Theorem / Eliashberg​, Tomita, Borchers / 27 February 2009

Theorem / Eliashberg​, Tomita, Borchers

Symplectic Language Theory 

TANAKA Akio 

Note 1 

Symplectic Topological Existence Theorem​

​

​

[Theorem]​

(Eliashberg)​

Symplectic homeomorphism   is C0 convergent to differential 

homeomorphism .​

Under the upper condition, φ is symplectic homeomorphism.​

​

​

[Note]​

1​

For language's understandability, differential homeomorphic C0 convergence is related with 

the finiteness and infinity of language. ​

2​

For the finiteness and infinity of language, next theorem is efficient to solve the problem.​

​

(Tomita's fundamental theorem)​

H       Hilbert space        ​

B(H)  Banach space B(H, H)​

N       B(H)'s *subalgebra that contains identity operator and closes for τuw topology​

J        Conjugate linear equidistance operator​

Δ       Unbounded positive self-adjoint operator​

Δit     τs-continuous 1 parameter unitary group​

(1) ​

(2) ​

​

(Borchers' theorem 1992)​

The theorem is deeply connected with Tomita's theorem.​

​

​

[Impression]​

Symplectic geometric structure is seemed to be solvable for language's
understandability that simultaneously connotes finiteness and infinity within. ​

​

To be continued​

Tokyo February 27, 2009​

Sekinan Research Field of language​

Source:

  

    
                   https://writer.zoho.com/public/sekinan/SLTNote1SymplecticTopologicalExistenceTheorem1

What facts does Three Conjectures for Dimension, Synthesis and Reversion show us? / 20 November 2014

What facts does Three Conjectures for Dimension, Synthesis and Reversion show us?
Based on Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement. 

• Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement / 19 November 2014

TANAKA Akio

1.
True-false problem of the Crete gives us the infinite circulation of true-false value.
This fact indicates us the existence of deep structure or hierarchy in language.
The Crete's true-false is solved by the perspective from 2-dimension to 3-dimension on structure in language world.

2.
Language has long history as the system of etymology. Apparently language has gradually added the  new meaning on the old established meaning in word. At this point new meaning is synthesised to the old meaning. At synthesis word mathematically reduces its dimension to the lower one. As the result time in word relatively occurred in the new word and inevitably connected with  dimension.

3.
Where and how does word exists in the world?
The distance from a certain point is absolutely demanded for measuring or observing for knowing the word's place.Reversion is a result for measuring or observing from a point.

4.
For precise description of dimension, synthesis and reversion mathematical tools are definitely needed and for more simple describing algebraic method is the most useful to approach for me and in order to easy-seeing and clear intuition geometrical approach is always inevitable to searching. I am greatly thanks to relevant mathematicians researching against severe problems still now for contemporary times.

Kodaira, Tokyo
20 November 2014
SIL

Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement / 19 November 2014

Paper

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

Disposition of Language / 12 September 2014 / With supplement / 18 September 2014

18/09/2014 20:18

Disposition of Language / 12 September 2014 / With supplement

 

Disposition of Language

TANAKA Akio

Language probably possesses the disposition not to disturb the thinking of human being.
Now  I cannot find any clue for entering this difficult theme. What I  know is that I can show some examples for the wonder of the disposition of language as the following.
Notation mark # shows the mathematical approach to the themes.
..............................................................................................................

Chinese classical writing form is one variation of vast forms of languages. It is strictly depending the disposition as the following.
<Wo ai ni.> means <I love you.>
The upper example shows the strict direction rule to read from left to right.
If this rule is neglected and the below example to read from right to left,
<Ni ai wo.> means <You love me.>

Disposition 1.
Language has direction.

I ever wrote a trial paper titled "Direction" in 2004, that is dedicated to Sergej Karcevskij.

• Direction / For KARCEVSKIJ Sergej / 26 November 2004 (The first intuitive paper of SRFL on direction)

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

Language frequently shows True-false problem like "The Crete's lie".
The details are shown at the papers in SRFL's library.

• True-false problem of the Crete / The example of what language has structure / 22 July 2013 
• # Dimension of Word / Arithmetic Geometry / 24 December 2012 
• # Word construction and its dimension / 4 September 2013
• # Dimension Conjecture at Synthesis of Meaning / 9 September 2013 (One of the recent papers on dimension)
• # Supposition on Dimension / 25 October 2013 (One of the kernel papers on Disposition till now)

Disposition 2.
Language has dimension.

