.12 Resolved conifold that has parameter t = 0 and is deformed becomes deformed conifold that has S3.13 Parameter t of deformed conifold S3 means time of word’s meaning variation in language.14 Deformed conifold S3 means word in language.15 P1× P1 becomes square that is connected by world sheets.16 P1× P1 means sentence in language.Refer to the following paper.Cube Theory Structure of Cube Tokyo March 25, 2006Cube Theory Cube Word Hakuba April 1, 2006Tokyo May 23, 2007Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/symmetry-flow-language-2-time-shift-of-meaning-in-moduli-space-7th-for-karcevskij-sergej/ ............................................................................................................. 15.Derived category Time conjecture of languageAt language universals, distance and time are the kernel concepts for my language models.Measure of distance is deeply related with time which is transcendental unit still now.Category theory is probably very useful for the relation between distance and time.For these concepts, I ever wrote several trial papers. Refer to the next one.
Language and Spacetime Shift of TimeFrom SAPIR Edward to KAWAMATA Yujiro TANAKA Akio 1 Language is expressed as structure of spacetime.2 Spacetime is expressed as manifold.3 Affine algebraic variety is selected for description of spacetime.Algebraic variety is pasted together from affine algebraic variety.Affine algebraic variety is irreducible affine algebraic set.Affine algebraic set is the set that consists of common zero point of finite polynominalPolynominal is in n-dimensional complex affine space.4 Now n-dimensional projective spaceP n is presented.Cn+1 \ {O} / ~O is the coordinate’s origin of complex affine space.~ is mathematical equivalence on elements of set.5 Projective space P n is covered by n+1 affine space.6 Now abelian category and derived category are presented.Abelian category and algebraic variety is placed together.Derived category is abelian category’s coherent sheaf’s complex that is composition of successive arrows becomes 0.7 From derived category, distinguished triangle is presented.8 Here time conjecture of language is presented.(1)Distinguished triangle makes the model for shift of time on language.(2)Time on language is closed, successive and circular in word.Circulation is worked between starting point and ending point of word.The origin of shift of time is derived from the following.On Time Property Inherent in Characters Hakuba March 28, 2003The concept of time in language is taught from the following.SAPIR Edward LANGUAGE An Introduction to the Study of Speech Harcout, Brace & Co. IncSpecial thanks to KAWAMATA Yujiro for the mathematical approach on language research, especially from the following.KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1, January 2006Tokyo April 20, 2007Sekinan Research Field of Languagewww.sekinan.org Read more: https://srfl-collection.webnode.com/news/language-and-spacetime-shift-of-time-from-sapir-edward-to-kawamata-yujiro-2007/ Read more: https://srfl-collection.webnode.com/news/what-is-signal-a-mathematical-model-of-nerve-22-december-2018/-----------------------------------------------------------At this paper, now I extract the next phrases. Derived category is abelian category’s coherent sheaf’s complex that is composition of successive arrows becomes 0. 7 From derived category, distinguished triangle is presented.8 Here time conjecture of language is presented.(1)Distinguished triangle makes the model for shift of time on language.(2)Time on language is closed, successive and circular in word. Circulation is worked between starting point and ending point of word. Paper group, Language and Spacetime is especially focused at time in space.Every paper of Language and Spacetime, Symmetry Flow Language and Symmetry Flow Language 2can be seen at the at the site, SRFL Paper Top pager's right column's Paper 2003-2007 .
Read more: https://srfl-paper.webnode.com/
Language and Spacetime
Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-contents/ Papers at Time and Spacetime, next two papers are also important to time concepts for me.Especially No.2 paper is dedicated to Mac Lane for his Category Theory's work.No.9 Paper is dedicated Kohari Akihiko and his days for his early death at unhappy accident in 1970s.
Two papers text are the next.
Language and Spacetime Word Containing Time and 4 Dimensional SphereDedicated toMAC LANE Saunders TANAKA Akio 1 Word contains time inside.Refer to the following paper.On Time Property Inherent in Characters 1 Generation in Characters Hakuba March 28, 20032 Word has construction that is expressed by category.On category, refer to Categories for the Working Mathematicians by Saunders Mac Lane, 1998 Springer-Verlag New York, LLC.3 Time has starting point and ending point in word.4 Meaning has starting point and ending point in word.5 Generally word shifts meaning from starting point to ending point by time.Refer to the following paper.On Time Property Inherent in Characters 2 Function of Characters Hakuba March 28, 20036 Primitive word does not shift time and stays in the same point.7 In category, the names of language are called by following terms.Meaning is called object.Shift is called arrow.Starting point is called domain or source.Ending point is called codomain or target.No shift or stay is called identity.Arrow can be composed. The composed arrow is called composite.In category two axioms are presupposed.One is associativity.The other is unit law.These terms are all complied with above quoted Mac Lane.8 Word with starting point is expressed on Gauss plane.9 Word with ending point is also expressed on Gauss plane.10 Shift time from starting point to ending point is expressed by coordinates’ transference.11 Here Riemann sphere is putted with having the same origin to Gauss plane.12 Word with starting point is projected toward the North Pole of Riemann sphere.13 Word with starting point has coordinates ws (xs ys, zs) on Riemann sphere’s surface.Refer to the following paper.Aurora and Riemann Sphere Tokyo October 2 – October 3, 2006Aurora Plane Tokyo October 14, 2006Word, phrase and Sentence Tokyo October 25, 200614 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, 2007Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-word-containing-time-and-4-dimensional-sphere-dedicated-to-mac-lane-saunders/
Language and SpacetimeTime Flow in WordFor KOHARI Akihiro and His TimeTANAKA Akio 1Word 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) = x2In 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).3Now 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’4The 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)5Now 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=0The flow has solution as equation φt(x)/dt = Xφt(x)6Here set {φt(x) | t∈R } is presented. The set is called orbit.7In word, meaning is expressed by flow and time is expressed by orbit.Tokyo May 3, 2007Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-time-flow-in-word-for-kohari-akihiro-and-his-time/ ------------------------------------------------------------------------------------------------------------------------------- What is signal? A mathematical model of nerve Preparation 1-15is over 29 December 2018 ------------------------------------------------------------------------------------------------------------------------------- SRFL PaperTokyo29 December 2018 --------------------------------------------------------------------------------------------------------------------------------
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 2NoteGeneration 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 = *AnSpectrum deconstruction An = ∫1-1 λdEλ(n)C*algebra that is generated by set { Eλ(n) ; λ∈Q∩[-1, 1], n∈N} AA’’ = NA is commutative.I∈AExistence of compact Hausdorff space Ω = Sp(A )A = C(Ω)Element corresponded with f∈C(Ω) A∈AN is generated by A. [Index of Terms]|A|Ⅲ7-5|| . ||Ⅱ2-2||x||Ⅱ2-2Ⅱ2-1*algebraⅡ3-4*homomorphismⅡ3-4*isomorphismⅡ3-4*subalgebraⅡ3-4adjoint spaceⅠ12algebraⅠ8axiom of infinityⅠ1-8axiom of power setⅠ1-4axiom of regularityⅠ1-10axiom of separationⅠ1-6axiom of sumⅠ1-5B ( H )Ⅱ3-3Banach algebraⅡ2-6Banach spaceⅡ2-3Banach* algebraⅡ2-6Banach-Alaoglu theoremⅡ5basis of neighbor hoodsⅠ4bicommutantⅡ6-2bijectiveⅡ7-1binary relationⅡ7-2boundedⅡ3-3bounded linear operatorⅡ3-3bounded linear operator, B ( H )Ⅱ3-3C* algebraⅡ2-8cardinal numberⅡ7-3cardinality, |A|Ⅱ7-5characterⅡ3-6character space (spectrum space), Sp( )Ⅱ3-6closed setⅠ2-2commutantⅡ6-2compactⅠ3-2complementⅠ1-3completeⅡ2-3countable setⅡ7-6countable infinite setⅡ7-6coveringⅠ3-1commutantⅡ6-2D ( )Ⅱ3-2denseⅠ9dom( )Ⅱ3-2domain, D ( ), dom( )Ⅱ3-2empty setⅠ1-9equal distance operatorⅡ4-1equipotentⅢ7-1faithfulⅡ3-4Gerfand representationⅡ3-7Gerfand-Naimark theoremⅡ4HⅡ3-1Hausdorff spaceⅠ5Hilbert spaceⅡ3-1homomorphismⅡ3-4idempotent elementⅡ9-1identity elementⅡ9-1identity operatorⅡ6-1injectiveⅢ7-1inner productⅡ2-1inner spaceⅠ6involution*Ⅰ10linear functionalⅡ5-2linear operatorⅡ3-2linear spaceⅠ6linear topological spaceⅠ11locally compactⅠ3-2locally vertexⅠ11NⅢ3-8N1Ⅲ3-8neighborhoodⅠ4normⅡ2-2normⅡ3-3norm algebraⅡ5norm spaceⅡ2-2normalⅡ2-4normalⅡ3-4open coveringⅠ3-2open setⅠ2-2operatorⅡ3-2ordinal numberⅡ7-3productⅠ8product setⅡ7-2r( )Ⅱ2R ( )Ⅱ3-2ran( )Ⅱ3-2range, R ( ), ran( )Ⅱ3-2reflectiveⅠ12relationⅢ7-2representationⅡ3-5ringⅠ7Schwarz’s inequalityⅡ2-2self-adjointⅡ3-4separableⅡ7-7setⅠ7spectrum radius r( )Ⅱ2Stone-Weierstrass theoremⅡ1subalgebraⅠ8subcoveringⅠ3-1subringⅠ7subsetⅠ1-3subspaceⅠ2-3subtopological spaceⅠ2-3surjectiveⅢ7-1system of neighborhoodsⅠ4τs topologyⅡ7-9τw topologyⅡ7-9the second adjoint spaceⅠ12topological spaceⅠ2-2topologyⅠ2-1total order in strict senseⅡ7-3ultra-weak topologyⅢ6-4unit sphereⅡ5-1unitaryⅡ3-4vertex setⅡ3-3von Neumann algebraⅡ6-3weak topologyⅡ5-3weak * topologyⅡ5-3zero 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 induction0-3 Formula defined by induction <1 Set>1-1 Axiom of extensionality ∀x∀y[∀z∈x↔z∈y]→x=y.1-2 Set a, b1-3 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 ofpower 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>2-1Set XSubset of power set P(X) TT 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.2-2Set 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.2-3Topological space (X, T)Subset of X YS ={A∩Y ; A∈T}Subtopological space (Y, S) Topological space is abbreviated to subspace. <3 Compact>3-1Set XSubset of X YFamily of X’s subset that is not empty set U = <Ui; i∈I>U is covering of Y. ∪U = ∪i∈I ⊃YSubfamily of U V = <Ui; i∈J > (J⊂I)V is subcovering of U.3-2Topological space XElements of U Open set of XU 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 XPoint of X aSubset of X AOpen set Ba∈B⊂AA 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) UElement of U BArbitrary element of V(a) AWhen 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 UNeighborhood of b VU∩V = Ø <6 Linear space>Compact Hausdorff space ΩLinear 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 RWhen 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∈Sab∈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 XSubset of X YArbitrary open set that is not Ø in X AWhen 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*∈AArbitrary 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 KLinear space over K XWhen 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∈XBasis of neighborhoods of X’ zero element 0 VWhen V⊂V is vertex set, X is called locally vertex. <12 Adjoint space>Norm space XDistance 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<1Stone-Weierstrass Theorem>Compact Hausdorff space ΩSubalgebra 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∈ALocally compact Hausdorff space ΩSubalgebra 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<2Norm algebra>C* algebra AArbitrary element of A AWhen 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 CLinear space over K XArbitrary 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) , λy+z> = λ, y> + , z>Linear space that has inner product is called inner space. <2-2>||x|| = <x, x>1/2Schwarz’s inequalityInner 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|| = 0u∈X limn→∞||un – u|| = 0Complete 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, GOpen set of X U, VF⊂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 AArbitrary A∈ACharacter 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 VSubset of V DElement of D xMap T : x → Tx∈VThe map is called operator.D is called domain of T. Notation is D ( T ) or dom T.Set A⊂DSet 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+βTyT is called linear operator. <3-3 Bounded linear operator>Norm space VSubset of V Dsup{||x|| ; x∈D} < ∞D is called bounded.Linear operator from norm space V to norm space V1 TD ( T ) = V||Tx||≦γ (x∈V ) γ > 0T 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 ,KBounded linear operator from H to K B (H, K )B ( H ) : = B ( H, H )Subset K ⊂HArbitrary x, y∈K, 0≦λ≦1λx + (1-λ)y ∈KK is called vertex set. <3-4 Homomorphism>Algebra A that has involution* *algebraElement of *algebra A∈AWhen 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 BB * := B*∈BWhen B = B*, B is called self-adjoint set.Subalgebra of A BWhen B is adjoint set, B is called *subalgebra.Algebra A, BLinear map : A →B satisfies next condition, π is called homomorphism.π(AB) = π(A)π(B) (∀A, B∈A )*algebra AWhen 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 AHomomorphism ∧: 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 AHomomorphism ππ(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 VFunction 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 VArbitrary x∈VIx = xI is called identity operator. <6-2 Commutant>Subset of C*algebra B (H) ACommutant 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) AWhen 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 τWhen α→∞, Aα →τ AHilbert space HArbitrary {xn}, {yn}⊂H∑n||xn||2 < ∞∑n||yn||2 < ∞|∑n<xn, (Aα- A)yn>| →0A∈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, BMap f : A → BAll of B’s elements that are expressed by f(a) (a∈A) Image(f)a , a’∈AWhen 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, Bx∈A, y∈BAll 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 RR 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∈ax∈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 αα 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 setSet of which cardinarity is natural number finite setAddition of countable infinite set and finite set is called countable set. <7-7 Separable>Norm space VWhen 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 HA∈B ( H )Sequence of B ( H ) {Aα}{Aα} is convergent to A∈B ( H )Topology τWhen α→∞, Aα →τ A|| (Aα- A)x|| →0 ∀x∈HNotation is Aα →s A<7-9-2 τw topology>Hilbert space HA∈B ( H )Sequence of B ( H ) {Aα}{Aα} is convergent to A∈B ( H )Topology τWhen α→∞, Aα →τ A|Aα- A)y>| →0 ∀x, y∈HNotation 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・ SElement of S ee 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 continuedTokyo April 20, 2008Sekinan Research Field of Languagewww.sekinan.org 2Generation 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 2008adding their days and after A conclusion for the present on early papers of Sekinan Library TANAKA Akio 23 January - 26 January 2018TokyoSekinan Library 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)On Time Property Inherent in Characters 2003Manuscript of Quantum Theory for Language 2003Quantum Theory for Language 2004Reversion Theory 2004Prague Theory 2004Distance Theory 2005Generation Theorem 2008Generation of Word 2008Homology Generation of Language 2009Homology Structure of Word 2009(2)von Neumann Algebra 1-4 2008Functional Analysis 2008Complex Manifold Deformation Theory 2008-2009Floer Homology Language 2009(3)The Time of Quantum 2008The Days of von Neumann Algebra 2015The Days between von Neumann Algebra and Complex Manifold Deformation Theory2015Connection between early paper's quantum and recent paper's geometry 2017The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 2017 11.Basis of On Time Property Inherent in Characters 2003, Manuscript of Quantum Theory for Language 2003 and Quantum Theory for Language 2004 are all led by Qing Dynasty's linguistic (Xiaoxue) tradition, especially from WANG Guowei, whose influence is written at The Time of WANG Guowei in December 2011. 