In http:/arxiv.org/hep-th/0104028, a paper titled What is Quantum Gravity begins by addressing the question What is Quantum Mechanics. Building on several years of work (cited in the paper as reference ) the authors derive non-relativistic quantum mechanics from two principles: I. Quantum observations are statistical. That is each observation defines a probability distribution, and the space of such distributions, with a natural (Fisher) metric is the world of quantum observation. II. The kinematics of quantum mechanics is a Hamiltonian flow on the space of distributions. So far, the ideas could have been stated in the 19th century. But the geometric ideas necessary to flesh out the principle only became available in the later 20th century. The upshot is this: The above geometric structure describing canonical QM, beautifully tested in numerous experiments, is also very robust from the purely geometric point of view . A consistent generalization of QM would doubtlessly be interesting from both the experimental and theoretical viewpoints. Unlike various generalizations proposed in the past (which in many instances have lead to difficult conceptual problems) the one put forward in  extends the kinematical structure so that it is compatible with the generalized dynamical structure! The quantum symplectic and metric structure, and therefore the almost complex structure become fully dynamical. By the way, in this approach the complex projective n-space arises naturally, leading us perhaps a little way toward twistor space.