whether or not we live in a continuous or discrete universe, this is an insufficient argument for (popular interpretations of) computational functionalism
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if you accept the premise that what a theory of consciousness has to do is provide a mapping from physics to qualia, this mapping still has to a) be principled and b) not violate classical local causality (unless you're a QM ToC advocate, which neither myself or joscha are)
if you want to propose a mapping from physics to qualia which can account for a language model's causally connected experience, these are the spatiotemporal obstacles you have to surmount. please understand that any mapping you propose will not just have to work here; but for all beings no matter their shape or form I asked: "Do the calculations performed to run a language model in a data center tend to be spatiotemporally disparate?"
if you accept this premise, and also believe that it would be a good thing for a being like a language model to have a subjective experience congruous with what we might fancifully imagine them to have – then we are going to need quite different hardware
otherwise, here's what you have to contend with
(and fwiw, i do suspect that functionalism may ultimately prove reconcilable with physicalism – just not *computational* functionalism)
anyway, what i'm saying is that this is all ultimately indifferent to a continuous vs. discretised universe; causality and parsimony still hold. for more on all this, see here
Btw the Navier Stokes problem comes down to: if we lived in a truly continuous universe, fluids might sometimes explode. It’s an issue for the universe of classical mathematics, but does not apply to the computational universe we are in.
