  Anthropic reasoning is a critical tool to understand probabilities,
especially in a large universe or multiverse. According to anthropic reasoning,
we should consider ourselves typical among members of a reference class that
must include all subjectively indistinguishable observers. We discuss here
whether such a reference class, which we assume must include computer
simulations, must also include computers that replay previous simulations,
magnetic tapes that store but do not "run" the simulation, and even abstract
mathematical functions. We do not see any clear criterion for excluding these
anomalous observers, but their presence is deeply troubling to the idea of
anthropic reasoning.
