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Wikipedia:Featured article candidates/Euclidean algorithm/archive1

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Euclidean algorithm

Nominator(s): Proteins (talk) 16:22, 27 April 2009 (UTC)[reply]
Toolbox

I am nominating this mathematical article because I believe it meets the Featured Article criteria. In its simplest form, the Euclidean algorithm is often taught to 10-year-old children; for many, it is the only algorithm they encounter in school. It has several important applications, such as the RSA algorithm (often used in electronic commerce) and solving Diophantine equations. Although the oldest known algorithm (23 centuries), it continues to play a role in developing new mathematics. It would be helpful for Wikipedia to have an excellent article on this topic, both for itself and for the introduction it provides to advanced mathematics such as abstract algebra. Proteins (talk) 16:22, 27 April 2009 (UTC)[reply]

I'm a bit concerned about the inclusion of the "Game of Euclid" in the historical development section. It doesn't seem to be very important as a research topic or achievement, and it certainly doesn't even come close to the other developments in that section. What was the reason for including this? --C S (talk) 17:19, 27 April 2009 (UTC)[reply]
The FA criteria require that the article be "comprehensive" (criterion 1b). I admit that the game of Euclid is relatively unimportant, but it has been discussed in mathematical journals and textbooks, as referenced in the article. There didn't seem to be a better place to put that material besides "Historical development". Proteins (talk) 17:43, 27 April 2009 (UTC)[reply]
Well, I spy less than half a dozen "mathematical journals and textbooks" that mention the game. Surely there are many topics with more coverage that have not been included in this article. So I can't see how omitting this game would violate criterion 1b. Not to mention, these math journals you talk of are mainly math education related ones, except the journal INTEGERS, which seems like an ok journal but not particularly well-known. Of course, I don't mean to disparage journals whose primary audience may be math educators, but in terms of using such journals as a justification for including a mathematical topic in this article, I don't think it is sufficient. One has to separate a topic which is primarily used as an educational device from a topic which is considered an important development in understanding of the Euclidean algorithm. --C S (talk) 19:23, 27 April 2009 (UTC)[reply]

I think that the sentence "The Euclidean algorithm is the oldest algorithm in the historical record" is wrong because of Old Babylonian algorithms used to solve problems. --El Caro (talk) 18:04, 27 April 2009 (UTC)[reply]

This is a good point. The passage stated is uncited, but there is further down a box with a quote by Knuth which makes the nuanced observation that it is the "oldest nontrivial algorithm" that has survived to the present day. Since Knuth actually wrote an article in 1972 on ancient Babylonian algorithms [1] where he examined written records of their algorithms, presumably he was aware that the "nontrivial" is an important and necessary modifier. "Oldest nontrivial...", of course, is his opinion. --C S (talk) 19:21, 27 April 2009 (UTC)[reply]
I've read the quote in the box. Is this "only" Knuth's opinion or a statement on whom most specialists agree ? --El Caro (talk) 19:39, 27 April 2009 (UTC)[reply]
If "algorithm" is defined only as a set of numerical rules (without requiring proof that the rules always work or understanding why they work), then surely there were algorithms for thousands of years before Euclid. I'll review the literature and list the opinions of other people besides Knuth. Proteins (talk) 20:25, 27 April 2009 (UTC)[reply]
I corrected this in the text before, but that is indeed what "algorithm" means. I have never seen anyone define algorithm to mean it must come with understanding of the person using it or a proof that it works. So I can't imagine Knuth would use some nonstandard definition of "algorithm", as you suggest, especially since he is a computer scientist and certainly computer scientists do not require algorithms come with proofs. That is probably why he says "nontrivial" as I mentioned above. --C S (talk) 20:40, 27 April 2009 (UTC)[reply]

"Euclid's algorithm can be applied to real numbers, as described by Euclid in Book 10 of his Elements" looks like an anachronism. Did Euclid know real numbers ? --El Caro (talk) 18:17, 27 April 2009 (UTC)[reply]

