Saturday, 30 March 2019

What is signal? The existence that generates language Preface-Main Issue 4 / 30 March 2019

What is signal? The existence that generates language Preface-Main Issue 4 


The existence that generates language
2018-2019
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References
Reference is cited from the papers written
at SekinanLibrary and SRFL
28 February 2019
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Main Issue 1

Quantum Group 
Main Issue will be written from the angle of Quantum group. 

2 March 2019
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Main Issue 3

Broad language


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Main Issue 4

Space and Boundary

Contents

  1. Why is boundary necessary in language?
  2. Boundary of Words
  3. Frame-Sentence Language  Boundary
  4. Language and Spacetime
    1 Language   Definition for the Child who Lost the World
    2 Word Containing Time and 4 Dimensional Sphere
    3 Structure of Word
    4 Generation of Sentence
    5 Description of Meaning
    6 Shift of Time
    7 Construction of Spacetime specially on Transformation with boundary for  Dimensions
    8 Stability of Language
    9 Time Flow in Word


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Text 1

Why is boundary necessary in language?


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1.
I have thought of language as a physic existence that has inevitably boundary to the outer world.
My question is simple and primitive. I ever wrote about the change of language - If there be change, there are exactly the situations before change and after change. Just where does changing substance exist? In the essay, rotten apple was used as the symbol of changing language.

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Presupposition on Natural Language

TANAKA Akio
                               
1.
Language is variable. If it be true, what is the base of variability?
2.
Language is pronounceable. If it be true, what is emerged by pronounced?
3.
Language is recordable. If it be true, what is emerged by recorded?
4.
Example.
An apple is variable and will be rotten by time proceeding.
An apple is pronounced at a glossary shop and will be bought by a home-maker.
An apple is recordable  and will be recorded in a photo.
5.
What distinguishes language from apple? The answer is uncertain. So I make the language models parting from natural language.

Reference
For WITTGENSTEIN Ludwig / Position of Language / 10 December 2005-3 August 2012

                                                              Tokyo
                                                       22 August 2012
                                       Sekinan Research Field of Language　
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2.
Language&s substantiality has been considered since I returned to the mathematical approach for learn language universals from the utterly beginning. In 2005 I wrote a tiny trial paper on the substantiality of language for thinking the study course hereafter.

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Substantiality
Dedicated to SAPIR Edward
TANAKA Akio
1 Substance of language is completion which possesses the distance from the real world.
2 The distance is sustained by the fixation for which meaning and time are abstracted.
3 If language has not distance, language appears and disappears following the real world proceeding.
4 Language is substantially unchangeable. Changeability occurs on surrounding.
5 The distance is measured by the longitude from the real world to the substantiality that meaning and time possess.
6 Substantiality is a frame of language.
7 Substantiality is free from the real world.
8 Substantiality is powered by outer energy.
9 Powered substantiality moves complied with possessed command, namely meaning and time.
10 Powered moving substantiality of language is called .
11 The idea of quantum is partially realized by in the supermarket or bookstore.
12 Substantiality is bar code of can or book. Outer energy is bar code reader. Quantum moves in a cash register. Language generates price addition in the real world.
13 Bar code is not language. Bar code is substantiality of language. Bar code does not move by itself. When bar code reader becomes energetic, bar code generates in a cash register. Language, namely, price-additional-work, starts at bookstore of station front in the bustling evening.    
Tokyo February 27, 2005
For the Memory of Tanashi Station Front Street February 26, 2005
Sekinan Research Field of Language
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3.
In 2013, I again wrote on the substantiality of language at the new level containing the determinate essence of language, dimension and  time. The title is Macro Time and Micro Time. In this paper I thought that dimension is the essential factor of meaning, especially containing Infinitive meaning.

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Macro Time and Micro Time


TANAKA Akio

24 July 2013
atbankofdam

1.
Through natural language, in human being, occurred the electrical signal by eye or ear. These complex situations are beyond this paper’s limits.
2.
Language is a physical object as signal and its transmission. At this circumstanstances, langauge must be recognised to be the existence that has finite time.
3.
An apple on the desk gradually becomes rotten by passing the time very after the crop in the orchard. #0
4.
Like an apple, language has passing physical time in oneself.
5.
Language is metamorphosed  by the time progressing.  #1
6.
Language includes the outer world from human being to universe. At this declaration, I recall Blaise Pascal’s Pensées. XXXIII. PROOFS OF JESUS CHRIST 308 The infinite distance between body and mind symbolizes the infinitely more infinite distance between mind and charity, for charity is supernatural.(Translated by A.J. Krailsheimer, 1966) #2
7.
Language’s time goes freely from the present to the future or the present to the past. #3
8.
Language symbolises the time from finiteness to infinity. #4
9.
Human being recognises this vast language world perfectly. #5

