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Talk:Sign language

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Deaf communities and Deaf culture
There were three paragraphs in § Deaf communities and Deaf culture: one general and vague one about the title topic, and two, very confusing and badly written, about native American signing. I'm cleaning these up and am going to integrate them into §Use of signs in hearing communities, where there is already a paragraph about the topic.

Some parts of § Deaf communities and Deaf culture were so confusing I could make no sense of them, and the best I could do was to remove them completely. Those parts are in boldface below. For the record, here's what it said before:
 * Deaf communities are very widespread in the world and the culture which comprises within them is very rich. Sometimes it even does not intersect with the culture of the hearing population because of different impediments for hard-of-hearing people to perceive aurally conveyed information.

 * There are many theories indicating what native American sign language were applied for. One theory indicates that the sign system's development provided great ease for the local inhabitants to talk with each other: In the 1500s, a Spanish expeditionary, Cabeza de Vaca, observed using sign language with the natives on the west part of modern day Florida. In mid 16th century, Francisco de Coronado also mentioned that communication with the Tonkawa using signs, was possible without the  presence of a translator.

 * Ideas narrate to doing business with the use of sign as a common understandable language, and even exaggerated ideas of Native American using sign because they were perceived to be "exotic" and "uncivilized" group also prevail. Nevertheless, the sign adhered by the Indians were used primarily with communication between tribes or for the usage of hunting. If gestures that were used by primitive individuals or Native Indians did in fact or not quite reach the stage of being official languages, excluding the usage of oration and still having full communication, is still up for debate.There are estimates indicating that as frequent as 15 in 650 Native Americans have serious deafness or are completely deaf. These estimates are more than twice the national medium.

To discuss this with me, please me. --Thnidu (talk) 23:46, 28 January 2015 (UTC)

 * I like what you did. Sorry to jump in to do other things while you were still working on it.  Are you done now? AlbertBickford (talk) 23:55, 28 January 2015 (UTC)

Sign languages in society: technology Suggestion
Currently, there is a hearing-centered bias in the article, in that discussions of technology (in the section on Sign languages and society) tend to assume that there are interpreters involved, for communication between deaf and hearing (or, more likely in many hearing people's minds, from hearing to deaf). This is a common bias in society, of course, but it doesn't reflect a WP:NPOV. I made some changes a couple years ago, distinguishing the use of videophones for deaf-to-deaf communication from their use with interpreters, but I notice the bias is still there. What brought it to my attention was inclusion of material by from an old article about sign languages on television. I fully support merging of that article into this one, but I notice that the new material seems to talk exclusively about interpretation of programs that are aimed primarily at hearing people. There's nothing explicitly stated (unless I missed it) about programs that use a sign language as a primary language, created by Deaf people for other Deaf people. More generally, we don't cover other uses of technology for primary communication by sign language users without an interpreter, such as vlogs and other video on the internet, video communication other than videophones (Skype, etc.), distribution of sign language material on phones, etc.

So, what I think is needed is to separate out the technological developments about the way video technologies are being used for sign languages into a section separate from sign languages in society. Comments? AlbertBickford (talk) 21:42, 9 March 2015 (UTC), updated AlbertBickford (talk) 21:43, 9 March 2015 (UTC)
 * I agree with Albert's changes. By way of explanation, I came across the Sign language on television article because it was listed at . Since the proposal had been neglected for more than three years, I decided to merge it into the end of the article. I'm glad Albert identified an appropriate location for its insertion.
 * Together with Albert's comments above on what is lacking, I'd also like to note that the contents that are there are also stale, for example quoting a 2008 article about "emerging technologies". Hopefully more current information on the television interpretation aspect can also be added. AtHomeIn神戸 (talk) 02:47, 10 March 2015 (UTC)

