What about a bouncing ball? In terms of raw physics the ball technically bounces an infinite number of times but because the interval between bounces are increasingly short the total time converges to a finite sum (rather than diverging to infinity which would mean it bounces forever). This seems to be a supertask that happens all the time in the world. But if that is so then what does that mean? --Mike (July 24th 2006)
An infinite number of people sneezing simultaneously - is this a supertask? By the current definition it is since an infinite number of actions have been performed in a finite space of time. However I'm not sure I would classify this as a supertask and so believe the definition needs refining. Anyone any opinions?? --NoizHed 20:17, 30 August 2005 (UTC)
You're right. This isn't a supertask, since these infinite actions would take place in parallel. It's only a supertask when an infinite number of actions happen sequentially. For that reason, I don't see Hilbert's Hotel scenarios as a supertask either. —Preceding unsigned comment added by 22.214.171.124 (talk) 16:23, 21 May 2008 (UTC)
Ok I've completely redone this page, although only given a bare backbone to each section. Hopefully someone can bust it up a bit. NoizHed 18:10, 2005 Aug 23
Newton and determinism
I just came across this article and was thinking about some things. "Laraudogoitia’s Beautiful Supertask" reminds me of Zeno's arrow paradox (at least, one aspect of it). Even though the arrow has to travel through an infinite number of points, it still travels through all of them. Likewise, the moving particle in this "Beautiful Supertask" still transfers its motion (which travels at a constant speed through the line of particles) and causes the "last" particle to come off the end at whatever that speed is. In fact, couldn't this physical fact be used to dispute the assumption that an finite-length space can hold an infinite number of particles? 12:54, 11 September 2005 (UTC)
- The particles in the experiment are point masses so that would beg the question. However you could do a similar experiment where all the particles have non-zero volume, provided there is no lower bound on the radius a particle can have. You have each particle having half the radius of the one to its right, and let the far right particle have a radius of 10cm say. Also there is no "last" particle, so nothing comes out of the end after one second. That is part of strangeness of this experiment since when time is reversed there are no moving body's yet they spring into motion nontheless. --NoizHed 16:27, 11 September 2005 (UTC)
- Pardon my last question about if "finite-length [spaces] can hold an infinite number of particles"; it would seem I forgot they are point masses.
- Well my point is that assuming each point mass passes all of its kinetic energy on to the next mass in line, the effect would be that of one point mass traveling from one side of the line to the other at a constant speed (even though at every collision, the mass stops and the one it collided with continues on). This means that collisions would be happening more and more frequently (first after X/2 time units, then X/4, then X/8, etc.) until at X time units when the particle (if uninhibited by other particles) would have reached the end of the line. According to the supertask, all of the kinetic motion ceases immediately at the end of the line because there is no last particle on line. It is -that- which is violating conservation of energy, not the time reversal. The time reversal is just the same violation in reverse. So assuming that conservation of energy must hold, and assuming the existence of point masses and a non-discrete space in which they may reside and collide with perfect elasticity, does that not invalidate this supertask? 20:10, 11 September 2005 (UTC)
- That is exactly correct. However it isn't claimed that the time reversal is the cause of the violation of conservation of energy, it's the time reversal that causes the violation of determinism which was commonly thought to be a property of Newtonian particle mechanics. It is also true that if you assume conservation of energy the supertask is a contradiction. However Laraudogoitia considers CoE to be a derived result (so to assume CoE would be to beg the question against him), and he gets his conclusion from more basic assumptions - namely that particles draw continuous space-time paths, the exchange of velocity for equimassive particles (finally he assumes time reversal invariance - however that isn't needed to derive the violation of CoE as you quite rightly pointed out)--NoizHed 21:54, 12 September 2005 (UTC)
- It is assumed that Newtonian/Classical mechanics govern the environment in which the point masses exist? Determinism, etc. 22:57, 12 September 2005 (UTC)