References
#0 For WITTGENSTEIN Ludwig Position of Language / December 10, 2005 – August 3, 2012 / Sekinan Research Field of Language
#1 Time of Word / Complex Manifold Deformation Theory / January 1, 2009 / sekinanlogos
#2 PASCAL PENSÉES. Translated with an introduction by A.J. Krailsheimer. PENGUIN BOOKS 1966.
#3 Escalator language and Time For SHINRAN’s Idea and BOHDISATTVA / Escalator Language Theory / December 16, 2006 / Sekinan Research Field of Language
#4 From Finiteness to Infinity on Language / Topological Group Theory / February 1, 2009 / sekinanlogos
#5 Understandability of Language / Complex Manifold Deformation Theory /January 9, 2009 / sekinanlogos
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4-1
Boundary is related with dimension through  Poincaré Theorem. Details are next.
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Dual 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 :=   M Boundary of language :=   p Dual 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 2012
Sekinan Research Field of Language

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5.
Relation between boundary and synthesis in language is utterly unknown field for me. Study has just started from the entrance position. Recent results are the next.

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Synthesis Conjecture
Conjecture for synthesis of meaning in word 

TANAKA Akio 


Synthesis 
1  Conjecture for synthesis of meaning in word 
29/09/2013 19:25
For synthesis of meaning in word,  Conjecture: Condition for synthesis of meaning in word i s proposed by cohomological expression.

2  Conjecture: Condition for synthesis of meaning in word 
29/09/2013 18:38
On condition for synthesis of meaning in word,  at conjecture is proposed  by the next result of etale cohomology.
Result
——————————————————-
Canonical natural equivalence 
The next two are left exact additional functors.
F :  A   ->  A’  
G :  A’  ->  A” 
A  and  A’  have enough many injective objects.
If  F  transfers  A’  s injective object to  G  acyclic object, the next canonical natural equivalence is concluded.
R  (  G  O  F  ) =~  RG  O  RF .
——————————————————–
Conjecture
Preparation 
Word is shown by  R . This word is called  old word .
Base meaning in word is shown by  F .
Word that has base meaning is shown by  RF .
Additional meaning to word is shown by  G .
Word that has additional meaning is shown by  RG . This word is called  intermediate word .
Word that has base meaning and additional meaning is shown by  R  (  G  O  F  ). This word is called  new word .
Conjecture 
For completion of new word, old word and intermediate word have the condition shown by the canonical natural equivalence of etale cohomology. 

3  Canonical natural equivalence 
29/09/2013 18:08
Canonical natural equivalence 
The next two are left exact additional functors.
F :  A   ->  A’  
G :  A’  ->  A” 
A  and  A’  have enough many injective objects.
If  F  transfers  A ‘s injective object to  G  acyclic object, the next canonical natural equivalence is concluded.
R  (  G  O  F  ) =~  RG  O  RF .

Source:  Conjecture for synthesis of meaning in word / sekinanlatest 2013 

Tokyo
1 May 2014
Sekinan Research Field of Language
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6.
Three Conjectures containing Synthesis Conjecture are shown at the next.These conjectures are the latest result of language universals at SRFL Sekinan Research Field of Language.

  1. Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement
  2.  
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Tokyo
21 December 2014
SIL


