​How is the time alive in language? 2014

 

 

How is the time alive in language?

TANAKA Akio

1.
When one first hear the existence of time in language, he may doubt its certainty. But I have intuitively believe it since I learned the ancient Chinese inscription on bone ad tortoise shell (in Chinese called Jiaguwen). In my early 20s, I met with the book of Chinese modern linguists, WANG Guowei, this belief changed the conviction. His lifework book Guantangjilin is hard to read till now.  But some papers in it are always inspires me by his deep and vast insight to character, language and history of ancient China. He also wrote fine criticism on Chinese pre-modern poem Ci.The title is RenjianCihua. The book is one of my favourite books of Chinese literature. People sometimes say that he was the highest genius after Song Dynasty, 1,000 years.In 2003 I wrote a tiny paper hinted by WANG's paper. It was the first paper for me that I directly faced the time inherent in inscription using Jiaguwen's update linguistic results. The title is " On Time Property Inherent in Characters".

• On Time Property Inherent in Characters / 28 March 2003
  
  

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.

•     Quantum Theory for Language / 15 January 2004
  
  

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. 

•          Complex Manifold Deformation Theory / 2008-2009
  
  

Above all, the first paper in this group, I first defined the concept, distance by complex manifold.

•          Distance of Word /  30 November 2008
  
  

The concept of distance was one of the most important themes on language, so I at early times wrote the intuitive paper, "Distance Theory".

•          Distance Theory / 5 May 2004
  
  

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".

•       Time of Word / 1 January 2009 
  
  

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.

•          Symplectic Language Theory / 2009
  
  

    In the group, a paper focused on mirror phase on language became one peak for my writing.

•          Homological Mirror Symmetry Conjecture by KONTSEVICH​ / 26 April 2009
  
  

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.

•           Floer Homology Language / 2009
  
  

In this group, the eighth paper was dealt with the quantization and discreteness of language.

•           Discreteness of Language / 19 July 2009
  
  

      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.

•           Prague Theory / 2 October 2004
  
  

 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.

•           Word as Infinite Loop Space / 6 December 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.

•           Arithmetic Geometry Language (AGL) / 2013
  
  

From these four papers, I concisely extracted the next three conjectures.

•           Dimension Decrease Conjecture
  
  
•           Synthesis Conjecture
  
  
•           Reversion Conjecture
  
  

At these conjectures, time inherent in language is in the basis of describing dimension, synthesis and reversion. The process of leading to the conjectures is over viewing the next.     

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

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. 

• 40 years passed from I read WANG Guowei / 16 November 2013
  
  

• Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij's paper "Du dualisme asymetrique du signe linguistique" / Print, 2012
  
  

Tokyo
26 November 2014
SIL

To Winter RI Ko. 14 John Peabody Harrington, Roman Jakobson, FUKAYA Kenji, Maxim Kontsevich, ZHANG Binglin and Roger Penrose. Translated by Google translate 2020

 

05/05/2020 18:29

To Winter
RI Ko
2015

14  
John Peabody Harrington, Roman Jakobson, FUKAYA Kenji, Maxim Kontsevich, ZHANG BInglin and Roger Penrose

From author:
This text’s translation by Google translate is a little hard to be accurate at the present, especially on mathematical explanation 

You can see the whole city from the library on the hill. The east side of the third floor is a computer room. The internet was always connected there, and I could use any table freely. I often spend my holidays near the window. A group of tall blue-green buildings rises to the northeast of the left side of the window. Seen from here on the hill, it is much higher. Only there is towering above the sky. Immediately south, there should be A’s home. Did the bulbul hit a tall building like that? The glass walls were distant and dull, reflecting the light of the autumn afternoon. 

When I was cleaning the room where the birds were gone for the first time in a while, I found some furrowed flock in the corner. The soft wings floated in the air for a while when released. Have you lived in the city because of your childhood? I wished that I was now resting slowly in the grove of the hills. A created Web pages and Dreamweaver, but since the amount has gradually increased, I switched to Expression Web from the middle. I used Office for documents at first, but soon I switched to Zoho.

