Talk:Zeno's paradoxes
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Removed from the main page:
- These paradoxes can also be explained by quantum physics, since certain particles can only occupy discrete positions and can "move instantaneously" from one point to another without crossing the space between. (this is known as "tunneling" and is related to the "probability wave" nature of particles at the subatomic level.)
Sorry, I don't think this does anything to resolve the paradox. In quantum mechanics, position is a continuous variable. If the person who added this thinks it is correct, please explain further.CYD
You are the quantum physics guy, not me, and I didn't even write the stuff removed but:
Zeno's paradox is based on the given that to get from point a to point b, you have to pass through all points in between. Since position is continuous, thats impossible. If quantum physics says (and I have no idea if it does truly or not) that a particle can travel from point a to b without traversing the points in between, then a particle is not going to be bound by Zeno's paradox. That said, someone would have to make the case that ALL motion by particles is achieved by tunneling. Is this the case? Again, I'm not a physics person so I don't know, but I suspect thats never been proven or demonstrated. Again, since position is continuous, this could never be observed, so it would have to be shown theoretically at best.
Copies of the newly released papers by Peter Lynds talking about this subject can be found at the following locations: at http://cdsweb.cern.ch/search.py?recid=624701 and "Zeno's Paradoxes: A Timely Solution" is available at http://philsci-archive.pitt.edu/archive/00001197/
- A brusque dismissal of Lynds's approach by me can be found at http://sl4.org/archive/0308/7012.html -- mitch, not yet a user 24 Jan 2004
Brusque is right. Going by your dismissal, you might as well have just said "I don't like it because I don't like it." Better still, "I don't like because I don't understand it".
Why the page move (from Zeno's paradoxes)? I mean, there's more than one of them... --Camembert
- I was thinking of wikipedia:naming conventions (pluralisation), but re-reading that it's not as simple as I had thought! Move it back if you like. Martin 20:32, 23 Sep 2003 (UTC)
- I do like, and I shall move :) --Camembert
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Re: Peter Lynds
To the anonymous editor (User:81.80.88.113 etc.):
Please read Wikipedia:What Wikipedia is not and Wikipedia:No original research. Then please list on this page, which authoritative texts and/or prominent scientist/philosphers lists Peter Lynds as having solved Zeno's paradoxes. You might also want to mention, why they did not think it already was solved by calculus.
When you have done so, read Wikipedia:Neutral point of view. Then you can add to the article that these people believe that the paradoxes needed solving, and how Peter Lynds managed to do it.
Rasmus Faber 13:16, 28 Jan 2004 (UTC)
A few I quickly found
"Author's work resembles Einstein's 1905 special theory of relativity", said a referee of the paper, while Andrei Khrennikov, Prof. of Applied Mathematics at Växjö University in Sweden and Director of ICMM, said, "I find this paper very interesting and important to clarify some fundamental aspects of classical and quantum physical formalisms. I think that the author of the paper did a very important investigation of the role of continuity of time in the standard physical models of dynamical processes." He then invited Lynds to take part in an international conference on the foundations of quantum theory in Sweden.
Another impressed with the work is Princeton physics great, and collaborator of both Albert Einstein and Richard Feynman, John Wheeler, who said he admired Lynds' "boldness", while noting that it had often been individuals Lynds' age that "had pushed the frontiers of physics forward in the past."
http://www.newscientist.com/opinion/opletters.jsp?id=ns24249 http://ciencia.astroseti.org/astrofisica/entrelynds.php http://www.space.com/scienceastronomy/time_theory_030806.html http://gauntlet.ucalgary.ca/story/6121 http://www.thescotsman.co.uk/international.cfm?id=827792003 http://www.dagbladet.no/kunnskap/2003/07/31/374849.html http://www.physics4u.gr/articles/2003/lynds.html http://perso.wanadoo.fr/marxiens/sciences/lynds.htm http://www2.uol.com.br/cienciahoje/chdia/n935.htm
Page entry already indicates what is wrong with the calculus solution (assumes determined position at each instant (and the existance of instants), so doesn't actually solve paradoxes and show how motion is possible) - it's just a mathematical trick to get rid of the infinity.
There are multitudes of scientists and philosophers who don't think the calculus approach provides a solution (obviously more so since Lynds work). Just have a look around the web, read a book on the paradoxes, or read the work of someone like Bertrand Russell.
- Repeatedly quoting Khrennikov out of context, do not exactly increase your credibility. He also said: "It's interesting but it's not great." Wheeler might have had the credibility needed, but he has not claimed to accept the conclusions of the paper, only that he "admired Lynds' boldness". (Note, however, Decumanus' objections on Talk:Peter Lynds).
- If you feel that the article incorrectly claims that calculus solves the paradoxes, you might want to add to the article why Russell questioned this solution. Something about Grünbaum and McLaughlin would probably also be appropriate. But do not add Peter Lynds.