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Text 2

Boundary of Words   ​

q.v. Zoho Paper. SIL
Topological Group Language Theory  
TANAKA Akio 
    
​
Preliminary Note 3  
Boundary of Words ​
​
​
[Theorem] ​
1 ​
Distance space     ( X , d) ​
Gromov product ( y | z ) x ​
2 ​
Hyperbolic space      X ​
point sequence     { x i  X } ​
Set of all the { x i  X }      S ∞ ( X ) ​
Point sequence of  X       { y i }     ​
When { y i } is lim i →∞ ( x i | y i ) = 0, { y i } is in  S ∞ ( X ). ​
​
​
[Explanation] ​
1 ​
Hyperbolicity for general distance space is defined by Gromov product. ​
Details are below. ​
2 ​
Distance space is defied by the next.  ​
Distance space that has basic point  x 0        ( X, d ) ​
Arbitrary 3 points of  X         x, y, z ​
When ( X, d ) satisfies the next, it is called  δ -hyperbolic. ​
( x | y ) x 0   min{( x | z)x 0 , ( y | z ) x 0 }- δ ​
When distance space ( X, d ) is  δ -hyperbolic for arbitrary base point,  X  is called  δ -hyperbolic. ​
Here for a certain   ,  δ -hyperbolic space is abbreviatedly called hyperbolic. ​
3 ​
The next condition is equivalent with what ( X, d ) is  δ -hyperbolic. ​
d ( x, y ) +  d ( z, w )    max{  d ( x, z ) +  d ( y, w ),  d ( x, w ) +  d ( y, z ) } +2 δ ​
4 ​
Distance space        X ​
Arc of X      α  : [0,  λ ] →  X ​
Arbitrary  s, t   [0,  λ ] ​
d ( α ( s ),  α (t)) = | s-t | ​
Arc  α  is called geodesic segment. ​
Geodesic segment from x to y that is x,y  X is expressed by   . ​
When arbitrary 2 points of distance space ( X , d) are combinable by geodesic segment,  X  is 
called geodesic space.  xyz  =     is called geodesic triangle. ​
​
​
[Impression] ​
1 ​
Word is identified with point sequence { x i  X }. ​
Language is identified with  S ∞ ( X ). ​
New generated word is identified Point sequence of  X , { y i } that has condition lim i →∞ ( x i | y i ) . ​
The new generated word is also in language, that is to say,  S ∞ ( X ). ​
2 ​
From the condition lim i →∞ ( x i | y i ), spherical surface is considered as boundary at infinity by 
the comparison with Poincaré model. ​
3 ​
Spherical surface is considered as the unit of language.  ​
Language's distance and warp is also considered under hyperbolic space. ​
References are below. ​
​
​
[References] ​
#1  Quantum Theorey for Language ​
#2  Distance Theory ​
#3  Warp Theory ​
The upper papers and the related papers with the themes are seen at  Sekinan Linguistuic 
Field . ​
​
​To be continued  
Tokyo February 12, 2009  


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Text 3
Frame-Sentence Language
Boundary



1 Language consists of frame and sentence.
2 Frame consists of words.
3 Sentence consists of quanta.
4 Frame is duplicable.
5 Sentence is not duplicable.
6 Word has no energy.
7 Quantum has energy.
8 Quantum’s energy comes from outside.
9 Outside energy is brought by human being or electric power.
10 Words are separated each other.
11 Quanta are connected each other.
12 Quanta’s connection is brought by reversion to boundary.
13 Boundary is shown by sentence’s end that is marked by period(.).
14 Word and frame has not boundary.
15 Boundary is expressed by unit element in mathematics.
16 Two quanta are connected by associative law in mathematics.
17 Words /flowers/ and /blossom/ are connected and become sentence [flowers blossom].
18 In sentence [flowers blossom], two quanta [flowers] and [blossom] are connected by associative law.
19 In sentence, associative law works as addition.
20 Sentence has not vacant space. 
21 Notation of vacancy in sentence substantially shows additional mark(+).
22 In sentence [flowers], sentence starts by [flowers] and sentence ends by [flowers]. 
23 One quantum sentence, likely [flowers], has energy 1.
24 Two quanta sentence has energy 2 .
25 Energy goes to sentence’s end in accordance with the system of reversion that is essence of language.


Tokyo November 30, 2005




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Text 4-1

Language
Definition for the Child who Lost the World 


0 The world spreads around the human being.
1 Language divides the world.
2 Language connects the world.
3 Language bends the world.
4 Language stretches the world.
5 Language shrinks the world.
6 Language extinguishes the world.
7 Language creates the world.
8 Language gives despair.
9 Language gives hope.
10 Language is pasting on spacetime with energy.
Tokyo March 3, 2007
Tokyo November 3, 2008 Added
Postscript
[Referential note / November 29, 2007]
For Authentication of Solidity 
[Definition added / November 3, 2008]
Definition 10, the part of <with energy> is newly added.


