On Monday, October 29, 2018 at 7:06:47 PM UTC, Philip Thrift wrote: > > > > On Monday, October 29, 2018 at 1:55:27 PM UTC-5, [email protected] > wrote: >> >> >> >> 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 <[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. >>> >>> *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* >> >>> >>> >> > Spacetime is a mystery, and it's discrete vs. continuous is perhaps an > oversimplification. > > There are other mathematical models theorists pursue (check arXiv), e.g. > fractal. >
*Whatever it is, it's not continuous. I think my analysis of Zeno's paradox is conclusive. Call the Nobel committee. AG * > > Scale relativity and fractal spacetime: theory and applications > Laurent Nottale > <https://arxiv.org/search/physics?searchtype=author&query=Nottale%2C+L> > https://arxiv.org/abs/0812.3857 > > - pt > -- 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.
