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Klee鈥揗inty cube article. This is not a forum for general discussion of the article's subject. |
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A fact from Klee鈥揗inty cube appeared on Wikipedia's
Main Page in the
Did you know column on 5 April聽2011 (
check views). The text of the entry was as follows:
|
I nominated this hook ( 聽Kiefer.Wolfowitz聽聽( Discussion) 18:58, 26 March 2011 (UTC)):
DYK Views: The article Klee鈥揗inty_cube has been viewed 5883 times in 201104.
聽Kiefer.Wolfowitz聽聽(
Discussion)
00:31, 6 April 2011 (UTC)
While pretty good at explaining the features of a KMC, I'm afraid the article fails to explain what it actually is.
As it is, the article only states that it's a "perturbation of a standard cube", but perturbed in what manner? What does it look like? Is it a three-dimensional thing that I could touch? A simply abstract concept? I'm at a loss here. -- Syzygy ( talk) 08:57, 5 April 2011 (UTC)
I agree with above critiques - given this article appeared as featured on wikipedia homepage I have to say it is more an example of poor writing example than a masterpiece. Even the image caption says nothing to clarify itself nor illuminate the piece. Suggestions include a lay summary intro with mentioning what branch of math or science this relates to, and any possible relevant fields of application. Say who/what Klee minty are and what problem they solved and what issues/anomalies remain as a result of their work. Then delete it. Nobody but someone who already knows what kmc is would ever have interest in such a horribly written article. Sadly it is not alone here - I find many highbrow esoterica lacking in common overviews for the bulk of site readership. 71.190.22.8 ( talk) 11:58, 5 April 2011 (UTC)
So, do I understand correctly that -- in layman's terms -- the KMC is simply a regular n-dimensional cube whose corner points have been slightly displaced, and the problem in question is to find the shortest route from the bottommost corner to the top corner? ("Short" as "smallest distance travelled along the path", or "least number of corners visited"?) If that is a the core, I'd be happy to update the main article accordingly. -- Syzygy ( talk) 10:26, 5 April 2011 (UTC)
I was bold. Please, pros, correct me where I erred. -- Syzygy ( talk) 12:44, 5 April 2011 (UTC)
Relax, Kiefer, I didn't remove anything from the link list but only suggested it be removed. I'm seeking a consensus, which is why I am posting here. -- Syzygy ( talk) 10:22, 7 April 2011 (UTC)
(And, BTW, note that many of the comments above were one thread at one point but have now been broken into sections. Some of my comments now look out of place... SGBailey)
At present we have "The Klee鈥揗inty cube (named after Victor Klee and George J. Minty) is a geometrical example that is used in mathematical optimization. The planar square [0,1]2 is defined by four linear inequalities, namely the inequalities that the two coordinate is greater than zero and less than one. Similarly, the cube in 3 or more dimensions is defined by a system of linear inequalities. Klee and Minty perturbed the inequalities defining the standard cube, so as to create a squashed cube, which serves as an important example in mathematical optimization."
Sentence 1 talks about a cube. Sentence 2 about a square. A square is not a cube. Indeed a hyper-cube is not a cube. Are we sayin that a KMC is an N-dimension (nominally) unit-vector thingy - that is a unit line, a unit square, a unit cube, a unit hyper-cube ... If so it would help to actually say it rather than leave it to be inferred. Whatever, leaping into a square after saying it is a cube doesn't come across well.
Sentence 2 comes across as gobbledegook "The planar square [0,1]2 is defined by four linear inequalities, namely the inequalities that the two coordinate is greater than zero and less than one. I'm fine with the sentence as far as "inequalities". What is "the two coordinate"? Is that meant to be plural "both coordinates" (Should it be N-dimensionalised and read "all coordinates"?)
Sentence 3 doesn't seem to add anything. What is its purpose?
The last sentence says squashed which suggests all 1 coordinates get smaller and all 0 coordinates get bigger. I suspect "distorted" is a better word here. An example would be worth a lot here. Thus perhaps: "A proper cube has coordinates {0,0,0}, {0,0,1}, {0,1,0}, {0,1,1}, {1,0,0}, {1,0,1}, {1,1,0}, {1,1,1} a sample KMC cube might have coordinates {0,0,0}, {0,0,1.1}, {0,0.9,0}, {0,1,0.9}, {0.9,0,0}, {1.1,0,1.1}, {1.1,1,0}, {0.9,0.9,1}"
Then it becomes clear that it is easy to evaluate a shortest route between two points on a proper cube as all edges are 1 so any direct route will be one of the potentially many optimal paths. But on the KMC cube in general or a particular sample KMC cube in particular it may be that "up, left" is better than "left, up" - and that is what the optimisation methods are trying to determine. (I think...)
