Sunday, 31 August 2025

Functional Analysis 2 Conjecture 1 Generation of Word

 

Functional Analysis 2 Conjecture 1 Generation of Word


Functional Analysis 2

Conjecture 1

Generation of Word 

TANAKA Akio

1 Let it be supposed that meaning of word is expressed in pre-Hilbert space H.
2 There exists Hilbert space H~ that contains pre-Hilbert space H as dense subspace
3 H’s linear operation and inner product is in H~.
4 Extension of meaning at word is guaranteed in space.
5 Geometrically let it be supposed that word is open sphere which is countable closed set.
6 Language is considered in succession of spheres that is expressed as <Quantum Theory for Language>.
[References]
<Hilbert space>
<Extension of meaning>
<Generation of hierarchy in language>
<Sphere>

Tokyo May 30, 2008
Sekinan Research Field of Language
www.sekinan.org

Quantum Theory for Language 2004

 

Quantum Theory for Language

Synopsis

Revised and Noted from Prototheory Paper   On Time Property Inherent in Characters


TANAKA Akio

1
The object of this theory is isolating languages. #1
2
The Chinese language is adopted for the model of isolating languages. #2
3
In this theory the Chinese character is regarded as the Chinese language.
Therefore this theory is the theory for written language. #3   
4
The Chinese character is the basis of this theory.
5
The Chinese character is the quantum of language. #4
Quantum is defined.
The quantum of language is the smallest unit of language.
The quantum of language has the force.
This force propels oneself to the next quantum.
Force is defined.
6
The quantum consists of indicators. #5
7
The indicator is the shape abstracted from the real world.
Indicator is defined.
The indicator has the signification and the period inherently.
8
The inherent signification of the indicator is produced from the work of the real world.
Inherent signification is defined.
The inherent period of the indicator is produced from the time of the real world.
Inherent period is defined.
9
The quantum consists of one or more than one indicators.
10
The quantum has the inherent meaning and the inherent time that is produced from one or more than one indicators. #6
11
The inherent meaning of the quantum is produced from the indicator or the combination of the indicators.
Inherent meaning is defined.
12
The inherent time of the quantum is produced from the indicator or the combination of the indicators.
Inherent time is defined.
13
The period of indicator has the start point and the end point.
The length of two points is called the period zone.
Period zone is defined.
The time of quantum have the start point and the end point.
The length of two points is called the time zone.
Time zone is defined.
14
The time zone of the quantum decides the state of the connection of the two quanta.
This state of the connection is called <time principle of quantum>.#7
15
The front quantum that has the short time zone can connect the rear quantum that has the long time zone.
This qualification is called <connection rule>.
This situation of connection is called word.
Word is defined.
16
The front quantum that has the long time zone cannot connect the rear quantum that has the short time zone.
This qualification is called <separation rule>.
This situation of separation is called sentence.
Sentence is defined.
17
Language has the gathering of words.
This gathering is called territory.
Territory is defined.
18
Language has the gathering of sentences.
This gathering is called province.
Province is defined.
19
The quantum appears for the purpose of adding the new value of the territory. #8
The value can spread the recognition of the human being.
This value is called harvest.
Harvest is defined.
20
Quantum propels oneself to the next quantum on a line.
This line is called orbit.
Orbit is defined.
21
Quanta propel on an orbit by the force of quanta.
The force of the quantum is produced from the indicator.
The indicator is the shape abstracted from the real world.
Therefore the indicator constantly approach to the real world.
This approach makes the force of quantum.
The force is placed in this theory.
The quantum connects real world by the force of approach.
This connection guarantees the existence of the quantum.
The quantum makes the word.
The quanta make the word.
The word is guaranteed.
The quanta make the sentence.
The sentence is guaranteed.
The quanta make the language.
The language is guaranteed.
22
A sentence needs an orbit.
Another sentence needs another obit.
Two sentences cannot propel on the same orbit.
This qualification is called <propelling rule>.
23
A sentence becomes at rest when a quantum approaches the most nearly to the real world.
The force of the quantum disappears because of no use of approaching to the real world.
This phenomenon is called standstill.
Standstill is defined.
Standstill phenomenon is concerned with the prayer of belief in human being.
Because the prayer is the act of constantly approach to the real world of religion.
Standstill phenomenon is a subject for the anthropology of religion. #9
24
The orbit is linear.
Next orbit is under the former orbit in this theory.
The quantum of next orbit is located just below the quantum of the former orbit.
For example from Chinese, / Wo shuo de shi jiade. /In English, What I say is a lie.
By the combination rule, the separation rule and propelling rule, this Chinese is showed below.
     Wo
shuo
             de
               shi jia
                    de.
This showing of the orbits is called orbit table. #10
Orbit table is defined.
The quanta on the same orbit is called phrase.
Phrase is defined.
In the orbit table, the place of the each orbit is called the layer.
Layer is defined.
25
In upper orbit table, the orbit of /shuo/, say, and /shi jia/, is a lie, is located in another layer. 
The orbit of /shuo/ is guaranteed.
The orbit of /shi jia/ is also guaranteed.
26
The orbit of /shuo/ and the orbit of /shi jia/ are different.
Two orbits belong to another place of the language.  
Language is made from orbits on which quanta are located.
27
/Wo shuo de shi jia de. / becomes contradiction in the current recognition of language.
But in this theory /shuo/ and /jiade/ are located another orbit.
Therefore contradiction is avoided.
Two orbits are equally guaranteed.
But the quantum of /shuo/ is farther than the quanta of /shi jia/ from the standstill.
/shi jia/ is nearer to the real world than /shuo/.
In the linear obit, nearer quantum to the standstill is stronger to the real world.
This is called <strength rule>.
Strength is a quantity of distance, from one quantum to the real world.
Strength is defined.
28
/Wo shuo de shi jia de. / is recognized below.
“The world is a lie. One place in this world I tell someone something.”
There is no contradiction here.

