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.

Why I started Quantum-Nerve Theory? Note and Note 2 for The Time of Language 2012-2019

 

 Why I started Quantum-Nerve Theory? Note and Note 2 for The Time of Language

The Time of Language
Ode to The Early Bourbaki To Grothendieck

TANAKA Akio 

In early 1970s, I had think of language from the side of mathematics, that level of mine is very low and primitive, moreover I never had any talent to mathematics.

But my eager to trying the approach was going to overcome hard barriers before me. So the route had really fascinated my mind for long time. At that time I had read Chinese classics almost every day. WANG Guowei, DUAN Yucai and WANG Yingzhi. They were giants on Chinese language historically and modern.

On the other hand I had thought of language generally, not defined by Chinese. But in front of the vast world of language, I had stood still lonely, not taking any method for approaching.

Mathematics was the only gleam of hope in the wasteland.

 

The rest is omitted.
For more details refer to the next.

https://srfl-paper.webnode.com/news/the-time-of-language-ode-to-the-early-bourbaki-to-grothendieck-note-and-note-2-added/

Tokyo
January 10, 2012
Sekinan Research Field of Language

[Note, 28 October 2014]

When I first learnt French in 1964, I was the second grade of high school. My aim to learning was to get the lowest readable situation for modern poems of French Symbolism represented by Arthur Rimbaud and Paul Verlaine. Afterwards in 1969 I knew the importance of Martinet’s work at the linguistic class of university. Probably in the early 1970s, I bought Bourbaki’s books at the old-book-shop at Kanda, Tokyo, when Bourbaki’s fame reached to the poor-talented linguistic student like me.

I was enchanted Bourbaki’s works and I somehow would like to adopt their results to my linguistic study. But my mathematical level was too low to get near Bourbaki’s world. From those days my wandering around mathematics and linguistics kept long long way like the Beatles song, The long and winding road.

What I again met mathematics, especially algebraic algebra was already over the twentieth century.

From 2003 I began to write papers being assisted with CHINO Eiichi’s advice and Sergej Karcevskij’s work. At that times Chinese Qing dynasty’s vast linguistic works topically represented by WANG Guowei was also assisting my study. At the result my first satisfied paper, “On Time Property Inherent in Characters”1 was completed. The theme in my life, model making of  language universals was begun further later in 2008 at Zoho site, sekinanlogos. At Complex Manifold Deformation Theory  I started writing more clearer descriptive papers by mathematics especially according to algebraic geometry. And now I step up one more and entered in arithmetic geometry  for solving more difficult themes such as dimension, synthesis and fusion of meaning in word.

Refer to the next.

1. On Time Property Inherent in Characters
2. Zoho site
3. sekinanlogos
4. Complex Manifold Deformation Theory
5. Arithmetic geometry

[Note 2 2 May 2019]

5 years passed from I wrote Note at October 2014.

The situation for the research changed rather largely.

I and wife became older and I become 72 years old this summer while the both have illness.

We often go to the hospital for the treatment for what I often think that all the illness are probably on the nerves which make persistent flows in our body, which inevitably need energy for fluidity.

At these circumstances  I began to write a new paper titled What is signal? The existence that generates language, What is signal?, original title,   What is signal? A mathematical model of nerve. The text is the next.

https://srfl-theory.webnode.com/news/what-is-signal-total-edition-21-november-2018-23-april-2019/

So far I have thought of language at the point from language universals which are the most fantastic theme for me. But illness and its base nerve showed me the new site of language that is the real base of language. It was the signal which has energy and flows and hatch language in the human being.

Now I stand back at the manuscript written in 2003 at Hakuba, Nagano, Japan titled Manuscript of Quantum Theory for Language. The text is the next.

https://srfl-paper.webnode.com/news/manuscript-of-quantum-theory-for-language-with-preface-note-and-note-2-2003-2018/

Quantum is the real kernel of my research, by which signal and language may be constructed for human being.

