Sunday 31 July 2022

Friday 29 July 2022

Site Sekinan Nerve 2022

 Sekinan Nerve



Nerve Theory Trilogy

Sekinan Nerve shows the newest theory researched at Sekinan Library.
Since 2018 I have studied a new theory aimed human beings nerve's mathematical structures based algebraic geometry.
In 2018 I wrote Signal-Nerve Theory, Old title What is Signal?
In 2019 I wrote Quantum-Nerve Theory.
In 2020 I start Energy-Nerve Theory.

Please refer to the next.

1. Signal-Nerve Theory, Old title What is Signal?
2. Quantum-Nerve Theory
3. Energy-Nerve Theory


Tokyo
12 July 2020
Sekinan Nerve

Thursday 28 July 2022

For WITTGENSTEIN Ludwig 2005-2009

 

For WITTGENSTEIN Ludwig

02/08/2014 10:22
For WITTGENSTEIN Ludwig0
 
Position of Language
 
 
 
Quantization1 is a cliff for consideration of language.
2 Mathematical interpretation of quantized language is now a first step to the theoretical ascent.
3 If there is not mathematics, next conjectures are impossible.
(i) Difference between word and sentence---Commutative and noncommutative ring
(ii) Continuation from word to sentence---Tomita’s fundamental theorem
(iii) Word’s finiteness and sentence’s infinity---Property infinite and purely infinite
(iv) Cyclic structure of word’s meaning---Infinite cyclic group
Meaning minimum2mirror language3 and mirror symmetry4 are inevitable approach to the study of language especially for language universals5.
 
[References]
0<WITTGENSTEIN Ludwig>
1<Quantized Language>
2<Meaning minimum>
4<Mirror symmetry>
5<Language universals>
 
Tokyo December 10, 2005
Now traveling to a northern more place from the encounter
Tokyo November 27, 2008 Revised
Tokyo March 24, 2009 Revised
Tokyo June 27, 2009 Revised
www.sekinan.org


Hatonosu Ravine, West Tokyo, 29 July 2014
 


Read more: https://srflnote.webnode.page/news/for-wittgenstein-ludwig/

Language stability and triangulated category

 

Language stability and triangulated category

 
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://srflnote.webnode.page/news/language-stability-and-triangulated-category/

In the 21st century, language will definitely become one of the most important theme and target of mathematics for us all

 

In the 21st century, language will definitely become one of the most important theme and target of mathematics for us all

 

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.

 
Language
 
 
Tokyo
8 February 2016

 



Read more: https://geometrization-language.webnode.page/products/in-the-21st-century-language-will-definitely-become-one-of-the-most-important-theme-and-target-of-mathematics-for-us-all/

Energy Distance Theory Conjecture 2 Geometry of Word

 

Energy Distance Theory Conjecture 2 Geometry of Word

 
Conjecture 2
Geometry of Word
 
 
 
[Conjecture]
Word is infinite cyclic group.
 
[Explanation]
(Preissmann’s theorem)
When (Mg) is connected Riemann manifold and sectional curvature of M is always KM < 0, non-trivial commutative subset of functional group of Mπ1(M) always becomes infinite cyclic group.
Preparatory proposition for Preissmann’s theorem
(Proposition 1)
When (Mg) and (Nh) are compact Riemann manifold and N is non-positive curvature KN≤0, arbitrary continuous map f ∈C0(MN) is free homotopic with harmonic map uC(M, N).
(Proposition 2)
When M is compact Riemann manifold, Ricci tensor of M is positive semidefinite RicM≥0 , is non-positive curvature KN≤0, and harmonic map is u : MN,  the next is concluded.
When N is negative curvature KN<0, u is constant map or map of u coincides with map of closed geodesic line.
Consideration for the theorem and propositions
1
m-dimensional C class manifold     M
Point of M     x
Tangent space of x     TxM
Inner product of TxM   gx
Coordinate neighborhood of     U
Local coordinate system of U     (x1, …, xm)
Function     gij : gx ( (∂/∂xi)x, (∂/xj)x), 1≤i, jm
gij is C class function over U.
Family of inner product     g = {gx}xM
g is called Riemannian metric.
When M has g, (Mg) is called Riemannian manifold.
2
Riemann manifold      (Mg)
M’s C class vector field    (M)   
Linear connection of M     ∇
XYZ∈X(M)
What ∇ and XYuniquely satisfy the next is called Levi-Civita connection.
(i) Xg(YZ) = g(∇XYZ) + g(Y, ∇XZ)
(ii) ∇XY -YX = [XY]
3
m-dimensional Riemann manifold (Mg)    M
Levi-Civita connection of M     ∇
XYX
R(XY) : = ∇XY - ∇YX - ∇[XY]
Map R : = X(M) ×X(MX(M) → X(M)
R(XYZ) : = R(XY)Z
R is called curvature tensor of M.
4
xM
2-dimensional subspace of tangent space TxM     σ
σ’s normal orthogonal basis on gx     {vw} {v’w’}
K(vw) = R(x)(vwwv) = gx(R(x)(vw)wv)
v’ = cosθv + sinθww’ = ∓sinθv±cosθw  (double sign directly used)
K(σ) : = R(x)(vwwv) = R(x)(v’w’w’v’)
K(σ) is called sectional curvature.
 