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Text 4-9


Time Flow in Word
For KOHARI Akihiro and His Time


1
Word is expressed by phase space in the situation on dynamical system.
Phase space M has a point x.
Continuous time t is expressed by group R that consists of real number.
Homomorphism φt(x)expresses the system.
φs+t(x) =φs (φt(x)), φ0 (x) = x
2
In thermodynamics, equilibrium is presented.
Equilibrium situation is expressed by (U, V, n).
U is energy in the system. V is volume. n is material.
Here new equilibrium is expressed by (U’, V’, n).
3
Now a category is presented.
(U, V, n) →f (U’, V’, n)
f is function of entropy.
Here (U, v, n) is expressed by P. (U’, V’, n) is expressed by P’.
The situation of equilibrium is expressed by the following.
f : P → P’
4
The situation of equilibrium is rewritten by phase space.
Each situation of equilibrium is expressed by a point x.
After time t, point x and x’ is presented by the following.
φ : φs(x) →φs+t(x)
5
Now equilibrium system is expressed by {φt} that is called flow.
Here phase space M can take tangent vector X.
Point x has tangent vector Xx = dφt(x)/dtt=0
The flow has solution as equation φt(x)/dt = Xφt(x)
6
Here set {φt(x) | t∈R } is presented. The set is called orbit.
7
In word, meaning is expressed by flow and time is expressed by orbit.
Tokyo May 3, 2007


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Text 4-8

Stability of Language


1
Language has stability.
2
Stability is defined by the following.
From KAWAMATA Yujiro, Stab X that consists of the set having all <locally finite> and <numerical>< stability condition> on derived category D(X) has finite dimensional complex manifold’s structure. Stab (X) is conjectured to be connected and simply connected. In derived category, exact sequence is extinct and distinguished triangle is generated.
Refer to the next paper. KAWAMATA Yujiro   Daisukikagaku to doraiken   Sugaku 58-1   Iwanami Shoten   2006
3
Now blow up and blow down is presented.
φ: QY(M) → M
M is nonsingular variety. Y is M’s submanifold.
QY(M) is blow up along Y.
φis arrow of algebraic variety
φis called QY(M)’s blow down.
4
Also birational mapping that is extension of blow up and blow down is presented.
Birational mapping is what rational mappingφ: V→W  has  mapping ψ: W→V.     Here existsφ∘ψ= idV ψ∘φ=idW .
5
By birational mapping, algebraic variety V, W and X is presented. These three are formed to be new distinguished triangle that is supposed to be equivalent with V, W and X.
6
Word that consists of category makes sentence that consists of distinguished triangle by birational mapping with algebraic method.

Tokyo April 30, 2007


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Text 4-7




Construction of Spacetime
Especially on Transformation with Boundary for Dimensions




1 Spacetime is putted to manifold.
2 When spacetime is expressed by sphere, spacetime becomes sphere symmetry.
Refer to the following paper.
3 The symmetry is special orthogonal transformational group.
4 Generally n-dimensional SO(n) is compact Rie group.
5 On symmetry of spacetime, geometric invariant is presented.
Now on invariant, metric tensor g is presented.
g = Σgij dxidxj
g’s invariant transformation is isometry group.
When gij → gji is established, infinitesimal motion (Killing vector field) is 0.
6 Here Ricci flow is expressed by the following.
g(t) = gij(t)
∂gij / ∂t = -2Rij 
Rij is Ricci curvature tensor.
7 M defined by a time interval [0, T] has a unique g(0) = go on Ricci flow.
8 (S4,g0) is 4 dimensional sphere surface with radius 1.
g(t) = r(t)2g0
g(t) has finite time  T = 1/2(n-1).
Ricci flow becomes a point after finite time.
Phenomenon what manifold becomes smaller dimensional space is called collapse.
9 Now word has meaning and time.
10 Here word is expressed by manifold.
Refer to the following paper.
Also refer to the following paper.
On time of language, refer to the following paper.
On time principle of language, refer to the following paper.
10 Here time of word is defined by manifold’s time of Ricci flow’s collapse.
11 By Thurston conjecture, when compact 3 dimensional manifold is cut and separated by 2 dimensional sphere and torus, while generated compact manifold has sphere boundary, sphere is put together there. As the result new generated manifold has locally uniform structure.
Refer to the following paper.
Also refer to the following paper.
12 Peculiar solution of Thurston conjecture is Poincaré conjecture that is what simply connected 3 dimensional compact manifold is homomorphic to 3 dimensional sphere surface S3.
13 According by Thurston conjecture, what put together newly generated 3 dimensional manifold is called connected sum.
Connected sum is expressed by M1#M2. M1 and M2  are 3 dimensional manifolds.
14 Here sentence is defined by manifold’s connected sum.

