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Starting clean

I think it's worthy of a B+ Now.....64.6.88.31 (talk) 17:22, 24 May 2008 (UTC)

Let's start the talk page clean, alright?Le Blue Dude (talk) 19:05, 4 May 2008 (UTC)

It seems to be starting on it's way to being a good, simple, article again. Whoot! 21:04, 13 May 2008 (UTC) —Preceding unsigned comment added by 64.6.88.31 (talk)

I agree. The biggest problem with the old version was that it argued fervently against the calculus solution (which led me to make all those long posts on the old discussion page). Now the article treats the "issues with the calculus solution" in a fully encyclopedic manner: it states that there are people who think that there are issues, and something about why they believe that, but it doesn't take a stance in the matter. Well done. Sthinks (talk) 23:49, 13 May 2008 (UTC)

Question

"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. If this assumption is challenged, the infinite sequence of events is avoided, and the paradox resolved."

Can someone explain how matter has the special property of being able to translate itself to an adjacent point in space from rest? I think there's an assumption inherent somewhere here. —Preceding unsigned comment added by 99.225.160.154 (talk) 05:03, 6 June 2008 (UTC)

I'm with you, and I think your question closely resembles Zeno's question as posed in the Arrow paradox. Indeed, Zeno raised some deep metaphysical questions in general about motion that don't seem to have been resolved. That is, as engineers we can talk about motion as simply being at different points in space at different points in time and, as such, we can make all kinds of predictions about when and where some object is going to be, often using calculus. However, what goes on metaphysically that makes this work is not clear at all. For one, there is the problem of the infinite sequence of points, and for another, is motion really a point-to-point kind of process? Indeed, is there even anything in reality corresponding to our notion of a 'point' in the first place? —Preceding unsigned comment added by 72.226.66.230 (talk) 13:12, 6 June 2008 (UTC)

Phraseology

"Aristotle remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small.[8] Such an approach to solving the paradoxes would amount to a denial that it must take an infinite amount of time to traverse an infinite sequence of distances."

I would hazard to suggest rephrasing the second sentence to read "Such an approach to solving the paradoxes would amount to a denial that it must take an infinite amount of time to traverse an infinite sequence of divisions of a finite distance." —Preceding unsigned comment added by 128.244.96.176 (talk) 04:24, 14 June 2008 (UTC)

Painting Pictures

Mathematical solutions aside, let's see if we can't expose any flaws intuitively.

Dichotomy:

Take a video of a person walking 60 yards in 60 seconds. Start replaying the video and pause it when the person has walked half the distance. Wait five seconds. Resume the video and pause it again when the person has walked half the remaining distance. Wait five seconds. Continue ad infinitum. Will you ever see the person reach the 60 yard mark? No. Will you ever finish watching the video? No. Does that mean that the person never really walked 60 yards in 60 seconds? No.

(Note: the above assumes that you have an infinitely fast thumb on an infinitely responsive pause button!)

Arrow:

Q: What would it be like to live in a universe where there are only three spatial dimensions and no time dimension? A: Motion would be nonsensical (how can there be distance divided by time when there's no such thing as time?). This is effectively what Zeno is asking us to consider when he begs the question of time being made up of an infinite sequence of timeless "now"s (an infinite sequence of timeless "now"s can certainly be located in time - but since their temporal sum is zero is it possible for them to constitute time?). Not only that, he's asking us to accept that his thought-experiment appearance of "rest" in a timeless "now" is more real than the empirical-experiment appearance of motion in a continuous-time sensing of the world.

While we're at it, let's try another tack. The arrow paradox presupposes continuous space and an infinitely discrete time where each "now" has no temporal extent and the arrow occupies a continuous spatial extent equal in size to its physical being. Let's reverse that and presuppose continuous time and an infinitely discrete space where each "here" has no spatial extent. For any given "here" through which the arrow's (apparent) motion takes it, there is a temporal extent associated with the arrow - that is, the arrow occupies the spaceless "here" for the amount of time it takes for the (apparent) motion of the arrow to carry it through the spaceless "here". Rationalize (literally) these two artificial perspectives - the spatial extent of the arrow in a timeless "now" with the temporal extent of the arrow in a spaceless "here" - and we get a measurement of: motion. —Preceding unsigned comment added by 128.244.96.176 (talk) 05:17, 14 June 2008 (UTC)

While I've been fascinated by the idea that that the Galilean priests who refused to look through Galileo's telescope have reincarnated into contemporary times (replete with their refusal to look through the 'quantum telescope' and offer theories to match observable reality), it seems you've made an effort to look, and to question.
However, your "rationalising" is, in my opinion, the point at which you paused in your questioning. Rational thinking and reason is derived from the Latin ratio. In a sense, to reason is to separate and compare (to objectify), and such objectification (by definition) won't get you within a hoot or a holler of "timelessness" or "spacelessness" (for how are you going to separate yourself from no-thing?). But you have at least questioned without referring back to the Gospels (of "science").
While I may make light of the general refusal to "look through the 'quantum' telescope" it is, I think, highly pertinent to remember that the human race has grown through the art of looking and questioning. So for all our sakes, I encourage you to continue questioning.
Steaphen (talk) 15:12, 14 June 2008 (UTC)
"... derived from the Latin ratio ..." - and it is precisely this limited literal sense that I intended ... the ratio of the spatial extent of the arrow in a timeless "now" to the temporal extent of the arrow in a spaceless "here" is distance/time - that is, the speed of the arrow. It seems to me that Zeno strips away an entire dimension under the guise of colloquial language ("now"). I thought it only fair to complete what Zeno started by stripping away the other three dimensions and seeing where that led (whether I did a good job is open to question). And what's interesting is that in re-integrating these two orthogonal projections of space-time through an operation as simple as the ratio, we regain what Zeno asserts is lost: motion! ;-) —Preceding unsigned comment added by 128.244.96.176 (talk) 20:19, 14 June 2008 (UTC)
By my rationlization :) working with spacelessness and timelessnesss, on a logical basis reveals the following: Starting with velocity=distance/time (v=d/t), and taking d=0 (since spacelessness presumably means zero distance) and t=0 (same again for timelessness) then you are suggesting that velocity v=d/t (e.g. of an arrow) is somehow derived from dividing zero by zero?
Once again, I think most contributors on this and the preceding "archived" page have what I call "GPS" .. Galilean Priest Syndrome. Here's a thought experiment. Imagine that the priests in Galileo's time were intelligent people (perhaps equal or greater than our intelligence). Why might they have, despite their intelligence, avoided looking through the telescope? The thought experiment is basically asking why might quite sane, intelligent folk avoid the scientific method: observing evidence and then working towards a new theory to fit said evidence?
As I previously made quite clear on the "archived" page, Zeno's arrow, hare or runner MUST inevitably pass through quantum scale increments, since by definition, geometric series require continuity ad infinitum. We know from quantum physics research that simple geometric continuity ceases. Accordingly, the standard mathematical treatment as provided by others at this forum, does not fit observed reality. It is indicative of GPS that no one has once made any attempt to address that basic flaw ... that of the discontinuation of continuity (and thus of the applicability of standard mathematical solutions as provided on this and the main page).
Your theories do not fit the facts. That is fertile ground for all manner of modern superstitions that are counterproductive to advancing the human race.
Steaphen (talk) 22:58, 20 June 2008 (UTC)Steaphen
Actually, what I propose simply reinstates time into Zeno's arrow "paradox". Zeno's arrow paradox is the t=0 projection of space-time. I merely illuminated the complementary d=0 projection of space-time and then re-integrated the two projections. The reason Zeno's arrow paradox looks like a paradox in the first place is that Zeno strips away the time dimension with a sleight of hand - he relies on imprecise colloquial language to hide the fact that an infinite sequence of t=0 "now"s can only exist within time and cannot possibly constitute time. That is, Zeno shows you a t=0 projection of space-time and rightly asserts that motion is nonsensical (in such a projection), but he weasel-words things to lead you to believe that he's talking about normal space-time. Again, I just called his bluff and shined a light on the complementary d=0 projection of space-time.
The calculus, on the other hand, doesn't solve Zeno's arrow paradox - it's just not relevant. Calculus deals with limits, and so can only approach Zeno's t=0 case; calculus looks at things as t tends toward 0, and so space-time remains fully intact (there is no t=0 projection).
That said, I see that you assert that Zeno's paradoxes "MUST inevitably pass through quantum scale increments". Okay, fine. But let's also illuminate the fact that many of Zeno's paradoxes pass through macro-scale increments, as well. The implication then is that quantum mechanics is relevant to Zeno's paradoxes at best only a small fraction of the time (the small fraction associated with quantum-scale increments). But again, I don't think you need to look beyond Zeno's sleight of hand in order to resolve the arrow paradox.
On the other hand, that very small fraction of relevance may be of critical importance to Zeno's dichotomy paradox. A space-time that is infinitely divisible by two into smaller and smaller halves is the mathematical model that Zeno shows us in order to "demonstrate" that motion is impossible. But this time he's begging the question. A more scientific way of looking at this is to start by asking the question, "Is space-time continuous?" Zeno's paradox can be seen as a counter-example, and thus by reductio ad absurdum space-time cannot be continuous. A smallest (quantum) increment is then potentially where the continuous-space-time mathematical model "bottoms out". (Much like how a fractal-geometry model of Britain's coastline "bottoms out" at a grain of sand.)—Preceding unsigned comment added by 97.73.64.154 (talk) 04:56, 24 June 2008 (UTC)
I was intrigued to note that your original reply (sans the last paragraph above) was eventually augmented with an astute observation concerning fractals.
Fractals, in broad terms, reflect various interfaces between the infinite and the finite - which of course is highly relevant to resolving Zeno's Paradoxes.
It seems to me that your next step would be to question what might lay between the various "grains" of physicality.
Steaphen Pirie (talk) 05:06, 11 January 2009 (UTC)
Director
Belief Institute
see also "Congruent Solutions to Zeno's Paradoxes"
Further to your excellent analogy of "grains" of space-time, is this extract from a recent NewScientist article (universe-as-hologram) -- :
"According to Craig Hogan, a physicist at the Fermilab particle physics lab in Batavia, Illinois, GEO600 has stumbled upon the fundamental limit of space-time - the point where space-time stops behaving like the smooth continuum Einstein described and instead dissolves into "grains", just as a newspaper photograph dissolves into dots as you zoom in."
Steaphen (talk) 10:11, 17 January 2009 (UTC)
which echos similar commentary from around 10 years ago...
"We know now, however, that it is Einstein's theory that ultimately fails. On extremely fine scales, space-time, and thus reality itself, becomes grainy and discontinuous, like a badly overmagnified newspaper photograph. The equations of general relativity simply can't handle such a situation, where the laws of cause and effect break down, and particles jump from point A to B without going through the space in between."[1]Steaphen (talk) 06:24, 20 February 2009 (UTC)

I don't get it

From the article: "Yet another proposed solution, that of Peter Lynds, is to question the assumption that moving objects have exact positions at an instant and that their motion can be meaningfully dissected this way. If this assumption is challenged, motion remains continuous and the paradoxes are avoided"

I don't understand how motion remains "continuous" if objects no longer have exact positions at an instant. I can make sense of the notion of "continuous motion" if objects do have exact positions at exact moments: continuous motion would then be that the objest goes through positions/moments that can be quantified by locations on a real number line, or at least that between any two positions/moments there is another position/moment. But when the requirement of objects having exact positions in space or time is dropped, I can no longer make sense of the notion of "continuous motion". But, of course, just because I can't, doesn't mean that there isn't a way to make sense of this. Can anyone make sense of this? —Preceding unsigned comment added by 128.113.89.96 (talk) 15:13, 23 August 2008 (UTC)

A Solution?

These arguments don't work because things have thickness. One object will catch up with the other object once the distances you keep dividing in half get less than or equal to their thickness. Or am I saying something stupid? —Preceding unsigned comment added by 71.135.44.251 (talk) 03:49, 21 September 2008 (UTC)

I don't think you're saying anything stupid. Since Zeno's argument treats the objects as points, and since actual objects have thickness, indeed a little more work needs to be done in order for Zeno's argument to apply to the motion of real objects. However, one relatively easy thing to do would be to consider (at the various points in time) the point in space of the object that is closest to the destination. If you do that, then Zeno can still point to the existence of an infinite sequence, and from there his argument can proceed as normal. So, I don't think that the fact that real objects have thickness solves anything. —Preceding unsigned comment added by 128.113.89.96 (talk) 17:26, 25 September 2008 (UTC)

Perhaps whether or not there are infinite points along the path is irrelevant. A point in space is just that, it does not itself have mass (and so we can easily wrap out minds around there being an infinite number of them) or move (rather, objects move relative to these points). But even if we think of a moving object as not having mass (ie, not having thickness), there could very well be a limit to the smallest distance that objects can move (like the Planck length).

If that were the case, the "object will catch up with the other object" when the "halfway" distance is less than or equal to the absolute minimum distance that an object (even one without thickness) can move. The infinite sequence relies on the assumption that this minimum distance will always be less than the next halfway length, or that such a minimum does not exist. —Preceding unsigned comment added by 68.8.181.178 (talk) 08:09, 16 July 2009 (UTC)

A question?

