How many universes are in the multiverse?
  We argue that the total number of distinguishable locally Friedmann universes
generated by eternal inflation is proportional to the exponent of the entropy
of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the
number of e-folds of slow-roll post-eternal inflation. For simplest models of
chaotic inflation, N is approximately equal to de Sitter entropy at the end of
eternal inflation; it can be exponentially large. However, not all of these
universes can be observed by a local observer. In the presence of a
cosmological constant \Lambda the number of distinguishable universes is
bounded by e^{|\Lambda|^{-3/4}}. In the context of the string theory landscape,
the overall number of different universes is expected to be exponentially
greater than the total number of vacua in the landscape. We discuss the
possibility that the strongest constraint on the number of distinguishable
universes may be related not to the properties of the multiverse but to the
properties of observers.