12.In 1970s at my age 20s, while I had read WANG Guowei, also read Ludwig Wittgenstein, from whom I narrowly learnt writing style that was maintained through early papers. On Wittgenstein I wrote The Time of Wittgenstein in January 2012. Especially written essayFor WITTGENSTEIN Ludwig Position of Language intermittently wrote from December 2005 to August 2012. 13.WANG Guowei taught me the micro phase of language and Edward Sapir taught me the macro phase of language. His book, Language 1921 shows us the conception of language's change system, Drift. I ever wrote some essays on him and his book titled Flow of Language in September 2014.On Edward Sapir I recently wrote a essay titled Edward Sapir gave me a moment to study language universals together with Sergej Karcevskij in July 2017. 14.I met again with CHINO Eiichi in 1979, from whom I learnt almost all the contemporary linguistics' basis, because of my bias to Chinese historical linguistics ( Xioxue) and Japanese classical phonology in characters. Reunion with CHINO was written at a essay titled Fortuitous Meeting What CHINO Eiichi Taught Me in the Class of Linguistics in December 2004. Also wrote Under the Dim Light in August 2012, CHINO Eiichi and Golden Prague in June 2014, Coffee shop named California in February 2015 and Prague in 1920s in April 2016. 15.CHINO Taught me the existence of Linguistic Circle of Prague and Sergej Karcevskij at Prague in 1920s. I wrote Linguistic Circle of Prague in July 2012 and also wrote on Karcevskij, Gift from Sergej Karcevskij in October 2005, Sergej Karcevskij, Soul of Language in November 2012, , Follower of Sergej Karcevskij in November 2012 Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi in April 2013 and For KARCEVSKIJ Sergej from time to time. 16.In 1970s, I also learnt mathematics for applying to describe language's minute situation. I had thought that language had to be written clear understanding form for free and precise verification going over philosophical insight. When set theory led by Kurt Godel was raised its head to logical basis, I was also deeply charmed by it. But even if fully using it, language's minute situation seemed to be not enough to write over clearly by my poor talent. The circumstance was written titled Glitter of youth through philosophy and mathematics in 1970s in March 2015. . 17.One day when I found and bought Bourbaki's series Japanese-translated editions, which were seemed to be possibility to apply my aim to describe language's situation. But keeping to read them were not acquired at that time. So I was engrossed in Chinese classical linguistics achieved in Qing dynasty, typically DUAN Yucai, WANG Niansun, WANG Yinzhi and so forth. The days were written as The Time of Language Ode to The Early Bourbaki To Grothendieck. 18.Algebraic geometry began from von Neumann Algebra. After these days, Zoho time came to me. Its first result is shown as the title Complex manifold Deformation Theory in 2008. Distance of Word in November 2008 is a mathematical conclusion of Distance Theory in May 2005. Zoho's main papers were seen at the site Sekinan Zoho. 19.Distance Theory has some derivations towards physical phases in my thought. Distance Theory Algebraically Supplemented Brane Simplified Model was written in October-November 2007. Each paper is the following. Distance Theory Algebraically SupplementedBrane Simplified ModelBendDistance S3 and Hoph Map Physics was one of the most fantastic fields in high school days. I ever wrote the days of yearning for physics and after that. Perhaps Return to Physics in April 2014, Winding road to physics in January 2015, Thanks to physics about which I ever dreamt in my future in April 2015, 20.After 2008 at Zoho sites, mathematics based language papers were successively written aiming clearer definition. Zoho's annual papers are shown at Sekinan Zoho's Zoho by year from 2008 to 2013. While I continued writing papers, my aim was gradually changed to confirm language's basis through mathematical, especially algebraic geometrical description by language models a little parting from natural language. The circumstances behind confirmation was written at Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague in October 2013 and 40 years passed from I read WANG Guowei in November 2013. Read more: https://geometrization-language.webnode.com/products/quantum-language-between-quantum-theory-for-language-2004-and-generation-of-word-2008-adding-their-days-and-after/ 3Energy 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 languageTANAKA Akio The energy of language seems to be one of the most fundamental theme for the further step-up study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory papers written so far.
Tokyo3 April 2015Sekinan Library
Read more: https://geometrization-language.webnode.com/news/preparation-for-the-energy-of-language/ .......................................................................
Floer Homology LanguageTANAKA 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 at Tokyo April 29, 2009 Newly planned on further visibility at Tokyo June 16, 2009 Sekinan Research Field of language
Read more: https://geometrization-language.webnode.com/news/floer-homology-language-note-1-potential-of-language/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=https%3A%2F%2Fgeometrization-language.webnode.com%2Fnews%2Ffloer-homology-language-note-1-potential-of-language%2F .................................................................... 4Energy 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.Amplitude of meaning minimum / Complex Manifold Deformation Theory 20082.Time of Word / Complex Manifold Deformation Theory 2008 ------------------------------------------------ Complex Manifold Deformation Theory Conjecture A4 Amplitude of Meaning Minimum TANAKA Akio ConjectureMeaning 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. 1Bounded domain of Rm ΩC∞ function defined in Ω u, Fu, F satisfy the next equation.F(D2u) = ΨD2u is hessian matrix of u.F is C∞ function over Rm×m .Open set that includes range of D2u UU satisfies the next.(i) Constant λ, Λ (ii) F is concave.2(Theorem)Sphere that has radius 2R in Ω B2RSphere that has same center with B2R and has radius σR in Ω BσRAmplitude of D2u ampD2uampBσRD2u = supBσRD2u – infBσRD2u0<σ<1C 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 FieldTo be continuedTokyo December 17, 2008Sekinan Research Field of language[References 4 / December 23, 2008 / on time of word]#18 Time of Word / Tokyo December 23, 2008 / sekinan.wiki.zoho.com
Read more: https://srfl-paper.webnode.com/news/amplitude-of-meaning-minimum/ ------------------------------------------------------------- Complex Manifold Deformation Theory Conjecture A5 Time of Word TANAKA Akio ConjectureWord 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. 1Kähler manifold XKähler form wA certain constant cCohomology class of w 2πc1(X)c1(X)>0Kähler metric gReal C∞ function f∫X (ef- 1)wn = 0Ric(w) -w = f2Monge-Ampère equation (Equation 1)Use continuity method(Equation 1-2)Kähler form w' = w + fRic(w') = tw' + (1-t)w'δ>0I = { }3 is differential over t.Ding's functional Fw4(Lemma)There exists constant that is unrelated with t.When utis the solution of equation 1-2, the next is satisfied.Fw(ut)C5Proper 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 Language2If 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 Theory3If 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.#1On Time Property Inherent in Characters#2From Cell to Manifold#3<For meaning minimum's finiteness>Amplitude of Meaning MinimumTokyo January 1, 2009Sekinan 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. 6Understandability 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. ---------------------------------------------------------
TANAKA Akio ConjectureLanguage is understandable. [View]0(Eells-Sampson Theorem)Compact Riemannian manifolds (M, g), (N, h)Section curvature of (N, h) everywhere non-positiveArbitrary C∞ map f : M → NEquation 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]1From 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. 2In 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, 2009Sekinan Research Field of language
------------------------------------------------------------- 7Understandability 2 Understandability of signal and language is dependant on time processing.Finite time is generally understandable for human or human assisted machine.In case of infinite time, what situation occur to understandability?I once think about infinity's details at the next two papers at von Neumann Algebra 3 in 2007. Properly Infinite / von Neumann Algebra 2008Purely Infinite / von Neumann Algebra 2008 ---------------------------------------------------------- von Neumann Algebra 3 Note 1Properly 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 HLinear subspace of H SubspaceSubspace that is closed by norm || ・|| of H Closed subspaceArbitrary subspace of H KK⊥: = {x∈H ; <x, y> = 0, ∀y ∈K} Orthogonal complement of KSubspaces 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∈Hd = dist(x, K) : = inf{||x-y|| ; y∈K}z∈Kd = ||x-z||z : = PKxPK is called objection operator from H to K.<1-3>von Neumann algebra NAll 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, KSubspace of H DMap AA(λx+μy) = λAx+μAy, ∀x, y∈D, ∀λ, μ∈CA 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 = HConstant M>0||Ax|| ≦M||x|| (∀x∈H)A is called bounded operator from H to KAll of As B(H, K)H = KB(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* = A2A 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 NCommutant of N N ‘Center of N Z := N∩N ‘ Z = CIN 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∈NF1∈P(N)F1≦FE ~ F1Situation 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, Bx∈A, y∈BAll 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 RR 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∈ax∈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 αα 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 setSet of which cardinarity is natural number finite setAddition 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 continuedTokyo May 1, 2008Sekinan Research Field of Languagewww.sekinan.org -------------------------------------------------------------------------- von Neumann Algebra 3 Note 2Purely 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∞ := 0τ 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 continuedTokyo May 1, 2008Sekinan Research Field of Languagewww.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 2011Finiteness of Words / Diophantine Language 2012Word as Infinite Loop Space / Infinite Loop Space Language 2012
8Signal
At this paper, signal is belonged to human world not belonged to outer world or universe.But Signal itself exists to go abroad to the widely opened worlds or universe.Understanding signal may be able to possess if there be energy which dispatch to the outer.Decipherment of the all the signals maybe a dream but the routes to decipher areternally remained by the very human ourselves. Refer to the next.The Days of Decipherment 2016Basis of the further study on language - Potential 2009-2015
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31/07/2016 14:46The Days of Decipherment TANAKA Akio On 20 July 2016 I went Tokyo National Museum, Ueno Park, Tokyo to see the exhibition AJOURNEY TO THE IMMORTALS: TREASURES OF ANCIENT GREECE, where I saw the linear A and B. It reminds me the youth days, so to say, the days of decipherment. 1960s -1970s is the age of decipherment in a sense. I was age 20 in 1967 and was learning language and literature at university. In 1958 John Chadwick's THE DECIPHERMENT OF LINEAR B was published from Cambridge University Press. At the preface of the book he wrote that the decipherment of linear B was told at Documents in Mycenaean Greek (Cambridge University Press, 1956) and Michael Ventris that deciphered the Linear B. In the same age in Japan, Xixia wenzi (Xixia characters) in China was deciphered byNISHIDA Tatsuo (1928-2012) who wrote the analysis and grammar of Xixia characters through the paper Seikamoji no bunseki narabini Seikago bunpou no kenkyuu in 1962.In almost the same time, Inca characters were studying to decipher. I frequently heard that Russian team developed largely. In early 1970s I frequently went to Kanda, Tokyo where old bookshops were selling vast Oriental books at the Hakusan street and Yasukuni Street. I bought Chinese classics, especially linguistic classics written in the Qing dynasty and I read them almost every day containing the comparison with the western linguistic results. The Qing dynasty's heritage were DUAN Yucai, WANG Niansun, WANG Yingzhi and WANG Guowei and so forth. DUAN Yucai's Showenjezi zhu and WANG Guowei's Guantang jilin were the most important for me. In France, 1960s was the days of Bourbaki that was one of the decipher of geometry by algebra, at least I thought so at that time. I sought and bought several Bourbaki's books at the old bookshops in Kanda, Tokyo,which is the largest old bookshop streets in Japan. But from my ability to mathematics Bourbaki was too much difficult to read on. From the days the long and winding road began to mathematics and its applicable study for language universals. At the exhibition of ancient Greece I confirmed in particular that the stability of language was kept by letters and characters from the Linear A and Linear B. Exhibition Catalogue numbers are the next.