Notes
#1
This theory originates in the concept <drift> of Edward Sapir.
#2
This theory is indebted to the book of Wang Yingzhi, Jingzhuanshici.
#3
Chinese characters are almost the Chinese language itself.
Because Chinese syllabic sounds always request the own images for the memories.
Therefore Chinese characters can also act as the spoken Chinese. 
#4
This Concept originates in the paper of Wang Guowei, Yinbucizhong suojian xiangong xianwang kao.
#5
Chinese character /yu/ generally means give birth to in English.
In ancient style of character /jia gu wen/ inscriptions on bones or tortoise shells, it has three indicators, woman bending forward, body fluid at childbirth, new born baby.
Therefore this character has the inherent meaning and time.
In other words, there are three successive categories of meaning and time, pregnancy, birth and support.
The quantum is essentially structural.
#6
This concept originates in the paper of Sergej Karcevskij, “Du dualisme asymetrique du signe linguistique”.
#7
The quantum of language disappears when the meaning of the quantum goes out of use.
For example, Chinese character /bu/ not originally meant a part of flower.
But this notional meaning disappeared early in the Chinese language.
Later instead of this meaning, /bu/ possessed the denial function. 
#8
Chinese character /jiao/ means teach in English, containing short time.
Chinese character /shi/ means room in English, containing long time.
Time of existence is longer than time of movement. Therefore /jiao shi/ makes one word. It means classroom.
But /shi jiao/ make one sentence, not one word. It means in the classroom I teach.
So connection and separation of the quanta are the new syntactic principle of the Chinese language.
It is called< time principle of quantum>.
#9
This theory is also a gift to anthropology, which always gives the theory flashes of thinking.
Many thanks for anthropology, especially for the book of Kawada Junzo, Mumoji shakai no rekishi.   
#10
In Chinese traditional syntax, characters have been classified into two groups, /shi ci/ notional words and /xu ci/ functional words.
In this quantum theory, notional words have long time, functional words have short time.
Orbit table is made by the time measuring of this traditional classification.
<Quantum Theory for Language> inherits the linguistic method from /xiaoxue/ small study of the /Qing/ Ching dynasty.


