Saturday 27 April 2024

Aurora Theory Dictoron and Time

Aurora Theory Dictoron and Time Aurora Theory Dictoron and Time TANAKA Akio 1 Objection 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] 2 Situation 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] 3 Now Riemann sphere has a unit radius. Refer to the following paper. Aurora Theory Limitation of Meaning Tokyo October 9, 2006 [AT7] 4 When 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] 5 Word 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 Selgej Tokyo March 13, 2005 Quantum Linguistics Solidity and Flexibility Tokyo January 14, 2006 Quantum Linguistics Quantum Language Machine For Forth Time to KARCEVSKIJ Tokyo January 23-29, 2006 Quantum Language Frame and Transmission For Quantum Language Machine 3 Tokyo February 26, 2006 Also refer to the following papers groups. Frame-Quantum Theory Map 3 Hakuba March 28, 2005 Quantum Linguistics Physical Substantiality of Language 6 Dictoron has spin. Refer to the following paper. Aurora Theory Dictoron as Language Quantum Tokyo October 1, 2006 [AT4] 7 Dictoron has two units of information at the same time. Refer to the following paper. Quantum Language Substantiality of language Tokyo February 21, 2006 8 Dictoron has ability to work as quantum computing. Refer to the following paper. Quantum Semantics Topological Entangled Language For KITAEV Alexei Yu Tokyo June 5, 2006 9 When 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, 2005 10 When dictoron moves between the origin and surface of Riemann sphere, phrase is generated and extinguished. 11 Generation and extinction of phrase are called time progression and time regression. 12 Now place of dictoron is expressed by the combination of longitude, latitude, direction and time. 13 The combination is indicated by the coordinates (x, y, z, and t). 14 The coordinates has symmetry. Refer to the following paper. Aurora Theory Dictoron, Time and Symmetry Language Multi-Time Conjecture Tokyo October 6, 2006 [AT6] 15 From symmetry of coordinates, there exists reverse phrase point on Riemann sphere by symmetric transformation. 16 Dictoron’s movement to the point has reverse progression. 17 Time 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, 2006 18 Place on Riemann sphere expresses time and imaginary time of dictoron. 19 Place 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, 2004 20 Word and imaginary word indicate language universe. Refer to the following paper. Reversion Theory Tokyo September 27, 2006 21 The universe is measured by distance. Refer to the following paper. Distance Theory Tokyo May 5, 2004 22 Time concerning about dictoron is also measured by distance. Refer to the following paper. Cube Theory Cube Word Hakuba April 1, 2006 23 Distance makes matrix (x, y, z, t) (-x, -y, -z, -t). 24 There comes matrix (-x2, -y2, -z2, -t2). 25 Now becomes function – (x2+y2+z2+t2). The function is called function I. 26 Function I specifies a line segment. 27 The segment expresses dictoron’s movement containing progression and regression of time and imaginary time. Tokyo October 21, 2006 Sekinan Research Field of Language Read more: https://srfl-paper.webnode.com/products/aurora-theory-dictoron-and-time/ at September 28, 2019 Email This BlogThis! Share to Twitter Share to Facebook Share to Pinterest
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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
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 model of language universals  2017
6.  Mathematical description for three elements of language universals  2017
 
 
................................................................................................................
 
 
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
 
 
................................................................................................................
 
 
 
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
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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

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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 15
He 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. 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

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


Kitayama Iris Park, Higashikurume, Tokyo
26 June 2014

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Friday 19 April 2024

Hills West Time Hills West Tokyo New Home Site 2024

 

Hills West Tokyo  New Home Site

Hills West Time

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What is signal? The existence that generates language Preface-Main Issue 5 Time and ideogram / 5 April 2019

 

What is signal? The existence that generates language Preface-Main Issue 5  Time and ideogram   /   5 April 2019


The existence that generates language
2018-2019
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References
Reference is cited from the papers written
at SekinanLibrary and SRFL
28 February 2019

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Main Issue 1
Quantum Group 
Main Issue will be written from the angle of Quantum group. 

2 March 2019
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Main Issue 3

Broad language

Read more: https://srfl-paper.webnode.com/news/what-is-signal-the-existence-that-generates-language-preface-main-issue-3-over-edition/#.XJNS5wHse0g.blogger

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Main Issue 4

Space and Boundary

Contents

  1. Why is boundary necessary in language?
  2. Boundary of Words
  3. Frame-Sentence Language  Boundary
  4. Language and Spacetime
    1 Language   Definition for the Child who Lost the World
    2 Word Containing Time and 4 Dimensional Sphere
    3 Structure of Word
    4 Generation of Sentence
    5 Description of Meaning
    6 Shift of Time
    7 Construction of Spacetime specially on Transformation with boundary for  Dimensions
    8 Stability of Language
    9 Time Flow in Word


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Main Issue 5

Time and ideogram

Contents

  1. On Time Property Inherent in Characters 
  2. Aurora Theory Distance and Time  <Language Multi-Time Conjecture 3>  5th Time for KARCEVSKIJ

