CHINO Eiichi and Golden Prague

CHINO Eiichi and Golden Prague


TANAKA Akio

C also died early, who had taught me Russian and linguistics. He loved
the old city that had the beautiful towers and bridges.

In C‘s many works there was the essay “The Moon of Carpathians”. He wrote
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached “Golden Prague”. Prague, it was his youth itself.

Now I cannot hear his voice telling the various anecdotes on languages,
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as  “the genius of linguistics”.

[References]

                                                              Tokyo
28 June 2014
Sekinan Research Field of Language

Time of Word

Complex Manifold Deformation Theory
 
 
Conjecture A 
5 Time of Word 
 
TANAKA Akio 
     
 
Conjecture 
Word has time.
[View]
¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains 
and vigorous port towns at dawn.  
1
Kähler manifold     X
Kähler form     w
A certain constant     c
Cohomology class of w     2πc1(X)
c1(X)>0
Kähler metric     g
Real C function     f
X (ef– 1)wn = 0
Ric(w) –w = f
2
Monge-Ampère equation 
(Equation 1)
Use continuity method
(Equation 1-2)
Kähler form     w’ = w +  f
Ric(w‘) = tw‘ + (1-t)w
δ>0
I = {  }
3 is differential over t.
Ding’s functional     Fw
4
(Lemma)
There exists constant that is unrelated with t.
When utis the solution of equation 1-2, the next is satisfied.
Fw(ut)C
5
Proper of Ding’s functional is defined by the next.
Arbitrary constant     K  
Point sequence of arbitrary P(Xw)K     {ui}
(Theorem)
When Fw is proper, there exists Kähler-Einstein metric.
[Impression]
¶ Impression is developed from the view.
1
 If word is expressed by u , language is expressed by Fw and comprehension of human 
being is expressed by C, what language is totally comprehended by human being is 
guaranteed.
Refere to the next paper.
#Guarantee of Language
2
If language is expressed by being properly generated, distance of language is expressed by 
Kähler-Einstein metric and time of language is expressed by tall the situation of language 
is basically expressed by (Equation1-2).
Refer to the next paper.
#Distance Theory
3
If inherent time of word is expressed by t‘s [δ, 1], dynamism of meaning minimum is 
mathematically formulated by Monge-Ampère equation.
Refer to the next papers.
#1<For inherent time>
On Time Property Inherent in Characters
#2<For meaningminimum>
From Cell to Manifold
#3<For meaning minimum’s finiteness>
Amplitude of Meaning Minimum
Tokyo January 1, 2009
Sekinan Research Field of language
 

Amplitude of Meaning Minimum

Complex Manifold Deformation Theory 
 
Conjecture A 
4 Amplitude of Meaning Minimum 
 
TANAKA Akio 
     
 
Conjecture 
Meaning minimum has finite amplitude.
[View*]
*Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains 
and vigorous port towns at dawn.  
1
Bounded domain of Rm      Ω
C function defined in Ω     uF
uF satisfy the next equation.
F(D2u) = Ψ
D2u is hessian matrix of u.
F is C function over Rm×m .
Open set that includes range of D2u     U
U satisfies the next.
(i) Constant λΛ     
(ii) F is concave.
2
(Theorem)
Sphere that has radius 2R in Ω       B2R
Sphere that has same center with B2and has radius σR in Ω      BσR
Amplitude of D2u     ampD2u
ampBσRD2u = supBσRD2u – infBσRD2u
0<σ<1
and e are constant that is determined by dimension m and .
ampBσRD2ue(ampBRD2u +  supB2R|D| + supB2R |D2| )
[Impression]
1 Meaning minimum is the smallest meaning unit of word. Refer to the reference #2 and 
#2′.
2 If meaning minimum of word  is expressed by BσR, it has finite amplitude in adequate 
domain.
[References 1 On meaning minimum]
#1 Holomorphic Meaning Theory / 10th for KARCEVSKIJ Sergej
#2 Word and Meaning Minimum
#2′ From Cell to Manifold
#3 Geometry of Word
[References 2 On generation of word]
#4 Growth of Word
#5 Generation Theorem
#6 Deep Fissure between Word and Sentence
#7 Tomita’s Fundamental Theorem
#8 Borchers’ Theorem
#9 Finiteness in Infinity on Language
#10 Properly Infinite
#11 Purely Infinite
[References 3 on distance and mirror on word]
#12 Distance Theory / Tokyo May 5, 2004 / Sekian Linguistic Field
#13 Quantification of Quantum / Tokyo May 29, 2004 / Sekinan Linguistic Field
#14 Mirror Theory / Tokyo June 5, 2004 / Sekinan Linguistic Field
#15 Mirror Language / Tokyo June 10, 2004 / Sekinan Linguistic Field
#16 Reversion Theory / Tokyo September 27, 2004 / Sekinan Linguistic Field
#17 Mirror Theory Group / Tokyo December 9, 2008 / Sekinan Linguistic Field
To be continued
Tokyo December 17, 2008
Sekinan Research Field of language
[References 4 / December 23, 2008 / on time of word]
#18 Time of Word / Tokyo December 23, 2008 / sekinan.wiki.zoho.com

