Talk:Zeno's paradoxes: Difference between revisions

Resolution of bias and POV

Subsequent to the above, a POV has been inserted on the main page, pending resolution through Formal Mediation.Steaphen (talk) 06:34, 28 November 2009 (UTC)

I think that the discussion is not about the content of the Zeno paradoxes, but about there are some people that think the paradoxes are not. Maybe we can set it as "Mainstream physics claim that paradoxes are solved" and that's it. And maybe we have to set a better mainstream explanation of the solution of the paradoxes. I read a lot of inconsistent claims in this discussion page, but it is not really worthy lost time in this, just open the possibility of another interpretation and that's it. —Preceding unsigned comment added by 190.247.72.15 (talk) 23:36, 10 December 2009 (UTC)

The mediation has been called because there are statements on the main page expressing unsupportable points of view. The statement "using ordinary mathematics we may arrive (or calculate") is fundamentally wrong, and needs correcting. If you think statements that have no basis in fact are able to posted in an encyclopaedia as being fact, then your definition of what constitutes an encyclopaedia is worlds apart from mine.Steaphen (talk) 02:51, 14 December 2009 (UTC)

btw, hands up allll those competent physicists (not mathematicians off in cloud-cuckoo land) who believe we can precisely calculate the location and speed of anything. Anyone? Are there any physicists, any at all, willing to commit career suicide by stating categorically we can calculate location and speed of stuff -- irrespective of size -- at and below the Planck length? Please also provide the research institution at which you work used-to work.Steaphen (talk) 03:11, 14 December 2009 (UTC)

I am not quite sure why you want to exclude mathematicians. In the end the arguments count, and your arguments aren't dismissed because of the fact that you are neither a physicist nor a mathematician. They are dismissed because of the content. That you believe that mathematical proofs are less rigorous than physical experiments, and subject to experimental validation, doesn't speak for your credentials in either area, but it wouldn't exclude you from making a valid point.

The problem is that Steaphen (currently) wants to remove any mention of any algebraic description of motion. To clarify this position to 190.247.72.15, lets give an example.

Suppose you have an object A that moves at twice the speed of object B. Suppose further that object A start at 0, and object B at 1. Assume that this speed is 1, then the position of object A can be described by $p_{a}=2t$, and the position of object B would be $p_{b}=1+t$, where t is time.

Steaphen now claims that we cannot solve these equations for t. He say that it is fundamentally wrong to solve them, and wikipedia should nowhere on wikipedia say that such equations can be solved. Steaphen even goes further and claims that you should not even mention the equations in the first place, because they are fundamentally wrong. He even goes further and claims that no physicist in his right mind would use algebraic equations to describe motion. It might sound extreme, but this appears to be his position. Please correct me if I am wrong.

To insert "mainstream" would give undue weight to a fringe position, that as far as I know only Steaphen holds. You will be hard pressed to find a single book on physics that does not use mathematical, geometric or algebraic descriptions of motion. Any textbook, look for example at Kreizig's Advanced Engineering Mathematics, but also any scientific paper, like Bohm's A suggested interpretation of the quantum theory in terms of “hidden variables”, Phys. Rev. 85, 166(I) – 180(II), 1952. As said, you will be hard pressed to find one, pulished in the last 100 years, that doesn't.

If Steaphen complains about unsupported, speculative and demonstrably erroneous suppositions, then it might be him who is sitting in the glasshouse.Ansgarf (talk) 03:50, 14 December 2009 (UTC)

I personally feel that the algebraic solution should not be included because it's unrelated to Xeno's paradox, which is a sigma addition problem, not an algebraic problem. The algebra does not solve the 1/2 1/4 1/8 series. Sigma addition does. --71.213.238.190 (talk) 16:48, 16 December 2009 (UTC)

A runner leaves the starting blocks. Picking his nose as an example location on which to focus, his nose (along with the rest of his body) beginning moving. It (his nose) moves 1/10 of a Planck length (he's quick to finish). What mathematical/geometric/algebraic expression can predict or plot his nose's movement? Explain what experimental data and theories support your thesis. Hey, was that Heisenberg rolling over in his grave (Not to mention Bohr, Bohm, Schrödinger et al)? Oh dear, someone has let the cat out of the bag. It's run away, but wins by a nose. Steaphen (talk) 04:48, 14 December 2009 (UTC)

You are indeed wrong. Perhaps English is not your first language. Reread my words. Please be more exacting in your analysis. I said, and this is quite clear, no-one is able to state categorically, with any credibility or substance that we may precisely calculate the physical qualities of momentum and location of anything. By all means apply your theories, your mathematical expressions, but there is NO evidence they can be correlated to actual physical reality -- you know, like the actual movement of things like, gee I don't know ... arrows, runners, tortoises. Yes, of course, none of this has any relevance to the issue of Zeno's Paradoxes, the apparent paradox of movement of physical things. Right. Which planet are we on? Cloud-cuckoo land? As for "mainstream" ah, yes, the crowd opinion. Do I smell smoke? As I said, the nonsense on this page beggars belief. Where's that mediator? Steaphen (talk) 04:12, 14 December 2009 (UTC)

Steapen, according to your own demands you just made a fundamental error, because under your own definition it is wrong to state that a runner is at a 1/10 of a Plank length distance from anything. And you gave yourself the algebraic equation, even if you phrased it in natural language. Namely that the movement is 1/10th of a Planck length. And Heisenberg's Uncertainty Principle is still just about the measurement of momentum and position.

You probably know that the level of Planck distances, the point of the nose is an abstraction at best. And you probably know that at Planck distances the QM description of the particle that forms the tip of the nose is given by the wave function, which can be interpreted as a probability distribution. And according to Ehrenfest's theorem the centre of particle that is the point of the nose behaves like a classic particle, and its behaviour can be described by an ordinary differential equation. And if this is too deterministic for you, use Schroedinger's equation, it also describes the motion of the particle that forms the point of the the nose, mathematically, but in a bit more detail.

I am surprised that you want me to be more exacting, since I got the impression that you found it already fairly burdensome. But maybe you are right, and I have been to easy on you. Anyway, I am not quite sure why you think that I misunderstood you, if you are actually confirming in the same paragraph my interpretation. You just said "By all means apply your theories, your mathematical expressions, but there is NO evidence they can be correlated to actual physical reality", didn't you? And this while you would be hard pressed to find a single physicist who does not believe that their equations are correlated to actual physical evidence. This is entailed in the very definition of being a physicist; using mathematical tools to describe physical phenomena, and then try to find experimental evidence. That is the reason why I actually object to include the qualifier "mainstream", since there would be no actual physicist who shares your view that you cannot use mathematical, geometric or algebraic means to describe motion. Ansgarf (talk) 12:24, 14 December 2009 (UTC)

re your "because under your own definition it is wrong to state that a runner is at a 1/10 of a Plank length distance from anything." no, that is not my definition, it is my question. What happens at those scales.

re your "And Heisenberg's Uncertainty Principle is still just about the measurement of momentum and position." WRONG. it is about the relationship between momentum and position. It is independent of all measurement. The Uncertainty Principle is a PRINCIPLE. Again, it must be that your first language is not English. If you tell me what it is, I'll see about speaking in your native tongue. I might have some trouble with Swahili though.

"I am surprised" ... I would think you're mostly surprised by everything.

I loved this "the point of the nose is an abstraction at best." Priceless. Absolutely priceless. You must get somebody else to pick your nose for you. By your definition, you can't pick it. Did I say, 'priceless.'? It must look awful to repeat myself so much.

And this (it only gets better. Hell, this is better than any entertainment you'd pay for): "And you probably know that at Planck distances the QM description of the particle that forms the tip of the nose is given by the wave function, which can be interpreted as a probability distribution." A probability distribution? Wow, that's really impressed me. So your nose, that you can't pick, is probably there, exactly where you calculate it to be with your slide rules and equations? So, the mathematics is precise about the possibilities and probabilities, but not the actual particles.. Gee, I wonder what that says. How many priceless moments are you allowed?

"the point of the nose behaves like a classic particle," you're not serious, are you? There's that question I need to keep asking "he's not serious, is he?". "we can calculate" requires ABSOLUTE precision and determinism. No if, or buts, or 'acts like" ... "acts like"? You're not really serious, are you, you're just teasing me aren't you?

But waaaaiit, there's more: "hard pressed to find a single physicist who does not believe that their equations are correlated to actual physical evidence." Right. Name one who will argue that we can correlate their equations (precisely) with the actual physical evidence (even theoretically, for distances around the Planck scale)? Just one, name one itty-bitty little short physicist, maybe, or one lying down who's still asleep, or even a dead one. Hell, I'm not choosy.

Priceless.

Steaphen (talk) 22:06, 14 December 2009 (UTC)

You know, I'm not sure why, but whenever I read the replies on this site by Ansgarf et al, I'm reminded of Monty Python's "Life of Brian". So, Ansgar, you'd like to have a baby (idea). But where's it going to gestate? In a box? Yes, you're all individuals. Well, I'm not. What has Quantum Theory ever done for us? Uhm, most success. Well okay, beside most success in predicting reality, what else? Er, ah, enabled DVD players, and lasers and a whole stack of really cool things. Right, what else? Brought new insights into possibilities? (paraphrasing) REG: Oh. Possibilities? Shut up!

Steaphen (talk) 22:26, 14 December 2009 (UTC)

Can you please make up your mind. Do you want me to be more exacting, or to just to "shut up"? I'll try to be more burdensome first, if that is o.k with you.

• When you say, what happens if a runner is at 1/10th of a Planck length you are assuming that he can be at 1/10th of a Planck length distance. So, can you make up your mind whether distances can be smaller than a Planck length or not?
• The article on Uncertainty Principle says In quantum mechanics, the Heisenberg uncertainty principle states that certain pairs of physical properties, like position and momentum, cannot both be known to arbitrary precision. The website of American institute of Physics says about the Uncertainty relations The uncertainty relations have to do with the measurement of these four properties; in particular, they have to do with the precision with which these properties can be measured.[1]
• No, you might not be able to pick your nose exactly, and you mentioned yourself repeatedly that the exact position of anything can not be determined exactly. So, could you make up your mind as to whether a point of the nose is a deterministic point mass, or not. Because in your question you assume it is, in your answers you ridicule it. So what do you want to assume?
• So, you do ridicule the notion of distributions, while you at the same time embrace QM? You might know that QM, the most successful theory, uses distributions over possible states at its core. So, please could you make up your mind, do you think that the distributions in QM provide a successful theory that has been experimentally validated, or do you think its description based on distributions is utter nonsense that has no correspondence with reality?
• I am not teasing you when I point to Ehrenfest's theorem, although, to be frank, I do enjoy to see how you struggle with the concept. When you assume that an object is defined by a wave-function as QM does, you can define its centre as a point. There is nothing particularly impossible about this. You can define the centre of an object, even if it is not a point itself. And if you do this for the wave function, you end up with an ordinary differential equation. That is the core of the theorem. Or do you see any mistake in the theorem?
• When a physicist writes down an equation that describes behaviour, he really says that the object in question behaves like that equation. Although, he'll probably admit that you cannot measure it precisely. I get the impression that you are not too familiar with the scientific method. It is not required to have have confirmed every theoretically possible prediction to accept a theory. To the contrary, a theory, if consistent, can be accepted unless it is falsified by previous or current experiments. These experiments confirm only all actual predictions, not every possible prediction. Your problem actually is that at Planck scale it might be very difficult if not impossible to falsify any prediction. How do you check that your runner is not already past his finish?
• I enjoy your references to popular culture. It is actually ironic that you tell me to shut up about distributions in QM. There is a famous quote, frequently attributed to Feynman, but that was actually coined by David Mermin, as response to people asking what really happens below quantum level. The quote is "Shut up and calculate!". It seems that at least this physicist thinks that you can calculate. Ansgarf (talk) 01:14, 15 December 2009 (UTC)

Dear Ansgar, I am so sorry, but I think I've used up my quota of 'priceless' responses -- otherwise I would provide you a detailed reply (I confess, mostly multiples of 'priceless', or variations therefore) but alas, as I said, I've exhausted my stock of 'piceless'es. Besides I start to look a bit silly, repeating myself ad infinitum, like one of your runners on his way, running through his infinite points as he calculates his way through timelessness. Awh, maybe one more. Priceless. Blessings on your path.Steaphen (talk) 04:28, 15 December 2009 (UTC)

Hi Steaphen, we have been over this a few time before, haven't we. And it does not surprise me that you cop out as soon as you are asked to give an exact answer. Neither does it surprise me that instead you try to get away with a few off-topic facetious remarks and references to popular culture. Not that I don't enjoy them. In this spirit I just want to share that your replies remind me of another gem of British comedy. You make very few responses that couldn't be summarised by ""Yeah but no but yeah but no but yeah but...", or "Don't go giving me evils!", or "Shut up! I ain't even dun nuffin' or nuffin'!" and of course the priceless "Oh my god! I soooooo can't believe you just said that!". Ok, enough silliness, let us indeed wait for the mediator to come to a conclusion.Ansgarf (talk) 04:48, 15 December 2009 (UTC)

