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Meaning minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi 2013

 

Meaning minimum
On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi

TANAKA Akio
ifbetrue
6 April 2013

1.
Meaning minimum is one of the kernel concepts for the model of language universals on my study. The concept was at first thought from Roman Jakobson's semantic minimum on which I first read at his book, ESSAIS DE LINGUISTIGUE GENERALE, 1973.　His concept was yet intuitive at the linguistic study  history in the latter half of the 20 th century. Comparison with his concept, my definition of meaning minimum was a certain basis prepared in the learning of mathematics, especially on algebraic geometry, that is the most fantastic approach to the construction of the language model. But the contents of meaning minimum is vacant. This concept shows the minimum unit of one big constructive meaning of word. meaning minimum seems to be correspondent with element of set theory, which theory and foundations of mathematics had been my favourite mathematical basis in 1970s, my youth time. Bourbaki was always echoed around us. Grothendieck was a highest star in this world.

2.
Time went vast from at that time. Set theory became one of the premise field of mathematics. But in my part, set theory's agenda was put at a another point. Because language has a certain expanded world that seems to be continuous. Set theory's atomic discreteness does not match in my primary learning level.  So, in my  age 30s, I had sank in the philosophically intuitive thinking often referring the tradition of 1920s, especially of the Linguistic Circle of Prague. On the circle my teacher CHINO Eiichi had taught me from time to time on the campus of university or coffee shop near the station we used. CHINO had gone to the Czechoslovakia Republic from 1959 to 1967. I first met him in 1969 at his Russian class at my  third year of university student. I was the age 21 and he was 37.

3.
At the age 23's 1971 spring,  I graduated university and  once became a high school's teacher and again returned back to university in 1979 after 8 year job of the school. At that time I thought of characters' distinctive features on Written  Chinese classics. I mainly read WANG Guowei, ZHANG Binglin, DUAN Yucai, WANG Yinzhi guiding by Japanese modern scholar KANO Naoki. Expressly I had attracted to  WANG Guowei and his book Guantangjilin. Besides reading these China's Qing dynasty's linguistic peaks, I had always thought on Ludwig Wittgenstein for his endless pursuit on language. So I resigned school and came back to the campus where I again met with CHINO. I was age 30s and he was 50s. He was already the big scholar at the linguistic field  but I was a poor return student. But I dare to say we were colleagues for language study. He taught me the detailed and strict tradition of the linguistic Circle of Prague. He frequently talked on Sergej Karcevskij and his eminent discernment on language. In the later year's masterpiece, Janua Linguisticae Reserata, 1994, he wrote only Karcevskij as genius in the great linguists.

4.
Being led by CHINO, I again started linguistic learning on meaning that I had been interested in from my 20s but too hard to approach by my talent. This time I had Karcevskij's fine insight to meaning enough absorbing the fertile tradition of Prague, where also exist Jakobson and Mathesius. Through the learning I gradually lean to desire to write clear definitions on language. I again remembered the little learning of my 20s age's mathematics. Bourbaki, Gödel, TAKEUCHI and their set theory, foundations of mathematics and that Incompleteness theorem. I had learnt mathematics little by little, inch by inch.

5.
CHINO Died in 2002 at age 70 and I became 55. The next year 2003, I wrote a short paper titled "Quantum Theory for Language". This paper was showed at a international symposium on Silk road for dealing with language from Chinese characters on linguistic viewpoint. I knew  that Asian civilisation and history had great concern not only from Asia but also European continents. At the symposium some 400 researchers gathered in the various scholarly fields. It was a awesome encounter for my study, namely, East meet West. Probably Chinese character's agenda will be written by Europe oriented mathematics. WANG Guowei will meet with Karcevskij mediated through mathematics' description. The target confronted at that time was time inherent in characters, or time in word.  In Chinese, particularly in classical written Chinese, all the characters show enough independent meaning in one character probably including even time. It was my first conjecture taught from Karcevskij and CHINO. Meaning minimum is on the boat going across to the opposite shore. This metaphor was derived from WANG Guowei's famous paper, "Yin- bu zhong suojian xiangong xianwang kao"

6.
The concept of time inevitably led to the distance of distance. In 2004, I wrote a paper titled "Distance Theory". But the paper was yet intuitive and not clear for descriptive definition. So hereinafter I learnt algebra inch by inch assisting with the rich imagine of geometry. In the centre of learning, always exist time that connotes finiteness and infinity. But infinity is not easily obtained without probably only loop space at the present. And again returns back to meaning minimum as the passenger of the boat named time property inherent. This time the passenger on the boat  is called operad or algebraic language.

