Talk:Algorithm/Archive 5

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About the etymology section

usually this section precedes all others. Why then is it postponed till section 9 where it makes no sense at all? Is it maybe because we have a hard time accepting that such a crucial concept, without which we wouldn't have had computers, actually goes back to and bears the name of a brilliant Muslim, who we would prefer to see as a terrorist? Shame on you! — Preceding unsigned comment added by 87.212.38.229 (talk) 16:58, 29 December 2011 (UTC)

I tried to do something about this but apparently user Wvbailey is convinced that the authors he mentions (is it Sonya Kleene, Stephen Kleene, who?, no idea who is meant by "Rogers") are somehow definitive. I don't get into edit warring, disputes with such users so others will have to pick up from here. Maybe the tagging is the best that can be done under these circumstances. Lycurgus (talk) 02:17, 17 January 2012 (UTC)

Also, I would take the approach of defending Arabic or Iraqi culture in this case rather than Islam/Muslims, they're not the same. 72.228.177.92 (talk) 02:43, 17 January 2012 (UTC)

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The etymology has been an ongoing issue here. Clearly anonymous has a (Muslim, Arab or Persian) ax to grind and is attempting to inject their religious faith or jingoistic intent into a difficult article that needs (quite clearly as demonstrated in anonymous's rant above) extremely tight sourcing. This problem of edit warring over their favorite son Al Kwarizmi has been ongoing between Iranians and Moslems, Shiites and Sunnis: the Iranian Shiites want to claim Al Kwarizmi as an Iranian (he was a Persian), the Arabs who swept through his region of Persia and converted his family by the sword from Zoroastrianism to Islam want to claim him as a Moslem and/or Arab. What his faith was, and his nationality, is absolutely irrelevant to the definition of "algorithm". The edit that you redacted and I reverted is flat out wrong. If anonymous can produce sourcing, then we can entertain a dialog. Or better yet, anonymous can add the definition and sourcing to Algorithm characterizations. But first I suggest that anonymous actually read the article, the footnotes and consult the relevant attached sources. And by the way it's Stephen Kleene 1952, Hartley Rogers 1967, and add Donald Knuth various dates); see the sourcing references. wvbaileyWvbailey (talk) 02:48, 17 January 2012 (UTC)

tldr; I should think Knuth or somebody would be a name to drop if that was the approach being taken. 72.228.177.92 (talk) 03:26, 17 January 2012 (UTC)

I'd also like a bit of clarity on the issue. While the article implies that the word algorithm is taken from Al Kwarizmi's name, the concept of an algorithm had been around for several centuries already. If that is true, then that perhaps needs to be made more explicit. Kmasters0 (talk) 08:37, 22 February 2012 (UTC)

Can you source this or be more explicit (who, what, when, where, how) about someone actually intentionally creating a generalization of the notion "step-by-step procedure for how to perform calculations" (i.e. concept)? If there's something that can be sourced and is relevant we should add it. It would be an interesting addition. (The history indicates it was a long process that culminated only in the 1930's, altho there were major strides (not mentioned in the article, I believe) in the mid-late 1880's around a formalization of the notion of recursion, in fact the more I think about it, the more "key" this seems; I bumped into this accidentally not so long ago but I can't remember who was responsible for formalizing the notion.). Bill Wvbailey (talk) 15:05, 22 February 2012 (UTC)

RE recursion: Bill's note to Bill: See Dedekind 1887. But what was I reading that sent me there? Cf Dedekind's definition 71 of the natural numbers, then his theorem 80 complete induction, of mathematical induction §124-125. Also Berlinski (unfortunately he does not give a history of recursion): "Recursion is an example of a mechanical process. The steps are broken down so simply that no though is involved in carrying them out. . .."/"And the importance of this?"/"It gives prceise meaning to the intuitive idea of effective calculability."/"Meaning?"/The dialog goes in a bit of a circle]/"It was clear to me," the cardinal finally said, "that recursion would be a subject to my taste" (pages 134-135)

RE recursion: Note to Bill part 2: Here's Dedekind 1887 as translated by Beman 1901: " . . . therefore the definition by induction (or recursion) is determinate and consistent (126)) (page 33). Bill Wvbailey (talk) 23:40, 24 February 2012 (UTC)

No, I can't source it, which is why there is confusion. My argument is that the article implies this. It does this by introducing Euclid’s algorithm as a matter of fact. Because it doesn't say that the process did not exist, this would imply that the concept of an algorithm had existed at (or even before) Euclid's time. Then the article goes on, much later, to explain that the word for the process comes from Kwarizmi's name. If that is not true, then I think it should be made more explicit. (BTW, while I don't support anonymous's rant, I also found it strange that the etymology of the word was placed so late in the article. Perhaps this can be moved, but by one who is more familiar with the wikipedia's editing principles than I.) Kmasters0 (talk) 10:01, 24 February 2012 (UTC)