The numbers 39 and 40 are Linear A. 41 and 77 are Linear B.
39. Clay juglet c. 1800 B.C. ~ c. 1700 B.C.
40. Clay bar c. 1700 B.C. ~ c. 1650 B.C.
41. Clay tablet c. 1375 B.C. ~ c. 1350 B.C.
77. Linear B bar and tablet c. the 13th century B.C. For my part the stability has been one of the biggest themes on language phenomena since I was taught from CHINO Eiichi through the results of the Linguistic Circle of Prague, especially of Sergej Karcevskij. The exhibition catalogue and Chadwick's book Japanese translated edition. Reference
References 2
References 3
References 4
References 5
Tokyo30 July 2016Sekinan Library
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01/05/2016 18:46Basis 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 fundamentalfactors on language.In 2003 I wrote Quantum Theory for Language , before which I wrote the manuscript focusing the concept of quantum abstracted from the ideogram of classical Chinese written language. The last target of manuscript was energy and meaning of quantum that was the ultimate unit of language. Refer to the next.Manuscript of Quantum Theory for Language. Hakuba, Nagano. March 2003 ------------------------------------------------------------------------------------------------------------------------------- What is signal? The existence that generates language Preparation 2 1-8is over 15 January 2019 -------------------------------------------------------------------------------------------------------------------------------
ReferencesReference is cited from the papers written at SekinanLibrary and SRFL
by TANAKA Akio
at Tokyo from 2003................................................................................................................
Contents 0Manuscript of Quantum Theory for Language with Preface, Note and Note 2 2003-2018 1Under the Dim LightLanguage, amalgamation of mathematics and physics
2Language and I
Language and PhilosophyHow is the time alive in Language? 3Egyptian Hieroglyph ExhibitionEssence of LanguageArs longa 4The 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
5IdeogramLetterThe Days and The TimePraguePioneerLinear B
6Genealogical Tree of Sekinan's Paper 7th Edition 7
What is letter?
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Selected Texts 0
Manuscript of Quantum Theory for Language TANAKA AkioPreface
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 2015Sekinan Library-----------------------------------------------------------------------------------------------
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。
---------------------------------------------------------------------------------------------------
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 229 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 paperInherent energy in language has been become a little updated after writing in 2003.
Now arranged at the next.
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Tokyo
20 June 2018
Read more: https://srfl-lab.webnode.com/news/manuscript-of-quantum-theory-for-language-with-preface-note-and-note-2-2003-2018 ........................................................................................................................... 1-1Under the Dim Light
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 LanguageAbout
Table
Read more: https://srfl-essay.webnode.com/news/under-the-dim-light1/ ....................................................................................................................................... 1-2
Language, amalgamation of mathematics and physicsTANAKA Akio
2 April 2013Language 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]
Tsugaike Highlands, Nagano. 30 August 2011
Read more: https://srfl-paper.webnode.com/news/language-amalgamation-of-mathematics-and-physics/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=https%3A%2F%2Fsrfl-paper.webnode.com%2Fnews%2Flanguage-amalgamation-of-mathematics-and-physics%2F ..................................................................................................................................................2-1Language and I
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
........................................................................................................................................
3-1Egyptian Hieroglyph ExhibitionJourney 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
...................................................................................................................................3-2Essence of Language
Seeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum
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
Read more: https://srfl-paper.webnode.com/news/the-essence-of-language/...........................................................................................................................................3-3Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow
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 exhibitionFrench Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow [Note]6 June 2018Time and EternityTANAKA AkioWhen 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
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.Geometrization LanguageSRFL LabThe two sites are connected through ideogram.Ideogram Paper. Sekinan ZohoIdeogram.SekinanzohoSekinan Zoho has the invitation to it.SRFL collection has general relevant information for the present research.Sekinan ZohoSRFL Collection
............................................................................................................................................ 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
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.
...................................................................................................................
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.....................................................................................................................
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.
......................................................................................................................
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........................................................................................................................
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
Read more: https://srfl-theory.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory1/
Read more: https://srfl-collection.webnode.com/news/the-days-when-i-was-thinking-on-energy-distance-theory1/ ................................................................................................................................. 4-2Thanks to physics through which I ever dreamt in my future
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:
Tokyo
24 April 2016
11 December 2017 Text partially revised
Read more: https://srflnote.webnode.com/news/thanks-to-physics-through-which-i-ever-dreamt-in-my-future/
Read more: https://geometrization-language.webnode.com/products/thanks-to-physics-through-which-i-ever-dreamt-in-my-future/.......................................................................................................................4-3Glitter of youth through philosophy and mathematics in 1970sTANAKA AkioIn 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, CHINOEiichi Russian language, the Linguistic Circle of Prague. At last dear friend of high school days KANEKO Yutaka mathematics and our youth.Tokyo6 March 201524 March 2018 Text revised and link addedSekinan LibraryRead more: https://srfl-collection.webnode.com/products/glitter-of-youth-through-philosophy-and-mathematics-in-1970s/?utm_source=copy&utm_medium=paste&utm_campaign=copypaste&utm_content=http%3A%2F%2Fsrfl-collection.webnode.com%2Fproducts%2Fglitter-of-youth-through-philosophy-and-mathematics-in-1970s%2F........................................................................................................................5-1Ideogram Paper Enlarged Edition1. On Time Property Inherent in Characters 20032. Ideogram 20053. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 20124. ONO Shinobu and Bernhard Karlgren 20155. Essence of Language 20166. The Days of Decipherment 20167. The Days of Ideogram 20178. The Days of Ideogram Note added Edition 20179. 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 201711. Connection between early paper's quantum and recent paper's geometry 7th edition 201712. Letter to Y. Of the century of language 201813. Letter to Y. Of Broad Language 4th edition 201814. Determination of the concept, Broad Language 201815. Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018
.............................................................................................................
5-2Letter
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.............................................................................................................
5-3The Days and The Time
Tokyo13 August 2018 Arranged
Read more: https://srfl-lab.webnode.com/news/the-days-and-the-time/........................................................................................................... 5-4Prague
Tokyo
2 August 2016
30 May 2018 Revised
Sekinan ZohoRead more: https://srfl-collection.webnode.com/news/prague/ ............................................................................................ 5-5Pioneer
The Time of Language, Ode to The Early Bourbaki To Grothendieck
Bourbaki' ELEMENTS DE MATHEMATIUE Troisieme edition, 1964
ONO Shinobu and Bernhard Karlgren
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
Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi
Uniformity For SAUSSURE Ferdinand
40 years passed from I read WANG Guowei
The days of von Neumann Algebra
The days between von Neumann Algebra and Complex Manifold Deformation Theory
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/ ................................................................................................... 5-6Linear BFrom seeing the exhibition TREASURES OF ANCIENT GREECE, Tokyo National Museum, Ueno, Tokyo. 2017
Reference
Derived Category Language Read more: https://srfl-collection.webnode.com/news/linear-b/ ..................................................................................................... 7What is letter?
TANAKA Akio
23 February 2019
1
Provisional definition of Letter, word and sentence.
2Letter is assumed to be generated from signal.Provisional definition of signal.
References
1
What is signal?Preface, Preparation and Preparation 2 Completed21 November 2018 - 15 January 2019Zoho Edition
2
How the language has been sought for ? 1-8
Read more: https://srfl-paper.webnode.com/news/what-is-letter-23-february-2019/ ...................................................................................................... SRFL PaperTokyo27 February 2019
Read more: https://srfl-paper.webnode.com/news/what-is-signal-the-existence-that-generates-language-preface-references-28-february-2019/ ............................................................................................................. Main Issue
1
Quantum Group Language Main Issue is written titled as Quantum group language abbreviated to QGL.
1 March 2019 ---------------------------------------------------------------------- 1QGL Preparation Paper
....................................................................................................
2General Preparation Paper Preparatory paper
3. Floer Homology Language Note 7 Quantization of Language 20094. Floer Homology Language Note 8 Discreteness of Language 20095. Simplicial Space Language Composition of Word 2013Preparatory Paper 2
3. Proto Arithmetic Geometry Language
4.Language, Word, Distance, Meaning and Meaning Minimum ................................................................................................................ Basic paper
3. Quantum Theory for Language Theoretical Summarization and Problem in Future 20044. Noncommutative Distance Theory Note 2 C*-Algebra2007 5. Kac-Moody Lie Algebra 2008 ................................................................................................................ Ideogram Paper1. On Time Property Inherent in Characters 20032. Ideogram 20053. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 20124. ONO Shinobu and Bernhard Karlgren 20155. Essence of Language 20166. The Days of Decipherment 20167. The Days of Ideogram 20178. The Days of Ideogram Note added Edition 20179. 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 201711. Connection between early paper's quantum and recent paper's geometry 7th edition 201712. Letter to Y. Of the century of language 201813. Letter to Y. Of Broad Language 4th edition 201814. Determination of the concept, Broad Language 201815. Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018
................................................................................................................ Overview Paper
5. The comparison between 2003 and 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 20176. Mathematical description for three elements of language universals 2017 ................................................................................................................ Concept Paper1. Letter to Y. Of the century of language 20182. Letter to Y. Of Broad Language 4th Edition 20183. Determination of the concept, Broad Language 2018 ................................................................................................................ Archive of Paper1. Genealogical Tree of Sekinan's Paper 7th Edition 2018
2. Zoho paper by year 2016 ----------------------------------------------------------------------------------------------
Read more: https://srfl-lab.webnode.com/ ................................................................................................................ 3Selected Paper (1)Kac-Moody Lie AlgebraNote 2Quantum GroupTANAKA Akio 1Base field KFinite index set ISquare matrix that has elements by integer A = ( aij )i, j∈ IMatrix that satisfies the next is called Cartan matrix.i, j ∈ I(1) aii = 2(2) aij ≤ 0 ( i ≠j )(3) aij = 0 ⇔ aji = 02Cartan matrix A = (aij)i, j ∈IFamily of positive rational number {di}i∈IArbitrary i, j∈I diaij = djajiA is called symmetrizable.3Finite dimension vector space hLinearly independent subset of h {hi}i∈IDual space of h h*= HomK (h, K )Linearly independent subset of h* {αi} i∈IΦ = {h, {hi}i∈I, {αi} i∈I }Cartan matrix A = {αi(hi)} I, j∈IΦis called fundamental root data of A that is Cartan matrix.4Symmetrizable Cartan matrix A = (aij)i, j ∈IFundamental root data {h, {hi}i∈I, {αi} i∈I }E = αi ⊂h*Family of positive rational number {di}i∈Idiaij = djajiSymmetry bilinear form over E ( , ) : E×E → K ( (αi ,αj ) = diaij )The form is called standard form.5n-dimensional Euclid space RnLinear independent vector v1, …, vnLattice of Rn m1v1+ … +mnvn ( m1, …, mn ∈ Z )Lattice of h hZ6From 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 ∈ hz7Vector space over K ABilinear product over K A×A → AWhen A is ring, it is called associative algebra.8Integer mt similarity of m [m]t[m]t = tm-t-m / t- t-1Integer m, n m≧n≧0Binomial coefficient (mn)t similarity of m! [m]t! = [m]t! [m-1]t!...[1]tt similarity of (mn) [mn]t = [m]t! / [n]t! [m-n]t![m0] = [mm]t = 18Integer 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∈IAssociative algebra U over K (q), that is defined the next relations, is called quantum group associated with Ψ.(1) khkh’ = kh+h’ ( h, h’∈hZ )(2) k0 = 1(3) KhEiK-h = qαi(h)Ei ( h∈hZ , i∈I )(4) KhFiK-h = qαi(h)Fi ( h∈hZ , i∈I )(5) Ei Fj – FjEi = ij Ki - Ki-1 / qi – qi-1 ( i , j∈I )(6) p [1-aijp]qiEi1-aij-pEjEip = 0 ( i , j∈I , i ≠j )(7) p [1-aijp]qiFi1-aij-pFjFip = 0 ( i , j∈I , i ≠j ) [Note]Parameter q in K is thinkable in connection with the concept of at the paper Place where Quantum of Language exists / 27 /.Refer to the next.Place where Quantum of Language exists / Tokyo July 18, 2004Tokyo February 9, 2008Sekinan Research Field of Languagewww.sekinan.org (2)Symplectic Language Theory TANAKA Akio Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH1R Commutative ring over CC R module that has degree(ΠC)k = Ck+1BC Free coassociative coalgebraEC Free coassociative cocommutative coalgebraBkΠC BΠC that has k number tensor productEkΠC EΠC that has k number tensor productmk : BkΠC → ΠClk : EkΠC → ΠC2 CoderivativeA∞-algebra = 0 at (BΠC, mk) (k>0)Weak A∞-algebra = 0 at (BΠC, mk) (k≥0)L∞-algebra = 0 at (EΠC, mk) (k>0) Weak L∞-algebra = 0 at (EΠC, mk) (k≥0) 3 M(C) Complex structure's moduli space over compact manifold c Unobstructed Weak A∞-algebra that satisfies M(C) 4 M Symplectic manifoldM† Complex manifold that is mirror of ML Lagrangian submanifold of M that Weak A∞-algebra is unobstructed FL Object of M† 's analitic coherent sheaf's category(Conjecture)For L there exists FL. FL's infinite small transformation's moduli space is coefficient to M(L). 5[b] Element of M(L)[b] defines A∞-algebra.[b] defines chain complex's boundary map m1bCohomologyy of m1 b is called Floer cohomology.Floer cohomology is expressed by HF((L, b), (L, b)) 6 (Impression)Word is seemed as L.For L there exist language FL and M(L).Mirror theory on language is supposed by the existence of FL and M(L).Mirror Theory papers in early stage of Sekinan Linguistic FieldTo be continued Tokyo April 26, 2009 Sekinan Research Field of language
Read more: https://srfl-lab.webnode.com/products/symplectic-language-theory-note-6-homological-mirror-symmetry-conjecture-by-kontsevich/ (3)Home Site: ifbetrueAutor: TANAKA AkioTheme: Language UniversalsMethod: Homotopy TheoryTitle: Homotopy LanguagePaper 1: Simplicial Space Language----------------------------------------- Simplicial Space LanguageComposition of WordTANAKA Akio20 January 2013ifbetrue 1. is topological space. is simplicial space. is represented by geometric realization of as the next.2. 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.3.Interpretation.Word is given by geometric realization of simplicial space .Meaning unit in word is given by free Abel group .(Paper end) Read more: https://srfl-lab.webnode.com/products/simplicial-space-language/mutative-distance-theory-note-2-c-algebra/ (4)
TANAKA Akio
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:
Reference:
Reference 2:
References 3:
References 4:
Reference 5:
[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
..................................................................................................................................... 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.
