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In this paper, we outline a new approach to quantum gravity; describingstates for a bounded region of spacetime as eigenstates for two classes ofphysically plausible gedanken experiments. We end up with two complementarydescriptions in which the point set continuum disappears.  The first replaces the continuum of events with a handlebody decomposition ofloop space. We conjecture that techniques fron algebraic topology will allow usto extend state sum models on spacetime to loop space.  The second picture replaces the continuum with a nondistributive lattice; theclassical limit seems more tractible in this picture.

A Pointless Model for the Continuum as the Foundation for Quantum Gravity