The same argument could be made for sound, and yet digital computers have no problem approximating it to sufficient precision as to make it indistinguishable from the original.

Discretization works fine and is not the problem. The problem is that the “AI” everyone’s so hyped up about is nothing more than a language model. It has no understanding of what it’s talking about because it has not been taught or allowed to experience anything other than language. Humans use language to express ideas; language-model AIs have no ideas to express because they have no life experience from which to form any ideas.

That doesn’t mean AGI is impossible. It is likely infeasible on present-day hardware, but that’s not the same thing as being impossible.