Talk:Balls and vase problem
From Wikipedia, the free encyclopedia
Contents |
[edit] History
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)
[edit] sci.math newsgroup
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)
[edit] Solution
The solution is 10-1+10-1+10-1+...
By straightforward arrangement, it is also 1-1+1-1+1-1+...
Therefore, according to Bolzano's Paradoxien des Unendlichen, the serie can be prooved to be any number and the problem has no mathematical solution.
AlainD 08:57, 13 January 2007 (UTC)
[edit] Article title
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)
- 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)
[edit] References in BJPS
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)
- 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)
[edit] The Lamp Paradox
Shouldn't there be a mentioning of the Lamp Paradox? It is basicily the same as the Vase Paradox, it goes at follows: "Let there be a Lamp which can have two states: "on" or "off". At t=1 the lamp is off, t=1/2 the lamp switches on, t=1/4 the lamp switches off and so on. The question posed is: what will the state of the lamp be at t=0?"
One of the suggested answers is that the lamp is neither on nor off, because it never reaches t=0. Maest 20:19, 4 March 2007 (UTC)
- Well, the two problems are similar, but they are not the same. The first asks for the final sum of balls based on adding and removing them from the vase, while the second asks what the "final" state of the lamp will be. The first question can be answered assuming that the time t=0 can be defined well enough. The second cannot be answered because even if time t=0 is defined, the answer relies on knowing the "last" step prior to t=0, when the lamp was switched on or off for the "last" time. The first problem needs no "last" step to be answered. It would be nice to have a "Lamp Paradox" article that could be added to the "See also" section, though. — Loadmaster 00:31, 6 March 2007 (UTC)
- I found the article, named Thomson's lamp, for the paradox you describe. I've added it to the "See also" section appropriately. And I added a redirect for Lamp paradox as well. — Loadmaster