This is more of a question than anything else, but given that in general the simplest solution to a problem is to be preferred to the more complex one, could it not be the case that Zeno (and Parmenides) were in fact right, and that motion is (simply) an illusion? (If that's wrong, why is it wrong?) Thanks! —Preceding unsigned comment added by 79.97.236.37 (talk) 05:24, 30 December 2008 (UTC)

I think time is the illusion. I am actually intrigued by what a lot of spiritual teachers are saying, that time does not exist and that it is really just a mental construct. I actually read a pretty interesting argument about time on youtube (surprise!) where two guys were discussing how cause and effect is impossible because for one "event" to affect another, they would have to exist in the same, exact moment in time. But if time exists, then each are in different moments in time (however finely divided..), so how can they affect one another? And even if time could be divided into infinitely small segments, then just like the argument 0.999... = 1, we could say that time would never pass (because each segment basically approaches zero). And if time could be broken down into discrete lengths, then the "jumps" between different moments wouldn't make sense, and cause and effect would be broken because each event is fundamentally separated from the other. When you observe reality, you can find no *direct* evidence that time exists, there is only a continuous present moment (I don't know what this means in terms of allowing for motion either, though).

So basically, I think there is a whole new order of reality that we don't understand yet (a greater reality), or are somehow oblivious to, but that currently the "theory" that "time" exists is impossible and as far as I see it, basically just a mental construct (i.e. you never experience past or future) 142.150.72.132 (talk) 16:31, 15 January 2009 (UTC)

Quantum zeno effect

We should discuss the pros and cons of including this section (rather than edit warring over it). Any thoughts? hgilbert (talk) 17:06, 4 March 2009 (UTC)

Good idea. I think the section should go, because I think it isn't related to Zeno's paradox. Zeno's paradox is fundamentally about infinite sequences, whereas the Quantum Zeno effect is not. —Preceding unsigned comment added by 67.244.167.93 (talk) 03:02, 13 March 2009 (UTC)

Why resort to calculus or infinite series?

The Achilles/Tortoise problem is exactly the sort of thing I would expect to see on a Physics I exam, and the solution can be found using algebra and not calculus or infinite series. I don't think this simple solution is adequately described in the article even though the results are mentioned. A more detailed explanation is below, but maybe it could be shortened for the article.

Using the numbers currently in the article we can form two equations. One equation for the X position of the tortoise (Xt) and the other for the X position of Achilles (Xa). Both equations are with respect to time, t.

The tortoise starts out 100 feet ahead and runs at 10 feet per minute: Xt = 100 + 10*t

Achilles runs at 100 feet per minute: Xa = 100*t

Assuming we are neglecting time dilation due to their different speeds and the issues with simultaneity these two share the exact same time, t. We want to know how long it will take for Achilles to reach the tortoise, when Xt = Xa. Setting the two equations equal we get:

100 + 10*t = 100*t
100 = 90*t
t = 100/90 = 10/9 = 1 + 1/9 = 1.11111... minutes

All we would have to do to make Achilles arrive at the tortoise at an even 2 minutes is set the tortoise's lead to 180 feet instead of 100. Doing this may make the numbers a little more clear since some people may be confused by the infinitely repeating decimal. I would have added this explanation to the article myself, but I figured I should check the talk page first.

If you graph the two equations it's plain to see the point where Achilles overtakes the tortoise. You can pick as many points along those lines as you want and call each segment a task, but it doesn't change the fact that the lines intersect. We know that Achilles moves at 100 feet per minute, this 100 feet can be divided into infinitely many sections but he will still traverse it in 1 minute. Using the given data the solution is straightforward. The only way this solution can be false is if one of the givens are false, in which case this problem is irrelevant. —Preceding unsigned comment added by 97.104.127.235 (talk) 00:01, 15 April 2009 (UTC)

Hi. The third paragraph under Proposed Solutions in the main article provides the kind of calculus based solution you are proposing. This is indeed the most common way in which people react to Zeno's paradox. But the article also points out a problem with this kind of solution, which is that it really doesn't get at the heart of the paradox. To be specific, calculus will tell us where and when Achilles will overtake the Tortoise, but it doesn't explain how this point in space and time can ever be reached, and it was the latter that Zeno as concerned about. Put another way, calculus gives us the exact time and location of Achilles overtaking the Tortoise if such an event were to take place, but the problem is that Zeno gave us an argument that concludes that this event cannot take place. Now, of course, all this sounds pretty ridiculous, as we know that this event will take place! But please understand that that is exactly what makes this a paradox, i.e. how is it possible to have a logical sounding argument with such an obviously false conclusion?!? And the answer to that is that there must be something wrong with the argument, either in its logic, or in its assumptions. So, any resolution to the paradox will have to figure out exactly where Zeno's reasoning is going wrong. A solution has to point to some assumption or to some inference that is mistaken. And unfortunately, it doesn't look like calculus points to any such flaw in Zeno's argument. It merely provides us with a separate line of reasoning (a calculation, really), that verifies that Achilles will overtake the Tortoise. But we already knew that. And, much more importantly, it doesn't question any of the inferences or assumptions made by Zeno. So, it doesn't solve anything. But to make things more complicated, there is in fact a version of Zeno's argument you will often hear, and in which there is an obvious flaw, and where calculus can be used to point out that flaw. This is where near the end of the argument, it says something like "and because Achilles needs to do infinitely many things, each of which takes some finite amount of time, it will take him an infinite amount of time to do these things, and so he will never overtake the Tortoise". Now in this line of reasoning is an obvious flaw, as it assumes that the sum of an infinite number of terms needs to be infinite, which calculus can easily show to be incorrect. And I have to believe that this is why so many people believe calculus provides a solution to the paradox. But, this version of the paradox misrepresents Zeno's argument. Zeno would simply proceed at the previous point with "and because Achilles needs to do infinitely many things in order to overtake the Tortoise, he cannot, because you simply cannot reach the end of an infinite sequence; by definition, you can't finish doing infinitely many things (sequentially that is, but that is what we are indeed dealing with in Zeno's paradox)". Of course, at this point people will say: "Wait a minute, but you can do an infinite number of things, simply do each thing at half the time you did the previous thing. Again, calculus will then show that if you do the first thing at t = 1, then you will have done an infinite number of things at t = 2". But again this response doesn't work, because it assumes that time is able to progress to t=2 even as there are an infinite number of points of time t = 1, t = 1.5, t = 1.75, for time to go through, i.e. you would have to assume that an infinite sequence can be finished in order to show that an infinite sequence can be finished. So this is a circular argument. But this also explains why some other people propose as a solution to Zeno's paradox that not all of these mathematical points in time have a counterpart in real life, i.e. that time (and space) are not continuous, as that would avoid getting into infinite sequences in the first place. —Preceding unsigned comment added by 67.244.167.93 (talk) 12:41, 15 April 2009 (UTC)
Fascinating to watch Galilean Priest Sydnrome at work here (Douglas Adams explained it wonderfully with his Somebody Else's Problem). Okay, some suggestions:
1. Begin with evidence from quantum physics (e.g. little things, ipso facto big things like spaceships, cricket pitches, arrows & hares etc jumping around without travelling the space in between).
2. Surmise, reasonably, that space-time is not infinitely divisible (since quantum theory indicates otherwise, and besides, uhm, like where's the physical evidence to show that it is infinitely divisible, aka perfectly geometrically continuous). Okay now the fun bits...
3. Imagine (if you will) a dimension that is, and will remain "immathematical" (ie. the infinite). Next, since our physical reality appears fairly stable and solid, assume it must somehow be 'cycling' into actuality exceptionally fast, like ~10**whatever times per second to give the comforting illusion of stability and order. The actual figure is not important. In other words, surmise some process cycling us through immathematical -> mathematical, back into immathematical. Now, since we're obviously doing this 'cycling' along with everything else, what do we notice about our everyday experiences that might suggest some mechanism for this process? Hint: where do thoughts come from? Brain. Wrong (mostly), since thoughts require firing of neurons, which require rising potentials & collapsing of wave-functions -> waves -> future ("everything in the future is waves"/Sir Bragg). Physical things e.g. neurons can't be causing prephysical possibilities to occur and to 'congeal' into whatever we're currently thinking ... such as what you thinking about this post. What's really causing you to think what you think? How do we tap and work prephysical possibilities? 2nd hint: check out Dr Damasio's work.
While I'm being fairly flippant here, it behoves all of us to reflect on what results we're inviting into reality by sticking with mechanistic cause-effect beliefs. So many wonderful potentials being wasted, ignored and denied through allegiance to outmoded belief-systems. We're capable of far more than what we think and we do ourselves (and others) an immense disservice by expecting that we can entirely count/calculate that which will remain uncountable (as Einstein remarked, not everything that counts can be counted, not everything that's countable, counts).
You're able to follow my comments in more detail at twitter.com/beliefdoctor or at The Belief Doctor
With good wishes, Steaphen (talk) 05:07, 19 April 2009 (UTC)


This problem essentially reduces to "is motion possible" since any motion can be thought of an infinite series of smaller motions. If we are given that there is motion then it follows that infinite series are completable. The point I tried to make earlier (towards the end of the first post in this section) is that if we are given that there is motion then there is not problem, if we are not given that motion is possible then that is the problem we need to solve and we can forget the tortoise stuff. If motion is not given as possible then I think the rest of the problem is just fluff. 97.104.152.15 (talk) 23:26, 27 April 2009 (UTC)
Well, there is certainly a large group of people who regard Zeno's paradox as one about the possibility of motion. The paradox according to these people is that Zeno gives us an argument against the possibility of motion, while at the same time motion certainly seems possible. To resolve that paradox, you either have to agree that apparently motion isn't possible after all, or you need to find a flaw in Zeno's reasoning.
However, a second group of people don't regard Zeno's paradox as a question of "is motion possible", but rather as a question of "how is motion possible". And now the paradox is that while many people think of motion as an infinite series of smaller motions (you seem to be one of those), Zeno argues that under such a view of motion, motion becomes impossible (which, by the way, goes directly against your claim that if motion is possible then infinite series can be completed), and since motion is possible (on this view, the possibility of motion is indeed a given), this view of motion is incorrect (and so motion is a given, but we also have a problem, which goes directly against your claim that if motion is a given, then there is not a problem). In short, the paradox is while we see motion as an infinite series, Zeno argues that that cannot be what motion is like. To resolve this paradox, you either need to agree that apparently motion is not an infinite series of smaller motions (for example, maybe space and time are not continuous), or you need to find a flaw in Zeno's reasoning.
Well put. However, I would suggest going further, by accepting the enormous successes of calculus, and standard geometric approaches as pointing towards validity within some deeper, or expanded context. In other words, we accept the power of infinite series, but we don't necessarily assume they apply exclusively to our physical system. The enormous, unparalleled success of quantum theory rests on the 'and' operative (e.g. Feynman's Sum Over Histories approach, reliant on summations of history A and history B and ... all alternative paths, not one-track Newtonian mechanics).
With an expanded understanding, we can recognise the error in attempting to undermine Zeno. He was right, motion is impossible if one assumes perfect continuity of our physical space-time. If that weren't the case we could perfectly track and predict itty-bits of stuff, without any problems. Plus we wouldn't be seeing the experimental evidence of quantum mechanics. In the end, Zeno wouldn't have had a leg to stand on. (Please excuse the pun)
I think the reason for the clear examples of GPS (above) is that without that expanded framework of understanding, many will hang on to their limited (one-track, one history) world view, despite consistent evidence that their belief-system is no longer congruent with reality.
The worthwhile question then becomes, how do those who are constrained by their beliefs, step into a new abyss, one that cannot be entirely reasoned, or analyzed, and do so without going insane (as many inventors, creative scientists, artists, writers, entrepreneurs, leaders and deep thinkers have done, and do). This is not a trivial consideration or question. Those who remain locked within the old Newtonian one-track, one-past belief system (and who rest on the validity of a mechanical world-view) are particularly in danger ... as exampled by the experiences of Cantor.
This is not to suggest that all artists, writers, creative entrepreneurs and leaders navigate the abyss with ease and impunity. Merely that they at least have sufficient faith to step and explore, rather than resting on top (not even near the edge) criticizing those who are in amongst it, feeling their way, hoping to report back their discoveries for the benefit of one and all.
Yes, some (artists) go too far, too deep and stay too long in that great chaos, and don't altogether make it back, but they at least acted on their intuitions.


Actually I wasn't saying that I believe motion involves an infinite series of smaller motions, but that was brought up during this discussion and I wanted to address it. Someone argued against my earlier post using that idea. I wouldn't be all that surprised if space-time was quantized.
The poster immediately above me mentioned quantum mechanics, I don't have a thorough enough understanding of quantum physics but perhaps part of the answer to the paradox lies in the fact that at the quantum level determinism disappears and the locations of particles becomes probabilistic. Particles don't necessarily need to travel the distance in between two locations, there is a certain probability that they will simply appear in the new location. The scale at which particles jump instead of travel normally could be seen as the point where the "infinite series of smaller motions" idea breaks down. 97.100.232.24 (talk) 20:09, 29 April 2009 (UTC)

Quantized spacetime, infinite sequences, and the state of this article

See and feel free to contribute to the extensive discussion of this important topic at /Quantized spacetime. The discussion has unfortunately grown too long for the main talk page; please continue it on the sub-topic page above. hgilbert (talk) 11:12, 11 July 2009 (UTC)

For those interested in a condensed version of the discussion in the above section, we may boil down the issue at hand as a failure to recognise the natural reduction of dimensionality involved when attempting to explain, portray or describe any phenomena or experience.

