Symplectic Language Theory
TANAKA Akio
Conjecture 1
Structure of Meaning
[Conjecture]
1
Meaning has structure.
(Perspective 1)
2
Structure's basis is given by symplectic manifold.
(LMT Note 1)
3
Meaning has symmetry.
(SLT Note 3)
4
Symmetry is given by homological mirror symmetry.
(SLT Note 3)
5
Meaning has meaning minimum.
(SLT Note 1)
6
Meaning minimum is given by Riemann surface's element.
(SLT Note1)
7
Meaning is given by group of Riemann surface's elements.
(SLT Note 2)
8
Meaning is variable by time.
(SLT Note 3)
9
Time is given by differential equation's variable.
(SLT Note 3)
10
Language has mirror language.
(SLT Note 3 / SLT Note 4)
11
Language's basis is given by Calabi-Yau manifold.
(SLT Note 4)
12
Mirror language's basis is given by isotopy class of symplectic submanifold.
(SLT Note4)
[Complement]
1
Homology mirror symmetry is also given by the next.
Complex manifold M♦
Structure sheaf of M♦ OM♦
Category of all the continuous OM♦'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
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