[References]
 
To be continued
Tokyo November 23, 2008
 
Postscript
[Reference November 30, 2008]
 
Tokyo
7 January 2018 Reprinted

 



Read more: https://geometrization-language.webnode.page/products/energy-distance-theory-conjecture-2-geometry-of-word/

Letter to Y, Of S.W. Hawking's THE CHRONOLOGY PROTECTION CONJECTURE 2018. Translated by Google 2022

  

Letter to Y, Of S.W. Hawking's THE CHRONOLOGY PROTECTION CONJECTURE 2018

06/08/2018 23:42

Dear Y,

 

Thank you for your email while you are busy.

 

I am also studying little by little for autumn.

As with anything, the more you do, the more things you don't understand.

 

It's also related to my main subject, so in relation to time,

I am now reading a 1991 academic lecture on the Chronology Protection Conjecture by Dr. Hawking, who died this spring .

The full text is also available in English at NTT Publishing.

The original title is THE CHRONOLOGY PROTECTION CONJECTURE.

I used to understand the word Chronology in the sense of chronology,

The historical order of time certainly does not reverse, so this word is appropriate.

I simply translated the time order as Time Order, but this would allow any order.

If you look at Shorter Oxford, the word first appeared in 1593, and it says The science of computing time or periods of time, which includes Latin and its original Greek. When Greek is written in alphabet, it becomes kronos- + logia, and I felt the historical depth of English from the etymology of the vocabulary.

 

Dr. Hawking is trying to demonstrate from a physics point of view that time does not reverse and that time machines cannot. He's not a mathematical method, so I'm calling it a hypothesis, but I think it's physically advanced.

 

I've been thinking about Imaginary Time for a while, and I've written a small paper from his dissertation, so I've always been curious about his views.

My Paper is:

 

In the fall, I would like to take the main subject, Quantum Group Language, which is a linguistic theory based on quantum groups in mathematics, which has continued since 2003, a little further .

Now it's preparatory work.

 

It's still fun to be able to clearly describe ideas in mathematics, hopefully.

There aren't many approaches to these languages, and they are pioneer-like and attractive.

 

Then how are you?

 

Cordially,

4 August 2018

SRFL

T.A.



Read more: https://srfl-lab.webnode.page/news/letter-to-y-of-s-w-hawkings-the-chronology-protection-conjecture-2018/

Letter to Y, Of S.W. Hawking's THE CHRONOLOGY PROTECTION CONJECTURE 2018

 

Letter to Y, Of S.W. Hawking's THE CHRONOLOGY PROTECTION CONJECTURE 2018

06/08/2018 23:42

Dear Y,

 

ご多忙の中、メールをありがとうございます。

 

私も秋に向けて少しづつ勉強をしています。

なんでもそうでしょうが、やればやるほどわからないことが増えてきます。

 

私の本題とも関連しますので、時間のことに関連して、

この春に亡くなられたホーキング博士の、時間順序保護仮説という、1991年の学術講演を今読んでいます。

NTT出版で、英文も全文載っています。

THE CHRONOLOGY PROTECTION CONJECTURE が原題です。

Chronologyということばは、私は年代順というような意味でこれまで理解していましたが、

時間の歴史的な順序は確かに、逆転はしませんので、このことばが適切なのですね。

時間順序を私は単純に Time Order などと訳していましたが、これではどのような順序も許容してしまうことになります。

Shorter Oxford を見ると、この語の初出は1593年で、The science of computing time or periods of time, と書かれていて、ラテン語とその元のギリシャ語が載っています。ギリシャ語をアルファベット表記にしますと、kronos-+logia となり、あらためて語彙の語源から英語の歴史的な奥深さを感じました。

