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> Which is a property of our formalism, not reality. Any state we'd care to actually observe necessarily has finite precision, so the internal mechanics of our

> Which is a property of our formalism, not reality. Any state we'd care to actually observe necessarily has finite precision, so the internal mechanics of our formalism to model this process utilizing infinities is an artifact only of our formalism, not of reality. But this is exactly my point. The fact that our observations have finite precision doesn't say anything about the underlying reality. That's the part that you're asserting. If it also turns out that assuming the underlying system is continuous results in much more compact theories than assuming otherwise, why is the obvious conclusion that spacetime is in fact discrete?

naasking 10y ago
> But this is exactly my point. The fact that our observations have finite precision doesn't say anything about the underlying reality. That's the part that you're asserting. I'm not sure what you think I've asserted, but my only actual assertions are that all of modern physics requires only computable abstractions, and thus, continuous abstractions aren't strictly necessary. I can certainly make the case that a continuous ontology requires more ontological commitments than a discrete ontology, but I haven't said anything along those lines thus far. > If it also turns out that assuming the underlying system is continuous results in much more compact theories than assuming otherwise, why is the obvious conclusion that spacetime is in fact discrete? What is the meaning of "compactness"? A proper comparison of theoretical parsimony requires comparing the Kolmogorov complexity. Compressing ontologies positing reals and/or rationals are definitely less parsimonious than ontologies positing only naturals.
- Jweb_Guru 10y ago
  > What is the meaning of "compactness"? A proper comparison of theoretical parsimony requires comparing the Kolmogorov complexity. Compressing ontologies positing reals and/or rationals are definitely less parsimonious than ontologies positing only naturals. As far as I can tell, by this argument there is literally nothing that would convince you that anything but a discrete theory was correct. So I don't think it's a very interesting argument, sorry. But thank you for explaining your viewpoint.
  - naasking 10y ago
    I've presented my argument why I don't think it's possible for a continuous ontology to be simpler than a discrete ontology, but if you think that's incorrect, then let's hear it.

naasking 10y ago

> But this is exactly my point. The fact that our observations have finite precision doesn't say anything about the underlying reality. That's the part that you're asserting. I'm not sure what you think I've asserted, but my only actual assertions are that all of modern physics requires only computable abstractions, and thus, continuous abstractions aren't strictly necessary. I can certainly make the case that a continuous ontology requires more ontological commitments than a discrete ontology, but I haven't said anything along those lines thus far. > If it also turns out that assuming the underlying system is continuous results in much more compact theories than assuming otherwise, why is the obvious conclusion that spacetime is in fact discrete? What is the meaning of "compactness"? A proper comparison of theoretical parsimony requires comparing the Kolmogorov complexity. Compressing ontologies positing reals and/or rationals are definitely less parsimonious than ontologies positing only naturals.

Jweb_Guru 10y ago
> What is the meaning of "compactness"? A proper comparison of theoretical parsimony requires comparing the Kolmogorov complexity. Compressing ontologies positing reals and/or rationals are definitely less parsimonious than ontologies positing only naturals. As far as I can tell, by this argument there is literally nothing that would convince you that anything but a discrete theory was correct. So I don't think it's a very interesting argument, sorry. But thank you for explaining your viewpoint.
- naasking 10y ago
  I've presented my argument why I don't think it's possible for a continuous ontology to be simpler than a discrete ontology, but if you think that's incorrect, then let's hear it.