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 9th September 2021, 07:37 PM #161 HansMustermann Penultimate Amazing     Join Date: Mar 2009 Posts: 19,189 Originally Posted by Robin What's the problem. Well the problem is that infinity doesn't finish. And again, the problem is that you just ignore what's being told to you earlier in the thread, and continue just repeating the same nonsense anyway. Because you were already explicitly told earlier in the thread that you're confusing movement with computation. That infinite sum only needs an infinite number of steps to compute. It doesn't require anything even remotely infinite for the object to pass through all those points. The arrow just moves between those points, it doesn't compute the sum of a series, or really anything else. And even ending up computing the series is only an issue because you arbitrarily picked that model. As I keep telling you, if your model prevents you from solving a problem, just pick a different model. __________________ Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? Last edited by HansMustermann; 9th September 2021 at 07:40 PM.
 9th September 2021, 07:39 PM #162 Meadmaker Penultimate Amazing     Join Date: Apr 2004 Posts: 26,743 [quote=Robin;13595272] Originally Posted by Meadmaker Well, then, he had better use an infinite number of steps. What's the problem. Well the problem is that infinity doesn't finish. If you take an infinite number of steps then finish that infinity, what was your last step? Basically there was none because infinitely many steps don't have a last step. So you have then contradicted the definition of "continuous" and the argument succeeds. Every time you perform an integral, you are summing up an infinite number of steps. And back in Real Analysis class, we prove a whole lot of things about infite series, and integrals, and continuous functions. I got an A in the class. It was a long time ago, but I don't see any contradictions involved in not having a last step. __________________ Proud of every silver medal I've ever received.
 9th September 2021, 07:41 PM #163 Robin Penultimate Amazing   Join Date: Apr 2004 Posts: 13,219 Originally Posted by HansMustermann That was already told to you in the other thread by both me and Ziggurat: that's not what QM says. ALL that the Planck unit was supposed to be is a limit on the accuracy you can measure with, NOT any kind of proof that space is quantized. Well you and Ziggurat were wrong then, weren't you? It is built into QM in so many ways. Lose it and break QM. In any case a fundamentally unmeasureable area of space would break the definition of a continuum which is supposed to be infinitely divisible. Quote: In fact, as I told you in the other thread too, there's a fundamental problem with thinking that space is neatly on integer coordinates, because you can't square that even with SR. Just out of interest, who was it that said that space is neatly on integer coordinates? Some friend of yours? Also ... why are you telling me about it? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 9th September 2021, 07:42 PM #164 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 Originally Posted by Robin So the best solution anyone has found for it in 2,500 years and it is, as you say, using a convergent series for what it is not for. And it failed to solve the paradox. And therefore Zeno was wrong? Something is wrong with that. Only your analysis. Convergent series isn't a solution to Zeno's paradox. It's a more rigorous and complete mathematical description of what he was trying to say. Convergent series was the wrong tool for the job when he was trying to invent it, and it's the wrong tool for the job today. The only thing that's changed in the past 2,500 years is that we've vastly improved the usefulness of the tool for other jobs. __________________ There is no Antimemetics Division.
 9th September 2021, 07:42 PM #165 Robin Penultimate Amazing   Join Date: Apr 2004 Posts: 13,219 [quote=Meadmaker;13595280] Originally Posted by Robin Every time you perform an integral, you are summing up an infinite number of steps. And back in Real Analysis class, we prove a whole lot of things about infite series, and integrals, and continuous functions. I got an A in the class. It was a long time ago, but I don't see any contradictions involved in not having a last step. But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
 9th September 2021, 07:45 PM #166 Meadmaker Penultimate Amazing     Join Date: Apr 2004 Posts: 26,743 [quote=Robin;13595285] Originally Posted by Meadmaker But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion. Well, I certainly don't think modelling motion as an infinite number of steps is a very useful model, but if you did it that way, it would still work. __________________ Proud of every silver medal I've ever received.