7.
After all I came back to the very dream that I had embraced since the high school days. It was  a fundamental ask on language related with mathematics and physics. The root of language would be able to describe by mathematics and physics. In my mind language is always put at the centre of the pursuit that was what anyone can clearly understand. Description by mathematics, but physics why. Physics treats with substance that constructs the world in which I had desire to let language enter. Substantial language. It was my dream and will be hereafter.

References
1.
<Meaning minimum>
Cell Theory Continuation of Quantum Theory for Language / From Cell to Manifold For LEIBNIZ and JAKOBSON / Tokyo June 2, 2007
<Bourbaki>
The Time of Language Ode to The Early Bourbaki To Grothendieck / January 10, 2012
2.
<CHINO Eiichi>
Fortuitous Meeting What CHINO Eiichi Taught Me in the Class of Linguistics / Tokyo December 5, 2004
<The Linguistic Circle of Prague>
Linguistic Circle of Prague / Tokyo 13 July 2012, 19 July 2012 Added
3.
<WANG Guowei>
The Complete Works of WANG Guowei / Tokyo 24 May 2012
<Ludwig Wittgenstein>
The Time of Wittgenstein / Tokyo January 20, 2012
<Sergej Karcevskij>
Notes for KARCEVSKIJ Sergej / Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique" / Tokyo September 8, 2011
4.
<Set Theory>
Quantum Linguistics / Growth of Word Dedicated to TAKEUCHI Gaishi / Tokyo January 30, 2006
5.
<Quantum Theory for Language>
Quantum Theory for Language Synopsis / Tokyo January 15, 2004
<Time inherent in characters>
On Time Property Inherent in Characters / Hakuba March 28, 2003
6.
<Distance>
Distance Theory / Tokyo May 5, 2004
<Meaning minimum and distance>
sekinanlogos / Floer Homology Language / Supersymmetric Harmonic Oscillator / Tokyo May 6, 2009
<Loop space>
sekinanmodel / Infinite Loop Space Language / Word as Infinite Loop Space / 6 December 2012
<Operad>

ifbetruezoho / Operad Meaning Theory / From Cell to Operad / 4 March 2013

7.
<Description>
sekinanmetria / Notes for KARCEVSKIJ Sergej / Description of Language / September 9, 2011
<Substantiality>
sekinanlogos / Floer Homology Language / Potential of Language / Tokyo June 16, 2009
<amalgamation>
Language, amalgamation of mathematics and physics / ifbetrue 2 April 2013

# Here ends the paper.

Stable and Unstable of Language Meaning Minimum of Language For the Supposition of KARCEVSKIJ Sergej

 

 

Stable and Unstable of Language

For the Supposition of KARCEVSKIJ Sergej

Meaning Minimum of Language

TANAKA Akio

October 5, 2011

[Preparation]

 ,

is graded ring and integral domain.

For negative e,  .

R's quotient field element is called homogenious when R's quotient field element is ratio f/g of homogenious element  .

Its degree is defined by .

<Definition>

At R's quotient field, subfield made by degree 0's whole homogenious elements,

 ,

is expressed by  .

For homogenious element  ,

subring of field  ,

 ,

is expressed by  .

For graded ring,

 ,

algebraic variety that  is quotient field that whole  for homogenious element  is gotten by gluing in common quotient field is expressed by Proj R.

Proj R of graded ring

,

 ,

is called projective algebraic variety.

<Composition>

Projective algebraic variety is complete.

◊

<System>

Moduli of hypersurface,

,

is complete algebraic variety.

◊

 ,

is sum set of,

 ,  .

◊

[Interpretation]

Word is expressed by,

 .

Meaning minimum of word is expressed by,

,  .

For meaning minimum,

refer to the next.

[References]

Cell Theory / From Cell to Manifold / Tokyo June 2, 2007

Holomorphic Meaning Theory 2 / Tokyo June 19, 2008

Amplitude of meaning minimum / Complex Manifold Deformation Theory / Conjecture A4 / Tokyo December 17, 2008

Gromov-Witten Invariant / Symplectic Language Theory / Tokyo February 27,2009

Generating Function / Symplectic Language Theory / Tokyo March 17, 2009

This paper has been published by Sekinan Research Field of Language.
Tokyo

4 June 2025
© 2011 by The Sekinan Research Field of Language

Sunday, 30 November 2025 From Gromov-Witten invariant to quantum cohomology ring and Gromov-Witten potential, in the centre considered homological mirror symmetry

 

Sunday, 30 November 2025

 

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

TANAKA Akio

From  Print  2012, Chapter 15He considered the direction of his work. He would create a simple model. He would represent that model using figures. The figures would be expressed using geometry. Following Kenji Fukaya, he defined geometry as "the set of a group and the space in which it acts." The appeal of Fukaya's books was that they allowed him to constantly confirm and look ahead at such fundamental things.



