Saturday 28 February 2015

Energy Distance Theory / Conjecture 1 / Word and Meaning Minimum

Energy Distance Theory

Conjecture 1
Word and Meaning Minimum

TANAKA Akio


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.
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 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 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>
Cell Theory / From Cell to Manifold / Tokyo June 2, 2007
<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
Sekinan Research Field of Language


 [Reference December 22, 2008]

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