In this way, I was able to quickly write small mathematical expressions using LaTex. When Backup was run automatically using SugarSync, all traces of A were on Cloud. The document was written in English. Regular sentences other than mathematical expressions are relatively easy to write with a limited vocabulary. This could lead to someone seeing somewhere. I had little hope, but there was little response. 

Of course, I thought it would be nice if there could be one or two people in this wide world who could sympathize with me, but that didn’t bother me that much. I just keep writing. There is no guarantee that there will be someone like John Pepody Harrington, who continued to record the American Indian languages. 1920 The photographs in the Smithsonian Institution’s collection, which are doing field research around the year, look somewhat like the pioneers of the West. It’s okay to wait quietly for the future of Harrington in the corner of the city. 

It was a fun task to think of a language containing time as a possibility using a model. However, in reality, it is rarely something that can be created, such as an original one. I couldn’t exceed the conventional idea. He arranged the work procedure little by little. First create a simple model. Select the shape suitable for the model. How much is the figure written? 

According to Kenji Fukaya, the geometry was “a group of groups and the space in which it acts”. It was Fukaya’s charm that he was able to briefly confirm and look at the fundamental things. By referring to Jacobson’s “semantic minimum”, a new geometric “minimum of meaning” is set, and the time t is included as a meaning by moving the time t in the closed interval. Defined the geometric word.

I repeated this direction many times with different levels of geometry. The universality of language was thought to be closely related to the invariant of mathematics. In Fukaya’s book, I learned that the quantum cohomology ring can be obtained from the Gromov-Witten invariant and the Gromov-Witten potential can be obtained. Language approached mathematics and physics. It has become possible to logically check the symmetry that has long been a concern. Under certain assumptions, the character of various languages can be inspected as a model from, for example, one figure or manifold. One of the centers was homological mirror symmetry, which was proposed by Kontsevich.

When I got tired of working in the library, I went out to the rooftop. The city, which spreads under the dark maroon autumn sky, conveyed the grandeur of human activities. The sounds of distant cities echo like a chord. Are people flying in this city as birds are flying in the sky? Just as birds sometimes crash into the ground by colliding with the turquoise glass of tall buildings, will people crash into the ground and crash somewhere?

 I once read a story about birds in the book Shorin no Fubun. “According to the poem of the 3rd year of the Emperor Hansho, a bird of five colors, it passes over the prefectures in which it belongs.” It seems that 10,000 birds of five colors flew in the sky. As for the beginning, I continue to cite Chinese books. According to the poem’s third year of honor, he gathered New Year’s lords, Otori, Emperor and Kanro to the Kyoto teacher, and according to the flock of birds, the findings of the Han book were true.

The contents of this Chinese book, in which 10,000 birds gathered in search of it, are true. It is unknown whether Shorin believed in these statements. However, according to Shorin’s habit, he might have believed it as a natural thing. 

Autumn flowers were dancing in the strolling garden on the roof of the library. White autumn Ming chrysanthemum, yellow Maru chrysanthemum, Nozoku chrysanthemum Soothing Hottogigisu and the white and white Arissum flowers crawling on the ground. Sky blue salvia, red cherry sage, purple rosemary and light blue basil. Dark blue Saintpaulia, white sapphinia, crimson geranium bowls and hanging. Huquera, Drachina consenna, Sansevieria houseplant. Spatti is also rich in green, and the red sea urchin is already red. Various sasanqua that began to inflate the buds, the last cosmos flowers that sway in the wind Winter clematis that has been quite tall, large leaves on the grape rack with few remaining, and a large red or white large ball swaying occasionally in the strong wind . 

If you look closely, you can also see the pink bokeh flowers that change the season. Shala beautifully turns red, and dogwood turns the leaves brown. On the other hand, rhododendrons had already inflated the buds considerably. Autumn was getting deeper. 

You can hear the sound of the city line riding on the wind. How is K doing? Well, let’s make a dedication to the document. For familiar days with K. I continued to write documents when I got home. The linguistic space including time gradually expanded from a straight line to a plane and from there to a sphere. Attracted by the work of Roger Penrose, I made a projective model. 