For example, a motion picture film on a screen is a 2-dimensional representation that might portray the general flow of actual physical events, such as a car-chase. But viewing the film can not substitute the rich, sensate experience of actually being in that car-chase. The sights, smells, forces and accelerations of real life are only vaguely hinted at in any film.

Similarly, our lived 3 or 4-dimensional physicality is a reduction of a deeper multidimensional meta-physicality, which is only hinted at in our daily physical lives. Artists, writers, sages and others who succeed in feeling this reality intuitively know that our physicality is only a limited reflection of deeper meta-physical dynamics and potentials.

Much mention is made of infinite series in regards to solving Zeno's Paradoxes. These series echo a deeper base or ground from which only limited "frames" (pops, pulses, coagulations, choices and experiences) occur in physicality.

The efficacy of calculus and mathematics is not the issue ... the issue at hand is to realise that they (the infinite series solutions) echo or reveal how our limited-frame world is, and will continue to be an on-going reduction or congealment of a far richer, multidimensional meta-physical existence. The experimental results of quantum physics reveal a limited, or finite-framed actuality reduced (or "collapsed") from infinite possibilities.

To suggest that we tangibly (in literal terms) experience this infinite-dimensionality is to suggest that watching a film is the same as living the experience portrayed by the film.

Just as a film of other lifestyles or circumstances can hint of possibilities that we ourselves might wish to live, so too do the mathematical solutions hint of the underlying possibilities and potentials not yet physically experienced.

Good wishes
Steaphen (talk) 09:46, 7 July 2009 (UTC)
Belief Institute

Infinity

There is absolutly no proof that a infinate sequence of points exist, one could argue that for an object to get from A to B it would have to pass an infinate amount of points, and therefore it would require infinate time. This is wrong however, consider an object leaving A, as it changes from from motionless to moving it must reach the first point. Likewise when it arrives at B it changes from moving to motionless and therefore must reach the last point. The infinate number of points does not exist in reality, just in the mind 193.120.116.183 (talk) 00:23, 28 May 2009 (UTC) shane mc donnell

That reality contains infinitely many places or instants has never been disproved, either. First or last points in the sense you use them do not exist, and arguments for the impossibility of changing between motion and rest are in the article. Regards, Paradoctor (talk) 08:19, 28 May 2009 (UTC)

Infinity . . .

Does the fact that it has never been disproved make it any less probable? If so, one could argue for the existence of lepracauns, goblins and fairies also! The arrow paradox only works if you remove the element of time, the idea of motion being impossible without time is no paradox, simply common sense. The clever wordplap may lead you to think the time has simply reduced, when in fact it has been removed completly 193.120.116.147 (talk) 19:43, 29 May 2009 (UTC) shane mc donnell

Anon, I don't know how long you've been around, but there are a lot of rules on Wikipedia. These may seem daunting at first, but you can always ask for help, and the better you get to know the rules, the better your editing experience will be. You may want to start here. The statements in your above comment do not appear to come from any reliable source, and thus should not be discussed in here. If they do come from a reliabe source, please tell us from which one, so we can start discussing how to integrate them into the article. Regards, Paradoctor (talk) 21:35, 29 May 2009 (UTC)

Not seeing the trees for the forest

It seems many have difficulty understanding the essential dilemma posed by the advances in quantum theory in relation to Zeno's Paradoxes. Some respondents at this website have even suggested that quantum physics has “nothing” to do Zeno's Paradoxes.

Zeno's observations concerned the movement of physical things such as arrows, runners and the like.

The use of Newton's or Leibniz's calculus (based on infinite series) was and is used to great effect to track and predict the movement of everyday objects, such as an arrow as it travels along its trajectory.

The efficacy of such tools (differential/integral calculus) is taken to mean that such tools are entirely sufficient for explaining the full and complete nature of physical movement.

This appears to be the reason for the almost universal use of standard Newtonian solutions (involving infinite series) on this and similar websites.

However, a thought experiment was previously introduced (on the “Archive Page”) that calls into question this assumption. The thought-experiment (with some minor amendments) is repeated here for clarity and convenience:

From the section Zeno's Paradoxes, Wikpedia and Apple Carts

Part A:
The arrow moves through physical space in a trajectory in accord with Newton's laws (e.g. in a parabolic curved trajectory). At each point along that trajectory, mathematically we can say at point 'x' along its path, the arrow will be at 'y' height. Moreover, at any point along its path we can mathematically determine its physical characteristics of position, momentum and rate of acceleration (given known initial conditions).
The variables in describing the flight of an arrow all have physical attributes (e.g. momentum, position, rate of acceleration etc.).
Let’s imagine (a thought-experiment) in which we fashion ourselves a particularly fine arrow (one so fine that its tip has been honed to just one iron atom). Since, according to classical physics we can accurately determine the arrow's trajectory, we can likewise accurately determine the position of the atom.
Lets imagine we fire the arrow in a complete vacuum, so as to not to confuse the issue with friction losses, cross winds and other physical influences.
According to classical physics, at any time during its flight (assuming known initial velocity, weight of the arrow) we can apply classical equations to physically predict not only the arrow’s (and the atom’s) position, but also its momentum.
Note: we were particularly diligent and analysed the arrow to determine not only its weight but also the number of atoms and types of atoms it contained (with their respective atomic masses), thus enabling momentum for the lead atom to be accurately determined.
When geometric series are used to “resolve” Zeno’s Paradoxes, the assumption is made of perfect continuity – that is, there are infinite points along its path.
Accordingly, at any point in time, we can precisely determine the position of the arrow’s lead atom, and its momentum. Unless there is something wrong with my reasoning, this means we’ve busted the Uncertainty Principle of quantum theory. Nobel Prize please.

This thought-experiment is used to demonstrate how standard mathematical solutions that rely on infinite series are not relevant or applicable to the finer movement of physical things.

Quantum theory and experiment exposes the error of such treatments. Quantum theory has a pivotal role (at least until superseded or eclipsed by a better theory) in regards to solving Zeno's Paradoxes.

To suggest otherwise by quoting or considering solutions involving infinite series, which necessitates avoiding the reality of the experimental evidence of quantum physics, is to offer theories without a modicum of clarity of reasoning or observation.Steaphen (talk) 09:37, 31 May 2009 (UTC)

Clarity of cause

In reviewing the intransigence over accepting the idea that Zeno's Paradoxes cannot be solved using infinite series (see the above section "Not seeing the trees for the forest") I began to reflect on the deeper issue at play.

I believe the core of the issue is one of immaturity and short-term expediency.

Specifically, when we believe in a mechanical, objective universe, we are able to disconnect, or distance ourselves from intimate association with the resulting system. We are, in effect, able to lay blame elsewhere, claiming that we are victims in a random, senseless universe, or at the mercy of a vengeful God (science and religion, resp.).

A mature self-organising (holodynamic) systems world-view carries with it the responsibility for the reality we share.

To quote Freeman Dysan, Emeritus Professor of Physics, Princeton.

Quantum mechanics makes matter even in the smallest pieces into an active agent, and I think that is something very fundamental. Every particle in the universe is an active agent making choices between random processes.

...consciousness is not just a passive epiphenomenon carried along by the chemical events in our brains, but is an active agent forcing the molecular complexes to make choices between one quantum state and another. In other words, mind is already inherent in every electron.

As within the part, so within the whole. As within the micro, so within the macro.

Zeno's Paradoxes telegraph that the accepted objective view of our physical universe is untenable. The world we experience, one amongst limitless others, is intimately connected with, and co-created through our choices.

Objective science is a limited snapshot of a far deeper multidimensional existence. To say or believe otherwise requires a small-ego persona that seeks to remain disconnected in order to avoid responsibility for the resultant reality.

While appearing expedient in the short term (e.g. enabling fast food production using antibiotics/ growth hormones / caged hens / testing medications & cosmetics on animals etc) we ultimately debase ourselves, deepening our disconnect with the natural world.

That, I sense, is the reason many will continue to avoid recognising why we cannot solve Zeno’s Paradoxes using infinite series.

Steaphen Pirie
Director
Belief Institute —Preceding unsigned comment added by Steaphen (talk • contribs) 15:12, 2 July 2009 (UTC)

The ultimate issue in Dichotomy Paradox - Walking the Planck

Eventually the distance in the The Dichotomy Paradox will equal the Planck Length. For the moment, I will assume there is no length shorter than the Planck Length. When the distance reaches this lenght, a decision must be made. Round up, or Round down. Zeno might be happy to know that rounding down would mean not moving. However, rounding up is kind of cheating, since the distance is literally divided by nothing (note, this is point where nothing reveals itself to be not equal to 0. To bad the Greek philosophers didn't spot that one earlier). Technically, you can't divide it ad infinitum. Thus you cannot fulfill the conditions of the paradox. Thus the paradox is not valid. But wait, by Walking the Planck or more, which everybody capable of walking can do, don't you have to pass half the length of the Planck Length before passing a full Planck Length? Well, nothing is smaller than a Planck Length so obviously not. Zeno might have a point about movement. Suppose moving from one Planck Length to the next is not accomplished by movement, but rather the object simply is in another place than where it was. This is known to happen in quantum physics (unless QP is completely baseless). But wait, its more complicated than that. Light traverses 1 Planck Length in a 1 Planck time. If Homer is not traveling at least the speed of light, then its impossible for him to move at all, because he'd travel less than a Planck Length. Traveling less than a Planck Length is not possible so Homer must not be moving when he appears to move or is moving at least the speed of light. Maybe there are no Planck units. Or maybe I'm just to tired to be reading about Zeno and responding at this time --Zerothis (talk) 06:17, 13 July 2009 (UTC)

Looks good to me :) Particularly your conclusion, "Suppose moving from one Planck Length to the next is not accomplished by movement, but rather the object simply is in another place than where it was." - that sounds suspiciously like a description for quantum superpositions. Which, when applied to everyday life, means as we step, there's two of us, one of the front foot, one on the back. But hey, maybe some prefer to stay on the back foot, destined to repeat what's been done, what's been said, what's been written, never managing another step forward. Ciao Steaphen (talk) 12:27, 14 July 2009 (UTC)
For those interested, Microsoft has made Richard Feynman's lectures available online.Steaphen (talk) 22:34, 16 July 2009 (UTC)
From Lecture 7, Seeking New Laws:
"...that space is continuous is, I believe, wrong. Because we get these infinities and other difficulties ...I rather suspect that the simple ideas of geometry extended down into infinitely small space is wrong."
- Professor Richard Feynman
The Messenger Series: Seeking New Laws
Many-worlds QM does not require discrete spacetime or the invocation of Planck lengths. mike4ty4 (talk) 20:55, 17 July 2009 (UTC)
Also, discrete motion would not require such a "bifurcation" process either. If you read what you just quoted, they say : "the object simply is in another place than where it was." Nothing bifurcates, nothing "superposes", at one discrete point of time, the thing occupies one discrete unit of space, then in the subsequent one the thing occupies the next. I.e. continuous-vs-discrete spacetime is irrelevant to the question of existence of quantum superpositions. mike4ty4 (talk) 20:59, 17 July 2009 (UTC)
There was no explicit statement suggesting Many-worlds required discrete spacetime. As offered elsewhere you appear to be unable to do rudimentary analysis (e.g. of statements by others). The vast majority, if not all of your posts are about what isn't needed or proved, not about what is physically occuring. You have written of step functions without any connection with, or direct relationship to what IS actually occuring in physicality. Here, in this fine posting by someone who has at least attempted to suggest what IS happening, you again go the negative with what ISN'T needed. This page is about the dilemma of understanding the movement of physical things. It is not, contrary to what many might wish, about the mathematics, although mathematical descriptions might help some.
The point of the step functions and Dirichlet functions argument, and I don't see why you keep missing this, is to try show you that motion exhibiting "jumps" can be accomodated in both a discrete and a continuous space-time, as they are examples of discontinuous functions defined on continua. If you took one as "position" as a function of "time", then it would describe a motion with a discontinuity. That is, its point is to invalidate your claim that such "jumping" motion (which by the way you have not yet provided evidence for -- unless you want to call misunderstandings and misinterpretations of QM theory "evidence". Please, for the gazillionth time, tell me what on Earth is this experiment where one can actually observe the particle "jumping"??? How did they manage to observe the particle in-flight to determine its jumping? And so on...) is proof or evidence of discrete space-time. It is not. What I am doing overall is not just saying "oh, that isn't needed". What I am doing is saying "that argument/evidence doesn't support your claim. Do you have a better one?". mike4ty4 (talk) 07:41, 26 July 2009 (UTC)
Once again, you appear to be unable to perform rudimentary analysis. Any claim as to what a thing is NOT, involves an implicit comparison to what it IS (try thinking complete and utter "nothingness", if you have difficulty understanding this). All of your posts implicitly involve your theories about what reality is. I've simply asked that you be more explicit (and honest) in your descriptions and theories.
As for your "what is this experiment?" confuses me ... it's a nonsensical question: The root of Quantum Theory (Latin root "quantas" for "how much") is about measurement of, and theories relating to discrete lumps and jumps (no one has ever measured a continuous wave, or seen one, they've only ever, and will only ever measure and observe discrete, discontinuous entities, or quanta, that when observed together appear to form waves. If you have difficulty understanding my point, I suggest you go off and search for a forest without trees, and report back when you have found one).
In view of the above, the question that therefore needs to be asked, and answered is: What experiment or physical evidence do you have that supports your theories of absolute, endless continuity of physical movement, and of space-time? Steaphen (talk) 22:19, 8 August 2009 (UTC)
I think that for credibility, if you continue in the negative without substantive ideas of what is PHYSICALLY occuring, mediation will need to be requested. Again, if you wish to offer ideas and theories to explain the experimental evidence, well and good. Otherwise, I think it best you discontinue your negative statements concerning other postings that at least offer some ideas as to what IS physically occuring.
That's because that has not been the point. The point is not to propose a new theory. You have not provided this experimental evidence yet. If you can, I'd like to see it. Because, say, the 2-slit experiment is totally consistent with ordinary QM. These are the things that led to the development of QM! So what is this experimental evidence? Tell me right here, and I'll talk about it. Rather, you came in here proposing a new theory, and you offered arguments to try and back it up. I saw flaws in those arguments, and then decided to point them out to you. As for what is occuring, for all the experiments you have so far mentioned, I'll refer you to QM theory. mike4ty4 (talk) 07:41, 26 July 2009 (UTC)
Many, if not all of my references were to existing interpretations of (or combinations of interpretations of) quantum theory, which, as anyone with some rudimentary ability to reason will concur, must relate to the finer movements of physical things, i.e. quantum theory must be relevant to the issue of Zeno's Paradoxes. To suggest otherwise is a disconnect of a theory about reality, with experienced reality. I seem to recall that psychiatrists have a term for such disconnects ...
As the award-winning physicist Dr Fred Alan Wolf explained, "At the smallest level of space-time-matter, space-time is continually fluctuating— creating momentary bubbles of matter, which just as quickly vanish into nothingness again." If you have ideas or theories of what is actually happening experimentally, and it indicates Dr Wolf's statement is incorrect, then by all means share your thoughts.Steaphen (talk) 23:57, 17 July 2009 (UTC)
I do not see why this must be incorrect, nor why it proves or evidences your theory, nor why it is incompatible with models like QM. mike4ty4 (talk) 07:41, 26 July 2009 (UTC)

