Talk:Proposed solutions to Zeno's paradoxes

Merge
No reason for this to be an independent article and if we push it back to the main article we'll get more readers & higher quality. Eusebeus (talk) 14:56, 19 November 2008 (UTC)

Comments
The treatment of the paradoxes here is an utter farce; why hasn't anyone cleaned this up? —Preceding unsigned comment added by 70.22.85.104 (talk) 01:36, 6 October 2008 (UTC)

The dichotomy solution answers the wrong question. It's not a matter of whether Homer can get to the bus but whether he can start to move, regardless of the way the original paradox was stated. You are making the assumption that he can begin to move in the former case but the paradox argues against the latter case equally.

Also, "Many mathematicians and engineers believe..." Disregarding for a moment that this is weasel worded and is uncited (like the other article on the paradoxes), why does it matter what mathematicians and engineers believe when this is clearly a physics problem? How does calculus alone tell us about the nature of space and time? —Preceding unsigned comment added by 207.245.46.103 (talk) 16:57, 20 June 2008 (UTC)


 * I think you explained exactly why these kinds of assertions are uncited. Many high school math teachers like to think that somehow the Greek didn't have an understanding of calculus and that they didn't realize that an infinite amount of terms can sum up to a finite amount, and use that to 'explain' the paradox. But, aside from this being completely implausible (if Zeno starts out by diving a finite distance between A and B into infinitely many intervals, one would think that he perfectly well realizes that those infinitely many intervals make up the original finite interval!)), they are completely missing the point, which is why this 'solution' never makes it into any kind of professional journal. The only places where something does appear in print about Zeno's paradoxes is in philosophy journals, and here it is generally recognized that calculus does indeed nothing to resolve the paradox. You're right, a solution to the paradox will have to be deeply metaphysical. —Preceding unsigned comment added by 128.113.99.141 (talk) 14:20, 23 June 2008 (UTC)


 * mathematics (High level mathmatics) are intrinsically bound up in physics. Go to college. Ask a physicist or a mathematician with a PHD and you will get an answer involving mathematical attempts to prove that infinite summations can occur. There are several. It might take some time. Of course... there's 'one in every department' who would fail to agree. But it's actually usually a lot smaller then one in every department. And it really is a problem of mathematics more so then physics. In physics the solution is "This works, and the behavior is most accurately modeled by this equation. QED no paradox." Unless you want to get into quantum crap, which requires a more then functional knowledge of set theory. See in physics we don't know or care how it actually works, we just want the most accurate model possible of it's behavior. In mathematics the solution requires one prove that it's possible to get infinitely small slices and to sum them infinitively, which is an axiom and therefore unprovable128.255.187.32 (talk) 15:18, 2 October 2008 (UTC)

Why is it "proposed" solutions? It's been solved. Here's one reference, at a highly reputable source: []. It doesn't appear in professional mathematics, physics, or engineering journals because it appears in basic mathematics / physics / engineering coursework, as in [] and also []. The deeply metaphysical part is admitting that the calculus is relevant, that time is continuous, that infinitely many moments of time are traversed in any finite interval, that the very phrase "next moment in time" is invalid. Endomorphic (talk) 13:29, 21 July 2008 (UTC)


 * Given from Mathworld: "The resolution of the paradox awaited calculus and the proof that infinite geometric series such as can converge, so that the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances."


 * Your reputable source gives a less than acceptable resolution of the paradox.


 * Quoting directly from Wesley C. Salmon, who compiled the best essays on the subject in a book titled "Zeno's Paradoxes" (you can find it on Google Book Search):
 * "It would be a mistake to suppose that Zeno's paradoxes are fully resolved if it is possible to give a logically consistent characterization of the continuum. There is, in addition to the logical question, also a semantical one. Zeno's paradoxes deal with physical extension, physical duration, physical process, and physical motion. These problems are not answered merely by developing a consistent system of of pure mathematics. It is also necessary to show how the abstract mathematical system can be used for the description of concrete physical reality."


 * So, find a resolution that does this and everyone will be satisfied.


 * This is about as brief as I can make it:
 * ?? -> ?? -> calculus doesn't work -> paradoxes!
 * ?? -> Time and space are continuous -> calculus works -> no paradoxes.
 * The idea is that noone has any idea what makes time move or what allows spatial seperation. If you don't want time and space to be continuous then you don't know anything and the paradoxes still kick you in the ass. If you assume time and space are continuous then the various infinite sequences converge and Zeno's paradoxes are solved; the remaining questions are not paradoxical.
 * The open questions are things like "what causes time to (appear to) pass?" and "what causes (the appearance of) spatial distribution?". All the contradictory stuff about trying to step through infinite sequences in finite time is gone. You might not have answered all the questions that were raised, but you've dealt with the paradoxes.
 * Incidently, you could run the argument the other way as "Time and space have to be continuous otherwise Zeno breaks you with his paradoxes." Endomorphic (talk) 15:40, 25 July 2008 (UTC)


 * http://www.mathpages.com/rr/s3-07/3-07.htm This treatment of the paradoxes confirms my thoughts that you can't just say "calculus" and "continuous" and be done with the paradoxes. Physics is necessary to begin to resolve anything. In any case, there is no consensus. —Preceding unsigned comment added by 207.245.46.103 (talk) 18:33, 28 July 2008 (UTC)
 * I don't really see how "www.mathpages.com", a collection of articles by some guy identified only as "Kevin Brown", without any contact details or advertised academic / professional affiliations, stands as a reputable source when conflicting against Mathworld.
 * Secondly, the arguments in the mathpages article aren't entirely valid. Sequence divergence itself isn't paradoxical; Zeno's paradox lies not in "omg! series divergence!" but in the conflict between "omg! series divergence!" versus "but the arrow *does* actually move!". From the very first paragraph in the article Zeno's Paradoxes: "contrary to the evidence of our senses, the belief in plurality and change is mistaken". The two examples using infinite collections of mirrors are deliberately divergent - they're just thomson's lamp in velocity / momentum; but until you see someone bounce a photon with infinately many mirrors in a finite amout of time, proof of their imposibility isn't a paradox. The nested mirrors don't demonstrate that anything is missing from the calculus. Endomorphic (talk) 16:01, 31 July 2008 (UTC)

Arrow Paradox
Is there not a fundamental flaw in this paradox? Namely assuming that instants in time can be added up to make time as an active dimension. Assume time is the fourth dimension; an instant in time is devoid of time, therefore it comprises of only 3 dimensions. Adding together instants of time is akin to adding 2 areas to make a volume, therefore, surely, the paradox is fundamentally flawed. Jagar Tharn (talk) 19:01, 24 October 2008 (UTC)