Measuring Space-Time Geometry over the Ages
  Theorists are often told to express things in the "observational plane". One
can do this for space-time geometry, considering "visual" observations of
matter in our universe by a single observer over time, with no assumptions
about isometries, initial conditions, nor any particular relation between
matter and geometry, such as Einstein's equations. Using observables as
coordinates naturally leads to a parametrization of space-time geometry in
terms of other observables, which in turn prescribes an observational program
to measure the geometry. Under the assumption of vorticity-free matter flow we
describe this observational program, which includes measurements of
gravitational lensing, proper motion, and redshift drift. Only 15% of the
curvature information can be extracted without long time baseline observations,
and this increases to 35% with observations that will take decades. The rest
would likely require centuries of observations. The formalism developed is
exact, non-perturbative, and more general than the usual cosmological analysis.