 * Video technologies on the internet, of course, are hardly "emerging" any more. But, from what I can tell, there really isn't much new to update, except that things have gotten faster and better quality.  Maybe vlogs came out since 2008, and that's something that should be included. In particular, I don't know of anything that has changed in terms of how interpretation is handled on television, but then, I don't watch those programs (don't watch TV at all, in fact).  AlbertBickford (talk) 02:56, 10 March 2015 (UTC)

janelli joyce batchar — Preceding unsigned comment added by 121.54.54.164 (talk) 05:59, 24 March 2015 (UTC)

Section to Add
I am editing the baby sign language page and am looking to remove a section from it. The section I wish to remove is a journal study discussing a bilingual hearing child born to deaf parents and raised with both spoken and signed speech. I think this could be a good asset to this page as it talks about using authentic Italian sign language and the influence of sign language on hearing children's abilities. I am adding the section onto this talk page with the citations so it can be treated accordingly.

Case study on bilingual exposure A study entitled "Hearing Children Exposed to Spoken & Signed Input" investigated the transition from gesture to sign in a case study of an Italian, hearing, bimodal, bilingual child.

Marco was "a bilingual hearing child of deaf parents exposed to sign and [oral] language from birth". Though both parents were deaf, they used both Italian Sign Language (LIS) and spoken Italian, at some times simultaneously. Marco was also regularly enrolled in a day care with Italian-speaking peers.

Gesture was considered anything that a hearing (Italian) monolingual child had also been observed producing, whereas LIS was only considered in use if it resembled an adult speaker's LIS or a simplified sign, as judged by a native signer.

Under these criteria, Marco did not appear to have a "sign advantage." "Sign advantage" refers to the hypothesis that children who learn sign language and spoken language simultaneously will reach early linguistic milestones more rapidly in sign than in speech. Differences appeared in Marco's use of deictic and representational gestures as compared to those of monolingual children. "While Marco used proportionately more representational than deictic gestures at both comparison points, monolingual children produced deictic gestures much more frequently than representational gestures." He was able to use representational gestures more comfortably and practically, showing that "exposure to sign language may enhance a children's appreciation of the representational potential of the manual modality; this may, in turn, generalize to gesture use." Marco differed from all the studied monolingual peers in that he was able to combine and use two representational gestures.Sarah.Monk (talk) 15:56, 3 March 2016 (UTC)

 * This seems like it would be an interesting addition to the Sign Language article. However, I'm puzzled as to why you want to remove it from the Baby Sign article, as it seems to be relevant to it (although I think in both cases I'd suggest shortening and summarizing it, and maybe rephrasing to make it clearer to a non-technical audience). AlbertBickford (talk) 16:20, 3 March 2016 (UTC)
 * I also wonder why it is removed from Baby Sign. I don't believe that the Baby Sign article should exclude studies with deaf parents or deaf children. I also am concerned that legitimate sources were removed simply because they "could no longer be accessed". Sometimes the locations of online sources change. Better to mark them as "dead links"; someone may find them. Even better is to try to find them yourself. Sundayclose (talk) 17:02, 3 March 2016 (UTC)

Baby sign is not in fact a language as ASL, BSL or ISL are languages that have grammar, syntax and punctuation. Baby sign is an extension of symbolic gesture and therefore using this study, since it talks directly about a specific form of sign language being taught as a language, does not apply to baby sign. Although I do agree that it could use some simplification before it is accessible to the public. The goal of the baby sign article is to inform readers of what baby sign is, how it can be implemented, and what affects it can have on language acquisition for children. For a child who is bilingual and learning a legitimate sign language it does not apply to the article. Although we do provide a link to this sign language article on the baby sign page.Sarah.Monk (talk) 18:13, 3 March 2016 (UTC)

