Wikipedia:Mediation Cabal/Cases/2009-08-09/Zeno's Paradoxes

Where is the dispute?
Zeno's Paradoxes and Talk:Zeno's_paradoxes

Who is involved?
User:Steaphen User:JimWae

What is the dispute?
The generally accepted mathematical solutions (specifically infinite-series solutions) to Zeno's Paradoxes, based on the assumption of continuity (of physical movement) are in conflict with the evidence of quantum physics, which reveals that movement is not fundamentally continuous.

Accordingly, the main article Zeno's Paradoxes contains many errors. I have edited the content to more correctly explain how such mathematical treatments, while useful to engineers, are not technically correct when considered in detail.

However, such edits have been deleted by those who argue that the theory (relating to physical movement of things, such as runners, hares and arrows) need not account for the actual, experimental, physical evidence (of the finer movement of physical things at quantum scales).

As a result, the main article misinforms the reader.

What would you like to change about this?
Sections rewritten, highlighting the inability of applying infinite-series solutions to Zeno's Paradoxes.

How do you think we can help?
I have presented arguments why the existing content is in error. I have presented a simple thought-experiment to show that either quantum theory is incorrect, or the infinite-series solutions are incorrect. If the main article is to maintain credibility, it would need to explain the inapplicability of infinite-series solutions.

Adjudication should confirm the inapplicability of infinite-series solutions, thus alerting the reader that the Paradoxes remain profound reflections of the deeper nature of reality, and that simple geometric, mechanistic world-views do not fit, explain or "solve" the paradox of everyday physical movement.Steaphen (talk) 03:25, 11 August 2009 (UTC)

Mediator notes
Picked up the case. Someone put it as open without entering their name! Xavexgoem (talk) 22:05, 27 October 2009 (UTC)

Discussion

 * In answer to Blippy's question on Talk:Zeno's_paradoxes, the issue is one of undue weight, unsupported assumptions, and clear errors (based on simple analysis (see Proof 1)).

Sme examples:


 * In the lead, main section --


 * "Zeno's paradoxes were a major problem ...". "were a problem" presupposes they aren't now.


 * "Many philosophers still hesitate ..." I don't hesitate at all. I actually disprove they have been solved. Specifically:


 * Proof 1: In simplistic terms, the de Broglie wavelength of an object is :λ = h / p (where p = momentum) [NB. The quantum state of a large body would not be so simplly defined]. The infinitesimal precision of the object's position (as required by infinite-series solutions) requires that λ approaches zero (since the de Broglie wavelength of the object indicates the range of possible positions and momentums of the object. Ignoring of course the constraints imposed by the Uncertainty principle). But as λ approaches zero (to ensure a short sharp pulse with infinite precision), p (momentum = mass x velocity) approaches infinity. Despite the fact that the calculated wavelength for a runner, tortoise or arrow is unnoticeably small (short), it is still some finite wave-length. Thus, infinite-series or simple algebra is most definitely not able to be used to calculate precisely where and when Achilles will overtake the tortoise (even in theory). Infinite series solutions most emphatically do not solve Zeno's Paradoxes.


 * in the section "The paradoxes of Motion" --


 * "because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise." ...this is an unsuspported assuption. Quantum theory says "movement is not fundamentally continuous". If Zeno assumed there were infinite points, then there should be specific mention of that, while also explaining the assumptive basis of that statement.


 * "Of course simple experience say ...", simple experience while watching a motion-picture film is that movement is continuous, but detailed observationv(e.g. by examining the film) shows that is an illusion.


 * In the section "Proposed Solutions" --


 * "These methods allow construction of solutions stating that under suitable conditions (i.e. the distances are progressively decreasing), the travel time is finite (bounded by a fixed upper bound)." This is clearly incorrect, if we allow Proof 1. In any event, the case has been not been confirmed or proven sufficient to assert that "These methods allow construction of solutions."


 * "Using ordinary mathematics we can arrive at a specific time when and place where Achilles would be able to catch up to the tortoise." This is unambiguously WRONG. See Proof 1. My work to correct this error was deleted on more than one occasion, hence the mediation request.