As I was thinking about it at midnight, I thought it would be beautiful if the language danced in the sky like an aurora. A complex plane is created by mapping all complex numbers to planes, as if all real numbers were mapped to straight lines. A complex number defined by two real numbers is placed on the plane as a language unit, and it is called a language point. Establish a vertical third coordinate axis from the origin of the plane and make a sphere with a unit radius centered on the origin. The spheres intersect at a radius of 1 on the new coordinate axes. If that point and a linguistic point on the complex plane are connected by a straight line, when the linguistic point has a distance of 1 or more, it intersects with the sphere at one point. When the distance is less than 1, the linguistic point is inside the sphere and does not intersect the sphere. 

This shows the limits of the language. Ordinary language points are projected on the spherical sky when the distance exceeds 1. The projection is called aurora. Language points at infinity converge on a sphere on the Z axis. You can capture an infinite number of languages in a finite way. A straight line connecting two points on the complex plane draws an arc in the spherical sky. The two straight lines form two arcs in the sky, and connecting four points creates a distorted quadrilateral in the sky. 

If we model the points in the sky as words, arcs as sentences, and quadrilaterals as sentences, the language will emerge there. The language becomes Aurora and dances in the sky. Language is aurora dancing above us.

 

Coffee shop named California 2012

 

Coffee shop named California

TANAKA Akio

From Print 2012, Chapter 10

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.

Source: Tale / Print by LI Koh / 27 January 2012 

References: 

1. Under the Dim Light / 1 August 2012
2. Road to Language Universals / 31 December 2012
3. Half Farewell to Sergej Karcevskij and the Linguistic Circle of Prague with References / 23 October 2013

Tokyo
23 February 2015
29 July 2016 Add image
Sekinan Archive

Read more: https://srfl-collection.webnode.com/products/coffee-shop-named-california-with-image/

Language and I 2017

 

Language 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.

TANAKA Akio

Tokyo
26 June 2017
Sekinan Library

Connection between early paper's quantum and recent paper's geometry 7th edition 2017

 

Connection between early paper's quantum and recent paper's geometry 7th edition

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

 

7th edition

 

TANAKA Akio

 

0.

Autumn in 2002, I entered hospital by contracting pneumonia, at where I thought that learning on Chinese characters heretofore seemed to be able to used for the model of language universals. Spring 2003 at Hakuba, Nagano I wrote a trial paper titled On Time Property Inherent in Characters, that was focused on the time inherent in characters using the Chinese written language appeared in typical philological text of the Five Classics of Confucianism. After all, this paper led me the long road to try solving language universals in language.

 

1.

On language universals my early papers are frequently concentrated in quantum's situation applied from theoretical physics. But at recent papers quantum's themes are almost disappear at least from the surface of theoretical progress.

This notable difference  is occurred through language's whereabouts, that is generally called space at scientific field. One of my important quest has been  at this whereabouts description.

Physical space is very hard to describe clearly by my ability. Probably I have not been able to understand physical space for using and observing the situation of language models. On the contrary mathematical spaces are very clear by using minimum axioms and theorems.

 

2.

Another quest is occurred from natural language's quality.

Natural language consists of physical elements - voice and hearing, writing and seeing. But what being carried by upper elements are going over physical world - thought, remembrance, feeling and so forth. I ever wrote these situation using a sample that is a changing apple passing in the time.

This quest is paraphrased in concrete - physics and abstract - mathematics.

 

3.

Geometry is a field of mathematics, which I select because of being easily visualised thinking for my approach to the language problems. Geometry hands out intuitive ideas to me not using any formulas, for example even at the time of tea.I consent that geometry is the queen of mathematics. I also remember the saying of Roger Penrose, "We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics."

 

4.

At the geometry field, now I am charmed to W. T. Thurston's geometrization concept, that opens 3-dimensional manifold to hyperbolic geometry's model. This model will probably hint me the new landscape for language models, that will show us more exhaustive language universal theory.

5.
What now I say as language universals is energy ,distance, dimension and so forth.
Brief comments on the three themes are time to time mentioned through my milestones to the upper steps for the research.

6.
The hardest theme has been in energy all through the research. But Perelman has opened the narrow and steep lane to the aim by physics-mixture mathematics approach,  especially thermodynamics-based means. It was a surprise which way was seemed to be the very hard way or despaired way at my present ability.
  

 

References

0.

