i had some more crackpot thoughts if you don't mind hearing them lol
the set of all strings is countably infinite like the natural numbers
however human language when actually spoken can contain recursive implicit meanings and subtext, so maybe even though it's just strings, if you made the implicit context explicit it would be uncountably infinite, much like the real numbers, even though in practice the meaning a human can grok from any given sentence is bounded like a ieee floating point number.
but i find it somewhat interesting that whereas all ieee floats have a certain amount of meaning they can carry around/a set amount of decimal places, the way we encode implicit meanings and tones into language is uneven, it's not character by character (but it can be if you add an accent or tone to a character even in non tonal languages),
like, what if you could design a number system more like human language where the decimal places somehow only showed up under certain conditions (maybe you could argue complex numbers are kinda like that, since the imaginary or real parts will appear and re apper under certain operations)
could you design a number system or an algebra in such a way that it was up for interpretation lol (or if not why not)
one thing is that you can interpret numbers in terms of geometry, but the interpretation is one to one, and thus boring compared to the interpretability of strings.
also maybe lambda calculus is somewhat interpretable in this way, and it can encode numbers and algebraic rules
maybe logical conclusion of this train of thought is the IO monad XD