(talk) We are not excluding studies with deaf parents, this one was solely excluded for the use of a legitimate sign language with a bilingual child because it brings about situations that apply directly to learning a sign language not baby sign. As for the worry about legitimate sources I assure you I spent countless hours searching for them on numerous academic, google, and other search engines. Sources that could no longer be found were removed but that does not mean that all information was removed, previously existing information that applies to baby sign has now been cited from sources that can be accessed. Certain information was removed because it can not be substantiated from more than one source. Studies regarding deaf children, if we find them, will be touched on briefly with a link to the sign language pages since deaf children are going to be learning a true sign language after basic introduction to baby sign. I welcome more comments about the Baby sign language page but do ask that you post them on the Baby sign talk page itself. Thank you. Sarah.Monk (talk) 18:13, 3 March 2016 (UTC)

 * Thanks, for your explanations. Now that I understand your goal for the Baby Sign page, and I agree with it completely: Keep the page focused on the use of signs with babies where there is no intention for the child to acquire a natural sign language, and use cross-references to this or other articles when a real natural sign language is to be discussed.  Also agreed--further discussion of that page should be done on its own talk page. AlbertBickford (talk) 22:25, 3 March 2016 (UTC)

The lead: teaching sign language to non-humans
The lead states unequivocally that non-human primates have been taught to use sign language. I think if we look at the entirety of the research on this issue conducted over that last 30 years and the response of linguists, we can only conclude that such a claim carries with it considerable controversy and disagreement on a number of issues. Some of the details in this regard are discussed later in the article and at Great ape language. There is also discussion of this issue on this talk page at Talk:Sign language. I'll acknowledge that this article and Great ape language probably need better sourcing on both sides of the issue. But in the mean time I would like to get the lead consistent with the information that is already in the articles.

First, I should emphasize that my main concern is the unequivocal firmness that it is stated in the lead that non-humans use sign language. There is some research supporting that possibility, but there are also challenges to both the methodology and the conclusions that have been made by the researchers. The criticism is particularly strong by some linguists (Chomsky, for example). The gist of the criticisms has been that it is unclear at best that the non-humans are using language rather than simply signs. An analogy would be a person's use of a few words of a foreign language that can be described as communication but not language as defined by the linguistic rules that qualify the communication as language. There also has been criticism that some of the conclusions about non-human use of language have come from the trainers who are biased and do not necessarily understand what constitutes a "language." Other arguments that the research fails to distinguish between "communication" and "language" have come from observation by native users of the sign language watching videos of the animals; some of the native users commented that the communications did not follow the usual syntactic and grammatical rules of the sign language and that some of the signs were not recognizable if the viewer did not know the context of what the animal was trying to communicate about.

The main point I am trying to convey here is not a definitive conclusion that non-humans have not or could not learn a sign language. My point is that the conclusions have enough dispute and criticism that the statement in the lead needs to be toned down so that it doesn't indicate without reservation that non-humans have learned a language. That would make the lead consistent with other parts of the article (and with Great ape language), as well as the overall research data. Sundayclose (talk) 19:04, 10 June 2016 (UTC)
 * Agree generally. I'm of the camp that non-humans haven't learned a sign language, just some symbols, but that doesn't seem to be what you're asking. There is definitely a controversy, and the statement in the lead does not reflect that and so should be changed. Wugapodes [thɔk] [kantʃɻɪbz] 20:06, 10 June 2016 (UTC)
 * Actually I personally agree that nonhumans that are described in the literature have not learned language. I've discussed this with many native ASL users and none are convinced that it's language. But that's only my anecdotal experiences, and there's enough evidence on both sides that NPOV requires us to present both sides. And actually that seems to be the case for the articles as a whole, but not the lead of this article. I'm not opposed to moving the current statement out of the lead to another part of the article. Sundayclose (talk) 21:32, 10 June 2016 (UTC)

 * I agree. Given the controversy, we should not make a blanket statement in the lead. There's a further issue: the use of sign languages (or some facsimile of them) with primates is a *very* small part of the article overall--just a tiny section at the very end. I'd suggest that the appropriate solution would be to take the one sentence that mentions primates in the lead, remove it from there, and meld it into the section on primate use of language. What do the rest of you think? AlbertBickford (talk) 20:16, 10 June 2016 (UTC)