 

ホーキング博士は、時間は逆転しない、タイム・マシンはできないということを物理学の見地から論証しようとしています。数学的な方法ではありませんので、仮説と表題にしていますが、物理的に高度の内容だと思います。

 

私もしばらくの間、虚時間 Imaginary Time のことを考えていましたし、博士の論考から小さなPaperをひとつ書いていますので、博士の見解はいつも気になっていました。

私のPaper は以下のものです。

 

秋になりましたら、本題の、2003年から継続する数学の量子群による言語論 Quantum Group Language をもう少し進めたいと思っています。

今は準備作業です。

 

観念的なものを数学で明瞭に記述できるのはやはり楽しいです、うまくできればですが。

こうした言語へのapproach は、あまりないでしょうし、pioneer的で魅力的です。

 

それではお元気で。

 

Cordially,

4 August 2018

SRFL

T.A.



Read more: https://srfl-lab.webnode.page/news/letter-to-y-of-s-w-hawkings-the-chronology-protection-conjecture-2018/

Tuesday 26 July 2022

​Letter to WPM Along the ridges of the mountains On Aurora Theory 3rd Edition 2 December 2019

 

​Letter to WPM Along the ridges of the mountains On Aurora Theory 3rd Edition 2 December 2019



Why climb mountain.
Climb for existence.
MIYATA Hachiro
Mountain photographer, Japan
– 2018

Letter to WPM  
Along the ridges of the mountains
On Aurora Theory

Dear WPM,
Thanks a lot for RTs and probably for your lasting love on language.
Now I am uploading Aurora Theory 2006 and its relevant papers to WordPress.
At this occasion, I will write some memories on Aurora Theory.
1
In August 2003, I stayed at Hakuba, Nagano, Japan, where Japan North Alps can be seen under the cerulean sky. I love the place for long time. Nagano is the place father and mother was born and grew up. So I also visited time to time, especially summer seasons escaping the heat at Tokyo. Ancestors’ land is the west from Hakuba over the one mountain range where Chikuma River flows north to Niigata area at where I enjoyed fishing in child days.
At this summer I would write over a paper to send a certain  international symposium’s secretariat to announce a theory in December 2003 at Nara, old capital of Japan in early 700s A.D.
But the theory is deadlocked at the minimal unit of language, which form cannot be seen in my mind.

One night I took a walk to renew my mind and dropped in a only-one-light-upped convenience store.
In the store I saw a leaflet of electric device. This was a opportunity to solve a question of the paper.
Inspiration The Time of Quantum
At that time, quantum was definitely put in my mind succeeding a manuscript written also at Hakuba’ s hotel in March 2003.
Manuscript of Quantum Theory for Language
2
But precise mathematical definition of quantum was not uncertain at that point in summer 2003.
Clear description of mathematical quantum was waited till 2008.
Kac-Moody Lie Algebra Note 2 Quantum Group

3
Aurora theory and Aurora Time Theory was written in 2006 at the premonition of quantum’s transcendentality for its  flexibility and freedom through Time in Language.

