Talk:Angel problem

message: Is the power measured as Pythagorean or New York distance? Or some other metric? -- The Anome 10:55, 17 Oct 2004 (UTC)
thread_title: Defn of distance

message: Is there a known lower bound for the angel's power C in the three-dimensional case so that the angel has a winning strategy? I.e., is a number c known such that a winning strategy exists for all C >= c? -- Schnee 00:04, 25 Oct 2004 (UTC)
replies: text: Cool, thanks. I'll check out that dissertation. ^^ -- Schnee 18:28, 5 Nov 2004 (UTC)
thread_title:  Lower bound for ''C'' in 3D case? 

message: Shouldn't Tom Körner be credited for the proof? Gdr 19:41, 2004 Nov 7 (UTC)
As I understand Tom Körner showed that for high enough dimension the angel can escape but not for 3 dimensions.  Imre Leader gave a seminar about his proof which Tom Körner knew about (They are in the same department).  But Tom did not ask for credit.  So probably not.  This other guy who published the paper linked to above should probably be mentioned though.  I'll do that.  Barnaby dawson 21:39, 7 Nov 2004 (UTC)
thread_title:  Multi-dimensional angels 

message: Hello, the above was referred to in the article. Which topology is that? --AlephNull 16:08, 25 November 2005 (UTC)
thread_title:  The Natural Topology on the Set of all Plays 

message: Hi Barnaby
I made the edit, because I thought it would be clearer to a lay person who would have no idea what "the angel has power k" means. They might think it means something like in a role playing game. So, I think it's more than style, it's about a better understanding for the reader. Hope you can live with my edit. Mccready 01:49, 30 April 2006 (UTC)
thread_title:  Style 

message: I have removed the not verified message.  The anonomous editor who added it did not specify what information in the section was not verifiable.  For the record all the results in there (apart from the recent proof claims) come from the notes I took at a seminar on the angel problem (including a solution for the 3D case) given by Imre Leader.  I have seen proofs of all of them bar the last.  We might not be able to find these proofs in print.  Barnaby dawson 08:01, 30 September 2006 (UTC)
thread_title: Verified

message: I have removed a sentence saying that two of the claimed proofs have been accepted in a peer reviewed journal on the suggestion of the author of one of them.  He felt that this was not normally general knoledge and that it might seem to give priority to those solutions.  Barnaby dawson 13:08, 2 October 2006 (UTC)
replies: text: Well, that's very nice of him, but really priority isn't based on publication date, as well he knows.  A more important issue is that we need to provide important information like this to our readers as appearing in some peer-reviewed journal is an integral part of whether the general reader will accept something to be solved or not.  For example, I had to revert an edit from another article that removed a description of the problem as "solved".  But it's solved by reasonable standards.  It would be absurd to not provide this info and wait until all these solutions get published or an author retracts his paper.  So I'm going to reinstate the information on publication.  --C S (Talk) 12:41, 13 May 2007 (UTC)

text: The Bowditch and Máthé papers have been published in the May issue of Combinatorics, Probability and Computing.  So the justification for removing the info (that it is not generally known info) is not really a good one anymore.    --C S (Talk) 12:51, 13 May 2007 (UTC)
thread_title: Avoiding interference with the academic process

message: Is this still supposed to have the "Unsolved Problems" tag?  The article states flatly in the end of the introduction that the problem is solved, but later doubt is raised as to whether the proofs actually work. --Whiteknox 12:37, 28 July 2007 (UTC)
thread_title:  Remove unsolved tag? 

message: After reading the article, I was still uncertain about the status of the 2D problem. Suppose the angel has power k and the devil has power m. What is the result of the game for different values of k and m?
As I understood:
k=1: Devil wins (Conway)
k>=2, m=1: Angel wins. (Máthé, Bowditch)
How about the cases k>=2 and m>=2? Were these results proved too or are they still open?
There must be some limit, i.e. even if the angel has power 1000, if the devil has enough power (take 10^10 for example), he can bound the angel.  —Preceding unsigned comment added by 212.50.147.101 (talk) 07:36, 26 October 2007 (UTC)
thread_title:  Different powers of angel and demon? 

