tag:blogger.com,1999:blog-3457668362098152413.post8061806970050849875..comments2016-03-17T07:25:59.559-07:00Comments on Thoughts on Science and Pseudoscience: One Simple Counter to Zeno's Dichotomy ParadoxThe Other John Mchttp://www.blogger.com/profile/06648184479112487844noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3457668362098152413.post-46312181639556295332016-03-17T07:25:59.559-07:002016-03-17T07:25:59.559-07:00Really your post is very informative
http://awaren...Really your post is very informative<br />http://awarenesspost.blogspot.com<br />computer Awareness Post<br />Welcome To computer Awareness Post Here You Can Learn About Computer Studies...syed dureali Kazmihttp://www.blogger.com/profile/18370871857700642535noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-24015503147314708062014-11-25T14:26:59.170-08:002014-11-25T14:26:59.170-08:00Thanks for the thoughts Jimmy. Isn't there sti...Thanks for the thoughts Jimmy. Isn't there still a contradiction in the argument, in assuming that motion from 0 to 0.5 (or any distance) is possible but the whole trip from 0 to 1.0 is not?The Other John Mchttp://www.blogger.com/profile/06648184479112487844noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-3181601549075840792014-11-25T09:36:34.917-08:002014-11-25T09:36:34.917-08:00Zeno presents the argument as a reductio ad absurd...Zeno presents the argument as a reductio ad absurdum, so the form of the argument is to assume a hypothesis and prove that the hypothesis, when assumed to be true, leads to absurdity. So he can legitimately assume the premise, "motion is real," to prove that this hypothesis leads to a contradiction. You've got the proposed contradiction right (you cannot complete the infinite task), the contradiction encountered thus proving the hypothesis that "motion is real" is false. So he is allowed to assume the premise, to prove it leads to absurdity.<br /><br />Additional note - in the modern "refutations" of Zeno's paradoxes that use calculus or infinite sums, you still are not resolving Zeno's paradox. Just because the math works, doesn't mean you can complete an infinite task in the physical world. Simply acknowledging that modern math allows that the infinite sum equals 1 does not show you can cross an infinite number of physical spaces - completing an infinite task in physical space/time is not the same as summing an infinite series (which you also cannot actually "do" in real space/time). The dot-dot-dot hides the task, but doesn't complete it!Jimmy Allenhttp://www.blogger.com/profile/09231542592695193360noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-83062835110460469612014-08-15T00:23:48.249-07:002014-08-15T00:23:48.249-07:00Even after clarifying this there are still some in...Even after clarifying this there are still some interesting thought experiments left. If we are drawing a line from 0 to 1 in infinitely many steps within one second:<br /><br />time t = 0: drawing a line segment from 0 to 0.5 in 0.5 seconds<br />time t = 0.5: drawing a line segment from 0.5 to 0.75 in 0.25 seconds<br />time t = 0.75: drawing a line segment from 0.75 to 0.875 in 0.125 seconds<br />...<br /><br />At which point exactly can we lift the pen in order to finish the line?<br />netzweltlerhttp://www.blogger.com/profile/03615165470672352773noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-55917247181411880192014-08-13T12:10:57.241-07:002014-08-13T12:10:57.241-07:00Yes! That one is much more compelling. This one is...Yes! That one is much more compelling. This one is dismantled via more modern mathematical thinking than was available in Zeno's time: the infinite sum IS mathematically equivalent to the final value 1. An infinity of numbers exist within any finite magnitude.The Other John Mchttp://www.blogger.com/profile/06648184479112487844noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-58586060083900719162014-08-13T11:59:06.449-07:002014-08-13T11:59:06.449-07:00By the way, there is a way more compelling "m...By the way, there is a way more compelling "motion impossible" argument from Zeno.<br /><br />If you want to reach 1 you have to reach 0.5 before<br />If you want to reach 0.5 you have to reach 0.25 before<br />If you want to reach 0.25 you have to reach 0.125 before<br />...<br /><br />Since there is no first step you can take you cannot even start moving.netzweltlerhttp://www.blogger.com/profile/03615165470672352773noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-8779887546231084632014-08-12T22:19:36.401-07:002014-08-12T22:19:36.401-07:00Of course we can start with
time t = 0: moving fr...Of course we can start with<br /><br />time t = 0: moving from 0 to 1 in 1 second<br /><br />and there we go. We can use any finite number of steps to reach point 1 like<br /><br />time t = 0: moving from 0 to 0.5 in 0.5 seconds<br />time t = 0.5: moving from 0.5 to 1 in 0.5 seconds<br /><br />The process described in my previous post is also accomplished in a finite amount of time. At t = 1 we have done infinitely many steps, but none of these infinitely many steps is targeting point 1. Zeno's conclusion, that this means, motion is impossible, is arbitrary. My conclusion is, that<br /><br />time t = 0: moving from 0 to 0.5 in 0.5 seconds<br />time t = 0.5: moving from 0.5 to 0.75 in 0.25 seconds<br />time t = 0.75: moving from 0.75 to 0.875 in 0.125 seconds<br />...<br /><br />is not a complete description of what is really going on.<br />netzweltlerhttp://www.blogger.com/profile/03615165470672352773noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-72580609068645584962014-08-12T14:28:02.068-07:002014-08-12T14:28:02.068-07:00Right but my point was that if we can assume that ...Right but my point was that if we can assume that moving any distance is possible (half the distance) in a finite amount of time, then the paradox disappears under its own argumentThe Other John Mchttp://www.blogger.com/profile/06648184479112487844noreply@blogger.comtag:blogger.com,1999:blog-3457668362098152413.post-9947214051962229042014-08-10T02:08:00.725-07:002014-08-10T02:08:00.725-07:00The puzzling part is not that we cannot move (that...The puzzling part is not that we cannot move (that's a nonsensical conclusion). The puzzling part is that there is no last step. You are moving on the number line from zero to one like this:<br /><br />time t = 0: moving from 0 to 0.5 in 0.5 seconds<br />time t = 0.5: moving from 0.5 to 0.75 in 0.25 seconds<br />time t = 0.75: moving from 0.75 to 0.875 in 0.125 seconds<br />...<br />There is no step on the list above like<br /><br />time t = x: moving from x to 1 in ? seconds<br /><br />So, take all the infinitely many steps on this list, and you still don't cover point 1.Anonymousnoreply@blogger.com