Sunday, 27 June 2021

Farewell to Language Universals Revised. 2021

 

Farewell to Language Universals

18/03/2020 19:40 ;  First uploaded date to Sekinan View 

I ever thought of language from the vie point of the core elements usually assumed as one of language universals.
Every element has been important for language phenomena, but selecting these elements from the infinite language world, they are seemed to be arbitrary pointing-out act for me now.
So the below quoted  facts at paper 1 and paper 2 are, at the end, considered to be one of important aspects on vast and boundless language for me now.

Tokyo
18 March 2020 First uploaded 
27 June 2021 Text revised
Sekinan Library


Paper 1

Mathematical description for three elements of language universals

Energy, dimension and distance can be described by mathematical writing.

Energy in language is now preparatory description til now.
vide:

  1. Energy of Language / Stochastic Meaning Theory
  2. Energy and Distance / Energy Distance Theory
  3. Energy and Functional / Energy Distance Theory
  4. Potential of Language / Floer Homology Language

For dimension, definite results are presented being aided by arithmetic geometry.
vide:

  1. Three Conjectures for Dimension, synthesis and Reversion with Root and Supplement

For distance, its vast and vagueness of the concept can not be grasped up. But related papers of mine are probably the most in number.
vide:

  1. Distance / Direct Succession of Distance Theory / Distance Theory Algebraically Supplemented
  2. Distance of Word / Complex Manifold Deformation Theory

This paper is not finished.

Tokyo
27 February 2015
SIL 

Read more: https://srfl-essay.webnode.com/news/at-least-three-elements-for-language-universals/


The upper paper, titled as Mathematical description for three elements of language universals, is now one of the most fundamental studies of language at present outlook.

Tokyo
28 February 2020
SRFL Paper

[Note]
28 February 2020
I ever wrote a essay titled Half Farewell to Sergej Karcevskij and the Linguistic Circle of Prague

Read more: https://srfl-paper.webnode.com/news/half-farewell-to-sergej-karcevskij-and-the-linguistic-circle-of-prague-with-references/


Paper 2

Half Farewell to Sergej Karcevskij and the Linguistic Circle of Prague with References

TANAKA Akio

I have thought on language through the rich results of the linguistic Circle of Prague and its important member Sergej Karcevskij.

But now my recent thinking has inclined towards algebraic or arithmetic geometrical method and description. Probably it is the time of half farewell to those milestones which led me to the standing place here with rather sufficient results in my ability. Great thanks to all that always encouraged me for hard and vague target on language especially meaning and its surroundings. And also to CHINO Eiichi with love and respect who taught me all the bases of language study.

For recent results see the following papers group named AGL Arithmetic Geometry Language and related essays.

Tokyo
23 October 2013
Sekinan Research Field of Language

[References]

Papers

Arithmetic Geometry Language (AGL)

  1. Dimension of Language (AGL 1)
  2. Synthesis of Meaning and Transition of Dimension (AGL 2)
  3. Birth of Word, Synthesis of Meaning and Dimension of New Word (AGL 3)
  4. Dimension Conjecture at Synthesis of Meaning (AGL 4)

Essays

  1. Parts and Whole
  2. Edward Sapir’s Language, 1921
  3. Macro Time and Micro Time
  4. Meaning Minimum
  5. Disposition of Language

24 September 2014, references added
Sekinan Research Field of Language

Read more: 
https://geometrization-language.webnode.com/news/farewell-to-language-universals/

Read more: 
https://srfl-paper.webnode.com/news/farewell-to-language-universals1/

Saturday, 26 June 2021

Days with CHINO Eiichi. 2012

Days with CHINO Eiichi
He led me the present study on language


TANAKA Akio

               
                         

I first met CHINO Eiichi at his Russian language class in 1969. He was 37 and I was 21 years old. He returned to Japan from Czechoslovakia in December 1967. It was only one and half years after. In Czech at Carrel university he studied Ancient church Slavic and the Prague School. 

We met again at his linguistic course in 1979 when I returned to study. Since then ten years passed by. He was 47 and I was 31. From that year to March 1986 I learnt from him on linguistics, especially The Linguistic Circle of Prague.

