Birth of Word, Synthesis of Meaning and Dimension of New Word

 

Birth of Word, Synthesis of Meaning and Dimension of New Word

TANAKA Akio

Tokyo

8 September 2013

hillseversunlit

1.

The image lm(δX) of Map δ_χ  is expressed by Zr(X)rat .

Here the next Chow group of r-cycle is defined.

CHr(X):=Zr(X)/Zr(X)rat .

<Birth of New Word>
Bass conjecture

For scheme X that is finite type on Z≥0 and intger r≥o, CHr(X) is finite generative Abel group.

♦

If language be the upper X, word is defined by  CHr(X) that is finite generative.

2.
<Synthesis of Meaning>

Transition theorem
The next i and j are regular closed immersion of codimension c,d. 

i:X→Y, j:Y→Z

Here is  given Cartesian diagram of the next scheme.

X'—^i'→Y'— ^j'→Z'
↓         ↓          ↓
X— ⁱ→Y — ^j → Z

At this time the next equality sign is set up.

(j O i)^! = i^! O j^! : CH_r(Z') → CH_r–c–d(X')

♦

If additional meaning be defined by the upper i and j, there is synthesis of meaning. 

3.

<Dimension of New Word>

If word be defined by CHr(X) and additional meaning is defined by i and j, the dimension of new word  is deduced from old word's r to r-c-d.

[Reference]

W. Fulton. Intersection Theory. Berlin, Springer. 1988.

 

Dimension Conjecture at Synthesis of Meaning

TANAKA Akio

Tokyo

9 September 2013

hillseversunlit

1.

The image lm(δX) of Map δ_χ  is expressed by Zr(X)rat .

Here the next Chow group of r-cycle is defined.

CHr(X):=Zr(X)/Zr(X)rat .

<Birth of New Word>
Bass conjecture

For scheme X that is finite type on Z≥0 and intger r≥o, CHr(X) is finite generative Abel group.

♦

If language be the upper X, word is defined by  CHr(X) that is finite generative.

2.
<Synthesis of Meaning>

Transition theorem
The next i and j are regular closed immersion of codimension c,d. 

i:X→Y, j:Y→Z

Here is  given Cartesian diagram of the next scheme.

X'—^i'→Y'— ^j'→Z'
↓          ↓          ↓
X— ⁱ→Y — ^j → Z

At this time the next equality sign is set up.

(j O i)^! = i^! O j^! : CH_r(Z') → CH_r–c–d(X')

♦

If additional meaning be defined by the upper i and j, there is synthesis of meaning. 

3.

<Dimension of New Word>

If word be defined by CHr(X) and additional meaning is defined by i and j, the dimension of new word  is deduced from old word's r to r-c-d.

4.

<Dimension Conjecture at Synthesis of Meaning>

When word synthesises meaning, word reduces own dimension according to codimension of additional meaning.

[Reference]

-On dimension

• Dimension of Word / 30 January 2012 / serkinanlum
• True-false problem of the Crete / 22 July 2013 / atbankofdamzoho

-OnTransition theorem

• W. Fulton. Intersection Theory. Berlin, Springer. 1988.

Operad Meaning Theory From Cell to Operad

 Operad Meaning Theory

From Cell to Operad

TANAKA Akio

ifbetrue

24 March 2013

1.

I ever wrote a next paper in which cell and meaning minimum  are defined.
Cell Theory. From Cell to Manifold For LEIBNIZ and JAKOBSON. Tokyo June 2, 2007.
In the paper, through Roman Jakobson's intuitive assist, the concept of meaning minimum is described by the elementary algebraic  geometry. At the deeper basis, Gottfried Leibniz's Monadologie , 1714 may influence for making this Cell Theory.   

2.

The main target of Cell Theory was in the generation of meaning in word. This target was more clearly described soon later at the next paper.
von Neumann Algebra 2. Generation Theorem. Tokyo April 20, 2008.

3.

But the balance of soft part and hard part in word, that was conjectured by Sergej Karcevskij in 1920s,  is very hard theme to describe. For solving the hardness, trial papers were proposed at the next paper group,  Notes for KARCEVSKIJ.

Notes for KARCEVSKIJ Sergej. 2011.

At the first paper of the Notes, Note for KARCEVSKIJ Sergej, the soft part in word was described by the free group's definition.

Notes for KARCEVSKIJ Sergej. Note for KARCEVSKIJ Sergej's "Du dualisme asymetrique du signe linguistique". Tokyo September 8, 2011 

4.

There is more difficult theme on the gradual changeable addition of meaning for which language has always efficiently useful in the thus complicated contemporary world. 

For this theme, I ever tried to write some papers related with time shift. The example is the next.

Symmetry Flow Language 2. Time Shift of Meaning in Moduli Space 'th for KARCEVSKIJ Sergey. Tokyo May 23, 2007.

5.

From another view on language, I had thought brane model for the connection of words or construction of language. The example is the next.

Distance Theory Algebraically Supplemented. Brane Simplified Model. 1 Bend. Tokyo October 17, 2007.

6.

Briefly summarising I have thought on language from its freeness, flexibility and changeability against long stern structure of soft and hard magical amalgam.

The gist is as the following.

Sayama Assumption on language. Sayama Hills, Tokyo 21 September 2012.

7.

Language shows many phases from thinking levels and viewpoints. 