Tokyo 
January 15, 2004
For the memory of Hakuba August 23, 2003
Sekinan Research Field of Language


Postscript
[References / January 21, 2008]
<On the property of quantum>
Clifford Algebra / Note 1 / From Super Space to Quantization / Tokyo January 10, 2008
<On orbit and orbit table>
Clifford Algebra / Note 3 / Anti-self-dual Form / Tokyo January 15, 2008

[References / December 21, 2008]
<Survey at the time>
Quantum Theory for Language / Simplified Review
Brief History of Quantum Theory for language
Log of Quantum Theory for Language / Love and Thanks to the Pioneers
Log of Quantum Theory for Language / On the Themes of SAPIR and KARCEVSKIJ
<Following theory at the time>
Mirror Theory
<A conclusion at the time>
Warp Theory

[Reference / January 1, 2009]
<On meaning and grammar>Orbit of Word / Complex Manifold Deformation Theory / sekinanlogos


RIREI Mathematical Based Language Study Succeeds Sekinan Library and SRFL August 2025

 

RIREI

Mathematical Based Language Study

Succeeds
Sekinan Library 
and 
SRFL

Sekinan Library was founded at Tachikawa, Tokyo in 1 April 1986.
Till March  of that year I was a student of the post graduate course
for cultural sciences and also worked at a night course of a high school
for keeping daily life. 


At university I studied the history of Buddhism of ancient Japan mainly
reading old Japanised Chinese writings while learning the history of
European linguistics typically represented by 
The Linguistic Circle of
Prague
 in 1920s.

 Buddhism was taught from Prof. KAWASAKI Tsuneyuki and linguistics
was  from Prof. 
CHINO Eiichi. In those days I had been concerned with the
presentation of historical text by Chinese characters which was not any
inflections in sentence, so usually called isolated language, which grammar
only being controlled by word order.

I wondered that what is word order, how the grammar changes in the
non-inflation words
. All were in the utterly dark world because European
linguistics had not made up the developed isolated language like classical
Chinese. But in China especially in the era of Qing dynasty, many linguists
had studied Chinese classics using vast methods historically formed since
circa 500 B.C.

At March 1986, I determined that study theme was limited in the linguistic
study of ideogram like Chinese character, for the study of which a new
perspective would be appeared from our Oriental region still now using
ideogram like China and Japan
. From April I started my study while
teaching modern and classical Chinese at Sekinan Library. At night
frequently being called as the lecturer of Buddhism and Chinese of civic
education. At that time the most interesting theme of the study was
 
ancient Chinese characters inscribed on oracle bones and tortoise shells,
which already showed the perfect system of ideogram and had been studied
in the Qing dynasty's linguists
, in which I was deeply fascinated by 
WANG Guowei's work Quantangjilin.

Over decade after, in Spring  2003, I wrote a manuscript for my study,
titled "
Manuscript for Quantum Theory for Language". Continuing
this work, 
I could first written a paper on diagram focused on inherent
time in Chinese characters
. The title was " 
On Time Property Inherent
in Characters
" and its direct succession, "Quantum Theory for
Language
 " 
which was presented at a conference opened at Nara in
December 2003.


RI Kohr (TANAKA Akio) 

28 August 2025
RIREI(New Site by RI Kohr)



Afar Sayama Hills, Tokyo

The comparison between 2003 and 2017 From Chinese character's meaning structure to Homological algebraic model of language universals

 

The comparison between 2003 and 2017
From Chinese character's meaning structure to Homological algebraic model of language universals 

 
TANAKA Akio
 
1. Between 2003 and 2017
In 2003 I wrote a paper that showed meaning's inner structure of Chinese characters.
The paper was based on Chinese character's old form, Jaguwen, Chinese inscriptions on animal bones and tortoise carapaces that was first found at Henan-sheng, China in 1999. I wrote the paper mainly depending on WANG Guowei's work. My paper is the following.

On Time Property Inherent in Characters. 28 March 2003 

 
In this 2017 I wrote a related paper with the 2003's paper, which mainly focused on ideogram's general purpose property from hieroglyph to LATEX symbols. My paper is the next.
 
The Days of Ideogram. 20 April 2017


2. From philology to algebra
The 2003 paper is on the continuation of Qing Dynasty's classical philologists in China.
The 2017 paper is on the extension of Category theory's homological approach.



