  The mathematical formalism of Quantum Mechanics is derived or "reconstructed"
from more basic considerations of probability theory and information geometry.
The starting point is the recognition that probabilities are central to QM: the
formalism of QM is derived as a particular kind of flow on a finite dimensional
statistical manifold -- a simplex. The cotangent bundle associated to the
simplex has a natural symplectic structure and it inherits its own natural
metric structure from the information geometry of the underlying simplex. We
seek flows that preserve (in the sense of vanishing Lie derivatives) both the
symplectic structure (a Hamilton flow) and the metric structure (a Killing
flow). The result is a formalism in which the Fubini-Study metric, the
linearity of the Schr\"odinger equation, the emergence of a complex numbers,
Hilbert spaces, and the Born rule, are derived rather than postulated.
