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The Basic Universal Deformation Formula is proven and applied to show thatWeyl algebras, which encode Heisenberg's uncertainty principle, are effectivedeformations of polynomial rings, and that uncertainty is necessary forstability. Deformation problems may have associated modular groups an algebraicexample of which is given. Poisson structures on $C^{\infty}(\mathbf R^d)$,shown by Kontsevich to be infinitesimal deformations integrable to fulldeformations, here are shown to be the skew forms of those infinitesimaldeformations of $C^{\infty}(\mathbf R^d)$ with vanishing primary obstructions.In dimension 3 any smooth multiple of such an infinitesimal again has vanishingprimary obstruction. This exceptional property suggests that in our universe alarge disturbance like the Big Bang can be confined to an arbitrarily smallinterval in time and almost completely confined to an arbitrarily small regionin space.

On the quantization of $C^{\infty}(\mathbb R^d)$