Thursday 25 April 2024

Pre-history for Quantum Group Language

 


Pre-history for Quantum Group Language



TANAKA Akio


................................................................................................................
 
 
Main paper
1. Kac-Moody Lie Algebra Note 2 Quantum Group 2008
2. Symplectic Language Theory Note 6 Homological Mirror Symmetry Conjecture by KONTSEVICH​ 2009
3. Floer Homology Language Note 7 Quantization of Language 2009
4. Floer Homology Language Note 8 Discreteness of Language​ 2009
5. Simplicial Space Language  Composition of Word 2013
 
 
................................................................................................................
 
 
Basic paper
1. Manuscript of Quantum Theory for Language Note added 2003
2. Quantum Theory for Language 2004
3. Noncommutative Distance Theory  Note 2  C*-Algebra 2007 
4. Kac-Moody Lie Algebra 2008 
 
 
................................................................................................................
 
 
Overview Paper
1. In the 21st century, language will definitely become one of the most important theme and target of mathematics for us all 2016
2Operad 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 model of language universals  2017
6.  Mathematical description for three elements of language universals  2017
 
 
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Concept Paper
 
1. Letter to Y. Of the century of language 2018
2. Letter to Y. Of Broad Language 4th Edition 2018
3.  Determination of the concept, Broad Language 2018
 
 
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Tokyo
16 February 2018
SRFL Lab

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About from 1980s

 


About


TANAKA Akio

SRFL Sekinan Research Field of Language was established in 2003 for the study on language universals, that was the core theme since my youth time some 40 years ago in the 1970s. But real start was much later in the late 1980s.

In 1986 I established the Sekinan Library for the base of study at Tachikawa, Tokyo. At that time my main theme was declined to the study of old Chinese character’s classical semantics using the traditional study of the form of characters reading Qing Dynasty’s WANG Guowei. The study from the direction had not given me so rich results. I at the same time read some mathematical books influenced from Bourbaki that was the big stream in 1970s in Japan. Set theory represented by Godel was also the favourite at the time.

In 1990s I determined the direction of study only to language universals taught from CHINO Eiichi, one of the modern typical philologists of Japan. He taught me almost all the aspects of European philology that were unknown for me. In the various themes he gave me, the most impressive was the existence of the Linguistic Circle of Prague. Above all Sergej Karcevskij was overwhelmingly deep and moving. But Karcevskij’s approach was seemed to be intuitive and far from clear descriptiveness.

I began to learn the theme hinted by Karcevskij while learning Godel, Bourbaki and Wittgenstein that was also gave me the big influence form the age 20s. I had frequently read Wittgenstein’s TRACTATUS. But my base of math was so poor and never became the descriptive use for language’s delicate phases. So I again restarted math from geometry that gave the most familiar and clear image for me. My intuitive image and basic math description were seemed to be able offer in nearly millennium days.

In spring 2003 I knew the application paper for the international symposium held by a certain institute. I arranged the short paper for it till early summer and sent it. The paper was happily adopted as one of the language and literature section of the symposium. The paper’s title was Quantum Theory for Language. It was again arranged next year 2004 as the title Quantum Theory for Language synopsis.

The establish date of Sekinan Research Field of Language was 23 August 2003, that was the date of completion of proto-conceptive paper of Quantum Theory for Language at the hutte in Hakuba, Nagano. Now the time passed rapidly 10 years. All things are now very dear for me with fine landscape of Japan Alps.

Tokyo
14 August 2013
Sekinan Research Field of Language


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Language and I. 2017

 

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

Sunday 21 April 2024

 DUAN Yucai and WANG Guowei

For the memory of Book shop streets at Kanda, Tokyo

From Author;
This essay is translated by Google.
So ambiguous sentences are seen.
I humbly beg your pardon.
Original text is Japanese.
Refer to the next please.

