  We present a new framework for defining fuzzy approximations to geometry in
terms of a cutoff on the spectrum of the Dirac operator, and a generalization
of it that we call the Dirac-Flux operator. This framework does not require a
symplectic form on the manifold, and is completely rotation invariant on an
arbitrary n-sphere. The framework is motivated by the formalism of Holographic
Space-Time (HST), whose fundamental variables are sections of the spinor bundle
over a compact Euclidean manifold. The strong holographic principle (SHP)
requires the space of these sections to be finite dimensional. We discuss
applications of fuzzy spinor geometry to HST and to Matrix Theory.