 9th September 2021, 07:57 PM #167 HansMustermann Penultimate Amazing     Join Date: Mar 2009 Posts: 19,189 Originally Posted by Robin Well you and Ziggurat were wrong then, weren't you? Nope. It's still just you not even trying to understand. You just postulate that whoever disagrees with your bare postulates must be wrong. Well, you know, "show, don't tell": Originally Posted by Robin It is built into QM in so many ways. Lose it and break QM. List one way in which space being quantized is built into QM, and where losing quantization of space would break QM. Originally Posted by Robin In any case a fundamentally unmeasureable area of space would break the definition of a continuum which is supposed to be infinitely divisible. Why? Your ability to measure something doesn't really mean anything else than just that: ability to measure it. I mean, if I only have a yardstick, I can't measure the 7nm gates on my Ryzen CPU, but that doesn't mean that those sizes don't exist. In QM case, we just have a fundamental limit in how small a yardstick we can use, that's all. (Well, that and other strange phenomena might happen at that scale, but that has nothing to do with whether the space is divisible or not.) Originally Posted by Robin Just out of interest, who was it that said that space is neatly on integer coordinates? Some friend of yours? Also ... why are you telling me about it? So you don't even understand what it means when you say space is quantized, but just use that word anyway? Because that's all you've told me in the paragraph quoted above. But yeah, that's been your underlying problem in both threads: the whole attitude of why are people telling you the ways in which you're wrong __________________ Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? Last edited by HansMustermann; 9th September 2021 at 08:03 PM.
 9th September 2021, 08:02 PM #168 HansMustermann Penultimate Amazing     Join Date: Mar 2009 Posts: 19,189 Besides, the more fundamental problem is that you're making a hash of different things, ad hoc. Whether or not QM even exists, has nothing to do with Zeno's problem. It's just a random dodge you pulled out of the rear at some point. Try to actually define the problem you're trying to solve and stick to that. __________________ Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand?
 9th September 2021, 08:20 PM #169 xjx388 Moderator Moderator     Join Date: Nov 2010 Posts: 10,062 Now I’m not a math or physics guy, but I know that I get from my car door to my front door. I guess I could walk half way there, then half the rest of the distance, then half of the rest of the distance, etc, forever, but what I’d physically be doing is lowering my rate of motion -slowing down. I guess I could slow down enough so that I never actually reach my front door. This would be stupid. What I actually do is keep my rate of motion relatively constant so that I actually reach my front door. I hope this helps. __________________ Hello.
 9th September 2021, 08:52 PM #170 Robin Penultimate Amazing   Join Date: Apr 2004 Posts: 13,219 OK, look at it this way. Suppose I have defined those points just above and I have some sort of a marker for where they are. Now I follow my point object to the first and it passes it and the second. But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same. OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last. Now what I am doing is passing a set of points that will look the same but it will never end. How do I get past the last one? The object is going the same speed but I am slowing down my perception of time __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 9th September 2021 at 08:58 PM.
 9th September 2021, 08:57 PM #171 HansMustermann Penultimate Amazing     Join Date: Mar 2009 Posts: 19,189 Which is really the same issue. You just arbitrarily redefined the problem into "if you infinitely slow down time, you'll need infinite time to watch it." Well, sure, but that's not very deep or enlightening. Actually let me be even more specific: if the time you need to watch each segment is constant -- let's say 1s for simplicity -- then all you have as seconds is the number of points you've been through so far. That's all you're doing: you've turned your watch into counting members of an infinite set. To go through an infinite series that way, duh, you go through an infinite number of such steps. So basically all you're saying is: infinite set has infinite members. And sure, it does, but it's like saying that water is wet. It's not exactly much of an epiphany. __________________ Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? Last edited by HansMustermann; 9th September 2021 at 09:04 PM.
 9th September 2021, 09:00 PM #172 llwyd Muse   Join Date: Sep 2010 Posts: 830 Anyway, the interesting thing is that time in modern physics is a way less self-evident phenomenon than it is in our everyday experience, and this makes spacetime also way less self-evident. Of course, much of this is due also to the fact that our everyday language is Newtonian and Cartesian, and absurdly clumsy in trying to describe the universe as it really is.
 10th September 2021, 05:04 AM #174 bruto Penultimate Amazing     Join Date: Jun 2005 Location: Way way north of Diddy Wah Diddy Posts: 29,342 Originally Posted by Robin The argument does not suggest at all that the object is travelling by division. That is nowhere in the premises. So the word does not occur. If you say that an object cannot reach its destination because the process of slicing its progress into halves does not allow it, what else are you talking about? __________________ I love this world, but not for its answers. (Mary Oliver) Quand il dit "cuic" le moineau croit tout dire. (When he's tweeted the sparrow thinks he's said it all. (Jules Renard)
 10th September 2021, 05:18 AM #175 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,946 Originally Posted by smartcooky Is all this anything like the old schoolboy story of the insect flying along the railway track and hitting a 100mph locomotive coming the other way? No. That's a legitimate math problem, and has well-defined answers when the parameters are fully specified. Robin has set out to demonstrate something quite different: That an infinite sequence of confused intermediate states will never arrive at a sensible conclusion. Which is not at all what Zeno set out to demonstrate. Where Zeno failed, however, Robin has succeeded.
