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

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