We time to time walked together to the station after the lecture, and sometimes at the small coffee shop named “California” near the station, we talked on the various themes from the daily trivial things to abstract language agenda. The room was almost always vacant and dim light was threw over us.

They were irreplaceable days and recently more and more have become dear in my life.

He wrote more than ten books and my favorite one is Opened the Door to LinguisticsJanua Linguisticae reserata, 1994. In the book he only crowned Genius to Sergej Karcevskij.

He died by disease in 2002 at age 70.

Under the Dim Light
Linguistic Circle of Prague

From Distance to Pseudo-Kobayashi-Distance

                                                            
                                                                Tokyo
                                                      16 November 2012
                                       Sekinan Research Field of Language

Tuesday, 15 June 2021

Fireworks. From Story To Winter 2015. By RI Ko. Translated by Google.

There has been steady progress in the world's quantization. According to Fukaya, Konzevich presented a formal conjecture in his 1997 paper, which he himself proved in his 2003 paper. "Transformational quantization of Poisson manifolds". Fukaya outlines the proof in his book only for nR. The whole proof is immeasurable.

Quantum space, that may not be a dream anymore. At the end, finite and infinite. Confine infinity to finite. Janos Corral and Shigefumi Mori tell. Any sequence of 3D standard flops is finite. If you think of the flop as a kind of mapping, assume that the meaning is a finite sequence, and project this four-dimensional world made of solids and time onto the three-dimensional world made of planes and time, it will occur infinitely. All the events of the four-dimensional world that have been lost will be confined to the finite three-dimensional world. There, the letters on the plane that embody the meaning including time project and confine this four-dimensional world including time.

 -So what should I do?

When I stood up and looked at the eastern window, there were few people going under the muffled sky. A tram with lights on passes silently through the thick fog that has become thicker than before. Street lights are lit all at once. The distantly forgotten festival begins.  

From the prints hung in the kitchen, a band of light rises silently toward the cold, dark room, and large fireworks bloom one after another, leaving a shimmer. The fireworks are reflected in the glass, and eventually spread over the glass onto the street where the fog flows. Fireworks are now wide open in the dark and foggy sky, and a tram with no passengers passes below it without sound. 

-Why are you so lonely?  

Garsin. A soul who lived and died like a light beam at the end of Russia's imperial rule. The "red flower" desperately seeks a single red flower that doesn't matter and finally gets it. Husevorod Mihailovic Garcin, oh, Mikhail is in your name. 

Angel Michael rises up. The last words of the Old Testament book of Daniel.    
Go to the end of you, and you will rest, and you will reach the end of the day, and you will get up and enjoy your share. 

Light a light in a dark room. The light that the bulbul gave me to live. What should I do. I have to eat a little food. Let's eat rice together. Everyone ate the bread yesterday morning. What was left behind. 

In the chilly weather, I put my hand on the cardigan beside the sofa. Bulbul, are you warm in the hills? 

In retrospect, the prints have finished all the flow and have returned to their original form. Someday the outside of the window became sleet. 

The door is knocked small. When I opened the door that wasn't standing upright, She stood uneasy, holding a white vinyl bag heavy and holding a wrap of French bread in one hand. The sleet was shining lightly on the short hair.

quantization

世界の量子化 quantization については着実な進展があった。 深谷によれば、コンツェヴィッチは1997年の論文で形式性予想を提示し、2003年の論文に至って、みずからその予想を証明 した。「ポアッソン多様体の変形量子化」。深谷は彼の本の中でその証明の概略をnRの場合に限って述べている。証明の全容は計り 知れない。

量子による空間、それももう夢ではないかもしれない。 その果てにある、有限と無限。無限を有限に閉じ込めること。 ヤーノシュ・コラールと森重文は伝える。三次元標準フロップの任意の列は有限である、と。今フロップを一種の写像と考え、意味 を有限の列と仮定し、立体と時間で作られたこの四次元世界を平面と時間で作られた三次元世界に射影すれば、無限に生起するとおも われた四次元世界の出来事のすべてが、三次元の有限の世界に閉じこめられることになる。 そこでは、時間を含む意味を体現した平面 上の文字が、この私たちの時間を含む4次元世界を射影し閉じ込めたものとなる。

