On Monday, October 29, 2018 at 6:36:47 PM UTC, 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 <agrays...@gmail.com> 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. > > *What if Tegmark is right, and one should banish the word "infinite" once > and for all, so "sum of the infinite series" could not even be mentioned!* > > The problem is we do not know what spacetime is, really. > > > https://blogs.unimelb.edu.au/sciencecommunication/2017/10/22/zenos-paradox-the-puzzle-that-keeps-on-giving/ > > : > ... > > *So, has this puzzle been solved once and for all?* > > *Quantum physics has probably given us our most convincing answer to the > paradox so far, but it is not a certainty. The question of whether space is > continuous or made up of discrete units is still debated among physicists > (there are experiments currently trying to test this), and quantum > mechanics itself is known not to be a complete theory of the universe. If > history is any indication, this isn’t the last we’ll hear of Zeno’s > paradox.* > > > - pt >
*Clark misstated the paradox, but it seems clear it depends on assuming space is infinitely divisible. So the resolution MUST be that space is discrete even though our most sensitive measurements to date have not detected it. LC can speak to this. And the problem has nothing to do with whether the word 'infinite" enters the analysis. One can do calculus without ever using that word to describe limits, etc. Great! So now I know the resolution of Zeno's paradox, and the physical fact that space must be discrete! Gotta love it. AG* > > -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