..................................................................................................................................Notes for KARCEVSKIJ SergejTANAKA Akio
The papers on this site have been published by Sekinan Research Field of Language ..................................................................................................................................... Entering in this year 2016, I read TODA Yukinobu's book, Several Problems on Derived Category of Coherent sheaf, Tokyo, 2016. The book shows me the update overview on derived category of coherent sheaf. The essence of my notable points are noted at the following. ................................................................................................................................... Kontsevich's conjecture
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 2009Homological Mirror Symmetry Conjecture by KONTSEVICH
/ Symplectic Language Theory / 26 April 2009Quantization of Language / Floer Homology Language / 24 June 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 2Kawamata Conjecture Conjecture is birational map between smooth objective algebraic manifolds.And.At This condition,there exists next fully faithful embedding.. [Reference]
[References 2]
[Reference 3]
Tokyo19 May 2016SRFL Theory ................................................................................................................................... Kawamata conjecture will hint me the new meaning's entrance in the old meaning at a word. Notes for KARCEVSKIJ Sergej that I ever wrote will be newly revised through TODA's fine work over viewing the recent 20 year development on derived category that began by Grothendieck. For TODA's book, refer to the next my short essay. ....................................................................................................................................
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016 TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on. [References]Distance Theory Algebraically Supplemented
[References 2]Isomorphism of map Sequence / Symplectic Language Theory Tokyo
19 May 2016
SRFL Theory ................................................................................................................................. This paper is unfinished. Tokyo20 May 2016SRFL Theory Read more: https://srfl-theory.webnode.com/news/karcevskij-conjecture-1928-and-kawamata-conjecture-2002/
(5)
TANAKA Akio The main reasons are the following.
1.Language is the most convenient tool for human being.2.Language has the vast variations in natural language and technical language. 3.Natural language has speech language, written language and their recorded language, for example books, records, CD and so on.4.Technical language has many computer languages and their related devices.5.At natural language, there exists many meanings not to confirm clear definitions, for example finite,infinite, discrete, continuity, universal and super. 6.Technical language has naturally defines the meanings by its discrete arithmetical basic using of discreteness.7.Mathematics is probably belonged to natural language, that uses speech and written language by usual conversations and papers or books. 8.But mathematics can clearly define the meaning through a few axioms and derived theorems. for example boundary, continuity, distance, finite, infinite and space.9.Mathematics has many strong tools for description, for example mapping, projection and identification.10.Mathematics has solid structure through long historical verifications from ancient Greece. References
Boundary:
Why is boundary necessary in language?
Description
THE ROAD TO REALITY A Complete Guide to the Laws of the Universe
Dimension
Distance
Geometry
Arithmetic Geometry LanguageLanguagePresupposition on Natural Language
Meaning
Space
Structure
True and False
The True-false problem of the Crete
Tokyo8 February 2016Geometrization Language
.............................................................................................................. Main Paper1Over TANAKA Akio SRFL PaperTokyo
2 March 2019
Read more: https://srfl-paper.webnode.com/news/what-is-signal-the-existence-that-generates-language-preface-quantum-group-language-2-march-2019-revised/ ...................................................................................................................... Main Issue 2
The Premise for Quantum Group Language
Contents
Derived Category Language, 23 July 2016 Edition 1. Bridge between mathematics and physics / revised2. Kontsevich's conjecture Category theoretic mirror symmetry conjecture3. Derived Category Language 14. Karcevskij conjecture 1928 and Kawamata conjecture 20025. Additional meaning and embedding6. Derived Category Language 27. Language stability and triangulated category8. Derived Category Language 39. Stability of Language10. Duality of Language
Read more: https://srfl-theory.webnode.com/news/derived-category-language-23-july-2016-edition/ Text 1
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016 TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.
I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on. [References]Distance Theory Algebraically Supplemented
[References 2]Isomorphism of map Sequence / Symplectic Language Theory
2Kontsevich's conjecture
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 2009Homological Mirror Symmetry Conjecture by KONTSEVICH
/ Symplectic Language Theory / 26 April 2009Quantization of Language / Floer Homology Language / 24 June 2009
Tokyo
10 May 2016
Read more: https://srfl-theory.webnode.com/news/kontsevichs-conjecture-category-theoretic-mirror-symmetry-conjecture/Tokyo
19 May 2016
Read more: https://srfl-theory.webnode.com/news/bridge-across-mathematics-and-physics-revised/ 3
Derived Category Language 1 |
Category theoretic mirror symmetry conjecture 1.
Fukaya category is
Fuk(X, ω).2.
General symplectic manifold is .
3.Derived category of A∞ is .4.
ConjectureWhen and have physical mirror relation, there exists the next triangle category's equivalence [Reference 1]
[References 2]
Tokyo18 May 2016SRFL Theory
Read more: https://srfl-theory.webnode.com/news/derived-category-language-1/ 4Karcevskij conjecture 1928 and Kawamata conjecture 2002 TANAKA Akio
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:
Reference:
Reference 2:
References 3:
References 4:
Reference 5:
[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
....................................................................................................................................
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.
......................................................................................................................................Notes for KARCEVSKIJ SergejTANAKA Akio
The papers on this site have been published by
Sekinan Research Field of Language
.................................................................................................................................... Entering in this year 2016, I read TODA Yukinobu's book, Several Problems on Derived Category of Coherent sheaf, Tokyo, 2016. The book shows me the update overview on derived category of coherent sheaf. The essence of my notable points are noted at the following. ....................................................................................................................................
Kontsevich's conjecture
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 2009Homological Mirror Symmetry Conjecture by KONTSEVICH
/ Symplectic Language Theory / 26 April 2009Quantization of Language / Floer Homology Language / 24 June 2009
Tokyo
10 May 2016
............................................................................................................................................
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
Kawamata Conjecture Conjecture is birational map between smooth objective algebraic manifolds.And.At This condition,there exists next fully faithful embedding..
[Reference]
[References 2]
[Reference 3]
Tokyo19 May 2016SRFL Theory ............................................................................................................................ Kawamata conjecture will hint me the new meaning's entrance in the old meaning at a word. Notes for KARCEVSKIJ Sergej that I ever wrote will be newly revised through TODA's fine work over viewing the recent 20 year development on derived category that began by Grothendieck.
For TODA's book, refer to the next my short essay.
...........................................................................................................................................
TODA Yukinobu. Several problems on derived category of coherent sheaf. Tokyo, 2016 TODA Yukinobu's Several problems on derived category of coherent sheaf has built across mathematics and physics. For my part, further more, physics and language seem to be expected to build over from the book.Chapter 5. Page 116. Conjecture 5.16 shows us the connection between symplectic geometry and algebraic geometry.
I ever wrote several notes on language related with string theory. Now TODA's book newly lights up the relation between physics and language. This relation is really fantastic for me from now on. [References]Distance Theory Algebraically Supplemented
[References 2]Isomorphism of map Sequence / Symplectic Language Theory Tokyo
19 May 2016
SRFL Theory ............................................................................................................................................... This paper is unfinished. Tokyo20 May 2016SRFL Theory
Read more: https://srfl-theory.webnode.com/news/karcevskij-conjecture-1928-and-kawamata-conjecture-2002/ 5
Category theoretic mirror symmetry conjecture 1.Fukaya category is
Fuk(X, ω).2.
General symplectic manifold is .
3.Derived category of A∞ is .4.
ConjectureWhen and have physical mirror relation, there exists the next triangle category's equivalence
Derived Category Language 2
Kawamata ConjectureConjecture is birational map between smooth objective algebraic manifolds.And.At This condition,there exists next fully faithful embedding.
Notes for KARCEVSKIJ SergejCondition of Meaning
TANAKA Akio
September 11, 2011[Preparation]Graded differential algebra Minimal model of graded differential algebra Degree of homogenious element x of graded differential algabra |x|Basis of linear space is given by homogenious and elements x1, ....., xnΛ (V) = Λ(V)k =Λ (x1, ....., xn )Operation of minimal model Spherical surface Sn, n≥2de Rham complex *(Sn)When n is even number,Volume element of Sn Mn = Λ (x), |x| = n, dx = 0,, M2n-1 gives minimal model Sn to de Rham complex .When n is odd number,Mn gives minimal model Sn to de Rham complex .[Interpretation]Word is given by spherical surface.Meaning of word is given by elements x1, ....., xn.Word has minimal model.Word becomes formal.Fundamental group of word contains free group of rank b1(M).Here KARCEVSKIJ's "stable part" is identified to fundamental group and " mobile part" is identified to free group.Refer to the paper Notes for KARCEVSKIJ Sergej, "Du dualisme asymétrique du signe linguistique" .
This paper has been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Stable and Unstable of LanguageFor the Supposition of KARCEVSKIJ SergejCompletion of LanguageTANAKA AkioSeptember 23, 2011[Preparation]1.n dimensional complex space CnOpen set Whole holomorphic function over U Ring sheaf for U →Oan(U)Complex analytic manifold CannAlgebraic manifold An multinomial of CannIdeal of multinomial ring a [x1, x2, ..., xn]V(a) = {(a1, a2, ..., an) Cnf (a1, a2, ..., an) = 0, a }Whole closed set of V(a) Fundamental open set D(f) = {(a1, a2, ..., an) Cn | f (a1, a2, ..., an) ≠ 0}Arbitrary family of open set {Ui} Easy sheaf F Zariski topological space Ring sheaf OAffine space An = ( , O)Ring RSet of whole maximum ideal Spm R1Spm R Spectrum of RSpm R is Noether- like.◊R is integral domain.Whole of open sets without null set UxQuotient field KMapping from Ux to whole partial set of K OO(V(a)c) = Rfc expresses complementary set.O is easy sheaf of ring over Spm R that is whole set K.◊R is finite generative integral domain over k.Triple (i) (ii) (iii) is called affine algebraic variety.(i) Set Spm R(ii) Zariski topology(iii) Ring's sheaf OO is called structure sheaf of affine algebraic variety.◊Ring homomorphism between definite generative integral domains Upper is expressed by .Ring holomorphism OX(U) → OY((t )-1U)Morphism from affine algebraic variety Y to X ( OX(U) → OY((t )-1U), X→Y )When is surjection, t is isomorphism overclosed partial set defined by p= Ker .Upper is called to closed immersion.2.Ring holomorphism Morphism between affine algebraic varieties Kernel of pImage of It is called that when is injection is dominant.◊R is medium ring between S and its quotient field K.When that is given by natural injection is isomorphism over open set, is called open immersion.◊When X is algebraic variety, longitude of maximum chain is equal to transcendental dimension of function field k(X).It is called dimension of algebraic variety X, expressed by dim X.◊Defined generative field over k KSpace ( X, Ox )added ring that is whole sets of K that has open covers {Ui} satisfies next conditions is called algebraic variety.(i) Each Ui is affine algebraic variety that has quotient K .(ii) For each i, j I, intersection is open partial set of .◊3.Tensor product between ring and itself becomes ring by each elements products.Elements that defines surjective homomorphism is expressed by .Image of closed embedding defined by is called diagonal.◊Field KRinged space that have common whole set K (A, OA) (B, OB)Topological space COpen embedding A and B have common partial set C.Topological space glued A and B by C Easy sheaf over W OWahere, arbitrary open set Ø ≠ Ringed space is called glue of A and B by C.◊Intedgral domains that have common quotient field K R, SElement Ram ≠ 0Element S bn ≠ 0Spm T Spm R, Spm T Spm SGlue defined by the upper is called simple.◊Affine algebraic varieties U1, U2Common open set of U1, U2 UCDiagonal embedding When the upper is closed set, glue is called separated.◊For simple glue , next is equivalent.(*) It is separated.(**) Ring is generated by R and S.◊R and S are integral domains that have common quotient field K.For partial ring T=RS generated by R and S, when simple is satisfied, it is called "Spm R ad Spm S are simple glue."◊Projective space Pn is simple glue.◊Algebraic Variety's morphism is glue of affine algebraic variety's ring homomorphism image.Algebraic direct product is direct product of affine algebraic variety.◊4.Affine algebraic variety XRing over k R is called R value point of X.Whole is called set of R value point of X, expressed by X(R).Ring homomorphism over k X(f) := X(R)X(S)Ring homomorphism , is function from ring category over k to category of set.◊Functors from ring category to set category F, GRing RFamily of over ring R {}{} has functional morphism.Functors F,G have isomorphism ( or natural transformation).Functor from ring's category to set's category that is isomorphic to algebraic variety, is called representable or represent by X, or fine moduli.◊Functor from ring's category to set's category FWhen satisfies the next conditions, X is called coarse moduli.(i) There is natural transformation : .(ii) Natural transformation ,Morphism that satisfies is existent uniquely.(iii) For algebraic close field k' k, (k') is always bijection.◊Algebraic variety G that is functor to group's category is called algebraic group.◊Finite generative ring over k AWhen G = Spm A satisfies 3 conditions on the next triad is called affine algebraic group.TriadConditions(i) are commutative for .(ii)There is identity map for A.(iii) There is coincident with for A.◊5.Projective space over C Pn(2n+1) dimensional spherical surface {}Pn has continuous surjection from .Pn is compact.Map is called closed map when is closed set image becomes closed set.◊Algebraic variety X is called complete when projection is closed map for arbitrary manifold Y.◊Morphism from complete algebraic manifold X to separated algebraic manifold Y, is closed map.◊Projective space Pn is complete.◊Algebraic manifold that has closed embedding at Pn is complete.This algebraic manifold is called projective algebraic manifold.[Interpretation]Here language is expressed by Pn.Word is expressed by projective algebraic manifold.Meaning of word is expressed by closed embedding. Thispaper has been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language
Provisional philosophic conjecture on additional meaning is the following.