 ―それで私はどうするのか。

 立って東の窓を見ると、外はこごえるような空の下に、行く人もまばらだ。さっきより一段と濃くなった厚い霧の中を、ライトを点 けた路面電車が音もなく過ぎて行く。街灯が一斉にあかりを灯している。 遠く忘れられていた祝祭がはじまる。  

台所にかけられた版画から、冷えきった暗い室内に向かって、光の帯が音もなくのぼり、大輪の花火がゆらめきを残してつぎつぎに 開花してゆく。花火はガラスに映り、やがてガラスを超えて霧がながれる街路の上へとひろがってゆく。 暗く霧におおわれた空一杯に、今、花火が大きく開き、その下方を乗客も絶えた路面電車が音もなく過ぎて行く。 

―なぜこんなにさびしいのか。  

ガルシン。ロシアの帝政末期を光芒のように生きて逝った魂。 「赤い花」は必死に、どうでもよい一輪の赤い花をもとめて、遂にそれを得る。 フセヴォロド・ミハイロヴィッチ・ガルシン、ああ、あなたの名まえの中にもミハイルがいる。 

天使ミカエルが起ちあがる。旧約聖書ダニエル書終章のことば。    
汝終りに進み行け、汝は安息に入り、日の終りに至り、起て汝の分を享ん。 

暗い室内にあかりを灯す。ヒヨドリが私に与えてくれた生きるというあかり。 どうしようか。すこしものを食べないといけない。ありあわせでごはんを食べようか。パンはたしかきのうの朝、みんな食べてし まった。あとなにが残っていただろう。 

染み入ってくるような寒さの中で、ソファの脇のカーディガンに手を通す。ヒヨドリよ、おまえも丘陵で暖かにしているか。 

ふりかえると版画は、すべての流動を終えて、もとのしずけさに返っていた。 窓の外はいつか霙になった。 

ドアが小さくノックされる。 立て付けのわるいドアを開くと、白いビニールバッグを重そうに持って、片手にフランスパン の包みを抱えて、Iが不安そうに立っ ていた。 その短い髪に、霙が淡く光っていた。

Monday, 14 June 2021

15 Silk Road and 16 Story. 2021

 

15 Silk Road and 16 Story. 2021

 

15.
2003
Silk Road
 

In the fall of 2002, I had pneumonia and was admitted to Ome Municipal General Hospital for about two weeks. Fortunately, the progress after admission was smooth, and after one week, my breathing and physical condition returned to normal, but my doctor was cautious about whether I was exhausted, and it took another week before I was discharged. Looking out the window at the mountains of Okutama, I was keenly aware that I hadn't written anything about the subject of the language I finally found. When I was discharged from the hospital, I was repeatedly checking the words and phrases of the treatise to be written, thinking that I should give priority to that first and foremost.

The essence of the discussion was gradually coming together. There was something unwavering about the pursuit of what the essence of language was the subject of my dissertation, but considering the depth and vastness of the language itself, I have accumulated myself so far. Based on this, I focused on kanji, and while using the Qing dynasty's elaborate linguistics, elementary school, I was aiming for a universal linguistic theory, and from there I was thinking of a direction to approach the language itself.

As a result, by the time of discharge, I found that some of the typical forms and meanings of the oracle bone script contained time in those letters, referring to Wang Guowei's papers, etc. Based on this, I considered the direction in which the syntactic theory, in which a sentence is formed by concatenating words that include time, is the second essay. However, my traditional dream was to set them in a physically verifiable direction rather than in a philosophical direction. My longing for theoretical physics, which has existed within me since high school, was still at the core of my thinking. And now  I was learning the basics of the magnificent algebraic geometry systematized by the French Bourbaki group Nicolas Bourbaki by the 1960s.

When I was a research student, Sergej Karcevskij's paper "Du dualisme asymmetrique du linguistique 1929" by Sergej Karcevskij of the Prague Linguistic Circle of Prague continued to come and go in me. For example, I had just set up a base camp far below this high peak.

Regarding "asymmetric duality of language symbols", I have written a short sentence before, so I will reprint it below.

