  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 at the future boundary of
bubbles with negative vacuum energy density may lead to bounces, where
contraction is replaced by inflationary expansion driven by different vacua in
the landscape. Similarly, singularities inside of black holes might be gateways
to other inflating vacua. This would drastically affect the global structure of
the inflating 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. We compare this to previous approaches to the measure problem. The
watcher's measure is independent of initial conditions and does not suffer from
ambiguities associated with the choice of a cut-off surface. Another potential
benefit from passing through crunches is that the observations collected by the
watcher may easily depart from ergodicity, in very generic landscapes. This may
significantly alleviate the problem of Boltzmann Brain dominance.
