  We show that the geometry of cutoffs on eternal inflation strongly constrains
predictions for the timescales of vacuum domination, curvature domination, and
observation. We consider three measure proposals: the causal patch, the fat
geodesic, and the apparent horizon cutoff, which is introduced here for the
first time. We impose neither anthropic requirements nor restrictions on
landscape vacua. For vacua with positive cosmological constant, all three
measures predict the double coincidence that most observers live at the onset
of vacuum domination and just before the onset of curvature domination. The
hierarchy between the Planck scale and the cosmological constant is related to
the number of vacua in the landscape. These results require only mild
assumptions about the distribution of vacua (somewhat stronger assumptions are
required by the fat geodesic measure). At this level of generality, none of the
three measures are successful for vacua with negative cosmological constant.
Their applicability in this regime is ruled out unless much stronger anthropic
requirements are imposed.