1. Manuscript of Quantum Theory for language
2. On Time Property Inherent in Characters

1.

1. The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 
2. Quantum Theory for Language
3. Property of Quantum
4. Quantification of Quantum
5. Homology Generation of Language
6. Homology Structure of Word

2.

1. Presupposition on Natural Language
2. Macro Time and Micro Time
3. Sayama Assumption on Language   
4. True-false problem of the Crete The example of what language has structure

3.

1. For me geometry is the only one expression to describe the universal language containing the time which is also one of the meanings
2. Mathematics and sculpture
3. Roger Penrose. Understanding the laws of the universe
4. Description 

4.

1. Geometrization Note 1 - Note 2
2. Hyperbolic language Connection of Words

 

5.

1. Road to language Universals
2. At least three elements for language universals 
3. Mathematical description for three elements of language universals

5-2

1. The days when I was thinking on Energy Distance Theory 
2. Energy Distance Theory Note 1 Energy and Distance
3. Floer Homology Language ​ ​Note 1 ​ Potential of Language

5-3

1. Papers on language dimension  In chronological order

5-4

1. Distance Theory Algebraically Supplemented / Brane Simplified Model 
2. Distance Theory Algebraically Supplemented / Brane Simplified Model / Distance 

6.

1. Interpretation on Perelman's work, Ricci flow and Geometrization conjecture by KOBAYASHI Ryoichi 
2. Work of Perelman 
3. The books on Grisha Perelman
4. Perelman's Approach 1
5. Perelman's Approach 2

 

This paper is unfinished.

 

Tokyo

8 November - 13 November 2017

Geometrization language

Read more: https://srfl-lab.webnode.page/products/connection-between-early-papers-quantum-and-recent-papers-geometry-7th-edition/

Quantum-Nerve Theory With References 2019

 

14/10/2019 17:39

 

Quantum-Nerve Theory
Abbreviation  :  QNT

 

TANAKA Akio

 

 

 

Part 0

Cicerone to QNT
 

 

Macro Time and Micro Time  2013
 

For WITTGENSTEIN Ludwig  Position of Language  2005 - 2014

 

Connection between early paper's quantum and recent paper's geometry  7th edition

 2017

 

TANAKA Akio

 

0.

Autumn in 2002, I entered hospital by contracting pneumonia, at where I thought that learning on Chinese characters heretofore seemed to be able to used for the model of language universals. Spring 2003 at Hakuba, Nagano I wrote a trial paper titled On Time Property Inherent in Characters, that was focused on the time inherent in characters using the Chinese written language appeared in typical philological text of the Five Classics of Confucianism. After all, this paper led me the long road to try solving language universals in language.

 

1.

On language universals my early papers are frequently concentrated in quantum's situation applied from theoretical physics. But at recent papers quantum's themes are almost disappear at least from the surface of theoretical progress.

This notable difference  is occurred through language's whereabouts, that is generally called space at scientific field. One of my important quest has been  at this whereabouts description.

Physical space is very hard to describe clearly by my ability. Probably I have not been able to understand physical space for using and observing the situation of language models. On the contrary mathematical spaces are very clear by using minimum axioms and theorems.

 

2.

Another quest is occurred from natural language's quality.

Natural language consists of physical elements - voice and hearing, writing and seeing. But what being carried by upper elements are going over physical world - thought, remembrance, feeling and so forth. I ever wrote these situation using a sample that is a changing apple passing in the time.

This quest is paraphrased in concrete - physics and abstract - mathematics.

 

3.

Geometry is a field of mathematics, which I select because of being easily visualised thinking for my approach to the language problems. Geometry hands out intuitive ideas to me not using any formulas, for example even at the time of tea.I consent that geometry is the queen of mathematics. I also remember the saying of Roger Penrose, "We cannot get any deep understanding of the laws that govern the physical world without entering the world of mathematics."

 

4.

At the geometry field, now I am charmed to W. T. Thurston's geometrization concept, that opens 3-dimensional manifold to hyperbolic geometry's model. This model will probably hint me the new landscape for language models, that will show us more exhaustive language universal theory.

5.
What now I say as language universals is energy ,distance, dimension and so forth.
Brief comments on the three themes are time to time mentioned through my milestones to the upper steps for the research.