The new religion of mathematics

There are some respondents at this site who refer to various mathematical theories in order to account for, or solve the dilemma of physical movement, as was perhaps first queried methodically by Zeno of Elea.

However, as experimental evidence of quantum physics is now revealing, mathematical theories that rely on continuity cannot be directly and continually applied to account for or explain the evidence of physical movement.

Either something is wrong with the evidence which can be repeatedly and independently observed, or the "simple ideas of geometry extended down into infinitely small space is wrong."

To hark back to theories that once worked reasonably well (Newtonian physics), but which no longer fit the evidence, is no different to superstitiously citing some religious text as being the complete and final truth, in the face of glaring evidence to the contrary.

The travesty of, and blind adherence to religious dogma in Galileo's time is again surfacing in our time, as the blind adherence to "simple ideas of geometry".

As was exemplified in Galileo's time, the superstitious adherence to old belief-systems can do immeasurable harm to humanity's advancement and well-being.

Steaphen Pirie
Director
Belief Institute
www.beliefinstitute.com
Steaphen (talk) 09:45, 18 July 2009 (UTC)

In view of the "invitation" to clarify the errors in modern scientific thinking, I've expanded the above materials into two articles/posts on the Belief Institute website:
The Travesty of Modern Science
Moving Beyond a 2,450-year-old era
From the book An Introduction to the Study of Experimental Medicine by renowned French scientist, Dr Claude Bernard:
If a doctor imagined that his reasoning had the value of a mathematician's, he would be utterly in error and would be led into the most unsound conclusions. This is unluckily what has happened and still happens to the men whom I shall call systematizers. These men start, in fact, from an idea which is based more or less on observation, and which they regard as an absolute truth. Then they reason logically and without experimenting, and from deduction to deduction they succeed in building a system which is logical, but which has no sort of scientific reality.
Superficial persons often let themselves be dazzled by this appearance of logic; and discussions worthy of ancient scholasticism are thus sometimes renewed in our day. The excessive faith in reasoning, which leads physiologists to a false simplification of things, comes, on the one hand, from ignorance of the science of which they speak, and, on the other hand, from lack of a feeling for the complexity of natural phenomena. That is why we sometimes see pure mathematicians, with very great minds too, fall into mistakes of this kind; they simplify too much and reason about phenomena as they construct them in their minds, but not as they exist in nature. Steaphen (talk) 07:37, 21 July 2009 (UTC)

Order, please!

Might I remind everyone of WP:SOAP and WP:TALK? Paradoctor (talk) 08:43, 21 July 2009 (UTC)

Thank you for this reminder. It was good to read the list of "Do not"s (I must admit I had not previously read them). I note that one of the "do nots" is "Wikipedia is not a collection of unverifiable speculation."
Without getting on my soapbox (another 'do not') I think that policy is quite appropriate for this Discussion page. If it is not verifiable, we should not include reference to it. But that begs the question, in regards to this particular topic (Zeno's Paradoxes), isn't the idea of solving Zeno's Paradoxes entirely speculative, in that no one has ever actually verified moving through an infinite series? In the above section, I included the quote by Claude Bernard because, as he so eloquently puts it, to only rely on logic to explain real life leads to being utterly in error.
Perhaps on that basis, the main article should be rewritten to reflect the speculative nature of the mathematical theories contained therein. Or perhaps on purely technical grounds, references to infinite series in relation to Zeno's Paradoxes should be removed entirely, given that they remain speculative and therefore contrary to Wikipedian good policy.Steaphen (talk) 00:32, 22 July 2009 (UTC)

Paradoctor - in reviewing my posts (above) it would seem I have breached Wikipedia policy. On that basis, I'd be happy for you, or whoever would be appropriate to remove all my posts for the sake of adherence to good policy (The key issues and implications covered above are on the Belief Institute website).Steaphen (talk) 14:41, 23 July 2009 (UTC)

I just saw this. I'm going to quit right now (as of this posting) and take this to a different forum if I want to continue it further. So don't bother responding to the posts I already left a few minutes before this specific writing. mike4ty4 (talk) 08:04, 26 July 2009 (UTC)

Proof of the impossibility of movement

1. Scientific Assumption #1: The standard, widely-accepted scientific solution for explaining the paradox of physical movement (often referred to as Zeno's Paradoxes) is fully resolved by the mathematics of infinite series - that we are able to traverse each point in an infinite sequence of small 'infinitesimal' contiguous and continuous steps in finite time, thus enabling everyday movement of our bodies etc.

The mathematics is more like that you can define a continuous function from a continuum to a continuum, but go on... mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
more like ...? what? we're talking reality here. Physical stuff. What are on Earth, are you on about (pun intended).

2. Assume that the common denominator for all experience of physical movement is our personal thoughts and feelings (awareness). As a corollary, events that we believe occur independent of our awareness, cannot be classed as events per se, but as unverified, speculative beliefs about imagined events (since we have not experienced them).

3. Scientific Assumption #2: Neurological activity (namely, firing of neurons in the brain, electrical signalling in the body) is the cause for all our thoughts and feelings (awareness).

Materialism! But OK, if you want... mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
Materialism? Moi? That is the assumption of mainstream, classical science - hence the impossibility of movement - see below (pun intended).

4. Scientific Assumption #3: Physical movement of our bodies directly corresponds to, and results from neurological activity, and that 'subconscious' processes are still the result of neurological activity.

Not yet a problem, at least when not taken as seriously as you attempt to do it NEXT... mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
"Not yet a problem", yet you respond. Why? Your posts will stretch the patience of any visitor to this site.

5. Scientific Assumption #4: Each thought, choice and movement we initiate originates with electrical activity in the brain (namely, with the firing of neurons).

Again not a problem yet... mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
Again, courtesy, please. Consider other visitors to this site.

6. In view of the fact we cannot think the infinite, for whatever we think, we will need to think again, and again ... ad infinitum (thus never fully completing our task of thinking the infinite), there can be no 1:1 correspondence of neurological/thought activity, with each infinitesimal step in movement, since there is no corresponding "infinite firing" of neurons. (In any event, the carriers of electrical signals (electrons) are quanta that, according to quantum theory, do not move continuously, thus do not provide the continuity required by point 1).

And why should there be a 1:1 correlation? See below, this has nothing to do with the fundamental structure of the universe. mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
mike4ty4, you appear to misunderstand the assumptions of materialistic science (e.g. the vast bulk of science). Each infinitesimal sub-Planck movement either has a physical cause, or it does not (i.e. the cause is non-physical). I'll assume you would assert the former, namely each infinitesimal movement has a physical, and physiologic cause. Please explain what that physiological cause is. If no such explanation, then you have confirmed that due to the assumptions as given, movement is impossible.

7. Ipso facto physical movement of our bodies is impossible, since by definition the neurological activity that causes infinite infinitesimal physical movements, has yet to occur, and cannot occur.

That assumes that every portion of the movement down to arbitrarily small scale requires neurologic activity.
CORRECT! That is the assumption of deterministic science. Perfect determinism requires an absolute, unambiguous correspondence between physical effect and some physical, identifiable cause. No exceptions.
This is the problem.
Not at all. It is only a problem for those anchored to old-paradigm deterministic theories, such as infinite series solutions to Zeno's Paradoxes.
To make muscle, for example, move a distance, does not require continuous stimulation.
Analyse what you have written. You are suggesting the physical atoms within a finger that moves, for example, have no identifiable physical cause for their continued, sub-Planck movements. But this makes a mockery of the perfect determinism required by infinite-series solutions. Even the momentum of an atom (that would continue an atom's movement in the absence of resistance, and forces from adjoining atoms in the finger) is a physically identifiable and measurable aspect of reality.
Even a pulse can do it. In any case, nerves sure don't fire at 1043 times a second, so their firing rate obviously has nothing at all to do with how quantized space and time are, and also, therefore, with whether or not continuous motion is physically possible. This neurobiological problem does not prove anything about space and time.
Perfect determinism (aka infinite-series solutions to Zeno's Paradoxes), absolutely and totally requires that there is a neurological cause for moving a finger (for example) through sub-Planck level movements.
It has nothing to do with the structure of the universe. Therefore once again you have failed to provide a good argument for your theory! mike4ty4 (talk) 08:00, 26 July 2009 (UTC)
Nonsense. Determinism requires identifiable physical causes for physical effects. For every effect, a physical cause can be determined. The world is one big machine, according to standard scientific assumptions. Even chaos theory is deterministic at core. As for mention of 10**43 times a second, what has that got to do with this proof?Steaphen (talk) 09:51, 3 August 2009 (UTC)
Once again, Scientific Assumption #4 states that movement of muscles is biological and neurological in origin. However, there can be no direct biological/neurological origins for infinitesimal sub-Planck length movements, unless the cause for them is "magical".
This section "Proof of the impossibility of movement" made no reference to space-time, merely the fact that if you rely on a materialism to explain physiological movement, you would need to explain how neurological processes create movement on sub-quantum (sub-Planck length) scales. As for the issue of space-time, this post did not reference the issue, nor is it relevant to this proof. It is simply an exercise in applying standard scientific assumptions, to highlight the error of Assumption no. 1. The proof still stands. One or more of the above Assumptions is in error.
Excerpt Belief Institute
Additional comments and implications:
Further to point 6., point 1 (Scientific Assumption 1) requires infinite infinitesimal movements, including movements that must occur at and below quantum scales. In other words, the standard, widely-accepted infinite series solutions to Zeno's Paradoxes requires that our physiology initiates movements shorter than the Planck length – well beyond any measurable limits of quantum theory, and well beyond any currently proposed or theoretical neurological/physiological/quantum-physical processes.
Finally, Scientific Assumption 1 involves absolute determinism (in that for each point within the infinite sequence of points when traversing any arbitrary length) there exists an associated physicality ('particle' or frames of particles).
Thus, string theories and other theories involving multi-dimensional solutions are disallowed by the strict deterministic requirements of Assumption 1, again confirming that physical movement, based on these assumptions, is impossible. Steaphen (talk) 09:50, 27 July 2009 (UTC)

8. Thus, a runner can never start a race; (and assuming a similar necessary neurological base for animal behaviours and actions) a hare can never catch a tortoise, as Zeno originally posited.

♥

If some of you mathematicians would like to help me reframe the above into more formal-logic language, that would be enjoyed and appreciated. In any event (this is my initial rendering of this proof/updated), I'm well enough pleased with it as is. Thanking and appreciating everyone who's 'motivated' me to fire up a few neurons to prove the impossibility of movement.

Steaphen (talk) 05:46, 23 July 2009 (UTC)

2nd Proof of the Impossibility of Physical Movement

Proving the impossibility of physical movement, based on the assumptions of modern science

This proof, based on the assumptions of modern science and medicine, reveals how we are unable to move our bodies even for the simplest of tasks, such as blinking an eye, or lifting a finger.