Thus the first, the second, the forth papers of Aurora Theory was presented at my Web in 2006.
1st
Aurora Theory Dictoron <Quantum and Trace> For FINKELSTEIN David
2nd
Aurora Theory  Dictoron and Aurora <Language is aurora dancing above us.> For SAEKI Shizuto
4th
Aurora Theory Dictoron as Language Quantum
Added from 2nd Edition
For quantum’s transcendentality on time in language, refer to the next papers.
Aurora Theory
Dictoron, Time and Symmetry
<Language Multi-Time Conjecture>
 [AT6]
Dictoron and Time [AT9]
Distance and Time
<Language Multi-Time Conjecture 3>   5th Time for KARCEVSKIJ
 [AT11]
Why Human Time Flows Fast and Slow on Occasion
 <Interlude for Multi-Time Conjecture>
 [IL1]
Aurora Time Theory
Time on Aurora [ATT1]
Imaginary Time and Imaginary Space   From HAWKING Stephen [ATT2]
Opened Time and Closed Time Revised   For WANG Guowei and DELBRÜCK Max [ATT4-2]
Added from 3rd Edition
It maybe that time contained in language is thought suspiciously. In Japan, of course in China, Chinese character is used till now, at least historically from Yin Dynasty, some 2400 years ago.
Chinese character is one of ideograms, almost of which are not used at present day by various reasons, such as not-easy to writing, typically hieroglyph at old Egypt.
It is not so questionable that these ideograms has time in their characters.
Fortunately we can verify through Chinese characters that they contain time in themselves or not.
But almost Westerner do not use ideograms now. So I wrote several papers to mainly Westers taking broad sense of ideograms, for example picture, pictograph, LATEX and so forth.
One question.
Do you think that picture contains time in it?
Now my relevant papers are arranged and titled to Ideogram Paper.
Refer to the next.
Ideogram Paper 1-16 With Addition
Ideogram Paper
1. On Time Property Inherent in Characters 2003
2. Ideogram 2005
3. Egyptian Hieroglyph Exhibition, Journey through the Afterlife Ancient Egyptian Book of the Dead by The British Museum 2012
4. ONO Shinobu and Bernhard Karlgren 2015
5. Essence of Language 2016
6. The Days of Decipherment 2016
7. The Days of Ideogram 2017
8. The Days of Ideogram Note added Edition 2017
9. The comparison between 2003 and 2017
From Chinese character’s meaning structure to Homological algebraic model of language universals 2017 
10. Time and Shape of Language from How is the time alive in language 2017
11. Connection between early paper’s quantum and recent paper’s geometry 7th edition 2017
12. Letter to Y. Of the century of language 2018
13.  Letter to Y. Of Broad Language 4th edition 2018
14. Determination of the concept, Broad Language 2018
15. Ars longa Seeing Masterpieces of French Landscape Paintings from the Pushkin State Museum of Fine Arts, Moscow 2018
16.Letter to Y. Of Broad Language 4th Text revised edition With Note 2019
[Addition]
The upper Ideogram Paper is now  placed at the basis of a new theory titled Quantum-Nerve Theory.
Refer to the next.
Quantum-Nerve Theory With References 2019
Added Note of The Days of Ideogram 2019
Added from 3rd Edition
Now above 16 papers, I present one invitational paper titled The Days of Ideogram 2017.




The Days of Ideogram ​​​Ideogram from hieroglyph to LATEX Symbol List Note added Edition
​The Days of Ideogram
​​​Ideogram from hieroglyph to LATEX Symbol List

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.
  1. Ideogram can contain rich information in small space. 
  2. Ideogram can show information at a glance.
  3. Ideogram can sustain information stably in long time*1-7.
  4. ​Ideogram has fertile capability to superb diversity of languages*8-5. 

2. Set theory
Probably in summer 1977, I was  designing for a paper on the sentence in language. The central part of the paper was connection between words or sentence, in which the logic of  language would be shown using the set theory as a simplified model of true and false. I was strongly influenced from Kurt Godel, Gaishi Takeuchi and Bourbaki*1-1. But this design was abandoned for my lack of mathematical basis keeping on.

3. Qing dynasty’s linguistics
In 1980s and 1990s I was lost in learning Chinese classical character theory, Xiaoxue, especially Qing dynasty for ideogram’s fundamental property*2-1. At this period I did not write any paper on language. I solely read WANG Guowei*1-2, WANG Yinzhi, DUAN Yucai and Qing dynasty’s linguists.

4. Time property in characters
In Autumn 2002 I got pneumonia and was hospitalized about 2 weeks, where I thought of 1970s’ dream, writing clear description on language universals by mathematics. The theme was as hard as ever. So, at the bed I thought the basis of language from a side of Chinese character’s classical approach which had vast heritage till Qing dynasty. I directed my attention to the character’s figure which had compound meanings containing time elements continuing from Yin dynasty’s hieroglyphic characters left on bones and tortoise carapaces some 2400 years ago. I thought that Chinese characters had containing time and its structure could be written by geometric approach once I had abandoned for difficulty. After leaving hospital, I wrote a paper titled On Time Property Inherent in Characters*3-1.  

5. Quantum elements 
In 2003 staying at Hakuba, Nagano, I wrote a rial paper on language universals from the viewpoint of physics. This was remained manuscript till now. The title was Manuscript of Quantum Theory for Language*3-2 for the time being. Because in summer 2003 I wrote the first paper on language universals from physics titles as Quantum Theory for Language*3-3 which was read at a conference held in winter  2003 of Nara Japan. 

6. Finite generative
Language probably begins from finite elements and generates.*3-6, 3-7 its world responding to outer world. I learned the concept of finite generative from von Neumann Algebra*4-1 at around 2006 and 2007. 


