Talk:Effective method

message: There are a Effective method that is not a Algorithm?  —Preceding unsigned comment added by 187.39.184.57 (talk) 12:54, 8 May 2010 (UTC)
replies: text: According to the generally accepted Church-Turing thesis, the answer is no. 67.117.130.143 (talk) 19:46, 12 December 2010 (UTC)
replies: text: Church-Turing thesis unnecessary. These are synonyms. The Church-Turing thesis is that any effective method / algorithm can be implemented by a Turing machine / Lambda-calculus term. I second the merge proposal. AmirOnWiki (talk) 16:40, 12 October 2011 (UTC)

text: As I read the article, plus the article on algorithm, there is indeed a distinction between an effective method and an algorithm. One could for example demonstrate that there is an effective mechanism for a given task (purely for illustration, let us say using trial and error to fit polyominoes into a given knapsack, when it is known that they have come out of that knapsack, and is not known how much spare space, if any, there had been before they had been emptied out). Having done so, it does not follow that any algorithm, let alone a most efficient algorithm had been demonstrated or designed. If the algorithm had indeed been designed, it would have followed that it could be directly translated into a computer program, given the necessary primitive operations and resources of space and processing power, none of which are conceptually requisite to demonstrate the existence of an effective method in principle. Also, it often is quite possible to construct many algorithms to implement a given effective method. JonRichfield (talk) 08:44, 9 January 2013 (UTC)

text: It's an open question whether a real world example exists. For reference, take a look at Church–Turing thesis#Philosophical implications, particularly "2." and "3.". You might also want to look at Supertask#Super_Turing_machines, Super-recursive_algorithm, Hypercomputer and Digital_physics#The Church–Turing (Deutsch) thesis. I think some related stuff was also in Chaitin's_constant, I just can't recall where exactly in that article. Anyway, if we had such an example of an effective method that was indeed realizable in the real world, we would have refuted the Church-Turing thesis – which is an open question (but generally considered impossible, see the article). Se'taan (talk) 05:00, 23 March 2013 (UTC)
thread_title:  Please add example 

message: Not being a math geek, I fail to see any notability behind the article's title. Is "effective method" really a phrase that means "an algorithm that does this thing that we can't quite agree on" and nothing else? In my opinion this article isn't very effective without more reliable sources. Krushia (talk) 04:53, 31 December 2012 (UTC)
replies: text: I have provided an additional reference just for your benefit. Greg Bard (talk) 05:20, 31 December 2012 (UTC)

text: Not having seen this page before, I have just added a remark at the end of the first section of this talk page. I hope that it is sufficiently clear.JonRichfield (talk) 08:47, 9 January 2013 (UTC)

text: Well, effective descriptive set theory and effective Polish space both have the word effective in it. I assume it means the same thing, as the "effective" being described in this article. So it would seem to be in current usage... ? 67.198.37.16 (talk) 01:29, 29 November 2023 (UTC)
thread_title:  Notability 

message: Is almost surely halting good enough to satisfy our definition of an effective method?
Classical (not quantum) bogosort, which almost surely halts, is conventionally classified as a sorting algorithm, which depends on the definition of an algorithm and thus an effective method. To what extent is this valid? --SoledadKabocha (talk) 19:06, 3 November 2015 (UTC)
replies: text: Classical computability is entirely deterministic. So, even before you run into the question about the fact that the algorithm for bogosort doesn't always halt, there is the deeper question that there is no deterministic way for a human to simulate the algorithm with only pencil and paper, without an additional source of randomness. So the bogosort algorithm is not an effective method in the sense of classical computability. This is OK, because that definition is not trying to capture everything that could possibly be computed, only the things that could be computed deterministically by a human with unlimited time, pencil, and paper. — Carl (CBM · talk) 20:19, 3 November 2015 (UTC)

text: However, if we treat bogosort as an algorithm that takes a finite list to sort and also an infinite oracle to query for "random" bits, then the resulting oracle computation is effective in the classical sense. It will not halt for every oracle, but it will halt for many of them. In this way, the classical setup is able to handle nondeterminism by treating the nondeterminism as given by an oracle, resulting in a deterministic computation. — Carl (CBM · talk) 20:51, 3 November 2015 (UTC)
thread_title:  Almost surely halting