**Lotus Flowers at Ueno**

Lotus flowers are always beautifully bloom at the pond of the Tokyo National Museum, Imperial-gift Ueno Park , Tokyo. When I was a student of the university, I frequently went to see the garnered items of the some museums located in the park. The photo was taken at 25 May 2011.

I also like the National Museum of Western Art in the Ueno park, that was designed by Le Corbusier. This lotus photo’s colour is a little similar with the Monet’s paintings themed on lotus flowers.

18 July 2012

Sekinan Research Field of Language

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Today I and wife went to Hanno, Saitama that is located at the next to my home town, north-west of Tokyo . The city was the very intimate place for some dear fiends of high school days.

We were always play in home town in the long vacations of summer, winter and spring, but sometimes using bicycles we went to Hanno to play the baseball at the city ground and see the Iruma River that flows the centre part of the city and rarely learnt the vacation work at the old city library alike a tiny elementary school building.

Along the bicycle road used to go and back, fantastic silver grasses were calmly swaying in the Autumn wind. We run fast the slope road seeing the rail road at right side. Occasionally we met the diesel train.

Today I went there with wife, with whom I went camping or barbecue at the river side far old days together with two children. Now they are already growing up and working in the central Tokyo. I and wife are enough old and feel tranquil seeing the river and the hills behind.

When the children were very young, we let them buy some confectioneries at the river side tiny shops that are still remain in the same old style. The time flew fast and all afar went. The river is only sparkling with same beauty.

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**Old Shops in Home town **

My home town belongs Metropolis Tokyo, located at the west suburb, some 40 km afar. I was born and grew up here, so many tiny shops were very intimate and to them I have dear feelings.

There are some old shops still now, where in the boy’s days I bought the daily use things for being ordered by mother sometimes from father. The remained styles of them are now all off-painted wall, unreadable signboards and rough roofs. Nowadays people including with my family always go to the big supermarket or shopping mall having very wide parking lots. Old main roads and shops decline day by day. It is surely modern social phenomenon. But we that know the ever busy conditions of the shops, feel very sad and lonesome.

Glossary shop unopened now

Tokyo 30 October 2012, Sekinan Library

Tokyo 30 October 2012, Sekinan Library

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TANAKA Akio

I frequently talked with

The subject he gave me were impressive and useful for me, in which the most important is the history of

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

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

1 August 2012

Sekinan Research Field of Language

**Under the Dim Light**

**Sergej Karcevskij, Soul of Language**

**Follower of Sergej Karcevskij**

**For KARCEVSKIJ Sergej**

**Linguistic Circle of Prague**

**Half Farewell to LCP with References**

**Prague in 1920s**

**40 years passed from I read WANG Guowei**

**The Complete Works of WANG Guowei**

**For WITTGENSTEIN Ludwig Revised**

**The Days of von Neumann Algebra**

**The Days between von Neumann Algebra and Complex Manifold Deformation Theory**

Early summer in Kirigamine Highlands, Nagano, Japan.

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1. Repeated Integral Model

1.1 Hyperbolic volume Volume of Language

1.2 Hyperbolic space Hyperbolic Space Language

2. Minimal Model

2.1 Free group Notes for KARVESKIJ Sergej, “Dusualisme asymétrique du signe linguistique”

2.2 Fundamental group Description of Language

2.3 de Rham complex Structure of Word

2.4 de Rham complex on spherical surface Condition of Meaning

3. Knot Theory Model

3.1 Hida deformation space Loop Time f Character

4. Jones-Witten Theory Model

4.1 Witten invariant Symmetry of Language

5. Moduli Model

5.1 Projective algebraic manifold Completion of Language

5.2 Projective algebraic manifold Meaning Minimum of Language

6. Arithmetic Geometry Model

6.1 Riemann-Roch Formula Language, Word, Distance, Meaning and Meaning Minimum

7. Projective Space Model

7.1 Grothendieck theorem Vector Bundle Model

8. Diophantine Approximation Model-Diophantine Language

8.1 Faltings theorem Finiteness of Words

8.2 Noguchi, Winkelmann theorem Dimension of Words

Tokyo

January 25, 2012

February 1, 2012 Added

Sekinan Research Field of Language

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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

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TANAKA Akio

**Supposition 1:**

**Three elements for language universals**

For language universals, now I suppose at least three elements being based from mathematical description.

Three elements for language universals are **energy**, **dimension** and **distance**.

The most fundamental element is energy. By this energy, all the movements and changes occur in language.

vide:

All the languages are located at a certain dimension in space. By this dimension, confusions in language are averted.

vide:

In language, all the movements and changes inevitably make distance occurred. By this distance, important phases of language are clearly defined.

vide:

……………………………………………………………………………………………………………

**Supposition 2:**

**Mathematical description for three elements of language universals**

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

Energy in language is now preparatory description til now.

vide:

- Energy of Language / Stochastic Meaning Theory
- Energy and Distance / Energy Distance Theory
- Energy and Functional / Energy Distance Theory
- Potential of Language / Floer Homology Language

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

vide:

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:

- Distance / Direct Succession of Distance Theory / Distance Theory Algebraically Supplemented
- Distance of Word / Complex Manifold Deformation Theory

…………………………………………………………………………………………………….

