Talk:Zeno's paradoxes/Archive 4

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Archive 1

Archive 2

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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)

(Ansgar) 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)