 * "While this solves the mathematics for this one paradox" - This is also incorrect. The mathematics of solving Zeno's Paradoxes has not been invented yet. See Proof 1. Even if you disallow Proof 1 as relevant, the assumptions still would need mention.

In the section "Status of the paradoxes today" --


 * "Mathematicians today tend to regard the paradoxes as resolved, but some philosophers disagree." The  and  has been added recently (not by me), but at least gets the article headed in the right direction.


 * "That is, while mathematics tells us where and when Achilles will overtake the Tortoise" Mathematics clearly DOES NOT tell us where and when Achilles will overtake the tortoise" See Proof 1. In the very least (ignoring Proof 1) the assumptive basis, and that the infinite series solutions do not meld with quantum theory has to be mentioned, if the article is to be credible.


 * "According to the uncertainty principle those distances are so small that taking a measurement would be pointless" This statement implies the error is with quantum theory, and that it is "poiintless" to attempt to use quantum theory, or to even rely upon it. It is also incorrect, technically speaking, for reasons provided in Proof 1.


 * "Infinite processes remained theoretically troublesome in mathematics until the early 20th century" implies they still aren't for physical processes. Instead it should read "infinite series", and that such theories are incapable of solving Zeno's Paradoxes.


 * "argues rigorous formulation of logic and calculus has resolved theoretical problems involving infinite processes, including Zeno's" is again, clearly incorrect, for the foregoing reasons (See Proof 1).Steaphen (talk) 08:13, 16 August 2009 (UTC)

Comment I think you are conflating thought experiments with real world situations. Zeno's Paradox is itself purely a thought experiment. It assumes in the first place that you can define the location of both Achillies and the tortoise at any and all times in the experiment with infinite precision. This patently cannot be done in any real world situation, even ignoring uncertainty and quantum effects. For example, how do we define Achille's position? Do we use his centre of gravity? Where is that? Plus it moves as Achilles moves his body, breathes in and out, sweats out fluid and otherwise experiences dynamic changes from moment to moment, like any living thing. No, we cannot do the most basic thing required to consider the paradox as a real world experiment (locate the protagonists) so other considerations about real world behaviours such as quantum effects and so on are entirely irrelevant. As a thought experiment, Zeno's Paradox lends itself completely and appropriately to mathematical analysis and so the use of infinte series to solve the problem is appropriate. - Nick Thorne  talk  00:51, 21 September 2009 (UTC)


 * Your response, and I give you credit for using your (presumed) real name, is highly disingenuous, to say the least. On one hand you say, we cannot define Achilles' (or modern day runner's) location in the real world, yet on the other that we can justifiably use mathematics to account for such movement in the real world.


 * Upon what basis do you argue that you may apply the magic of mathematics, any more than you could apply the divination of angels on pinheads? What is the actual verification that your theory accounts for the facts?


 * Your opinions do not serve this mediation. I'll get around to formal mediation in due course. Please save any further comments that you may have for another forum. They are not appropriate hereSteaphen (talk) 17:16, 27 September 2009 (UTC)


 * And your response, sir, shows a lack of reading comprehension skills. I said nothing about applying mathematics to the real world situation, I said that Zeno's Paradow is a thought experiment and so lends itself to mathematical analysis.  For what it is worth, in the real world the best we ever have is (close) approximation.  The real world is not an idealised state and to ask for absolute precision and accuracy - such as exists in mathematical models - is to fundamentally misunderstand the nature of both reality and mathematics.  BTW, mathematics is not magic.  Frankly you entire case here seems to be an example of tilting at windmills and POV pushing and I reiterate the fact that you continue to confuse the real world with the idealised world of mathematics.  Your problem not mine.  Finally, you are not entitled to tell any editor not to edit any page on Wikipedia or to engage in any discussion.  It is one of the fundamentals of this place that anyone is enttled to edit anything.  You do not own this page or this discussion. -  Nick Thorne  talk  22:25, 27 September 2009 (UTC)


 * Nick, you may be correct, in that I lack reading comprehension skills, and understanding of the 'real world'. Be that as it may, this mediation was initiated in response to many comments similar to yours over on the discussion page -- I don't recognise anything new in what you have offered, that has not been covered before. As stated above, I said your opinions do not serve this mediation. They are not offering solutions to the issues I've raised, and on that basis would best be posted on the discussion page.