Homology Structure of Word​

Floer Homology Language 
TANAKA Akio 
     
 
Note6 
 
Homology Structure of Word
§ 1
1
Compact manifold in small diameter      M
Inner product space     h (M)
Map      h (Mk→  h (M)     
2
A model and B model by Witten, E.
A model     M as symplectic structure
B model     M as complex structure  
3
(A model)
(Definition)
kA (M) = H k(M;C)
*A (M) = kA (M
Inner product <. , .>A     <uv>A =      (  ; cup product)
mA, 02(uv) = 
4
(Theorem)
*A (M), mA, 02, <. , .>A ) is Frobenius algebra.
5
Oriented  2-dimensional manifold with genus g     Σg
6
J (Σg) = {JΣg | Smooth complex structure over Σg }
Integer over 0     k
Different k-number points over Σg     z1, …, zk     (Gathered points are expressed by . )
Diff (Σg) = {ψ : Σg → Σg | ψ() = ψ is differential homeomorphism. }
Quotient space      g,k J (Σg) / Diff (Σg
Rieman surface of genus g with k marked points     (Σ
(Σg,k 
Autmorphism group     Aut (Σ= { ψ : Σ → Σ | ψ is biregular.ψ() = }
Compactification of  g,k      CM g,k 
§2
Symplectic manifold    M
Differential 2-form over M     wM
Well-formed almost complex structure with wM     JM
βH2(MZ)
 (is pseudoholomorphic.)
(Σ,φ) 
2
[(Σ,φ)] 
Evaluation map     ev[(Σ,φ)]=
3
Forgetting map    fg : 
Enlarged Forgetting map    fg : 
3
(Definition)
(Gromov-Witten invariant)
(ev, fg)*
Gromov-Witten invariant is expressed by GWg,k(M, wMβ)
4
(Theorem)
Sumset    is compact.
5
(Associative law)
(Theorem)
[Image]
Meaning minimum of word is identified with .
Word is identified with 
Commutativity of meaning minimums in word guaranteed by theorem of associative law. 
[References]
Homology on Language / Symmetry Flow Language / Tokyo May 15, 2007
From Cell to Manifold / Cell Theory / Tokyo June 2, 2007
Deep Fissure between Word and Sentence / Algebraic Linguistics / Linguistic Result / Tokyo 
September 10, 2007
Reversion Analysis Theory / Tokyo June 8, 2008
Reversion Analysis Theory 2 / Tokyo June 12, 2008
Holomorphic Meaning Theory 10th for KARCEVSKIJ Sergej / Tokyo June 15, 2008
Holomorphic Meaning Theory 11th for KARCEVSKIJ Sergej / Tokyo June 19, 2008
Word and Meaning minimum / Energy Distance Theory / Conjecture 1 / Tokyo September 
22, 2008
Geometry of Word / Energy Distance Theory /  Conjecture2 / Tokyo November 23, 2008
Amplitude of meaning minimum / Complex Manifold Deformation Theory / Conjecture A4 / 
Tokyo December 17, 2008
Tokyo June 16, 2009
Sekinan Research Field of Language
[Related Note / June 18, 2009]
Potential of Language / Floer Homology Language / June 18, 2009