  3. Aurora Theory

    From Gauss Plane to Aurora

    Dictoron   Quantum and Trace [AT1]

    Dictoron and Aurora
    ＜Language is aurora dancing above us.> [AT2]

    Aurora and Curvature [AT3]

    Dictoron as Language quantum [AT4]

    Aurora and Riemann Sphere [AT5]

    Dictoron, Time and Symmetry
    ＜Language Multi-Time Conjecture> [AT6]

    Limitation of Meaning [AT7]

    Aurora Plane [AT8]

    Dictoron and Time [AT9]

    Word, Phrase and Sentence
    ＜Language Multi-Time Conjecture 2> [AT10]

    Distance and Time
    ＜Language Multi-Time Conjecture 3>   5th Time for KARCEVSKIJ [AT11]

    Why Human Time Flows Fast and Slow on Occasion
     <Interlude for Multi-Time Conjecture> [IL1]


    Read more: https://srfl-paper.webnode.com/products/aurora-theory-contents/

  4. Aurora Time Theory

    From Gauss Plane to Aurora 2

    Time on Aurora [ATT1]

    Imaginary Time and Imaginary Space   From HAWKING Stephen [ATT2]

    Enlarged Distance Theory [ATT3]

    Opened Time and Closed Time   For WANG Guowei <Bridge between Physics and Linguistics> [ATT4]

    Opened Time and Closed Time Revised   For WANG Guowei and DELBRÜCK Max [ATT4-2]


    Read more: https://srfl-paper.webnode.com/products/aurora-time-theory-contents/



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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 <time inherent in characters>, time has various longitudes, from short to long. As the case stands that two times in two characters touch in succession and the former character’ time is longer than the latter character’ time, these two characters connect tightly and generate a new aspect complex. But on the reverse situation, that is to say, the former character has shorter time than the latter character, these two characters have the difficulty to generate a new aspect complex, every individual character has a tendency to stand alone each other.

As for characters connection /heng yan/, character /heng/ has <an eternally long time> inherent, on the other hand, character /yan/ has <a temporary short time>. Like this connection of characters that the former is long time inherent and the latter is short time inherent, a new aspect complex is generated in principle.

Therefore characters /heng yan/ become one word and characters /yan heng/ become one sentence which is constituted from the two characters.

That is to say, on Chinese language that is classified to isolating language in linguistic typology, for there are no phenomena of declension, the main them of the grammatical functions is the break of words, namely characters, and the selection of parts of speech.

On the decision of grammatical functions, now I institute two conceptions for language. One is <time inherent in characters>. The other is <self selectivity of aspects on the combination of characters>.

<Time inherent in characters> is above mentioned. <Self selectivity of aspects> is also above mentioned. Say over again, when time inherent in the successive character is shorter than the former character’s, two characters are composed and become one word. But the latter is longer than the former; two characters are not composed and become one sentence.

As a result, there become two divergences. One is the generation of a new aspect complex. The other is succession of two individual aspects. The former become a word. The latter become a sentence.

This distinction leads a new view for the generation of lexis and the structure of syntax. Time inherent in characters is examined by the property of characters, especially by the inscriptions on bone and tortoiseshell in ancient China. Therefore <self selectivity of aspects on the combination of characters> is a hypothesis in the present stages.

4 Time principle on language

 Generally, recognition of word or structure of meaning on word, which is estimated one of the most important themes on linguistics, is extremely difficult to examine for long time. For the examination of the theme, now I chose the inscriptions on ancient China. These inscriptions are the most effective materials for analyzing the structure of meaning on language. Then, one of the most effective means is to verify <Time inherent in characters> and <Self selectivity of aspects on the combination of characters>. Now I collectively call these two factors as <Time principle on language>.


Hakuba March 28, 2003
Written by Japanese
Original Edition

Tokyo January 3, 2005
Translated into English
Standard Edition

Sekinan Research Field of Language
 
[Postscript June 23, 2008]
†0<WANG Guowei>
  1. Sekinan Research Field of Language / 5 WANG Guowei / Tokyo November 8, 2004
  2. For WANG Guowei

†1<Period>
  1. Stochastic Meaning Theory / June 22, 2008

†2<Multi-time>
  1. Clifford Algebra / Note 5 / TOMONAGA’s Super Multi-Time Theory / Tokyo January 25, 2008

†3<Time flow>
  1. Time Theory / Tokyo December 25, 2004
  2. Language and spacetime / Time Flow in Word / Tokyo May 3, 2007

<More details on the theme>
  1. Invitation by Theme-Time / Tokyo January 6, 2008

[Postscript July 11. 2008]
  1. Solid Trace Theory / Solid Trace / Tokyo April 19, 2006
  2. For Authentication of Solidity / Tokyo November 6, 2005

[Postscript December 23, 2008]
  1. Energy Distance Theory / Conjecture 2 / Geometry of Word / Tokyo November 23, 2008
  2. Complex Manifold Deformation Theory / Conjecture 5 / Time of Word / sekinan.wiki.zoho.com

[Postscript July 30, 2014]
  1. TOMONAGA’s Super Multi-time Theory / Clifford Algebra Note 5 / 25 January 2008 / Note added 30 July 2014


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Text 2





Distance and Time
<Language Multi-Time Conjecture 3>
 5th Time for KARCEVSKIJ




1
Sentence that appears aurora is expressed by integral on Riemann sphere.
Refer to the following paper.
2
Sentence has distance that is expressed by the height of trapezium on sentence plane.
Refer to the following paper.
3
Sentence 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.

