  An unresolved question in inflationary cosmology is the assignment of
probabilities to different types of events that can occur in the eternally
inflating multiverse. We explore the possibility that the resolution of this
"measure problem" may rely on non-standard dynamics in regions of high
curvature. In particular, "big crunch" singularities that develop in bubbles
with negative vacuum energy density may lead to bounces, where contraction is
replaced by inflationary expansion. Similarly, singularities inside of black
holes might be gateways to other inflating vacua. This would drastically affect
the global structure of the multiverse. We consider a measure based on a probe
geodesic which undergoes an infinite number of passages through crunches. This
can be thought of as the world-line of an eternal "watcher", collecting data in
an orderly fashion. This watcher's measure is independent of initial conditions
and does not suffer from ambiguities associated with the choice of a cut-off
surface.