Tokyo
2 May 2019
Sekinan Library

Tokyo
27 November 2019 Text revised
SRFL Paper

Another pass way to mathematics 2013

      Saturday, 27 July 2013

Another pass way to mathematics 

02jan13

In some 40 years 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 them 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 anymore, 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 logics for its long history while the poets make poems that need severe rules of rhythm and meaning. That is all, for my standpoint on mathematics or Chinese classics or my life.

 

Word as Infinite loop Space 2012-2022

 

 

Word as Infinite loop Space

TANAKA Akio

1. 

Result of D. G. Quillen by Annals of Mathematics, 96 (1972).

Algebraic K theory over commutative ring R.

 is classifying space of   .

Quillen showed that  is infinite loop space.

2.

Interpretation of Quillen's result.

Meaning of word is expressed by .

Word is expressed by , .

Saying in other words. 

Word is expressed by high dimensional algebraic K group over commutative ring R.

Conclusion at the present.

Word has meaning that is expressed by infinite loop space.

Word has parameter that is expressed by commutative ring.

Word has dimension that belongs to algebraic K group.

Tokyo
6 December 2012

Zoho Sites of Sekinan

Sekinan Research Field of Language

[Reference added]

NISHI Junzo, Philosopher of Modern Japan, What NISHI Junzo remained for us

12 September 2022
Quantum-Nerve Theory

Energy Distance Theory Conjecture 2 Geometry of Word 2008

 

Energy Distance Theory Conjecture 2 Geometry of Word

TANAKA Akio

[Conjecture]

Word is infinite cyclic group.

[Explanation]

Ⅰ

(Preissmann’s theorem)

When (M, g) is connected Riemann manifold and sectional curvature of M is always K_M < 0, non-trivial commutative subset of functional group of M, π₁(M) always becomes infinite cyclic group.

Ⅱ

Preparatory proposition for Preissmann’s theorem

(Proposition 1)

When (M, g) and (N, h) are compact Riemann manifold and N is non-positive curvature K_N≤0, arbitrary continuous map f ∈C⁰(M, N) is free homotopic with harmonic map u_∞∈C^∞(M, N).

(Proposition 2)

When M is compact Riemann manifold, Ricci tensor of M is positive semidefinite Ric^M≥0 , N is non-positive curvature K_N≤0, and harmonic map is u : M→N,  the next is concluded.

When N is negative curvature K_N<0, u is constant map or map of u coincides with map of closed geodesic line.

Ⅲ

Consideration for the theorem and propositions

1

m-dimensional C^∞ class manifold     M

Point of M     x

Tangent space of x     T_xM

Inner product of T_xM   g_x

Coordinate neighbourhood of M     U

Local coordinate system of U     (x¹, …, x^m)

Function     g_ij : g_x ( (∂/∂xⁱ)_x, (∂/∂x^j)_x), 1≤i, j≤m

g_ij is C^∞ class function over U.

Family of inner product     g = {g_x}_x∈M

g is called Riemannian metric.

When M has g, (M, g) is called Riemannian manifold.

2

Riemann manifold      (M, g)

M’s C^∞ class vector field    X (M)   

Linear connection of M     ∇

X, Y, Z∈X(M)

What ∇ and X, Y, Z uniquely satisfy the next is called Levi-Civita connection.

(i) Xg(Y, Z) = g(∇_XY, Z) + g(Y, ∇_XZ)

(ii) ∇_XY -∇_YX = [X, Y]

3

m-dimensional Riemann manifold (M, g)    M

Levi-Civita connection of M     ∇

X, Y∈X

R(X, Y) : = ∇_X∇_Y - ∇_Y∇_X - ∇[X, Y]

Map R : = X(M) ×X(M)×X(M) → X(M)

R(X, Y, Z) : = R(X, Y)Z

R is called curvature tensor of M.

4

x∈M

2-dimensional subspace of tangent space T_xM     σ

σ’s normal orthogonal basis on g_x     {v, w} {v’, w’}

K(v, w) = R(x)(v, w, w, v) = g_x(R(x)(v, w)w, v)

v’ = cosθv + sinθw, w’ = ∓sinθv±cosθw  (double sign directly used)

K(σ) : = R(x)(v, w, w, v) = R(x)(v’, w’, w’, v’)

K(σ) is called sectional curvature.

