  We develop a new method for decomposing Witten diagrams into conformal
blocks. The steps involved are elementary, requiring no explicit integration,
and operate directly in position space. Central to this construction is an
appealingly simple answer to the question: what object in AdS computes a
conformal block? The answer is a "geodesic Witten diagram," which is
essentially an ordinary exchange Witten diagram, except that the cubic vertices
are not integrated over all of AdS, but only over bulk geodesics connecting the
boundary operators. In particular, we consider the case of four-point functions
of scalar operators, and show how to easily reproduce existing results for the
relevant conformal blocks in arbitrary dimension.