Basis of the further study on language – Potential

Basis of the further study on language – Potential 
 
Floer Homology Language 
 
TANAKA Akio 
  
Note1 
Potential of Language 
   
¶ Prerequisite conditions 
Note 6 Homology structure of Word
  
(Definition) 
(Gromov-Witten potential)  
 
(Theorem) 
(Witten-Dijkggraaf-Verlinde-Verlinde equation)  
  
(Theorem) 
(Structure of Frobenius manifold) 
Symplectic manifold     (MwM
Poincaré duality     < . , . > 
Product     <V1 V2V3> = V1V2V3
(MwM) has structure of Frobenius manifold over convergent domain of Gromov-Witten potential. 
 
(Theorem) 
Mk,β (Q1, …, Qk) =  
 
N(β) expresses Gromov-Witten potential. 
 
  
[Image] 
When Mk,β (Q1, …, Qk) is identified with language, language has potential N(β). 
     
[Reference] 
Quantum Theory for language / Synopsis / Tokyo January 15, 2004 
 
First designed on   
Tokyo April 29, 2009 
 
Newly planned on further visibility  
Tokyo June 16, 2009  
Sekinan Research Field of Language 
 
[Note, 31 March 2015] 
This paper was first designed for energy of language. But at that time, I could not write 
the proper approach from the concept of energy by mathematical process. So I wrote 
the paper through the concept of potential. Probably energy is one of the most fundamental
factors on language.
In 2003 I wrote Quantum Theory for Language , before which I wrote the manuscript focusing 
the concept of quantum abstracted from the ideogram of classical Chinese written language. 
The last target of manuscript was energy and meaning of quantum that was the ultimate 
unit of language. 
Refer to the next. 
 

Preparation for the energy of language

Preparation for the energy of language

TANAKA Akio

The energy of language seems to be one of the most fundamental theme for the further step-up  study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory  papers written so far.

  1. Potential of Language / Floer Homology Language / 16 June 2009
  2. Homology structure of Word / Floer Homology Language / Tokyo June 16, 2009
  3. Amplitude of meaning minimum / Complex Manifold Deformation Theory / 17 December 2008
  4. Time of Word / Complex Manifold Deformation Theory / 23 December 2008

Tokyo
3 April 2015
Sekinan Library

How does the language models connect with natural language?

How does the language models connect with natural language?

TANAKA Akio

 

Natural language contains many important factors theoretically abstracted in the long philological studies.
At the contrast the language models made by mathematical description are themselves have not any connections with natural language.
The models by mathematics, which is totally composed from a few premises, contains many theorems and their understructures.
In these underconstructures, natural language’s factors are resembled with mathematical factors.
At the result, some resemblances are compared between mathematical models and natural language.
From these works, some resemblances to language universals may be appeared in the factors of mathematical models modified by natural language.
7 April 2014

Original: SRFL Note / How does the language model connect with natural language?

[5 May 2014 Reference added]
True-false problem of the Crete 

Tokyo
5 May 2014

Sekinan Research Field of Language        

Substantiality, Dedicated to SAPIR Edward

Substantiality

Dedicated to SAPIR Edward

TANAKA Akio

1 Substance of language is completion which possesses the distance from the real world.

2 The distance is sustained by the fixation for which meaning and time are abstracted.

3 If language has not distance, language appears and disappears following the real world proceeding.

4 Language is substantially unchangeable. Changeability occurs on surrounding.

5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.

6 Substantiality is a frame of language.

7 Substantiality is free from the real world.

8 Substantiality is powered by outer energy.

9 Powered substantiality moves complied with possessed command, namely meaning and time.

10 Powered moving substantiality of language is called <quantum>.

11 The idea of quantum is partially realized by <bar code system> in the supermarket or bookstore.

12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.

13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates <quantum> in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening.