3. From intuitive to definitive
The 2003 is not openly used mathematical approach, as a result  writing style is considerably intuitive.
The 2017 is also intuitive, but in its base, more sufficient mathematical data in the 17 year study result. The most recent work is Derived Category Theory. The theory is at the next.


Derived Category Language


Now the  upper two papers, the 2003 and the 2017 and their related papers are seen at Sekinan Paper and Sekinan Theory.


Sekinan Paper
Sekinan Theory


4. Starting place
The new theory is now being prepared for more mathematical-descriptive expression titled Homology Language.Starting place is at the following papers.

Karcevskij conjecture 1928 and Kawamata conjecture 2002
Language stability and triangulated category


5. Gist of  Homology Language
 The fundamental essences are the next.
(1)
Set is defined as Universe which can avoid set theory's contradiction.
(2)
Set is considered as Category which can get back to all the concepts to Object and Morphism.
(3)
Topological space is considered as Homology which can get back all the work to algebra.
(4)
Language model is considered as Sheaf which can past functions to the more big function.
(5)
Language can take Contractible which can describe free concepts as meaning.  
 
 
6. Aim of Homology Language
(1)
Language will get near to finite generative a little alike natural language.
Fundamental work was done at the next from set theory but not definitive as universe

 
von Neumann Algebra 2 Note Generation Theorem
 
(2)
Category theory seems to be a one-step-up stage to write on language from the days of Maclane Saunders. Refer to the next.
 Topological Semantics. Torus Chain. For MAC LANE Saunders
Language and Spacetime. Word Containing Time and 4 Dimensional Sphere. Dedicated to MAC LANE Saunders
Language and Spacetime. Structure of Word. From KARCEVSKIJ to MACLANE
For MAC LANE Saunders. Categorical Approach toward Language
 
(3) Homological approach
In 2009 I wrote a trial papers titled Floer Homology Language. Still now the papers are important for my study.


Floer Homology Language
   |
   Potential of Language
   Supersymmetric Harmonic Oscillator
   Grothendieck Group
   Reversibility of Language
   Homology Generation of Language
   Homology Structure of Word
   Quantization of Language
   Discreteness of Language



In Floer Homology Language, the next two papers will become the guidepost for new theory Homology Language

Homology Generation of Language
Homology Structure of Word


(4) Symplectic algebra
Symplectic algebra is one of the most fantastic fields of the contemporary mathematics.
I also ever wrote simple invitational papers for applying to language universals.
The papers are next.

Symplectic Language Theory
     |
     Symplectic Topological Existence Theorem     
     Gromov-Witten Invariant     
     Mirror Symmetry Conjecture on Rational Curve     
     Isomorphism of Map Sequence     
     Generating Function  
     Homological Mirror  Conjecture by KONTSEVICH
     Structure of Meaning
     On Structure

In the papers, The next contains the update result of homological approach.

Homological Mirror Symmetry Conjecture by KONTSEVICH


(5) Bridge to resolve
Relationship between symplectic geometry and derived category shows the realization of clearer description on  language.universals Because for my part, Symplectic Language Theory and Floer Homology Language seems to be the nearest way to resolve the hardship of natural language's inner structure.
The details are the next.

 Additional meaning and embedding

 
(6) Symmetry
The concept called symmetry is very important to describe the complex situation of natural language.
Symmetry contains undifferentiated factors in itself, for example mirror, distance,ant-world and so forth.
I ever tried to cultivate this fantastic field to resolve the hardship on language universals one more step up. 

My trying paper is the following.

Mirror Theory
Mirror Language

 
 ..............................................................................................................
 
This paper in unfinished.
 
 
Tokyo
6 July - 9 July 2017
Sekinan Library

Read more: https://srfl-paper.webnode.com/news/the-comparison-between-2003-and-2017-from-chinese-characters-meaning-structure-to-homological-algebraic-model-of-language-universals/




Quantum Language between Quantum Theory for Language 2004 and Generation of Word 2008. 2018. Note on David Marr and Grisha Perelman. 2020

 

Quantum Language between
Quantum Theory for Language 2004
and
Generation of Word 2008
adding their days and after

 

..........................................................................................................................................