"Symmetry. That's what I once talked to C in linguistics. Prague in the 1920s. Karzewski's paper in the magazine TCLP," Asymmetric duality of linguistic signs. " The coexistence of absolutely contradictory flexible and rigid structures where the language continues to hold, thereby the language remains the language. An eternal contradiction that will continue to be doubly inherent in language. Karzevski presented the duality of why the language can be so flexible and so robust, and that it is almost absolutely inconsistent. A scholarly essay left by Sergei Karzevskiy, a linguist whom C called the only genius in his last book. A consistent understanding of this duality as to why this coexistence is possible has probably not yet been submitted. "

Discussion of Karutsuefusukii is a NanOsamu in linguistics was almost a breakthrough shown for sense had not untouched the macro structure was briefly bisected.

In 2003, I began to put together the two directions mentioned above in parallel, but spring came without being able to construct the logic of the language that connects the two of vocabulary and syntax. Two children went out for spring skiing in Yuzawa, Niigata prefecture, which has been continued in recent years, because the school was on spring break, and the children and my wife enjoyed skiing according to their respective strengths, but I went to the hotel alone. For the rest, I focused on following the invisible logic for building the word-to-syntax connection that was absolutely necessary for my dissertation .

As a result, I didn't bring any reference materials, so the day after I arrived in Yuzawa, I wrote with almost no writing brush and summarized the principle logic that connects vocabulary and syntax. I was able to do it. This sentence was scribbled and incomplete, so I didn't upload it on the Web even after I finished writing the two articles, but in 2015, when I reread it in detail, I found that this sentence Since I recognized most of the sprout of the subject I continued to write about my language, I decided to add a short preface and  upload  it under the title of Manuscript of Quantum Theory for Language . ..

Around April, a while after I returned to Tokyo, I opened the site of the National Institute of Informatics, which I used to see at that time, and announced that an international symposium on Silk Road would be held in Nara, co-sponsored by the Institute and the Ministry of Education. The call for papers to be published there was posted. Since I had written two articles based on the draft I wrote in Yuzawa, I decided to submit the article on syntactic theory as an application paper, and since it was an international symposium, the papers should be written in English in principle. Since it was said that it was supposed to be translated into English, I corrected a part to make it more logical and clear, and I was able to apply safely by the submission deadline in May. The treatise was entitled Quantum Theory for Language  , which regarded language as a physical quantum and formed sentences by its combination.

Although I felt common sense anxiety about treating language as a quantum, I was sensuously convinced of the future prospects in that direction, so I hardly hesitated. Fortunately, this treatise was adopted as one of the four oral presentations in the symposium's linguistic literature section, and I was on December 23 and 24, 2003, on the far right of Nara Todaiji Temple. It will be announced on the 23rd at the symposium held at the public hall. The presenters in this department were a professor at Hokkaido University, a member of the Toyo Bunko Museum, a researcher at a company, and myself.

After the oral presentation on the afternoon of the 23rd, I was really relieved. On the afternoon of the 24th of the second day, when I went to the hall, which was the main venue, researchers from various countries gathered and various languages ​​were spoken. Perhaps because of the subject of the symposium, there seemed to be a large number of people attending from Central Asia. Starting with an invited lecture, there were lectures by department, oral presentations, panel presentations, posting of related information, etc. were held throughout the public hall, and it was reported that the total number of participants was close to 400. To me, the venue itself seemed like the end of the modern Silk Road.

Quantum, which is the center of my discussion, is a concept of physics, but it was also very attractive from the viewpoint of mathematics, so it was taken into group theory in mathematics and defined as a quantum group in the 1980s. Proposed by VG Grinfeld.
Hopf algebra and the quantum Yang-Baxter equation. 1985 is the first paper. In the same year, Michio Jimbo of Japan also published a treatise A  q -difference analogue of  U (g) and the Yang-Baxter equation. 1985, which bridged physics and mathematics.

It was later in the late 2000s that it became clear to me that it became possible to use quanta strictly in mathematics. My sensory direction to the quantum can thus be used as being determined by a completely strict mathematical definition.