Tokyo February 27, 2005

For the Memory of Tanashi Station Front Street, Tokyo at  February 26, 2005
Mother has lived in Tanashi City.

Sekinan Research Field of Language

How is the time alive in language?

How is the time alive in language?

TANAKA Akio

1.
When one first hear the existence of time in language, he may doubt its certainty. But I have intuitively believe it since I learned the ancient Chinese inscription on bone ad tortoise shell (in Chinese called Jiaguwen). In my early 20s, I met with the book of Chinese modern linguists, WANG Guowei, this belief changed the conviction. His lifework book Guantangjilin is hard to read till now.  But some papers in it are always inspires me by his deep and vast insight to character, language and history of ancient China. He also wrote fine criticism on Chinese pre-modern poem Ci.The title is RenjianCihua. The book is one of my favourite books of Chinese literature. People sometimes say that he was the highest genius after Song Dynasty, 1,000 years.In 2003 I wrote a tiny paper hinted by WANG’s paper. It was the first paper for me that I directly faced the time inherent in inscription using Jiaguwen’s update linguistic results. The title is ” On Time Property Inherent in Characters”.

2.
In summer 2003, I stayed at Hakuba, Nagano for a while for writing over the paper that was intended to present a symposium  at Nara in winter. The paper was taking up the structure of written language that was dealt with the relation between time and grammar. But I did not solve the question on with what shape language exists in the language world. What shape has language and at where space does language exist or float? The theme on space was hard to deal at that time. I only concentrated to the shape in space. At 28 August I was fatigued to think and went  for a stroll outside  the inn putting up. The place was at the mountain side of the Hakuba Range and there was only one convenience store, where I walked in the shop and saw one advertisement of electric pocket dictionary. I returned having this advert to the inn and read its sentences. At the very time I found the shape of language I sought was sphere that was inherited time in it, also having grammatical functions. The paper’s title was named to ” Quantum Theory for Language” by the shape of language. This was a really product of clear and fine atmosphere of Hakuba with a distant view of the North Alps of Japan.

3.
From 2004 to 2008 I wrote some papers on inscription and language. But I was not satisfied inwardly for the style of intuitive approach to language. I wanted to write more simple and clear expression. For being realised of my wish, I definitely needed to use mathematical tools. I returned to my 20s days’ reading of Bourbaki that was desperately difficult for may ability. I again gradually read mathematical books and journals for seeking useful source of my hope to converting to language study. A certain results that came to my papers with satisfaction was appeared in 2008 by the papers titled Complex Manifold Deformation Theory.

Above all, the first paper in this group, I first defined the concept, distance by complex manifold.

The concept of distance was one of the most important themes on language, so I at early times wrote the intuitive paper, “Distance Theory”.

At the fifth paper of Complex Manifold Deformation Theory, I again challenged the hard theme of the time in language, titled to ” Time of Word”.

4.
The definition of space in which language exists is one hard target for me to write satisfactory. A fixed results came to me at the papers group titles Symplectic Language Theory in 2009.

In the group, a paper focused on mirror phase on language became one peak for my writing.

5.
Related with the shape of language, quantization and discreteness on language was the urgent    themes for the further step of studying the total image of language I was pursuing. Floer Homology  Language was the one milestone for me to overcome to the next stage.

In this group, the eighth paper was dealt with the quantization and discreteness of language.

6.
What situation does the time in language have? This question exists in my mind at the early days when I wrote the paper “On Time Property Inherent in Characters”. The first step to solution was described at the paper ” Prague Theory”. The group of Prague Theory was written due to dedicate to Prague, The Linguistic Circle of Prague and Sergej Karcevskij with the memory of my teacher CHINO Eiichi.

In this paper, Chinese Character /kun/, that meaning is difficult in English, was used for the eternity of loop time. This loop time was also appeared in the paper ” On Time Property Inherent in Characters”. But Prague Theory shows more direct and compact by growing tree and its obstructive enclosing fence. This intuitive image was more clearly described at the paper ” Word as Infinite Loop Time ” at Infinite Loop Space Language in 2012.

In this paper, time in language is clearly connected with dimension of algebraic group saying as the next. Word has dimension that belongs to algebraic K group.