 * I agree--the sentence in the lead is disproportionate to the content in the article and should be moved to the primate section at the end. I'd recommend keeping this article and Great ape language mostly separate. This article is really about human sign language, so I would recommend a hatnote saying something like "This is about human sign language. For a discussion of sign language in other primates, see Great ape language." --Mark viking (talk) 20:43, 10 June 2016 (UTC)
 * I would be opposed to a hatnote worded like that, or honestly any hatnote at all. I think it's disproportionate coverage to be at the very top in a hatnote. I think the main link to Great ape language in the "in primates" section as it currently stands is enough. Wugapodes [thɔk] [kantʃɻɪbz] 22:00, 10 June 2016 (UTC)

If there's no objection, I will reword and move the sentence out of the lead. Sundayclose (talk) 13:29, 11 June 2016 (UTC)
 * It sounds like we're all agreed that we should move the one sentence out of the lead and into the section about primate use of sign language. The sentence itself is fine, and it has useful links to the various apes involved, it's just in the wrong place. I'm not totally decided about the hatnote issue, but tend to agree with the idea of not having a hatnote at the top of the article. Hatnotes in that position are important for guiding people to other articles that a reader may be looking for. There's a hatnote there now, guiding people to an article on manual codes for spoken languages. Those are often confused with natural sign languages, so that is a useful hatnote. But, if someone was interested in sign language use in research with primates, they are most likely going to go to an article on primates. Or, if they do start with the article on sign languages, they'll scan it for mention of primates, and fine the section that refers them to the relevant article. So, although I wouldn't object strongly to a hatnote, I think it is better without one. Let's just move the one sentence and then see what it looks like. AlbertBickford (talk) 01:23, 12 June 2016 (UTC)
 * BTW, I was about to make the change, but then I saw Sundayclose had volunteered to do so, so I'll defer to you. AlbertBickford (talk) 01:23, 12 June 2016 (UTC)
 * So, we're to mention it in the Lede, since it's a topic in the body of the article (as per what we're supposed to do), but perhaps trim it down to just mentioning that - according to the references we have on hand - primates have been taught to use a form of sign language for inter-species communication. It shouldn't vanish out of the Lede, is what I'm saying. - Jack Sebastian (talk) 01:38, 12 June 2016 (UTC)
 * It's disputed that it is a "form" of sign language, rather than just memorization of signs. An analogy is someone who knows 100 or so words in a foreign language. They can use words, but they do not use the "language" (which includes syntax and grammar). No linguist that I know of would state that someone who knows a few words actually is using the language, just a component of the language. It is disputed that nonhumans use more than signs, which alone are not a language but a component of the langauge. Another issue by some who commented above is whether the lead should have any mention of the issue since it's a small part of this article and is covered in more detail in another article. Sundayclose (talk) 01:53, 12 June 2016 (UTC)
 * That's a point worth considering that the lead/lede should include a mention of a topic that is included later in the article. As I read the guidelines on the lede, the concern is not to include every topic from the article in the lede, but to give an overall summary of the article, one which is sensitive to the relative importance of the topics within the article. In this case, I'd argue that the section on primate use of signs is so small, compared to the overall size of the article (especially considering ways that it could be reasonably expanded), that it doesn't deserve mention in the lede. AlbertBickford (talk) 01:58, 12 June 2016 (UTC)
 * The hatnote was a navigation suggestion and if the consensus is to leave it out, no worries. --Mark viking (talk) 02:43, 12 June 2016 (UTC)
 * I think that we have references referring to primate sign language and it bears repeating that our reasoning regarding the quality of that sign language is immaterial, since our opinions are not usable as sources of references. Of course, if Sundayclose is an expert in primates or sign language, then we should cite an article that (s)he has written in real life, noting one of those linguists they "know" explaining the differences. As editors, we cannot make that distinction.
 * I think - if anything - that a bit more of the primate stuff should be in the article as well. A LOT of our readers who come across sign language as an article are going to want to know why primate sign language isn't a part of the article. If expansion of the topic in the article is necessary, I'd be happy to do so. - Jack Sebastian (talk) 03:10, 12 June 2016 (UTC)
 * Just as an aside, I was looking over the article in question with an eye towards expansion, and it would appear that reference #89 (Premack & Pemack (1983), Premack (1985), Wittmann (1991) ) would appear to not actually exist. If it does, we need a reference that more clearly verifies the statement it is supposed to be supporting - Jack Sebastian (talk) 03:17, 12 June 2016 (UTC)
 * The article already has reliable sources regarding the dispute about whether or not nonhumans (apes) use sign language and whether it should be referred to as "language", in the section on "Primate use". And it's sourced even further at Great ape language. Sundayclose (talk) 03:20, 12 June 2016 (UTC)
 * The 1983 book Premack book exists with GBooks link The Mind of an Ape and we have an article on it: The Mind of an Ape. --Mark viking (talk) 03:24, 12 June 2016 (UTC)
 * Ahh, the reference was simply written incorrectly. And I was aware of the side article, but its cool that you do, too. While Premack is pretty well-known in the field, his opinion about the inability to teach sign language to primates other than humans is a minority one. Would it be unfair to give Premack's view more weight than, say Washoe's or the others who believe differently? I'll fix the citation, so someone else doesn't get confused by it. However, since I cannot find the subsequent dates of studies noted in the reference apart from the book by the Premacks (1983), I'd probably correct the spelling of Premack and remove the others; they deserve separate references anyway. - Jack Sebastian (talk) 03:35, 12 June 2016 (UTC)