I have further geometrically transformed this quantum, and with the help of the achievements of Perelman and others who introduced the calories of physics into mathematics, I have extended it from natural language to signals and further to the energy elements that are the basis of them. Quantum-Nerve Theory, which advances to representation and its application and tries to quantum-transform human nerves to lead to applied science, has almost finished its preparatory consideration from 2018 to 2019, and is now We have reached the direction of developing the mathematical structure algebraically. At the same time, I  would like to continue learning important directions such as David Marr's work Vision, which passed away at the age of 35 in 1980, which created the skeleton of neural theory, and "visual calculation theory and brain expression" as a subtitle.

Let's go back to 2004.
In January 2004, the Institute of Informatics sent me a completed manuscript because I would like to publish an oral presentation paper as a booklet, and I received an e-mail saying that the oral presentation manuscript was further corrected and sent. In May, a thick booklet containing papers was delivered to the people concerned. To distinguish it from conventional manuscripts, the title on the booklet is Quantum Theory for Language Synopsis  .

In 1967, I was thinking of a big direction from Asian languages ​​to European languages. Nearly 40 years later, my first booklet containing a thesis summarizing my subject was sent from Japan to Central Asia and then to Western Europe. It may have become one of the wisdom delivered on the modern Silk Road. 


 

16 .
2015 
Story

In the winter of 2012, when I felt that the Paper dissertation on the universality of the Language Universals language, which I had been writing since 2003, had settled down in my own right, at the age of 65, I derived the language from axioms and theorems. However, in some respects, the desire to take a step away from the ruthless world of mathematics and to warmly portray the human beings living there has become stronger, and one youth that includes autobiographical elements. I wanted to portray the possibilities as two people who are both lonely but never isolated.

The main character, A, the reunited I, and the bulbul that hurt his wings were all, in a sense, the alter ego of the author. As an amateur, I can't judge whether the story is complete, but as I write this story, I hope that one day I will express what I should call salvation while wandering in the days of youth. became.

In their lifetime, they have met many people, received unpredictable support, and faced unexpected farewells, and would have continued their journey to discover their own subject of life. I was one of them.

One will never be able to continue when he is strong. So, there, you might come across something that could be called salvation somewhere without realizing it. It wasn't because it was weak, or because it was weak, and it wasn't sought because it was weak, but in life itself, perhaps inevitably, salvation would have existed as something that would come unknowingly. One day I naturally became like that.

The story begins with the cold of the wind and the days of autumn, and ends with a day full of light that makes you feel the loneliness of winter.
I pray that everyone is the two of the day.

"Winter is coming to them like grace now."

I conclude this story so.

Friday, 11 June 2021

15 Silk Road and 16 Story. 2021

 


15.
2003
Silk Road
 

2002年の秋、私は肺炎となり、青梅市立総合病院に2週間ほど入院した。幸いに入院後の経過は順調で、1週間後には呼吸も体調もほぼ平常に戻ったが、体力の消耗があったのか主治医の先生は慎重で、退院まではもう1週間を必要とした。私は窓外に奥多摩の山々を見ながら、ようやく見いだした言語の主題について、まだ何も書き上げていないことを痛切に感じていた。退院したら、まず何よりもそのことを優先しなければならないとおもいながら、書かれるべき論文の片言や字句を繰り返し点検していた。

論考の骨子は、少しずつであったがまとまりつつあった。言語の本質とは何かを追求することが私の論考の主題であることに対しては揺るぎないものがあったが、言語そのものの深淵と広大を考える中で、私は今までの自己の集積を踏まえて、漢字を中心に置き、清代の精緻な言語学である小学を援用しながら、普遍的な文字論をめざし、そこからさらに言語そのものへと迫る方向を考えていた。

その結果、退院時までに、私は甲骨文として典型的な形態と意味を有するいくつかについて、それらの文字の中に時間が内包されていることを、王国維の論文等を参照しながら単語論としてまとめることを第一の論考とし、それを踏まえて、次に時間を内包する単語が連接することによって文が形成されることとなる統語論を第二の論考とする方向を考えた。しかしそれらを、言語哲学的な方向で進めるのではなく、あくまでも物理的な検証可能な方向で設定したいというのが、私の従来からの夢であった。高校時代から私の内に存在する理論物理学へのあこがれは、依然として私の思考の中核をなしていた。そして今はフランスのブルバキ集団 Nicolas Bourbaki が1960年代までに体系化した壮大な代数幾何の初歩を私は学んでいた。

