alt Hacker NewsThere's actually a lot of math trying to describe the types of space you mention - non quantized, non 'granular', they're not made of points, or distances (metrics). One deep idea is to define space through which symmetries hold (Klein's Erlangen program). Topology itself is not interested in distances per se, only properties of a space invariant under homeomorphisms (a fancy way of saying you can continuously deform a cup to be a donut). Thurston's Geometrization Theorem outlines the 8 geometries that a closed 3 manifold can have. Topos theory studies space in a very general setting that connects logic to it. You may like the books "The Shape of Space" and "Surreal Numbers". The Numbers 1, 2, 3 is not the only in which mathematicians abstract reality.
I know I failed to explain this correctly and was downvoted for it
But I think you got my point. “Granularism” itself is an approximation of a specific set of dimensions of space.
Tokenizing reality so far is somewhat incompatible with say real time forces (new dimensionalism as you sort of describe here) Even if there are granularities representations of them.
So whatever hasn’t been granulized so far AI can’t understand because it would need to verify in reality through observation if the new units of granularity align with outcomes.
This is of course possible to some degree but runs into a paradox if it is a portion of reality than is irreducible or works in a fundamentally “non granular” way.
I have no proof of this but of course already at the quantum level we are running into to “non granular” realities