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This is an old revision of this page, as edited by Lowercase sigmabot III (talk | contribs) at 00:01, 18 September 2018 (Archiving 2 discussion(s) from Talk:Algorithm) (bot). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.
Archive 1←Archive 3Archive 4Archive 5

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)

---

  • 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)

The section 'Why algorithms are necessary' doesn't seem to explain "why algorithms are necessary"

When I red the title I expected to find an explanation to why we have to use algorithms instead of just using singular expression. I understand that it would be hard to do that, but I don't really understand 'why' in a mathematical sense. Can all algorithms be translated to expressions? If not, why? Has this question been answered? Has it been asked? By whom? Etc... Have I missed a part of the article here?

An algorithm reduces a problem to a number of simpler steps. A single step algorithm is the ultimate algorithm. Algorithms refer to operations. The expression x = a + b + c boils down to two operations in a machine that can add no more than two numbers: "add a and b and save the intermediate result", and "add c to the intermediate result". "Simpler steps" is context-dependent. A very basic computer that only can add and subtract requires more elaborate algorithms if effectively multiplication an division operations are needed. Advanced subroutine libraries can cope with problems forumulated in matrix operations. Rbakels (talk) 13:15, 9 December 2013 (UTC)

Is it possible to get a patent or software patent for an algorithm? For examples the algorithm pairs the describe lossy (or lossless) compression and decompression of video or audio data. They are said to be maybe subject of patents. Even though patent holders usually take royalties only for encoding... This is why FFmpeg or Libav are not found in many software repositories. User:ScotXWt@lk 23:16, 30 June 2014 (UTC)

I am not an expert on algorithms but there definitely are many patented algorithms. Examples include data compression algorithms. Many are listed here. Wqwt (talk) 04:59, 9 August 2014 (UTC)

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Etymology and True Word Origins

It is obvious the editor of this article has control issues.

It is a fact that al-Khwārizmī studied Greek source material extensively to make his unique contribution to the world of mathematics.

It is a fact that most of the word algorithm just as word the logarithm come from a Greek language origin.

To state that two syllables of a word come from a certain language (in this case Greek and NOT Arabic) and then refuse to give credit, shows true ignorance, ethnic bias and revisionism.


It is in fact important to begin to understand any concept by beginning with where the notion comes from and what it means, this is fundamental.

Since "al" is a reference to the name Khwārizmī and not part of the name or nomen itself, then there is no evidence that this is related to the etymology of the word algorithm and not irrelevant to the issue. The word 'the' or 'of' have no contextual or descriptive relationship to the entire word, al-gorithm.

It is widely accept that logarithm is short for the Greek logos-arthimos or literally translated "why-arithmetic" and most evidence supports the idea that algorithm is a further development of the same arithmetic concept allo-logos-arthimos or translated from the Greek: "another-why-arithmetic".

"Most evidence"? Where? Yours appears to be a false etymology, even though it's a reasonable mistake to make. See this for example:
ALGORITHM. n. 1690s, from French algorithme, refashioned (under mistaken connection with Greek arithmos "number") from Old French
algorisme "the Arabic numeral system" (13c.), from Medieval Latin algorismus, a mangled transliteration of Arabic al-Khwarizmi
"native of Khwarazm," surname of the mathematician whose works introduced sophisticated mathematics to the West (see algebra ). 
The earlier form in Middle English was algorism (early 13c.), from Old French.
Source: Online Etymology Dictionary. 200.127.158.54 (talk) 21:26, 1 October 2015 (UTC)

al-Khwārizmī developed the algorithm from reference to Greek math texts, not in a vacuum, but by study of preexisting knowledge and he innovated from that point. This has nothing to do with opinions it is "the story", historical fact. — Preceding unsigned comment added by 69.183.30.237 (talk) 06:41, 8 May 2012 (UTC)

You are certainly full of opinions (or as Bertrand Russell would call them -- "beliefs"), but you have not backed them up with even a single source. Wikipedia requires sources, not beliefs. If you have credible sources, in particular research on the etymology of this particular word algorithm, we would like to see them. Bill Wvbailey (talk) 14:40, 8 May 2012 (UTC)

There are sources in the article itself, an article which has contradictions. Some related articles that conflict are also found. The use of language fragments or combined words means that it is already proven. Arabic and Greek merging of words is common throughout history, there is a shared influence from Egypt and the Phoenician root. The close trading relationship between these cultures translated into intellectual exchange as well. The alphabet was created from a Phoenician arithmetic notation of items of trade, ie. Ox-head or alpha etc. The Greeks combined these symbols with there own glyph-ic scripts and writing was also adopted in more widely in the mid east. Arabic followed a similar genesis preceding written script.

The article itself is not consistent and was revised to remove pertinent information. I don't agree that any "belief" system enters into the debate. History at one point in time became an instrument to convey knowledge as imperfect as that can be. Politicizing something that can be clearly pointed out does not accomplish anything. It is not belief that leads me to think this, it is disdain for a new culture that has disregard for the past. — Preceding unsigned comment added by 69.182.147.217 (talk) 04:36, 11 May 2012 (UTC)

Etymology: algorithm. Sources? BillWvbailey (talk) 23:00, 11 May 2012 (UTC)

first paragraph covering Euclid's

I improved the section covering Euclid's algorithm by mentioning that it's to determine the greatest common divisor. See the edit. A good understanding of English and language in general will tell you that even though the usual use of adjectives is that you put it before the noun that it demonstrates, when the demonstrative (is predicate a better word?) is more a phrase than a single word--in this case, "common to two numbers"--it makes it easier to parse to put the adjectival phrase after the noun. user:98.229.184.161 disagrees, and made this edit with the claim that my usage was invalid. See his edit. On the other hand, now the wording is "greatest common divisor (GCD) to two numbers" which, to me, seems very clunky. I would edit it back to return it to my wording, but I don't feel like starting an edit war over something so simple. I'll leave it to the rest of the community to decide. D. F. Schmidt (talk) 21:48, 14 December 2015 (UTC)

Word origin and Etymology

There are two sections ("word origin" and "etymology") in article about one and the same topic. I think these sections need to merge. --Treisijs (talk) 14:37, 21 December 2015 (UTC)

"Most algorithms are intended to be implemented as computer programs."

"Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device."

Where is the evidence for this? This sounds like a view of a computationalist. Yoga Conflagration (talk) 19:36, 5 June 2016 (UTC)

Can you suggest a rewrite? E.g. "The most common algorithms are hand-calculations for [arguably, source?] common arithmetic computations: addition, subtraction, multiplication and division, square-root and exponentiation. Algorithms are implemented as computer programs [source? See the Bohm-Jacopini theorem ] and by other means, such as computer programs, biological neural networks (for example, the human brain implementing arithmetic or an insect looking for food), and [combinatorial and sequential] electrical circuits , or a mechanical device ." Bill Wvbailey (talk) 23:45, 5 June 2016 (UTC)

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