研究生時代、プラハ言語学サークル Linguistic Circle of Prague のセルゲイ・カルツェヴスキイ Sergej Karcevskij の「言語記号の非対称的二重性」Du dualisme asymmetrique du linguistique 1929 という論文が、私の中で去来し続けていた。例えて言うならば、私はこの高峰のはるか下方の裾野にベースキャンプを設営したばかりであった。

「言語記号の非対称的二重性」については、かつて短くまとめた文を書いたことがあるので、以下に再掲する。

「対称性。それはかつて言語学のCと繰り返し話した内容だ。1920 年代のプラハ。雑誌 TCLP に載ったカルツェフスキイの論文、 「言語記号の非対称的二重性」。言語が保持し続けるところの、それによって言語が言語であり続けるところの、絶対的に矛盾する柔 構造と硬構造の共存。言語において二重に内在し続けるだろう永遠の矛盾。言語がかくも柔軟でかくも堅固でいられるのはなぜか、そ のほとんど絶対的に矛盾するかともおもわれる二重性をカルツェフスキイは提示した。Cがその最後の本の中でただ一人天才と称した 言語学者、セルゲイ・カルツェフスキイが残した白眉の論考。なぜこの共存が可能なのか、この二重性に対する整合的な理解は今もなお、たぶん提出されていない。」

カルツェフスキイの論考は、言語学において難攻とされ、ほとんど手を付けられないでいた意味についてそのマクロな構造を簡潔に二分して示した画期的なものであった。

2003年に入り、私は上述した二つの方向をほぼ並行してまとめ始めたが、単語論と統語論の二つを繋ぐ言語の論理を構築できないまま、春を迎えた。この年も近年続けてきた新潟県湯沢での春スキーに、二人の子供が学校が春休みになったので出かけ、子供と家内はそれぞれの力に応じたスキーを楽しんだが、私は一人ホテルに残り、私の論考にどうしても必要であった、単語から統語への連結部分構築のための見えない論理を追うことに集中した

結果的には、却って何も参考となる資料を持ってこなかったために、湯沢に到着した翌日、私はほとんど筆をおくことなく書き進め、単語論と統語論を結ぶ原理的な論理をまとめることができた。この文章は、走り書き的でありかつ未完であったために、二つの論考を書き終えた後も、Web 上に Upload することはなかったが、2015年、あらためて子細に読み直してみると、この文章の中に私の言語についてその後書き続けた主題のほとんどの萌芽を認めたため、あらためて短いまえがきを付し, Manuscript of Quantum Theory for Language 「言語の量子論のための草稿」と題して Upload することとした。

東京に戻ってからしばらくした四月ごろ、その頃時々見ていた国立情報学研究所のSite を開くと、研究所と文部省の共催で、Silk Road に関する国際シンポジウムが奈良で開催されることの予告とそこで発表する論文の募集が掲載されていた。私は湯沢で書いた草稿を元に二篇の論考を書き上げていたので、そのうちの統語論に関する論考を、応募論文として提出することを決め、国際シンポジウムであったため、論文は英文表記を原則とするとされていたので英語へ翻訳することとし、一部をより論理的に明瞭にするために添削し、5月の提出期限までに無事応募することができた。その論文はQuantum Theory for Language と題され、言語を物理的な量子とみなし、その結合によって文が形成されるというものであった。

言語を量子として扱うということに、常識的な不安を感じながらも、その方向に私は未来的な展望を感覚的に確信していたので、ほとんどためらうことはなかった。幸いにこの論文はシンポジウムの言語文学部門の4編の口頭発表論文の一つに採用され、私はその年2003年の12月23日と24日 に奈良東大寺の向かって右奥にある奈良県立公会堂で行われたシンポジウムで 23日に発表することとなった。同部門の発表者は、北海道大学教授と東洋文庫員および企業の研究者と私の4名であった。

23日午後の口頭発表を終えるとさすがに安堵した。二日目の24日の午後、メイン会場となるホールに行くと各国の研究者が集い、さまざまな言語が話されていた。シンポジウムの主題からか、中央アジアから出席された方々が特に多いようであった。招待講演から始まり、部門別の講演があり、口頭発表、パネル発表、関連情報の掲示等が公会堂全体で行われていて、延べ参加数は400名近くと伝えられた。私にはこの会場そのものが、現代のSilk Road の終着のようにおもわれた。

