What is signal? Preparation 2 / 6 Understandability / 9 January 2019

What is signal? 

The existence that generates language

TANAKA Akio
SRFL Paper
Tokyo

21 November - 6 January 2019

Original Title

 What is signal? A mathematical model of nerve  

Preparation 1-15

For father and mother 

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Preparation 2

4

Energy 2

Signal and language send message, for which they need energy directly or indirectly.

What exists between message and energy?

I ever wrote several trial papers on this theme.
Here I show the two of them

1.

Amplitude of meaning minimum / Complex Manifold Deformation Theory   2008

2.

Time of Word / Complex Manifold Deformation Theory   2008

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Complex Manifold Deformation Theory 

​

Conjecture A 

4 Amplitude of Meaning Minimum 

​

TANAKA Akio 

     

​

Conjecture 

Meaning minimum has finite amplitude.​

​

[View*]​

*Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains 

and vigorous port towns at dawn.  ​

1​

Bounded domain of Rm      Ω​

C∞ function defined in Ω     u, F​

u, F satisfy the next equation.​

F(D2u) = Ψ​

D2u is hessian matrix of u.​

F is C∞ function over Rm×m .​

Open set that includes range of D2u     U​

U satisfies the next.​

(i) Constant λ, Λ     ​

(ii) F is concave.​

2​

(Theorem)​

Sphere that has radius 2R in Ω       B2R​

Sphere that has same center with B2R and has radius σR in Ω      BσR​

Amplitude of D2u     ampD2u​

ampBσRD2u = supBσRD2u – infBσRD2u​

0<σ<1​

C and e are constant that is determined by dimension m and .​

ampBσRD2uCσe(ampBRD2u +  supB2R|D| + supB2R |D2| )​

​

​

[Impression]​

1 Meaning minimum is the smallest meaning unit of word. Refer to the reference #2 and 

#2′.​

2 If meaning minimum of word  is expressed by BσR, it has finite amplitude in adequate 

domain.​

​

​

[References 1 On meaning minimum]​

#1 Holomorphic Meaning Theory / 10th for KARCEVSKIJ Sergej​

#2 Word and Meaning Minimum​

#2′ From Cell to Manifold​

#3 Geometry of Word​

​

[References 2 On generation of word]​

#4 Growth of Word​

#5 Generation Theorem​

#6 Deep Fissure between Word and Sentence​

#7 Tomita’s Fundamental Theorem​

#8 Borchers’ Theorem​

#9 Finiteness in Infinity on Language​

#10 Properly Infinite​

#11 Purely Infinite​

​

[References 3 on distance and mirror on word]​

#12 Distance Theory / Tokyo May 5, 2004 / Sekian Linguistic Field​

#13 Quantification of Quantum / Tokyo May 29, 2004 / Sekinan Linguistic Field​

#14 Mirror Theory / Tokyo June 5, 2004 / Sekinan Linguistic Field​

#15 Mirror Language / Tokyo June 10, 2004 / Sekinan Linguistic Field​

#16 Reversion Theory / Tokyo September 27, 2004 / Sekinan Linguistic Field​

#17 Mirror Theory Group / Tokyo December 9, 2008 / Sekinan Linguistic Field​

​

To be continued​

Tokyo December 17, 2008​

Sekinan Research Field of language​

​

[References 4 / December 23, 2008 / on time of word]​

#18 Time of Word / Tokyo December 23, 2008 / sekinan.wiki.zoho.com

Read more: https://srfl-paper.webnode.com/news/amplitude-of-meaning-minimum/

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Complex Manifold Deformation Theory​

​

Conjecture A 

5 Time of Word 

​

TANAKA Akio 

     

​

Conjecture 

Word has time.​

​

[View¶]​

¶Mathematics is a view in which I freely appreciate objects as if I see flowers, mountains 

and vigorous port towns at dawn.  ​

1​

Kähler manifold     X​

Kähler form     w​

A certain constant     c​

Cohomology class of w     2πc1(X)​

c1(X)>0​

Kähler metric     g​

Real C∞ function     f​

∫X (ef- 1)wn = 0​

Ric(w) -w = f​

2​

Monge-Ampère equation ​

(Equation 1)​

Use continuity method​

(Equation 1-2)​

Kähler form     w' = w +  f​

Ric(w') = tw' + (1-t)w'​

δ>0​

I = {  }​

3 is differential over t.​

Ding's functional     Fw​

​

4​

(Lemma)​

There exists constant that is unrelated with t.​

When utis the solution of equation 1-2, the next is satisfied.​

Fw(ut)C​

5​

Proper of Ding's functional is defined by the next.​

Arbitrary constant     K  ​

Point sequence of arbitrary P(X, w)K     {ui}​

(Theorem)​

When Fw is proper, there exists Kähler-Einstein metric.​

​

[Impression¶]​

¶ Impression is developed from the view.​

1​

 If word is expressed by u , language is expressed by Fw and comprehension of human 

being is expressed by C, what language is totally comprehended by human being is 

guaranteed.​

Refere to the next paper.​

#Guarantee of Language​

2​

If language is expressed by being properly generated, distance of language is expressed by 

