  We argue that the Lorentzian path integral is a better starting point for
quantum cosmology than the Euclidean version. In particular, we revisit the
mini-superspace calculation of the Feynman path integral for quantum gravity
with a positive cosmological constant. Instead of rotating to Euclidean time,
we deform the contour of integration over metrics into the complex plane,
exploiting Picard-Lefschetz theory to transform the path integral from a
conditionally convergent integral into an absolutely convergent one. We show
that this procedure unambiguously determines which semiclassical saddle point
solutions are relevant to the quantum mechanical amplitude. Imposing
"no-boundary" initial conditions, i.e., restricting attention to regular,
complex metrics with no initial boundary, we find that the dominant saddle
contributes a semiclassical exponential factor which is precisely the {\it
inverse} of the famous Hartle-Hawking result.