 * As best as I can see, all of those sources exist. They're listed in the Bibliography. Sundayclose (talk) 03:27, 12 June 2016 (UTC)
 * Unfortunately, "as best as I can see" doesn't constitute verifiability. If you could provide more detailed sources, that would be great. - Jack Sebastian (talk) 03:36, 12 June 2016 (UTC)
 * RE: "it would appear that reference #89 (Premack & Pemack (1983), Premack (1985), Wittmann (1991) would appear to not actually exist". From the Bibliography in the article:
 * Premack, David, & Ann J. Premack (1983). The mind of an ape. New York: Norton.
 * Premack, David (1985). "'Gavagai!' or the future of the animal language controversy". Cognition 19 (3): 207–296.
 * Wittmann, Henri (1991). "Classification linguistique des langues signées non vocalement." Revue québécoise de linguistique théorique et appliquée 10:1.215–88.
 * Sundayclose (talk) 21:54, 12 June 2016 (UTC)
 * And that's the way they should have been entered into the article, and not as a misspelled grouping. - Jack Sebastian (talk) 23:41, 12 June 2016 (UTC)
 * Yes, thanks for pointing out that one letter was omitted. I had to look a little. One of the three "Premack" entries omitted a letter. What made it a little easier for me to find was that everything else was spelled correctly. Sundayclose (talk) 00:19, 13 June 2016 (UTC)