6.
The hardest theme has been in energy all through the research. But Perelman has opened the narrow and steep lane to the aim by physics-mixture mathematics approach,  especially thermodynamics-based means. It was a surprise which way was seemed to be the very hard way or despaired way at my present ability.
  

 

References

0.

1. Manuscript of Quantum Theory for language
2. On Time Property Inherent in Characters

1.

1. The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals 
2. Quantum Theory for Language
3. Property of Quantum
4. Quantification of Quantum
5. Homology Generation of Language
6. Homology Structure of Word

2.

1. Presupposition on Natural Language
2. Macro Time and Micro Time
3. Sayama Assumption on Language   
4. True-false problem of the Crete The example of what language has structure

3.

1. For me geometry is the only one expression to describe the universal language containing the time which is also one of the meanings
2. Mathematics and sculpture
3. Roger Penrose. Understanding the laws of the universe
4. Description 

4.

1. Geometrization Note 1 - Note 2
2. Hyperbolic language Connection of Words

 

5.

1. Road to language Universals
2. At least three elements for language universals 
3. Mathematical description for three elements of language universals

5-2

1. The days when I was thinking on Energy Distance Theory 
2. Energy Distance Theory Note 1 Energy and Distance
3. Floer Homology Language ​ ​Note 1 ​ Potential of Language

5-3

1. Papers on language dimension  In chronological order

5-4

1. Distance Theory Algebraically Supplemented / Brane Simplified Model 
2. Distance Theory Algebraically Supplemented / Brane Simplified Model / Distance 

6.

1. Interpretation on Perelman's work, Ricci flow and Geometrization conjecture by KOBAYASHI Ryoichi
2. Work of Perelman
3. The books on Grisha Perelman
4. Perelman's Approach 1
5. Perelman's Approach 2

 

This paper is unfinished.

 

Tokyo

8 November - 13 November 2017

Geometrization language

 

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

 

 

Part  1

Making nerve's mathematical model
 

 

What is signal? The existence that generates language

Preface, Preparation, Preparation 2, References, Main Issue 1-5,  Anticipation - FAQ

and Comment
Contents Edition

21 November 2018 - 24 April 2019

TANAKA  Akio

Sekinan Library

Tokyo

 

Original Title 

 

What is signal? A mathematical model of nerve  ​

 

For father and mother

 

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

 

 

 

 

 

 

 

 

 

Quantum-Nerve Theory

 

Part 2

Physical mathematics from quantum group

 

 

0

Inspiration The Time of Quantum 2008

 

1

Quantum Theory for Language 2004

Place where Quantum of language Exists 2004
Frame-Quantum Theory 2005

Frame-Quantum-Time Theory 2005

Quantum Warp Theory Warp 2005

Quantum Linguistics Solidity and Flexibility 2006

Quantum Language Substantiality of Language 2006

 

 

2

1.Clifford Algebra Note 1 From Super Space to Quantization 2008

2. Kac-Moody Lie Algebra Note 2 Quantum Group 2008

3. Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH​ 2009

4. Floer Homology Language Note 7 Quantization of Language​ 2009

5. Floer Homology Language Note 8 Discreteness of Language​ 2009

6. Simplicial Space Language  Composition of Word 2013

 

3

1. Floer Homology Language 2009

2. Homology Structure of Word 2009

3. Quantization of Language 2009

4. Discreteness of Language 2009

5. Proto Arithmetic Geometry Language 2009

6.Language, Word, Distance, Meaning and Meaning Minimum 2009

 

 

4

1. Manuscript of Quantum Theory for Language Note added 2003

2. Quantum Theory for Language 2004

3. Quantum Theory for Language  Theoretical Summarization and Problem in Future 2004

4. Noncommutative Distance Theory  Note 2  C*-Algebra 2007

5. Kac-Moody Lie Algebra 2008

Read more: https://srfl-paper.webnode.com/news/quantum-nerve-theory-2019/

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Part 3 
Basic Paper

 

 

Kac-Moody Lie Algebra

Note 2

Quantum Group

 

TANAKA Akio

 

 

1

Base field     K

Finite index set     I

Square matrix that has elements by integer     A = ( a_ij )_{i, j ∈ I}

Matrix that satisfies the next is called Cartan matrix.

i, j ∈ I

(1) a_ii = 2

(2) a_ij ≤ 0  ( i ≠j )

(3) a_ij = 0 ⇔ a_ji = 0

2

Cartan matrix     A = (a_ij)_i, j ∈I

Family of positive rational number    {d_i}_i∈I

Arbitrary i, j∈I    d_ia_ij = d_ja_ji

A is called symmetrizable.

