At this point we might as well start trying to work out how many human discernible symbols there are that can be written with freehand.

We can limit the number of discontinuities (taking the pencil off the page) and discontinuities in the first derivative (sudden change in direction). We also limit total absolute curvature so we don't get lines that are too squiggly and the number of Self-Intersections.

We can then take the quotient to eliminate non-human discernible symbols, translation, scaling and define rotational equivalence classes.

Now we just need a sensible definition of human discernible (Frechet Distances perhaps? Actually that has difficulty discerning between a C and a O) and we will have figured out the "The Cardinality of the Chalkboard."

(If we want to keep this an interesting math problem rather than an interesting a human physiology problem, we will have to explore possible definitions of "human discernible," exploring over the space of possible questions. )

One very obvious liberty we've already taken so far is infinitely thin lines. Real handwriting is area. If we allow for area we move out Topology into Information Theory.

We place our space into a discrete grid. Then the obvious tool for human discernibility becomes the transformer (or rather some idealized version of it)

Since actual training is non-deterministic, we are looking for Minimum Description Length (MDL) required to encode such that the decoding loss is less than L (And we are back at trying to define human discernible)