I suspect that if you follow this distinction out all the way, you'll find that ideographic writing is also a collection of symbols that can be considered digits, although the base is much higher... while English might have an effective base around thirty (if you allow for some punctuation), Kanji has an accepted common base of a few thousand and if you held some professor's feet to the proverbial fire, you could probably establish some mathematical bound for this base.

Check out syllabaries. Some writing systems are really quite close to an extremely compressed trace of the analog signal, while still being a linear sequence of symbols.