This paper is not finished.

Tokyo

27 February 2015

SIL

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TANAKA Akio

In 1970s or in my age 20s there surely exists glitter of youth in my life, now I remember.

In those days, in Japan many fabulous magazines were successively published. *Episteme*,*Toshi*（City）、*Chugoku*（China) and the likes. Especially I loved reading * Episteme* which had printed many philosophical or philological articles as the form of special issues concentrated important philosopher, thinker and writer. The chief editor of

In my life, Wittgenstein gave the big influence for thinking and writing style, never entering or approaching his essential philosophical themes.After millennium year when I started the regular writing on language universals, my writing style was resembling in his * Tractatus Logico-Philosophicus*. My paper written in 2003,

1970s was a relatively calm times after those university’s revolution in the late 1960s in which I also compellingly rolled in. In those days I almost had been wandering between library and old book shops aiming my life-time true themes cowardly avoiding the turmoils of university and towns. **Blaise Pascal**（1623-1662）’s * Pansees* was my favourite one. One day at Kanda’s Taiwan chinese book shop Kaifu Shoten, I bought

In 1970s, I had cherished a dream in which I wanted to use mathematical description and get the essential of language. But I had not any ability to proceed the study for it while I read at random several mathematical books. One day I found and bought the amount **Nicolas Bourbaki**（1935-）’s text books at old book shop in Kanda, Tokyo. They were hard to keep reading for my talent in those days. After all, the books were put aside the desk. The remaining in my mind was adoration to Bourbaki and their brilliant achievement. My return to Bourbaki was long after in 1990s when I again tried the pursuit of language having a clear vision to study **language universals** according to **the Linguistic Circle of Prague**, especially aiming to resolve the supposition presented by **Sergej Karcevskij**（1884-1955).

Turning round the past days, my way was always narrow and winding road. But it keeps till now not breaking off in any situations. The way was finely glittering in my youth days despite under the cloudy sky. Probably I have kept happily walking till now being assisted by many people especially at the field of language, mathematics and relevant studies.

At random now I remember the dear names from whom I never cannot hear their voices. **HASEGAWA Hiroshi, CHEN Donghai **

Tokyo

6 March 2015

Sekinan Library

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# Applied papers with this essay are reprinted at this SRFL News.

von Neumann Algebra was written from 3 April 2008 to 2 May 2008. And Complex Manifold Deformation Theory was written from 30 November 2008 to 9 January 2009. In the days between the two theories I wrote the following 4 paper groups.

- Functional Analysis
- Reversion Analysis Theory
- Holomorphic Meaning Theory
- Stochastic Meaning Theory

These days were the preparatory time for regularised writing by algebraic geometry at Zoho site. But they were relatively precious days for thinking about the reshuffling mathematics and physics related with language. Especially Stochastic Meaning Theory was a milestone for mathematical approaching to physical phenomenon of language.Stochastic Meaning Theory’s titles are the next.

**Stochastic Meaning Theory**

On the other hand, I really realised that mathematical writing of natural phenomenon, for example natural language, inevitably needed clear routes by mathematics that was represented by function analysis approach. Functional Analysis and Reversion Analysis Theory were the trial papers aiming for new ground, especially the comparison of finiteness and infinity in generation of words and sentences.

**Functional Analysis 1**

Note

1. Baire’s Category Theorem

2. Equality and Inequality

3. Space

4. Functional

Conjecture

1. Finiteness of Vocabulary

2. Distance at Hypersurface

**Functional Analysis 2**

Note

1. Pre-Hilbert Space and Hilbert Space

2. Orthogonal Decomposition

Conjecture

1. Generation of Word

**Reversion Analysis Theory**

1. Reversion Analysis Theory

2. Reversion Analysis Theory 2

But at that time I could not decide the main field of mathematics for applying to language study. Moreover I never thought about language models parting from natural language and constructing the new field for thinking about language universals.

After these preparation of algebra that was started from *Premise of Algebraic Linguistics 1 -1* at 11 September 2007, I barely reached to the entrance of algebraic geometry’s use for language and making the language models. It was Complex Manifold Deformation Theory which began to write at 30 November 2008 titling *Distance of Word*, one of my main themes for language universals from the very starting of language study. Thus my study first focused to making language models of algebraic geometry using complex manifold.

**Complex Manifold Deformation Theory**

- Distance of Word
- Reflection of Word
- Uniqueness of Word
- Amplitude of Meaning Minimum
- Time of Word
- Orbit of Word
- Understandability of Language

# Here ends the paper.

**Tokyo**

**6 January 2015**

**Sekinan Library**

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viz. The cited papers’ texts are shown at the blog site SRFL News’ January 2015 blogs.

