Talk:Maze: Difference between revisions

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Where did that definition of labyrinth came from? That's not the common definition. --Voodoo 23:30, 18 Apr 2004 (UTC)

This is not advertising, since the book is long out of print and the Web sites do not contain advertising. Please restore this material as this is a very popular puzzle book. Canon 19:57, 22 January 2006 (UTC)[reply]

OK Canon, I have restored it. If the material is of use to people other than the promoters of the book, then I guess it deserves to stay. I'm sorry to have deleted it so hastily. --Heron 20:58, 22 January 2006 (UTC)[reply]

Thanks very much. Canon 00:20, 23 January 2006 (UTC)[reply]

Does someone want to back up the claim made in the opening paragraph that a maze is different from a labyrinth? If not it is both wrong and a distraction. Canon 23:41, 25 March 2006 (UTC)[reply]

The terms "maze" and "labyrinth" seem to have been used interchangeably for centuries, and still are. However, since this topic began to be the subject of scholarship and comparative theorising, scholars have needed to differentiate between the entertaining puzzle (in which one gets lost in dead-ends), and the unicursal type (which takes just one, very convoluted, path to its centre). They have settled upon "maze" for the former and "labyrinth" for the latter: see the reading list and many of the external links cited for examples of this usage. Admittedly it can be confusing for non-specialists and specialists alike (eg most of the structures generally known as turf mazes are unicursal labyrinths); perhaps this distinction needs to be summarised in the introductions to both the Maze and Labyrinth pages. SiGarb | Talk 22:23, 26 March 2006 (UTC)[reply]

I did as you recommended and the earliest mention of a difference in the meanings occurs in the book by Matthews (1922):

We might perhaps point out that a slight shade of difference may be assumed to exist between "labyrinth" and "maze," even when these words are used in their metaphorical sense. We may take "labyrinth" to signify a complex problem involving merely time and perseverance for its solution, "maze," on the other hand, being reserved for situations fraught, in addition, with the elements of uncertainty and ambiguity, calling for the exercise of the higher mental faculties--in short, we may regard the two words as having reference respectively to the unicursal and multicursal types of plan (see Introduction). A distinction of this kind adds point to a sentence like that which occurs, for instance, in Mr. Lytton Strachey's "Queen Victoria," where he tells us (p. 178) that the Prince Consort "attempted to thread his way through the complicated labyrinth of European diplomacy, and was eventually lost in the maze."

This looks like an example of the refinement of meaning that occurs in many disciplines (e.g., the words "force" and "energy" mean something to a physicist that is much more precise than the meanings of these words to the non-physicist). I agree that this needs to be spelled out in the introduction, which at the moment is off-putting to non-specialists. Perhaps something like:

Specialists use the term "labyrinth" to refer to paths that do not branch and "maze" to refer to paths that do branch.

I would make this change myself but as a non-specialist I think it is inappropriate for me to speak for specialists. Canon 01:11, 27 March 2006 (UTC)[reply]

I think the distinction between branching and non-branching for maze and labyrinth should be made early. It is easy to grasp and remember. Stephen B Streater 06:55, 27 March 2006 (UTC)[reply]

I always learned that a maze has branches and is designed to be difficult to navigate, and labyrinths have a single, non-branching path. I don't have any sources to back this up, except for experience. I learned that labyrinths were used for spiritual purposes, and they were always a curving path that led to a center region, and the center represented God, and the curving path represents a spiritual journey. Labyrinths also (I think) usually come out the way that they came in, where as a maze usually involves going from point A to point B. At least that's always what I believed. --Sbrools ^{(talk . contribs)} 03:40, 17 January 2007 (UTC)[reply]

I wouln´t quarrell if my edit was reverted. But see Talk:Maize first. --Ezeu 08:26, 30 April 2006 (UTC)[reply]

It has been disputed if the of an image in this article, Image:Rats running around in a maze.png, qualifies as fair use. Please add a fair use rationale to the image description page, explaining why the image quallifies as fair use. --Fritz S. (Talk) 09:02, 29 July 2006 (UTC)[reply]

Who is Jon Pledge of Exeter? Does he exist? Does anybody know? - RTH 17:28, 13 November 2006 (UTC)[reply]

I wonder. It's been around since this edit [1] in 2004, made by an editor whose other contributions (most of which are made in 2004) seem quite sensible. However, googling for "Jon Pledge" mostly gives hits that are either totally unrelated to mazes, or that are mirrors of en.wikipedia. An independent source would be really good here! —The preceding unsigned comment was added by Noe (talk • contribs) 17:47, 13 November 2006.