https://hillswest.blogspot.com/2024/04/duan-yucai-and-wang-guowei.html


It was a sunny Sunday, so I took the tram and went to the used bookstore district. After walking along the wide main road for ten minutes, you will enter a used bookstore district. The ginkgo trees on the street are still a little early in their leaves turning yellow. The brown brick buildings on either side blend in with the old cobblestone sidewalks. Once upon a time, I took the City Line, got off at the old D station, and headed south along the cobblestone pavement into the used bookstore district. So it's easier now. Just south of the tram stop is N Bookstore, a Chinese book store that I often go to. I find it easiest to walk as a routine, so before I knew it, I ended up stopping at the same bookstore often. N Bookstore is customary for bookstores around here, with a narrow frontage and a long back. There are two aisles and four rows of bookshelves. There is a clerk at the very back. Once before, he came across a book that he vaguely remembered and asked what it had in stock. Then, a thick catalogue was handed to me without a word, which caused me some trouble. Since then, I have not asked questions carelessly. I've looked all around the entrance, so today I'm going to go inside. It takes a while for my eyes to adjust to the dim light. A large, old, bespectacled clerk continues to work silently on the package, probably to be shipped to the library. The slips that were left there are listed with unknown book titles. A moved out of the way and decided to look at the bookshelf right in front of it. I reached for the oracle bone dictionary on the pale grey cover of a large volume that was easily visible in the middle row. It feels heavy when you pick it up. It has a unique oil smell. There may not be many true oil-sealed books like those of olden days, but Chinese books have a unique sense of him. Inside, there is a black frame with vertical ruled lines, and handwritten letters are printed on them. The lettering is not that bad. Many handwritten letters are so skilful that they are difficult to read, but this one is manageable. The preface is long, so if you look at the end, it says that it took eight years to create this dictionary. In the catalogue after the preface, there are oracle bone characters for headings. Looking at the text, there are quite a few that are written as ``the shape of the letters is quite unknown'' or ``the meaning is unknown.'' He decided to buy her because she was honest and likable. It was inconvenient to walk if it was this heavy, but I didn't want to stop by again on the way home, so I just bought it. If you go a little south on the opposite sidewalk, you'll find an old two-story coffee shop. The first floor is like an office, and going up the stairs is a store. Since I left without having lunch, I decided to take it easy. There are always very few customers. I think this is okay, but he's still here. I look down from the window and see people rushing along the sidewalk. Perhaps he is from a bookstore, as he pedals a sturdy bicycle with a large bamboo carrier attached. he asked as the tram passed by. This scenery has not changed for a long time. He has wandered here alone like a rhinoceros. He became interested in oracle bone script a long time ago. The origin of anything is fascinating. This is where writing began, and that alone was enough evidence. After that, I spent some time reading introductory books and explanations. A certain concept, the shape that represents it, and its deformed depiction change with the times. But soon I wondered what lay before the beginning. Nothing. What happens when you go to a place where there is nothing? Concepts become increasingly simple and childish, and there is nothing beyond them. Once I thought about it, I didn't feel like continuing. Then I moved, and some of the books I had collected were lost. However, recently I have become concerned about oracle bone characters again because of the fireworks prints. As I was thinking about the flow of the screen, I realized that time was inherent in the shapes, and the oracle bone characters showed this. In the print, fireworks are launched and opened one after another. This is repeated in infinitely small prints. You could say that it happened within a closed period of time. I thought that this kind of closed time might exist in the written word as well. He was once looking at Guantang jilin in the Kingdom of Wei, and he came across a sentence. It was written about the character ”``gen''``(亙). This character has the meaning of "to cross'' or "to last forever". WANG Guowei says that in the oracle bone script, the two horizontal lines drawn up and down are the banks of the river, and between them is a small crescent-shaped boat, which goes back and forth between the two banks. SO the meaning became "to be repeated.'' When he felt that WANG Guowei had clearly demonstrated the immanence of time in kanji as a structure, he was struck by her precise reasoning, but at that time he was completely lost. Now, with the prints of fireworks, it has been brought back to light. When he returned to Guantang jilin during his wandering days, he could barely understand a part of it, but there was a feeling of hope shining like a ray of straw for him. . That has now become a reality. In the Guantang jilin, the character ``west'' indicates a bird's nest, and in the another paper, the character ``chu'' indicates that the flag is waving in the same direction in the wind. . That is, the birds return to their nests at sunset, and the flag flutters in the wind at the centre of the group. Time truly flowed through the words. In particular, the character shape for "zhong" (中), in which the flag flutters from side to side, is a phenomenon that cannot occur in the same wind, and the character form is said to have been erroneously copied and to be a ”wei” (譌)character. All of the texts in WANG Guowei are relatively short, but each piece of information in the small annotation is filled with dazzling and sharp insights that evoke a vast historical reality behind them. Even in literature, we can say in fine detail in human speech, the sounds in the air, the colons in the sky, the shadows in the water, the image in the mirror, the will is limitless because words are exhausted. It touches on the finiteness of language and the infinity of meaning. He also says that the five characters in the phrase "drifting light to moisten the light"' capture the spirit of Spring grass. He was born in 1877 and died in 1927. Did he live in the modern era with his honed talent, or did he himself create the modern era? When he returned to his room, he read through the dictionary he had picked up, and was drawn to the oracle bone character for "yu"(育). It is clear that the upper part of this character represents a woman giving birth, and the lower part represents a child being born. In the old form, the child is therefore written upside down. Some documents clearly show amniotic fluid at the time of birth. In other words, the original meaning of this character is childbirth itself, but care begins immediately after birth. Therefore, it was written that the meaning of "to grow"' appears. Considering the concept of time inherent in this character, we can understand him from preparation for childbirth to childbirth itself to child rearing. I was curious about this character, so I took a look at the explanatory annotations for the Duan Yucai, which WANG Guowei taught most in elementary school, and found that since an upside-down child is not good, it has the meaning of making it good. It was written that. Although the explanation retains some traces of the original material in the ``upside-down child'' part, it is abstract as a whole, and combines the original material's figures showing the specific process of childbirth with the idea that there is something inherent in it. It had become quite distant from the time when it was revealed. Duan Yucai, a rare scholar, died in 1815. The oracle bone script discovered in 1899 had never been seen before.

