Symplectic Language Theory / Structure of Meaning

TANAKA Akio

Conjecture 1

Structure of Meaning


[Conjecture]
1
Meaning has structure.
(Perspective1)
2
Structure's basis is given by symplectic manifold.
(LMTNote1)
3
Meaning has symmetry.
(SLTNote3)
4
Symmetry is given by homological mirror symmetry.
(SLTNote3)
5
Meaning has meaning minimum.
(SLTNote1)
6
Meaning minimum is given by Riemann surface's element.
(SLTNote1)
7
Meaning is given by group of Riemann surface's elements.
(SLTNote2)
8
Meaning is variable by time.
(SLTNote3)
9
Time is given by differential equation's variable.
(SLTNote3)
10
Language has mirror language.
(SLTNote3/Note4)
11
Language's basis is given by Calabi-Yau manifold.
(SLTNote4)
12
Mirror language's basis is given by isotopy class of symplectic submanifold.
(SLTNote4)

[Complement]
1
Homology mirror symmetry is also given by the next.
Complex manifold     M^♦
Structure sheaf of M^♦   O_M^♦
Category of all the continuous O_M^♦'s module     Coh(M^♦)
Symplectic manifold     M
Lagrangian submanifold of M     L
Floer homology     HF(L₁, L₂)
Morphism set from L₁ to L₂     Lag (M)
(Conjecture)
Derived category of Coh(M^♦) and derived category Lag (M) is isomorphic.
2
(Language symmetry by Floer homology mirror symmetry conjecture)
Language is given by Coh(M^♦).
Mirror language is given by Lag (M).

^{_{To be continued}}

^{_{Tokyo March 10, 2009}}

^{_{Sekinan Research Field of language}}