Kähler-Einstein metric and time of language is expressed by t, all the situation of language 

is basically expressed by (Equation1-2).​

Refer to the next paper.​

#Distance Theory​

3​

If inherent time of word is expressed by t's [δ, 1], dynamism of meaning minimum is 

mathematically formulated by Monge-Ampère equation.​

Refer to the next papers.​

#1<For inherent time>​

On Time Property Inherent in Characters​

#2<For meaningminimum>​

From Cell to Manifold​

#3<For meaning minimum's finiteness>​

Amplitude of Meaning Minimum​

​

​

Tokyo January 1, 2009​

Sekinan Research Field of language​

Read more: https://srfl-paper.webnode.com/news/complex-manifold-deformation-theory-conjecture-a-5-time-of-word/

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From upper two papers, Amplitude of Meaning Minimum and Time of Word, I think that energy, distance, meaning and time are closely related.


6
Understandability

Meaning is understood in the finite time by human or machine assisted by human. 

Understandability of meaning is closely related with time.

At this situation I ever wrote a following trial paper titled understandability of language in 2008.

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Complex Manifold Deformation Theory

Conjecture B

2 Understandability of Language

TANAKA Akio

    

Conjecture

Language is understandable.


[View]
0
(Eells-Sampson Theorem)
Compact Riemannian manifolds (M, g), (N, h)
Section curvature of (N, h) everywhere non-positive
Arbitrary C∞ map     f : M → N
Equation 
Solution of the equation exists at .
When there exists ,  is convergent to harmonic map  and  is free homotopic with .
1
(Harmonic map)
Arbitrary variation of  { } 
2
(Section of )
3
(Levi-Civita connection)
Levi-Civita connection of (M, g) and (N, h)     

[Impression]
1
From Eells-Sampson Theorem, if language is supposed to be expressed by the equation and word is supposed to be expressed by  , language is understandable in finite time.The situation contributes guarantee of language. 
2
In infinite time, Language still can be understood by word's generation system  .  

[References]
For impression, refer to the next.
<Understandability of language>
#1 Finiteness in Infinity of Language / Kac-Moody Lie Algebra / Conjecture 1 / Tokyo February 10, 2008
#2 Properly Infinite / von Neumann Algebra 3 / Note 1 / Tokyo May 1, 2008
#3 Purely Infinite / von Neumann Algebra 3 / Note 2 / Tokyo May 1, 2008
<Guarantee of language>
#4 Guarantee of Language / Tokyo June 12, 2004
<Generation system>
#5 Generation Theorem /von Neumann Algebra 2 / Note / Tokyo April 20, 2008



Tokyo January 9, 2009
Sekinan Research Field of language

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Arithmetic Geometry Language​

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TANAKA Akio​

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[DRAFT] 

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Language, Word, Distance, Meaning and Meaning Minimum​

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by Riemann-Roch Formula​

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1​

Finite generated Z module          M​

Positive Definite Hermitian form of M          <  ,   > : M × M → C​

Hermitian Z module           (M, <  ,  >)​

M's volume on <  ,  >          vol (M, <  ,  >) = exp(-

 (M, <  ,  >))​

M           free Z module.​

Free basis of M          e1, ..., er​

vol (M, <  ,  >) = 

​

​

2​

Reduced integer ring          R​

Total quotient ring of R       K​

Z free basis of R                 {w1, ..., wn}​

DR:= det(TrK/Q (wi ・wj))​

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3​

(Proposition)​

vol(R, < , >

hcan = 

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4​

Hermitian R module          (H, h)​

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​

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5​

(Theorem)​

Order        r​

Hermitian R module          (H, h)​

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6​

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Metric of V        

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​​

7​

Impression​

Language := (H, h)​

Word       := 

  ​

Distance  := hV​

Meaning   := V​

Meaning minimum  := H​

​

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[Reference]​

Cell Theory / Continuation of Quantum Theory for Language / From Cell to Manifold / 

June 2, 2007​

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​

​

Tokyo August 15, 2009​

Sekinan Research Field of Language​

sekinan.org​

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