Steaphan's comments included in this series of posts indicates a complete lack of awareness regarding the difference between simple algebra & calculus. The point about "Using simple mathematics we can calculate..." is to point out that calculus is NOT needed to determine the point at which Achilles catches the tortoise. If we are given each runner's speed and the amount of the head start, then using simple math (6th grade level or less) we can determine the relative position of each runner at every second. With the numbers in the article, Achilles "catches" the tortoise sometime between whole number values for the seconds. Algebra (9th grade math or so) can be used to calculate the specific (fractional) time & distance at which Achilles catches the tortoise. To say it is a "specific" time and distance is not the same as saying we can determine the time & distance to an infinite degree of precision. Each runner's speed is already a rounded-off value, as is the head-start. Most people understand that speeds, distances, and times are not usually given to an infinite degree of precision. I have a proposed solution to this impasse, but I wish first to determine whether settling this one point will settle the controversy, and if Steaphan will be content if the solution does not result in including his beliefdoctor thesis in the article--JimWae (talk) 05:52, 11 December 2009 (UTC)

I must also repeat: The paradoxes are not about whether or not we can find a precise point in space and time at which Achilles is located. (In fact, the arrow paradox depends on the arrow having a precise location at a precise point in time.) Zeno paradoxes do not stand or fall based upon whether we can model motion mathematically to calculate some points along the way. Zeno's paradoxes are based on the impossibility of completing an infinite number of tasks.--JimWae (talk) 06:05, 11 December 2009 (UTC)

I would never suggest that "the fact that measurements are approximate suggests QM is irrelevant". My point is that the uncertainty within measurements made regarding race-courses has a far more significant bearing than QM on how precise our calculations can be - and that it would be ludicrous to introduce QM as the main factor of uncertainty in such calculations. --JimWae (talk) 06:13, 11 December 2009 (UTC)

JimWae, you can't be serious. Regarding your "The paradoxes are not about whether or not we can find a precise point in space and time at which Achilles is located." On the front page you state that "Using ordinary mathematics we can arrive at a specific time when and place where ...". Are you serious? that you can make both statements, and remain credible? Are you aware of the disconnect that your theories require, not to mention that they lack even a modicum of consistency. Enough of this nonsense. Let the mediator(s) sort it, and failing that, the arbitrators. And failing that Jimbo. After around a century of having quantum theory (beginning with Einstein's 1905 paper on the photo-electric effect), there is simply no excuse for clinging to old, deterministic, clockwork-universe beliefs. Steaphen (talk) 04:01, 14 December 2009 (UTC)

There are competent physicists who affirm that we cannot precisely "calculate" the location of anything, no matter what its size or circumstance. Even the moon is accepted as having a wave-function which requires that we cannot exactly calculate its location and momentum (speed) (at and below Planck scale increments). The argument that we can "arrive at a specific time" is not even 'bad science' or any form of science. Such statements fail to observe the basic principle of the scientific-method.

The comments by various respondents on this site have degenerated into the unimaginably absurd. Case in point: JimWae said that

"The uncertainty in finding the point at which Achilles catches the tortoise comes more than 2 dozen magnitudes of distance before QM enters the picture. QM is an issue at around 10⁻³⁵ metres. We measure distances on a racecourse to a certainty of - at the very best - about 5 millimetres. Stopwatches at races record differences only as small as 1/100 second, whereas QM enters as an issue at about 10⁻⁴⁴ seconds. We do not have instruments than get anywhere near the theoretical limits of QM, and introducing QM as the primary uncertainty in a race is absurd."

If we analyse JimWae's comments, he suggests that to solve movement of racehorses, for example, we may theoretically use mathematics/algebra/calculus/geometry to plot their exact location and speed, irrespective of whatever distances they move, including at and below the Planck length. According to JimWae, we can only measure to around 5mm, therefore QM is irrelevant to the issue of Zeno's Paradoxes? He appears to misunderstand QM, in that reference to the requirement for actual measurement is not dictated by the Quantum Theory. The mathematical expressions stand independent of experimental evidence for them. It just so happens that every experiment (and there have been many tens of thousands of them) have not once disproved Quantum Theory. Hence why many physicists readily accept it to be the most successful physical theory, in history.

JimWae and Ansgar both appear to think that it is valid to apply geometric/algebraic/mathematical expressions to some phenomenon, even when there is overwhelming evidence revealing that it is invalid to do so. The Uncertainty Principle disallows application of any mathematical/algebraic/geometric expression to precisely define (to infinite precision) momentum and position of physical matter. The Uncertainty Principle requires that we may only approximate the location and speed of objects, irrespective of whatever mathematical/algebraic/geometric expression is used. This has nothing to do with the failure of measurement. It is simply reflecting the deeper non-deterministic nature of reality. If there are any Reliable Sources who can assert otherwise, they're welcome to state as much.

The statement "using ordinary mathematics we may calculate" requires perfect determinism (requiring INFINITE precision through INFINITE orders of magnitude below the Planck length), and that any such calculation is reflected in fact. The statements in contention and under scrutiny in this mediation have not been of the kind "Using ordinary mathematics we may approximate ...". Instead they have stated categorically, "we may calculate", with perfect determinism, requiring absolute correspondence with reality: no such absolute correspondence has been observed in actuality. Furthermore, the Uncertainty Principle requires that we may not even do so theoretically, by any mathematical/geometric/algebraic means whatsoever. The Quantum Theory and the experimental FACTS work together to reveal infinite-series/ordinary mathematics cannot precisely calculate an objects position and momentum, time and energy. The statement "using ordinary or simple mathematics we can calculate" is so fundamentally and deeply in error, as to be on par with "using ordinary mathematics we may calculate the number of angels on pinheads" ... both statements show an equal lack of correspondence with observable reality, and are therefore about as useful, meaningful or rational.

At what point does Wikipedia rein in unsupported, speculative and demonstrably erroneous suppositions of editors? Steaphen (talk) 04:01, 14 December 2009 (UTC)

Arbitrary break

• I doubt any mediator will want to take this case on unless the discussion becomes more focussed. I see there is no response yet to my statement that I have in mind a possible way to resolve this "impasse" --JimWae (talk) 22:20, 14 December 2009 (UTC)

Impasse? I've simply and repeatedly asked that you provide a Reliable Source who states that we may precisely calculate the momentum and position of a runner, or hare, or any part thereof, at all increments in movement, including at and below the Planck length. It doesn't get much simpler or more focused, does it?Steaphen (talk) 22:31, 14 December 2009 (UTC)

• The text does not say "precisely". Please try to focus. Nor does it say "momentum and position", nor "momentum" at all.--JimWae (talk) 23:46, 14 December 2009 (UTC)

Well, it's either precise or approximate. State your case. Precise (to infinite precision, as required by infinite-series solutions, and all mathematical solutions) or approximate.

Approximate or infinitely precise? If precise, and you define position then you won't have a clue as to the arrow's, or hare's velocity.

Is that clear enough for you? And if "precise" then tell me, what happens precisely at and below the Planck length?

Is that focused enough for you? Precise or approximate? WHICH IS IT? Steaphen (talk) 04:19, 15 December 2009 (UTC)

Dear JimWae, you appear to have sufficient intellectual horsepower to see where all this is headed. Now, to make it easy for you: I believe physical stuff and physical reality exists (at and below the Planck level) in superpositions of possibilities, all of which emerge from, and ride deeper nonlocal fields of potential. In which case, you're peeing into a hurricane if you think you can precisely define bits of "physical stuff" that aren't even technical real, or tangible. So, the best you'll do is "using ordinary mathematics we can approximate ..." yadda yadda. But to argue that you can precisely calculate is, as explained, 'peeing into a hurricane" ... If you want to accept that change on the main page (from "we can arrive" to "we can approximately arrive" or words similar), then we're done, mostly. There's a few other statements that need sorting, but in no way are you, or anyone else, justified in saying "using ordinary mathematics we can arrive (or calculate)." It's just bad science, or not even science at all to suggest theories that are demonstrably wrong. Steaphen (talk) 05:14, 15 December 2009 (UTC)

This discussion could go on indefinitelly. Steaphen you need to accept the fact that there are many different physical models of reality (Newtonian, Einsteinian etc) all of them based in the same language - mathematics. Then, you have the calculus which allows us to calculate (pretty much) anything within your model to an arbitrary precision/accuracy (which only depends on the calculus method that was used). So to say that you cannot precisely calculate a property within a specific physical model, when mathematical formulas are given, is simply false. Within the Newtonian model, I can do exactly what is said: use the ordinary math to calculate all those properties listed, even though the model, and the properties themselves (who is to say that physics in 1000 years is still going to use properties like velocity, momentum?) are, if you want, entirely fictional their only relation with actual reality is that mathematical models behaving similar to our perception of reality, may be found. They are similar, but still fictional. Even QM might be. As for the paradox itself could it be possible that what Zeno really meant was not, 'motion is impossible' but 'motion as we perceive it intuitively, is impossible, therefore our intuitive grasp of motion must be false'. Since motion is clearly possible, his purpose couldn't have been to prove that motion is impossible, so it must have been something else. The paradox itself rests on the continuous (or, at minimum, dense) model of space and time, therefore, maybe what Zeno actually wanted to imply is that our intuitive, continuous model must be false, and that reality works in a different way from what we perceive. A number of questions stem from that speculation, for example why would the mechanism for interpreting our reality be false, it sounds like something that nature doesn't usually do. Sort of like giving us hands that we couldn't use to pick up things with... On the other hand this does seem to validate some more discussion on the QM topic within the scope of the article. As others have pointed out, this is an article about paradox so references to physics should be kept to required minimum, still the primary topic of this paradox appears to be motion, so to me it makes sense to include as much essential information humanity has gained about motion so far, as possible. Cheers, Zibbo. (89.142.158.223 (talk) 09:24, 15 December 2009 (UTC))

JimWae, Ignoring the somewhat nonsensical responses by others: precise or approximate?

State your case. If precise, then as above, if not, then what justification can you make for 'we can calculate'?

Cheers, Steaphen (talk) 19:19, 15 December 2009 (UTC)

• The precision of the calculation is limited only by the precision of the measurements of distance and speed, just like all calculations using measurements are. When measurements are used, there is no absolute precision - all precision is relative. Calculations using measurements are not themselves approximations, the measurements are what is approximate. The calculation produces a quantity, say time (in seconds), the precision of which depends on the precision (the significant figures) given in the measurements. Neither Achilles nor the tortoise can run at a constant speed over the entire race - each must accelerate to start. 11 1/9 seconds is more specific and more precise than "somewhere between 11 seconds and 12 seconds"--JimWae (talk) 23:17, 15 December 2009 (UTC) ---- The implication of the Planck units is that we will never have instruments able to measure quantities smaller than them. (We are not even close with our present instruments.) We cannot know for certain what happens between Plank lengths & Planck times, but by continuing to use a "continuous model" at that level, we do not have to discard laws of physics such as the conservation of momentum. We do not have to conclude that space and time are some kinds of entities with a "fabric" composed of jumps, just like we do not have to conclude from looking at still frames from a movie that the subject actually "jumped" in space.--JimWae (talk) 02:03, 16 December 2009 (UTC)

Good, I'm glad we're in agreement. Due to angles on pinheads, that we can't actually see or verify with our instruments, we may conclude that Zeno's Paradoxes are solved by said angels transporting runners and hares and the like. No evidence, buy hey, it's only because the instruments can't see them.

You have now stated that the quantum theory, as in the wave nature of matter, is, at a root level, still able to be precisely determined. Hands up all those physicists who agree with JimWae that we can precisely calculate the physical characteristics of physical things. Anyone?

While it is entertaining to watch the contortions to which people go to defend the indefensible, nonetheless, it behoves all of us that this nonsense is stopped.

Unless you can provide a reliable source stating that we can precisely CALCULATE the whereabouts (speed and location) of physical things like runners, and hares (as in the quandry first proposed by Zeno) -- including and especially at and below the Planck length, I'll update the front page to say "approximate" where required. You have posted POV, with no supporting Reliable Sources. Steaphen (talk) 06:19, 16 December 2009 (UTC)

• Which of every high school algebra, high school physics, and college physics textbook is not a reliable source? Are you not at all interested in a proposed way out of this impasse? I repeat, the text does not say we can "precisely calculate". Precision is a relative term (as is approximation) -- neither is a useful adjective in this context and both would be POV. --JimWae (talk) 08:19, 16 December 2009 (UTC)

• I see you've gone ahead and started what could well become an edit-war. It is pure syntactic error to write "approximately arrive at a specific time" and "approximately calculate" --JimWae (talk) 08:30, 16 December 2009 (UTC)

Once again, there is no justification for saying "we may arrive" -- it implies we may accurately do so. The school texts don't cover the issues we are dealing with here ... namely, movement through the Planck scale.