 

Quantum Language between
Quantum Theory for Language 2004
and
Generation of Word 2008
adding their days and after
A conclusion for the present on early papers of Sekinan Library
2018

 

 

 
Quantum Language 
between Quantum Theory for Language 2004 and Generation of Word 2008
adding their days and after
 A conclusion for the present on early papers of Sekinan Library
 
 
 
23 January - 26 January 2018
Tokyo
 

1.
I wrote a paper titled Quantum  Theory  for Language in 2004.
This paper was read at the international symposium on Silk Road at Nara, Japan in December 2003.
The encounter with this time's persons and thoughts are written at The Time of Quantum  in September 2008.

2.
This paper's concept was prepared at Hakuba, Nagano, Japan in March 2003.
This concept was jotted down at the hotel of Hakuba so the publication became late till 2015. The title was named Manuscript of Quantum Theory for Language.
 
3.
In Autumn 2002 I was hospitalized by pneumonia for two weeks, when I thought to put the linguistic research on old Chinese characters so far in order. The result was arranged as a paper titled On Time Property Inherent in Characters also at Hakuba in March 2003.
 
4.
Quantum Theory for Language was added proviso, Synopsis, because the paper was thought at that time as a role of a rather long mathematical paper's preface on quantum theory on language.
 
5.
In 2005 Distance Theory was written as a successive paper of Quantum  Theory  for Language. In those days Reversion Theory in September 2004, Prague Theory in October 2004 were successively written.
 
6.
Time passed by rapidly.
After some preparations of mathematics, I wrote successive papers related with Quantum Theory for Language. von Neumann Algebra was put at the centre of preparation. The days at that time was simply wrote titled as The Days of von Neumann Algebra and The Days between von Neumann Algebra and Complex Manifold Deformation Theory in 2015.
 
7.
von Neumann Algebra succeeds from 1 to 4. 2's Generation Theorem was written in April 2008. After von Neumann AlgebraFunctional Analysis was written. 2's Generation of Word 's result is directly connected to Quantum Theory for Language's mathematical background.
 
8.
From 2008 I frequently used Zoho site because of easily writing by mathematical equation system. Complex Manifold Deformation Theory was the first result of Zoho. At Floer Homology Language some complementary fruits were gotten for Quantum Theory, Homology Generation of Language in June 2009 and Homology Structure of Word also in June 2009.
 
9.
Algebraic geometry had been consistently flowing in Quantum Theory.
Recently written Connection between early paper's quantum and recent paper's geometry, November 2017 summarizes the situation at that time concisely.
 
10.
Quantum Theory's time series representative is the following.
(1)
(2)
(3)
 
11.
Basis of On Time Property Inherent in Characters 2003, Manuscript of Quantum Theory for Language 2003 and Quantum  Theory  for Language 2004 are all led by Qing Dynasty's linguistic (Xiaoxue) tradition, especially from WANG Guowei, whose influence is written at The Time of WANG Guowei in December 2011.

12.
In 1970s at my age 20s, while I had read WANG Guowei, also read Ludwig Wittgenstein, from whom I narrowly learnt writing style that was maintained through early papers. On Wittgenstein I wrote The Time of Wittgenstein in January 2012. Especially written essayFor WITTGENSTEIN Ludwig Position of Language intermittently wrote from December 2005 to August 2012.    
 
13.
WANG Guowei taught me the micro phase of language and Edward Sapir taught me the macro phase of language. His book,  Language 1921 shows us the conception of language's change system, Drift. I ever wrote 
some essays on him and his book titled Flow of Language in September 2014.
On Edward Sapir I recently wrote a essay titled Edward Sapir gave me a moment to study language universals together with Sergej Karcevskij  in July 2017
 
14.
I met again with CHINO Eiichi in 1979, from whom I learnt almost all the contemporary linguistics' basis, because of my bias to Chinese historical linguistics ( Xioxue) and Japanese classical phonology in characters. Reunion with CHINO was written at a essay titled Fortuitous Meeting What CHINO Eiichi Taught Me in the Class of Linguistics in December 2004. Also wrote Under the Dim Light in August 2012, CHINO Eiichi and Golden Prague in June 2014, Coffee shop named California in February 2015 and Prague in 1920s in April 2016.

