Glitter of youth through philosophy and mathematics in1970s

Glitter of youth through philosophy and mathematics in1970s

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 Episteme was NAKANO Mikitaka(1943-2007), probably one of the best editors in the latter half of the 20th century in Japan.  The most impressive number was Ludwig Wittgenstein(1889-1951), probably in 1977. Also influenced from the issue of Kurt Godel(1906-1978)who gave me the possibility of set theory.

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, Quantum Theory for Language shows a very imitative style to him. This tendency kept on for some time till I changed to adopt algebraic method for more clear description to the themes.

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 WANG Guowei(1877-1927)’s Guantangjilin that opened the new frontier for classical Chinese philology mainly streamed by “Small Study”, traditional exegetics in China. Influenced WANG Guowei I wrote a paper titled On Time Property Inherent in Characters, 2003 by which I began the latter start of language study.

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 Chinese languageKAJIMURA Hideki, CHO Shokichi Korean languageNatary Muravijowa Russian languageONO Shinobu Chinese literatureMIIYAZAKI Kenzo, FURUTA Hiromu, KONDO Tadayoshi Japanese literatureANDO Tsuguo French poemSAEKI Shoichi HaikuIKEDA Hiroshi Japanese classical dramaSAITO Kohei sculptureYAMAGISHI Tokuhei bibliographyNISHI Junzo Chinese philosophyKAWASAKI Tsuneyuki BuddhismCHINO Eiichi Russian language, the Linguistic Circle of Prague. At last dear friend of high school days KANEKO Yutaka mathematics and our youth.

Tokyo
6 March 2015
Sekinan Library

The days between von Neumann Algebra and Complex Manifold Deformation Theory

The days between von Neumann Algebra and Complex Manifold Deformation Theory

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

TANAKA Akio

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
  1. Period of Meaning
  2. Period of Meaning 2 
  3. Place of Meaning
  4. Energy of Language
  5. Language as Brown Motion

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
  1. Distance of Word
  2. Reflection of Word
  3. Uniqueness of Word
  4. Amplitude of Meaning Minimum
  5. Time of Word
  6. Orbit of Word
  7. Understandability of Language

# Here ends the paper.

Tokyo
6 January 2015
Sekinan Library

The Days of von Neumann Algebra

The Days of von Neumann Algebra

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

TANAKA Akio

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

Gift from Sergej Karcevskij

TANAKA Akio

1.
Is language variable? If so, where is substance of variability?
2.
Variability occurs in substance.
3.
What is not substance is untrue in variability.
4.
Where is substance of language?
5.
Letters are substance. Pronunciations are substance. Meanings are substance?
6.
Meanings occurs in inner human being.
7.
The sun rises in the east. It is true. The sun also rises. It is true in Hemingway.
8.
Meaning is variable.
9.
At where occurs variability of meaning?
10.
If variability of meaning is true, substance in which variability occurs must be shown in front of us.

Tokyo
October 23, 2005
Sekinan Research Field of Language

Postscript [References January 1, 2008]
Substantiality / Tokyo February 27, 2005
Substantiality of Language / Tokyo February 21, 2006

Coffee shop named California

From Print 2012, Chapter 10

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.

Source: Tale / Print by LI Koh / 27 January 2012

References:
Under the Dim Light / 1 August 2012
Road to Language Universals / 31 December 2012
Half Farewell to Sergej Karcevskij and the Linguistic Circle of Prague / 23 October 2013

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

I need not more wander the book shop streets

From Print 2012, Chapter 10

I need not more wander the book shop streets. The object exists in my mind. I would better watch the canal. Wandering is over now.  Perhaps I would not become meister  forever. In my narrow working place, I ‘d better do my work till sunset. So out of the window by the working place,  the saint passes by. I ever read the Russian folk tale like that.

The Autumn evening is fast. The headlight of streetcar  is dazzling. In the yellow-lighten window the passengers are picked out by the light. The car disappeared  to the book streets. The station shop is also lighted up by the yard’s busy orange light.

Read more: http://srflnote.webnode.com/news/i-need-not-more-wander-the-book-shop-streets-from-tale-print-2012/

[Reference]

  1. 40 years passed from I read WANG Guowei / 16 November 2013
  2. Prague in 1920s, The Linguistic Circle of Prague and Sergej Karcevskij’s paper “Du dualisme asymetrique du signe linguistique” / Print, 2012

[Note  1 October 2014]
“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.