If you cannot furnish a reliable source, you are pushing a POV. However, you are not justified in asserting that my "approximate" is a POV, in that you have not established a case for 'precise' which is implicit in the statement, "we can arrive". In other words, the onus is not upon me to 'prove' approximate' it is upon you to 'prove' precision, which is implicit in the statement "we may arrive'.

Furthermore, if you don't believe "precise" is implicit in saying "we can arrive" than you will not argue with clarification "we may approximately arrive".

In any event, Zeno's Paradoxes is about the precise means by which movement occurs (it is about the precise means by which Achilles catches the tortoise). That's why they have caused serious thinkers difficulty for 2,400+ years. In that context, precision is an absolute, unremitting requirement for any valid treatment.

You have not provided precise explanations, and therefore the statements "we may arrive" need to be prefaced with 'approximately' etc.

It would seem no mediators are going to step in. Arbitration will be called in due course. Steaphen (talk) 09:55, 16 December 2009 (UTC)

I see that you changed my addition of 'approximately' to the article. I'll expedite the call for arbitration.Steaphen (talk) 10:04, 16 December 2009 (UTC)

• "approximately arrive at a specific time" is semantic and syntactic gibberish --JimWae (talk) 10:40, 16 December 2009 (UTC)

that's a lame comment. You knew it was a simple grammatical error. It should have read "approximately arrive at a time" . Seriously, I expected better of you.Steaphen (talk) 12:43, 16 December 2009 (UTC)

• Apparently you revert before you read comments here (before you can "decide" if they are "lame" or not), otherwise you would not have reverted to the syntactic goop that you wrote. By the way, I have no problem in saying that the value calculated has limited precision, but it is not the calculation itself that is approximate, it is the resulting quantity of the calculation that has limited precision (otherwise we have goop again). But the level of precision with the numbers given in the example is already far less than the level of precision at which QM would be a paramount consideration. It's all (QM included) about the imprecision of measurements.--JimWae (talk) 22:58, 16 December 2009 (UTC)

You may be proficient in mathematics, but your understanding of quantum theory is simply wrong. The quantum theory does not allow precise knowledge (e.g. of location and speed, time and energy) of physical matter (including that which comprises arrows and the like). This is independent of the actual measurement. At the root level, matter exists in superpositions, which 'coagulate' in our reality as a point particle, a point arrow, etc., but the indeterminacy remains at the root level. that is why the position and speed of an arrow cannot be precisely calculated, because in real terms, it isn't even there, until we observe it.

It seems I'll need to write an article for the arbitrators, listing all those physicists and their quotes concerning the root level indeterminacy of physical reality, and the inability to say, with any substance "using ordinary mathematics we may arrive" or "calculate".

If you want to leave in "we may calculate" for Zeno's arrow, fine, but include angels on pinheads as well, because each have been as equally substantiated in fact (i.e. none).Steaphen (talk) 06:02, 17 December 2009 (UTC)

JimWae, simple question. Do you believe that at the root level of physical reality, at and below the Planck length and time, we may IN THEORY, precisely determine location and speed of physical stuff, at every and any point we choose? Leave aside any reference to measurement. Take it out of the picture completely. IN THEORY are we able to precisely calculate speed and location of physical particles? Simple question, yes or no. No need to waffle on, or deflect or avoid the issue, just a simple answer "yes I believe we can precisely calculate the precise location and momentum of physical matter at and below the Planck length and time" or "no, I don't". NB - this question has been repeated below, with additional commentary.Steaphen (talk) 22:10, 17 December 2009 (UTC)

Revert

It is extremely rude to make changes to an article that are currently under mediation. I'll revert the paragraphs affected by Steaphen's recent edits, pending mediation, back to the what they were on 7 December.Ansgarf (talk) 11:40, 16 December 2009 (UTC)

While I agree that the paragraph on computing when Achilles can pass the tortoise can be improved, or alternatively could be even omitted completely, as long as it is tagged POV, and we are waiting for mediation, we probably should keep it as is. Ansgarf (talk) 21:47, 17 December 2009 (UTC)

Righteo then

All of you stop writing to the article, kay? There's a difference between a mathmatical model, a philosophical model, and reality. We accept this when we attempt moddling. It's theoretically possible to determine the position of the runner to within plank's measure (Not constant, that's something different but related to plank's measure... which is related to plank time and plank space) distance of a single point, (Actualy it's not but that's because you're determine it's relation to a point that you don't actualy know where it is and it gets really messy but it can be simplified to say "You can to no better accuracy (Always worse accuracy) then plank's constant) and we can do this with a fairly simple experiment. But that's entirely irrelevant. Completely and totaly irrelevant.

Similarly the fact that we can calculate the theoretical position with algebra is irrelevant. All of this is irrelevent.

All we need is a rundown of the paradox, a rundown of the three (Two rather) solutions, and a run down of why philosophers disagree.

If the article is only about the historical problem, by all means, delete all that is superfluous to the 'rundown of the paradox'. Interesting pun.

I.e. delete the section "proposed solutions" -- scrap them entirely, since none are substantiated in fact, and are all POV. Or include the angels on pinheads as well. Equally valid, and equally substantiated.Steaphen (talk) 22:04, 16 December 2009 (UTC)

Needs rescraping

This page has gotten too complex again, and needs to be started clean... again. *Sigh* 71.213.238.190 (talk) 16:27, 16 December 2009 (UTC)

If you find this page tiring "sigh", I suggest you go lie down for awhile, and leave it to those with focus, energy and ability to sort out the nonsense.Steaphen (talk) 22:08, 16 December 2009 (UTC)

Bad math

"Another proposed solution is to question the assumption inherent in Zeno's paradox, which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence the infinite sequence of events is avoided, and the paradox resolved."

To whomever said that... Euclidian space (Which is what we live in) is hausdorf, regular, normal, metric, locally compact, and Lindiloff. That means that, amoung other things, between any two points there is another point. --71.213.238.190 (talk) 16:44, 16 December 2009 (UTC)

"Euclidian space (which is what we live in)... is hausdorf, regular..." Really? We live in Euclidean space? Really? What evidence do you have for that supposition, or that the reality we live in, is "hausdorf, regular ..."? Have you read and understood anything on this page? Upon what basis do you make that assumption? What experimental evidence supports your wild assumption.Steaphen (talk) 22:13, 16 December 2009 (UTC) btw, it's bad English to say 'math', which is an abbreviation of mathematics.

71.213.238.190 you fell right in the middle. While I don't agree with Steaphen on this page that often, this topic has been discussed on this page exhaustively. First, space-time uses Non-Euclidean geometry, but this is just an aside, and not relevant for the paradox. But whether it is Haussdorff is relevant; or whether space is dense to be precise. There are many people, like Steaphen, who assert that space-time is not dense, but discrete. Which might be wrong. But even if true, if space-time is discrete, then you wouldn't be able to construct an infinite series of tasks. The statement you mention is not bad math, but part of a case distinction. The case it describes might be bad physics, but isn't bad math. Ansgarf (talk) 22:51, 16 December 2009 (UTC)

The point of this mediation (and it seems, arbitration) is the statement "using ordinary mathematics we may arrive" , or 'calculate'.

Discrete space or dense space is irrelevant to this mediation. The statement "using ordinary mathematics we can calculate (or arrive)", is, on the evidence, plain and simply WRONG.

As before, Zeno's Paradoxes is about the precise means by which movement occurs (it is about the precise means by which Achilles catches the tortoise). That's why they have caused serious thinkers difficulty for 2,400+ years. In that context, precision is an absolute, unremitting requirement for any valid treatment.

To suggest we need not concern ourselves with whether the calculation is precise or approximate, and yet assert that this is the precise explanation for how movement occurs, is a contradiction that beggars belief.

either the calculation perfectly reflects the actual location of an arrow (or its lead atom), or it's approximate. If it perfectly defines its location, then how is it that this process (of using 'ordinary mathematics') clearly, unequivocally and repeatedly has been shown to be wrong -- it doesn't work. It doesn't fit the facts (of being able to perfectly predict/calculate the location of physical stuff at small increments in movement).

Any competent physicist reading this page would agree that we can't precisely 'calculate' the position and speed of anything, no matter what its size. To then suggest we can precisely account for physical movement while ignoring this key fact is just plain ... well, I'd have to say, stupid.

In any event, does anyone reading this page, really, genuinely believe that when we blink an eye, or lift a finger, we move the finger or eye-lid through endless, endless, endless, endless, endless, endless (endlessly repeated) little physical movements? Does anyone seriously believe we physically do that?

Is there anyone reading this page who has the courage to not hide behind descriptions and mathematics, who says 'yes, I believe I move my hand through an endless sequence of little physical movements"?

If there is someone so courageous, explain to me, like a 5 year old, how do you physically do that? Move through an endless number of 'infinitesimal' real little steps? And in each of those steps, minutely and infinitesimally small, below the Planch length, what's happening in that space, because physicists sure as hell have no idea.

Why don't you enlighten them, and save them the expense of operating the LCH

Steaphen (talk) 06:27, 17 December 2009 (UTC)

You should know by now that I am not joking. But I am used to the fact that whenever you can't admit that you are wrong you feel the need to flamebait. Also, I noticed that you are repeating yourself, but not just the arguments, but almost verbatim. I'll skip some of your old arguments, and just respond to some that are somewhat new.

First, if you think that the difference between a discrete model of space and a dense model doesn't matter, explain, how you define an infinite series of non-zero distances, on a finite set of points in space. You don't need to give a lengthy argument, just give the series.

Furthermore, I didn't say that we need not to be concerned about the accuracy of the computation. Accuracy is an important issue in numerical analysis , but that has little to do with QM. I said that applying QM to mathematics is a category mistake. I coincidentally chatted with a researcher from the LHC recently, and he called questioning accuracy of mathematics for quantum systems a red herring.

To illustrate why it is besides the point take the following set of algebraic equations $p_{a}=2t$ and $p_{b}=1+t$. For which $t$ will $p_{a}=p_{b}$? The solution is $1$. Not approximately $1$, because there simply does not exist a value other than 1 that could be a solution. You mention angles on pinheads frequently, implying that you can make up solutions for mathematical descriptions at will. I wonder, can you think of a value for t, that is not 1, and that would solve the equation?

Whether we move though an infinite or finite number of steps whenever we make a movement is in my humble opinion still an open question. A finite number of steps might make some things easier to explain, but I don't see much of a problem either way. But I commend you for making a comment that is actually related to Zeno's paradox. Because, the uncertainty in QM isn't.

Finally a comment unrelated to your latest reply. On Friday you ridiculed the use of distributions [2] to describe physical objects, but since then you have shared with us already twice that you believe that matter exists in superpositions. The way you argue seems to be the following: First, you ask people what to assume that an object is at a certain point in the order of a Planck length. Then you have the following strategy:

• If that person uses your assumption that the object is at the point you ridicule them as ignorant because at that order of magnitude particles are best described by superpositions and not points.
• If that person points out that that at that level particles are best described by superpositions, you ridicule them because they cannot even pick a point.

Of course, maybe you use the word "superposition" unaware of its meaning. Or what reason do you have to criticise me for referring to distributions, and Jim for not referring to them? Ansgarf (talk) 08:59, 17 December 2009 (UTC)

Note: This above reply is based on thisversion. Just another observation. You do not only have split opinions on distributions, apparently. In this thread you first pound 71.213.238.190 for suggesting that space/time is not discrete but Hausdorff, and just one reply later you claim that you couldn't be bothered at all whether spacetime is discrete or not. The only constant here is that your replies look like flamebaits. Although I have to grant you that you toned down your last reply a bit. Ansgarf (talk) 09:18, 17 December 2009 (UTC)

As before, blessings on your journey. Steaphen (talk) 21:47, 17 December 2009 (UTC)

JimWae, (in case you missed this question above): simple question. Do you believe that at the root level of physical reality, at and below the Planck length and time, we may IN THEORY, precisely determine location and speed of physical stuff, at every and any point we choose? Leave aside any reference to measurement. Take it out of the picture completely. IN THEORY are we able to precisely calculate speed and location of physical particles? Simple question, yes or no. No need to waffle on, or deflect or avoid the issue, just a simple answer "yes I believe we can precisely calculate the precise location and momentum of physical matter at and below the Planck length and time" or "no, I don't".

Can you reference any competent physicists who agree that we can IN THEORY precisely calculate position and momentum of physical stuff at and below the Planck length and time?