At the time anonymous raised the complaint, the etymology of the word was not mentioned in the lead section at all. Now it is in the first sentence. Since then it seems that the etymology discussion has cooled off a bit. Isheden (talk) 15:24, 24 February 2012 (UTC)

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• RE Euclidean "algorithm": Good point about the usage "Euclidean algorithm". I understand your concern. I think the approach to take (see the quotes below) will be to change the wording under the drawing, and perhaps in the body too. Euclid (at least in Heath 1908 translation) begins with a Proposition" which he then proves. Heath in his commentary calls it a "method" and "process" (cf footnote page 67) and refers to Nichomachus' rule:

"Here we have the exact method of finding the gratest common measure given in the text-books of algebra . . .. The process of finding the greatest common measure is simply shown thus: [demo goes here, is confusing]. ¶ Nichomachus gives us the same rule (though withut proving it) . . ." (pages 66-67 from Euclid's Elements Book VII appearing Hawking 2005).

Knuth starts with a little history re al Kwarizmi, and then jumps right in with the Euclidean "algorithm" as his first example. Knuth notes that the word did not appear in Webster's New World Dictionary until 1957. He also cites the Oxford English Dictionary about the etymology being confused with arithmetic. He calls it a process once and thereafter "algorithm":

"By 1950, thw word algorithm was most frequenty associated with "Euclid's algorithm", a process for finding [etc]" (Vol 1 Knuth 1972:2)

Berlinski starts this way (first para in the Preface of the book):

"More than sixty years ago, mathematical logicians, by defining precisely the concept of an algorithm, gave content to the ancient human idea of an effective calculation." (Berlinski 2000:xi)

"The idea of algorithm had been resident in the consciousness of the world's mathematicians at least since the seventeenth century; and now, in the third decade of the twentieth century, an idea lacking precise explication was endowed with four different definitions . . . the four quite different definitions, it is worthwhile to recall, were provided by Goedel, Church, Turing, and Post." (Berlinski 2000:20)

Definition from my Merriam-Websters Ninth New Collegiate Dictionary (1990) gives a first occurrence in ca 1894:"a procedure for solving a mathematical problem (as of finding the greatest common divisor) in a finite number of steps that frequently involves repetition of an operation; broadly a step-by-step procedure for solving a problem or accomplishing some end."

• RE The etymology section: it has moved around any number of times. As I note above, it has been a "bone of contention" for a long time, almost to the point of having to place the article under a "review" process. A prominent position near the top seems to inflame the passions of those who then read no further and then engage in an edit war. Since appearing now far down in the article I've noticed the flaring of passions has been greatly reduced. Actually, even the mention of his name in the lead paragraph has been a cause of inflammation. Bill Wvbailey (talk) 16:35, 24 February 2012 (UTC)

Search and enumeration

It's simply very badly written: First, it's unclear if 1) and 2) are meant to be examples or types. Second, it looks like other (heuristic) algorithms are mentioned in this section. 68.183.23.147 (talk) 04:47, 17 January 2013 (UTC)

Go to 2 0r 3

I am a layman who doesn,t know much about algorithm. But I think something is wrong in the flow chart of Euclid's algorithm. see the figure. after A is assigned the value A-B why go to 2? Isnt it 3 to where the arrow should lead? see that will once again check whether B>0 ,which is not needed as we reach the step assigning A the new value after checking it? Sorry if my question is an idiotic one. --binu (talk) 07:36, 10 August 2013 (UTC)

This version of the algorithm -- the "elegant" version (there's more about it in the article) -- is also a bit subtle. There's also a less-subtle version (Knuth's version)further down in the article, too. Knuth observed that the best way to understand an algorithm is to try it out. You can do it either by hand or by use of an Excel spreadsheet, or if you can program e.g. in Basic; see further in the article where the Basic program is listed. Bill Wvbailey (talk) 16:05, 10 August 2013 (UTC)

Finite number of steps?

I never understood why algorithms are supposed to be limited to a finite number of steps. An algorithm to calculate the square root of a number requires an infinite number of steps. But "infinite" in mathematics does not mean a prohibitively large number, but only that the result can be achieved with arbitrary (although never complete) precision. Rbakels (talk) 09:18, 6 December 2011 (UTC)

Well the algorithm on computer would be to "calculate the square root to within 1 ULP" rather than just calculate the square root. --Salix (talk): 10:40, 6 December 2011 (UTC)

Alternatively, wouldn't it be correct to say that (e.g.) the Newton-Raphson algorithm can calculate the exact square root of any number in an infinite number of steps, as a mathematical way of saying that the exact value can be approached (not: reached) in any level of precision if only the number of iterations is increased? (Of course, I am aware that this presumes calculations with infinite precision). Rbakels (talk) 13:05, 9 December 2013 (UTC)