 10th September 2021, 05:34 AM #176 Steve Philosopher     Join Date: May 2005 Location: Sydney Nova Scotia Posts: 9,814 Originally Posted by xjx388 Now I’m not a math or physics guy, but I know that I get from my car door to my front door. I guess I could walk half way there, then half the rest of the distance, then half of the rest of the distance, etc, forever, but what I’d physically be doing is lowering my rate of motion -slowing down. I guess I could slow down enough so that I never actually reach my front door. This would be stupid. What I actually do is keep my rate of motion relatively constant so that I actually reach my front door. I hope this helps. Nope. Didn't help. Robin still 'thinks' that nothing ever gets where it is going. Makes me wonder how his fingers ever reach the keys on his keyboard. Maybe they don't! (now there is a paradox). __________________ Caption from and old New Yorker cartoon - Why am I shouting? Because I'm wrong!"
 10th September 2021, 05:34 AM #177 Meadmaker Penultimate Amazing     Join Date: Apr 2004 Posts: 26,743 Originally Posted by Robin OK, look at it this way. Suppose I have defined those points just above and I have some sort of a marker for where they are. Now I follow my point object to the first and it passes it and the second. But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same. OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last. Now what I am doing is passing a set of points that will look the same but it will never end. How do I get past the last one? The object is going the same speed but I am slowing down my perception of time It will take infinite perceived time to watch. You will never get to the end. __________________ Proud of every silver medal I've ever received.
 10th September 2021, 08:10 AM #178 JoeMorgue Self Employed Remittance Man     Join Date: Nov 2009 Location: Florida Posts: 34,787 Okay but if Zeno is the one replacing the parts on the Ship of Theseus.... __________________ "When enough people make false promises, words stop meaning anything. Then there are no more answers, only better and better lies." - Jon Snow "Every lie we tell incurs a debt to the truth. Sooner or later, that debt is paid." - Valery Legasov
 10th September 2021, 09:03 AM #179 Myriad The Clarity Is Devastating     Join Date: Nov 2006 Location: Betwixt Posts: 18,234 Originally Posted by Robin Um yes, pretty much what Zeno said. That there is no difference between an arrow in flight and a stationary arrow. Movement is the consequence of comparing two positions. It took centuries before the rest of humanity woke up to the fact that movement was not some property of the thing moving. But, yeah, silly old Zeno pointing out that there was no such thing as movement and being right about it. I'm pretty sure even the ancients understood that movement involved a change of position. For instance, when conducting one-stade (about 200 yard sprint) foot races, do you think they figured out that the finish line had to be located at some particular distance from the starting line, or were they stumbling around in confusion on that point? There being different ways to model movement isn't evidence that movement doesn't exist. Rather the contrary. __________________ A zømbie once bit my sister...
 10th September 2021, 12:43 PM #180 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 I keep having trouble finding this thread. I just realized it's in R&P, and that I don't actually care so much anymore. Definitely a case of "okay, so motion doesn't happen. Now what?" for me. __________________ There is no Antimemetics Division.
 10th September 2021, 01:03 PM #181 xjx388 Moderator Moderator     Join Date: Nov 2010 Posts: 10,062 Originally Posted by Robin OK, look at it this way. Suppose I have defined those points just above and I have some sort of a marker for where they are. Now I follow my point object to the first and it passes it and the second. But I have a good infinite zoom lens and whenever the object passes points I start zooming in so as to make the distances between seem the same and then I employ my slomo device to slow it down so that the time interval seems the same. OK, I keep on like this, zooming in the lens and turning up the slomo device so that each moment seems the same as the last. Now what I am doing is passing a set of points that will look the same but it will never end. How do I get past the last one? The object is going the same speed but I am slowing down my perception of time The object still got where it was going. You are just slowing down time. Much like I could slow down my speed and never reach my front door. You get past the last one by zooming out and turning off your slow mo doohickey. __________________ Hello.
