Sunday 31 January 2016

Direction, SRFL Essay / New way to language universals

Direction

Why is boundary necessary in language?

31/01/2016 14:21
Why is boundary necessary in language? q.v. Boundary of Words ​/ 12 February 2009 TANAKA Akio 1. I have thought on 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...

At least three elements for language universals

30/01/2016 20:37
At least three elements for language universals TANAKA Akio Supposition 1: Three elements for language universals For language universals, now I suppose at least three elements being  based from mathematical description. Three elements for language universals...

Preparation for the energy of language

30/01/2016 20:35
Preparation for the energy of language TANAKA Akio The energy of language seems to be one of the most fundamental theme for the further step-up  study on language at the present for me. But the theme was hard to put on the mathematical description. Now I present some preparatory...

Thanks to physics about which I ever dreamt in my future

30/01/2016 20:34
Thanks to physics about which I ever dreamt in my future TANAKA Akio In the days of high school, I deeply dreamt that someday physics would perfectly write over this world's phenomena by the clearest descriptions. So I longed for studying physics in the future. But I selected language's diverse...


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Saturday 30 January 2016

SRFL Essay. New essay site of SRFL

Lead

History of SRFL

30/01/2016 17:46
History SRFL Essay is the essay site of Sekinan Library which was founded in 1986 at Tachikawa, Tokyo.  Sekinan Library at first aimed to study ideogram's relationship between figure and meaning mainly using Chinese characters. But the study gradually declined to the essences...



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SRFL Paper, Easier seen Top page



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Boundary of Words

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  Î´ -hyperbolic. ​
( x | y ) x 0   min{( x | z)x 0 , ( y | z ) x 0 }- Î´ ​
When distance space ( X, d ) is  Î´ -hyperbolic for arbitrary base point,  X  is called  Î´ -hyperbolic. ​
Here for a certain   ,  Î´ -hyperbolic space is abbreviatedly called hyperbolic. ​
3 ​
The next condition is equivalent with what ( X, d ) is  Î´ -hyperbolic. ​
d ( x, y ) +  d ( z, w )    max{  d ( x, z ) +  d ( y, w ),  d ( x, w ) +  d ( y, z ) } +2 Î´ ​
4 ​
Distance space        X ​
Arc of X      Î±  : [0,  Î» ] →  X ​
Arbitrary  s, t   [0,  Î» ] ​
d ( Î± ( s ),  Î± (t)) = | s-t | ​
Arc  Î±  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  

Thursday 28 January 2016

Genealogical Tree of Sekinan's Paper Sixth Edition / 1 September 2015 / SRFL Theory

Genealogical Tree of Sekinan's Paper Sixth Edition

TANAKA Akio

Tokyo
18 July 2015 First Edition
1 September 2015 Sixth Edition
SRFL Theory
_________________________________________________________________________________
Genealogical Tree
Sixth Edition


Manuscript of Quantum Theory for Language
|
On Time Property Inherent in Characters
|
Quantum Theory for Language
|                                                 |
Distance Theory                      Property of Quantum
|                                                 |
Prague Theory                        Quantification of Quantum
|
Reversion Theory
|
Mirror Theory
|
Mirror Language
|
Guarantee of Language
|
Actual Language and Imaginary Language
|
Direction
|
Uniformity
|
Changeability
|
Individuality
|
Time
|
Fixation
|
Grammar
|
Substantiality
|
Frame
|
Recognition
|
Ideogram
|
Conversation
|
Descriptiveness
|
Lineation
|
System
|
Automaton
|
Vector

|
Cell Theory
     |
     From Cell to Manifold      
     Conifold as Word     
     Projective Space as Scheme for Word Order 
     |
Algebraic Linguistics
     |     
     Sentence versus Word
     Deep Fissure between Word and Sentence
     |
Distance Theory Algebraically Supplemented
     |
     Bend     
     Distance 
     S3 and Hoph Map 
     |
Noncommutative Distance Theory
     |
     Groupoid     
     C*-Algebra
     Point Space     
     Atiyah’s Axiomatic System
     Kontsevich Invariant
      |
Clifford Algebra
      |
     From Super Space to Quantization
     Anti-automorphism
     Anti-self-dual Form
     Dirac Operator
     TOMONAGA's Super Multi-time Theory 
     Periodicity
     Creation Operator and Annihilation Operator
     Meaning Product 
     |
Kac-Moody Lie Algebra 

     |
     Kac-Moody Lie Algebra
     Quantum Group
     Finiteness in Infinity on Language
     |
Operator Algebra