7. Structure and dimension
Language probably has structure, which details are unknown now for me. But several phenomena hints me the existence of structure containing dimension. Its example is shown at the Crete’s lie, on which I wrote a tiny paper titled as True-false problem of the Crete*3-8in 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

0
  1. Ideogram. 4 March 2005.
  2. Quantification of Quantum. 29 May 2004. 

1
  1. The Time of Language
  2. The Time of WANG Guowei
  3. The Time of Wittgenstein 
  4. The Time of Quantum
  5. The Days of Distance
  6. The days when I was thinking on Energy Distance Theory
  7. The Days of Decipherment
  8. The days of von Neumann Algebra
  9. The days between von Neumann Algebra and Complex Manifold Deformation Theory
  10. Language between Sergej Karcevskij and string theory, one century’s trace

2
  1. 40 years passed from I read WANG Guowei
  2. For WITTGENSTEIN Ludwig Revised with Symplectic Language Theory and Floer Homology Language
  3. Language between Sergej Karcevskij and string theory, one century’s trace Preface
  4. Karcevskij conjecture 1928 and Kawamata conjecture 2002

3
  1. On Time Property Inherent in Characters
  2. Manuscript of Quantum Theory for Language
  3. Quantum Theory for language 
  4. Prague Theory
  5. Distance Theory
  6. von Neumann Algebra 2 Note Generation Theorem
  7. von Neumann Algebra 3 Note 1 Properly Infinite
  8. True-false problem of the Crete
  9. Word as Infinite Loop Space
  10. Disposition of Language
  11. Distance of Word
  12. Flow of language
  13. Boundary of language
  14. At least three elements for language universals​​

4
  1. von Neumann Algebra
  2. Algebraic Geometry Language
  3. Derived Category Language

5
  1. Early Paper
  2. ​Early paper 2
  3. Early Paper 3
  4. Recent Paper
  5. Recent Paper 2
  6. Recent Paper 3

6
  1. Appendix / Language between Sergej Karcevskij and string theory, one century’s trace The 30th Anniversary of Sekinan Library Memorial Essay
  2. Genealogical Tree of Sekinan’s Paper Sixth Edition

7
  1. SRFL Paper
  2. Sekinan Study
  3. Twitter. Sekinan Library. Moments​​

Outer sites and publication
​8
  1. The Comprehensive LATEX Symbol List Scot Pakin 19 January 2017.
  2. The exhibition catalogue of The British Museum ANCIENT EGYPTIAN BOOK OF THE DEAD JOURNEY THROUGH THE  AFTERLIFE. Asahi Shinbun.
  3. Steven Snape. Decoding the stone. George Weidenfield and Nicolson Ltd. 1997.
  4. John Chadwick. THE DECIPHERMENT OF LINEAR B. Cambridge University Press. 1958.
  5. The exhibition  catalogue of A JOURNEY TO THE IMMORTALS : TREASURES OF ANCIENT GREECE.  Asahi Shinbun et al.  2016.
  6. Unicode® Technical Report #51 UNICODE EMOJI.
This essay is unfinished.

Tokyo
20 April 2017
Sekinan Zoho
[Note]
7 March 2018
From 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.
Read more: https://srfl-lab.webnode.com/products/the-days-of-ideogram-ideogram-from-hieroglyph-to-latex-symbol-list/




Added from 3rd Edition
The mathematical expression of Time itself was afterwards written at the papers titled Clifford Algebra.
Refer to the next.
Clifford Algebra
Note
From Super Space to Quantization
Anti-automorphism
Anti-self-dual Form
Dirac Operator
5 TOMONAGA’s Super Multi-time Theory
Periodicity
Creation Operator and Annihilation Operator
Conjecture
Meaning Product 
In these papers, the most directly refer to time is No. 5 paper, TOMONAGA’s Super Multi-time Theory .
This paper is also a survey of time from modern physics side, Schrodinger, Tomonaga and Dirac.
Please read this paper by the upper paperbottom’s PDF Edition which is no errata of Web-print-version.




Best regards,
T. A.
Tokyo
2 December 2019
SRFL Paper
P.S.
The latest work on quantum theory is shown at the next.
Quantum-Nerve Theory
​Abbr: QNT
Quantum-Nerve Theory With References
​Reference
Ideogram 1-16 With Addition
​References 2
 1. 
Manuscript of Quantum Theory for Language 2003-2019 / Newly revised edition
2.
From Quantum Theory for Language to Quantum-Nerve Theory / 16 July 2019 Edition
3.
What is signal? Total Edition  / 21 November 2018-23 April 2019
4. 
What is signal? Contents  / 24 April 2019