 10th September 2021, 01:10 PM #182 JoeMorgue Self Employed Remittance Man     Join Date: Nov 2009 Location: Florida Posts: 34,787 Basically Robin has a bad understanding of a Supertask, a purely mathematical (as in doesn't actually work in reality) concept concerning an infinite number of events happening in a finite amount of time. __________________ "When enough people make false promises, words stop meaning anything. Then there are no more answers, only better and better lies." - Jon Snow "Every lie we tell incurs a debt to the truth. Sooner or later, that debt is paid." - Valery Legasov
 10th September 2021, 01:23 PM #183 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 My favorite part of this thread is when Robin switched from "Zeno is right, and convergent sums prove motion doesn't happen!" to "I've been saying all along that Zeno was wrong and convergent sums are the wrong tool for the job!" __________________ There is no Antimemetics Division.
 10th September 2021, 01:29 PM #184 LarryS Graduate Poster   Join Date: Oct 2014 Posts: 1,312 Originally Posted by Robin But the sum of an infinite number of steps in mathematics is not the problem, as I said. He is referring to motion. Well is there is no absolute space-time (and space-time may be doomed: https://www.cornell.edu/video/nima-a...time-is-doomed then there can be no motion as there is no place to move to or from
 10th September 2021, 01:31 PM #185 Dave Rogers Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles     Join Date: Jan 2007 Location: Cair Paravel, according to XKCD Posts: 32,744 Originally Posted by theprestige Definitely a case of "okay, so motion doesn't happen. Now what?" Since motion is impossible, nothing. Dave __________________ There is truth and there are lies. - President Joseph R. Biden, January 20th, 2021
 10th September 2021, 02:53 PM #186 Hevneren Critical Thinker   Join Date: Jul 2007 Posts: 308 I sort of wish doronshadmi would visit this thread now, to help us sort this out. He has thought a lot about Zeno’s paradox.
 10th September 2021, 02:57 PM #187 bruto Penultimate Amazing     Join Date: Jun 2005 Location: Way way north of Diddy Wah Diddy Posts: 29,342 The answer to the paradox exists but it cannot be known. You can't respond to the problem because every time you get halfway to the end you have to halve your speed and you'll never finish before the world ends. Actually if you think about it forget Zeno. Gorgias was right! __________________ I love this world, but not for its answers. (Mary Oliver) Quand il dit "cuic" le moineau croit tout dire. (When he's tweeted the sparrow thinks he's said it all. (Jules Renard)
 10th September 2021, 03:26 PM #188 llwyd Muse   Join Date: Sep 2010 Posts: 830 Well, Zeno was totally amazing for his age (as far as we can see from the Platonist tradition), and this ridicule here is rather unseemly. It is easy for us to belittle after 2500 years of progress, but we are standing on the shoulders of generations of giants. One of my own insights from this forum is that the run of the mill scientists tend to be rather like engineers: not very insightful or imaginative and possessing a rather painfully facile sense of humour...
 10th September 2021, 03:55 PM #189 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 I don't think any of us here have a problem with Zeno as such. I certainly don't. I don't know if he was joking or serious. I assume he wasn't an idiot, though. __________________ There is no Antimemetics Division.
 10th September 2021, 03:57 PM #190 Steve Philosopher     Join Date: May 2005 Location: Sydney Nova Scotia Posts: 9,814 Originally Posted by llwyd Well, Zeno was totally amazing for his age (as far as we can see from the Platonist tradition), and this ridicule here is rather unseemly. It is easy for us to belittle after 2500 years of progress, but we are standing on the shoulders of generations of giants. One of my own insights from this forum is that the run of the mill scientists tend to be rather like engineers: not very insightful or imaginative and possessing a rather painfully facile sense of humour... If you read more closely I think you might discover that ridicule and belittlement directed at Zeno is non-existent here. And exactly how many "run of the mill scientists" do you imagine are participating in this thread? __________________ Caption from and old New Yorker cartoon - Why am I shouting? Because I'm wrong!"
 10th September 2021, 04:03 PM #191 LarryS Graduate Poster   Join Date: Oct 2014 Posts: 1,312 Originally Posted by Steve And exactly how many "run of the mill scientists" do you imagine are participating in this thread? I think it's reasonable to believe that no successful and inciteful scientist, philosopher or religious person would participate in threads such as in this forum.
 10th September 2021, 04:15 PM #192 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 Jay Windley is pretty active here. __________________ There is no Antimemetics Division.
 10th September 2021, 04:29 PM #193 Steve Philosopher     Join Date: May 2005 Location: Sydney Nova Scotia Posts: 9,814 Originally Posted by LarryS I think it's reasonable to believe that no successful and inciteful scientist, philosopher or religious person would participate in threads such as in this forum. Pretty hard to find accurate spellers here too, I'll bet. __________________ Caption from and old New Yorker cartoon - Why am I shouting? Because I'm wrong!"