1.

My study’s turning point from intuitive essay to mathematical writing was at the days of learning von Neumann Algebra, that was written by four parts from von Neumann Algebra 1 to von Neumann Algebra 4. The days are about between 2006 and 2008, when I was thinking about switching over from intuitive to algebraic writing. The remarkable results of writing these papers were what the relation between infinity and finiteness in language was first able to clearly describe. Two papers of von Neumann 2. Property Infinite and Purely Infinite, were the trial to the hard theme of infinity in language.The contents’ titles are the following.

**von Neumann Algebra**

On Infinity of Language

1 von Neumann Algebra 1

2 von Neumann Algebra 2

3 von Neumann Algebra 3

4 von Neumann Algebra 4

References

1 Algebraic Linguistics

2 Distance Theory Algebraically Supplemented

3 Noncommutative Distance Theory

4 Clifford Algebra

5 Kac-Moody Lie Algebra

6 Operator Algebra

………………………………………………………………………………………………………………….

2.

The papers of von Neumann Algebra and References are the next.

**von Neumann Algebra 1 **

1 Measure

2 Tensor Product

3 Compact Operator

**von Neumann Algebra 2**

1 Generation Theorem

**von Neumann Algebra 3**

1 Properly Infinite

2 Purely Infinite

**von Neumann Algebra 4**

1 Tomita’s Fundamental Theorem

2 Borchers’ Theorem

**Algebraic Linguistics <Being grateful to the mathematical pioneers>**

On language universals, group theory is considered to be hopeful by its conciseness of expression. Especially the way from commutative ring to scheme theory is helpful to resolve the problems a step or two.

1 Linguistic Premise

2 Linguistic Note

3 Linguistic Conjecture

4 Linguistic Focus

5 Linguistic Result

**Distance Theory Algebraically Supplemented**

Algebraic Note

1 Ring

2 Polydisk <Bridge between Ring and Brane>

3 Homology Group

4 Algebraic cycle

Preparatory Consideration

1 Distance

2 Space <9th For KARCEVSKIJ Sergej>

3 Point

Brane Simplified Model

1 Bend

2 Distance <Direct Succession of Distance Theory>

3 S3 and Hoph Map

**Noncommutative Distance Theory**

Note

1 Groupoid

2 C*-Algebra

3 Point Space

4 Atiyah’s Axiomatic System

5 Kontsevich Invariant

[References]

Conjecture and Result

1 Sentence versus Word

2 Deep Fissure between Word and Sentence

**Clifford Algebra**

Note

1 From Super Space to Quantization

2 Anti-automorphism

3 Anti-self-dual Form

4 Dirac Operator

5 TOMONAGA’s Super Multi-time Theory

6 Periodicity

7 Creation Operator and Annihilation Operator

Conjecture

1 Meaning Product

Kac-Moody Lie Algebra

Note

1 Kac-Moody Lie Algebra

2 Quantum Group

Conjecture

1 Finiteness in Infinity on Language

**Operator Algebra **

Note

1 Differential Operator and Symbol

2 <A skipped umber>

3 Self-adjoint and Symmetry

4 Frame Operator

Conjecture

1 Order of Word

2 Grammar3 Recognition

……………………………………………………………………………………………………………………

3.

After writing von Neumann Algebra 1 – 4, I successively wrote the next.

**Functional Analysis
Reversion Analysis Theory
Holomorphic Meaning Theory
Stochastic Meaning Theory**

Especially Stochastic Meaning Theory clearly showed me the relationship between mathematics and physics, for example Brownian motion in language. After this theory I really entered the algebraic geometrical writing by Complex manifold deformation Theory. The papers are shown at Zoho site’s sekinanlogos.

- sekinanlogos

**Complex Manifold Deformation Theory**

- Distance of Word
- Reflec bsp;of Word
- Uniqueness of Word
- Amplitude of Meaning Minimum
- Time of Word
- Orbit of Word
- Understandability of Language
- Topological Group Language Theory
- Boundary of Words

**Symplectic Language**

- Symplectic Topological Existence Theorem
- Gromov-Witten Invariantational Curve
- Mirror Symmetry Conjecture on Rational Curve
- Isomorphism of Map Sequence
- Homological Mirror Symmetry Conjecture by KONTSEVICH
- Structure of Meaning

**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

…………………………………………………………………………………………………………………….

4.

The learning from von Neumann Algebra 1 ended for a while at Floer Homology Language, where I first got trial papers on language’s quantisation or discreteness. The next step was a little apart from von Neumann algebra or one more development of algebra viz. arithmetic geometry.

# Here ends the paper.

## The cited papers’ texts are also shown at this site.

vide: The days between von Neumann Algebra and Complex Manifold Deformation Theory

Tokyo

3 December 2015

SIL

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