Wikipedia:Featured article candidates/Euclidean algorithm/archive1: Difference between revisions

Revision as of 06:34, 29 April 2009

Revision as of 06:56, 29 April 2009

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:::::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. --[[User:C S|C S]] ([[User talk:C S|talk]]) 20:40, 27 April 2009 (UTC)

::::::After consulting more than a dozen mathematical sources, I concede that you are entirely correct. An algorithm is any well-defined (alpha)numerical procedure, and can well be incorrect. Thus, pre-Pythagorean carpenters constructing a right angle by a 3-4-5 triangle were using an algorithm, and so were carpenters who used a 2-3-4 triangle. I accepted the proof requirement (which I read elsewhere) because Knuth's argument for the EA's priority seemed incompatible with the obvious prior existence of many algorithms, such as calendars, money changing, tax and inheritance systems, measurement of area, architecture, multiplication and division, etc. I have also not found a reliable source besides Knuth that identifies an oldest nontrivial algorithm. The solution for this FAC may well be to leave the quote box from Knuth, but to change the assertion in the article. How about "oldest numerical algorithm still in common use", or "one of the oldest algorithms in the historical record"? Would either of those wordings be acceptable? [[User:Proteins|Proteins]] ([[User talk:Proteins|talk]]) 02:45, 29 April 2009 (UTC)

Hi Proteins. Well, as you said, multiplication algorithm was around before, so I'm unhappy with the first phrasing. The second seems acceptable. Actually, I had a bit of fun digging around the Google searches for "euclidean algorithm oldest". I had no idea that there was such a common misconception of the Euclidean algorithm being the oldest algorithm (with no qualification). Perhaps Wikipedia itself has had a role in perpetuating this. In "Mathematica in Action" by Stan Wagon [http://books.google.ca/books?id=vpYmj7ohofsC&pg=PA332&lpg=PA332&dq=euclidean+algorithm+oldest&source=bl&ots=TrzJiLLaFV&sig=HpohbX7gFDCvAeKBdvueJaBvPCU&hl=en&ei=Pe73Sf_wHKToswO38-XrDg&sa=X&oi=book_result&ct=result&resnum=2], Wagon asserts "The Euclidean algorithm for computing the gcd of two numbers is arguably the best algorithm in all of mathematics. According to Knuth, it is the oldest nontrivial algorithm that has survived to the present day." So here Knuth's assertion of "oldest nontrivial..." is repeated with the addition that it is the ''best'' algorithm bar none. However, misleadingly, the section heading proceeding the passage states "The oldest surviving algorithm"! In [http://books.google.ca/books?id=--Ih9bv0m_AC&pg=PA3&lpg=PA3&dq=euclidean+algorithm+oldest&source=bl&ots=Fpfc6FT1lb&sig=fA8HF9MElQ7rJO1g_SKzIQFcSnY&hl=en&ei=Pe73Sf_wHKToswO38-XrDg&sa=X&oi=book_result&ct=result&resnum=6 this book], the author asserts, the "Most likely, it is the oldest mathematical algorithm in existence". Oops! Anyway, although the Wagon claim is on the strong side, I think the Knuth quote really has some content there. So I think we ought to keep that in the box, while in the text we can make a more unobjectionable assertion like "one of the oldest...record". --[[User:C S|C S]] ([[User talk:C S|talk]]) 06:56, 29 April 2009 (UTC)

;Applied to real numbers