On Wed, Sep 4, 2024 at 8:08 AM Alan Grayson <[email protected]> wrote:
> *> it seems that the metric tensor FIELD is NOT well defined. AG* *The metric tensor encodes spacetime curvature, and for every point in spacetime that you can name I can give you a 4x4 matrix of unique computable numbers that defines the curvature at that point. What's ambiguous about that? It's true that I can't do that for points in spacetime that you cannot name, but that is not a problem because you cannot get experimental results from points that you cannot name. * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> wai > > On Wednesday, September 4, 2024 at 6:02:17 AM UTC-6 John Clark wrote: > >> On Tue, Sep 3, 2024 at 6:44 PM Alan Grayson <[email protected]> wrote: >> >> * > I fail to see how your comments relate to the possibly ambiguous >>> concept of the latter. The metric tensor field seems ambiguously defined.* >> >> >> *A N dimensional space is composed of an uncountable number of real >> numbers but it can be unambiguously defined by just N countable rational >> numbers, you can pair them up one to one. This is possible because there is >> only a countably infinite number of COMPUTABLE real numbers, the same rank >> of infinity as the rational numbers. So you can in effect give a rational >> number name to every real number you are able to find on the number line. >> You can do this even for a number such as π which is not only irrational, >> it's transcendental, because it is also computable. You can use an infinite >> series to get arbitrarily close to π. * >> >> *The vast majority of numbers on the number line are NOT computable (and >> have no name) but that's not really a problem despite the fact that the >> vast majority of numbers on the number line are NOT computable because, >> except for Chaitin's Omega Number, every number that a mathematician has >> ever heard of is a computable number. Computable numbers can have names, >> uncomputable numbers can not.* >> > -- 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/CAJPayv3MbDFig6j5-e-J2ZKACFe5pCSnefA3nrCeXqb_SHHJbA%40mail.gmail.com.
