I don't think you understand the issue. Velocities greater than c in the underlying spacetime manifold are allowed in the construction of the tangent plane, so the issue I raise has nothing to do with countable vs. uncountable, or computability. AG
On Tuesday, September 3, 2024 at 10:26:01 AM UTC-6 John Clark wrote: > On Tue, Sep 3, 2024 at 10:07 AM Alan Grayson <[email protected]> wrote: > > *> While spacetime might not have an infinite set of events, countable or >> uncountable, the tangent space is constructed via a vector space with at >> least a countable number of elements. * > > > Even though there are an uncountably infinite number of real numbers but > only a countable number of rational numbers, you can always find a rational > number that is arbitrarily close to any real number, provided that the real > number in question is computable. Thus the thing that you're so worried > about is not a concern for a physicist because, at least so far as anybody > knows, there is no physical experiment you can perform that can reveal the > difference between the countable infinite and the uncountable infinite. > > Mathematics is the language of physics but mathematics is not physics. And > any language can be used for both fiction and nonfiction, so it could be > that the hierarchies of infinity and even the very concept of infinity is > the mathematical equivalent of a Harry Potter novel. Mathematical > consistency may not be enough to ensure physical reality. > > John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis> > acr > > > > >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/531dd85e-aef9-4066-a1c9-eca79c887753n%40googlegroups.com.