I noticed Jack Sebastian's change of "basic signs" to "sign language" in the section about the issue. It seems to me that neither wording is NPV, so I changed this to simply "signs", and adjusted wording later to try to bring out the meat of the controversy. Also, I'm not aware that there is any controversy about animals' ability to communicate with signs (or by other means), so I removed that claim, which was unsourced. AlbertBickford (talk) 14:17, 12 June 2016 (UTC)
 * With regard to newer references, I'd recommend citing Doctor Doolittle's Delusion (2004) by Stephen R. Anderson. I haven't read it myself, but this issue is the main topic of the book. According to descriptions I've read, the book makes a sharp distinction between communication and language (language being one type of communication, but by far not the only one), and argues that although animals can use elements like signs to communicate in ways that share some traits with human language, their use of them is much more limited than what occurs in natural human language. At any rate, it presumably includes citations to more recent research. Hopefully, too, we can find more recent research that presents the opposite view.
 * Incidentally, this distinction between communication and language is an important one for the article on sign language as a whole, since it is also important for distinguishing natural sign languages from invented artificial systems like Signed Exact English. AlbertBickford (talk) 14:17, 12 June 2016 (UTC)
 * Hi Albert. I used 'sign language' as that was what was utilized in the book, not signs. So it isn't an issue of NPOV; its the language used. The litmus for inclusion in an article is verifiability, not truth (ie. we don't have to agree with what they say, but we do have to verifiably cite it). As for the distinction between communication and language, I agree that it would be a good one to make, so long as we have supporting documentation that makes the entirety of the arguments with relation to sign language. This allows us to avoid the problem of synthesis. We cannot be program managers by taking two seemingly unconnected pieces of information and joining them together in a new way. We can cite folk who do this, but we cannot do it ourselves. - Jack Sebastian (talk) 16:34, 12 June 2016 (UTC)
 * OK, granted, but if you look at even the advertising blurbs from Anderson's book, you could see that it could be cited as demonstrating that the term "sign language" itself is controversial--indeed, whether it is language or not is the essence of the controversy. Part of it is a matter of definition--linguists use the term "language" in a very precise way that is not shared by non-linguists. (So, as far as "truth" is concerned, what seems to me to be happening is that primatologists have a definition of "language" which does describe what the apes are doing, but the linguists' definition is stricter. What we're grappling with, though, is how to modify the article in a verifiable way. I'm sure Anderson's book could provide that, but not having read it, I can't do that. Maybe I'll just have to.)
 * Anyway, a to acknowledge the controversy while still being verifiable, respecting the writings of primatologists who claim that animals have learned "language", how about a wording something like this: "There have been several notable notable examples where scientists have attempted to teach sign language to non-human primates in order to communicate with humans, but it is a matter of substantial controversy whether these animals have learned language (as a complete system comparable to its use in humans) or simply a set of signs that they can use to communicate." Alternately: "There have been several notable examples of scientists who have claimed to teach sign language to non-human primates...". Both, I think, would state in a neutral way what these scientists have actually done, and what they believe has happened, without endorsing their claims. What do you think? AlbertBickford (talk) 18:46, 12 June 2016 (UTC), updated AlbertBickford (talk) 18:52, 12 June 2016 (UTC)
 * The best way to accomplish this modification of the article is to find references that talk about the controversy. We cannot use our knowledge of the controversy to talk about it. We can use that knowledge to guide our search for relevant citations, but without those citations, we cannot say anything about the controversy. - Jack Sebastian (talk) 23:39, 12 June 2016 (UTC)
 * I agree that more citations are needed, especially more recent ones, and I suggested one source above (but unfortunately don't have time to follow it up right now myself). However, we already have citations on both sides of the debate, don't we? And we have existing wording in the article that acknowledges a debate. Hence, we have an obligation to achieve a NPOV among the citations we already have. My edits and suggestions have been directed to that end. AlbertBickford (talk) 01:29, 13 June 2016 (UTC)