- Newtonian mechanics is assumed, (to be more precise the result is derived from even weaker assumptions, namely the three I listed above). Determinism obviously isn't assumed, especially since the experiment shows Newtonian mechanics isn't deterministic after all! --NoizHed 17:50, 13 September 2005 (UTC)
- If you begin with those three assumptions (particles draw continuous space-time paths, velocity exchange for equimassive particles, and time reversal invariance), you've assumed determinism. Every particle has one path and only one path it can take through space-time (in both "directions of time"); this is because of time reversal invariance and particles having continuous space-time paths. I believe the apparent contradiction stems from the infinite number of particles in a line. -- 21:50, 13 September 2005 (UTC)
- What you just described isn't *causal* determinism. Trivially, talking about 4 dimensional space-time always involves a brand of determinism, but of a different (weaker) sort. Causal determinism is the kind outlined by Laplace, where given the velocities and masses of every particle at a particular time means you can deduce their positions, velocities, masses etc... at every future point. --126.96.36.199 19:02, 28 September 2005 (UTC)
- You can align an infinite number particles on the number line, but on the other hand you can't let the momentum go through all of them? There seems to be some inconsistency in the modelling, and/or that some parts are not as clearly defined as they seem to be. One thing I would like to point out is, the set-up actually assumes a mathematical system different to that based on the real number set, on which Newtonian mechanics is defined, by allowing us to think of infinitesmal quantities besides of the dimensions of objects. 188.8.131.52 (talk) 08:44, 15 March 2008 (UTC)
- Newtonian mechanics simply do not apply well to infinite densities as here.--Hagman (talk) 20:34, 19 May 2011 (UTC)
- What's being claimed as infinitesimal? An infinite number of particles on a line seems trivially realizable in real numbers (say, take a particle at each integer). CRGreathouse (t | c) 20:45, 19 May 2011 (UTC)
What's the difference between causal determinism and what I've described? Unless it's something like "a particle's velocity remains the same unless it collides with another particle" (which I assumed but should have included). I also noticed the definition at the beginning of the determinism article: "Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences." (emphasis added) This seems to imply that the phrase "causal determinism" is redundant - in that determinism already implies causality. Your thoughts? -- 00:28, 9 October 2005 (UTC)
This article contains a lot of hefty (and obscure) "references" to literature on rather new/contraversial subjects. Maybe links would be appropriate? - JustinWick 18:59, 19 November 2005 (UTC)
The question of whether supertasks are possible - ie. can exist in the 'real' world (whatever that is) - hinges on whether or not infinite is meaningful in that same world. I believe that the intuitive answer is the correct one: infinite is not a meaningful term in the real world.
The thought exercises produce logical paradoxes because they are impossible. String an infinite number of point masses together and what do you have? A black hole that swallows the universe. At that stage it becomes rather pointless to consider what happens when you try to move one, doesn't it.
So as fun as it may be to think of these things, it just seems silly to consider them in relation to reality. 3:39, 21 March 2006 (UTC)
- The point of the Zeno paradoxes was to show that these supertasks actually *do* occur in the real world. The ensuing literature from Thomson and Benacerraf concerned the question as to whether this was really a paradox or not. Also a distinction should be made between physically possibility and logical possibility. Many of the experiments are physically impossible yet, the claim is, they are logically possible. --NoizHed 13:53, 25 May 2006 (UTC)
- I think we don't understand nearly enough about our universe to conclusively decide whether or not "infinite" is a meaningful word within it or not, or whether these supertasks actually are occurring or not (consider very-small-scale discrete time/space vs. continuous). -- Ben-Arba 11:03, 28 May 2006 (UTC)
Comuputer Science and Supertasks
The meaning of the term supertask in popular computer science and in hypercomputing agrees with the one from mathematics and philosophy. There is no need for additional definition of supertask in the context of computer science. As far as the article about supertasks in multi-processor scheduling is concerned , this is just one of the uses, that is not widely known and accepted. Using this narrow definition to computer science in general would be stretching the point. Maybe just adding a section about other uses of the term supertask would be appropriate. --Marni 00:30, 30 June 2006 (UTC)