It should be removed. I am tagging it as unsourced in the time being. --Ezeu 23:55, 15 December 2006 (UTC)[reply]

According to Abelson and diSessa, John Pledge discovered the method when he was 12 years old. (Turtle Geometry: the computer as a medium for exploring mathematics, page 177). I have added a "see the book". See here: http://books.google.com/books?id=3geYp44hJVcC&pg=PA179&lpg=PA177&vq=pledge&dq=Abelson+disessa&as_brr=3&output=html&sig=Bk5zudgf-MMb3FTUHz_rBpPBW2Y (you would need a Google acount) - 190.30.193.60 00:24, 31 May 2007 (UTC)[reply]

However, there seems to be a related result in searching mazes based on a grid, with a quite similar approach, keeping track of your turns and counting the number of grid squares you have passed. M. Blum, D. Kozen. On the power of the compass (or, why mazes are easier to search than graphs), in: Proceedings 19th FOCS (Annual Symposium on Foundations of Computer Science), 132--142, 1978. Jochgem 13:43, 15 March 2007 (UTC)[reply]

So called "Pledge" and other algorithms will work in computer programs, but only experts are able to use them - the paragraph should be removed. The "wall-follower" method (simple, but restricted) and the Trémaux method (more difficult) are the only algorithms that work in reality, too. (The explanation of the Trémaux method under [1] is not correct!) - It would be a good idea to separate the more mathematical problems of mazes from the history of the traditional hedge maze. Nowadays mazes seem to be very British... but the (puzzle) hedge maze is an old element of garden design, first developped during the late Renaissance in Italy. (Try to read "my" article de:Irrgarten) -- RTH 16:27, 30 March 2007 (UTC)[reply]

Actually the Pledge algorithm can easily be applied by hand, both when looking at a map and when actually inside a life size Maze. All you need is some way to determine whether you're facing a particular direction (such as you're looking at a map, have a compass, or have a fixed landmark like a mountain). Applying the Pledge algorithm is just like wall following, except you move forward (potentially between islands) when exactly facing the particular direction (assuming you haven't turned yourself around to the left or right one or more times). Assuming you can detect your direction, and count the number of times you've twisted yourself around, the Pledge algorithm can be done by hand or computer. Hopefully this is clear in the current version of the article. Thanks, Cruiser1 14:12, 19 September 2007 (UTC)[reply]

O.k., using a compass or a map... (why not GPS?). -- RTH (talk) 16:26, 9 January 2008 (UTC)[reply]

Hi all. Is anybody aware of either positive or negative results for 3d maze solving? (I understand this question is maybe slightly off topic, but thanks anyway for any info.) Regards,--Powo 13:23, 2 February 2007 (UTC)[reply]

I think you're going to have to be more specific to get an answer. What are positive or negative results? What is supposed to solve the maze in which way, and what makes 3D special? --Jonathanvt 20:07, 11 April 2007 (UTC)[reply]

Solving a 3D maze is exactly the same as solving a 2D maze if you see the maze as being a graph. Probably, the only solution would be to use brute force, i.e. you recursively choose a random path at each junction and backtrack to take a different one if it turns out to not be the right one. (That's exactly what "follow the wall" does.) If that doesn't answer your question, then please be more specific. 83.79.52.201 (talk) 17:07, 24 March 2008 (UTC)[reply]

"Recursive backtracking" is very different from "follow the wall". Recursive backtracking uses a stack to keep track of all junction choices you've taken to reach the current point, and marks the Maze when backtracking so you always visit every cell in the Maze exactly once (regardless of its topology). Following a wall just means always taking a particular junction choice relative to the direction you're facing, where this method may not visit all cells in Mazes with loops before returning to start, meaning unlike recursive backtracking, wall following isn't guaranteed to find the solution to a Maze (although it at least works on many Mazes). Thanks, Cruiser1 (talk) 22:33, 28 March 2008 (UTC)[reply]

Hi there just a suggestion/question, should the maze at stuart landsborough's puzzling world be included in the mazes open to the public section. it costs a small amount to enter and is "the worlds first"modern-styled" great maze

