Talk:Ross–Littlewood paradox

message: This article needs a History section detailing who first proposed it, historical arguments, etc. I have not yet found any good references on the web, but I remember seeing two or three good articles in the past. — Loadmaster 22:14, 6 November 2006 (UTC)
thread_title:  History 

message: This problem has been discussed to death on sci.math.  I've listed a few of the more recent (2005−2006) threads. — Loadmaster 22:14, 6 November 2006 (UTC)
thread_title:  sci.math newsgroup 

message: Would this article not be more accurated titled Ross-Littlewood paradox?  Also, Supertask#Ross-Littlewood_paradox contains more good information than this article; some content really should be moved to here, leaving a shorter summary in the Supertask article. ~ Booya Bazooka 04:01, 25 January 2007 (UTC)
replies: text: That's probably the best approach, to merge this article with Supertask#Ross-Littlewood_paradox into a new Ross-Littlewood paradox aticle. Then the contents of the section in Supertask can be condensed, being replaces with a "Main article" link to the new article. — Loadmaster 22:01, 15 February 2007 (UTC)
thread_title:  Article title 

message: The British Journal for the Philosophy of Science has two relevant publications regarding this topic:
* "On Some Paradoxes of the Infinite". Victor Allis; Teunis Koetsier. Vol. 42, No. 2. (Jun., 1991), pp. 187-194.
* "Ross' Paradox Is an Impossible Super-Task". Jean Paul Van Bendegem. Vol. 45, No. 2. (Jun., 1994), pp. 743-748.
Electronic versions are available on JSTOR if you have access to it. ~ Booya Bazooka 04:28, 25 January 2007 (UTC)
replies: text: I went ahead and added those two references to the "References" section of the article. They need to be wikified into ref form, though. — Loadmaster 17:19, 22 February 2007 (UTC)
thread_title:  References in BJPS 

message: A variation of the Balls and Vase problem is the Pearl of Wisdom. An example of the tale can be found at www.246.dk/pearl.html. — Loadmaster 22:03, 13 August 2007 (UTC)
replies: text: The link has disappeared, but can still be found in the WayBack Machine archive here or here. — Loadmaster (talk) 02:14, 8 February 2011 (UTC)
thread_title:  Pearl of Wisdom 

message: I think this problem simply shows that you have to be careful about your terms - in particular, when talking about limits, you have to define your topology first. 
The problem can be phrased like this: We have a function f from [0,1] to some state space of the vase, let's call it X. We have defined f on a sequence converging to 1 and would like to know the continuous continuation.
If we let X be the one-point compactification of the real numbers and f(1-2^-n)=9n, then the limit is infinity.
On the other hand, if we let X be 2^\mathbb{N} (each component representing the presence or absence of an individual marble) with the product topology or in other words the topology of pointwise convergence, and f(1)=(1,1,...,1,0,...) (10 ones, then zeroes) and f(2)=(0,1,1,...,1,0,...) (0, then 19 ones, then zeroes) and so on, then the limit is the zero sequence, since every component pointwisely converges to zero.
You see, it's just a matter of proper definitions. If there is a notable source for this argument, I strongly suggest adding it to the article. Functor salad 04:10, 16 October 2007 (UTC)
thread_title:  My 2 cents 

message: Another variation is Benardete's paradox, said to be an extension of Zeno's Paradox, which is described at thinkquest.org. Briefly, the god Zeus decides to kill Prometheus by issuing an order to an infinitude of his demons, ordering the first demon to kill Prometheus if he is not dead by 2:00, the second to kill him if he is not dead at 1:30, the third to kill him if he is not dead at 1:15, etc., each demon killing Prometheus in half the time interval of the subsequent demon. The strangeness comes in the realization that Prometheus is indeed dead by 2:00, but yet no specific demon killed him. — Loadmaster (talk) 04:11, 30 March 2008 (UTC)
thread_title:  Benardete's Paradox 

message: The Original Research tag is debatable. Set theorists are clearly in agreement that the first answer (zero balls left in the vase) is correct. The other solutions are variations on the conditions and "meaning" of the problem. — Loadmaster (talk) 02:25, 17 August 2009 (UTC)
thread_title:  Original research 

message: Talk:Balls and vase problem →  — This article was moved without moving the corresponding Talk page.  The new talk page only has a single edit, the addition of a wikiproject template. ~ Booya Bazooka 00:56, 1 November 2010 (UTC)
replies: text: . By the way, it's okay to just use  in clear-cut cases like this. Jafeluv (talk) 13:31, 7 November 2010 (UTC)
thread_title:  Requested move 

message: I think the section on the "no balls left in vase" solution needs to be rewritten. It really doesn't make sense on face-- of course there is always a step n at which ball n is removed, but it's just as obvious that at at every step n, nine more balls are added. I'm not trying to argue against inclusion of this section; I just think it needs to be rewritten so that it at least makes some small amount of logical sense on face... I hope this makes sense. Thanks  — Preceding unsigned comment added by 70.36.226.136 (talk) 21:50, 1 August 2013 (UTC)
thread_title:  Section needs rewriting 

