Arithmetic Geometry Language

TANAKA Akio



[DRAFT]

​

Language, Word, Distance, Meaning and Meaning Minimum

by Riemann-Roch Formula


1
Finite generated Z module          M
Positive Definite Hermitian form of M          <  ,   > : M × M → C
Hermitian Z module           (M, <  ,  >)
M's volume on <  ,  >          vol (M, <  ,  >) = exp(- (M, <  ,  >))
M           free Z module.
Free basis of M          e1, ..., er
vol (M, <  ,  >) = 

2
Reduced integer ring          R
Total quotient ring of R       K
Z free basis of R                 {w1, ..., wn}
DR:= det(TrK/Q (wi ・wj))

3
(Proposition)
vol(R, < , >hcan = 

4
Hermitian R module          (H, h)



5
(Theorem)
Order        r
Hermitian R module          (H, h)



6

Metric of V        
​
7
Impression
Language := (H, h)
Word       :=   
Distance  := hV
Meaning   := V
Meaning minimum  := H


[Reference]
Cell Theory / Continuation of Quantum Theory for Language / From Cell to Manifold / June 2, 2007



Tokyo August 15, 2009
Sekinan Research Field of Language
sekinan.org