April 04, 2024 Reprint

48 Letter

 

48 Letter

   This letter is translated by Google. So there are ambiguous expressions. 
   I humbly beg your pardon.
48
   
    I believe that Kenichi Yoshida was the one who said that time passes quietly when reading a book of letters, but that is probably the core of literature. So what I would like to add here is only in the vicinity. My conclusion is that literature is a defence. The defence is against what we call the heart, the hardness, the life, and so on.


 The literature referred to here is not limited to the so-called literature represented by poetry and novels, but also sometimes extends to newspaper fragments and advertisements. When I heard that a soldier during the war read and re-read the efficacy of his medicine over and over again, I felt the misery of war mixed with a faint sense of peace, and at the same time, I felt a sense of peace amidst the chaos. I also sensed a literary defence.

 I will use the word "heart" here. Literature protects the soul. I believe that people's hearts are easily hurt. If you don't have anything, it will probably get damaged easily. I'm not sure if literature can save a person's soul, but I think it can provide some protection to a vulnerable heart.

 In Tetsutaro Kawakami's ``Yushu Nikki'', I have read and re-read the part where he talks about the poems of Mallarme and Lafarge. I replaced the words ``autumn like a cymbal bang'' with the clear autumn of Japan that I had seen, and contrasted it with the golden yellow leaves around me. It may be a silly thing to say, but Mallarme's words certainly lifted my sometimes depressed heart. However, even if my heart is still depressed, through these words, autumn has appeared before me, and its reality has created an impression in my heart that is on par with the memories of autumn I actually saw. We have continued to give to My sense of reality is not limited to this ``autumn'' experience, but through various words, it gives me a new sense of reality.

 Was it Lafarge who said, "The rain falls with the kindness of angels?" Once these words were fixed in my heart, the rain always fell with such gentleness. It's as simple as it gets, but I'm sure everyone has had this experience. You could say that I viewed this as a joyous experience and have cherished it. No matter how many times I turned my pockets inside out, all that came out was dust. My few possessions were a collection of fragmented words.

