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Given a time length $s$, we say that something \definitie{happens rarely} if in any given unit volume of space the time between two occurrences of that something is at least $s$. One could give similar definitions based on the probability of an intelligent being observing that something.  [TODO: Say that we are using any reasonable definition for measuring things with a given precision at the beginning.]  Let us now do the following:  \begin{itemize}   \item Restrict ourselves to universes in which we can measure things with real numbers.