Language can be captured more clearly from discreteness but more flexibly thinkable from meaning variation and changeability.

Floer Homology Language. Discreteness of Language. Tokyo 2009.

Changeability To SAPIR and KARCEVSKIJ. Tokyo January 8, 2005.

8.

Changeability of language implies the eternity of time, but this eternity cannot be easily obtained probably without loop condition of movement. 

Time of WANG Guowei. Loop Time of Character. September 15, 2011.

Infinite Loop Space Language. Word as Infinite loop Space. Tokyo 6December 2012.

Loop space can capture this eternality, that is shown often by the repetition. I firmly noticed this situation at the Shinto dance performance at a shrine festival.

Sato-kagura, Village Shinto dance, Fuchu, Tokyo. 28 January 2013. 

9.

Loop space was also notified early stage of Chinese history in circa. 500 B.C. at one of the five classics Yijing that is the fortune-telling text of ancient China.

On Yijing, I was taught from philosopher NISHI Junzo.

NISHI Junzo, Philosopher of Modern Japan. Tokyo 30 August 2012.

10.

From Infinite loop space, the concept of operad is lead as the next.

10.1

 is the space that has base *.

 is the loop space over .

.

10.2

.

10.3

Theorem (J.P. May's recognition theorem)

 operates all the fold loop space. 

Continuous space  to which  operates is weak homotopy equivalent with a certain fold loop space. 

11.

 is  identified as a operator that has j number input and 1 number output.

12.

Here I think that  is identified as a word that has j number meaning minimums and 1 number compound meaning.

References

J. P. May. The Geometry of Iterated Loop Spaces. 1972.

Iek Moerdijk, Bertrand Toen. Simplicial Methods for Operads and Algebraic Geometry. 2010. 

Jean-Louis Loday and Bruno Vallette. Algebraic Operads. Version 0.999. 2012

♦Here ends paper.

Simplicial Space Language -Composition of Word

 

Simplicial Space Language -Composition of Word

Simplicial Space Language

Home Site: ifbetrue

Autor: TANAKA Akio

Theme: Language Universals

Method: Homotopy Theory

Title: Homotopy Language

Paper 1: Simplicial Space Language

-----------------------------------------

Simplicial Space Language

-Composition of Word

TANAKA Akio

20 January 2013

ifbetrue

1. 

 is topological space.

 is simplicial space.

 is represented by geometric realization of   as the next.

2.

 is topological space.

 is singular simplex.

 is free Abelian group generated by set .

 .

 is singular chain complex of  and has strongly convergence spectral sequence called Atiyah-Hirzebruch spectral sequence.

3.

Interpretation.

Word  is given by geometric realization of simplicial space  .

Meaning unit in word is given by free Abel group .

(Paper end)

Word as Infinite Loop Space

 

Word as Infinite Loop Space

TANAKA Akio

1. 

Result of D. G. Quillen by Annals of Mathematics, 96 (1972).

Algebraic K theory over commutative ring R.

 is classifying space of   .

Quillen showed that  is infinite loop space.

2.

Interpretationof Quillen's result.

Meaning of word is expressed by .

Word is expressed by , .

Saying in other words. 

Word is expressed by high dimensional algebraic K group over commutative ring R.

Conclution at the present.

Word has meaning that is expressed by infinite loop space.

Word has parameter that is expressed by commutative ring.

Word has dimension that belongs to albegraic K group.

Tokyo
6 December 2012

Zoho Sites of Sekinan

Sekinan Research Field of Language

Duality of Language

 Duality of Language

TANAKA Akio

1. Theorem(Poincaré duality)
For oriented compact n-dimension topological manifold M,
biliear form

is exact,
 and  become dual space each other.
♦

2. Interpretation
Word := MBoundary of language := pDual language :=  and Language := 

3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.

4. References
Distance Theory
Mirror Theory
Guarantee of Language

Tokyo
25 May 2012Sekinan Research Field of Language

Grassmann Language

 Grassmann Language

TANAKA Akio

1. is (N+1) dimensional complex space.
 is Grassmann manifold that is all the spaces which are made from (k+1) dimensional linear subspace of  .
Element of (k+1) dimensional exterior space of  is called (k+1) vector.
Elements of  is given by (k+1) vector of decomposable is givenby the below.
 .
 is one fixed base of .
 is also able to written.
 is called Cayley-Plücker-Grassmann coordinates.
 is unitary group.
 .
 .
Hermitian inner product is defined as the below.
 .
 .
 is called norm of  .
Over 
 .
.
.
 .
 .
 .
Kähler form is
.
The upper measuring is Kähler measuring.
 .
 .

2.(Theorem)
Grassmann manifold has invariant Kähler measuring by operation of  .
Its Kähler form is equal to  times of hyperplane section bundle's curvature form over  that is determined by immersion of Cayley-Plücker-Grassmann coordinates and hermitian norm  .

3.Grassmann language model is supposed as the below.
Word is expressed by grassmann manifold.
Word has location and distance, that are expressed by Cayley-Plücker-Grassmann coordinates and hermitian norm  .

4.
References are below.
<On distance of word>Distance Theory /Tokyo May 5, 2004 
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008
<On manifold>
From Cell to Manifold/ Cell Theory / June 2, 2007
[ Cell Theory / Continuation of Quantum Theory for Language / For LEIBNIZ and JAKOBSON ]

Tokyo
March 6, 2012Sekinan Research Field of Language