 * This is not about "ownership" but about courtesy to those readers seeking information on how mediation has progressed concerning the issues raised above. Simply repeating many of the arguments or style of responses posted on the discussion page is inappropriate to the intent (or at least my intent) of this mediation which names myself and JimWae as being the parties involved. If you are not a mediator, what is your purpose here? Is that purpose in accord with Wikipedia rules for resolution of mediations?Steaphen (talk) 23:39, 28 September 2009 (UTC)


 * You wrote above:
 * Adjudication should confirm the inapplicability of infinite-series solutions, thus alerting the reader that the Paradoxes remain profound reflections of the deeper nature of reality, and that simple geometric, mechanistic world-views do not fit, explain or "solve" the paradox of everyday physical movement.
 * this looks like you have assumed that your position is the only tenable one and that your initial position will therefor be the resultion of the mediation. This does not look like a good faith request for mediation at all, mediation is not proving you are right, it is about coming to an amicable agreement acceptable by both parties.  You do not seem to be trying to do this, rather it seems to me that you are attempting to use this forum to justify your position and silence your opposition.  You admit that many other people have been saying similar things to you as I have - has it not crossed your mind that this may be because your position is actually incorrect?  Perhaps it is time for you to drop the stick.  As for courtesy, you have filled this mediation request with multiple restatements of basically one idea, that the real world is not continuous.  This is hardly courteous to those who might wish to come here to help out.  If you simply stated your thesis once, clearly and concisely, you might get a better hearing.  Instead you provide us with a wall of words which looks very much like the efforts of someone trying to make their argument appear more impressive by sheer size.  This does not fool anyone.  Further, on the issue of my posting here, I might point out that this section is titled "Discussion", it is entirely appropriate for any editor with whatever level of interest in the subject to post here.  You do not get to choose who posts here and you do not get to decide beforehand how the mediation will work.  For what it is worth, I do not think you are likely to get a mediated resultion to your dispute for the simple reason that you do not seem to be prepared to accept anything less than your starting position as the resolution. -  Nick Thorne  talk  00:10, 29 September 2009 (UTC)


 * I have (yes, repeatedly) asked some basic questions of the assumptions made by others. If that is my pushing POV, then it would seem I have not interpreted the process of "scientific method" correctly. As for many others saying the same thing, I would expect that at any decent heretic-burning or witch-hanging spectacle in the past there would have been many saying the same sorts of things (as to their guilt). The opinion of the crowd does not particularly interest me. In this instance I have in effect asked this question (of the crowd): "If the theories espoused for solving Zeno's Paradoxes are based on the assumption of continuity of movement (which stands in contrast to the experimental evidence of quantum physics) then what is the justification for that assumption?"


 * If seeking mediation on that basis (of asking questions of the crowd) dooms this mediation, then perhaps as Giordano and Galileo et al. might have concurred, so be it. Steaphen (talk) 03:11, 29 September 2009 (UTC)

Alright, back to square 1
I'm a bit confused by this discussion. Can the parties please add a brief summary of the problem, as they see it? Thanks. Xavexgoem (talk) 22:04, 27 October 2009 (UTC)


 * Xavexgoem you're a bit late to the party. Formal mediation ( Requests_for_mediation/Zeno's_paradoxes ) has been initiated, due to the poor quality of the previous informal mediation (carried out on the talk page, by "informal mediator" Blippy). Steaphen (talk) 09:02, 10 November 2009 (UTC)
 * Sorry to hear that. Well, he probably won't return. Xavexgoem (talk) 09:15, 10 November 2009 (UTC)