On Monday, October 29, 2018 at 10:21:52 PM UTC+1, [email protected] wrote: > > > > 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.* >
Why not? Say you move at a constant speed v and you want to traverse distance d. To traverse half the distance takes time d/2v; to traverse a quarter of the distance takes time d/4v; to traverse an eighth of the distance takes time d/8v, etc. When you add up the times d/2v + d/4v + d/8v + ... with calculus you get total time d/v, a finite number. You traverse the distance in a finite time. -- 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.