     |
     Differential Operator and Symbol
     One Paper Lost
     Self-adjoint and Symmetry 
     Frame Operator             
     Order of Word     
     Grammar     
     Recognition
     |
von Neumann Algebra
     |

     von Neumann Algebra 1
      Measure
     Tensor Product
     Compact Operator 

     von Neumann Algebra 2
     Generation Theorem
     von Neumann Algebra 3
     Properly Infinite
     Purely Infinite
     von Neumann Algebra 4
     Tomita's Fundamental Theorem
     Borchers' Theorem
     Relation between Word and Sentence
     |
Functional Analysis
     |
     Functional Analysis
     Baire's Category Theorem
     Equality and Inequality
     Space
     Functional
     Finiteness of Vocabulary
     Distance at Hypersurface   
     Functional Analysis 2
     Pre-Hilbert Space and Hilbert Space
     Orthogonal Decomposition
     Generation of Word
      |
Reversion Analysis Theory
      |
      
      Reversion Analysis Theory      
      Reversion Analysis Theory 2
      |
Holomorphic Meaning Theory
      |

      Holomorphic Meaning Theory
      Holomorphic Meaning Theory 2
      |
Stochastic Meaning Theory
      |

      Stochastic Meaning Theory      
      Stochastic Meaning Theory 2
      Stochastic Meaning Theory 3
      Stochastic Meaning Theory 4
      Stochastic Meaning Theory 5
   
      Stochastic Meaning Theory Conjecture 1
      Stochastic Meaning Theory Conjecture 2 

      |
Energy Distance Theory
      |

      Energy and Distance
      Heat and Diffusion
      Energy and Functional
      Finsler Manifold and Distance
      Word and Meaning Minimum

      Geometry of Word  
      |
Complex Manifold Deformation Theory
      |

      Distance of Word
      Reflection of Word
      Uniqueness of Word
      Amplitude of Meaning Minimum
      Time of Word
      Orbit of Word

      Map between Words
      Understandability of Language
     |
Language Manifold Theory
     |
     Moser's Theorem
     |
Topological Group Language Theory

     |
     Word Problem of Word-hyperbolic Group 
     From Finiteness to Infinity on Language     
     Boundary of Words 
     |
Symplectic Language Theory
     |

     Symplectic Topological Existence Theorem     
     Gromov-Witten Invariant     
     Mirror Symmetry Conjecture on Rational Curve     
     Isomorphism of Map Sequence     
    Generating Function  (Text lost)   
    Homological Mirror Symmetry Conjecture by KONTSEVICH
    Structure of Meaning
    On Structure
    |
Floer Homology Language
   |
   Potential of Language
   Supersymmetric Harmonic Oscillator
   Grothendieck Group
   Reversibility of Language
   Homology Generation of Language
   Homology Structure of Word
   Quantization of Language
   Discreteness of Language
   |
Proto Arithmetic Geometry Language   
   |   
   Language, Word, Distance, Meaning and Meaning Minimum
   |

Imagenary Language
   |
   Volume of Language
   Hyperbolic Space Language
   |
Notes for KARCEVSKIJ Sergej
   |
   Notes for KARCEVSKIJ Sergej, "Du Dualisme asymétrique du signe linguistique"
   Description of Language
   Structure of Word
   Condition of Meaning 
    |
Time of WANG Guowei
   |
   Loop Time of Character
   Symmetry of Language
   |
Stable and Unstable of Language
   |
   Completion of Language
   Meaning Minimum of Language
   Additional Meaning in Word
   |
Projective Space Model
   |
   Vector Bundle Model
   | 
Diophantine Language
   |
   Finiteness of Words
   Dimension of Words
   |
Hyperbolic Language
   |
   Connection of Words
   |
Grassmann Language
   |
   Grassmann Language
   Grassmann Language   
   |
   Grassmann Language 2   
   Elements of Word
   |
Birational Language, Dual Language
   |
   Birational Language
   Birational Language
   Dual Language
   Duality of Language
   |
Infinite Loop Space Language
   | 
   Word as Infinite Loop Space
   |
Algebraic Geometry Language  
   |    
   Parts and Whole (AGL Preface)     
   Dimension of Language (AGL 1)       
   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)        
   |   
Three conjectures for dimension, synthesis and reversion with root and supplement
   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

   |
At least three elements for language universals
   |
   Disposition of Language
   Distance of Word
   Flow of Language
   |
   Papers for Language Dimension, In chronological order
   |
 Preparation for the energy of language


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