  1. A person chooses to begin walking. Neurons fire in his/her head, thus initiating electrical pulses sufficient to cause the relevant muscles to work the process of physical movement.
  2. Prior to the first signal being sent, a neuron is required to fire (note, see Scientific Assumptions identified earlier in the above section).
  3. Prior to this first neuron firing, sufficient electrical charge (potential difference) must be accumulated in order to fire the neuron - for the signal to leap the synapse.
  4. However, the building of electrical potential cannot be caused by the choice of walking itself, as it is the first neuron ("thought"/"feeling") in the chain of electrical signals sent to the muscles.
  5. Since, according to the Scientific Assumptions (see above), all physical movement originates with neurological activity (firing of neurons), there cannot be a neurological "first thought" or a "first feeling" associated with the choice to walk, as there is no cause of the building of electrical potential sufficient to enable the required neurological processes of "thinking" and "feeling", and the subsequent experience of walking.
  6. Ipso facto, physical movement, based on the Assumptions as defined, is impossible.

Steaphen (talk) 13:15, 27 July 2009 (UTC)

A Planck in the eye of Newton

It seems those who suggest or believe that infinite series offer solutions for Zeno's Paradoxes, forget such solutions are based on a "perfect" determinism" that requires a strict and unambiguous 1:1 correspondence of physical cause for each physical effect (e.g. the effect of physical movement of Zeno's runner, hare, tortoise etc).

This strict correspondence requires a physical, neurological cause for sub-Planck scale movements (which must occur due to the deterministic requirements of infinite-series solutions). To suggest that this is not required, is to suggest physical movements have a nonphysical cause.

To move one's finger, for example, through the required sub-Planck scales, begs the question: "what part of our thinking, or neurological activity is driving parts of our bodies through scales that go well below the theoretical limits of quantum physics?"

Imagine the power of our minds to move bodily atoms through scales of movement not only shorter than the Planck length, but infinitely shorter ... at will, on command and with intent.

Steaphen (talk) 10:29, 3 August 2009 (UTC)

Excerpt: "The Mental Universe"

"One benefit of switching humanity to a correct perception of the world is the resulting joy of discovering the mental nature of the Universe. We have no idea what this mental nature implies, but — the great thing is — it is true.
There is another benefit of seeing the world as quantum mechanical: someone who has learned to accept that nothing exists but observations is far ahead of peers who stumble through physics hoping to find out ‘what things are’. If we can ‘pull a Galileo,’ and get people believing the truth, they will find physics a breeze.
The Universe is immaterial — mental and spiritual. Live, and enjoy."

Prof. Richard Conn Henry
Henry A. Rowland Department of Physics and Astronomy
The Johns Hopkins University, Baltimore, Maryland 21218, USA.

and from the same article:

“It is difficult for the matter-of-fact physicist to accept the view that the substratum of everything is of mental character.”
Sir Arthur Eddington

and ...

“the stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter... we ought rather hail it as the creator and governor of the realm of matter.”
Sir James Jeans

Steaphen (talk) 07:52, 9 August 2009 (UTC)

Achilles and the Tortoise

Anybody else realize that this isn't actually a paradox? The reason Achilles never overtakes the tortoise is because the description of time is f(x)=1/x, which never reaches 0. The story takes smaller and smaller increments of time going into the infinitesimal range of numbers above zero, rather than following the linear trend of time progression. 204.158.149.12 (talk) 15:25, 6 August 2009 (UTC)

The use of mathematical functions such as f(x)=1/x (as applied to physical process of movement) relies on the assumption of continuity (of movement, and space-time). Upon what basis do you make such an assumption (of continuity)? What physical evidence supports this assumption, particularly in regards to physical movement at quantum scales, and at sub-Planck scales (as required by infinite series solutions)?Steaphen (talk) 22:27, 7 August 2009 (UTC)

Proof of the impossibility of physical movement (revised)

  • Please DO NOT edit or insert comments inside the points below. Add your comments in the comments section, leaving the points listed below unadulterated.*

This proof, based on the assumptions of modern science and medicine, reveals how we are unable to move our bodies even for the simplest of tasks, such as blinking an eye, or lifting a finger.

  • Assume that the common denominator for all experience of physical movement is our personal thoughts and feelings (awareness). As a corollary, events that we believe occur independent of our awareness, cannot be classed as events per se, but as unverified, speculative beliefs about imagined events (since we have not experienced them).
  1. Scientific Assumption #1: The standard, widely-accepted scientific solution for explaining the paradox of physical movement (often referred to as Zeno's Paradoxes) is fully resolved by the mathematics of infinite series - that we are able to traverse each point in an infinite sequence of small 'infinitesimal' contiguous and continuous steps in finite time, thus enabling everyday movement of our bodies etc.
  2. Scientific Assumption #2: Neurological activity (namely, firing of neurons in the brain, electrical signaling in the body) is the cause for all our thoughts and feelings (awareness).
  3. Scientific Assumption #3: Physical movement of our bodies directly corresponds to, and results from neurological activity, and that 'subconscious' processes are still the result of neurological activity. Any movement of bodies, or parts of bodies is controlled by neurological processes that start, continue and stop such movements. That is to say, for each and every physical effect (of physical movement) there is an identiable physical cause.
  4. Scientific Assumption #4: Each thought, choice and movement we initiate originates with electrical activity in the brain (namely, with the firing of neurons).
  5. In view of the fact we cannot think the infinite, for whatever we think, we will need to think again, and again ... ad infinitum (thus never fully completing our task of thinking the infinite), there can be no 1:1 correspondence of neurological/thought activity with each infinitesimal step in movement, since there is no corresponding "infinite firing" of neurons. (In any event, the carriers of electrical signals (electrons) required for muscular contraction and movement are quanta that, according to quantum theory, do not move continuously, thus do not provide the continuity of signal and muscular movement required by point 1)*.
  6. As a corollary of point 5 (above), Scientific Assumption 1 in conjunction with Assumption 3, requires that for each and every one of the infinite infinitesimal movements, including movements that must occur at and below the Planck length, there must be some identifiable physical, neurological cause, That is to say, the standard, widely-accepted infinite series solutions to Zeno's Paradoxes requires that our physiology initiates movements shorter than the Planck length – well beyond any measurable limits of quantum theory, and well beyond any currently proposed or theoretical neurological/physiological/quantum-physical processes. On this basis one or more of the above assumptions must be invalid, or the theoretical limits of quantum theory are incorrect. In addition, and as stated Scientific Assumption 1 involves absolute determinism, in that for each point within the infinite sequence of points when traversing any arbitrary length, there exists an associated physicality (measuable, tangible, physical 'particles' or frames of particles). In effect, movement of one's finger requires that it is composed of not only quantum particles, such as quarks, but also 'sub-quantum' particles - 'super-quarks', and 'super-super-quarks' ... ad infinitum. Thus, string theories and other theories involving multi-dimensional solutions (that extend beyond our tangible 3-dimensional physicality) are disallowed by the strict deterministic requirements of Assumption 1, again confirming that physical movement, when based on these assumptions, is impossible.
  7. Ipso facto physical movement of our bodies, when based on these Assumptions, is impossible since the neurological activity that causes infinite infinitesimal sub-Planck-scaled physical movements, has yet to occur, and cannot occur.

(Note, the understanding and explanation for how we move is more fully covered in various articles and courses provided by the Belief Institute)Steaphen (talk) 23:23, 7 August 2009 (UTC)

Comments and rebuttals to the above:

Your comments here ...

seriously Paradoctor (talk) 16:34, 8 August 2009 (UTC)
Paradoctor, as mentioned above, I'm happy for you to remove all those posts that breach the Wikipedian rules, including mine. But it seems to me that based on Wikipedian rules the whole of this and the archived talk pages should be removed.
Perhaps you would like to clarify what Wikipedia IS, rather than what it is NOT.
Please confirm which of the above posts (and those of the achived pages) entirely conform to Wikipedian rules.Steaphen (talk) 21:34, 8 August 2009 (UTC)
I agree. It is not up to us to wade through all this grandstanding drivel. Just stop this endless WP:OR --JimWae (talk) 03:37, 9 August 2009 (UTC)
Presumably, your posts (on the archived page) weren't "grandstanding drivel" .. upon what basis is yours not "grandstanding drivel"?
As a courtesy to visitors to this site, and potential contributors, perhaps you should at least cite one post that meets all the Wikipedian criteria.
Steaphen (talk) 07:05, 9 August 2009 (UTC)
This talk page is for improvements to the article - not a blog & not a place to hype your blog--JimWae (talk) 08:26, 9 August 2009 (UTC)
Once again, which of the posts conforms to Wikipedia criteria? In regards to your "improvements to the article" - correct, my work is to correct the untenable, unsupportable and erroneous opinions in the article, thus improving it. I think given the intransigence, and associated dogmatic assertions by the majority in this talk section, we should seek mediation by Wikipedia mediators.
Steaphen (talk) 08:43, 9 August 2009 (UTC)
It would not matter if ALL previous posts did not conform to Wiki policies. We still are expected to follow those policies. However, here is at least ONE that is abot improving the article-- and there are more in that archive. In order to include content in the article, we need to find reliable sources. Your blog does not count as a WP:RS. There are numerous faults easily found in your "Scientific Assumption" approach - but THIS is not the place for people to discuss YOUR theories--JimWae (talk) 20:25, 9 August 2009 (UTC)
Jim, good to see you occasionally dropping in to keep things in order (and all the while using your actual name!). Unfortunately, you appear to be biased in your criticisms. On the main page there is Original Research content in the "Proposed Solutions" section (e.g. by Lynds etc.). The bias appears to be based on your perception of which articles or references are "reliable sources". In Galileo's time, Galileo and his kind were "unreliable" sources, while the Church's authority and scriptures were deemed "reliable" views of reality. Giordana Bruno and to a far lesser extent Galileo experienced the fiery brunt of not obeying accepted opinion as to what constituted "truth." Then, as now, there's no excuse for accepting the prevailing dogmas, just because the crowd says they're reliable sources. "Peer reviewed" I hear you say ... again, by whom, which crowd, which Church?
I can easily gather a crowd of reliable sources, one of whom includes the late Richard Feynman (who, as quoted above believed that "the simple ideas of geometry extended down into infinitely small space is wrong.") Then there's the physicist Professor R.C.Henry from the John Hopkins University, who says that "If we can ‘pull a Galileo,’ and get people believing the truth, they will find physics a breeze. The Universe is immaterial — mental and spiritual." Not to mention a plethora of others voicing remarkably similar ideas, all of whom highlight the error of standard infinite-series solutions to Zeno's Paradoxes. I suppose because their beliefs and comments don't fit your world-view, they must be unreliable sources.
As for my blog, or reference to the Belief Institute website, again, there are many references to other websites that support various theories. I think the unbiased visitor will concur that you're selective in your criticisms. And as for "numerous faults" .. I've had dialogue with a number of folk (e.g. an emeritus professor of mathematics) and as usual, the counter arguments are all based on the assumption of continuity. Yours no different.
Jim, as much as all this might appear trivial, unfortunately there are quite deleterious consequences coming our way (and already upon us) from continued adherence to old mechanical world-views. In as much as I’m part of this reality, it behoves me to do something about the continued adherence to beliefs that served us well enough in a previous era, but which are now dangerously out of step with needed awareness and behaviours.
I set up the Belief Institute as a repository and centre for congruent world-views that go beyond old dogmatic, deterministic beliefs. While my manner is perhaps not as eloquent or as courteous to ensure the greatest acceptance of the message, I am willing to be a messenger in the face of naysaying, abuse and denials.
Steaphen (talk) 08:12, 10 August 2009 (UTC)

Errors on the main page

Jim, in regards to your comments of "improving the article", there are a number of errors on the main page.

Specifically, the comment "Using ordinary mathematics we can calculate both the time and place where Achilles overtakes the tortoise." is incorrect.

We now know that, with the benefit of quantum theory, we cannot precisely do as claimed - we cannot precisely calculate both the time and place where Achilles overtakes the tortoise. The sentence needs correction.

>>UpdateSteaphen (talk) 23:16, 10 August 2009 (UTC): The above sentence has been changed to "Using ordinary mathematics we can approximate (to the limits of quantum theory) the time and place where Achilles overtakes the tortoise."

For similar reasons the statement "More modern solutions using calculus have generally satisfied mathematicians and engineers" is also technically incorrect, as there is no confirmed "solution" to the paradoxes using calculus. Assumptions yes, but solutions, no.

The sentence should instead read "More modern methods using calculus have generally satisfied mathematicians and engineers." (note, change has now been committed).

I'll edit other errors, and add more appropriate content in due course.