[References]
Extract of Zoho papers at Sekinan Library.
More details refer to Sekinan Zoho.
Stable and Unstable of Language
Floer Homology Language Tokyo23 May 2016SRFL Theory Read more: https://srfl-theory.webnode.com/news/additional-meaning-and-embedding/ 6 Derived Category Language 2Kawamata Conjecture Conjecture is birational map between smooth objective algebraic manifolds.And.At This condition,there exists next fully faithful embedding.. [Reference]
[References 2]
[Reference 3]
Tokyo19 May 2016SRFL Theory
Read more: https://srfl-theory.webnode.com/news/derived-category-language-2-kawamata-conjecture/
7
T. Bridgeland defined stability conditions on triangulated categories in 2007.
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/ 8
[Epitome]T. Bridgeland defined stability conditions on triangulated categories in 2007.
Language's stability presented by Sergej Karcevskij in 1928.
Bridgeland's stability seems to hint for Karcevskij's stability. Stability conditions on triangulated categories Data ( Z, A ) satisfies the next condition. is bounded kernel of t-structure. gives stability condition on A .------------------------------------------------------------------------------------------------------
2.
[Paper on Karcevskij conjecture by TANAKA Akio 2011] Notes for KARCEVSKIJ SergejCondition of Meaning
TANAKA Akio
September 11, 2011[Preparation]Graded differential algebra Minimal model of graded differential algebra Degree of homogenious element x of graded differential algabra |x|Basis of linear space is given by homogenious and elements x1, ....., xnN (V) = L (V) k = N ( x 1 , ....., x n )Operation of minimal model Spherical surface Sn, n≥2de Rham complex *(Sn)When n iseaven number,Volume element of Sn Mn = Λ (x), |x| = n, dx = 0,, M2n-1 gives minimal model Sn to de Rham complex .When n is odd number,Mn gives minimal model Sn to de Rham complex .[Interpretation]Word is given by spherical surface.Meaning of word is given by elements x1, ....., xn.Word has minimal model.Word becomes formal.Fundamental group of word contains free group of rank b1(M).Here KARCEVSKIJ's "stable part" is identified to fundamental group and " mobile part" is identified to free group.Refer to the paper Notes for KARVESKIJ Sergej "asymmetric Dusualisme the linguistic sign" . -------------------------------------------------------------------------------------------- 3.
[Paper on description of language by TANAKA Akio 2011] Notes for KARCEVSKIJ SergejDescription of Language
TANAKA Akio
September 9, 2011Manifold MCup product map of M Dual map of Free Lie algebra that generates £ ( ) is identified as the partial space of £( ) that quadrastic Lie bracket of generates.Ideal of £( ) that Im η generates a Holonomy Lie algebra of M Completion of holonomy Lie algebra If M has quadrastic homology connection, Malcev completion becomes isomorphic with holonoly Lie algebra completion .Primary minimum model M(1)of differential manifold M is isomorphic with Malcev completion of of M's fundamental group.For the description of a language model there is a need primary minimum model M(1) of differential manifold M. This paper has been published by Sekinan Research Field of Language.
All rights reserved.
© 2011 by The Sekinan Research Field of Language ----------------------------------------------------------------------------------------------------------- 4.[Note]If word satisfies Bridgeland 2002's Data{Z, A] , word has a stability in language.For the problem of additional meaning refer to Karcevskij conjecture 1928 and Kawamata conjecture 2002. ----------------------------------------------------------------------------------------------------- #This paper is unfinished Tokyo
25 May 2016
Read more: https://srfl-theory.webnode.com/news/derived-category-language-3/
9
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
Read more: https://srfl-paper.webnode.com/news/perspective-for-derived-category-language-stability-of-language/
10Duality of Language TANAKA Akio1. Model
Calabi-Yau 3-folds.
2. Theorem
R. Pandharipande and R.P. Thomas.
Pandharipande-Thomas Theorem (1998).
K. Behrend.
Behrent contructable function (2009).
Y. Toda.
Generating functions of stable pair invariants via wall-crossing in derived categories in algebraic geometry. (2008)
Curve-counting theories via stable objects (2010).
T. Bridgeland.
Hall algebras and curve-counting invariants (2011).
D. Joyce and Y.Song.
A theory of generalized Donaldson-Thomas invariants. (2012)
3. Definition
Generalized DT invariants. ( Joyce and Song. 2012)
4. Isomorphism
Isomorphism is induced in the defined moduli spaces.
5. Duality and mirror
If language is identified as Calabi-Yau 3 folds, language inevitably induce dual or mirror element.
Reference
Rensetsuso no Doraiken ni kakawaru shomondai. TODA Yukinobu. 2016. Sugaku shobo. Tokyo.
Reference 2
Derived Category Language, 25 May 2016 Edition.
Reference 3.
Actual Language and Imaginary Language. To LÉVI-STRAUSS Claude.
Reference 4.
Symplectic Language Theory Note 3 Mirror Symmetry Conjecture on Rational Curve.
Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH.
Reference 5.
Main papers of Sekinan Library.
Paper ends.
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This paper is unfinished.
Tokyo
22 July 2016
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Issue Paper 2
Over
Read more: https://srfl-paper.webnode.com/news/what-is-signal-the-existence-that-generates-language-till-main-issue-2-over-edition/ ............................................................................... Main Issue 4
Space and Boundary
Contents
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Text 1
q.v. Boundary of Words / 12 February 2009
TANAKA Akio ................................................................................................................................ 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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Substantiality Dedicated to SAPIR Edward TANAKA Akio 1 Substance of language is completion which possesses the distance from the real world.2 The distance is sustained by the fixation for which meaning and time are abstracted.3 If language has not distance, language appears and disappears following the real world proceeding.4 Language is substantially unchangeable. Changeability occurs on surrounding.5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.6 Substantiality is a frame of language.7 Substantiality is free from the real world.8 Substantiality is powered by outer energy.9 Powered substantiality moves complied with possessed command, namely meaning and time.10 Powered moving substantiality of language is called .11 The idea of quantum is partially realized by in the supermarket or bookstore.12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening. Tokyo February 27, 2005For the Memory of Tanashi Station Front Street February 26, 2005Sekinan Research Field of Language ................................................................................................................... 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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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 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
.................................................................................................................................. 4-1Boundary is related with dimension through Poincaré Theorem. Details are next.
.................................................................................................................................. Dual Language Duality of Language TANAKA Akio 1. Theorem
(Poincaré duality)
For oriented compact n-dimension topological manifold M ,
biliear form
is exact,
and become dual space each other.
♦ 2. Interpretation
Word := M Boundary of language := p Dual language := and Language := 3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language. 4. References
Distance Theory
Mirror Theory
Guarantee of LanguageTokyo
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
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.
----------------------------------------------------------------------------------------------------------- Tokyo
21 December 2014
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Text 2
q.v. Zoho Paper. SIL Topological Group Language Theory TANAKA Akio Preliminary Note 3 Boundary of Words [Theorem] 1 Distance space ( X , d) Gromov product ( y | z ) x 2 Hyperbolic space X point sequence { x i X } Set of all the { x i X } S ∞ ( X ) Point sequence of X { y i } When { y i } is lim i →∞ ( x i | y i ) = 0, { y i } is in S ∞ ( X ). [Explanation] 1 Hyperbolicity for general distance space is defined by Gromov product. Details are below. 2 Distance space is defied by the next. Distance space that has basic point x 0 ( X, d ) Arbitrary 3 points of X x, y, z When ( X, d ) satisfies the next, it is called δ -hyperbolic. ( x | y ) x 0 min{( x | z)x 0 , ( y | z ) x 0 }- δ When distance space ( X, d ) is δ -hyperbolic for arbitrary base point, X is called δ -hyperbolic. Here for a certain , δ -hyperbolic space is abbreviatedly called hyperbolic. 3 The next condition is equivalent with what ( X, d ) is δ -hyperbolic. d ( x, y ) + d ( z, w ) max{ d ( x, z ) + d ( y, w ), d ( x, w ) + d ( y, z ) } +2 δ 4 Distance space X Arc of X α : [0, λ ] → X Arbitrary s, t [0, λ ] d ( α ( s ), α (t)) = | s-t | Arc α is called geodesic segment. Geodesic segment from x to y that is x,y X is expressed by . When arbitrary 2 points of distance space ( X , d) are combinable by geodesic segment, X is called geodesic space. xyz = is called geodesic triangle. [Impression] 1 Word is identified with point sequence { x i X }. Language is identified with S ∞ ( X ). New generated word is identified Point sequence of X , { y i } that has condition lim i →∞ ( x i | y i ) . The new generated word is also in language, that is to say, S ∞ ( X ). 2 From the condition lim i →∞ ( x i | y i ), spherical surface is considered as boundary at infinity by the comparison with Poincaré model. 3 Spherical surface is considered as the unit of language. Language's distance and warp is also considered under hyperbolic space. References are below. [References] #1 Quantum Theorey for Language #2 Distance Theory #3 Warp Theory The upper papers and the related papers with the themes are seen at Sekinan Linguistuic Field . To be continued Tokyo February 12, 2009 Sekinan Research Field of Language
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Text 3
Frame-Sentence LanguageBoundaryTANAKA Akio 1 Language consists of frame and sentence.2 Frame consists of words.3 Sentence consists of quanta.4 Frame is duplicable.5 Sentence is not duplicable.6 Word has no energy.7 Quantum has energy.8 Quantum’s energy comes from outside.9 Outside energy is brought by human being or electric power.10 Words are separated each other.11 Quanta are connected each other.12 Quanta’s connection is brought by reversion to boundary.13 Boundary is shown by sentence’s end that is marked by period(.).14 Word and frame has not boundary.15 Boundary is expressed by unit element in mathematics.16 Two quanta are connected by associative law in mathematics.17 Words /flowers/ and /blossom/ are connected and become sentence [flowers blossom].18 In sentence [flowers blossom], two quanta [flowers] and [blossom] are connected by associative law.19 In sentence, associative law works as addition.20 Sentence has not vacant space. 21 Notation of vacancy in sentence substantially shows additional mark(+).22 In sentence [flowers], sentence starts by [flowers] and sentence ends by [flowers]. 23 One quantum sentence, likely [flowers], has energy 1.24 Two quanta sentence has energy 2 .25 Energy goes to sentence’s end in accordance with the system of reversion that is essence of language. Tokyo November 30, 2005Sekinan Research Field of Languagewww.sekinan.org
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Text 4-1
Language and Spacetime Language
Definition for the Child who Lost the World TANAKA Akio0 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.Tokyo March 3, 2007
Tokyo November 3, 2008 AddedPostscript
[Referential note / November 29, 2007]
For Authentication of Solidity
[Definition added / November 3, 2008]
Definition 10, the part of is newly added.