Tokyo April 24, 2007


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Text 4-6


1 Language is expressed as structure of spacetime.
2 Spacetime is expressed as manifold.
3 Affine algebraic variety is selected for description of spacetime.
Algebraic variety is pasted together from affine algebraic variety.
Affine algebraic variety is irreducible affine algebraic set.
Affine algebraic set is the set that consists of common zero point of finite polynominal
Polynominal is in n-dimensional complex affine space.
4 Now n-dimensional projective space P n is presented.
C n+1 \ {O} / ~
O is the coordinate’s origin of complex affine space.
~ is mathematical equivalence on elements of set.
5 Projective space P n is covered by n+1 affine space.
6 Now abelian category and derived category are presented.
Abelian category and algebraic variety is placed together.
Derived category is abelian category’s coherent sheaf’s complex that is composition of successive arrows becomes 0.
7 From derived category, distinguished triangle is presented.
8 Here time conjecture of language is presented.
(1)Distinguished triangle makes the model for shift of time on language.
(2)Time on language is closed, successive and circular in word.
Circulation is worked between starting point and ending point of word.
The origin of shift of time is derived from the following.
The concept of time in language is taught from the following.
SAPIR Edward   LANGUAGE  An Introduction to the Study of Speech   Harcout, Brace & Co. Inc
Special thanks to KAWAMATA Yujiro for the mathematical approach on language research, especially from the following.
KAWAMATA Yujiro   Daisukikagaku to doraiken   Sugaku 58-1, January 2006

Tokyo April 20, 2007


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Text 4-5



Description of Meaning

6th Time For KARCEVSKIJ Sergej




1 Word consists of meaning and time.
Refer to the following paper.
2 Sentence consists of connection of words.
Refer to the following paper.
3 Now presheaf is presented by MACLANE Saunders.
Presheaf is contravariant functor F on small category C.   F: Cop → Set   (Set is all of small sets and functions.)
Category has duality principle by axiom.
Category C has opposite category Cop.
Arrow f has opposite arrow f op.
Object of Cop is object C.
Arrow of Cop is arrow f op.
4 Presheaf F gives homomorphism by the following.
V ⊂U    ( V and U  are arbitrary open sets.)
ρ : F (U) → F (V)
ρ gives restrictive mapping.
5 From category, word is given intuitively as below.
F (V) is starting point of meaning.
F (U) is ending point of meaning.
Presheaf F is time for shifting meaning.
6 Grp that consists of groups and homomorphisms are presented.
Now here exist a group G and other groups H.
Arrow’s set HomGrp( H,G) makes the relation between H and G clear. ( HomGrp( H,G) is all the arrows’ set connecting objects H and G in category Grp.)
Here G is meaning of word. H is elements of meaning G.
7 Meaning of word is clarified by all the arrow’s set.
8 The clarification is called description of meaning. 

Tokyo April 16, 2007


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Text 4-4




Generation of Sentence





1 Word consists of meaning and time.
Refer to the following paper.
2 Now word is expressed by cylinder.
In category, cylinder is made by the following.
X is topological space that has base point x0.
I is unit closed interval. 　I = {t ｜0≦t≦1}　
Cylinder is expressed by X×I.
Here t is time of word.
X × 0 is meaning of starting point. X × 1 is meaning of ending point.
3 Now Suspension ΣX of topological space X is presented.
ΣX is made by shortening of upper surface X × 0 and  under surface X × 1 of cylinder X × I.
4 Now Reduced suspension SX is presented.
SX= S1 ×X  
S1 is circumference that is stuck together of point 0 and 1 of closed interval I.
Here SSn =Sn+1  Sn is n-dimensional sphere.
SX is made by shortening of x0 × I from ΣX.
SX is expressed by point.
The point is base point of SX.
5 SX defines group in category.
6 SX has operation of group.
7 Now word follows operation of group in algebra.
8 Connection of words generates sentence.
9 Connection is made by the following.
Now H (I, X) is presented.
H ( I, X) is a road space of topological space X.
H ( I, X) is a set that consists of continuous mapping ψ: I → X at interval I = [0, 1].
Road isψ∈ H (I, X).
Ifψisψ(0) =ψ(1),space X becomes loop space ΩX.
10 If a topological space R is presented, H ( X, ΩR) becomes group.
11 If  an Abelian group A is presented, space Kn (n = 1,2,3….), a set H(X, Kn) becomes Abelian space.
This space is identified with connection of words, namely, sentence.