Any at all? Steaphen (talk) 22:14, 17 December 2009 (UTC)

• It would be rather ridiculous to leave measurement out of considerations of whether we can determine the speed and location of things. We cannot locate anything at all -- not even approximately --- without some framework of measurements.--JimWae (talk) 22:55, 17 December 2009 (UTC)
• Btw, please see this edit. I think you will find less to object to in it.--JimWae (talk) 22:59, 17 December 2009 (UTC)

You have avoided the question. Consider it a thought experiment, in that say in 500 years time they invent some amazing new device or some such that does what we can't now. Whatever. Is it possible IN THEORY, to ever (as in EVER, say in one million years) to precisely calculate position and momentum of stuff?

Yes or no? Simple question. It's a rhetorical question, because your statement "using ordinary mathematics we can calculate" requires that in theory you may do exactly that. In any event, your refusal to answer this question, despite asserting that it is possible via "using ordinary mathematics we may calculate/arrive" confirms the affirmative that you believe it is possible in theory. Now find a competent physicist who agrees with you.Steaphen (talk) 23:46, 17 December 2009 (UTC)

• I cannot think, nor do I think anyone can, of how to locate anything without using measurements. So, the question answers itself - we cannot (& will not ever) measure the exact location of anything to a degree of precision below Planck levels, so we cannot (& will not ever) determine such a precise location. That does not 'mean that space has jumps.
• And neither the paragraph you object to, nor the one I recently put up (which I think is tighter & leads better from one sentence to the next), requires what you say it requires.
• Besides, if we can show mathematically that Achilles can actually pass the tortoise, then we have gone at least part of the way to casting doubt on Zeno's arguments that Achilles can never catch the tortoise --JimWae (talk) 00:03, 18 December 2009 (UTC)

JimWae, you have again avoided the question. You either believe it can be CALCULATED in theory, or it can't. By your statements you believe position and momentum can be calculated. That is your statement, "using ordinary mathematics we can calculate". Your own statements confirm you can calculate position and momentum.

No competent physicist will agree with your assertion. None. Find one that does and I'll show you a physicist without (or soon to be without) a career in physics.

Your statements "using ordinary mathematics (or algebra, or whatever, by any means) we may calculate (at and below the Planck length) ..." is wrong. No physicist will agree with you. None. The front page is simply wrong. Find one physicist that confirms your POV. Just one. Steaphen (talk) 00:47, 18 December 2009 (UTC)

• It is ridiculous to keep repeating the question. I have answered it fully already. Location (for one) cannot ever be determined to a degree of precision below Planck units - BECAUSE we cannot ever measure below that level. It does not follow from that that space has jumps.--JimWae (talk) 01:00, 18 December 2009 (UTC)
• Nowhere in the article is there any suggestion that calculation to such a degree is possible. We do not measure to such a degree when determining if one runner has caught up to another. If Achilles can pass the tortoise, he has more than caught up to him.--JimWae (talk) 01:20, 18 December 2009 (UTC)

You have, yet again, avoided a very simple question: Do you believe the particle, or arrow or whatever, is physically 'there' for any calculation to be performed, irrespective of whether it can ever be experimentally verified. I'll answer for you. You believe physical stuff is entirely still physical, tangible and real, at every level and point down to infinitely short length and time. That is your belief, simply reflected by "we may calculate" .. otherwise, what is it that you are calculating if it is not something physical?

As before, you will not find any competent physicist agreeing with you. The front page is your POV, and unsupported by any competent physicist (Reliable Source).

Steaphen (talk) 01:29, 18 December 2009 (UTC)

• Are you trying to read my mind, now? You are misrepresenting my thoughts, my posts here, and what appears in the article - such has no applicability to what the article should cover. Just because we cannot assign an infinitely precise number to the location of an object, it does NOT follow that space has jumps. I have answered fully, and I will not repeat myself again.--JimWae (talk) 01:37, 18 December 2009 (UTC)

With all due respect, it is you who have stated "we may calculate" (to infinite orders of magnitude below the Planck length). That is a requirement of your statement since you have not stated limits to that calculation. "We may calculate" implicitly covers all orders of magnitude below the Planck length. ALL. Including distances such as 10^{-1,000,000,000,000,000,000,000,000}. and onwards to 10^-infinity metres. No competent physicist on this planet, or any other is going to agree to that. The front page is wrong. Plain and simple. Steaphen (talk) 01:46, 18 December 2009 (UTC)

btw, what on earth has "space has jumps" or not got to do with your statement "using ordinary mathematics we may calculate"? You've now mentioned it twice, yet it is completely irrelevant to the very simple question I have asked you: can you calculate the position and momentum of physical stuff all the way down to the infinitely short (distance and time). You require that you can. Fine. Find one physicist who agrees with you.

let's be clear on this. The mediation was called because of your statement "using ordinary mathematics we may arrive (or calculate)" This has nothing to do with measurement, or dense space or angels on pinheads, or anything else other than the validity or invalidity of that statement. Period. All your side-steps won't resolve that basic mediation issue. The statement is wrong and has to go. Steaphen (talk) 01:54, 18 December 2009 (UTC)

• If "We may calculate implicitly covers all orders of magnitude below the Planck length" were true, then there could be no calculations at all involving measurements. The precision depends on the precision of the starting measurements - any freshman college physical science student knows that.--JimWae (talk) 02:32, 18 December 2009 (UTC)
• I have no way of knowing what "really happens" below Planck levels. Neither do you, (though your writings seem to suggest you think you do, when you keep repeating "it is wrong") and likely nobody will ever know. We apply models until the model no longer works. Using a continous model, we do not have to discard all the laws of physics such as conservation of momentum--JimWae (talk) 02:32, 18 December 2009 (UTC)

re your "If "We may calculate implicitly covers all orders of magnitude below the Planck length" were true, then there could be no calculations at all involving measurements" -- If I am understanding you correctly, now, then your "we may calculate" implicitly means "we may approximately calculate". You either calculate precisely or approximately. Again, what exactly is it that you are calculating? Angels on pinheads? If you are accurately calculating physical stuff, then again, what happens below the Planck length?

re your "I have no way of knowing what "really happens" below Planck levels", and yet you claim you can calculate (at and below Planck levels)? You can't know what is really happening, but you believe you can nonetheless apply some mathematical/algebraic/geometric model to those realms? This has gone beyond entertaining, to surreal.Steaphen (talk) 03:48, 18 December 2009 (UTC)

So let me see if I understand you correctly. You can calculate when Achilles overtakes the tortoise? But, we can't calculate any movement if it involves sub-Planck level movements? So, that requires that when Achilles overtakes the tortoise, he "jumps" past any sub-Planck movements?

Do I understand you correctly now? Steaphen (talk) 04:54, 18 December 2009 (UTC)

So if Achilles overtakes the tortoise, say at 30 + 0.01^{-1,000,000,000} metres (i.e. at 30 metres + a sub-Planck fraction of a metre), we can't, according to your statements, accurately calculate this? But you say on the main page, "using ordinary mathematics we can arrive (calculate) ..." Which is it? We can calculate (in and through sub-Planck movements) or we can't? Steaphen (talk) 05:02, 18 December 2009 (UTC)

• As explained to you elsewhere on this page, by me & others, calculations are not what produces the lack of precision, it is the measurments we begin with. 100 metres does not mean 100.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000… metres. (This is taught in every freshman college physical science class) Have you given up on trying to read my mind now, or are you purposely misunderstanding me?--JimWae (talk) 05:20, 18 December 2009 (UTC)

You can reference "freshman", junior or elementary school mathematics/algebra or whatever. It is irrelevant, because none of them covered the issue of Planck length and below movements. NONE of them. I could say "the Earth is flat" because within certain approximations it is. We're dealing with the specifics here of how physical things move.

According to your statement above, it does indeed mean 100.0000001 or whatever, because you can calculate it precisely, to infinite degree. Either that or you cannot calculate precisely.

Again, simple question to what extent can you calculate the location and momentum of physical stuff. Forget about measurement, I'm asking you, THEORETICALLY, what is the limit of that calculation. You've said it is (implicitly) infinitely precise. I have not once seen you say otherwise. Having implicitly stated your case (since you've not denied otherwise) please find one physicist who will support it. Just one! Steaphen (talk) 06:30, 18 December 2009 (UTC)

In any event, irrespective of whatever measurements are made, theoretically, the de Broglie wavelength of an object is :$\lambda ={h}/{p}$ (where p = momentum). The infinitesimal precision of the object's position (as required by infinite-series/algebraic/geometric/mathematical solutions) requires that $\lambda$ approaches zero (since the de Broglie wavelength of the object indicates the range of possible positions and momentums of the object.). This requires the momentum to be infinite. This is nothing to do with measurement. This is quantum theory explaining the limits of theoretical knowledge.

The statement "using ordinary mathematics we can calculate' is wrong. The de Broglie relationship is most certainly important when considering movement of runners, arrows etc in the realm of Planck length increments, because to calculate them to such precision, requires they have large -> to infinite mass/momentum (depending on how 'precise' you want to 'calculate').

The mediation will not be settled unless you can find a Reliable Source who will state that exact calculation of position and momentum of physical objects is possible at and below the Planck length.

Any theoretical calculation within whatever degree of certainty (as given by the de Broglie relationship) limits the theoretical knowledge of its position. There is no way around this, unless you want to disprove the wave-nature of physical objects. The statement on the main page "using ordinary mathematics we can calculate" is deeply and comprehensively wrong.Steaphen (talk) 08:02, 18 December 2009 (UTC)

---

You keep mentioning de Broglie's wavelength. Just a simple question, does an object that has not infinite momentum a position? Ansgarf (talk) 09:00, 18 December 2009 (UTC)

Finally, you've started to ask some intelligent QUESTIONS. Do the maths (that's an abbreviation for mathematics), or algebra whatever, and starting asking some real questions as to what is really going on. So if velocity (non-relativistic) for an average size/weight runner of 90kg is say 5 m/s, that means ...

Email me when a mediator shows up. Otherwise I'll pop back in a few weeks or months to initiate arbitration.

Ciao Steaphen (talk) 20:04, 18 December 2009 (UTC)

Glad that you understood this question. I thought that if I tone it down and ask you in small steps you might be able to keep pace and provide at least some answers. Unfortunately, it seems you try to duck the question by being cute and saucy. Rather than seeing school yard antics, I would have preferred an answer. It shouldn't be hard to tell whether you assume that an object has a well defined position or not, regardless of momentum. Ansgarf (talk) 21:54, 18 December 2009 (UTC)

---

Steaphen, in case you missed my question. At or below the Planck length and time, do you think that it makes sense to ask at which point a particle is exactly, or do you believe that they are quantum superpositions? Just to put things in context, the Planck length is in the order of $10^{-35}m$, a hydrogen atom ($10^{-10}m$). This proportion is 100.000 times larger than our relation (order of $10^{0}m$) to the Milkyway ($10^{20}m$). Ansgarf (talk) 23:59, 17 December 2009 (UTC)

Dear Ansgar, I'm sorry, but I have simply lost patience or interest in your replies. They lack even a modicum of reasonable analysis. Seriously. I'm not able to offer you any replies that you seem to be able to comprehend. This latest by you is a good example. The solutions to Zeno's Paradoxes, by whatever mathematical means, whether by infinite-series, or whatever, must and do involve going through not only the Planck length and shorter increments, but infinite orders of magnitude shorter. We're not talking 10^-35 metres, we're talking 10^{-1,000,000,000,000,000,000} metres and on to infinity. Your inability to follow through with your statements and theories as to what that implies in terms of actual physical reality (e.g. the situation with runners, hares, arrows etc.) reveals a disconnect of theory with reality that I'm unable to bridge, or understand. As before, blessings on your journey. I genuinely mean that, because I can't help you, it seems, any other way.Steaphen (talk) 00:58, 18 December 2009 (UTC)

And I am well aware that you think about all order of magnitude, and I am well aware there exists an $n$ such that $1/2^{-n}$ will be smaller than any positive $e$. I do know the definition of convergence. And it is in all orders of magnitude a grave category mistake to apply uncertainty to calculations, because calculation work on dimensionless numbers. In the set of real numbers with addition it is true that 1+1 is exactly 2. And 100 +100 = 200. And $1*10^{-40}+1*10^{-40}=2*10^{-40}$. This follows from the simple fact that addition and multiplication on the reals is distributive. And no physicist assumes otherwise.

You said repeatedly that you "believe physical stuff (...) exists (at and below the Planck level) in superpositions of possibilities". But you still ask Jim and others what the exact position of physical stuff is. If there is a disconnect, then between what you claim to believe, and what your question and remarks reveal you actually believe. The statement about the relative size of hydrogen and the planck length, compared to you and the Milky Way, was intended to make you think about the concept of position. Because you keep asking at what postal address the Milky Way resides. Figuratively, speaking.