Tokyo October 28, 2006
Postscript January 25, 2008
[Basis]
[References]
<Past work on multi-time themes>
<For more details>



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Text 3



Dictoron and Time



1
Objection 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.
2
Situation of aurora’ phrase is expressed by longitude, latitude and direction to the next phrase.
Refer to the following paper on direction.
3
Now Riemann sphere has a unit radius.
Refer to the following paper.
4
When 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.
5
Word 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.
Also refer to the following papers.
Also refer to the following papers groups.
6
Dictoron has spin.
Refer to the following paper.
7
Dictoron has two units of information at the same time.
Refer to the following paper.
8
Dictoron has ability to work as quantum computing.
Refer to the following paper.
9
When 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.
10
When dictoron moves between the origin and surface of Riemann sphere, phrase is generated and extinguished.
11
Generation and extinction of phrase are called time progression and time regression.
12
Now place of dictoron is expressed by the combination of longitude, latitude, direction and time.
13
The combination is indicated by the coordinates (x, y, z, and t).
14
The coordinates has symmetry.
Refer to the following paper.
15
From symmetry of coordinates, there exists reverse phrase point on Riemann sphere by symmetric transformation.
16
Dictoron’s movement to the point has reverse progression.
17
Time to the reverse progression has reverse progression time.
The time is called imaginary time.
Refer to the following paper.
18
Place on Riemann sphere expresses time and imaginary time of dictoron.
19
Place of imaginary time makes imaginary word on complex plane.
Refer to the following paper.
20
Word and imaginary word indicate language universe.
Refer to the following paper.
21
The universe is measured by distance.
Refer to the following paper.
22
Time concerning about dictoron is also measured by distance.
Refer to the following paper.
23
Distance makes matrix (x, y, z, t) (-x, -y, -z, -t).
24
There comes matrix (-x2, -y2, -z2, -t2).
25
Now becomes function – (x2+y2+z2+t2). The function is called function I.
26
Function I specifies a line segment.
27
The segment expresses dictoron’s movement containing progression and regression of time and imaginary time.

Tokyo October 21, 2006



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Text 4




Dictoron, Time and Symmetry
<Language Multi-Time Conjecture>




A
1 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.
B
13 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.

Tokyo October 6, 2006


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Text 5





Why Human Time Flows Fast and Slow on Occasion




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.
3 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.

Tokyo October 28, 2006



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Text 6


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.
2 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.
4 Dictoron’s distance is expressed by ct.
c is light velocity. t is time.
ct is 1 after unit time.
x2 + y2 + z2 = (ct) 2
5 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, 2006


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Text 7




Imaginary Time and Imaginary Space

From HAWKING Stephen




1 Language is expressed by word, phrase and sentence in Aurora Theory, abbreviated to AT.
Refer to the following paper.
2 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.
3 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 phrase does 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 <should-not-be-existent-but-logically demanded> space in the ATT’s sphere.
The space is called imaginary space.

Tokyo November 11, 2006


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Text 8




Enlarged Distance Theory

For CELAN Paul
Ansprache anläβlich der Entgegennahme des Literaturpreises der Freien Hansestadt Bremen




1 Language was supposed to have distance for mainly making sentence.
Refer to the following paper under roughly sketched situation.
2 Distance in 4 dimensional space is indicated by Minkowski space.
(Δs)2≡(cΔt)2-(Δx)2-(Δy)2-(Δz)2
Δs is distance. c is light velocity. Δt = t2-t1. Δx = x2-x1. Δy = y2-y1 Δz = z2-z1.
3 Now if time is imaginary time it by being showed from HAWKING S., distance is indicated by Euclid space.
-(Δs)2≡(cΔt)2+(Δx)2+(Δy)2+(Δz)2
Here 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.
4 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.
4-2 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, 2006


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Text 9



Opened Time and Closed Time





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.
Also refer to the following papers.
Also refer to the following papers.
Perspective on the theme is indicated below.
4 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.
Perspective on the theme is indicated below.
5 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.
Perspective on the themes is indicated below.
6 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.
Perspective on the themes is indicated below.
7 In Aurora Time Theory, language is connected with time by Minkowski space.
Refer to the following paper.
8 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)2
Here 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)2
The 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.
Perspective on the themes is indicated below.
9 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, 2006
Tokyo November 26, 2006 Dedication, consideration 8 and Conjecture Revised
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