私の論考の中心となる量子は物理学の概念であるが、数学から見ても非常に魅力的なものであったため、数学における群論に取り込み量子群とみなして定義することが、1980年代にグリンフェルト V. G. Grinfeld によって提唱された。
Hopf algebra and the quantum Yang-Baxter equation. 1985 がその嚆矢となる論文である。同年、日本の神保道夫も論文 A q-difference analogue of U(g)and the Yang-Baxter equation. 1985 を発表し、この二者によって、物理学と数学が架橋されることとなった。

量子を数学で厳密に用いることが可能となってきたことが私にも明瞭となってきたのは、さらに後年となる2000年代後半であった。私の量子に対する感覚的な方向はこうして完全に厳密な数学的定義によって確定されたものとして、使用することができるようになった。

私はこの量子をさらに幾何学的に変形し、物理学の熱量等を数学に導入したペレルマン Perelman 等の業績を援用して自然言語から信号、さらにその元となるエネルギー要素へと拡張させた言語表象とその応用へと進み、人間の神経を量子的に変形させて応用科学へと導こうとする、Quantum-Nerve Theory を2018年から2019年にその準備的考察をほぼ終了して、現在はその数学的構造を代数幾何的に進展させる方向に至っている。あわせて神経理論の骨格を作った1980年に35歳で逝去されたDavid Marr の著作 Vision、副題として「視覚の計算理論と脳内表現」等の重要な方向も学び続けたいとおもっている。

2004年に戻ろう。
2004年1月に情報学研究所から、口頭発表論文等を冊子として刊行するので完成原稿を送られたし、とのメールがあり、私は口頭発表原稿をさらに添削して送付した。5月には論文等が掲載された厚い冊子が関係者に届けられた。従来の原稿と区別するために、冊子上の表題は、Quantum Theory for Language Synopsis とした。

1967年に、私はアジアの言語からヨーロッパの言語へ向かう大きな方向を考えていた。それから40年近くを経て、私が初めてみずからの主題をまとめた論文を掲載した冊子が日本から中央アジア、そして西欧へと送られることとなった。それは現代 のSilk Road で届けられる叡知の一つとなったのかもしれない。 


 

16 .
2015 
Story

2003年から書き続けてきたLanguage Universals 言語の普遍性に関するPaper 論考が、みずからの中で一段落したと感じた2012年冬、65歳となった私は、言語を公理と定理から導く、青春の日々から求め続けてきたものではあるが、ある点では非情な数学の世界そのものから一歩離れて、そこに生きる人間をあたたかく描いてみたいというおもいが強くなり、自伝的な要素を含んだ一つの青春の可能性を、ともに孤独ではあるが決して孤立してはいない二人として描いてみたくなった。

主人公の A も再会した I も、羽を痛めたヒヨドリも、みなある意味では作者そのものの分身であった。物語として完成しているかどうかは素人の私には判断できないが、私はこの物語を書きすすめるうちに、いつか、青春の日々にさまよう中での、救済とも呼ぶべきものを表現したいとおもうようになった。

人はみな生涯で、多くの人に出会い、おもいがけない支えを受け、不意の別れに接しながら、みずからの生の主題をいつかは見い出そうとする旅を続けてきたのだろう。私もまたその一人であった。

人は決して強いときばかりを続けることはできないだろう。だからそこでは、気づかないうちにどこかで救済とも呼ばれうる何かに出会うのではないだろうか。それは決して弱いからではなく、あるいは弱いから求めるのでもなく、生きることそのもののうちに、多分必然として、救済は見知らぬうちにもたらされるものとして、きっと存在していたのではなかったか。私はいつか自然にそんなふうにおもうようになっていた。

物語は、風に寒さをおもう秋の日々からはじまり、冬のおとずれを感じさせる二人の、光あふれる一日で終わる。
すべての人が、この日の二人であるかのようにと、私はねがう。

「二人に今、恩寵のように冬が来る。」

私はこの物語を、そう結んだ。