[References]

<Example of word’s infinite cycle is shown by the bellow.>

On Time Property Inherent in Characters / Hakuba March 28, 2003

Prague Theory / Tokyo October 2, 2004

Prague Theory 3 / Tokyo January 28, 2005

TOMONAGA’s Super Multi-Time Theory / Tokyo January 25, 2008

<On minimum unit of meaning, refer to the next.>

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

Reversion Analysis Theory / Tokyo June 8, 2008

Reversion Analysis Theory 2 /Tokyo June 12, 2008

Holomorphic Meaning Theory / Tokyo June 15, 2008

Holomorphic Meaning Theory 2 / Tokyo June 19, 2008

Energy Distance Theory / Conjecture 1 / Word and Meaning Minimum / Tokyo September 22, 2008

To be continued

Tokyo November 23, 2008

Sekinan Research Field of Language

www.sekinan.org

Postscript
[Reference November 30, 2008]

Distance of Word / November 30. 2008 / Sekinan.wiki.zoho.com

Deep Fissure between Word and Sentence 2007

 

Linguistic Result

Deep Fissure between Word and Sentence

　　  TANAKA Akio

Now language has some algebraic postulations below.

Word consists of elements R₁. The element has proto-meaning.

Word’s meaning is generated by product(・) of the elements.

The product of elements is called primary meaning (R₁, ・).

Word is group.

Another word ( R₂, ・)is generated.

New word is generated by addition (＋) of the elements of two words.

The addition of elements is called secondary meaning (R₁, R₂, ・, + ).

New word is ring.

The upper group and ring are regarded as commutative.

Sentence consists of words T₁.

Sentence is generated by product of words (T₁, ・).

But sentence is seemed to be non-commutative, i.e.T₁T₂T₃ is not T₃T₂T₁. /I/ /read/ /book/ is not /book/ /read/ /I/. Word is expressed by / /.

I call the situation <deep fissure between word and sentence>.

This <fissure> is seemed to be relative with true-false argument of sentences.

Tokyo September 10, 2007

Sekinan Research Field of Language

www.sekinan.org

Postscript January 21, 2008

[Basis]

<On differential structure between word and sentence>

Algebraic Linguistics / Linguistic Note / 12 / Coset / Tokyo August 6, 2007

[Foresight from past work]

<On true-false value>

Tube-Ring Theory / True and False Hierarchy of Language / For CHINO Eiichi and Prague / Tokyo July 25-28, 2006

Algebraic Linguistics / Linguistic Result / From Cut and Glue Dimension to Krull Dimension / 8^th for KARCEVSKIJ Sergej / Tokyo September 26, 2007

Postscript February 10, 2008

[Conjecture]

<On finiteness and Infinity on language>

Kac-Moody Lie Algebra / Finiteness in Infinity on Language / Tokyo February 10, 2008

Postscript August 2, 2008

[Conjecture]

<On Definition of word and sentence>

Stochastic Meaning Theory / Conjecture 1 / Tokyo July 12, 2008

<On warp and entropy of language>

Stochastic Meaning Theory / Conjecture 2 / Warp and Entropy / Tokyo July 25, 2008

Intuition and Mathematics 2012

 

Intuition and Mathematics

TANAKA Akio

                 Tokyo, 30 August 2012              

Intuition and mathematics are deeply concerned with each other. In my stand, intuitive concept is first flowing up and the next mathematical description is arranged. According to this situation, intuition is very important and if there is no such flowing up thinking, the development is almost not so easy proceeding.

The time concept in language is the key concept of my language model that is at first found from the ancient Chinese characters' construction and after writing a short intuitive paper, the more precise descriptions are took up using mathematics especially of geometry. 

But at the deepest basis of language, time is seemed to be infinitive but not spread tin a strait line to the future, more likely going round as  circle or circular situation. This conjecture was firmed by Yi-jing that is one of the Five Great Classics of China. I received the lecture on Yi-jing from philosopher NISHI Junzo some five years at the university. 