15.
CHINO Taught me the existence of Linguistic Circle of Prague and Sergej Karcevskij  at Prague in 1920s. I wrote Linguistic Circle of Prague in July 2012 and also wrote on Karcevskij, Gift from Sergej Karcevskij in October 2005, Sergej Karcevskij, Soul of Language in November 2012Follower of Sergej Karcevskij in November 2012  Meaning Minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi in April 2013 and For KARCEVSKIJ Sergej from time to time.

16.
In 1970s, I also learnt mathematics for applying to describe language's minute situation. I had thought that language had to be written clear understanding form for free and precise verification going over philosophical insight. When set theory led by Kurt Godel was raised its head to logical basis, I was also deeply charmed by it. But even if  fully using it, language's minute situation seemed to be not enough to write over clearly by my poor talent. The circumstance was written titled Glitter of youth through philosophy and mathematics in 1970s in March 2015. .

17.
One day when I found and bought Bourbaki's series Japanese-translated editions, which were seemed to be possibility to apply my aim to describe language's situation. But keeping to read them were not acquired  at that time. So I was engrossed  in Chinese classical linguistics achieved in Qing dynasty, typically DUAN Yucai, WANG Niansun, WANG Yinzhi and so forth. The days were written as  The Time of Language Ode to The Early Bourbaki To Grothendieck.

18.
Algebraic geometry began from von Neumann AlgebraAfter these days, Zoho time came to me. Its first result is shown as the title Complex manifold Deformation Theory in 2008. Distance of Word in November 2008 is a mathematical conclusion of Distance Theory in May 2005. Zoho's main papers were seen at the site Sekinan Zoho.

19.
Distance Theory has some derivations towards physical phases in my thought. Distance Theory Algebraically Supplemented Brane Simplified Model was written in October-November 2007. Each paper is the following.

Distance Theory Algebraically Supplemented
Brane Simplified Model
Bend
Distance <Direct Succession of Distance Theory>
S3 and Hoph Map 
 
Physics was one of the most fantastic fields in high school days. I ever wrote the days of yearning for physics and after that. Perhaps Return to Physics in April 2014, Winding road to physics in January 2015, Thanks to physics about which I ever dreamt in my future in April 2015, 

20. 
After 2008 at Zoho sites, mathematics based language papers were successively written aiming clearer definition. Zoho's annual papers are shown at Sekinan Zoho'Zoho by year from 2008 to 2013. While I continued writing papers, my aim was gradually changed to confirm language's basis through mathematical, especially algebraic geometrical description by language models a little parting from natural language. The circumstances behind confirmation was written at Half farewell to Sergej Karcevskij and the Linguistic Circle of Prague in October 2013 and 40 years passed from I read WANG Guowei in November 2013.
 
 

...............................................................................................
 
 
Note
On David Marr and Grisha Perelman 
5 June - 7 June 2020
 
David Marr's Vision 1982, Marr refers to possibility for the existence of modular design at the upper place in language. He also says that there needs multiple description to research meaning.
The book gives me a bit different way to approach to the root of language aparting from ordinary mathematical method of mine, but if anything, nearly to geometry, in my way, ,Perelman's.
Refer to the next two paper groups, especially at Heat equation and Geometrization Conjecture.
Heat and Geometrization has been the most important target of my research since about 2018. 
 

Perelman's Approach 2

31/01/2016 20:25

Geometry of Geometrization Conjecture

09/08/2015 19:08

Canonical resoresolution

09/08/2015 19:01

Geometrization Conjecture

09/08/2015 18:53

Poincare Conjecture

09/08/2015 18:46

Parabolic neibourhood

09/08/2015 18:41

Open metric ball

09/08/2015 13:15

Maximum principle

09/08/2015 13:14

Uhlenbeck's trick

09/08/2015 13:09

Developmental equation

09/08/2015 12:55

Epsilon-delta method

07/08/2015 13:25

Heat equation

07/08/2015 12:07

Statistical mechanics system

07/08/2015 11:55

Ricci flow's curvature tensor

07/08/2015 11:44

Ricci flow

06/08/2015 22:35

Ricci soliton

06/08/2015 22:23