You lost interest, because you have no reply, and probably also because you cannot stand exacting analysis. If my analysis looks absurd, then because it starts on purpose from some of your assumptions and statements, and reduces them to absurdity. Which is made easy, since I have seen very little evidence that you understand what it means for a set to be dense, what is meant by superposition, what model of time is used actually in QM, the nature of mathematical proof, the nature of physical models, the role of experimental evidence, or what assumption Zeno makes, just to name a few things. In your latest reply you just try to duck that you haven't thought about the fact that in the order of Planck levels, the naive notion of position of a particle may not apply. Or you only think about it if it suits you. Ansgarf (talk) 18 December 2009 (UTC)

Significant figures

Strictly speaking, 100 metres has only 1 certain significant figure and indicates any distance from 50 metres to less than 150 metres. To clearly signify the 3 significant figures usually intended by 100 metres, we could write instead the odd-looking "100. metres", indicating from 99.5 to less than 100.5 metres. "100.0 metres" indicates from 99.95 metres to less than 100.05 metres - that the value is less than one that would round to 100.1 and greater than one that would be rounded to 99.9. Standard 100-metre races are probably exact, at best, to 0.0005 metres (1/2 a millimetre). Even if exact to 1/20 of a millimetre, we should only specify the distance as 100.0000 metres. People who work in the physical sciences are expected to be aware of the limitations of all measurements, and avoid reporting with false precision. QM cannot be the primary cause of uncertainty when the measurements are at this level of precision. The main uncertainty comes from the fact that speed, distance, and time are measurements, not ideally exact numbers. Though there are less clear standards for fractions, 11 1/9 seconds indicates a time (in seconds) greater than what would round to 11 2/17 and less than one that would round to 11 2/19. If I thought the fractions were the reason for Steaphan's concerns, I would have used values that could be presented in decimal form long ago. Anyway, it does not matter how precise the figures in the example are, if it mathematically shows that Achilles will actually pass the tortoise. --JimWae (talk) 09:37, 18 December 2009 (UTC)

Not quite, "100" is simply ambiguous. With physical quantities, you have the option of using SI prefixes, as in 100±0.5 m = 1.00 hm or 10.0 dam. Regards, Paradoctor (talk) 19:29, 27 December 2009 (UTC)

But "100", unless otherwise specified, cannot be presumed to have more than 1 sig fig.--JimWae (talk) 22:56, 28 December 2009 (UTC)

That's what "ambiguous" means, you cannot presume. It may mean 1 hm or 1.00 hm, or if you prefer km, either 0.1 km or 0.100 km. Paradoctor (talk) 00:29, 29 December 2009 (UTC)

Stillness

It's rather strange. Here we are considering how motion is possible, when the present-day view is that stillness is impossible - at both the macro & sub-micro levels--JimWae (talk) 01:48, 18 December 2009 (UTC)

Do you realize that rest is an extreme case of motion? ;) Paradoctor (talk) 21:27, 12 February 2010 (UTC)

This page is crap

I read this entire page of arguments and its is crap, you guys are nerds who need to drink some beer, no one should care about philosophy this much when you will die one day. —Preceding unsigned comment added by 173.26.222.43 (talk) 11:20, 21 December 2009 (UTC)

My what a talk page. Is this guy Steaphen attempting to illustrate the paradox with infinitely recursive argument? --77.188.52.212 (talk) 16:45, 27 December 2009 (UTC)

Nope. I'm waiting for him to start arbitration. Paradoctor (talk) 17:38, 27 December 2009 (UTC)

No point waiting. You are not involved in this mediation (come arbitration)-- your comments and opinions are not relevant or required.Steaphen (talk) 20:01, 22 January 2010 (UTC)

(sipping tea) Paradoctor (talk) 22:04, 22 January 2010 (UTC)

Proposed changes

I propose the following changes:

1. Paragraph "Zeno's paradoxes were a major problem .... wrong with the argument."

I propose to replace this with

"Zeno's paradoxes were a major problem for ancient and medieval philosophers. More modern calculus has solved the mathematical aspects of the paradox, while many philosophers still hesitate to say that all aspects paradoxes are completely solved. Variations on the paradoxes (see Thomson's lamp) continue to produce philosophically and mathematically challenging problems. Developments in physics have called into question the idea that position, time, and speed are simple points, which undermines some of the implicit assumptions of Zeno paradox."

The reason for this change is that the previous version puts mathematics and physics needlessly in opposition. Physics is unrelated, and plays it own role. Also, the previous version does not explain its role.

2. Paragraph "Using ordinary mathematics (...) namely, "How is it that motion is possible at all?""

I propose to delete the entire paragraph. Zeno's paradox is not about algebra, or how to compute when two objects meet, or how to compute where two lines in Euclidean space intersect. This paragraph is also too specific for an encyclopaedic article.

3. I propose to not qualify the word "calculate". Within the scope of the paradox positions, times and limits of series are not "approximately calculated", or "more exactly calculated", but simply "calculated". The article is not about uncertainty, robustness, error bounds or numerical accuracy.

4. The paragraph "Physicists remark (...) about 10−16 seconds."

I propose to delete the last sentence "As of 2004, the shortest time difference capable of actually being measured was about 10⁻¹⁶ seconds." It is not relevant for the paradox, and this information should be mentioned in the article on the Planck length.

I propose to replace it with the sentence. "These findings suggest that for physical systems the infinite series that appear in Zeno's paradoxes may not occur at the sub-quantum level." Ansgarf (talk) 04:54, 29 December 2009 (UTC)

Mediation

Can I firstly apologise on behalf of MEDCOM for no mediator taking this case on. If you still need a mediator, I will happily take it on as I am available to mediate. Seddon ^talk|^WikimediaUK 07:01, 5 January 2010 (UTC)

This is not the appropriate section for mediation. The mediation page is at http://en.wikipedia.org/wiki/Wikipedia:Requests_for_mediation/Zeno%27s_paradoxes

Steaphen (talk) 13:19, 15 January 2010 (UTC)

I know :) but since im on medcom, I'm asking whether there is still a need for a mediator :) Seddon ^talk|^WikimediaUK 04:30, 31 January 2010 (UTC)

The mediation issues in the main have not been resolved. If you would like to make relevant representations on the appropriate pages, that would be appreciated. I expect you've noted that the POV notice in the main article was, in violation of Wikipedian guidelines, removed without the issues being resolved. Hence the likely need for arbitration, given the persistence of bias and POV in the main article.Steaphen (talk) 08:48, 1 February 2010 (UTC)

Arbitration called

Wikipedia:Arbitration/Requests/Case#Zeno.27s_paradoxes Steaphen 13:37, 11 February 2010

• I find the use of "called" (instead of "requested") ambiguous and confusing. Please cite reliable sources for this use of the word.--JimWae (talk) 20:35, 11 February 2010 (UTC)

Dear JimWae, "called", "requested" ... take you pick. It is irrelevant.

This arbitration is not about content! It is about inappropriate behaviour, of making statements that are not supported by Reliable Sources, and are thus speculative opinions and assumptions. Plain and simple.

If any competent physicist can assert that via ANY mathematical means, we may fully and precisely account for physical movement of physical objects (no matter what their size), I would like to see that statement presented here for the benefit of this arbitration.

Any by "fully account" that means experimentally and theoretically supported by the evidence, and the quantum theory, or whichever theory has peer-reviewed support, and accounts for the experimental data.Steaphen (talk) 00:57, 12 February 2010 (UTC)

Outside opinion by CBM

The underlying dispute is something that mathematicians can sometimes be insensitive to. It's certainly true that, in the standard Newtonian mathematical model of motion, Zeno's paradoxes are no issue. From the viewpoint of a mathematician, this is all that matters. Thus many calculus textbooks say that Zeno's paradoxes have been solved, because from a mathematical standpoint they have been.

However, this isn't a very pleasing answer for non-mathematician philosophers and physicists. Also, the general naiveté with which Zeno presented the paradoxes makes it difficult to tell what the paradoxes actually are. In our mathematical reductionism we can easily take them to be statements about Newtonian mechanics, while physicists might take them to be referring to actual motion rather than to our model of it. The same situation arises very often, when mathematicians approach a vaguely-worded philosophical problem by first making it mathematically precise and then solving the precise version as if it was the same as the original vague version.

In the article here, there is presumably space to cover both the mathematical solution and the more general philosophical discussion. I did a Google search earlier and it looks like there is a decent philosophical literature on the subject, which isn't surprising. I don't know if there is literature that explores the relationship between quantum physics and Zeno's paradoxes.

My general advice, as an outside observer, is that it might be best to discuss the mathematical solution in its own section, making a note that it relies on the Newtonian model of movement. Within that section, things like quantum physics are irrelevant. This is the solution that is commonly presented in calculus textbooks.

In a separate section, the article could discuss more general philosophical research on the paradoxes. The point here is not that the Newtonian solution is invalid, but that there may be other concerns that are not captured by the Newtonian model.

Of course these two approaches (mathematical/philosophical) are not in conflict. They complement each other by revealing different aspects of the situation. — Carl (CBM · talk) 17:52, 11 February 2010 (UTC)

"the general naiveté with which Zeno presented the paradoxes": I'll bet you a penny that you can't cite that to reliable sources. Paradoctor (talk) 18:22, 11 February 2010 (UTC)

A google books search for "zeno naive paradox" will find several interesting examples, but maybe not in the sense of "naive" that I had in mind. — Carl (CBM · talk) 20:54, 11 February 2010 (UTC)

Keep looking, that penny won't rust away. You might save yourself some work, though. Ask yourself: What would it take to make your statement true? Paradoctor (talk) 21:28, 11 February 2010 (UTC)

My opinion is quite simple: the paradoxes as originally stated refer to our naive conceptions of position, time, and motion, rather to any particular formalism in which they could be either proved or refuted. If we disagree on that, I don't think it's worth discussing in great depth. — Carl (CBM · talk) 21:55, 11 February 2010 (UTC)

"the paradoxes as originally stated": Stated where? Paradoctor (talk) 22:24, 11 February 2010 (UTC)

I agree with the thrust of CBM's comment, but with regards to "naiveté" consider the following:

In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance... Bertrand Russell, The Principles of Mathematics (1903)

Paul August ☎ 18:58, 11 February 2010 (UTC)

"two thousand years of continual refutation": I presume Mr. Russell has provided either citations to literature reviewing the reception history of Zeno's paradoxes, or a review of his own? Paradoctor (talk) 19:20, 11 February 2010 (UTC)

Doesn't that published quote constitute "a review of his own"? — Carl (CBM · talk) 20:10, 11 February 2010 (UTC)

Not in any understanding of the term "review" I know of, and most assuredly not in the specific meaning alluded to, I'm afraid. The quote might be considered a short statement of the conclusions drawn from such a review. Without supporting citations or argument, this is "just" Russell's opinion. Considering Russell's statement about the history of the topic, one should be able to find a lot of reliable sources contradicting Russell, which might lead an adventurous soul to worry about WP:UNDUE should those voices not get mentioned. Paradoctor (talk) 20:30, 11 February 2010 (UTC)

Thanks to Carl for making the discussion more promising. I always believed (naively, or not?) that Zeno hinted at something like that: it is unbelievable that mathematical models stipulating infinitely many points in a finite domain reflect the reality in this aspect (but of course they are quite good in many other aspects). (I never read something deep about Zeno paradoxes.) I wonder, do you agree or disagree? (Sorry if it is off-topic.) Boris Tsirelson (talk) 21:42, 11 February 2010 (UTC)

I apologize; I was not trying to start a long discussion about Zeno's paradoxes. I just wanted to point out that there is room to discuss both the formal mathematical solution (although it may not solve the original problem) and philosophical aspects of the original problem (although these may be philosophical, rather than mathematical). We don't have to choose between these alternatives, because they actually reinforce each other. — Carl (CBM · talk) 21:58, 11 February 2010 (UTC)

I agree, completely. Boris Tsirelson (talk) 22:16, 11 February 2010 (UTC)

Just as a reminder. The current article does mention the philosophical aspects as well as the mathematical aspects of the original paradox, and that more than once. It also mentions that when applied to physical reality quantum aspects may play a role. These paragraphs may be improved, but it is not the case that the current article doesn't mention it. It does.Ansgarf (talk) 23:27, 11 February 2010 (UTC)

Yes, you're right. I read through the comments higher on the page, and I thought that both sides were right, but about different things. The lede section of the article has a nice tone, I think. The difficulty is the section "Status of the paradoxes today" lower down, which tries to do too many things at once. I would propose adding a section "mathematical resolution" that discusses the calculus-textbook approach, and then editing "status of the paradoxes" to focus more on the philosophical reception of the mathematical solution. Looking through google books, I am sure there are enough sources to do all of this. — Carl (CBM · talk) 00:51, 12 February 2010 (UTC)

A textbook solution just got removed a few weeks ago, since too many people felt that the paradox is at its core not about calculus or algebra. In my opinion it wasn't worth the trouble to be included [3]. But if you can come up with a paragraph that that avoids the problems the old version had, I wouldn't object.