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Text 4-9
Language and SpacetimeTime Flow in WordFor KOHARI Akihiro and His TimeTANAKA Akio 1Word 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) = x2In 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).3Now 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’4The 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)5Now 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=0The flow has solution as equation φt(x)/dt = Xφt(x)6Here set {φt(x) | t∈R } is presented. The set is called orbit.7In word, meaning is expressed by flow and time is expressed by orbit.Tokyo May 3, 2007Sekinan Research Field of Language
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Text 4-8
Language and SpacetimeStability of LanguageTANAKA Akio 1Language has stability.2Stability is defined by the following.From KAWAMATA Yujiro, Stab X that consists of the set having all <locally finite> and <numerical>< stability condition> on derived category D(X) has finite dimensional complex manifold’s structure. Stab (X) is conjectured to be connected and simply connected. In derived category, exact sequence is extinct and distinguished triangle is generated.Refer to the next paper. KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1 Iwanami Shoten 20063Now blow up and blow down is presented.φ: QY(M) → MM is nonsingular variety. Y is M’s submanifold.QY(M) is blow up along Y.φis arrow of algebraic varietyφis called QY(M)’s blow down.4Also birational mapping that is extension of blow up and blow down is presented.Birational mapping is what rational mappingφ: V→W has mapping ψ: W→V. Here existsφ∘ψ= idV ψ∘φ=idW .5By birational mapping, algebraic variety V, W and X is presented. These three are formed to be new distinguished triangle that is supposed to be equivalent with V, W and X.6Word that consists of category makes sentence that consists of distinguished triangle by birational mapping with algebraic method.Tokyo April 30, 2007Sekinan Research Field of Language
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Text 4-7
Language and Spacetime Construction of SpacetimeEspecially on Transformation with Boundary for Dimensions TANAKA Akio 1 Spacetime is putted to manifold.2 When spacetime is expressed by sphere, spacetime becomes sphere symmetry.Refer to the following paper.Word Containing Time and 4 Dimensional Sphere Tokyo April 5, 20073 The symmetry is special orthogonal transformational group.4 Generally n-dimensional SO(n) is compact Rie group.5 On symmetry of spacetime, geometric invariant is presented.Now on invariant, metric tensor g is presented.g = Σgijdxidxjg’s invariant transformation is isometry group.When gij → gji is established, infinitesimal motion (Killing vector field) is 0.6 Here Ricci flow is expressed by the following.g(t) = gij(t)∂gij / ∂t = -2Rij Rij is Ricci curvature tensor.7 M defined by a time interval [0, T] has a unique g(0) = go on Ricci flow.8 (S4,g0) is 4 dimensional sphere surface with radius 1.g(t) = r(t)2g0g(t) has finite time T = 1/2(n-1).Ricci flow becomes a point after finite time.Phenomenon what manifold becomes smaller dimensional space is called collapse.9 Now word has meaning and time.10 Here word is expressed by manifold.Refer to the following paper.Topological Tolerance Tokyo Junr 7, 2006Super Fluidity Tokyo June 17, 2006Also refer to the following paper.Structure of Word April 6, 2007On time of language, refer to the following paper.On Time Property Inherent in Charaters Hakuba March 28, 2003On time principle of language, refer to the following paper.Quantum Theory for Language Synopsis Tokyo January 15, 200410 Here time of word is defined by manifold’s time of Ricci flow’s collapse.11 By Thurston conjecture, when compact 3 dimensional manifold is cut and separated by 2 dimensional sphere and torus, while generated compact manifold has sphere boundary, sphere is put together there. As the result new generated manifold has locally uniform structure.Refer to the following paper.Cut and Glue Cut-tube-ring generates multidimensional world Tokyo July 7, 2006Also refer to the following paper.Torus Chain Tokyo June 10, 200612 Peculiar solution of Thurston conjecture is Poincaré conjecture that is what simply connected 3 dimensional compact manifold is homomorphic to 3 dimensional sphere surface S3.13 According by Thurston conjecture, what put together newly generated 3 dimensional manifold is called connected sum.Connected sum is expressed by M1#M2. M1 and M2 are 3 dimensional manifolds.14 Here sentence is defined by manifold’s connected sum.Tokyo April 24, 2007Sekinan Research Field of Language
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Text 4-6
Language and Spacetime Shift of TimeFrom SAPIR Edward to KAWAMATA Yujiro TANAKA Akio 1 Language is expressed as structure of spacetime.2 Spacetime is expressed as manifold.3 Affine algebraic variety is selected for description of spacetime.Algebraic variety is pasted together from affine algebraic variety.Affine algebraic variety is irreducible affine algebraic set.Affine algebraic set is the set that consists of common zero point of finite polynominalPolynominal is in n-dimensional complex affine space.4 Now n-dimensional projective spaceP n is presented.Cn+1 \ {O} / ~O is the coordinate’s origin of complex affine space.~ is mathematical equivalence on elements of set.5 Projective space P n is covered by n+1 affine space.6 Now abelian category and derived category are presented.Abelian category and algebraic variety is placed together.Derived category is abelian category’s coherent sheaf’s complex that is composition of successive arrows becomes 0.7 From derived category, distinguished triangle is presented.8 Here time conjecture of language is presented.(1)Distinguished triangle makes the model for shift of time on language.(2)Time on language is closed, successive and circular in word.Circulation is worked between starting point and ending point of word.The origin of shift of time is derived from the following.On Time Property Inherent in Characters Hakuba March 28, 2003The concept of time in language is taught from the following.SAPIR Edward LANGUAGE An Introduction to the Study of Speech Harcout, Brace & Co. IncSpecial thanks to KAWAMATA Yujiro for the mathematical approach on language research, especially from the following.KAWAMATA Yujiro Daisukikagaku to doraiken Sugaku 58-1, January 2006Tokyo April 20, 2007Sekinan Research Field of Language
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Language and Spacetime Description of Meaning6th Time For KARCEVSKIJ Sergej TANAKA Akio 1 Word consists of meaning and time.Refer to the following paper.Structure of Word Tokyo April 6, 20072 Sentence consists of connection of words.Refer to the following paper.Generation of Sentence Tokyo April 13, 20073 Now presheaf is presented by MACLANE Saunders.Presheaf is contravariant functor F on small category C. F: Cop → Set (Set is all of small sets and functions.)Category has duality principle by axiom.Category C has opposite category Cop.Arrow f has opposite arrow fop.Object of Cop is object C.Arrow of Cop is arrow f op.4 Presheaf F gives homomorphism by the following.V ⊂U ( V and U are arbitrary open sets.)ρ : F (U) → F (V)ρ gives restrictive mapping.5 From category, word is given intuitively as below.F (V) is starting point of meaning.F (U) is ending point of meaning.Presheaf F is time for shifting meaning.6 Grp that consists of groups and homomorphisms are presented.Now here exist a group G and other groups H.Arrow’s set HomGrp( H,G) makes the relation between H and G clear. ( HomGrp( H,G) is all the arrows’ set connecting objects H and G in category Grp.)Here G is meaning of word. H is elements of meaning G.7 Meaning of word is clarified by all the arrow’s set.8 The clarification is called description of meaning. Tokyo April 16, 2007Sekinan Research Field of Language
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Language and Spacetime Generation of SentenceFor WANG Guowei and CELAN Paul TANAKA Akio 1 Word consists of meaning and time.Refer to the following paper.Structure of Word Tokyo April 6, 20072 Now word is expressed by cylinder.In category, cylinder is made by the following.X is topological space that has base point x0.I is unit closed interval. I = {t ｜0≦t≦1} Cylinder is expressed by X×I.Here t is time of word.X × 0 is meaning of starting point. X × 1 is meaning of ending point.3 Now Suspension ΣX of topological space X is presented.ΣX is made by shortening of upper surface X × 0 and under surface X × 1 of cylinder X × I.4 Now Reduced suspension SX is presented.SX= S1 ×X S1 is circumference that is stuck together of point 0 and 1 of closed interval I.Here SSn =Sn+1 Sn is n-dimensional sphere.SX is made by shortening of x0 × I from ΣX.SX is expressed by point.The point is base pointof SX.5 SX defines group in category.6 SX has operation of group.7 Now word follows operation of group in algebra.8 Connection of words generates sentence.9 Connection is made by the following.Now H (I, X) is presented.H ( I, X) is a road space of topological space X.H ( I, X) is a set that consists of continuous mapping ψ: I → X at interval I = [0, 1].Road isψ∈ H (I, X).Ifψisψ(0) =ψ(1),space X becomes loop space ΩX.10 If a topological space R is presented, H ( X, ΩR) becomes group.11 If an Abelian group A is presented, space Kn (n = 1,2,3….), a set H(X, Kn) becomes Abelian space.This space is identified with connection of words, namely, sentence. Tokyo April 13, 2007Sekinan Research Field of Language
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Language and Spacetime Structure of WordFrom KARCEVSKIJ to MACLANE TANAKA Akio 1 Word has structure.On one case of the structure, refer to the following papers.Cube Theory Dimension Tokyo March 22, 2006Cube Theory Structure of Cube Tokyo March 25, 2006Cube Theory Cube Language Hakuba April 1, 20062 Now the simplest structure example is presented.Word has starting point of meaning. The meaning is called ms.Word has time for shifting meaning. The time is called ts.Word has ending point of meaning. The meaning is called me.3 By category, word’s ms, ts and me are expressed below.ts : ms → meHere ts is replaced by arrow f. ms and me are replaced by objects a and b. The relation is expressed by diagram below.f : a → b4 Here word X and word Y are presented as category that consists of topological space or group.Word X is expressed by f : a → b.Word Y is expressed by g : b → c.Composition X and Y is expressed by compositef ∘g.f ∘g : a → c5 Here f ∘g is putted to h.The diagram that consists of objects a, b, c and arrow f, g, h is presented.6 Now category’s morphism is called functor.Functor that is commutatively transformed to another functor is called natural transformation.Natural transformation is called component.On component, refer to the following paper’s concept .Cube Theory Structure of Cube A 10 Tokyo March 25, 2006Natural transformation means functor’s morphism.7 Product of two categories B and C is defined by the following.B ×C’s arrow → is <f, g>. Here, f : b → b’ and g : c → c’ ∘ = ∘f, g’∘g>8 C×2 consists of C×0, C×1 and arrows combined C×0, C×1.Here when any natural transformation has unique functor, it is called universal natural transformation.9 Product category C×2 is expressed by concept in .10 By upper rough sketch, ’ concepts are transplanted to category. 11 Word is reconstructed by topological space or group.12 Structure of word that is presented by KARCEVSKIJ has the chance affirmatively verified in accordance with the concepts of MACLANE. Tokyo April 6, 2007Sekinan Research Field of Language
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Language and Spacetime Word Containing Time and 4 Dimensional Sphere Dedicated to MAC LANE Saunders TANAKA Akio 1 Word contains time inside.Refer to the following paper.On Time Property Inherent in Characters 1 Generation in Characters Hakuba March 28, 20032 Word has construction that is expressed by category.On category, refer to Categories for the Working Mathematicians by Saunders Mac Lane, 1998 Springer-Verlag New York, LLC.3 Time has starting point and ending point in word.4 Meaning has starting point and ending point in word.5 Generally word shifts meaning from starting point to ending point by time.Refer to the following paper.On Time Property Inherent in Characters 2 Function of Characters Hakuba March 28, 20036 Primitive word does not shift time and stays in the same point.7 In category, the names of language are called by following terms.Meaning is called object.Shift is called arrow.Starting point is called domain or source.Ending point is called codomain or target.No shift or stay is called identity.Arrow can be composed. The composed arrow is called composite.In category two axioms are presupposed.One is associativity.The other is unit law.These terms are all complied with above quoted Mac Lane.8 Word with starting point is expressed on Gauss plane.9 Word with ending point is also expressed on Gauss plane.10 Shift time from starting point to ending point is expressed by coordinates’ transference.11 Here Riemann sphere is putted with having the same origin to Gauss plane.12 Word with starting point is projected toward the North Pole of Riemann sphere.13 Word with starting point has coordinates ws (xs ys, zs) on Riemann sphere’s surface.Refer to the following paper.Aurora and Riemann Sphere Tokyo October 2 – October 3, 2006Aurora Plane Tokyo October 14, 2006Word, phrase and Sentence Tokyo October 25, 200614 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, 2007Sekinan Research Field of Language
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What is signal? The existence that generates language Preface-Main Issue 4 Space and BoundaryOver Edited30 March 2019ENSILA
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Time and ideogram
Contents
Ideogram Paper
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Text 1
On Time Property Inherent in Characters TANAKA Akio
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]
[Postscript December 23, 2008]
[Postscript July 30, 2014]
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Text 2
Aurora Theory Distance and Time 5th Time for KARCEVSKIJ TANAKA Akio 1Sentence that appears aurora is expressed by integral on Riemann sphere.Refer to the following paper.Aurora Theory Word, Phrase and Sentence Tokyo October 25, 20062Sentence has distance that is expressed by the height of trapezium on sentence plane.Refer to the following paper.Aurora Theory Aurora Plane Tokyo October 14, 20063Sentence has time that is expressed by the vector on the right or left side of trapezium.| AB | = S・tb-a Here | | is distance between phrase A and phrase B, abbreviated to DAB.S is velocity of moving DAB.tb-a is time-lag of phrase A and phrase B. Each phrase generates according to its peculiar time.Now the radius of Riemann sphere is r. The angle made by vector A and vector B is θ.Here θ is Function (xa, ya, xb, yb), and any point (x, y) is on complex plane.DAB is expressed by 2 r sinθ/2. S is expressed by 2 r sinθ/2 / tb-a.Now when tb-a is unit time 1, S is expressed 2 r sinθ/2.S is variable by pointing word on complex plane.So Dictoron’s velocity on Riemann sphere is variable.Refer to the following papers.Distance Theory Tokyo May 5, 2004Changeability To SAPIR and KARCEVSKIJ Tokyo January 8, 2005Time For KARCEVSKIJ Tokyo January 22, 2005Tokyo October 28, 2006Sekinan Research Field of Languagewww.sekinan.orgPostscript January 25, 2008[Basis]Clifford Algebra / TOMONAGA’s Super Multi-time Theory / Tokyo January 25, 2008[References]Aurora Theory / Dictoron, Time and Symmetry< Language Multi-Time Conjecture> / Tokyo October 6, 2006Aurora Theory / Word, Phrase and Sentence / Tokyo October 25, 2006Language and Spacetime / Time Flow in Word For KOBARI Akihiro and His Time / Tokyo May 3, 2007Invitation by Theme-Time / Data Arranged at Tokyo January 6, 2008Aurora TheoryLanguage and Spacetime
