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.

                                                                                           

The Time of Wittgenstein 2012

 The Time of Wittgenstein  

TANAKA Akio

                                        

There surely exists the time of Wittgenstein for me.
That time about in my 30s, in the middle of 1970s.
One may aware of the kernel of the problem after almost all the hardships were gone and the problem is going under pursuing in the daily work for oneself, as Wittgenstein wrote at 6.521 in TRACTATUS LOGICO-PHILOSOPHICUS. 

Wittgenstein wrote on language immanently at least in TRACTATUS.
He also said in TRACTATUS 6.432 that how world exists  does not care from the higher dimensions.
I also wanted to write on language from the immanent side in language.
But I had not any pursuing method for writing on language at that time, only remaining set theory typically presented by Bourbaki that some translations were surely on my desk.

Set theory was enough fascinating at the time, but it did not give me any relative and constructive situations on language or widely on the world. It was isolated and non-relative for writing on language. I wanted the bond of the world.

Now I have geometry for which the world can be bonded enough tightly. In 1970s I was never aware of the existence of geometry by myself, probably not being influenced from Wittgenstein's 6.35 in TRACTATUS, Geometry absolutely tell nothing on how the figure is and where the figure situated.

So I had remain silently in the days not being able to write on the theme, the basic essence of language. Then I never knew the object on language, language universals that was taught from CHINO Eiichi later in 1980s. CHINO showed me the paper of Sergej Karcevskij, Du dualisme asymétrique du  singe linguistique. The theme determined my remain life hereafter. CHINO was the true teacher of my study.

Wittgenstein wrote at the last 6.54 of TRACTATUS that his some propositions must be abandoned. I began to go through the wood of hard theme of language universals by mathematics especially using geometry. About what can be told to, I never must be silent.

Reference
Citation from Ludwig Wittgenstein


                                                              Tokyo
                                                  January 20, 2012
                                 Sekinan Research Field of Language

Through Models to Language Universals 2012

 Through Models to Language Universals

TANAKA Akio                                

1.
Language universals are essentially pursued through natural language.
2.
I pursue language universals through language models described by mathematics.
2.1
The reason is depended on natural language's nature that is partially pointed out at the paper, Presupposition on Natural Language 2012.
3.
On natural language, at least, even word cannot be defined by my study level.
4.
My main target pursuing language in at letters or characters that are stable and recordable, furthermore remained language's original images especially at Chinese characters.
5.
Models can be written by adequate mathematical description using adequate theorems already established in the history of mathematics.
5.1
In the latter half of the 20th century, mathematics is vastly developed for using and describing various themes of human beings. 
5.2
Kurt Gödel and Nicolas Bourbaki made the mile stones for application to the humane studies.
6.
Described mathematical models are reflecting some part of natural language.
7.
If a certain theorem is  effective to pseudo-language universals,  the theorem probably should be newly rewritten or constructed in the space of natural language. Its situation are perfectly unknown  in my present study stage.
7.1
For example, paper, Loop Time of Character 2011 describes the relationship between character and its time. From these presuppositions, meaning of word is defined by mathematics. But the situation of presuppositions does not become clear viewpoint in mathematics and natural language.
7,2
Vast cliffs are standing in front of the study. It is really starting point for me.
7.3
The forerunners ever said anyway that there exists a mountain, they climb it.

                                                                  Tokyo
                                                         25 August 2012
                                       Sekinan Research Field of Language

Tokyo Station Restoration Completed 2012

Tokyo Station Restoration Completed  

TANAKA Akio

                                        

Tokyo Station has been completed restoration work yesterday at 1 October 2012. The station is probably most favourite station in Japan for me. From my student times I have used it innumerably. In the late 1960, in my student days, the station's main gate Marunouchi was rather calm and lonesome except rush hours of business persons.

Now the situation has vastly changed. It has become the most wonderful station and around the station has also most lively space from early morning till late night. I love the atmosphere of this station and its around.

The bookstore Maruzen close Marunouchi gate is my pleasurable space for update information on near 2 million books published in Japan and abroad. If you come to Japan, please see the station and go outside to the Imperial Palace some 10 minutes walk from Marunouchi gate. You can appreciate the both faces of modern and classical Japan. Probably it will be the fantastic experience on Japan.

Tokyo Station was constructed at 5 December 1914. The original station was burnt at 25 May 1945 by the Tokyo attack of the World War 2.

  

       Newspaper advertisement of the Tokyo Station
                          Date: 1 October 2012

Tokyo
2 October 2012
Sekinan Research Field of Language

Tradition of Dictionary 2012

Tradition of Dictionary 

TANAKA Akio 

                                        

 

Walter W. Skeat's Concise Dictionary of English Etymology 2007 is compact but rich content dictionary of English etymology, that lets us feel the Great Britain's long tradition of philology and dictionary making.

When surveying the dictionary making in England, its typography's beauty and binding's durability are enough amazing for us Oriental.

Especially I really think that the leather spine of the book's stoutness make us feel the historical heaviness. Regretfully Japan's book spines are not so strong than the Great Britain.

My Shorter Oxford Dictionary was made in 1956 but after half a century the leather spine is very smooth and beautiful against my roughly handling.

Tokyo
25 May 2012
Sekinan Research Field of Language

Understandability of Language Historical Review 2012

 

Understandability of Language

Historical Review  

TANAKA Akio

         

Intuitive Concept
Guarantee of Language
Deep Fissure between Word and Sentence
Finiteness in Infinity of Language

von Neumann Algebra 2
Generation Theorem

von Neumann Algebra 3

Properly Infinite
Purely Infinite

Complex Manifold Deformation Theory
Understandability of Language



Tokyo
February 17, 2012
Sekinan Research Field of Language

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
They were receiving the hard cold winds at the mountains.

На севере Альп Японии.

В альпийских растений,
 которые получают жесткие холодные ветры в горах.

Tokyo
1 August 2012
Sekinan Research Field of Language