Mentioning Brouwer at that point was a compromise, on an earlier formulation. It claimed that Intuitionists reject to any use of infinites, which is not true. [4]. The most recent sentence on Brouwer was intended to keep those people happy, while at the same time keeping them from adding false claims about Intuitionists. I agree that the whole topic is a bit spurious, but it is a compromise. Ansgarf (talk) 01:14, 12 February 2010 (UTC)

I see now. Regarding the calculus solution: to many mathematicians, including me, the calculus solution "is" the solution of the paradoxes. It's certainly repeated as a solution in numerous calculus and analysis texts. Moreover, I saw several sources today that seemed interested in discussing whether it really was a solution. I think the article would be incomplete without covering the mathematical viewpoint. On the other hand, I understand the philosophical viewpoint that the mathematical solution is too idealized to address the original problem.

Regarding Goedel and Brouwer, as a logician I think discussing them at all is a red herring. The issues that the intuitionists have with infinity (and you are right that they do not reject it outright) are not related to infinite sums nor to classical mechanics, while Zeno's paradoxes are unrelated to the law of the excluded middle. Goedel's theorem is not related to the foundations of calculus, which were accomplished in the 19th century anyway, well before his time. — Carl (CBM · talk) 01:42, 12 February 2010 (UTC)

Ok, maybe there is something to be said to leave out everything that is too tangential. And Intuitionism probably is. If you can include a short treatment of the mathematics of the paradox - which might already be achieved by reorganising the current article a bit - then I'd be more than happy. The article does are ready contain references that calculus is not "the" solution to all aspects. By some reorganisation this might become more pronounced. Ansgarf (talk) 02:30, 12 February 2010 (UTC)

[From Steaphen] - The arbitration was called on the issue of inappropriate behaviour -- regarding statements being made that are not, and cannot be supported by real-world evidence, and thus remain in the domain of speculation. Zeno's Paradoxes concern the subject of movement of physical things -- runners, arrows etc. If mathematics can assist in that inquiry, well and good. If spirit-guides of recently deceased can assist in that inquiry, well and good. If a bumbling idiot can assist in that inquiry, well and good. Whether mathematics can assist in solving Zeno's Paradoxes is not relevant or useful until a competent physicist can detail how theory matches and accounts for reality (experimental data concerning the movement of physical things).Steaphen (talk) 01:20, 12 February 2010 (UTC)

As I was saying, there are two sides to resolving the paradox: the mathematical resolution within Newtonian classical mechanics, and the philosophical discussion about the real world. Each of these is, in its way, important to a complete understanding of the paradoxes. — Carl (CBM · talk) 01:42, 12 February 2010 (UTC)

[From Steaphen] - Upon what basis do you affirm that mathematics is important to this issue, if there is no reliable linkage, correspondence or congruency of theory with evidence and fact? A lack of correspondence (of theory with fact) is how people get burned at stakes. Please start with observable reality, and wind backwards into theory (as we might expect of any good scientist or serious thinker) -- if that theory involves mathematics, well and good. If not, so be it. Starting with observable reality is I believe valid and worthy. Let's leave speculation and baseless opinions for forums devoted to such things.Steaphen (talk) 02:06, 12 February 2010 (UTC)

I think that mathematics is important to the issue because large numbers of mathematics books bring up the issue in the context of infinite series. Most mathematicians learn of Zeno's paradoxes in this way. Moreover, I was looking at philosophical references today and many of them mention the mathematical solution (in some cases, only to criticize it). If you would like, I can make a list of such references. However, if you have looked into the literature on Zeno's paradoxes, I am sure you have already seen what I am talking about. — Carl (CBM · talk) 02:09, 12 February 2010 (UTC)

Carl, I am aware of the preponderance of opinions on this issue. Arbitration was called to seek some clarity amongst the clamour and noise of the crowd ("large numbers"). Scientific principles ('scientific method') regarding this subject have been discarded, ignored or simply denied. My intent is to bring some discipline to the issue, by reaffirming the root validity of applying the scientific method to the subject of Zeno's Paradoxes.

I have not seen any examples (regarding the subject of Zeno's Paradoxes at this site) of strict adherence to one of the root principles upon which great scientists and thinkers have stood since time immemorial - the scientific method of questioning observable reality and finding a theory which fits the facts. Steaphen (talk) 02:19, 12 February 2010 (UTC)

I'm not sure what you're saying. The goal of this article is to summarize what is already known and written about Zeno's paradoxes – including what is written in mathematics texts. The goal here is not to solve the paradoxes ourselves (which would be unlikely) or to decide that entire branches of the literature on the paradoxes should be discarded. — Carl (CBM · talk) 02:23, 12 February 2010 (UTC)

I called arbitration, not because of the historical content about the paradoxes, but about claiming (or even inferring) that said beliefs, theories or literature, actually account for physical movement. There's an important difference about reporting on the literature (and theories) and claiming that the theories are valid.

This arbitration would not have been called IF the theories were put in their proper context -- that they remain unsubstantiated theories! and do not (at least not from the evidence I've seen) offer congruent, verifiable solutions to the paradoxes. Statements like "Using ordinary mathematics we can calculate, (or arrive) ..." are simply biased opinions with no basis in verifiable fact.

By all means, report on those baseless opinions, but to state that "using ordinary mathematics, we may ... " is wrong until proven and confirmed by a Reliable SourceSteaphen (talk) 02:50, 12 February 2010 (UTC)

• Steaphan, are you even aware that the sentence you keep harping about has not been in the article since last year? Not that it was not true that "using ordinary mathematics, we can calculate a position and time at which Achilles would catch the tortoise". --JimWae (talk) 06:36, 12 February 2010 (UTC)

Surely, every given physical theory does not describe reality completely (and therefore will be replaced some day). Surely, this is true in particular for the concept of mathematical continuum as a model of space-time. However, all that does not mean that we should abandon all physical theories (as Steaphen seems to propose). Boris Tsirelson (talk) 07:22, 12 February 2010 (UTC)

[From Steaphen] -> From a verbatim extract of the front-page article as at 6.34 pm Australian Eastern Time, 12th February, 2010: ". While mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise, ..."

Wrong. It cannot. At least not on the available evidence. Hence the request for arbitration, re the persistent violation of Wikipedia policy regarding statements without merit, that pust POV, and lack Reliable Source support.

Boris, please re-read my words. It is not about denying the history of the paradoxes, or what's been said about them, it's simply the baseless claims (see above) that are being called into question.

It's really not that hard to understand ... if you want to make claims about theories that cannot be substantiated via physical experimentation or evidence. then you must also allow other claims such as astrology, or numerology or other belief-systems that have also not been strongly correlated with the facts of reality, or that have been experimentally substantiated. Steaphen (talk) 07:42, 12 February 2010 (UTC)

Yes, it's really not that hard to understand: every theory "cannot be substantiated via physical experimentation or evidence", if you require it to be absolutely right. Does it mean that we should stop using theories at all, however? Boris Tsirelson (talk) 08:09, 12 February 2010 (UTC)

When the article talks about "While mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise, ..." it refer to the tortoise and the runner in the mathematical model of the paradox. To solve the equations you are not doing "experiments", you do math. Which will give you mathematically precise solutions. That is much more rigorous than any experimentation can be. They are not any particular runners or tortoises that have a shoe size, a weight, or feeding habits. That Zeno's paradox is a thought experiment, a proof by contradiction, and not an actual physics experiment, is obvious from the context, and even mentioned explicitly in the article. Ansgarf (talk) 08:25, 12 February 2010 (UTC)

• @Steaphan::For this discussion to go anywhere, you will need to be more "on-target" about what parts of the article you are objecting to and not throw in red-herrings. While mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise could easily be changed to While mathematics can be used to calculate where and when the moving Achilles would overtake the Tortoise but I gather even that would not satisfy you. Just because we cannot specify to a million decimal points the time and position does not mean math cannot be used to calculate a time and position. Besides, Zeno's argument is that Achilles will never catch the tortoise at all, not that the position cannot be determined with infinite precision. If math can determine a time and position (even with lots of imprecision) at which Achilles has actually done more than caught but has actually passed the tortoise, math is still the tool that is being used to do so. If people do not maintain that Achilles actually catches and passes the tortoise, then they should not consider this to be a paradox at all, but some kind of "truth". --JimWae (talk) 08:44, 12 February 2010 (UTC)

It is not a problem to overtake the Tortoise (as Zeno surely understood). It is a problem, whether a finite time interval can contain infinitely many events, or not. Boris Tsirelson (talk) 10:05, 12 February 2010 (UTC)

As Carl emphasizes, we should take into account both sides of the story: (a) some models resolve the paradox admitting infinite divisibility of space-time (the mathematical side); (b) it does not mean that infinite divisibility is a property of reality (the philosophical side). Let me repeat Carl's phrase: "Of course these two approaches (mathematical/philosophical) are not in conflict. They complement each other by revealing different aspects of the situation." Boris Tsirelson (talk) 10:10, 12 February 2010 (UTC)

Hi, Steaphen. I've been reading the discussion with intense interest, and then I came to what seems to be the focus of your discontent. You feel that the claim that math can be used to calculate when and where Achilles will catch the tortoise, is an unsubstantiated claim that is wrong, incorrect, without merit and so forth? So I'm seeing this in my mind in the simplest possible, common-sense terms. Say that Achilles gives the tortoise a lead of 1000 feet. Now suppose the tortoise's speed is 1 foot per minute, and Achilles runs at a speed of 1000 feet per minute. One minute after the race begins, the tortoise will have moved 1 foot, and Achilles will have moved 1000 feet. At that point in time, Achilles would be exactly 1 foot behind the tortoise. In the next minute, the tortoise will have covered another foot, and Achilles will have covered another 1000 feet. So after two minutes, Achilles will then be 998 feet out in front of the tortoise. Common sense rules that, since Achilles now leads the tortoise, then at some point he had to have passed the tortoise. Are you then challenging whether or not math can be used to precisely determine that point in time and distance traveled, that brief instant, when Achilles and the tortoise were "neck-and-neck"? side-by-side?

Using the above figures, we can readily see that Achilles and the tortoise will be neck-and-neck at a time between 1 and 2 minutes, and the distance from Achilles' starting line will be between 1001 and 1002 feet. It is also certain that the time will be much closer to 1 minute than to 2 minutes, and the distance much closer to 1001 feet than to 1002 feet.

So how would we go about calculating the exact time and distance? Since few of us actually like math, I will not include it here save for an explanatory LINK that yields the outcome. Using our figures, Achilles will catch up to the tortoise when he has run 1001.001001 feet. And since his speed is 1000 feet per minute, he will be neck-and-neck with the tortoise when 1.001001001 minutes have elapsed. So it would appear, Steaphen, that the claim is substantiated, right, correct, has merit and so forth, don't you agree?

(Yes, I realize that this does not even come close to doing justice to the philosophical side of this near-2500-year-old-and-still-kickin' paradox; however, it does clearly show that those seedy, unphilosophical (aphilosophical?) mathematicians are certain that Zeno's paradox has been "solved".)

 —  Paine (Ellsworth's Climax)  11:36, 12 February 2010 (UTC)

[From Steaphen] - "My discontent' is with the clearly unscientific approach to this issue. You may perform calculations, but whether they have any relationship or correlation with reality is the question. If you've observed astrologers or numerologists, they apply similar thinking and arguments to what I have seen here. Theories and calculations can be cited, but without concrete correlations with the facts, they are of equal merit. The mathematics, irrespective of however strong the illusion, appearance or approximations is irrelevant if it cannot account for the minutia of physical movement.

As far as I'm concerned, the comments here at this site are no more valid, scientific or rigorous than those of astrologers and numerologists. I'm open to theories that show congruency to the facts -- irrespective of whoever espouses them.