Wouldn't Wikipedia be one, since everything must be sourced, and to be trusted, sources must be sourced, which must be sourced, ad infinitum? 184.108.40.206 00:19, 15 May 2007 (UTC)
- No. The regress stops at primary sources and secondary sources acceptable under WP:RS; meta-sourcing of sources is also stopped by WP:AGF. --Gwern (contribs) 02:41 15 May 2007 (GMT)
Would anyone object if I added an example from Kafka to the Interesting Examples section? - all his characters seem to be struggling with a supertask of one kind or other, often internal - but one of the clearest examples is from his story 'The Great Wall of China':
- ...The messenger started off at once, a powerful, tireless man. Sticking one arm out and then another, he makes his way through the crowd. ... he moves forward easily, unlike anyone else. But the crowd is so huge; its dwelling places are infinite ... If there were an open field, how he would fly along, and soon you would hear the marvelous pounding of his fist on your door. But instead of that, how futile are all his efforts. He is still forcing his way through the private rooms of the innermost palace. He will never win his way through. And if he did manage that, nothing would have been achieved. He would have to fight his way down the steps, and, if he managed to do that, nothing would have been achieved. He would have to stride through the courtyards, and after the courtyards the second palace encircling the first, and, then again, stairs and courtyards, and then, once again, a palace, and so on for thousands of years...
What do you all think? Adambrowne666 09:20, 27 July 2007 (UTC)
- Well, according to the definition a supertask is an infinite sequence of tasks that occurs in a *finite* amount of time. It is implied that Kafka's messenger carries out his tasks for ever. --NoizHed 12:35, 8 August 2007 (UTC)
Nonsense in section on Ross-Littlewood (infinitely many marbles) paradox
The section on the Ross-Littlewood paradox is filled with utter nonsense. Such as:
"Of course, it would be wise to heed Benacerraf’s words that the states of the jars before t = 1 do not logically determine the state at t = 1."
The following sentence is also unsupported by logic, for there is no reason to believe that this just-change-the-numerical-labels version ought to have the same result as the original problem (or any result at all!!!).
"A bare-naked variation that really goes straight to the heart of all of this goes as follows: at t = 0, there is one marble in the jar with the number 0 scribbled on it. At t = 0.5, the number 0 on the marble gets replaced with the number 1, at t = 0.75, the number gets changed to 2, etc."
Most important, this is not one of those paradoxes that remains ultimately unresolved! There is only one correct way to think of this, and all the ways of thinking that lead to different conclusions are flawed by reasoning that assumes facts not in evidence regarding infinities. A fully correct analysis of this paradox was given by Martin Gardner when he described the paradox's resolution in Scientific American. An erroneous analysis is given in the second edition of the book "Paradoxes from A to Z" by Michael Clark.Daqu (talk) 15:07, 9 July 2009 (UTC)
- You really need to explain why you make these statements. What is Gardner's analysis, and why is that one correct? What is Clark's analysis, and why is that one incorrect? And finally, the bare-naked variation is a variation, so why should one suppose that it should have the same result as the original problem? —Preceding unsigned comment added by 220.127.116.11 (talk) 13:35, 13 July 2009 (UTC)
- I will at some point explain why I have made these statements. But on what basis should *I* need to explain why I make these statements??? The ones who need to explain their statements are those who wrote unsupportable claims in the article (something I have not done).Daqu (talk) 10:46, 26 November 2009 (UTC)
- The idea that the state at t=1 is not determined is eminently sensible. Gardner's analysis is fine for supertasks done in a well-ordered manner, but nonsense otherwise. And what "fact in evidence" about infinity allows for only well-ordered supertasks? --Unzerlegbarkeit (talk) 01:22, 12 April 2010 (UTC)
Most subsequent philosophers reject Zeno's bold conclusion in favor of common sense.
no actual infinity
these supertasks only show that the nature of infinity is potential, not actual...such thought experiments are entertaining as novelties, but vacuous if meant to be taken seriously...