 10th September 2021, 04:38 PM #194 theprestige Penultimate Amazing   Join Date: Aug 2007 Location: The Antimemetics Division Posts: 53,572 And W D Clinger has been active in this very thread, as well as many others in the Science section. __________________ There is no Antimemetics Division.
 10th September 2021, 05:59 PM #195 HansMustermann Penultimate Amazing     Join Date: Mar 2009 Posts: 19,189 Originally Posted by theprestige My favorite part of this thread is when Robin switched from "Zeno is right, and convergent sums prove motion doesn't happen!" to "I've been saying all along that Zeno was wrong and convergent sums are the wrong tool for the job!" Which was already a hard U-turn from "Zeno was meaning something completely different" (and completely unsupportable based on any sources) in the other thread. I was kinda suspecting that this thread was some kind of trolling, tbh, especially when it took only a bit over 1 page to turn into spam-trolling and taunting. Not sure what got into Robin this time, tbh. I can't say I agreed with all their ideas over time (and sometimes I was wrong,) but you could hold a rational conversation with them. THIS is... rather unexpected. __________________ Which part of "Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn" don't you understand? Last edited by HansMustermann; 10th September 2021 at 06:11 PM.
 11th September 2021, 06:19 AM #197 W.D.Clinger Illuminator     Join Date: Oct 2009 Posts: 3,946 Originally Posted by Robin 1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed 2. Every first half of a part of a continuous path is a part of a continuous path 3. No part of a continuous path can be travelled. (1,2) 4. But we perceive travel through continuous paths Conclusion: Our perception of motion must differ from the underlying reality OK, put just almost exactly as Zeno put the first dichotomy argument. Again, I am just interested in exactly what is wrong with the argument. It seems to me that the premises are true and that 3 follows from 1 and 2 and that the conclusion is true and forms a satisfying resolution to the paradox. Your statement 3 does not actually follow from your statements 1 and 2.
 11th September 2021, 06:38 AM #199 Meadmaker Penultimate Amazing     Join Date: Apr 2004 Posts: 26,743 Originally Posted by Robin 1. No part of any continuous path can be fully travelled if the first half of that part has not first been completed 2. Every first half of a part of a continuous path is a part of a continuous path 3. No part of a continuous path can be travelled. (1,2) 4. But we perceive travel through continuous paths Conclusion: Our perception of motion must differ from the underlying reality OK, put just almost exactly as Zeno put the first dichotomy argument. Again, I am just interested in exactly what is wrong with the argument. It seems to me that the premises are true and that 3 follows from 1 and 2 and that the conclusion is true and forms a satisfying resolution to the paradox. There's the problem right there. 3 doesn't follow from 1 and 2. Quote: And the sum of a convergent sum really isn't something that can be calculated in time, So? And anyway, it can be calculated in time, algebraically. It's just that each term in the infinite sequence of partial sums can't be calculated in time. I can easily calculate the sum of a geometric series, quite rapidly. __________________ Proud of every silver medal I've ever received.
 11th September 2021, 06:43 AM #200 bruto Penultimate Amazing     Join Date: Jun 2005 Location: Way way north of Diddy Wah Diddy Posts: 29,342 I know I'm just being simple and all but I really don't understand why this argument has any merit. Of course if we count in a certain way, we get results in a certain way, but the paradox seems to require that we proceed from one point to another by going half way with each step. We don't. Sure, we can't complete the journey until we've passed the halfway point, but there is no requirement that we stop at each halfway point to catch our breath or to take out our abaci and calculate our progress, and no real world requirement that we cannot simply jump past a halfway point. If we take relatively uniform steps (or if our arrow proceeds at a fairly consistent speed) then as the halfway point becomes smaller and smaller we simply step past it. Our speed does not diminish to half every time a new halfway point is reached. It flies past. The real world abounds with examples, and though we can no doubt credit Zeno the sophist with many things, including an understanding of mathematics and an appreciation of the complexity of the world, one might consider for a moment why the word "sophistry" has come to imply what it does. If you count progress in a certain way, it is true that you cannot count your way to the target. But why does that in any way imply anything except that your method of counting is not appropriate? My previous somewhat flippant comment might be thought serious too. If you believe Zeno was right, I think in the end you had better believe Gorgias was right too. __________________ I love this world, but not for its answers. (Mary Oliver) Quand il dit "cuic" le moineau croit tout dire. (When he's tweeted the sparrow thinks he's said it all. (Jules Renard)

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