message: Does anyone know whether a 1-angel can win in 3 dimensions? --128.12.103.70 (talk) 19:36, 15 April 2008 (UTC)
thread_title:  3-D angels 

message: In Conway's paper the Devil is described as destroying or "eating" squares. But in the description here the squares are said to be "blocked". I think the original language should be preserved. Likewise, most descriptions follow Conway in describing the game as taking place on a checkerboard-style grid of squares, but the illustration here shows a Go-board style grid of intersections. The change is unnecessary and potentially confusing. One of the hallmarks of the original problem is its vivid and memorable imagery, I think the presentation here should preserve this.  67.83.200.217 (talk) 05:21, 19 April 2009 (UTC)
thread_title:  Description and Illustration 

message: The article contains some sketches of proofs for complex cases like a "high-powered 3D angel", but there is no indication of the proof for what I believe is the simplest case, the 1-angel in 2D. The article states that in this case the Devil wins, but wouldn't it make sense to have at least a sketch of this proof (or if it is too complicated, at least an indication of this)? 80.194.194.190 (talk) 09:29, 21 August 2009 (UTC)
thread_title:  Proof that the Devil wins againts a 1-Angel in 2D? 

message: How did anyone ever publish a paper on proving (say) the 4-angel? If I'm the angel, and my coordinates are the origin, I can just move 4 spaces to the top-right every turn and run away from the devil. If he blocks that one square, I'll just move four spaces to the top-left instead. In fact, I can't see how for any power, even 1, the devil has a prayer of winning. I feel this article must be really poorly explaining something because it seems a joke otherwise. Red Slash 23:57, 13 May 2013 (UTC)
thread_title: ?? Is this poorly explained or the easiest problem ever??

message: The proof that the 1-angel loses to the devil is quite easy, and it's found in Kutz's PhD paper (first few pages) http://www.mpi-inf.mpg.de/alumni/d1/2009/mkutz//diss/kutz_angel.pdf  — Preceding unsigned comment added by 2.24.200.212 (talk) 00:39, 12 December 2013 (UTC)
thread_title: Win for the Devil

message: "If we have an infinite number of devils each playing at distances d_1 < d_2 < d_3 < \cdots then the angel can still win if it is of high enough power."
This is obviously not true. For a given power k, there is a distance d where 8*k^3 devils can play. So if the angel goes that far out it can be trapped in one turn. So the angel is bounded and can be trapped by randomly adding blocks until it can't move. Folket (talk) 13:10, 1 April 2014 (UTC)
thread_title:  infinite devils 

message: I recently read through all four claimed solutions to the Angel Problem. I am confident that Kloster’s proof and Máthé’s proofs are correct. Kloster’s proof is the cleanest, simplest, one of the two strongest ones (k = 2), and of the two strongest proofs, the only one that directly provides a constructive algorithm. This article should therefore be updated (either by me or someone else) to include a description of this solution. Bowditch’s proof also seems correct (although it’s more complicated), but actually only proves the k =9 case, not the k = 4 case, since Lemma 3.7 (in the journal version; Lemma 2.7 in the arXiV version) is incomplete.
I spent quite a bit of time trying to read Gacs’ proof and found a potentially problematic section. Lemma 4.4 states, “Using the fact that the angel’s current position is in a (−1)-safe cell”; I do not know how to verify this claim though, especially since Lemma 4.4 doesn’t seem to make any reference as to the actual position of the angel at this time, merely about which cells are currently “clean” and “safe,” and I was also unable to verify that this claim is correct in general. I emailed Professor Gacs last month and he said he didn’t remember the proof in enough detail to answer my question.
I know this constitutes original research, and I am not a professional mathematician (I’m a software engineer);  is there any way to update the article with this information? If anyone else has read these proofs, did you notice the same issues? rdl381 (talk) 07:43, 29 October 2022 (UTC)
thread_title:  Is Gacs’ proof correct?