3

Finite dimension vector space     h

Linearly independent subset of h     {h_i}_i∈I

Dual space of h     h*= Hom_K (h, K )

Linearly independent subset of h*     {α_i} _i∈I

Φ = {h, {h_i}_i∈I, {α_i} _i∈I }

Cartan matrix A = {α_i(h_i)} _{I, j∈I}

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

4

Symmetrizable Cartan matrix    A = (a_ij)_i, j ∈I

Fundamental root data     {h, {h_i}_i∈I, {α_i} _i∈I }

E = α_i ⊂h*

Family of positive rational number     {d_i}_i∈I

d_ia_ij = d_ja_ji

Symmetry bilinear form over E     ( , ) : E×E → K     ( (α_i ,α_j ) = d_ia_ij )

The form is called standard form.

5

n-dimensional Euclid space    Rⁿ

Linear independent vector     v₁, …, v_n

Lattice of Rⁿ     m₁v₁+ … +m_nv_n     ( m₁, …, m_n ∈ Z )

Lattice of h     h_Z

6

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

(Φ, ( , ), h_Z )

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

 i ∈ I

(1)  ∈ Z

(2) α_i ( h_z ) ⊂ Z

(3) t_i :=  h_i ∈ h_z

7

Vector space over K     A

Bilinear product over K     A×A → A

When A is ring, it is called associative algebra.

8

Integer     m

t similarity of m    [m]_t

[m]_t = t^m-t^-m / t- t^-1

Integer   m, n   m≧n≧0

Binomial coefficient     (^m_n)

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

t similarity of (^m_n)    [^m_n]_t = [m]_t! / [n]_t! [m-n]_t!

[^m₀] = [^m_m]_t = 1

8

Integer fundamental root data that has Cartan matrix A = ( a_ij )_{i, j ∈ I}

      Ψ = ((h, {h_i}_i∈I, {α_i} _i∈I ), ( , ), h_z )

Generating set     {K^h}_h∈hz ∪{E_i, F_i}_i∈I

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

(1) k^hk^h’ = k^h+h’     ( h, h’∈h_Z )

(2) k⁰ = 1

(3) K^hE_iK^-h = q^αi(h)E_i    ( h∈h_Z , i∈I )

(4) K^hF_iK^-h = q^αi(h)F_i   ( h∈h_Z , i∈I )

(5) E_i F_j – F_jE_i = _ij  K_i - K_i^-1 / q_i – q_i^-1     ( i , j∈I )

(6) ^p [^1-aij_p]_qiE_i^1-aij-pE_jE_i^p = 0     ( i , j∈I , i ≠j )

(7) ^p [^1-aij_p]_qiF_i^1-aij-pF_jF_i^p = 0     ( i , j∈I , i ≠j )

 

[Note]

Parameter q in K is thinkable in connection with the concept of at the paper Place where Quantum of Language exists / 27 /.

Refer to the next.

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

 

Tokyo February 9, 2008

 

Sekinan Research Field of Language

 

www.sekinan.org

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

 

 

 

 

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References

 

 

Manuscript of Quantum Theory for Language  2013
 

​Language between Sergej Karcevskij and string theory, one century's trace  2016
 

 

 

Ideogram Paper  2003-2018
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

 

 

Overview Paper  2013-2017

 1. In the 21st century, language will definitely become one of the most important themes and targets of mathematics for us all 2016

2. Operad Meaning Theory From Cell to Operad Revised Edition 2013

3. Connection between early paper's quantum and recent paper's geometry 7th edition 2017

4. Karcevskij conjecture 1928 and Kawamata conjecture 2002 / I briefly wrote about the conjecture 2017

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

 

 

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Tokyo
14 October 2019
SRFL Paper


 

 

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