Additional errors that need correcting: "The paradoxes certainly pose no practical difficulties." This is incorrect, the quantum paradox (the uncertainty principle - the paradox being that a "thing" can be both entirely uncertain and certain at the same time) presents "difficulties" for those working on microchips, quantum computers and other devices that operate at such scales. —Preceding unsigned comment added by Steaphen (talk • contribs) 23:21, 10 August 2009 (UTC)

Cheers, Steaphen (talk) 18:04, 10 August 2009 (UTC)


You have not established that it is an error to say "we can calculate the time and place". We CAN calculate both. Your *claim* that it cannot be done precsely (whatever that means) is at least open to question. Saying "Using ordinary mathematics we can approximate (to the limits of quantum theory) the time and place where Achilles overtakes the tortoise" is needlessly opaque to the reader. I thus have reverted --JimWae (talk) 23:21, 10 August 2009 (UTC)
We CAN calculate both - whether it is "precise" (whatever that means) is a separate issue. --JimWae (talk) 23:24, 10 August 2009 (UTC)
Whether "Euclidean" mathematics is an accurate model of "reality" (whatever that means) is a separate issue --JimWae (talk) 23:26, 10 August 2009 (UTC)
"Whether "Euclidean" mathematics is an accurate model of "reality" (whatever that means) is a separate issue" Nonsense. Zeno's Paradoxes are about the movement of physical things. If "Brand A mathematics" (calculus) cannot be used in the detail of explanation (as the evidence of quantum physics now reveals), then get rid of it. Simple.Steaphen (talk) 23:33, 10 August 2009 (UTC)

Whoa there Jim! You have not established that we can "precisely and accurately" calculate the place and time. I'd enjoy seeing the mathematics that did that, in actual physical practice, not just theory. You realise of course that in doing so you'll have broken the Uncertainty Principle of quantum theory. Once again, if you have the physics to show how quantum physics (a real science, not just speculation and supposition) can do this, I'm very interested to learn.

Recorrecting. Mediation next step!Steaphen (talk) 23:28, 10 August 2009 (UTC)

We need not presume that time & space are the types of ontological entities that can be divided indefinitely (like the real number system can) to be able to calculate AN of answer using ordinary math ( w/o calculus). I contend it is a mistake to think that time & space can be "divided" at all - except as a conceptual exercise - they are not ontological entities like material objects are. Hold your own horses. Ordinary mathematics does not care about quantum theory; it is a system unto itself (whether it is a perfect model of "reality" is another matter). The point is that the calculation CAN be done (yes, even precisely) - and that still the issue is not resolved. That is what make it a paradox. If we do not point out that the calculation CAN be done, then the paradox is much less paradoxical. If you think what you have put in there is a *correction*, you are sadly mistaken - as you will see if you insist on mediation to determine how opaque your "correction" is. --JimWae (talk) 23:46, 10 August 2009 (UTC)
Using ordinary mathematics we CAN arrive at a precise calculation regarding the space & time when/where they meet. Whether that answer "mirrors" reality is what makes the paradox knotty. --JimWae (talk) 23:50, 10 August 2009 (UTC)
It doesn't make it "knotty", just wrong. Plain and simple. As Feynman said, "the simple ideas of geometry extended down into infinitely small space is wrong." Wrong content has no place in an encyclopedia.Steaphen (talk) 00:04, 11 August 2009 (UTC)
A calculation does not imply a "solution"--JimWae (talk) 23:51, 10 August 2009 (UTC)
Calculations using horoscopes and other superstitions can also be used. I don't see any credible reason for your bias to use calculus. (apologies) "algebra" !
Let's get some independent adjudication on this. [Initiated.] :) 124.189.34.79 (talk) 01:34, 11 August 2009 (UTC)
Please try to read my comments more carefully. It is the paradox that is knotty, not Euclidean geometry. I have not staked any of what I have said on calculus at all - I have repeatedly pointed out that calculus is NOT needed to get a precise (tho not necessarily accurate) answer -- just algebra --JimWae (talk) 00:23, 11 August 2009 (UTC)
Higher accuracy, but lower precision
Higher precision, but lower accuracy



(Reply by Steaphen):
And your point is? (pun intendend).
Irrespective of whether you argue for algebra, the fundamental issue still stands .. .the inapplicability of using any mathematics that is reliant on continuity to solve Zeno's Paradoxes. If such were the case we could dispense with quantum theory and simply use algebra to totally, accurately and precisely determine and predict the movement of quantum stuff (and ipso facto, the accurate and precise movement of hares, runners et al).
Jim, you appear to echo the disconnect of others with regards to the simple fact that physical movement has been found to be fundamentally discontinuous. If you have any evidence of its "endless" continuity, please enlighten the scientific community. That reminds me, where's my Nobel Prize! In the section Talk:Zeno's_paradoxes#Not_seeing_the_trees_for_the_forest I've disproved either the Heisenberg's Uncertainty Principle, or the validity of using infinite series to solve Zeno's Paradoxes. Which one do you wish to junk?
Let's see what the adjudicators say Steaphen (talk) 01:52, 11 August 2009 (UTC)
Do you really wish to maintain that it is an "error" to say that "using algebra, we can derive a (PRECISE) time & place at which Achilles catches the tortoise"?
Jim, your responses are getting embarrassing (for you). Do you not understand that according to quantum theory, there is nothing that can be precisely determined. Any macro-sized object will appear to be in a particular place, at a particular time. But drill down, and look at, say, an atom in the tip of the toe of Archille's front foot. Can you precisely know its location at a particular time, and by extension, that of all the atoms in his body?
This has been the glaring disconnect of basically all the respondents at this site - dsconnecting the proven science of quantum theory from some fanciful wish as to how they (and you) would like to think reality behaves.
So to answer your question: absolutely, categorically YES, it is WRONG to say that "using algebra, we can derive a precise time and place at which Archilles catches the tortoise." The main article needs to reflect this, for reasons outlined in the mediation request Wikipedia:Mediation Cabal/Cases/2009-08-09/. Steaphen (talk) 04:26, 11 August 2009 (UTC)
Neither space nor time are, in themselves, either continuous or discontinuous. Space & time (a la Kant) are unavoidable mental constructs with which we shape our world. We can both divide & separate matter. We can "divide" both space and time, but we can separate neither.--JimWae (talk) 03:30, 11 August 2009 (UTC)
Informal mediation requested Wikipedia:Mediation Cabal/Cases/2009-08-09/ Steaphen (talk) 03:32, 11 August 2009 (UTC)
Please stop breaking up my comments
Heisenberg Uncertainty Principle states that we cannot determine the position and momentum of microscopic particles of matter at the same time.
You are treating space and time as if they are analogous to matter. Your view is not supported by references to works in the field of quantum theory.
There is no denying that using algebra, a precise numerical answer can be calculated. It is another matter as to whether it gives a false precision. Before you can argue that it is false precision, it needs to be established that the calculation IS precise --JimWae (talk) 05:34, 11 August 2009 (UTC)
Btw, in case you have not noticed yet, I have never claimed the math solves the paradoxes. The section we are arguing about is entitled "Proposed solutions". There used to be a section for "issues with the proposed solutions" - but it lacked references. --JimWae (talk) 06:15, 11 August 2009 (UTC)
My apologies for the insertions. As I understand, Heisenberg's Uncertainty Principle applies to all conjugate quantities, including time-energy, and not just position-momentum. Once again, a precise value (location, time) cannot be meaningfully calculated, anymore than can the number of angels on pinheads. The Uncertainty Principle applies to large bodies as well. Even though some use simple ideas of combined mass to work out that the wavelength of the object becomes so small as to be unnoticable in everyday life, it does not matter how unnoticable or short the wave-length. It is not infinitely short!
Jim, to clarify - the infinite-series solutions ignore or deny the fundamental wave-particle duality of all matter (and all conglomerations of matter). Any large object will exhibit wave-like behaviour (according to the Wikipeida article wave-particle duality, this has been done for C60F48, a fluorinated buckyball with a mass of about 1600 u, composed of 108 atoms) which means the precise position and time of any object, even planets, cannot be precisely calculated or determined (even in theory).
Jim, given your penchant for simple algebra, perhaps I need to explain in your language. In detail, the de Broglie wavelength of an object is : (where p = momentum). The infinitesimal precision of the object's position (as required by infinite-series solutions) requires that approaches zero (since the de Broglie wavelength of the object indicates the range of possible positions and momentums of the object. Ignoring of course the constraints imposed by the Uncertainty principle's requirement that :). But as approaches zero (to ensure a short sharp pulse with infinite precision), p (momentum = mass x velocity) approaches infinity. Thus, to precisely know an object's location at some arbitrary point in time t, requires the object to have infinite mass, and/or infinite velocity (btw, this is a quick translation of basic concepts into the algebra, so might have to fine-tune the wording or some such. But I'm sure you'll get the gist).Steaphen (talk) 05:22, 12 August 2009 (UTC)
Despite the fact that the calculated wavelength for a runner, tortoise or arrow is unnoticeably small (short), it is still some finite wave-length. Thus, infinite-series or simple algebra is most definitely not able to be used to calculate precisely where and when Achilles will overtake the tortoise (even in theory).
The widely-accepted infinite-series solutions to Zeno's Paradoxes are clearly incorrect, lacking compatibility and congruency with the experimental facts, and the main article needs to reflect this.Steaphen (talk) 00:40, 12 August 2009 (UTC)
There is of course one one exception to what I have stated above: you can apply infinite-series solutions (simple algebra) to precisely calculate the position and time of an object ... the only problem is that the mass of the object must be infinite (thus having an infinitely short wave-length, enabling precise location). Actually, there's another problem, the infinite-mass runner would need infinite energy to start his race, as would the bowman who attempted to pick up and shoot an infinite-mass arrow. :) Steaphen (talk) 01:05, 12 August 2009 (UTC)
As for your reference to space-time, the mediation request does not mention space-time, merely that infinite-series should not be mentioned as having solved the paradoxes. The main reason for the request was your re-editing of my change of sentence from "we can calculate" .. to "we can approximate" and others that implied, inferred or stated infinite-series solved the paradoxes.
The thought-experiment provided in the section Talk:Zeno's_paradoxes#Not_seeing_the_trees_for_the_forest requires you either accept quantum theory, and dismiss infinite-series solutions or vice versa. If you have knowledge of how and why the Uncertainty Principle does not apply, please enlighten all of us. In which case, the Nobel is yours. It's a done deal.
But I remain curious. Just what is your opinion of those physicists who hold such esoteric, non-mechanistic views such as physicist R.C.Henry (see above)? Or Yale's Emeritus Professor of Physics Margenau (who explained that "...each of us is the Universal Mind but inflicted with limitations that obscure all but a tiny fraction of its aspects and properties.") or Schrödinger who wrote: "There is obviously only one alternative, namely the unification of minds or consciousness. Their multiplicity is only apparent, in truth there is only one mind".?
Do you believe they would (or do, for those still living) claim or agree that "simple ideas of geometry (can be) extended down into infinitely small space"? Perhaps you should ask them.

Steaphen (talk) 09:47, 11 August 2009 (UTC)

---

Two Trains and a Fly: Two trains are traveling towards each other on the same track. One train is traveling at 30 km/h, the other at 20 km/h.

When the trains are 100 km apart, a superfly leaves one and flies towards the other. When it reaches the other it immediately travels back to the first. Upon returning, it immediately starts back to the second, and so on, until the trains crash.

Question: When the trains crash, how far has the superfly travelled, if it flies continuously at 50 km/h? Or, if you prefer, what is the upper-bound?

Mediator on deck!

Hi folks. I'm willing to help out as a mediator here if you're still interested. I'm not entirely across the issues, but if I understand correctly so far, there is essentially a disagreement about a clash of Zeno's paradox and QM... is that right? Could someone give me a brief summary, from a content perspective, of how this impacts on the article? i.e. are there disputed sources, undue weight issues etc. Cheers, Blippy (talk) 05:43, 16 August 2009 (UTC)

Blippy, why have you responded here, and not on the mediation page Wikipedia:Mediation_Cabal/Cases/2009-08-09/?
In answer to your question, the issue is one of undue weight, unsupported assumptions, and clear errors (based on simple analysis (see Proof 1)).