-- SGBailey ( talk) 09:16, 7 April 2011 (UTC)
I'm basically happy with "2011-04-07T12:15:32" version. It is now readable. Thanks. -- SGBailey ( talk) 11:43, 7 April 2011 (UTC)
It seems weird that the article has an illustration of an ordinary cube (for readers who don't know what a cube is, presumably), but considers it unnecessary to illustrate a Klee-Minty cube. Maproom ( talk) 16:53, 9 October 2011 (UTC)
This is the
talk page for discussing improvements to the
Klee鈥揗inty cube article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources:聽 Google ( books聽路 news聽路 scholar聽路 free images聽路 WP聽refs)聽路 FENS聽路 JSTOR聽路 TWL |
This is the talk page for discussing changes to the Klee鈥揗inty cube article itself. Please place discussions on the underlying mathematical issues on the Arguments page. If you just have a question, try Wikipedia:Reference desk/Mathematics instead. |
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||||||||||||||||||||||||||
|
A fact from Klee鈥揗inty cube appeared on Wikipedia's
Main Page in the
Did you know column on 5 April聽2011 (
check views). The text of the entry was as follows:
|
I nominated this hook ( 聽Kiefer.Wolfowitz聽聽( Discussion) 18:58, 26 March 2011 (UTC)):
DYK Views: The article Klee鈥揗inty_cube has been viewed 5883 times in 201104.
聽Kiefer.Wolfowitz聽聽(
Discussion)
00:31, 6 April 2011 (UTC)
While pretty good at explaining the features of a KMC, I'm afraid the article fails to explain what it actually is.
As it is, the article only states that it's a "perturbation of a standard cube", but perturbed in what manner? What does it look like? Is it a three-dimensional thing that I could touch? A simply abstract concept? I'm at a loss here. -- Syzygy ( talk) 08:57, 5 April 2011 (UTC)
I agree with above critiques - given this article appeared as featured on wikipedia homepage I have to say it is more an example of poor writing example than a masterpiece. Even the image caption says nothing to clarify itself nor illuminate the piece. Suggestions include a lay summary intro with mentioning what branch of math or science this relates to, and any possible relevant fields of application. Say who/what Klee minty are and what problem they solved and what issues/anomalies remain as a result of their work. Then delete it. Nobody but someone who already knows what kmc is would ever have interest in such a horribly written article. Sadly it is not alone here - I find many highbrow esoterica lacking in common overviews for the bulk of site readership. 71.190.22.8 ( talk) 11:58, 5 April 2011 (UTC)
So, do I understand correctly that -- in layman's terms -- the KMC is simply a regular n-dimensional cube whose corner points have been slightly displaced, and the problem in question is to find the shortest route from the bottommost corner to the top corner? ("Short" as "smallest distance travelled along the path", or "least number of corners visited"?) If that is a the core, I'd be happy to update the main article accordingly. -- Syzygy ( talk) 10:26, 5 April 2011 (UTC)
I was bold. Please, pros, correct me where I erred. -- Syzygy ( talk) 12:44, 5 April 2011 (UTC)
Relax, Kiefer, I didn't remove anything from the link list but only suggested it be removed. I'm seeking a consensus, which is why I am posting here. -- Syzygy ( talk) 10:22, 7 April 2011 (UTC)
(And, BTW, note that many of the comments above were one thread at one point but have now been broken into sections. Some of my comments now look out of place... SGBailey)
At present we have "The Klee鈥揗inty cube (named after Victor Klee and George J. Minty) is a geometrical example that is used in mathematical optimization. The planar square [0,1]2 is defined by four linear inequalities, namely the inequalities that the two coordinate is greater than zero and less than one. Similarly, the cube in 3 or more dimensions is defined by a system of linear inequalities. Klee and Minty perturbed the inequalities defining the standard cube, so as to create a squashed cube, which serves as an important example in mathematical optimization."
Sentence 1 talks about a cube. Sentence 2 about a square. A square is not a cube. Indeed a hyper-cube is not a cube. Are we sayin that a KMC is an N-dimension (nominally) unit-vector thingy - that is a unit line, a unit square, a unit cube, a unit hyper-cube ... If so it would help to actually say it rather than leave it to be inferred. Whatever, leaping into a square after saying it is a cube doesn't come across well.
Sentence 2 comes across as gobbledegook "The planar square [0,1]2 is defined by four linear inequalities, namely the inequalities that the two coordinate is greater than zero and less than one. I'm fine with the sentence as far as "inequalities". What is "the two coordinate"? Is that meant to be plural "both coordinates" (Should it be N-dimensionalised and read "all coordinates"?)
Sentence 3 doesn't seem to add anything. What is its purpose?
The last sentence says squashed which suggests all 1 coordinates get smaller and all 0 coordinates get bigger. I suspect "distorted" is a better word here. An example would be worth a lot here. Thus perhaps: "A proper cube has coordinates {0,0,0}, {0,0,1}, {0,1,0}, {0,1,1}, {1,0,0}, {1,0,1}, {1,1,0}, {1,1,1} a sample KMC cube might have coordinates {0,0,0}, {0,0,1.1}, {0,0.9,0}, {0,1,0.9}, {0.9,0,0}, {1.1,0,1.1}, {1.1,1,0}, {0.9,0.9,1}"
Then it becomes clear that it is easy to evaluate a shortest route between two points on a proper cube as all edges are 1 so any direct route will be one of the potentially many optimal paths. But on the KMC cube in general or a particular sample KMC cube in particular it may be that "up, left" is better than "left, up" - and that is what the optimisation methods are trying to determine. (I think...)
-- SGBailey ( talk) 09:16, 7 April 2011 (UTC)
I'm basically happy with "2011-04-07T12:15:32" version. It is now readable. Thanks. -- SGBailey ( talk) 11:43, 7 April 2011 (UTC)
It seems weird that the article has an illustration of an ordinary cube (for readers who don't know what a cube is, presumably), but considers it unnecessary to illustrate a Klee-Minty cube. Maproom ( talk) 16:53, 9 October 2011 (UTC)