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We should note that in the second and third cases it can also happen that one can’t improve their axiom set to cover more even when using a statistical axiom set. One such case would be when the perceived laws of the universe change in unpredictable ways from day to day (of course, this can happen without any change in the actual axiom set for the universe).  Let us denote by \definitie{observable description} of a possible universe $U$ for some intelligent beings $B$ inside $U$ any axiom set that can make all possible predictions for $U$ that,  from the point of view of the beings $B$. [TODO: This is not a good definition, I should clarify what happens if there $B$,  can be a universe $U$ in which predict everything\footnote{With the assumptions above  there are predictions that can't be covered by any countable is an  axiom set. Maybe I should use only universes for which I set that  can make those, but then ours may not be such a universe. Or maybe I should use the paragraph below predict everything. In general, an observable description would have to predict as much  as it's possible.} about $U$ in the best way possible (i.e. predict precisely when possible or in  a definition.] statistical way if not).  Then, for the given intelligent beings we would say in the first case that their universe has a \definitie{finite observable description} and in the second and third case that it has an \definitie{infinite observable description}. Of course, a possible universe $U$ could have multiple types of intelligent beings, each type perceiving the universe in a different way. Because of this difference in perception, for some intelligent beings the universe $U$ may have a finite observable description while for others it may have an infinite observable description.