See the discussion section on Wikipedia:Mediation_Cabal/Cases/2009-08-09/ for details

Steaphen (talk) 08:14, 16 August 2009 (UTC)

Hi Steaphen. This is my first mediation - I'm used to 3O's - when I looked I saw that some do it this way, others on the mediation site. I'm happy to move the conversation there if you prefer. Can I slow things down a smidge and deal with one thing at a time? I note that that your first point concerns whether the ZP remains a problem. I appreciate that you are providing reasons why it is still problematic, but do you have a WP:RS for that assertion as well? I just want to make sure we tick all the boxes - so to speak. Cheers, Blippy (talk) 08:19, 16 August 2009 (UTC)
Blippy, I appreciate your interest in ticking the boxes, but the problem is this article (Zeno's Paradoxes) is in a class of its own for some very important reasons.
Let's consider "ticking the box" regarding "Reliable Sources" - in any era, the prevailing cultural belief-system will form a filter for acceptable ideas and behaviours. For example, the official verdicts of the Salem witch trials that saw 18 people executed for having practised "witchcraft", were "peer (court) reviewed" judgements (and that's official!).
Then there was the official "peer (church) reviewed" dogmas that saw Giordano Bruno burnt alive, and Galileo spend the remainder of his later years under house arrest.
Placing our faith in the Gospels of science (The Book of Mathematics) is really no different to putting our faith in the Gospels of religion. The superstition that movement is "perfectly continuous" and that infinite-series solve the paradoxes has parallels to the witch-burning attitudes of past eras.
What would navigate us out of the ruff, so to speak, is asking questions of the evidence, and to seek answers not based on the majority (crowd) opinion, but on good old-fashioned wisdom - timeless principles that will stand the test of time. What is a timeless principle? Ask the question, see what answers you get.
So in answer to your question, yes I have Reliable Sources (some of which have been mentioned on this talk pages), but I think, given the witch-hanging/burning penchant of people through the ages, I'm inclined to suggest that we play down the importance of crowd opinion.
The reason this article (Zeno's Paradoxes) is in a class of its own, is that it goes to the core of the fundamental nature of our physical reality, upon which various assumptions (and crowd opinions) are then formed. Get the base understanding wrong (i.e the nature of physical movement, and space-time), and all the following assumptions and theories become based on a house of cards, held in place only by dogmas and opinions held by scientists, philosophers and mathematicians.
Steaphen (talk) 10:26, 16 August 2009 (UTC)
Hmmmm, that's going to make it tricky then Steaphen. I'm all for wisdom and not being swayed by public opinion, or even scientific opinion come to that. But what you're wanting to do is to change a WP article in a particular way. Whilst I acknowledge that ZP may have fundamental, perhaps axiomatic and even ontological implications, perhaps WP is not the place for such wisdom to be imparted? The problem is that WP has a very distinct hang up on reliable sources and not promulgating original research. This is kind of handy though, because it stops all those Zeno deniers from running amok too :-) So I think that given we're discussing this in the context of WP, we'll need to play by the WP rules - which may preclude your insights from being utilised here. How does that sound? Cheers, Blippy (talk) 10:43, 16 August 2009 (UTC)
Blippy, my point is not to ignore Reliable Sources, but in how we select what is reliable, as the selection will be filtered based on one's world view. Physicist David Bohm expressed quite clearly that "according to the quantum theory, movement is not fundamentally continuous." In that case, infinite-series solutions, based on the assumption that physical movement IS continuous are invalid. But those who wish to maintain "movement is continuous" views will find reasons to dismiss David Bohm as a reliable source. Do you get my point?
Another way to consider this, is that the root assumptions we hold about physical movement will colour our perceptions. So, for the sake of "ticking boxes" perhaps a way to approach this is to be quite clear about those root assumptions, and the beliefs and theories that result from those root assumptions. At the very least, the fact that the root assumption of continuity has been taken for granted very much needs to be acknowledged.
Another dimension to this issue is your response here. Do you believe physical movement is "perfectly" continuous? Movement either is "perfectly continuous", or it isn't. It's a yes-no consideration, but how you answer will shape how you deal with this issue, and whether as a moderator you shift the issue towards "maybe we have to preclude your insights" etc... they're not originally mine, so they're not my insights. Are you suggesting that Bohm is not a reliable source, because your world view is one of continuity of movement? In other words, as a moderator, are you seeking to inject your bias in this matter?
I sense that your comment "because it stops all those Zeno deniers" (whatever that means), indicates your bias towards a "movement is continuous" world view, and therefore perhaps precludes your dealing with this issue. Steaphen (talk) 12:47, 16 August 2009 (UTC)
Hi Steaphen. I'm actually quite taken with Bohm's implicate order. But I'm not here to offer an opinion, rather mediation. And we can't get the mediation underway if we don't have at least two possible alternatives to choose from. We need to have RS's backing each of the contested positions, otherwise there is no contest - WP is only here for RS material. So let's start there - I don't recall Bohm dealing with Zeno's Paradox explicitly. Can you direct me to the source for that? Cheers, Blippy (talk) 13:34, 16 August 2009 (UTC)
"Reliable Sources" are many, but again, I'm keen to see how you select which are reliable and which are not. For example physicist Fred Alan Wolf explains in his award-winning book "Taking the quantum leap" how movement is discontinuous and that Zeno was right ("Werner Heisenberg was ... awarded the Nobel prize in physics for his realization that Zeno was correct after all"). Norman Friedman, author of "The Hidden Domain" explains how reality is flickering on and off, and so on. There's plenty of authors/physicists who concur with the basic understanding that movement is not fundamentally continuous. In fact, I'd enjoy seeing any physicist stating categorically that he/she believed that movement WAS entirely continuous. I'd like to see that.
Do you have any reliable sources claiming that physical movement IS entirely continuous, which would be necessary if one is to apply infinite-series to physical movement?
Let's do a quick whip-around, "Hands up all those physicists who believe physical movement is perfectly continuous" ... and please provide details with which university or research institution you're employed, and how long you predict you'll remain employed.Steaphen (talk) 16:32, 16 August 2009 (UTC)
Blippy, since you asked the question, what reliable sources do you have that supports the idea that physical movement is entirely continuous, including continuity through sub-Planck scaled increments (e.g. of Zeno's arrow)? If you can't answer the question that you've asked, perhaps you should disqualify yourself from further mediation and/or that I bump this to a request formal mediation Steaphen (talk) 16:48, 16 August 2009 (UTC)
Excerpt, from "Taking the Quantum Leap", (Publishder, Harper and Row, New York), winner of the American National Book Award, 1982, by Dr Fred Alan Wolf (regarding the assumed continuous movement of Zeno's arrow):

"to see the arrow move as a series of continuous dissolving movie frames, we must view many more than the modern filmaker's usual twenty-four frames per second. We need an infinite number of frames passing before our eyes each second. So dividing up motion into infinity is really no different than adding up to infinity.

This subtlety eluded Aristogle and everyone who came after him for the next two thousand years and more. By assuming that the arrow's motion was continuous, it was natural to imagine continuity as 'made up' of an infinite number of still frames, eve though we would never attempt to make such a movie picture. We just believed that 'in principle' it was possible.

By 1926 that hope was demolished. Werner Heisenberg, the young physicist, who demolished it, was later to be awarded the Nobel prize in physics for his realization that Zeno was correct after all. Heisenberg's Principle of Indeterminism (or Principle of Uncertainty, as it is often called) reaffirmed Zeno's objections that "an object cannot occupy a given place and be moving at the same time." Heisenberg recognized that observation, as we actually experience it does not allow us to analyze motion on to infinity. Sooner or later we see that our activity introduces discontinuities in whatever we are observing. These discontinuities are fundamental to the new physics of the twentieth century."

Blippy, if you can't cite a reliable source (within say one week from today's timestamp) that refutes Wolf's view, or offers a credible alternative to the idea that physical "movement is not fundamentally continuous", I'll bump this to formal mediation, since informal mediation has failed to resolve the issues I've raised in Wikipedia:Mediation_Cabal/Cases/2009-08-09/.Steaphen (talk) 23:15, 16 August 2009 (UTC)
  • Here and here are the edits that brought on the request for mediation. Algebra does not give an *approximate* answer. The section is proposed solutions, and the proposed solution should be allowed to be presented on its own terms. Since that edit, I have changed the wording to "Using ordinary mathematics we can arrive at a specific time when and place where Achilles would be able to catch up to the tortoise" towards eliminating the suggestion that the answer ordinary math & algebra gives is necessarily THE answer. There is no denying that algebra gives us AN answer that is as precise as the measurements of distance, speed and time are. Admittedly the answer is a false, overly-precise answer if the measurements of speed and distance and time are themselves approximations. It does, however, point out that neither calculus nor the sum of an infinite sequence is even needed. The limts of the algebraic solution is something that can be developed within the article later on -- without interjecting quantum theory even before the proposed algebraic solution is presented. The algebraic solution also applies ONLY to Achilles and the tortoise - and not to any other of ZPs. --JimWae (talk) 00:47, 17 August 2009 (UTC)
Your comment "Using ordinary mathematics we can arrive at a specific time when and place ...etc" is simply rehashing old ground. As I've named you as one of the parties involved (in the mediation docs), I'll extend to you the same courtesy of allowing time for you to cite reliable sources to support your assumptions, before requesting formal mediation.
Blippy, Jim, if a week is insufficient for either of you to cite reliable sources, what time-frame would you require? If you don't believe you can cite any reliable sources (asserting that physical movement is entirely continuous), let's not waste further time or dialogue and bump this straight to formal mediation, followed by, if necessary, arbitration.Steaphen (talk) 01:38, 17 August 2009 (UTC)
  • The point is that the article should not take a position on whether movement in general is continuous or not - nobody knows, despite what a few may assert. The TITLE of the SECTION we are dealing with is "PROPOSED SOLUTIONS"--JimWae (talk) 04:38, 17 August 2009 (UTC)
Jim, you have made certain statements as fact without basis - they are your personal opinions (and thus POV). It is irrelevant which section such assumptions-as-fact are made, reliable sources are rquired to substantiate such claims. If you can't supply any reliable sources to back up your "facts" (e.g. that we can calculate exactly where Achilles overtakes the tortoise etc) then let's not waste further time. I'll request formal mediation unless you can supply reliable sources to backup your statements. Keeping in mind that these reliable sources will need to assert that movement of physical things (e.g. Zeno's arrow) is perfectly continuous, as opposed to Wolf's asserting that it is not (perfectly continuous)124.189.34.79 (talk) 04:52, 17 August 2009 (UTC)
  • Simple mathematical calculations that anyone can follow do not require sources. Furthermore, this proposed simple mathematical solution can be found in nearly any discussion of ZPs. At the most, all I need to do is to find one reliable source that presents the same proposed argument. Algebra does not give us an approximation - though the limiataions of measurement do. However, the measurements are not given as approximations in the example - and that too is worth further discussion--JimWae (talk) 05:02, 17 August 2009 (UTC)
  • Furthermore, the argument that the algebraic solution does not solve every issue with Achilles and the tortoise does not need to involve quantum physics - much simpler, more accessible argumaents are available --JimWae (talk) 05:10, 17 August 2009 (UTC)
I'm not interested in what the crowd says about your assumptions. What reliable sources can you cite that says "movement is fundamentally continuous" in order for any mathematics (based on continuity) to be relevant and applicable to understanding and calculating the when and where of said movement?
Jim, with respect, I'll not respond to any more of your opinions. As a courtesy, I'll allow one week, unless you request more time to find a reliable source that confirms "movement is fundamentally continuous, which thereby enables and validates the use of mathematics that are based on algebraic continuity".Steaphen (talk) 05:20, 17 August 2009 (UTC)
Your referenced article says "Our belief that the mathematical theory of infinity describes space and time is justified to the extent that the laws of physics assume that it does," and you believe this qualifies as a reliable source? That if others assume something is true, and admit their assumptions, then that's good enough to assume it is true, and fact? That attitude and logic lands us all in serious witch-hanging, heretic-burning territory. See you in a week. CiaoSteaphen (talk) 05:50, 17 August 2009 (UTC)
  • All I have to do is provide a source that demonstrates the algebraic argument is relevant. I do not need to show that the argument is the correct & complete solution. If you could realize this, we could get on with improving the article--JimWae (talk) 05:59, 17 August 2009 (UTC)
  • It is not our task to present "the true nature of reality" to the reader. The best we can do, without doing WP:OR is present what reliable, and preferably scholarly, writers have to say on the subject--JimWae (talk) 06:09, 17 August 2009 (UTC)

Whoa!!

Hi JimWae and Steaphen (also 124.189.34.79?). Could I suggest we back up a bit here? Steaphen, you seem to think I'm here to refute or contribute to the content in some way - that's not my intention. You folk all seem eminently far more expert than I to take care of the content. It looks like you have a number of reliable sources Steaphen, would you agree JimWae? If so, is there any objection to changing the initial wording that Steaphen has raised that implies that there is no longer any controversy about ZP's? Cheers, Blippy (talk) 09:57, 17 August 2009 (UTC)