Well, now we're getting into metaphysical matters that I think are tangential. For example, when Euclid considered arithmetical operations on whole numbers, it's not the same in a sense as what we consider such arithmetic, nor is probably what the ancient Greeks considered whole numbers the same as what we do now. So strictly speaking Euclid did not know real numbers, but he didn't know whole numbers, addition, or subtraction either. So that makes your point kind of moot. --C S (talk) 19:21, 27 April 2009 (UTC)[reply]
The ancient Greek certainly knew about irrational numbers, at least as surds, even if they hadn't defined Dedekind cuts. Book X of Euclid's Elements is devoted entirely to questions of incommensurability, and this real-number version of Euclid's algorithm begins that exposition. Knuth states elsewhere that the Greeks treated real numbers by infinite continued fractions, but he doesn't explain his remark further; I took him to be referring to this version of Euclid's algorithm. One could argue, I suppose, that the modern concept of real numbers embraces more than just "the set of all rational and irrational numbers", but that seems beyond the level of this article. Proteins (talk) 20:18, 27 April 2009 (UTC)[reply]
Ancient Greeks considered numerical concepts mainly in terms of geometric constructions ala ruler and compass and that is how Euclid's treatment of commensurability goes. This is certainly not the way modern mathematicians think of them. Sure the ancient Greeks knew of some irrational numbers, but they certainly didn't know "e" or many other irrational numbers that are not constructible. So their concept of irrational number was far more limited than our modern understanding, even when one limits the concept of real number to mean "set of rational and irrational numbers". Even on the math where modern and ancient understanding would seem to overlap, it's clear the ancient Greeks just had a different way of thinking about it, so in a metaphysical sense, you could argue that the objects are really different. --C S (talk) 20:40, 27 April 2009 (UTC)[reply]

Oppose on criterion 3

  • File:Gabriel-Lamé.jpeg - There is no source, date, or author for this image that would lead us to believe that it is in the PD. We need to be able to verify that it is in the PD. More research on this image needs to be done.
  • File:Dedekind.jpeg - The website for this image does not indicate the 1870 date and we have no name or death date for the photographer, so we cannot verify the PD license listed. More research on this image needs to be done.

These issues should relatively easy to resolve. I look forward to reading the entire article. Awadewit (talk) 21:13, 27 April 2009 (UTC)[reply]

  • Problem - many of the paragraphs are lacking citations or, if having them, there are no citations covering many sentences. See the end of the section "Greatest common divisor" for just one example. This needs to be fixed before it can pass FAC. Ottava Rima (talk) 23:45, 27 April 2009 (UTC)[reply]
    • If you are referring to the subsection that begins, "Three related mathematical methods are used often in the arguments below..." That is an explanatory paragraph explaining the article elements, in particular, explaining what typical math proof method will be used further down. That does not require citation. Looking through the article, I see plentiful citations. I suspect what Ottava Rima is referring is to paragraphs where the initial statement might be sourced, but further explanation or example is not (although it is simply a further explication of what the initial sentence said). I wonder if Ottava Rima is familiar with WP:SCG, since I cannot see how the article fails the SCG. I think there is some confusion that would be remedied by reading "Examples, derivations and restatements" section of the SCG in particular. --C S (talk) 23:58, 27 April 2009 (UTC)[reply]
      • Unless it is sourced, it is possibly Original Research. Now, from the guideline that you quoted: "The no original research and verifiability policies are of paramount importance to Wikipedia. Information presented in Wikipedia should be easily verifiable by anyone who wishes to do so. To ease verification, sources should be detailed by the articles." This article fails that. The whole page has over 50 sections needing citations. Such things are 100% unacceptable in an FA. Ottava Rima (talk) 00:26, 28 April 2009 (UTC)[reply]
        • You've been claiming a lot citation violations, but have yet to demonstrate one example. Could you show me an example paragraph from the article that violates the SCG? You cited the opening sentences of the SCG, but I'm not sure you've read further past it since the rest of the introduction explains that there are different ways to satisfy these core polices. Then further on down in the first section it is explained that not every sentence or paragraph may require a citation depending on the type of material. --C S (talk) 01:27, 28 April 2009 (UTC)[reply]
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