Based on Jakobson's "semantic minimum," I set a geometric "meaning minimum" and defined a geometric word that encompasses time as its meaning by moving time t through a closed interval. I repeated this approach many times at different geometric levels.

The universality of language has approached the invariant of mathematics. From Fukaya's book, I learned that the quantum cohomology ring can be obtained from the Gromov-Witten invariant, and furthermore, that the Gromov-Witten potential can be obtained. Language has approached mathematics and physics. Symmetries that have long bothered me can now be examined in detail. At the heart of this is Kontsevich'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

Homological Mirror Symmetry Conjecture by KONTSEVICH / 26 April 2009
Supersymmetric Harmonic Oscillator / 6 May 2009

Kitayama Iris Park, Higashikurume, Tokyo

26 June 2014

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 Print 2012, Chapter 15

彼は作業の方向を考えた。簡潔なモデルをつくる。そのモデルは図形で表わす。図形は幾何で表記する。幾何は深谷賢治に従って、「群とそれが作用する空間の組」とした。そういう根本的なことを常に確認し展望することができるのが深谷の本の魅力だった。

ヤーコブソンの「意味最小体」semantic minimumを参考にして、幾何的な「意味の最小単位」meaning minimumを設定し、閉区間closed intervalで時間tを動かすことによって、時間を意味として包括する幾何的な語wordを定義した。この方向を異なる幾何のレベルで、幾度も繰り返した。

言語の普遍性は数学の不変量invariantに接近した。深谷の本で、グロモフ‐ウィッテン不変量Gromov-Witten invariantから量子コホモロジー環quantum cohomology ringが得られ、さらにグロモフ‐ウィッテンポテンシャルGromov-Witten potentialが得られることを知った。言語は数学と物理に接近した。むかしから気になっていた対称性も精密に点検できるようになった。その中心にコンツェヴィッチによるホモロジー的ミラー対称性homological mirror symmetryがあった。

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

Homological Mirror Symmetry Conjecture by KONTSEVICH / 26 April 2009
Supersymmetric Harmonic Oscillator / 6 May 2009

Kitayama Iris Park, Higashikurume, Tokyo

26 June 2014

Another pass way to mathematics / 2 January 2013

 

Another pass way to mathematics 
02jan13
  　

In some 40 years ago, I had concerned with mathematics to which I only had read several books as if it is  the books of arts, for example, the verses of Chinese classics that are always obscure to understand by my Chinese ability. 

On the Tang Dynasty’s famous poet, DU Fu’s work I had not clearly understood, probably till now. But the works are all pleasant in its own way. As like the, mathematics I had read some books and papers. 

Definitely  I could not make DU Fu-like work. But I liked DU Fu so much. And I also cannot understand mathematics any more, but also like it. 

If there be not valuation that is usual done at school, more people maybe like it as same as they read poems putted before them. Mathematicians are put to study stern logic for its long history while the poets make poems that need severe rules of rhythm and meaning. But we should read and understand them according to our ability. 

That is all. It is my standpoint on mathematics and Chinese classics, or all of my life.

TANAKA Akio2 January 2013
Sekinan Research Field of Language

Winter comes as if grace arrives 2012

 

恩寵のように冬が来る Winter comes as if grace arrives

From Print 2012, Chapter 19

信号が変わる。

―むかしね。谷山豊TANIYAMA Yutakaって人がいたんだ。

Ａは声をすこし大きくして言った。

―若くして亡くなった。婚約者もたしかまもなく亡くなった。彼とその友人が作った予想が、フェルマー予想Fermat Theoremを解くかぎになった。ワイルズWilesという人が解いてもう十年以上になる。それで谷山TANIYAMAの特集が雑誌に載ったことがあった。

Ｉはただ彼を見ている。

―そのときね、本屋で読みながら、すごくうらやましいとおもった。雑誌は買わなかったけど、買ってもしかたがないような気がしたから。自分にはそのときなにもなかったから。ただ、そんなふうに生きてみたい、死ぬことじゃないよ、一度生きるならそんなふうに生きたいとほんとうにおもった。それがたぶん自分には生涯できないとわかっていたから、よけいうらやましかったんだ。それがね、いまは谷山TANIYAMAのように生きている。彼のようにすごくもなんともないけど。おもいはまったく同じなんだ。

―すごいわね、ほんとうに。そんなにおもえるなんて。

書店が見えてきた。

ふたりに今、恩寵のように冬が来る。For the two, winter comes as if grace arrives.

Reference: The Complete Works of TANIYAMA Yutaka / 11 November 2012