 I learned a lot from Tetsutaro Kawakami. They protected my youthful heart. The scene in Zenzo Kasai's ``Bring the Child'' where the father opens the glass door and enters the dining room with his child gave me an infinite sense of relief. Perhaps somewhere in that sense of relief there was a projection of "Christ the Son," but such self-analysis was hindered by its own logic, and ultimately failed to reach the deeper parts of my heart. It seems that. Logic is sometimes easily incorporated into a system, but the senses do not belong to any of them and sometimes do not stop making their claims half-heartedly. Literature has often played such a role in our hearts, and unlike the words of our parents who lecture us logically, they sink into our hearts like the familiar country and western songs we listen to when we go back to our rooms. did.

 If Zenzo Kasai's ``Bring a Child'' had not been in my young heart, my heart might have been moved by any religion that came my way. I might have been happier that way, but I didn't take that direction and ended up wandering many times to get to where I am today. The scenery of ``Bringing a Child'' remains undifferentiated in my heart, and it continues to send me a deep sense of relief. Similarly, ``the rain falling with the gentleness of an angel'' transformed my cold, wet heart into a warm and gentle world.

 Words are not magic, nor are they anything like magic. It is just a message to send. However, the message reaches people's hearts as a reality, just as the colours created by a painter shine with light from the depths of the painting. Often with a sense of reality that goes beyond what my inexperienced self has experienced. When several of these messages are combined, the vulnerable heart becomes like a strong beaver's nest, protecting the child from the big bears. You can feel the autumn sound of cymbals in the gloomy sky, and a lonely father with his child gives a gift of supreme kindness to those who read it from the light of a bare light bulb.

 This is why literature has the ability to defend itself as an added value.


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48 Letter

 

48 Letter

 48 手紙
   
    本を読んでいるときはときが静かに流れると述べていたのは、吉田健一さんであっと思いますが、文学の中心はもうそれで尽きているでしょう。ですから私がここでさらに付け加えるのはその周辺のことに過ぎません。文学は防御になるというのが、私の結論です。何の防御であるかというと、心とかたましいとか人生とか、そんなふうに呼ぶものに対してです。


 ここでいう文学とは、詩や小説で代表されるいわゆる文芸にとどまらず、ときには新聞の断片や広告の文面にまで及びます。戦争で兵士が、薬の効能書きを何回も読みなおしたという話を聞いたとき、戦争の悲惨さとその中でのかすかなやすらぎとが私の中で混在し、それと同時にその混沌の中からも私は文学の防御を感じとっていたのです。

 私は、ここでは心ということばを使うことにします。文学は心を防御するのです。人の心は傷つきやすいものだと私は思っています。なにもなければ、多分容易に傷ついてしまうものではないでしょうか。文学が人の心を救うことができるかどうか、私にはよくわかりませんが、傷つきやすい心に一定の防御を与えることはできるのではないでしょうか。

 河上徹太郎さんの『有愁日記』の中で、私が幾度か読み返したのは、マラルメやラフォルグの詩のことを述べていたところです。「シンバルを叩いたような秋」ということばを私は見なれた日本の澄明な秋に置き換え、自らの周囲にある黄金色の黄葉に対比していました。たわいないことと言えますが、それでもこのマラルメのことばが、ときに沈んだ私の心を引き立ててくれたことは確かでした。しかしもし私の心が沈んだままだとしても、このことばを通してひとつ秋が私の前に現前し、その実在感は、私が実際に見た秋の記憶と決して遜色のない印象を私の心に与え続けてきたのです。私の中の実在感はこの「秋」の経験にとどまらず、いろいろなことばを通してそこからの新たな実在感を私に与えてくれるのでした。

 「天使の優しさで降る雨」と言ったのはラフォルグだったでしょうか。こうしたことばが私の心にひとたび定着すると、雨はいつもその優しさで降るのでした。単純と言えばこの上なく単純ですが、きっとこうした経験は誰にでもあるでしょう。それを私は自らの喜ばしい経験としてとらえ、大切にはぐくんで来たといえるかもしれません。両方のポケットを何回裏返しても、出てくるのは屑ぼこりだけだった私の数少ない財産がそうした断片的なことばの集積だったのです。