The mathematical arguments are, when studied in detail, irrelevant, or as relevant as astrology, in regards to the solution to Zeno's Paradoxes. Earlier I presented my understanding of the deeper nature of reality, which involves quantum superpositions of possibility and nonlocal fields of potentials, all of which will not, now or ever, be reducible to simple geometric analysis. But that is not what this arbitration is about ... it is the clear violation of Wikipedia policy of providing statements and theories that are not supported by Reliable Sources.Steaphen (talk) 12:06, 12 February 2010 (UTC)

But what about the solution (to the dispute, not to the paradox) proposed by Carl? Does it satisfy you? Any objections? Recall it: "Of course these two approaches (mathematical/philosophical) are not in conflict. They complement each other by revealing different aspects of the situation." OK? Or not? Boris Tsirelson (talk) 12:19, 12 February 2010 (UTC)

If I am not mistaken Carls proposal is to state that "(a) some models resolve the paradox admitting infinite divisibility of space-time (the mathematical side); (b) it does not mean that infinite divisibility is a property of reality". I am happy with this distinction, and I assume most people are, since this distinction is already reflected in the article, and has been in there for a long time. Ansgarf (talk) 14:07, 12 February 2010 (UTC)

Okay, Steaphen, I shall continue to look for reliable sources. I realize that WP sometimes frowns upon YouTube as a source, however since the content guideline clearly states that there is no blanket ban against YouTube, and since the LINK I gave above is a video made by a reputable professor of mathematics at U. of Helsinki and Florida State University, perhaps then we could begin with THIS LINK as a reliable source and an inline citation? That web page prominently links to the YouTube video I cited above. Please keep in mind that it is not our job to debate the TRUE vs. FALSE, the RIGHT vs. WRONG, SCIENCE vs. PSEUDOSCIENCE, etc. of any reliably sourced claim. All we must do is agree that the source(s) is reliable. So do you accept

THIS LINK 

as a reliable source for the claim:

"While mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise . . ."

 —  Paine (Ellsworth's Climax)  13:36, 12 February 2010 (UTC)

[From Steaphen] - does the Reliable Source account for/detail/explain the minutia of physical movement? No. Does astrology account for/detail/explain the minutia of physical movement? No. Then include both theories (astrology and mathematics) since "they complement each other by revealing different aspects of the situation."

Mathematics does not, in detail, determine when Archilles overtakes the tortoise. Provide one physicist who affirms that we can calculate such things, at and below the Planck length. The continued inclusion of mathematics (as offered above, and as per related links) is simply bad, incompetent science when applied to the issue of Zeno's Paradoxes.Steaphen (talk) 15:00, 12 February 2010 (UTC)

Please prepare yourself, Steaphen, because your argument is about to be refuted: The RS does NOT have to account for details/minutia of physical movement; it ONLY has to support the claim being made in the article. And just because math may "complement" the pseudoscience of astrology does not detract from the solid gold fact that math ALSO complements, supports, and even validates science, as well. Mathematics indeed DOES, in detail, determine when Achilles overtakes the tortoise, and it can do this to six decimal places for distance and nine decimal places for time. That's pretty precise, isn't it? That's pretty detailed. You won't find any physicists worth their salt who will affirm that anything at all can be calculated at or below the Planck length, simply because the Planck length is, BY DEFINITION, the shortest length that "has meaning". This in NO WAY cripples mathematics for yielding precise, detailed and PRACTICAL results ABOVE the Planck length. And once more, it simply does NOT matter what you or I think about the science, good or bad or competent or incompetent when applied to the issue of Zeno's paradoxes. All that matters is that the source is reliable and that it backs up the claim made in the article -- AND THAT IS ALL THAT MATTERS.

It is not up to me, and it is not up to you whether or not the claim is valid. The only thing that we editors get to decide is whether or not a claim can be reliably sourced. And the claim about the mathematics that, in the eyes of mathematicians resolves Zeno's paradoxes is a valid claim and can be reliably sourced.

 —  Paine (Ellsworth's Climax)  15:55, 12 February 2010 (UTC)

• PS. Would anybody else like to add their opinion about the reliable source I cited? If nobody objects and gives a reason to blackball the source, I shall add it soon to the article.
  • I don't see why we would ever cite a video in this article. But there are plenty of professionally published texts (in particular, calculus textbooks) that discuss Zeno's paradoxes from a mathematical viewpoint. — Carl (CBM · talk) 16:41, 12 February 2010 (UTC)

Great! Perhaps you can slip one or two of those PPTs after the claim in question? And just to provide a focus in case it might be needed, I'll place a {{cn}} template in the section of the article where the reliable source is called for by Steaphen.

 —  Paine (Ellsworth's Climax)  19:16, 12 February 2010 (UTC)

Steaphen: the underlying point of looking at a formalism such as Newtonian mechanics is that the formalism does not account for every possible detai. Neverthless, one can do calculations within the model to see what the model says. For example, when we want to see how high a launched projectile will fly in free fall, we don't ordinarily pull out our quantum physics textbooks. In situations like that, we just use the normal Newtonian equations to calculate it. We often ignore air resistance, too, which is much more important there than quantum effects. It seems to me that your argument would say equally well that we cannot compute how high a projectile will fly without quantum mechanics, and therefore Newtonian mechanics does not actually say how high a projectile will fly.

Similarly, if we just want to figure out when Achilles will pass some point, we can use the Newtonian model to see what it says. Of course the Newtonian model doesn't account for quantum mechanics; that's part of the point of using a model. The Netwonian model doesn't completely resolve Zeno's paradoxes, but seeing how those paradoxes play out in the Newtonian model is relevant to understanding the paradoxes, and it's also important for seeing why the Newtonian model is internally consistent. — Carl (CBM · talk) 16:41, 12 February 2010 (UTC)

Naïve question

Is this helpful? To wit, does anybody doubt that Achilles will overtake the tortoise at

$t_{\text{pass}}={\frac {l_{\text{tortoise}}}{v_{\text{Achilles}}-v_{\text{tortoise}}}}$

and

$l_{\text{pass}}=v_{\text{Achilles}}\cdot t_{\text{pass}}$,

where $t_{\text{pass}}$ and $l_{\text{pass}}$ are the time and distance from the start when Achilles passes the tortoise? Paradoctor (talk) 20:22, 12 February 2010 (UTC)

I don't doubt it, Paradoctor, however when another editor sees the need for a reliable source to support a claim, then I don't see how this can be ignored. I placed the cite-needed template at the precise place in the text that follows the claim that's in dispute just in case any other editors wanted a quick focus. Please note that I've checked the three cites that follow the next word, "Philosophers", and they do not appear to support the math claim.

I do not have access to, nor would I understand very well, the calculus text(s) that would make good, reliable sources, or I'd do it myself.

 —  Paine (Ellsworth's Climax)  20:33, 12 February 2010 (UTC)

'three cites that follow the next word, "Philosophers"': They are not meant to, they relate to the following claim.

As expected, JimWae came up with sources supporting my contention. The challenge has been met. Or does anyone have any source proposing alternative values for $t_{\text{pass}}$ and $l_{\text{pass}}$, Steaphen? Apart from suggesting that physics is so fundamentally wrong that it overlooks the impossibility of motion, of course. Paradoctor (talk) 21:22, 12 February 2010 (UTC)

Well, there again, it's very easy to get off the track here and start talking about the article's content. Seems to boil down to philosophy vs. mathematics/physics (theoretical? or is that too close to philosophy?). At any rate, reliable sources have been found, one has been chosen and added to the article, and hopefully this satisfies editor Steaphen's notable idea, and the POV maintenance tag can be dusted.

 —  Paine (Ellsworth's Climax)  22:50, 12 February 2010 (UTC)

Here are some text sources to choose from: --JimWae (talk) 20:38, 12 February 2010 (UTC)

• http://nongnu.askapache.com/fhsst/Mathematics_Grade_12_Ch40_Differential_Calculus.pdf pg 510
• http://cvs.gnowledge.org/episteme3/pro_pdfs/28-broni-prabhu.pdf p 178
• http://books.google.ca/books?id=QsJKB4V_DmkC&pg=PA43&lpg=PA43&dq=achilles+tortoise+%2Bgraph&source=bl&ots=67boCXfnQR&sig=RK13rCkMrbm7--S1iiHd1wit1qk&hl=en&ei=d0wDS_7kE4fqsQPv_8W4BA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CCEQ6AEwBw#v=onepage&q=achilles%20tortoise%20%2Bgraph&f=false
• http://www.learner.org/courses/learningmath/algebra/session5/part_c/index.html
• http://www.tc.umn.edu/~burc0050/math/achilles_paradox.html
• http://doctorlaismath.com/example2

I think that puts you firmly within the "No" coalition. ;) Paradoctor (talk) 21:22, 12 February 2010 (UTC)

Yes! definitely a "No". Jim, if I had to choose from these best of the best (hard choice, truly), I'd opt for the first one. No, No, don't sweat it, I'll add it in, and you and others can improve it if you feel the need. Thank you very much for your effort and time!

 —  Paine (Ellsworth's Climax)  21:54, 12 February 2010 (UTC)

 Done– That said and done, would anyone object to adding Mika Seppala's video link (a non-YouTube version) to the External links section?
 —  Paine (Ellsworth's Climax)  22:25, 12 February 2010 (UTC)

Add one pushover !vote. Paradoctor (talk) 22:52, 12 February 2010 (UTC)

Thank you all. You have clearly illustrated the process of witch-hanging, heretic-burning in detail. We may expect that onlookers at such spectacles in the past similarly remarked, "a pushover result, she didn't even try to jump on her broomstick while she hung."

Science and reasoning saved us from the superstitions of middle and later ages, but what or who is going to save us from the stupidity and cowardice of the contemporary dark-age of ignorance, dogma and fear? Steaphen (talk) 23:59, 12 February 2010 (UTC)

You're not satisfied. Noted. Can you provide arguments compatible with policy for making changes to the article? Paradoctor (talk) 00:26, 13 February 2010 (UTC)

I hesitate to use the video for several reasons 1>It is slow moving & 2>rather long & 3>the author states in text & voice that there is no paradox. Using basic arithmetic, we can arrive at a time when Achilles will have passed the tortoise. Using elementary algebra (and given sample speeds and distances), we can derive quite an exact time and position (not with infinite precision, however, because all speeds and distances have limited precision) at which A would catch (and after which would overtake) the tortoise. Using variables for speed and head-start distance is maybe intermediate algebra. We do not really need calculus for any of that. Calculus comes in when we want to find the sum of a diminishing geometric series, and Zeno could be counted as an inspiration for the development of calculus. Calculus (or geometric series math) is necessary for the dichotomy paradox, however. As has been pointed out to Steaphen many times, if you think space and time consist of quanta, there is no infinite series & thus no paradox - but he has some resistance to this that seems to involve infinities between quanta (or something like that) that he advocates on his website. There may even be a WP:COI involved. --JimWae (talk) 06:15, 13 February 2010 (UTC)

Okay on the vid, Jim, I understand. As for conflicts and paradoxes and math, all I can say is that if the arrow really can't move, then we are all being tricked by one hell of an illusion!

 —  Paine (Ellsworth's Climax)  21:55, 13 February 2010 (UTC)

Sometimes even knowing that we're being deceived won't get rid of the illusion. ;) Paradoctor (talk) 22:28, 13 February 2010 (UTC)

Grünbaum

It is very strange to me that Adolf Grünbaum's classic text Modern Science and Zeno's Paradoxes is nowhere referenced in the article. Sławomir Biały (talk) 12:50, 13 February 2010 (UTC)

Bibliography

This list is intended to collect references thought to be relevant for the article. Delete entries only when they are blatantly and obviously inappropriate. In general, we want not only to collect useful references, but also be able to check new additions against previous discussions that lead to exclusion. Provide diffs, and update section links when they get archived.

• Grünbaum, Adolf (1967). Modern science and Zeno's paradoxes. Wesleyan University Press. Retrieved 13 February 2010.
• Grünbaum, Adolf (1968). Modern science and Zeno's paradox. Retrieved 13 February 2010.
• Salmon, Wesley C. (March 2001). Zeno's paradoxes. Hackett Publishing. ISBN 9780872205604. Retrieved 13 February 2010.

Samon's book is one of the best on the subject. Huggett, in his article "Zeno's Paradoxes" in the Stanford Encyclopedia of Philosophy [5] writes: After the relevant entries in this encyclopedia, the place to begin any further investigation is Salmon (2001), which contains some of the most important articles on Zeno up to 1970, and an impressively comprehensive bibliography of works in English in the Twentieth Century . Paul August ☎ 14:22, 13 February 2010 (UTC)

Comment by Steaphen

[From Steaphen]: It seems that all editors (excluding myself) at this site lack the ability to ask of themselves one simple question: "is what I am calculating validated by experimental data?" -- "Is my method aligned with the fundamentals of the scientific method, of matching or accounting for experimental data with theory?"

None, based on the above, have followed the basic precept of the scientific method. None of you. Hence my reference to witch-hanging and the like, for none of you have applied sound, scientific principles in respect of Zeno's Paradoxes.

Despite all the clever calculations, none of you have shown that those calculations actually apply to tangible physical reality, at least not in the minutia of physical movement.

Any competent physicist will understand my issue here ... in the minutia of movement physical things do not follow Newtonian laws of motion ... it is only when sufficient quantities and distances are covered that macro-Newtonian physics applies. But in the minutia -- the very point of the paradoxes -- irrespective of the appearance of smooth movement of big things, Newtonian physics fails. That is the simple, undeniable reality of quantum theory and experiment.

You can calculate until all the witches in eternity are hung or burned, but you won't change the fundamental fact that Newtonian physics (and the mathematics it is based on) fails dramatically and conclusively in the minutia of physical movement.