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

Language is said to be changeable like "old meaning" and "new meaning".
If this changeability be true, from where one meaning becomes "old" and becomes "new".
This situation hints me the existence of basic point in language. In the papers so far, the same concept is called standstill point.

Disposition 3.
Language has basic point.

• Interpretation of Reversion Conjecture /20 May 2014

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

At Disposition 3. the difference between "old meaning " and "new meaning" is supposed to be shown by the distance from the basic point.

Disposition 4.
Language has distance.

• Distance Theory / 5 May 2004 
• Interpretation of Reversion Conjecture /20 May 2014

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

From the concepts of basic point and distance, the concept of reversion is proposed. One place has a certain distance from the basic point and the direction from the place to the basic point occurs the concept reversion.

Disposition 5,
Language has reversion.

• Reversion Theory / 27 September 2014 
• Warp Theory / 24 October 2004
• Reversion Analysis Theory / 8 June 2008
• Reversion Analysis Theory 2 / 12 June 2008
• Reversibility of Language / 5 June 2009   
• Reversion Conjecture Revised / 20 May 2014 
• Interpretation of Reversion Conjecture /20 May 2014
• Simplification of Reversion Conjecture / 14 May 2014

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

Language's disposition seems to be macro rule but also shows the phases of the micro rule like the description of "meaning"at Disposition 4. The example is the following.

• # Condition of Meaning / Notes for KARCEVSKIJ Sergej / 11 September 2011 (One of the mathematical approach papers on meaning)

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

Results till present

Disposition  shows the clear and linear development of human thinking from the so called chaos situation of human brain's inner events. But I do not deal with the situation related with inner events. I only deal with the outer and statistic situation being accomplished as language. Several concepts in mathematics are probably useful to describe the disposition, such as oriented, dimension, cardinal point, distance  and so forth. Some phases have been studied using mainly algebraic algebra at the Zoho sites of SRFL. Details are shown at the below. 

• # Zoho Past / SRFL Sekinan research Field of Language / 2008 2013
• # Zoho Now / SRFL Sekinan Research Field of Language / 2013 - 2014 

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

Study after this

I would challenge Disposition 1. Direction because this field seems to be related with group theory, especially with finitely generated group and its surroundings or development, for example Bers-Thurston conjecture, "All the infinitely generated Klein group is algebraic limit of geometrical infinite group".


Tokyo
12 September 2014
Sekinan Research Field of Language

Hatonosu Ravine, Tokyo

22 August 2014

.........................................................................................................................................
Supplement


[Reference added, 15 September 2014]

• # SRFLZoho, mathematical approach to language universals / 2008 - 2014

[Text added, 16 September - 18 September 2014]

      Text for reversion and Disposition 5 Language has reversion. are added.

[Papers added, 18 September 2014]
       Papers related with Disposition 3 and Disposition 4 are added.

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

Read more: http://srflnote.webnode.com/news/disposition-of-language-with-supplement/

...........................................................................................................................................
Tokyo
18 Novemebr 2014 Rebloged from SRFLNote.webnode
SIL

Writing Style of the Papers 2013 / 3 May 2014

Posted on May 3, 2014 

Writing Style of the Papers 2013

TANAKA Akio 
                                      

From 2013 I changed a little on the writing style of papers. I have always thought on the several concepts for language universals and their surroundings. Synthesis of old meaning and new meaning is one of the most important themes. Dimension of language is also a big theme for long time from my beginning of the study.

Recently I frequently use the web site, webnode, in which the top page almost has “News” column that is very convenient to write tiny memo-like ideas I have always been thinking. Ending the memo and uploading the site, writing date and time are inevitably mentioned. It is very useful for me because I always need the date of thinking the theme.

So I made some sites by the webnode. But after using for the facing work they are almost deleted for cleaning the history of my task. I do not want remaining the footprints of my trifling works. At the result my remaining webnode site is only one, that is named SRFLNote in which there are some trivial notes on the study now.

Several papers written by the webnode “News” column  are shown at this site.
For this writing situation , “Dimension Decrease Conjecture”,  “Conjecture for synthesis of meaning in word”and “Conjecture for reversion of language” have peculiar style from the ordinary papers.

From now on, what this style will be kept on is uncertain for me, but I think that adequate themes by this style will be remained, for example, on the field of the hierarchy of language related with dimension.

