If the observation time is finite, and the time resolution of the observation is limited, then you'd still only have a finite number of distinguishable symbols, wouldn't you?
That's true if the time resolution is limited. Theoretically there could be no limit. It would not make for a very practical alphabet, but it would still be an unlimited alphabet.
Just as Rorschach's mask always changes in Watchmen. We would have books with changing alphabet. In the library of babel, Harry Potter would be located in one section at a given time T1 but maybe at a different section at time T2.