message: I did a quick google search, and I can find no mention of the distinguishability of balls. In physics, the statistics of particles depends on whether the particles are distinguishable or not, i.e. does swapping ball 1 and ball 2 change the state of the system in some way. It seems in this case that the balls are being counted, but with indistinguishable balls, there is no ordering which is unique. It makes no sense to say "I removed the first ball, then the second, then..." since there is no ball #1, 2 or 3. In an indistinguishable case, you can only specify the states of the balls probabalistically. After the first step, there are 10 balls in there, each with a 1/10 probability of being removed. After this, I believe the math gets hairy, since you can't remove a ball you already removed, and thus you need to calculate the probability of each ball being removed given that it was not removed in any previous step. Then you have to do a sum to find the number of balls left 47.21.153.202 (talk) 15:31, 9 August 2013 (UTC)
replies: text: I'm not sure, but you seem to be confusing physical reality with abstract mathematics. It's an abstract mathematical/logical gedankenexperiment, wherein we use an infinite number of abstract "balls". We assume each ball is uniquely labeled (e.g., with the natural number reflecting the order in which it is inserted into the vase). Such labeling allows us to keep track of which balls were inserted and which were removed at any given moment during the procedure. Perhaps we need to add some verbiage making it clear that there is a labeling employed, or some other means used to uniquely distinguish between different balls. — Loadmaster (talk) 23:01, 9 August 2013 (UTC)
replies: text: I think my suggestion is that, when dealing with inifinites within the context of this problem, the ability to uniquely number the balls is broken. I suggest this due to what I percieve as a kind of "reductio ad absurdium", wherein changing which balls we remove, but not how many, changes how many balls are left in the vase. This challenges that we can uniquely number the balls we put into the vase, which seems to be a major premise of the proposed solutions to the paradox. I suppose my new premise, due to the statement of the problem not explicitly defining how we remove balls from this vase, is that they are removed at random, and that this may lead to a non-self-contradictory solution to the problem. Then again, it may just push the problem off on to how the probabilities are calculated, instead of which ball is removed. My parallel to physics is due to my personal training in physics and total lack of formal or significant informal education in the mathematics of infinites outside the scope of physics, which I can completely understand as significantly hampering my ability to comment on this problem. 47.21.153.202 (talk) 18:15, 12 August 2013 (UTC)
replies: text: Your suggestion sounds a lot like the assertion that the Axiom of Choice is required for the infinite case, which is by no means a principle that all mathematicians take for granted.  That's actually a very helpful observation for me, but seems a bit out of scope, as it is original research of the solution.  70.247.167.104 (talk) 13:59, 11 February 2014 (UTC)
thread_title:  Indistinguishability and probabalistic behavior

message: Who is the paradox named for?  70.247.167.104 (talk) 14:11, 11 February 2014 (UTC)
replies: text: Good question. The authors are listed in the "Further reading" section: John E. Littlewood (author of Littlewood's Miscellany, 1953) and Sheldon Ross (author of A First Course in Probability, 1988). A Google search also turned up this document (also here) that lists the same books and authors. I've added some links to the article for them. — Loadmaster (talk) 16:28, 11 February 2014 (UTC)
thread_title:  Ross Who?  Littlewood Who? 

message: In the introduction, it is never said how many balls are added or removed at each step. when reading the solution part, we have first "since at every step along the way more balls are being added than removed" but it was never assumed before. that is just a problem of formulation because after it seems obvious that 10 balls are added and 1 is removed at each step. but in the introduction, it seems that the problem is more general, and that any number of balls could be added and removed. 150.65.16.33 (talk) 12:27, 25 June 2014 (UTC)
replies: text: Yes, the article at present is a complete (erroneous) mess. The way Littlewood stated it, the answer is quite clear (not that this prevents crank nonsense, which WP seems to require equal attention to); the problem as stated in the article at present has no solution. (But I can't completely understand your comment either...) The article should be rewritten, starting by quoting the problem as posed by Littlewood... I have a copy of the Miscellany somewhere, and keep meaning to do it. Imaginatorium (talk) 15:31, 25 June 2014 (UTC)

text: I just edited the description of the task to say "at each step 10 balls are added to the vase and 1 ball removed from it". MaigoAkisame (talk) 13:56, 19 April 2017 (UTC)

text: Oh, I realized the text already contained this sentence in a different place. I removed the original sentence, so the effect of my edit is moving it to a place which makes the text more coherent. MaigoAkisame (talk) 15:23, 19 April 2017 (UTC)
thread_title:  Problem description is not precise 

message: The problem description adds the first balls at 11:59:30, while the figure adds the first balls at 11:59:00.  The figure matches the description in Ross, so I think the problem description should be changed.  Additionally, the problem structure is perhaps better revealed by this chart:
Cerberus (talk) 15:48, 19 September 2017 (UTC)
thread_title:  Figure vs Problem Description 

message: The "Vase is empty" solution uses this logic: "This means that by noon, every ball labeled n that is inserted into the vase is eventually removed in a subsequent step."
Now consider the question, "at what time, or in which step, is the last ball removed?" The answer is there is no last ball. But I don't think this question can go in that section, because it's not part of the logic leading to this solution. Where could it go? 23.121.191.18 (talk) 06:09, 28 January 2020 (UTC)
thread_title:  Where could this go in the article? 

message: Ross, of course, deserves credit for whatever work he did on the problem.
But: The paradox was invented by Littlewood, not Ross.  So Ross does not merit having his name attached to the paradox for developing it further, 35 years later!
(Also: The paradox was discussed by Martin Gardner in his Mathematical Games column in Scientific American long before Ross mentioned it.) 2601:200:C000:1A0:18:344C:F94C:B721 (talk) 00:55, 25 March 2022 (UTC)
thread_title:  Ross deserves credit ... but NOT for coming up with this paradox 

message: I propose either moving "depends on the conditions" under "vase is empty" or to a new section about "variants of the problem", since it follows the same logic as the "vase is empty" solution except with similar problems C7XWiki (talk) 05:56, 27 March 2022 (UTC)
thread_title:  Section "depends on the conditions"