take the case of "guessing the positive integer"...I am thinking of a positive integer, can you guess which one?...let's say you approach this in an orderly way and ask is it 1? is it 2? is it 3? etc... were I thinking of an integer between 1 and 10, there would be an N such that after N "no" answers, the answer would have to be a "yes" answer, i.e. N=9... but since there are infinite positive integers, in our case there is no such N...in other words, even though it is true that one of the integers is my number, it is also true that for any N, I can logically, without contradicting myself (lying), have given you a series of N "no" answers...put this in the form of a supertask, and at T = 1, you have run through all the positive integers, have not received a "yes" answer, and so have not been able to guess my integer, although it certainly seems as if you should have!
paradoxical results such as this only mean there is a mistake somewhere in our reasoning...the more intractable the paradox, the more subtle the mistake, that's all...and a mistake can be so damned subtle that most thinkers to this point have missed it, or for reasons of their own, chosen to miss it... 18.104.22.168 (talk) 22:41, 7 August 2010 (UTC)
Laraudogoitia’s supertask impossible
since all particles have width, it will be impossible to put infinity of them in a line, and all the particles will all be vibrating, so it is impossible for them to stop completely. —Preceding unsigned comment added by 22.214.171.124 (talk) 01:45, 24 February 2011 (UTC)
The version of the Supertask article edited by user:Quuxplusone at 18:40, May 1, 2013, in the section Davies' super-machine says that the Supertask construction in the Davies paper "Building Infinite Machines" is physically impossible because it requires the infinite divisibility of space and time. However I just read the Davies paper and it doesn't seem to mention that, nor does the Wikipedia article Atomic theory, cited by that same version of the article. While there are some speculative theories in which space and time are discrete (for example Causal sets), in both General Relativity and the Standard Model, currently the two most widely accepted fundamental theories of physics, space and time are explicitly formulated to be infinitely divisible. In both those theories events in space and time are represented using points in a Differentiable manifold, which is infinitely divisible. I'm going to edit the article to reflect the issues that Davies actually raised in his paper. Pmokeefe (talk) 14:52, 3 September 2013 (UTC)
Deleting the section The diary of Tristram Shandy
"A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time." "Tristram Shandy, the hero of a novel by Laurence Sterne, writes his autobiography so conscientiously that it takes him one year to lay down the events of one day." Shandy is only doing a finite amount of work (laying down the events of one day) in a finite amount of time (one year), so that is not an example of a supertask. I'm going to delete the section. Pmokeefe (talk) 15:33, 3 September 2013 (UTC)
- This contradiction appeared when you added
- 'a sequence of events that never stops',
- which itself contradicts the actual assumption:
- ' a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time'.
- And a finite interval obviously ends, hence anything that happens within the interval, stops.
- You may, of course, see a contradiction in the infinite sequence of events happening within a finite time, but that's a different topic. CiaPan (talk) 15:28, 6 April 2019 (UTC)
"In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time."
That is simply and fundamentally wrong: beside that "philosophy" proper has little to do with it (or "cardinality" for that matter), a "supertask" is the *limit* of any such sequence, and "time" is totally irrelevant if not as an expository device.
(For example, Achilles does eventually reach the tortoise, but how long it takes is irrelevant, crucial is that it happens in the *limit* of the sequence of steps taken.)
- Claims abaout correctness or wrongness of a definition should be supported by references to literature. No definition is inherently right or wrong. A definition is correct if it correctly identifies the meaning of the defined term. Unless otherwise specified the correct meaning is the one most commonly used in the literature. If there is variation in the literature that should be mentioned in the article. 2001:14BB:C3:9C72:5146:A4F2:587B:CD5 (talk) 10:42, 15 November 2023 (UTC)
- I understand the idea of backed-up by references, but that is just not all there is to any argument or article and certainly not in a comment: moreover here I should literally reference at least three centuries of mistakes pervading all the literature. This article does reflect common understanding and even common literature, that doesn't change that fact that it is essentially and fundamentally wrong and in a way that is blatant as I do have in fact explained, for how briefly. This article should be rewritten from scratch. LudovicoVan (talk) 11:27, 15 November 2023 (UTC)