  Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate,
co-closed four-form $C$ introduces a dual symplectic structure $\widetilde{B} =
*C $ independent of $B$ via the Hodge duality $*$. We show that the doubling of
symplectic structures due to the Hodge duality results in two independent
classes of noncommutative U(1) gauge fields by considering the Seiberg-Witten
map for each symplectic structure. As a result, emergent gravity suggests a
beautiful picture that the variety of six-dimensional manifolds emergent from
noncommutative U(1) gauge fields is doubled. In particular, the doubling for
the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of
Calabi-Yau manifolds such that they are mirror to each other. Therefore, we
argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for
the deformation of symplectic and dual symplectic structures.
