  Complex geometry and symplectic geometry are mirrors in string theory. The
recently developed generalised complex geometry interpolates between the two of
them. On the other hand, the classical and quantum mechanics of a finite number
of degrees of freedom are respectively described by a symplectic structure and
a complex structure on classical phase space. In this letter we analyse the
role played by generalised complex geometry in the classical and quantum
mechanics of a finite number of degrees of freedom. We identify generalised
complex geometry as an appropriate geometrical setup for dualities. The latter
are interpreted as transformations connecting points in the interior of the
Planck cone with points in the exterior, and viceversa. The Planck cone bears
some resemblance with the relativistic light-cone. However the latter cannot be
traversed by physical particles, while dualities do connect the region outside
the Planck cone with the region inside, and viceversa.