From this site, one cannot but conclude, based on the above dialogue, that mathematicians go sheepishly and quietly into that good night.Steaphen (talk) 03:28, 17 February 2010 (UTC)

I agree with you that Newtonian mechanics fail to accurately account for experimental reality at distances that are small enough so that quantum mechanical effects are not negligible. However, per WP:NOR we can't make a connection in this article between quantum mechanics and Zeno's paradoxes unless we are ready attribute it to a reliable source explicitly making that connection. Gabbe (talk) 12:09, 17 February 2010 (UTC)

The reason that people still study Newtonian mechanics, despite knowing they are not perfectly accurate due to relativity and quantum mechanics, is that Newtonian mechanics are experimentally verified to be in very close agreement with reality for objects of reasonable size moving at reasonable speeds. There is an enormous amount of experimental data that says that the predictions of Newtonian mechanics will be extremely accurate for objects the size of a runner and a tortoise moving at constant slow speeds.

So it makes perfect sense to ask whether Zeno's paradoxes cause an inconsistency in Newtonian mechanics. It turns out that they don't, as explained in many calculus books. This does not resolve the philosophical questions behind Zeno's paradoxes, but it does shed light on them. In the end, that's always the role of formalized models in physics: to shed light on physical reality by investigating what would happen in a system that we understand better than we understand physical reality. — Carl (CBM · talk) 12:54, 17 February 2010 (UTC)

I can see Steaphen's point in that the map is not the territory. That is, a model of reality is not reality itself. That we are able to construct a useful model of reality in which there is no paradox doesn't mean that there isn't any paradox in the real world. Notwithstanding this, we can't let the article make a connection between findings in quantum mechanics and Zeno's paradoxes unless we can find a reliable source willing to do so, as that would be original synthesis. Gabbe (talk) 13:27, 17 February 2010 (UTC)

Right; but to the extent that we think our model of reality is accurate, the reason that the paradox doesn't hold in our model can help us see why the paradox doesn't hold in the real world. This is the role that formal mathematical models (even quantum physics) have in physics, to help us understand reality by letting us study a mathematical model instead. In this case, it turns out that the Newtonian and quantum physics models give different reasons why the paradoxes don't hold, and both of these help us understand what is going on in the paradoxes. I agree that the article should include sources if it mentions quantum physics. — Carl (CBM · talk) 13:33, 17 February 2010 (UTC)

Precisely. Gabbe (talk) 13:34, 17 February 2010 (UTC)

There was an edit conflict, but I'll post a few comments anyway. They were meant as an addition on CBM's earlier comments.

We should keep in mind that Zeno used in his description a classical model of motion, which includes the assumptions that an object is a point, that in between any two points there is another, and that motion is on all scales essentially the same.

There are roughly two ways to deal with the paradox. The first is to use the assumptions made in the model as described by Zeno and show that even if you start from these assumption the numbers add up. And they add up mathematically exact, and not just approximately. An alternative, and complementary approach is to question the assumptions Zeno made. And modern physics does indeed invalidate some of his assumptions.

The first approach is not just historically the most common approach, it is also true to the original argument. If we just point out that his classical model is dated given our latest understanding of quantum mechanics we miss the point Zeno tried to make a few thousand years ago. Ansgarf (talk) 13:59, 17 February 2010 (UTC)

[Fron Steaphen] The witches will still burn, because your filters are simply blinding you to the Reliable Sources who link Zeno's Paradoxes with quantum mechanics. You can make excuses for being bad scientists (by not rigorously applying the scientific method), but that doesn't blind others to noting your behaviours, fears and beliefs. Scientific method has not been applied, or followed. That is the long and short of it (excuse the pun).

Perhaps, given that I have a 'higher' vantage point, I'm able to more easily see the unsupported, and unsupportable assumptions upon which many here base their contributions (a bit like seeing that the Earth is not flat, thus affording one to sail around the globe).

As I have explained previously, and which is repeated here, when we consider the minutia of movement, things get 'weird' -- and one theory, supported by the quantum evidence, is that our physical reality simply 'blinks off' very quickly, many times per second. And that the mathematics (quite valid -- particularly within an expanded framework) merely reveals the superpositions of probabilities that lie in potential, but unrealised in this probability. Thus the mathematics is still correct, it's just that the mathematical expressions are not entirely applicable or representative FOR THIS probability.

If, as good scientists, we take such a theory and bravely ask, "does this explain the facts?" we might be surprised by how well it explains the world we experience. The debate then would shift to a higher-vantage point of considering what else must be going on for that theory to be valid. Then we would enter a region in which we could more accurately and productively understand, explain and work the world we experience.

But alas, it seems there's no real scientists on this site, at least not ones that could be considered bona-fide scientists who openly seek ideas and theories to fit the facts.

"Ah' but you say, 'that would be original content, or POV or conflict of interest' ... or similar (ironically, JimWae took issue suggesting a conflict of interest by me, and this by a mathematics teacher pushing the validity of mathematics to 'solve' the paradoxes.).

As suggested above, it is exactly your bias that blinds you to the Reliable Sources who have quite a different, and better take on the nature of Zeno's Paradoxes.

But of course, you will find arguments why my statement here is wrong, or superfluous or ... whatever. All that you will have demonstrated is your lack of scientific credibility by not seeking theories to fit the facts.Steaphen (talk) 06:11, 18 February 2010 (UTC)

You have a point in criticising the statement "mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise". This is not strictly correct. While it is true in a Newtonian model, in a quantum physical model we can only calculate the expectation value of what their position will appear to be when we make an observation. This is because the value of their position is not a deterministic variable, but a stochastic one. However, in this case the expectation value equals the Newtonian value. The wave function of large, macroscopic objects like tortoises and hominids have very little variance, so for all practical intents and purposes it will appear deterministic when we make an observation.

To be more accurate we could let the article say "In a Newtonian model we can calculate the exact time when Achilles overtakes the tortoise, but in a quantum mechanical model we can only calculate the expectation value of what we will observe this instant to be. This expectation value is equal to the Newtonian value." But I fail to see why such formality is required in this article. How is the reader's understanding of Zeno's paradoxes improved by such rigid strictness? Gabbe (talk) 08:01, 18 February 2010 (UTC)

"How is the reader's understanding of Zeno's paradoxes improved by such rigid strictness?" -- how does the rigid strictness of observing a small curvature in the Earth improve the belief that the Earth is flat?

Within such "rigid strictness" are universes of possibility that are disallowed by standard Newtonian mechanics. That is, in the 'gaps' of physicality (and your perception) lay infinite potentials that are not 'realised' in this probability. No small 'improvement' in understanding.

But again, each of you here will disallow alternative views because none of you are sufficiently disciplined or honest to seek theories that fit the facts.

It is enough that you have been alerted to the error in your understanding; you have stumbled over the facts, and picked up yourselves up as if nothing had happened. Leave it to others to go noisily and confidently into that good night, bringing forth new light.

Ciao Steaphen (talk) 08:59, 18 February 2010 (UTC)

But to "seek theories that fit the facts" is not our task as Wikipedians. Our task is to report what others have concluded. Wikipedia is not the venue to follow the scientific method. Alternate views are only admissible in articles if they are

1. attributable (per WP:A)
2. not an instance of undue weight (per WP:UNDUE)

In other words, being true is not sufficient for including a statement per Wikipedia's policies. Gabbe (talk) 10:25, 18 February 2010 (UTC)

Hold it, pardner! Verifiability is a central concern of the scientific method: "Scientific method refers to " ... " or correcting and integrating previous knowledge." You could say that the job of scientists is to produce (scientific) libraries. The job of encyclopedists is to provide a useful guide to such libraries. What we don't do is produce substantially new knowledge (there is encyclopedic research, of course). Paradoctor (talk) 10:43, 18 February 2010 (UTC)

(continued at my talk) Paradoctor (talk) 11:29, 18 February 2010 (UTC)

There is more to the scientific method that empiricism. To use logic to check whether an argument or model is logically and mathematically sound is an essential part of the scientific method. To experimentally check his assumptions and predictions made by models is is another. Even though experiments are thought to be essential to the scientific method, there is nothing unscientific about the former, in Zeno's case in showing logically and mathematically that an apparent contradiction isn't a contradiction. You cannot get more rigorous than that. Just to make it explicit.

• It is a verifiable fact that Zeno assumed that the tortoise's and the runner's positions are points (He did not use quantum superpositions.)
• It is a verifiable fact that Zeno assumed that inbetween every two points is another point (He did not assume a Planck length)
• It is a verifiable fact that Zeno assumed that the entire distance that the runner has to complete is the simple sum of the smaller distances. Zeno did give no special rules for small distances. (No discrete quantum leaps)
• It is a verifiable fact that under these assumptions the sum is finite. Any textbook will do as reliable source.

There might be more to Zeno's paradox, but that doesn't take away that this kind of formal reasoning is not only consistent with the scientific method, it is an essential part of it. For the tortoise and the runner as described in the paradox you can compute when the latter passes the former. Ansgarf (talk) 12:58, 18 February 2010 (UTC)

BTW: I second Gabbe's bold edit, even thought a previous version of the deleted sentence was inserted by me. If we take out the particular link between QM and Zeno from the Proposed Solutions section, since there are no reliable sources for that particular claim, then it should also be removed from the introduction. Ansgarf (talk) 13:09, 18 February 2010 (UTC)

Dear dear Ansgar,

There is no evidence whatsover that Zeno assumed anything. There is only historical records of what others said of him. The only facts relating to Zeno is what is currently observable, in existence now, and that is stuff written on paper or stone or whatever, which we may assume was written by someone, but we have no evidence of who wrote that material, other than other bits of paper or stone 'saying' who wrote what.

You appear to lack even a modicum of understanding concerning the nature of 'facts'.

As for the other, dear me, you lack the simplest of understanding. You may calculate whatever you want, but there is absolutely no evidence (or tight correlations) between what you are calculating and what you assume those calculations relate to, or are correlated with. Could be angels on pinheads, for all the evidence I've seen.

From the contributions that have been provided by others, all of you would be accepted into the flat-earth society, or the brethren in Galileo's time, because you each have opinions and superstitions that are unfounded or unsupported by, or incongruent with the facts.

Is it not galling for you to realise that readers of this page will have solid grounds for recognising that you're no better than the priests in Galileo's time, or flat-earth believers -- due to your blind adherence to superstitions that cannot be verified in, or strongly correlated with fact?

Steaphen (talk) 00:16, 21 February 2010 (UTC)

But Newtonian mechanics has been thoroughly verified by centuries of experimental evidence. For object the size of a tortoise or runner moving at the speeds typical of these things, the experimental evidence is that the predictions of the Newtonian model will be extremely accurate. It's hardly a "superstition" that the objects we observe in everyday life act in accordance with Newton's laws. — Carl (CBM · talk) 00:29, 21 February 2010 (UTC)

Dear Ansgar,

The approximate value and efficacy of Newtonian mechanics has never been questioned or disputed.

Zeno's Paradoxes involve explaining movement in detail, in the minutia, which involves quantum mechanics, for all objects, irrespective of size. To say otherwise is just sloppy thinking, and that's being polite.

This page will, or should prove to be a classic textbook example of sloppy thinkers believing opinions and superstitions as 'fact'. The wonderful irony is that the contributors are supposedly scientists. That will be the icing on the cake for students in centuries to come. Delicious ironies that beggar belief.

"And to think", they will say, "that they had their fingers on the button. How on earth did civilisation survive." (that's the optimistic probability that may not eventuate, due to the ignorance and superstitions of this age.)

To highlight the irony: The extent to which the Earth is flat is the extent to which Newtonians mechanics (and the mathematics thereof)solves Zeno's Paradoxes. Both are crude limited-dimension perceptions of a deeper multi-dimensional reality (just like a motion picture film provides a compelling and believable 2D illusion of a 3D reality).

The illusion and crude efficacy of Newtonian mechanics has never been disputed.

You've continually been distracted by the action on the screen, not asking questions that would lead you to the projector, then to the director, the production process, and marketing thereof.

Steaphen (talk) 01:05, 21 February 2010 (UTC)

"Zeno's Paradoxes involve" ... "quantum mechanics": WP:PROVEIT Paradoctor (talk) 02:07, 21 February 2010 (UTC)

It is, once again, highly disingenuous of you to ask that I prove something that is not in contention. What is in contention is the use of Newtonian mechanics in solving Zeno's Paradoxes. The onus is upon you, and the rest of the brethren to prove correlations (at and below the Planck length) when discussing movement of physical things. Do any of you have even an ounce of scientific integrity? If those correlations of theory with fact involve quantum mechanics (which I believe does) then so be it. But start first with integrity, honesty and discipline, then see where that leads you.Steaphen (talk) 02:13, 21 February 2010 (UTC)