If the time exists some for me, I will write more several papers on the important themes using mathematical notations to the unknown world of language hereinafter.

Reference
webnode
HILLSSOUTHROAD / 2013 (Archive only)

Tokyo
18  November 2014 Rebloged
SIL

Dimension Decrease Conjecture / 1 May 2014

Dimension Decrease Conjecture 

TANAKA Akio

1  Dimension conjecture of word 
23/09/2013 23:04
Word has dimension. New addition of meaning to word makes dimension of word decrease. 
Basis
Pull back map of higher Chow group
23/09/2013 16:11 
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meabning, dimension of word is decreased by dimension of additional  meaning.
Refer to thenext.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho . 

2  SAITO Shuji, SATO Kanetomo 
24/09/2013 10:14S
SAITO Shuji, SATO Kanetomo. Algebraic Cycle and Etal Cohomology. 2012.

3  Pull-back map of higher Chow group 
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meabning, dimension of word is decreased by dimension of additional meaning. 
Refer to thenext.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho .

4  Y. Nesterenko, A. Suslin 
23/09/2013 15:30
Y. Nesterenko, A. Suslin.
Homology of the general linear group over a local ring, and Milnor’s  K -theory. Math. 1990.

5  Higher Chow ring 
23/09/2013 15:21
Double graded Abel group becomes double graded ring by defined intersection product.
Its product become commutative at one degree and become noncommutative at the another degree.

6  W.Fulton 
23/09/2013 11:01
W. Fulton.  Intersection Theory , 2nd ed. 1988.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho .

7  V. Vodoedsky 
22/09/2013 20:09V.
V. Vodoedsky
On motivic cohomology with Z/2-coefficients . Math.98. 2003.
On motivic cohomology with Z/l-coefficients . Ann. of Math.

8  Map that norm residue map induces 
22/09/2013 20:03
When  k  is field and  n  is commutative integer, map that norm residue map induces is bijection.


Tokyo 
1 May 2014 
SIL

Time in word, 24 October 2013 / Note added 17 November 2014, Note 2 added 3 December 2014

Time in word

TANAKA Akio

Time inherent in word has been one of the most fantastic theme for me for a long period. WANG Guowei’s paper was strongly hinted to the theme towards first writing a trial paper on it. Roman Jakobson was also gave me the basic notion related with the theme. Still now the problem has not solved as the starting point. But being aided by mathematical method and description,  learning on it has become more attractive in these days.

• Trial paper: On Time Property Inherent in Characters
• Basic notion: From Cell to Manifold
• Mathematical description: Dimension Decrease Conjecture

Tokyo
24 October 2013
SIL

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

[Note]

When I wrote this essay, "Time in Word" in the autumn of 2013, the relation between time and dimension cannot be thought clearly but now in 2014 I distinctly think that the relation exists at the situation of synthesis of the new meaning on the old meaning. The four papers of Arithmetic Geometry Language written between 4 September 2013 and 9 September 2013 are indicating the affinity with time and dimension. Now I show the compact paper in the four, titled " Synthesis Meaning and Transition of Dimension".

• Synthesis of Meaning and Transition of Dimension, 6 September 2014 

Four papers of Arithmetic Geometry Language are the following.

Arithmetic Geometry Language (Abbreviated AGL)

• Dimension of Language (AGL1)
• Synthesis of Meaning and Transition of Dimension (AGL 2)
• Birth of Word, Synthesis of Meaning and Dimension of New Word (AGL 3)
• Dimension Conjecture at synthesis of Meaning (AGL 4)

Tokyo
17 November 2014
SIL

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

[Note 2]

The relation between time and dimension is now arranged at the following paper.

• Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement / 19 November 2014

The overview of time in language is now shown at the following paper.

• How is the time alive in language?

On WANG Guowei and Roman Jakobson, refer to the next.

• 40 years passed from I read WANG Guowei / 16 November 2013
• Roman Jakobson /16 July 2012
• Meaning minimum On Roman Jakobson, Sergej Karcevskij and CHINO Eiichi / 6 April 2013
• From Cell to Manifold, On Meaning Minimum hinted by Roman Jakobson / 2 June 2007

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

[Note 3]
Essay "Pleasure of Mathematics" includes time notion related with Brownian motion.

• Pleasure of Mathematics / 15 December 2014 

Tokyo
3 December 2014
15 December 2014, Note 3 added

SIL