The world of Yi-jing consists from perfect infinitive circularity and this world is perfectly recognised by human for its closed situation of infinity. It is very hard to recognise infinity as perfect whole image and Yi-jing is resolved this baffling problem through the shut-in world, that is "compact" concept of mathematics.

                    

Intuition and Mathematics through Chinese classic Yi-jing. 2012-2019

 

Intuition and Mathematics through Chinese classic Yi-jing. 2012-2019

 

Sep 21, 2021

Intuition and Mathematics

What NISHI Junzo remained for us 2

TANAKA Akio                                    

Intuition and mathematics are deeply concerned with each other. In my stand, intuitive concept is first flowing up and the next mathematical description is arranged. According to this situation, intuition is very important and if there is no such flowing up thinking, the development is almost not so easy proceeding. 

The time concept in language is the key concept of my language model that is at first found from the ancient Chinese characters’ construction and after writing a short intuitive paper, the more precise descriptions are taken up using mathematics especially of geometry. 

But at the deepest basis of language, time is seemed to be infinitive but not spread with a strait line to the future, more likely going round as circle or circular situation. 

This conjecture was firmed by Yi-jing that is one of the Five Great Classics of China. I received the lecture on Yi-jing from philosopher NISHI Junzo some five years at the university. 

The world of Yi-jing consists from perfect infinitive circularity and this world is perfectly recognised by human for its closed situation of infinity. 

It is very hard to recognise infinity as perfect whole image and Yi-jing is resolved this baffling problem through the shut-in world, that is “compact” concept of mathematics.  

Tokyo
30 August 2012
8 September 2019 Text revised
SRFL Paper

My Haiku Teacher, SAEKI Shoichi 2012

 

My Haiku Teacher, SAEKI Shoichi 

TANAKA Akio 

Tokyo 4 July 2012  Revised 11 July 2025
                                

Haiku is the traditional Japanese literature since the Meiji Period some 140 years ago, the ancestor of which was called Haikai that was began in the Muromachi Period some 500 years ago.
I have made Haiku since age 20s. My Haiku's teacher is SAEKI Shoichi, one of the modern Haiku writers in Japan. SAEKI's spiritual teacher is probably ISHIDA Hakyo, famous Haiku writer in the Showa Period. Thus the tradition of the literature has been proceeded in Japan.
One of my youth age's Haiku ( at Tokyo, February 1970) is the following.

パンタグラフ冷たい隙間で発光す

Pantograph
At the coldest clink
Radiates light for me

Under the Dim Light 2012

 

Sekinan Research Field of Language

Under the Dim Light 

TANAKA Akio 





                                        

I frequently talked with CHINO Eiichi at the coffee shop near the station we used to get on. The shop was at the second floor and the steps upstairs always sounded squeaking. Under the dim light the topics of conversation was on language or linguistics after all. He was already the university professor but I was a poor research student. But he was always showed me the general tenderness.

The subject he gave me were impressive and useful for me, in which the most important is the history of the Linguistic Circle of Prague and the excellent pioneers of language study. He had of course the unique approach to the study but I had never any conspicuous one except boundless interest on the study.

In his wide and precious telling for me I gradually determined my course to proceed. It was the making of basic and radical foundation on natural language by searching the structure of language through simple and clear description. For keeping this difficult aim I had a decision that there was only way to use mathematics that I had abandoned at the past for its hardness.

In my age 20s, I had read Ludwig Wittgenstein and Nicolas Bourbaki in concentrating. I did not clearly understand  Wittgenstein's approach. But I borrowed his writing style that was simple and clear. So my early work's descriptions were nearly at him. But I decided that I never adopted strongly-intuitive thinking.

I always considered mathematical basis or analogy. My aim was the independence from the intuitive description. Keeping on this course, there was seen the mathematical basis that I must adopt the model in which language universals are clearly described. I entered to the mathematical description of study that was confirmed premises of my way.

At the North Alps of Japan.
The flowers are alike the time of my past.
They were receiving the hard cold winds at the mountains.

Tokyo
1 August 2012
Sekinan Research Field of Language