The paper presents a derivation of canonical quantum mechanics (QM) based on the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This approach is extended to provide a novel, non-perturbative formulation of quantum gravity. The key idea is that quantum mechanics can be understood geometrically through the complex projective space $ CP(n) $, which serves as the underlying manifold for statistical events with a well-defined Hamiltonian flow. The Fisher-Fubini-Study metric on $ CP(n) $ is shown to be equivalent to the quantum metric, and the Schrödinger equation emerges as a geodesic equation on this space. The paper also discusses the implications of this geometric structure for quantum gravity, proposing a non-perturbative formulation where the space of quantum events is a nonlinear Grassmannian $ Gr(C^{n+1}) $. This structure is compatible with the equivalence principle and allows for a diffeomorphism-invariant quantum phase space. The Hamiltonian is determined by the requirement that it defines a consistent quantum gravity in an asymptotically flat background. The paper also outlines possible observational implications of this approach, including deviations from the Planck law, the vacuum energy, and the double-slit experiment. The proposal is shown to be compatible with known non-perturbative formulations of quantum gravity, such as Matrix theory. The work is supported by references to previous studies and provides a geometric framework for understanding quantum mechanics and gravity.The paper presents a derivation of canonical quantum mechanics (QM) based on the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This approach is extended to provide a novel, non-perturbative formulation of quantum gravity. The key idea is that quantum mechanics can be understood geometrically through the complex projective space $ CP(n) $, which serves as the underlying manifold for statistical events with a well-defined Hamiltonian flow. The Fisher-Fubini-Study metric on $ CP(n) $ is shown to be equivalent to the quantum metric, and the Schrödinger equation emerges as a geodesic equation on this space. The paper also discusses the implications of this geometric structure for quantum gravity, proposing a non-perturbative formulation where the space of quantum events is a nonlinear Grassmannian $ Gr(C^{n+1}) $. This structure is compatible with the equivalence principle and allows for a diffeomorphism-invariant quantum phase space. The Hamiltonian is determined by the requirement that it defines a consistent quantum gravity in an asymptotically flat background. The paper also outlines possible observational implications of this approach, including deviations from the Planck law, the vacuum energy, and the double-slit experiment. The proposal is shown to be compatible with known non-perturbative formulations of quantum gravity, such as Matrix theory. The work is supported by references to previous studies and provides a geometric framework for understanding quantum mechanics and gravity.