7.
The relation between time and dimension was entered on a new phase at the learning of algebraic geometry, especially of arithmetic geometry. Arithmetic Geometry Language, abbreviated to AGL, was the starting papers for me to arithmetic method.

From these four papers, I concisely extracted the next three conjectures.

At these conjectures, time inherent in language is in the basis of describing dimension, synthesis and reversion. The process of leading to the conjectures is over viewing the next.

8.
Acknowledgement
Time inherent in language is a fantastic but as hard to pursue for me still now. I would examine this theme further more and more, probably till the end of my research life. Now all the thanks are going to The Linguistic Circle of Prague and especially its member Sergej Karcevskij, with my teacher CHINO Eiichi who taught me their precise information from his long study at Prague in 1960s.

9.
For CHINO Eiichi

9.1 Golden Prague
C also died early, who had taught me Russian and linguistics. He loved
the old city that had the beautiful towers and bridges.
In C’s many works there was the essay “The Moon of Carpathians”. He wrote
that the conference was over, departed at Kiev, saw the moon and
churches over the Carpathian Mountains, impetuously went to the west,
passed Slovakia, Moravia, Bohemia, and at last reached “Golden Prague”.
Prague, it was his youth itself.
Now I cannot hear his voice telling the various anecdotes on languages,
of which he freely had commanded. By the short heading, a newspaper
reported his death, naming as  “the genius of linguistics”.

– 9 October 2014 –

9.2 Coffee shop named California
If C live, he also may ask me, “What  are you researching now?”
And I also will answer him as same as ever.
“I have pursued universals, never done facts, without repenting.”
Oh C, if you live, will we also talk on language?
At the table facing each other under the low ceiling of the shop going up the steep stairs.
The name of the shop is California.
For the memory of our daily forgetful life,
its never miserable though poor all over,
I will write down our delight.

– 27 October 2014 –

10.
Ode to Kanda

“I need not more wander the book shop streets.” / From Tale, Print, 2012

This tale was written by TANAKA Akio, pen-named LI Koh in autumn 2012 for remembering the poor but brilliant youth time of myself. This is one of my favourite phrases in this tale.
The book shop streets described in the tale is Kanda, Tokyo, which is located in the central Tokyo, where I frequently walked seeking the old Chinese classic books for the study from Oriental way of linguistics. In late 1960s, the streetcars were surely running in the old fashioned streets of Kanda, now perfectly changed to the subway streets.

From Print 2012, Chapter 10

もはや本屋街をさまようことはない。I need not more wander the book shop streets. 対象は私のうちにある。The object exists in my mind. 私はただこの運河をながめていればいい。I would better watch the canal. 遍歴は終わった。Wandering is over now.  たぶん永遠にマイスターにはなれないだろうが、みずからの小さな仕事場で、日が落ちるまで作業をすればいい。Perhaps I would not become meister  forever. In my narrow working place, I ‘d better do my work till sunset. すると仕事場の窓辺を聖者が通って行く。 So out of the window by the working place,  the saint passes by. かつてそんなロシアの民話を読んだ。I ever read the Russian folk tale like that.

秋の日ぐれは早い。The Autumn evening is fast. 路面電車のヘッドランプがまぶしいくらいだ。The headlight of streetcar  is dazzling. 黄褐色の窓に少ない乗客が照らし出され、古本屋街の方へ消えて行った。In the yellow-lighten window the passengers are picked out by the light. The car disappeared  to the book streets. 駅の売店がにぎやかな橙の光に包まれている。The station shop is also lighted up by the yard’s busy orange light.

Tokyo
26 November 2014
SIL

Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement

Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement

TANAKA Akio

Root
Arithmetic Geometry Language

Three Conjectures
Dimension Decrease Conjecture (Conjecture 1)
Synthesis Conjecture (Conjecture 2)
Reversion Conjecture (Conjecture 3)

Supplement
Interpretation of Reversion Conjecture
Simplification of Reversion Conjecture
Reversion Conjecture Revised

Tokyo
19 November 2014
SIL News