> On 29 Oct 2018, at 19:55, [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!
Banishing the infinite from the ontology is a good idea, but it will kept playing an important role in the phenomenology, and in the meta-theories. > > 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/ > > <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? The original mathematical paradox has been solved. But physical version of it, in some theories, can be problematical. Bruno > > 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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
