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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, from the point of view of the beings $B$, can predict everything\footnote{With the assumptions above there is an axiom set that can predict everything. In general, an observable description would have to predict as much as it's possible.} that is reasonable\footnote{i.e. the \ghilimele{good enough} requirement from above.}  about $U$ in the best way possible (i.e. predict precisely when possible or in a 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.