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Showing posts with label Energy Distance Theory. Show all posts
Showing posts with label Energy Distance Theory. Show all posts

Friday, 19 December 2014

The days when I was thinking on Energy Distance Theory / 19 December 2014

The days when I was thinking on Energy Distance Theory
q.v. Energy and Distance in Language / 31 August 2008

TANAKA Akio

1.
Around 2008, I was thinking on energy in language related with distance in language. Distance is one of the kernel themes of my study of language universals in those days. In simply saying, distance is the result of movement and for movement there must inevitably needs energy. So I had thought that if language have distance, there must be energy or its alike in language that is supposed in mathematical models. But in my ability in 2008, I could not develop the deep and wide range of language from the theme, energy and distance. So Energy Distance Theory was still now unfinished.

2.
In another approach of my study on language universals, Edward Sapir's Language, 1921 was one of my favourite books between 1970s and early 1980s. In his book, the most fantastic concept for me was Drift, that indicated the vast movement of language system itself.  I ever gave brief account on it.

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Edward Sapir's Language, 1921 showed me the dynamism of language proposing the concept, drift.
Drift shows us the macro phase of natural language and I was hinted by Sapir's this concept and proposed the micro phase of natural language. The paper "Quantum Theory for Language" is my first total proposal paper describing the natural language's model.

Reference
Substatiality Dedicated SAPIR Edward / 27 February 2005

Tokyo
5 September 2014
Sekinan Research Field of Language 
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3.
My language study started from the reading of Old China's Qing dynasty's huge linguistic inheritance, "Xiaoxue", in English Small Study , that is contrary to the name, the most basic and difficult study of classical texts of old China. I particularly loved the books written by WANG Guowei and WANG Yinzhi and DUAN Yucai.
The main book list to which I referred in those days between the age 20s and 40s are shown  at the next.


Especially I was enchanted with WANG Guowei's work, whose selected papers' title was Guantangjilin. For him I wrote a short essay as below.

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TANAKA Akio
Guantangjilin is the selection of works by WANG Guowei, which contents contains vast area of history, literature and linguistics. Some people say that his works is a thousand-year peak from Song era’s philosopher SHU Xi. I bought his book at Haifeng shudian, Kanda, Tokyo in my mid 20s. The date  of colophon is February 1973, publisher is Zhonghua shuju Xianggang fenju.

Probably I bought it in 1973 or 1974. In those days I frequently went Haifeng shudian bookshop for buying Chinese classics,  mainly Qing Dynasty’s linguistic works that is called ” Xiaoxue”, Small study at China. Guantangjilin is a very difficult book to understand  by my poor study result.


His study era is from Yin Dynasty to Qing Dynasty some 2,500 years of Chinese literary history. At his vast works I was especially charmed in Qing Dynasty’s ancient Chinese hieroglyphic characters, Jiaguwenzi by Chinese. After 40 years, in 2003 I wrote a small paper on language universals through this  ancient Chinese hieroglyphic characters at the view point of written language.


The title is On Time Property inherent in Characters. From at that time 10 years passed by. Now I am still learning on language universals but its style is far apart from the days 2003 or 1973. Ambiguity of approach by traditional linguistics is not for my part. I dare challenge to a new frontier of description for language study using mathematics or algebraic geometry.

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4.
After all,Energy Distance Theory ended in the half-finished situation. But now I still eager to write and develop the papers on energy and distance. The road is long and winding as ever. I always accustomed to delay and stagnate. Some rays of light is emitting in the small study room of mine.


Tokyo
19 December 2014
SIL

Energy and Distance in Language / 31 August 2008

Energy and Distance in Language
Energy Distance Theory

Note 1
Energy and Distance

TANAKA Akio

1
Curvein 3-dimensional Euclidian space   : [0, 1] → 3
Longitudeof   ) = dt
2
Surface   S
Curvecombines and in   l
Coordinateof     φ → S
Coordinateof   2
φ = ( φ , φ , φ )
φ )
φ )
3
Curvein   : [0, 1] → 3
Curveon   )
Ω )= { : [0,1] → (0) = (1 ) = }
∈ Ω )
)= φ ) )
( 0 )= 0
( 1 ) = 1
) = dt     dt
ij isRiemann metric.
4
Longitudeis defined by the next.
x, xˑ     dt
5
Energyis defined by the next.
x, xˑ   =   ∑ I,j i,j )) xˑ xˑ dt
6
x, xˑ ≥ ( x, xˑ ) ) 2
7
Theorem
For ∈ Ω ), the nexttwo are equivalent.
(i) akesminimum value at .
(ii) takes minimum value at .
8
What longitudeis the minimum in curve is equivalent what energy is the minimum in curve.
9
Longitude is corresponded with distancein Distance Theory.

[References]
Distance Theory / Tokyo May 4, 2004
Property of Quantum / Tokyo May 21, 2004  
Mirror Theory / Tokyo June 5, 2004
Mirror Language / Tokyo June 10, 2004
Guarantee of Language / Tokyo June 12, 2004
Reversion Theory / Tokyo September 27, 2004

Tokyo August 31, 2008

Friday, 5 December 2014

Word and Meaning Minimum "Language has dimension." / 22 September 2008



Conjecture 1
Word and Meaning Minimum



1
Word is expressed by arbitrary figure W in space Rn.
Meaning minimum is expressed by n-dimensional sphere M that has diameter below δ.
W is covered by sequence of M.1, M2, M3, .
Lower limit of all the covering ∑k (diam ( Mk ) ) α is expressed by Hα,δ ( W ).
Hα,δ ( W ) = inf diam ( Mk ) <δ (diam ( Mk ) ) α
2
Hα ( W ) : = limδ 0 Hα,δ ( W )
3
Word has non-positive real number or by Hα ( W ).
Hα ( W ) is restricted by measurable sets.
Hα ( W ) is treated as Hausdorff measure.
4
Word is expressed by Hausdorff measure.
Meaning minimum is expressed by limδ 0 M .
5
Word has α dimension.
Meaning minimum has n dimension.
6
Language consists of word and meaning minimum.
7
Language has dimension.

[References]
<On meaning minimum>
<On place of meaning>
Stochastic Meaning Theory 3 / Place of Meaning / Tokyo July 11, 2008
<On confirmation of meaning>
Stochastic Meaning Theory 2 / Period of Meaning / Tokyo June 27, 2008
 
Tokyo September 22, 2008

 [Reference December 22, 2008]
Complex Manifold Deformation Theory / sekinan.wiki.zoho.com