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Aurora TheoryDictoron and Time TANAKA Akio 1Objection from words of complex plane to the Poles of Riemann sphere makes aurora plane that consists of phrases and sentences.Refer to the following paper.Aurora Theory Aurora Plane Tokyo October 14, 2006 [AT8]2Situation of aurora’ phrase is expressed by longitude, latitude and direction to the next phrase.Refer to the following paper on direction.Aurora and Curvature Tokyo September 30, 2006 [AT3]3Now Riemann sphere has a unit radius.Refer to the following paper.Aurora Theory Limitation of Meaning Tokyo October 9, 2006 [AT7]4When word is written on complex plane, phrase is indicated on Riemann sphere to which dictoron radiates from the origin of the sphere.Refer to the following paper.Aurora Theory Dictoron and Aurora For SAEKI Shizuto Tokyo September 24-28, 2006 [AT2]5Word on complex plane corresponds to frame on Frame-Quantum Theory.Phrase on Riemann sphere corresponds to quantum on Frame-Quantum Theory.Refer to the following paper.Aurora Theory Dictoron Quantum and Trace For FINKELSTEIN David Tokyo September 17, 2006 [AT1]Also refer to the following papers.Frame-Quantum Theory Dedicated to KARCEVSKIJ Sergej Tokyo March 13, 2005Quantum Linguistics Solidity and Flexibility Tokyo January 14, 2006Quantum Linguistics Quantum Language Machine For Forth Time to KARCEVSKIJ Tokyo January 23-29, 2006Quantum Language Frame and Transmission For Quantum Language Machine 3 Tokyo February 26, 2006Also refer to the following papers groups.Frame-Quantum Theory Map 3 Hakuba March 28, 2005Quantum Linguistics Physical Substantiality of Language6Dictoron has spin.Refer to the following paper.Aurora Theory Dictoron as Language Quantum Tokyo October 1, 2006 [AT4]7Dictoron has two units of information at the same time.Refer to the following paper.Quantum Language Substantiality of language Tokyo February 21, 20068Dictoron has ability to work as quantum computing.Refer to the following paper.Quantum Semantics Topological Entangled Language For KITAEV Alexei Yu Tokyo June 5, 20069When dictoron at the origin of the sphere reaches on Riemann sphere, phrase is generated.When dictoron on Riemann sphere returns to the origin of the sphere, phrase is extinguished.Refer to the following paper.Frame-Quantum-Time Theory Tokyo July 31, 200510When dictoron moves between the origin and surface of Riemann sphere, phrase is generated and extinguished.11Generation and extinction of phrase are called time progression and time regression.12Now place of dictoron is expressed by the combination of longitude, latitude, direction and time.13The combination is indicated by the coordinates (x, y, z, and t).14The coordinates has symmetry.Refer to the following paper.Aurora Theory Dictoron, Time and Symmetry Language Multi-Time Conjecture Tokyo October 6, 2006 [AT6]15From symmetry of coordinates, there exists reverse phrase point on Riemann sphere by symmetric transformation.16Dictoron’s movement to the point has reverse progression.17Time to the reverse progression has reverse progression time.The time is called imaginary time.Refer to the following paper.Tube-Ring Theory Imaginary Language Minus Dimensional Cut-Tube-Ring Tokyo July 8, 200618Place on Riemann sphere expresses time and imaginary time of dictoron.19Place of imaginary time makes imaginary word on complex plane.Refer to the following paper.Actual Language and Imaginary Language To LÉVI-STRAUSS Claude Tokyo September 23, 200420Word and imaginary word indicate language universe.Refer to the following paper.Reversion Theory Tokyo September 27, 200621The universe is measured by distance.Refer to the following paper.Distance Theory Tokyo May 5, 200422Time concerning about dictoron is also measured by distance.Refer to the following paper.Cube Theory Cube Word Hakuba April 1, 200623Distance makes matrix (x, y, z, t) (-x, -y, -z, -t).24There comes matrix (-x2, -y2, -z2, -t2).25Now becomes function – (x2+y2+z2+t2). The function is called function I.26Function I specifies a line segment.27The segment expresses dictoron’s movement containing progression and regression of time and imaginary time. Tokyo October 21, 2006Sekinan Research Field of Language
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Aurora Theory Dictoron, Time and Symmetry TANAKA Akio A1 Dictoron is language quantum that has meaning.Dictoron is now represented by photon.2 Meaning is indicated by quantum’s spin that is classified to upward and downward.3 Dictoron is discharged from Riemann sphere’s center point.Riemann sphere has the radius that is photon’s unit speed 1.4 Dictoron is on Riemann’s sphere after photon’s unit time.5 Here dictoron has time that is indicated by vector.6 Dictoron’s place is on Riemann sphere whenever dictoron has any vector.7 Projection of Riemann sphere’s surface from North Pole of Riemann sphere to orthogonal coordinates is expressed by complex plane.8 Riemann sphere of time’s expression is symmetry at any time that has various vectors.9 If Riemann sphere has electrical charge, dictoron is affected by the charge.10 Dictoron’ meaning, now indicated by spin, is expressed by quantum’s spin situation on Riemann sphere.11 Quantum’s situation is projected to complex number field.12 Dictoron is expressed by norm space.B13 Riemann sphere is symmetrical on time, namely any vector.14 Different time vector has different projected complex number field.15 Dictoron’s movement to Riemann sphere let us conjecture existence of multi-time.Refer to the following paper.On Time Property inherent in Characters Hakuba March 28, 2003Tokyo October 6, 2006Sekinan Research Field of Language
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Aurora Theory Why Human Time Flows Fast and Slow on Occasion TANAKA Akio 1 Word is expressed on complex plane and phrase is expressed on Riemann sphere.2 When word is presented at regular intervals, namely unit time 1, velocity of dictoron’s movement on Riemann sphere becomes to be variable.Refer to the following paper.Aurora Theory Distance and Time Tokyo October 28, 20063 Here human mind be on Riemann sphere and outer world be on complex plane, regular presentation of words on complex plane makes variable velocity consequence on Riemann sphere.4 Concentration is in whether human mind has Riemann sphere or not.Refer to the following paper in early work on characters.On Time Property Inherent in Characters Hakuba March 28, 2003Tokyo October 28, 2006Sekinan Research Field of Language
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Aurora Time Theory Time on Aurora TANAKA Akio 1 Language is expressed by word, phrase and sentence in Aurora Theory.Word is on complex plane.Phrase is on Riemann sphere.Sentence is trapezium in Riemann sphere.Aurora appears phrase on Riemann sphere.Aurora also appears sentence in Riemann sphere.Refer to the following paper.Aurora Theory Word, Phrase and Sentence Tokyo October 25, 20062 Surface of Riemann sphere is expressed by x2 + y2 + z2 = 1.3 Dictoron’s distance from coordinates’ origin after unit time is 1.After unit time, dictoron that is represented by photon reaches the surface that has distance 1.Refer to the following paper.Dictoron, Time and Symmetry Tokyo October 6, 20064 Dictoron’s distance is expressed by ct.c is light velocity. t is time.ct is 1 after unit time.x2 + y2 + z2 = (ct) 25 Now function F is presented from dictoron’s distance.Function is expressed by F = (ct) 2 - x2 - y2 - z2.6 Here F be invariant, F becomes Minkowski space.F’s invariant is given by interval.Interval is expressed by generating Riemann sphere’s surface. It is abbreviated to GRSS.7 GRSS is objected to complex plane by unit circle and its inside.The circle is on z = -1 plane.8 Minkowski space is expressed on complex plane containing time dimension. Tokyo November 5, 2006Sekinan Research Field of Language
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Text 7
Aurora Time Theory Imaginary Time and Imaginary SpaceFrom HAWKING Stephen TANAKA Akio 1 Language is expressed by word, phrase and sentence in Aurora Theory, abbreviated to AT.Refer to the following paper.Aurora Theory Word, Phrase and Sentence Tokyo October 25, 20062 Dictoron reaches Riemann sphere that has the radius r1 of 1 by the time t1 from the origin of coordinates.Riemann sphere is expressed by x2 + y2 + z2 = 1.Here c is light velocity, r1 = c t1 = 1.Refer to the following paper.Aurora Theory Dictoron For FINKELSTEIN David Tokyo September 17, 20063 Dictoron has distance that is abbreviated to ds.In Aurora Theory, phrase is expressed on Riemann sphere by dictoron’s radiation from coordinate’s origin.Phrase takes shape when ds = 1.Phrase does not take shape when ds < 1 or ds > 1.4 Now in Aurora Time Theory, abbreviated to ATT, 4 dimensional sphere that has the radius 1 is expressed by x2 + y2 + z2 + t2 = 1.Here t is time dimension.5 In ATT, phrase takes shape when ds = 1 and phrase does not take shape when ds < 1 or ds > 1.6 In ATT, t2 = 1 – (x2 + y2 + z2).When x2 + y2 + z2 > 1, t2< 0.t becomes imaginary number.7 In AT and ATT, word is expressed on complex plane and phrase is expressed on the sphere. ds has real number 1.8 In ATT, t is expressed by 1/c. Here c is light velocity. So t be imaginary number, the expression is i/c.9 4 dimensional coordinates in ATT, when t is expressed by i, the sphere is expressed by x2 + y2 + z2 = 2.10 In ATT, when ds = 1 and the sphere is x2 + y2 + z2 = 2, dictoron is in the sphere. So phrasedoes not make shape.11 Dictoron in ATT has magnitude by the definition that is expressed by ds.When t is imaginary unit i, remained magnitude to the destination for phrase is 1.12 If t be imaginary unit i, non-existential space that is measured by remained magnitude 1 is to be existent.13 When t is imaginary number, now verified imaginary unit i, t is called imaginary time.14 Imaginary time makes space in the ATT’s sphere.The space is called imaginary space. Tokyo November 11, 2006Sekinan Research Field of Language
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Text 8
Aurora Time Theory Enlarged Distance TheoryFor CELAN PaulAnsprache anläβlich der Entgegennahme des Literaturpreises der Freien Hansestadt Bremen TANAKA Akio 1 Language was supposed to have distance for mainly making sentence.Refer to the following paper under roughly sketched situation.Distance Theory Tokyo May 5, 20042 Distance in 4 dimensional space is indicated by Minkowski space.(Δs)2≡(cΔt)2-(Δx)2-(Δy)2-(Δz)2Δs is distance. c is light velocity. Δt = t2-t1. Δx = x2-x1. Δy = y2-y1 Δz = z2-z1.3 Now if time is imaginary timeit by being showed from HAWKING S., distance is indicated by Euclid space.-(Δs)2≡(cΔt)2+(Δx)2+(Δy)2+(Δz)2Here distance (Δs) becomes imaginary number.This distance means that 4 dimensional space has imaginary number’s distance. The distance is abbreviated to imaginary distance.Imaginary distance is in imaginary space.Refer to the following paper.Aurora Time Theory Imaginary Time and Imaginary Space Tokyo From HAWKING Stephen November 11, 20064 Imaginary distance is interpreted by the following.4-1 On complex plane imaginary number is objected to the circle that is expressed by y2 + z2 = 1.The circle is called to imaginary ring.Aurora Theory Aurora and Riemann Sphere For Mason L. J. Tokyo October 2-3, 20064-2 Imaginary ring expresses point at infinity of hyperboloid by Caley transformation.4-3 In consequence, on point at infinity,imaginary distance is expressed on the circle.4-4 In 4 dimensional space, on point at infinity, the imaginary distance is expressed on a circle.5 Thus supposition is the following.In 4 dimensional space, distance on point at infinity is definitely expressed by HAWKING’s imaginary time.Tokyo November 20, 2006Sekinan Research Field of Language
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Text 9
Aurora Time TheoryOpened Time and Closed TimeFor WANG Guowei and DELBRÜCK Max TANAKA Akio 1 Time is classified to opened time and closed time.2 Opened time is a real time in our world.3 Closed time is an artificial time in artificial things.For instance, Chinese characters have closed time.Refer to the following paper.On Time Property Inherent in Characters Hakuba March 28, 2003Also refer to the following papers.Warp Theory Dedicated to SAPIR Edward Tokyo October 24, 2004Direction For KARCEVSKIJ Tokyo November 26, 2004Time Theory Tokyo December 25, 2004Also refer to the following papers.Changeability To SAPIR and KARCEVSKIJ Tokyo January 8, 2005Individuality Tokyo January 10, 2005Time For KARCEVSKIJ Tokyo January 22, 2005Fixation Tokyo February 20, 2005Perspective on the theme is indicated below.Quantum Theory for Language Map 4 Hakuba March 28, 2005Quantum Theory for Language Theoretical Summarization and Problem in Future Tokyo November 28, 20044 Closed time has starting point and ending point.On Chinese character /kun/, meaning difficult in English, the situation of closed time is explained in the concrete.Refer to the following paper.Prague Theory Dedicated to KARCEVSKIJ, PRAGUE and CHINO Tokyo October 2, 2004Perspective on the theme is indicated below.Log of Quantum Theory for Language 3 Love and Thanks to the Pioneers Tokyo October 24, 2004Log of Quantum Theory for Language 4 On the Themes of SAPIR and KARCEVSKIJ Tokyo January 16, 20055 Now closed time be supposed to be a definite line or plane, the time is thinkable by closed set on topological space.Refer to the following paper.Quantum Semantics Lattice Tokyo May 15-28, 2006Perspective on the themes is indicated below.Top Quantum Semantics Tokyo May 15, 2006 and After6 In Aurora Theory, word of language is expressed on complex plane, phrase of language is expressed on Riemann sphere and sentence is expressed in Riemann sphere.Refer to the following paper.Aurora Theory Aurora and Riemann Sphere For MASON L. J. October 2-3, 2006Aurora Theory Word, Phrase and Sentence Tokyo October 25, 2006Perspective on the themes is indicated below.Top Aurora Theory Tokyo September 17, 2006 and After7 In Aurora Time Theory, language is connected with time by Minkowski space.Refer to the following paper.Aurora Time Theory Time on Aurora Tokyo November 5, 20068 In Minkowski space, distance of language is supposed to be measured by disparity between time and place.(Δs)2≡(cΔt)2-(Δx)2-(Δy)2-(Δz)2Here time be imaginary being showed by HAWKING S., distance is supposed to be measured by addition between time and place.-(Δs)2≡(cΔt)2+(Δx)2+(Δy)2+(Δz)2The distance becomes imaginary number.The distance is called to imaginary distance.Imaginary distance is expressed on a circle on point at infinity.Imaginary time, imaginary distance and infinity is defined by closed set on topological space.Refer to the following paper.Aurora Time Theory Enlarged Distance Theory For CELAN Paul Tokyo November 20, 2006Perspective on the themes is indicated below.Top Aurora Time Theory Tokyo November 5, 2006 and After9 There appears conjecture on time.Conjecture 1 Closed time is in writing.Conjecture 2 Imaginary time is in closed time.Conjecture 3 Imaginary distance is in imaginary time.Conjecture 4 Imaginary spacetime is in Riemann sphere by objecting from complex plane of word and phrase.Conjecture 5 Real time is in opened time and imaginary time is in closed time. Both are expressed by Riemann sphere.Tokyo November 25, 2006Tokyo November 26, 2006 Dedication, consideration 8 and Conjecture RevisedSekinan Research Field of Language
