Cell Theory Projective Space as Scheme for Word Order

Cell Theory

Continuation of Quantum Theory for Language

Projective Space as Scheme for Word Order

　　　TANAKA Akio

1 n-dimensional complex projective space Pⁿ is defined by the following.

Sch is category of scheme. Set is category of set. X is scheme.

Contravariant functor h_x : Sch → Set

h_x (S) = Hom_sch (S, X)

Pⁿ = h_x (Spec(C))

Pⁿ becomes scheme for expressing h_x.

2 P² that is defined by 2-dimensional homogeneous polynomial is presented.

Closed scheme of P², X = Proj C |x, y, z| becomes <line>, <circle> or <surface> by affine transformation.

<Surface> is projective manifold.

3 Weighted projective space that is projective algebraic manifold is defined by the following.

P (a₀, …, a_n) = Proj C |x₀, …, x_n|

4 Weight is identificated to word order of language.

5 Language is expressed by algebraic manifold, especially by projective scheme.

[Reference]

Cell Theory /  From Cell to Manifold / Tokyo June 2, 2007

Cell Theory / Conifold as Word / Tokyo June 9, 2007

Tokyo June 11, 2007

Sekinan Research Field of Languagewww.sekinan.org