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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