On Monday, October 29, 2018 at 8:33:32 PM UTC, Tomas Pales wrote: > > > > On Monday, October 29, 2018 at 7:36:47 PM UTC+1, Philip Thrift wrote: >> >> >> >> On Monday, October 29, 2018 at 11:07:41 AM UTC-5, John Clark wrote: >>> >>> On Sun, Oct 28, 2018 at 2:56 PM <[email protected]> wrote: >>> >>> > *What's your view of Zeno's paradox which implies motion is >>>> impossible.* >>> >>> >>> Zeno thought it was obvious if you added an infinite number of nonzero >>> lengths or nonzero times together you would always get something that was >>> nfinite, and that is the foundation of his paradox; but with modern >>> calculus we know that sometimes that isn't true, and when it isn't true >>> calculus can tell you exactly what the FINITE length or finite time >>> interval turns out to be. For example, the sum, of the infinite series: >>> 1+1/4+1/9+1/16+1/25 + 1/36 + .... 1/N^2 is EXACTLY equal to (PI^2)/6. >>> >>> John K Clark >>> >>> >>> >>> >> It is still a paradox as discussed in foundational physics and >> mathematical writing, when one leaves the naive calculus as taught in high >> school or college. >> > > The calculus solution seems fine to me, what's the problem with it? >
*If you try to traverse a unit distance in infinite steps such as 1/2, 1/4, 1/8, 1/16 and so forth, the sum converges to 1, but you will never traverse the distance even though the sum converges. This is Zeno's paradox. Clearly it depends on space being infinitely divisible. But since motion IS possible, the solution of Zeno's paradox must be that space is discrete (not "discreet"). AG* Of course if space is discreet then you can solve the Zeno paradox without > calculus. > > -- 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 post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