Tokyo April 13, 2007


Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-generation-of-sentence-for-wang-guowei-and-celan-paul/


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Text 4-3



Structure of Word

From KARCEVSKIJ to MACLANE




1 Word has structure.
On one case of the structure, refer to the following papers.
2 Now the simplest structure example is presented.
Word has starting point of meaning. The meaning is called ms.
Word has time for shifting meaning. The time is called ts.
Word has ending point of meaning. The meaning is called me.
3 By category, word’s ms, ts and me are expressed below.
ts : ms → me
Here ts is replaced by arrow f. ms and me are replaced by objects a and b. The relation is expressed by diagram below.
f  : a → b
4 Here word X and word Y are presented as category that consists of topological space or group.
Word  X is expressed by  f  : a → b.
Word Y is expressed by g  : b → c.
Composition X and Y is expressed by composite f ∘g.
f ∘g : a → c
5 Here f ∘g is putted to h.
The diagram that consists of objects a, b, c and arrow f, g, h is presented.
6 Now category’s morphism is called functor.
Functor that is commutatively transformed to another functor is called natural transformation.
Natural transformation is called component.
On component, refer to the following paper’s concept <passage>.
Natural transformation means functor’s morphism.
7 Product of two categories B and C is defined by the following.
B ×C’s arrow <b, c> →<b’, c’> is <f, g>.  Here, f : b → b’ and  g : c → c’
 <f’, g’>∘<f, g> = <f’∘f, g’∘g>
8 C×2 consists of C×0, C×1 and arrows combined C×0, C×1.
Here when any natural transformation has unique functor, it is called universal natural transformation.
9 Product category C×2  is expressed by concept <garden> in <Cube Theory>.
10 By upper rough sketch, <Cube Theory>’ concepts are transplanted to category. 
11 Word is reconstructed by topological space or group.
12 Structure of word that is presented by KARCEVSKIJ has the chance affirmatively verified in accordance with the concepts of MACLANE.

Tokyo April 6, 2007


Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-structure-of-word-from-karcevskij-to-maclane/


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Text 4-2



Word Containing Time and 4 Dimensional Sphere

Dedicated to MAC LANE Saunders




1 Word contains time inside.
Refer to the following paper.
2 Word has construction that is expressed by category.
On category, refer to Categories for the Working Mathematicians by Saunders Mac Lane, 1998 Springer-Verlag New York, LLC.
3 Time has starting point and ending point in word.
4 Meaning has starting point and ending point in word.
5 Generally word shifts meaning from starting point to ending point by time.
Refer to the following paper.
6 Primitive word does not shift time and stays in the same point.
7 In category, the names of language are called by following terms.
Meaning is called object.
Shift is called arrow.
Starting point is called domain or source.
Ending point is called codomain or target.
No shift or stay is called identity.
Arrow can be composed. The composed arrow is called composite.
In category two axioms are presupposed.
One is associativity.
The other is unit law.
These terms are all complied with above quoted Mac Lane.
8 Word with starting point is expressed on Gauss plane.
9 Word with ending point is also expressed on Gauss plane.
10 Shift time from starting point to ending point is expressed by coordinates’ transference.
11 Here Riemann sphere is putted with having the same origin to Gauss plane.
12 Word with starting point is projected toward the North Pole of Riemann sphere.
13 Word with starting point has coordinates ws (xs ys, zs) on Riemann sphere’s surface.
Refer to the following paper.
14 Word with ending point has also coordinates we (xe, ye, ze) on Riemann sphere.
15 Here 4 dimensional sphere is putted with having the same origin to Riemann sphere.
16 A indefinite strait line determined by coordinates ws and coordinates we makes coordinates wt (xt, yt, zt, tt) on 4 dimensional sphere’s surface.
17 Coordinates wt on 4 dimensional sphere’s surface is uniquely reflected in word with starting point and word with ending point.
18 Word containing time is uniquely expressed on 4 dimensional sphere’s surface.

Tokyo April 5, 2007


Read more: https://srfl-paper.webnode.com/products/language-and-spacetime-word-containing-time-and-4-dimensional-sphere-dedicated-to-mac-lane-saunders/


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What is signal? The existence that generates language Preface-Main Issue 4 
Space and Boundary
Over Edited
30 March 2019





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