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Simple physical reasoning shows, that although not themselves usually not conformally invariant, physical models quite generally can be formulated in terms of conformal geometry. The mathematical machinery underlying this development is a calculus of conformal invariance based around ``tractors''---sections of a bundle with connection intimately related to Einstein's equations. These ideas are also connected to approaches that describe dualities between models by introducing a second time coordinate. We describe how models arranging from gravity to higher spins may be described in this way.