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Text 10IdeogramTANAKA Akio 1 is a unit for of language.2 is a figure which has two parts, and .3 As a figure, is recognized in an instant.4 generates in .5 Now there are 5 s, namely, [ I, meet, he, library, yesterday].6 There becomes , namely, / I meet he library yesterday. /7 New returns to .8 New s are 6, [ I, meet. he. library, yesterday, I meet he library yesterday ].9 There add 3s. [met, him, at].10 New is generated, / I met him at library yesterday. / .11 is static and fixed but is dynamic and changeable.12 needs energy for its dynamism but does not need dynamic devices.13 resembles Nintendo’s FAMICON, but differs in the following 14-18.14 is a source of .14 is a part of automatic language generating machine.15 is a figure which is scanned and reproduced easily.16 ’s inputting devices are various, such as typing, voice inputting, manual writing, pictograph and so forth. 17 can install to language-answering-devices, such as telephone, vending machine, showing-way-machine and so forth. Answer is always individually different for the most adequate purpose.18 ’s is possible to be written as a sophisticated figure which is transformed to easy-readable style.19 ’s is enlarged by the adding-from-old-to-new system. See upper No.5-10. TOKYO
March 4, 2005Sekinan Research Field of Language
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Text 11
Egyptian Hieroglyph ExhibitionJourney 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 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
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
References 4
References 5
Tokyo
30 July 2016
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Text 13
The Days of Ideogram
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.
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
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5
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7
Outer sites and publication
8
This essay is unfinished.
Tokyo
20 April 2017
Sekinan Zoho[Note]
7 march 2018From the upper study, ideogram has special features as the next.1. Ideogram is one style of writing language, rather near to image than letter.2. Ideogram has potential to connects image and letter.3. One ideogram generally contains more information than letter.4. Ideogram has possibility to researching object by mathematics especially algebraic approach.5. Ideogram has geographical and historical rich fields from Mesopotamia, Egypt to China. 6. I take Chinese character for my research's object.
...............................................................................................What is signal? The existence that generates language Preface-Main Issue 5 Time and IdeogramCompleted Edited7 April 2019ENSILA
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Anticipation
FAQ
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Text 1
Presupposition on Natural LanguageTANAKA 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 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. 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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Text 2
Sayama Assumption on Language TANAKA Akio 1. Language is changeable.*12. Language has substance. Because it is changeable.*23. Language has time. Because it is changeable.*34. Language has boundary. Because it is substance.*45. Language has structure. Because it is substance.*56. Language is describable. Because it is substance.*6References
*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 Sayama Hills, Tokyo
21 September 2012
Sekinan Research Field of Language
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Text 3
Symplectic Language TheoryTANAKA Akio Dialogue 1 On StructureFor HORI Tatsuo, Footprints on the snow, 1946Why do you think that language has structure?_We have true-false problem since Greece had logic on language, Crete man tells himself a liar. The situation suggests that if language has structure and we see the structure's whole, there is no more problem in the upper funny but radical story.Do you mention that language has dimensions in it for preventing the confusion?_Surely dimension is an important factor of structure. But language is a vast building in which all the logisc and all the feelings are expressible for all the hope of human beings.Then how the structure is built, do you imagine?_I ever learned the history of Prague Linguistic Circle, in which the most important hypothesis is said that language has function. Function is inevitably occurred following after the completion of structure, I think.Do you say that from the observation of language function is adequately acceptable for structure's surface?_Yes, I think so.Then on inner structure of language, what do you think?_At first, language has meaning. But it was put aside by Prague Linguistic Circle as the hardest problem on language for its ambiguity as MATHESIUS V. gave the famous lecture, Latency of language phenomena, 1911. I attracted the theme, language has ambiguity.Did you go to Prague? _No. I only heard on PLC from CHINO Eiichi. He learned linguistics at Prague, from 1958 to 1967. He gave me the basis of linguistics after his returning to Tokyo. I first met him at Tokyo 1969. I learned Russian at that time in the small class. He was young at 37, and I also young too at 21. You really respect CHINO._I remember him respectfully, but more frequently merrily, for his fantastic conversation to the younger beginner, studying language from various fields, from art to classical languages at the university. On language, ambiguity is important?_Undoubtedly. CHINO gave me the concept of asymmetric dualism of linguistic sign. The paper was written by KARCEVSKIJ Sergej at 1929. Precisely to say, "Du dualisme asymétrique du signe linguistique", Travaux du Cercle Linguistique de Prague 1.From ambiguity to structure, through what course did you choose?_I took the road from the minimum unit of meaning that was extracted by WANG Guowei's GUANTANG JILIN, the book was real youth of my life, for which I named by reference of JAKOBSON Roman's concept . I dearly remember CHINO's warm advice "not to enter such a theme that are firstly treated by WITTGENSTEIN-like person. We are not invited", backing to the railway station from the university, after his lecture on linguistics at early summer twilight. is your starting point, I recognized. After that, To where did you go?_At first, from set theory. I ever learned it mainly from TAKEUCHI Gaishi's papers. Now I yet like his approch to the mathematical object. And I, at that time, also came under the influence of LÉVI-STRAUSS Claude.That course was productive to you?_It is a difficult question. For first step of my study, partly yes and mostly no.Mostly no, for what?_For me the most important is the relation between s. But set theory is not efficient for that direction.Is relation important?_Perhaps yes.Why?_Back to MATHESIUS's or KARCEVSKIJ's , there exists relationship between one meaning and another meaning. For me, this relationship is not able to be handled by my set theory's level. But set theory is enough charming for its elemental simplicity.And where did you go to the next?_ Geometry. It is the most natural and fantastic approach by its freely intuitive methods. Intuition is surely familiar. But selection is only done by such reason?_I have not any other choices at considering my mathematical level then.Geometry was respondent to your hope?_Yes, absolutely yes. As people say that geometry is a heimat of mathematics, I really think so.Geometry is more easily way to approach for you?_Repeatedly say, I have not any choices at that time. Meeting with geometry, I often wrote various figures containing topological ones, for instance at on the train to the town in which mother is under medical care.Such drawings can express language's validity?_Much interesting to express but the themes containing validity of language and so forth are very hard to access.Why?_Relationship among language inside is far away beyond my amateurishly imaginary figures.And after that?_I came here, at my present mathematical situation as PENROSE Roger said in his book THE ROAD TO REALITY, that mathematics is the most highly investigational way for the study of universe. His confidence to mathematics is put up on my home page of sekinan.org.Where do you stand now?_Symplectic geometry.Why do you stand there?_Also natural for me. And freely thinkable.Freely thinkable, what imagine by that?_Mathematics is radically free. Just like a wind at high lands, far-sighted and transparent.Mmm. Transparent. _Yes,perfectly transparent. In contrast with language. Language is always having ambiguity.Ambiguous language and transparent mathematics._That's all.Many thanks today._It's my pleasure. Tokyo
March 12, 2009
Sekinan Research Field of Language
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Text 4
TANAKA Akio
I was born in 1947 and become 68 years old this summer.
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.
In the gardenPeony begins to come out in the cold winter. If there be change in language, from which to which language changes in its true nature?At where is there the change's power or energy? Refer to the next. 0. General survey
1. Substantiality and time
2.Flow and energy
4. Stochastic theory, distance, functional, potential with energy
Tokyo
1 January 2015
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Text 5
q.v. Boundary of Words / 12 February 2009
TANAKA Akio ---------------------------------------------------------------------------------------------------------
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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Substantiality Dedicated to SAPIR Edward TANAKA Akio 1 Substance of language is completion which possesses the distance from the real world.2 The distance is sustained by the fixation for which meaning and time are abstracted.3 If language has not distance, language appears and disappears following the real world proceeding.4 Language is substantially unchangeable. Changeability occurs on surrounding.5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.6 Substantiality is a frame of language.7 Substantiality is free from the real world.8 Substantiality is powered by outer energy.9 Powered substantiality moves complied with possessed command, namely meaning and time.10 Powered moving substantiality of language is called .11 The idea of quantum is partially realized by in the supermarket or bookstore.12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening. Tokyo February 27, 2005For the Memory of Tanashi Station Front Street February 26, 2005Sekinan Research Field of Language ....................................................................................................................................
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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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
...................................................................................................................................... 4. Boundary is related with dimension through Poincaré Theorem. Details are next.
......................................................................................................................................... Dual Language Duality of Language TANAKA Akio 1. Theorem
(Poincaré duality)
For oriented compact n-dimension topological manifold M ,
bilinear form
is exact,
and become dual space each other.
♦ 2. Interpretation
Word := M Boundary of language := p Dual language := and Language := 3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language. 4. References
Distance Theory
Mirror Theory
Guarantee of LanguageTokyo
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.
....................................................................................................................................
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.
----------------------------------------------------------------------------------------------- Tokyo
21 December 2014
Read more: https://srfl-theory.webnode.com/news/why-is-boundary-necessary-in-language/
....................................................................................................
Text 6
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.
8.
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.
Tokyo
26 November 2014
Read more: https://srfl-theory.webnode.com/news/how-is-the-time-alive-in-language/
........................................................................................................................
Text 7
vide: Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement
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
.................................................................................................................
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.
01/07/2018 11:19 Manuscript of Quantum Theory for Language
TANAKA AkioPreface
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 2015Sekinan Library -----------------------------------------------------------------------------------------------
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 229 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 development of quantum group. Particularly from the Drinfeld's speech at the international mathematician conference in 1984.
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 paperInherent energy in language has been become a little updated after writing in 2003.
Now arranged at the next.
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Tokyo
20 June 2018
Sekinan Zoho -----------------------------------------------------------------------------------
Tokyo29 June 2018SRFL Lab
Here ends Manuscript of Quantum Theory for Language
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What is signal? The existence that generates language Preface-Comment Over Edited10 April 2019ENSILA
Read more: https://srfl-theory.webnode.com/news/what-is-signal-total-edition-21-november-2018-23-april-2019/