 河上徹太郎さんからは多くのことを教えてもらいました。それらが青春の私の心を防御してくれたのです。葛西善蔵の「子をつれて」で父親がこどもと一緒にガラス戸を開けて食堂へ入っていくところは、私に限りない安堵感を与えてくれました。その安堵感のどこかに「子なるキリスト」の投影があったのかもしれませんが、そうした自己分析はいわばその論理性そのものに邪魔されて心のより深いところへは遂に行き着かなかったようです。 論理はときには容易に体系の一部に組み込まれるものですが、感覚はそのどこにも属さず中途半端なままにその主張を止めないでくれることがあるものです。文学はしばしばそのような役割を心の中で演じましたから、理詰めで説教する親のことばとは違って、部屋に戻って聞く聞きなれたカントリー・アンド・ウエスタンのように心に染みてくるのでした。

 もしも私の若い心に葛西善蔵の「子をつれて」がなかったなら、私の心は近づいてきた任意の宗教に心動かされたかもしれません。その方があるいは幸せとなったかもしれませんが、私自身はそうした方向をとることなく、幾度も彷徨を繰り返しながら現在にまで来てきてしまったということになります。「子をつれて」の風景は私の心の中で未分化なまま、今も深い安堵感を私に送り続けてくれるのです。同様に「天使の優しさで降る雨」は冷たくぬれた私の心を、あたたかな優しい世界へと変えてくれたのです。

 ことばは別に魔法使いではなく、マジックでもなんでもありません。それはひとつのメッセージを伝えて寄越すに過ぎません。ただそのメッセージは、画家が作り出す色彩が画面の奥から光をともなって輝き出すように、人の心にひとつの実在となって届くのです。往々にして未熟な自らが体験したこと以上の実在感をともなって。そういうメッセージのいくつかが重なると、傷つきやすい心はまるで頑丈なビーバーの巣のように、大きな熊からもその子を護ってくれるのです。どんよりとした空にシンバルの秋を感じ、子をつれたわびしい父が暗いはだか電球の明かりの中から至高の優しさを読むものに贈ってくれるのです。

 文学がひとつの付加価値として防御能力を持っているというのは、以上のようなことなのです


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Saturday 20 April 2024

From Gromov-Witten invariant to quantum cohomology ring and Gromov-Witten potential, in the centre considered homological mirror symmetry

 

From Gromov-Witten invariant to quantum cohomology ring and Gromov-Witten potential, in the centre considered homological mirror symmetry



From Author;
This essay is translated by Google.
So there seem ambiguous expressions in the sentences
I beg your pardon. 


From  Print  2012, Chapter 15He considered the direction of his work. Create a concise model. The model is represented graphically. Figures are expressed geometrically. Following Kenji Fukaya, geometry was defined as ``a set of groups and the spaces in which they act.'' The appeal of Fukaya's books was that they allowed us to constantly check and look at fundamental things like this.



By referring to Jacobson's "semantic minimum" and setting a geometric "minimum unit of meaning" meaning minimum, and moving time t in a closed interval, we can create a geometric concept that encompasses time as meaning. Defined the word word. He repeated this direction many times, at different geometric levels.

The universality of language approaches the invariant of mathematics. I learned from Fukaya's book that a quantum cohomology ring can be obtained from a Gromov-Witten invariant, and a Gromov-Witten potential can also be obtained. Language has become closer to mathematics and physics. Symmetry, which has long been a concern, can now be precisely inspected. At the centre of this was Koncewicz's homological mirror symmetry. 
Source: Tale / Print by LI Koh / 27 January 2012 Reference: Mirror Language / 10 June 2004 Reference 2: Gromov-Witten Invariantational Curve /27 February 2009 Homology Structure of Word / 16 June 2009 Potential of Language / 29 April 2009-16 June 2009

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

Reference:
Mirror Language / 10 June 2004


Reference 2:
Gromov-Witten Invariantational Curve /27 February 2009 

Homology Structure of Word / 16 June 2009
Potential of Language / 29 April 2009-16 June 2009

References 3:
Mirror Symmetry Conjecture on Rational Curve / 27 February 2009


Kitayama Iris Park, Higashikurume, Tokyo
26 June 2014