- Rasmus Faber 08:39, 29 Jan 2004 (UTC)
You're mad
You're absolutely mad Rasmus. How could that khrennikov quote be out of context?! Lynds is right. Even if you disagree though, it should be included. It obviously deserves to be. What's your problem? personal attacks snipped
Politeness, Mr. Lynds, is always in order. — No-One Jones (talk) 13:32, 29 Jan 2004 (UTC)
- I apologize. It was not the Khrennikov quote that was out of context. It was the quote from the referee. You forgot to mention that the comparison to Einstein's paper was not about any particular brilliance or importance, but to defend the validity of the circular reasoning.
- Did you read Wikipedia:No original research? It explains Wikipedia's policy as to which theories deserves inclusion. Now please let me know which prominent people thinks Peter Lynds' research is important in the context of discussing Zeno's paradoxes. I don't want a listing of which popular science magazines have had articles about him. Nor do I want a listing of which scientists have similar theories. I want names and quotes from a few prominent scientists who say, that Peter Lynds' theory is an important new solution to Zeno's paradoxes.
- Rasmus Faber 13:53, 29 Jan 2004 (UTC)
What more do you want Rasmus? Lynds to firstly get a Nobel Prize? Khrennikof and the other referee made those comments about Lynds' paper.....it contains his solution to the paradoxes and much of the rest of the content is based upon the same reasoning and argument. The journal editor obviously also thought it important. Throw in general support for his work by the likes of Wheeler and Davies (and I'm sure many more), and his solution definately qualifies as "significant scientific minority".
As a side note, the referee who made the Einstein comparison obviously meant that the paper's arguments were still valid even if possibly circular.
Tortoise
This isnt a paradox, its simple. First you have to define the size of the tortoise. Next you have to decide when the distance between the tortoise and achilles is less than that size. Bensaccount 00:40, 14 Mar 2004 (UTC)
Dangerous minds
I found the associated work dangerously confident in its statements. As is correctly stated, Zeno based his paradoxes on the work of Parmenides. Reading 'Parmenides' by Plato, one is reminded that Zeno's examples were to show that Parmenides logic was true because if it was false, the universe as we know it is even crazier than if Parmenides is right. One should always bear in mind that mathematics is based on axioms and is subject to Godel's Incompleteness Theorem and is fraught with internal paradoxes and ambiguities, many of which are seriously close to the areas related to Zeno's paradoxes. My edit was minor, only intended to moderate the view that Zeno has been dealt with. Any quantum theoretical treatment (or use of infinities, limits etc) that purports to resolve Zeno's paradoxes, is founded in Parmenides 'World of Seeming' (his 'Way of falsehood') and so is no closer to resolving the foundations of the paradox at all. Lot's of people seem to miss this point. Zeno was not setting a mathematical problem, but a problem for the universe as we think it to be (eg quantum models and Hilbert's formalism). Centroyd 31 May 2004
This page needs a big edit
Rereading this page makes me nauseous. It is so full of people being certain about things that that are deeply flawed. Consider the Lynd's 'solution' that is put up as a solution to the paradox. I do not suggest that Lynd's is not right in limiting infinitessimals, but this is not a solution to the paradox - quite the opposite. If what I read on the page is representative of Lynd, then he is saying there are no infinitessimals, therefore there is no paradox. But Zeno would say 'So what? That is not my point.' As previously commented, a solution to Zeno needs to consider Parmenides in conjunction. In the meantime I think this article needs to be more balanced. Centroyd. 1st July 2004.
"The rock thrown towards a tree"? What is the source for this??
I've never heard of this paradox before. What is the source for it? I'm very familar with Aristotle's Physics and I don't find it there. Nor do I find it in Simplicius's commentary. I'd like to replace it with the "Dichotomy" paradox given by Aristotle. Any objections?
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Yes, I agree to replacing it - but Dichotomy is not very descriptive either, though it is the traditional heading. This is the sum of an infinite series of infinitesimals & the easiest to present arguments against - unless you are the subject walking towards the tree (or wall) & try to take just the first step.
The entire article needs to be laid out better. The arguments trying to overcome the paradoxes are presented before all the paradoxes are even presented -- and are not even clearly distinguished from them. --JimWae 05:17, 2004 Nov 17 (UTC)
Physical explanations afterthought
Just thinking after reading the section on physical explanations. "Lynds asserts that the correct resolution of the paradox lies in the realisation of the absence of an instant in time underlying a body's motion, and that regardless of how small the time interval, it is still always moving and its position constantly changing, so can never be determined at a time." First off, I think that sentence needs an edit. I'm not sure how to do it though. Also, isnt that precisely the fundamental calculus assumption? That regardless of how small the limit of time tends to, the velocity need not tend to zero, and can have a finite value. Thus even at a "still" moment, the arrow's position is changing at that finite rate. Or am I missing something? Ethan Hunt 00:40, 2 Sep 2004 (UTC)
Rival article
Someone just added Xeno's paradox. Might want to compare/merge. Ortolan88 18:33, 14 Nov 2004 (UTC)
- Now merged. Author of Xeno article can retrieve, merge content if they wish. -- Decumanus 18:37, 2004 Nov 14 (UTC)