That was never in dispute, and the article has long stated that some hold there's still controversy. I do not think it ever said that scholars agree the controversy has been resolved - quite the opposite --JimWae (talk) 18:15, 17 August 2009 (UTC)
OK, thanks JimWae. So Steaphen, are you happy to leave the first section as is, or do you have some specific changes to the wording you would like to see? Cheers, Blippy (talk) 09:24, 18 August 2009 (UTC)
However, isn't Steaphan taking the position that (according to him) quantum physics has solved ZPs and that (some) quantum physicists hold the matter is closed? There is an important difference between establishing that the smallest theoretically-possible measurement of space is one Planck length and establishing that the smallest possible unit of space is one Planck length.
The original impetus for the mediation was the statement "Using ordinary mathematics we can arrive at a specific time when and place where Achilles would be able to catch up to the tortoise." This is incorrect. With mathematics we can only approximate place and time. The other issues raised on the Mediation page have not been addressed either. Given Jim's (and others') expected continued obstinacy in the face of the facts, and your (Blippy) apparent misunderstanding of the issues, I'm happy to move this matter forward to formal mediation.
This issue is not a trivial matter. A shift in belief-systems is inevitable (and arguably well overdue). Limiting, reductionist scientific beliefs (and their related religious and political beliefs) are causing increasingly adverse consequences for all of us. Yes, that's correct, reductionist scientific world-views give rise to fundamentalist religious beliefs - they are sister-belief systems, both objectify the causal agent for self-organisation of "systems" (physical and spiritual, resp.). That disconnect (objectification) is the cause of most if not all of the world's ills. And that disconnect is maintained by adherence to beliefs as exemplified on the main page of this article.Steaphen (talk) 08:35, 20 August 2009 (UTC)
For the sake of clarity, and without recopying the text from the mediation page, any statement that implies mathematics can give correct (precise) location and speed of arrows, runners,tortoises is, based on the evidence, incorrect. Arguments to the contrary are simply highly biased points of view, speculative, and have no demonstrable basis in this reality. If you can cite reliable sources that state mathematics (in any form) can give precise physical details of objects, (and in the process disproving the Uncertainty Principle) then I'd be highly interested to see them. Since none will be forthcoming, I'll expect the change in the text as outlined on the mediation page.Steaphen (talk) 08:48, 20 August 2009 (UTC)
I'd like to make an observation at this point... mediation (formal or informal) strives to reach a point where all parties are happy with the outcome. You have raised a number of issues Steaphen, and as an independent third party, I am attempting to address them in a particular sequence. It is simply not possible to address all of the issues simultaneously. If you feel that I am misunderstanding something I am more than open to being told what that is, however large swathes of texts repeating contentious points will not help. I would like to proceed in an orderly fashion, identifying areas where we can find immediate agreement, and "creep up" on the bigger issues. If that doesn't suit I'm happy to bow out. Cheers, Blippy (talk) 10:43, 20 August 2009 (UTC)
I would question your status as an independent third party, given your earlier reference to "Zeno deniers", "leaving the first section as is" (when I had outlined the errors contained therein), and calling for me to cite reliable sources while not requesting reliable sources from those who had objected to my edits. I note that you have yet to call for reliable sources from Jim. These factors together would seem to indicate bias, and/or inexperience with this process, and/or not understanding the issues, leading me to expect that formal mediation will be a necessary next step.
Blippy, assuming for the moment your good intent (sans bias/prejudice), let's clarify matters: I've provided a reliable source (winner 1982 National Book Award), explaining that we cannot precisely determine the position of an arrow. To counter this reliable source, I'd expect that you call for a reliable source (from Jim, et al) that does claim we can precisely determine the position of the arrow. And by "precisely" that means stating that even at quantum scales and sub-quantum scales (since the arrow will at some stage travel through such increments, since the arrow must traverse infinite points, according infinite-series solutions) we can precisely and wholly determine the arrow's position and momentum. Totally, without error, and most importantly, without uncertainty. Perfect reductionism, as required by infinite-series solutions.Steaphen (talk) 14:38, 20 August 2009 (UTC)
Blippy, as you suggested, one thing at a time, so lets start with the first one:-
I suggest the paragraph in the first section on the main page that reads:

"Zeno's paradoxes were a major problem for ancient and medieval philosophers, who found most proposed solutions somewhat unsatisfactory. More modern methods using calculus have generally satisfied mathematicians and engineers. Many philosophers still hesitate to say that all paradoxes are completely solved, while pointing out also that attempts to deal with the paradoxes have resulted in many intellectual discoveries. Variations on the paradoxes (see Thomson's lamp) continue to produce at least temporary puzzlement in elucidating what, if anything, is wrong with the argument."

be changed to:
"Zeno's paradoxes were a major problem for ancient and medieval philosophers, who found most proposed solutions somewhat unsatisfactory. More modern methods using calculus have generally satisfied mathematicians and engineers. However, in 1926 physicist Werner Heisenberg formulated the Uncertainty Principle which disallows precise calculation of the speed and location of physical objects such as arrows, runners and tortoises. Variations on the paradoxes such as Thomson's lamp, together with the Schrödinger's Cat Paradox and the EPR Paradox provide further puzzlement for physicists and philosophers."Steaphen (talk) 02:11, 21 August 2009 (UTC)


1> When has this proposed paragraph ever been discussed previously?? If not, why is a mediator needed? 2> Please elucidate how Schrödinger's Cat Paradox and the EPR Paradox are "variations on the ZPs". 3> Heisenberg is not needed to cast uncertainty on measurements. 4> re Heisenberg - the principle is about simultaneously determining location and momentum, and applies much less to macroscopic objects 5> Heisenberg is not about calculating, but about determining. You've mixed-up the concepts again 6> Precision does not have the same meaning as correct. "I am 33.345678934503 metres tall" is very precise and very incorrect --JimWae (talk) 04:32, 21 August 2009 (UTC)

It's been discussed before, dating back about 2 years, if you recall.
If you were to attempt to reflect on this matter, you would find all paradoxes relating to the movement and reality of physical things share the same base issues, Zeno's included. The question "is the cat alive or dead", is the same as "is the arrow or Achilles actually there or not"? It relates to the fundamentals of quantum theory (which presumably you've not bothered to acquaint yourself with). And I wrote, "together with" meaning they are not specifically Zeno's Paradox, but nonetheless such paradoxes remain unsolved, as do Zeno's.
We cannot determine (or calculate) precisely both speed and location of anything, no matter what its size. Your reply that "applies much less to macroscopic object" beggers belief.
"Precision" is precisely what the solutions to Zeno's Paradoxes are about. I could say any number of things and argue they are close enough, so its good enough. They're not. As far as mixing up concepts, interesting response. I can argue that "precisely calculating" the number of angels on a pinhead indicates when Achilles will overtake the tortoise, and in some universe or other, I might be close enough to the truth. Who knows, because you are most certainly not referring to facts in your responses.
By the way Blippy, where's those reliable sources stating that we can precisely calculate (including 100% accuracy at quantum and subquantum scales) the exact location and speed at which Achilles is running, or the arrow is flying? By your own words, "We need to have RS's backing each of the contested positions, otherwise there is no contest - WP is only here for RS material. So let's start there" - so again, what reliable sources have you gained from Jim stating that we can totally, precisely and accurately calculate the actual location and speed of an object as it passes through the quantum scaled increments (that they inevitably MUST do, according to the requirements of infinite-series solutions, or any solution that is based on the implicit assumption of continuity?)Steaphen (talk) 05:18, 21 August 2009 (UTC)

If you re going to repeatedly use precision and 'accuracy interchangeably, we will never get anywhere in this discussion. Please acquaint yourself with the differences --JimWae (talk) 05:13, 21 August 2009 (UTC)

From Accuracy and precision "In the fields of science, engineering, industry and statistics, accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeatability, the degree to which further measurements or calculations show the same or similar results"
Blippy, what reliable sources have you gained stating that we can precisely calculate the actual, true value of an object's momentum and position, and that we can reproduce those calculations to show the same results (of their true values)?Steaphen (talk) 05:28, 21 August 2009 (UTC)
OK. I'm going to stick pretty much to the incremental approach here folks and not get sidetracked by issues yet to be addressed. I'm not sure whether you are wanting me to stay involved or not Steaphen. I'll assume the former at this stage. So, I note that in your preferred version the first issue is no longer disputed. You are happy to leave the first two sentences as they are. I presume you don't have an issue with this JimWae? That gives us Zeno's paradoxes were a major problem for ancient and medieval philosophers, who found most proposed solutions somewhat unsatisfactory. More modern methods using calculus have generally satisfied mathematicians and engineers. as agreed text. Yes? Cheers, Blippy (talk) 07:32, 21 August 2009 (UTC)
Agreed, but I wonder why we continue dialogue given your earlier request "We need to have RS's backing each of the contested positions, otherwise there is no contest - WP is only here for RS material." On that basis, there's no contest, unless Jim can provide a reliable source (a physicist) who's willing to commit career suicide and state that we can precisely and accurately calculate an arrow's or Achilles' momentum and location, at and below quantum scaled increments in the arrow's flight and during Achilles' run. There's plenty of reliable sources saying we can't. I'd like to see one that clearly says we can. Recognising of course that such a statement would necessarily (either implicitly or explicitly) refute the Uncertainty Principle, since such a statement would also affirm that the motion (speed and location) of any atom or particle within the arrow or Achilles could also be precisely and accurately calculated.Steaphen (talk) 23:52, 21 August 2009 (UTC)
We're getting there Steaphen, just slowly, slowly. Now, the first two sentences are fine, but you dispute the rest of that paragraph. So, firstly, what is it about this bit Many philosophers still hesitate to say that all paradoxes are completely solved, while pointing out also that attempts to deal with the paradoxes have resulted in many intellectual discoveries. Variations on the paradoxes (see Thomson's lamp) continue to produce at least temporary puzzlement in elucidating what, if anything, is wrong with the argument." that you dispute? Is there a lack of RS to back this up in your view, or something else? I know you wish to replace it with your preferred text, but why do you wish to delete this, specifically? Cheers, Blippy (talk) 02:21, 22 August 2009 (UTC)
The sentence "Zeno's paradoxes were a major problem for ancient and medieval philosophers" implies they aren't now. Turn the sentence around, if you like, or include the "however".. either way, the bias has not yet been addressed.
For example, we could say "Zeno's paradoxes have remained a major problem for philosophers since their origin. Many mathematicians using calculus hesitate to say that all paradoxes remain unsolved." What "reliable sources" have been cited to argue that they have been solved? And in solving them, how specifically did they address the uncertainty principle issue raised previously? Blippy, do you understand the bias implicit in the first sentence? If the first two sentences stay, then you will need the "however, in 1926 ..." or similar to address the biasSteaphen (talk) 07:36, 22 August 2009 (UTC)
Sadly Steaphen you are now wanting to change what you had just said you agreed to!! OK, so the very first sentence is back in dispute. Do you disagree with the substance of the sentence i.e. that ancient and medieval philosophers struggled with ZP's, or just the implication that they are no longer a problem, or both? Cheers, Blippy (talk) 07:53, 22 August 2009 (UTC)
The point of the reply is that if the first sentence stays (to which I agreed, as a first step) then you would need the "However, in 1926 ..." or similar to address the bias. I see no reason to be sad, other than for you to do your job, and address the bias. Perhaps though I do need to take you to task, because you have not directly addressed the first issue raised in this Wikipedia:Mediation_Cabal/Cases/2009-08-09/ mediation dispute. Allowing your first request (and my initial "agreed") was a small gesture of good faith, in that you would at some point seek to address the bias implicit in the disputed sentence. Perhaps you took my "agreed" reply as a fait accompli, independent of other sentences or issues. If so that was your incorrect assumption.Steaphen (talk) 09:15, 22 August 2009 (UTC)
  • The sentence "Zeno's paradoxes were a major problem for ancient and medieval philosophers" DOES NOT IMPLY that they are not now, though some with an inclination to jump to conclusions might infer so. It merely asserts what is agreed upon. For wikipedia to say they they REMAIN a problem would be a problem, since people disagree on that. Instead, the article does not take a stand on whether they actually remain a problem today & presents the differing viewpoints re the present on whether they are still a problem.
  • The other paradoxes are similar to ZPS only in being paradoxes. If the only standard for being similar is that they be paradoxes, we could include the Twin Paradox too--JimWae (talk) 19:24, 22 August 2009 (UTC)
  • "However, in 1926..." actually has wikipedia appear to take a position that in 1926 something happened to change whether the ZPs were still considered a problem -- but it remains glaringly ambiguos on whether the effect of the uncertainty principle was on the ZPs or on the calculus approach. The "however" is uncalled for. The relevance of the Uncertainty Principle is left dangling--JimWae (talk) 19:26, 22 August 2009 (UTC)
Blippy, I suggest, "Zeno's Paradoxes have been a problem for philosophers since Zeno's time" (to replace the entire paragraph in dispute). If there are any reliable sources (physicists) who now state that they aren't, perhaps you could call for them to be presented here. I have presented one who says they are. Any by "reliable" I mean a physicist, not some mathematician off in cloud-cookoo land who has lost connection with physical reality, and with any congruent, verifiable theories thereof.Steaphen (talk) 21:37, 22 August 2009 (UTC)
Jim, A reliable source says "it was natural to imagine continuity as 'made up' of an infinite number of still frames, even though we would never attempt to make such a movie picture. We just believed that 'in principle' it was possible. By 1926 that hope was demolished.
What part of "demolished" do you have problem with? To have Wikipedia include material that suggests that such "imaginings" have not been demolished, requires a reliable source who says they have been verified in fact. Simply citing 'noise of the crowd' is a disservice to yourself and Wikipedia. The case 'for' (that the Paradoxes remain unresolved) has been made. Now the case 'against' needs to be made, including reference to reliable sources.Steaphen (talk) 23:03, 22 August 2009 (UTC)
Blippy, the unbiased observer (of this discussion) will note that while I suggest amendments on this discussion page, Jim proceeds to make edits to the main article based on his beliefs, as if to suggest he is an authority on such matters. And all the while, doing so without referencing reliable sources. If you can't rein in the bias, and the clear breaches of Wikipeida policy, what point this mediation?Steaphen (talk) 22:14, 22 August 2009 (UTC)

Blippy, I've given this mediation process more time than is perhaps wise, allowing it to affect my focus on more important and relevant business matters. I won't spend more time responding to the style of responses so far. You'll need to cut to the chase, request reliable sources that support Jim's arguments, and definitively sort out the bias that I've highlighted. A lack of reliable sources (stating, as previously explained, that experimental and theoretical physicists can accurately and precisely, in theory and practice, determine the exact motion of physical objects, including arrows and the like) will confirm this mediation has failed.Steaphen (talk) 01:18, 23 August 2009 (UTC)

  1. ^ J. Madeleine Nash, "Unfinished Symphony", Time, December 31, 1999, page 61
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