The link to the german WP article Irrgarten might be misleading. The authors understand the article as purely garden-related, i.e. it only deals with botanical maze-like arrangements. Any reference to other representations (especially the mathematical stuff) seems to be very unwelcome there and are removed almost immediately. I have also doubts that "irrgarten" is equivalent to "maze". In german popular language, most people use the term "labyrinth" that, in modern times, seems to be almost equivalent to "maze". But maybe there is no fully equivalent German translation of "maze". Therefore I recommend removing the link to the German article.--SiriusB 10:50, 14 August 2007 (UTC)[reply]

I will add a description of wall-follower and Trémaux etc. in de:Irrgarten. (You are right: the main aspects are garden related.) -- RTH (talk) 16:33, 9 January 2008 (UTC)[reply]

Almost all the links to external sites in this article seem unnecessary. They are also really annoying an lead the casual reader on a wild internet goose chase. Most i'm guessing are just advertising. I'll leave it to someone who knows this article well to crop them out rather than just hack them out myself with no knowledge of the subject. thanks in anticipation! extraordinary 14:53, 23 August 2007 (UTC)[reply]

I made the following edits: (1) Moved the "Mazes open to the public" section to right before "External links", because they're both basically a list of links. (2) Moved the "Publications about mazes" section to right before "Further reading", because they both concern books about Mazes. (3) Moved the "Generating mazes" section to right after "Maze Construction", because they both deal with making Mazes. This didn't remove or change any content, but it does make the article a bit cleaner. Thanks, Cruiser1 12:50, 18 September 2007 (UTC)[reply]

Removed internal link to cut-the-knot. The cut-the-knot page doesn't even mention Mazes, much less why it's fundamental enough to be one of two "see also" links on the main Maze page. If cut-the-knot is notable with respect to Mazes, it should be added to Category:Mazes. Thanks, Cruiser1 (talk) 03:31, 7 February 2008 (UTC)[reply]

Ganna try t make the article better today. --Stealth500 (talk) 17:16, 24 November 2007 (UTC)[reply]

There are many important maze algorithms for when you can see the entire maze, but these are not discussed. They are used, for example, to solve mazes on paper, or with computer programs. Additionally, the algorithms give some insight into the mathematical structure of mazes. Would it be appropriate to discuss the dead end filling algorithm in this article? A good description of the algorithm is seen here: [2] (about 2/3 the way down the page), and a video of it in action is here: [3]. —Preceding unsigned comment added by 98.203.237.75 (talk) 12:38, 7 January 2008 (UTC)[reply]

Dead end filling algorithm: good idea, easy to understand. But don't add all algorithms, I think, it's too much. The differences between Dead End and Cul-de-Sac (french translation of dead end) should be explained. In German: possibly "Sackgasse" versus "tote Galerie". -- RTH (talk) 16:57, 18 January 2008 (UTC)[reply]

Any maze can be topologically mapped onto a three-dimensional maze. Does this mean that even a 42-dimensional (let's say rectangular) maze can be projected into a 3D space (naturally no longer being a rectangular one) without additional crossings? Is there any proof to this statement that could be cited here?--SiriusB (talk) 11:27, 29 January 2008 (UTC)[reply]

The above is indeed true. Beyond that, any Maze can be mapped to a 2D Maze if you allow over and under passages. A standard Maze (of any number of dimensions) is basically just a graph, where junctions are vertexes/points, and passages are edges/lines between vertexes. You can topologically move or flatten those vertexes so they're all in a plane. The edges between the vertexes will probably overlap, but as long as those overlapping edges are distinguished from actual vertexes, you can say the Maze has been reexpressed as a 2D Maze with crossings (also called a "weave" Maze). Thanks, Cruiser1 (talk) 12:48, 29 January 2008 (UTC)[reply]

Maybe one can understand this by reducing passages to thin lines (i.e. 1-dimensional manyfolds). Those only need to cross if the dimension of the surroundings space is 2-dimensional (and, of course, overlay if dim=1). And therefore a "weave" 3D maze (with 4D "bridges") would not make sense in general (i.e. if the maze is not restricted to a rectangular "box" pattern like that in the 4D Maze game in the external link list), would it?--SiriusB (talk) 09:08, 7 February 2008 (UTC)[reply]

Mazes have precise coordinates located on earth, i don't get that part...--Colonel Valh ala-112 02:44, 30 May 2008 (UTC)[reply]