I went ahead and moved the sentence out of the lead to the closing section, since it seemed like discussion on that aspect of the issue had died down. There's still the matter of how to describe the controversy over whether apes can have language, how much of it to handle in this article in addition to the main treatment elsewhere, and getting some newer citations in here. I also think we should check the citations about sign language being used with various specific types of primates, particularly the claim that Bonobos (pygmy chimpanzees) have learned it. AlbertBickford (talk) 01:43, 13 June 2016 (UTC)
 * I think you may have a misunderstanding of how editorial discretion and WP:NPOV works. As editors it is in fact our job to frame these issues, that's why WP:Due and undue weight exists. It is the job of editors to be able to weigh the substantiality of coverage. Being able to frame issues and make judgement calls is why NPOV exists and works, we are humans with brains not robots. Without discretion we would just be a list dueling of quotes from books and websites, not an encyclopedia. As people who have read substantial literature on this, our intuitions as to what is and is not neutral or undue are important, and our ability to frame it is not tied by WP:NPOV in the way you suggest. Considering multiple editors have said this term is not neutral, a controversy in the literature clearly exists, and a neutral descriptive way has been suggested to remedy those, I don't find your arguments particularly persuasive. Wugapodes [thɔk] [kantʃɻɪbz] 01:46, 13 June 2016 (UTC)
 * Respectfully, I think you are confusing an essay with policy. Apart from me in essence agreeing with your arguments, the point is, I am not asking you to be a "robot". I am asking you to realize that though you might be versed on a subject, you are not citable. This encyclopedia is built on references. Yes, we decide which references are from solid sources and which are fringe theories and so on, but we don't decide which side of a discussion/disagreement the article is going to fall on . We list both sides and allow the reader to make up their own mind. If a neutral remedy has been proposed tha tis supported by references pro and con, maybe I have missed that. If so, I'm sorry. Could someone present the nutreal descriptive way for me? - Jack Sebastian (talk) 02:42, 13 June 2016 (UTC)
 * The statements that I've suggested are based on the citations that we already have, some of which claim apes have learned sign language, some of which say it's not language. I don't know if anyone has come up with a neutral way of saying it in the literature, but I do believe that the citations we already have, both in this article and in the Great Ape Language article, are sufficient to justify the neutrality of the wording that I proposed. AlbertBickford (talk) 23:19, 13 June 2016 (UTC)
 * Respectfully, if the literature has not found a way to address or even identify the merits of the opposing viewpoints, I do not believe it is up to us to make that distinction. The possible reason why references regarding the comparisons of the differing viewpoints aren't being found is that they might not exist. This would suggest that the differences are likely less important than the body of work itself, which is still compiling information, studies and theories. The so-called "controversy" might in fact be an artificial construct for the purposes of this article only. If the latter is the case, any discussion of any dissent/controversy doesn't belong here. We can present both points of view, and allow the reader to make up their mind. - Jack Sebastian (talk) 18:49, 17 June 2016 (UTC)

With an eye towards resolving this discussion on the common ground we have found, I've made an edit that addresses the concerns:
 * Wherever communities of deaf people exist, sign languages have been developed. Signing is not only used by the deaf, it is also used by people who can hear, but cannot physically speak. It's also taught to other primates besides humans, such as common chimpanzees, Bonobos and Orangutans, though there is disagreement as to whether the language taught is true sign language. While they use space for grammar in a way that spoken languages do not, sign languages show the same linguistic properties and use the same language faculty as do spoken languages.

Thoughts? - Jack Sebastian (talk) 23:30, 24 June 2016 (UTC)
 * I disagree with the edit, which essentially undoes a change I made on 13 June. My change has in effect been reversed twice by Jack Sebastian, and was reinstated once by SundayClose, so clearly we need to talk about it more. Here's my case: I still feel that the treatment of non-human use of sign language is not sufficiently important to justify its inclusion in the lede. Furthermore, there are strong sources already cited in this discussion (though not yet incorporated in this article--I have Anderson's book on order so I can read it before actually introducing citations, although it is clear from previews that it claims to make a strong case against the claim that apes have learned sign language, and that they can only be claimed to have learned signs). Further, I would note that one of my specialties as a linguist is sign languages, and in my familiarity of the linguistic literature on sign languages I have not ever seen a single article or publication by a linguist that even mentions ape use of sign language. In an article about language, it should be linguists (who specialize in studying language) whose practice guides us as editors. Now, it is difficult to cite the lack of citation, but we should certainly pay attention to the absence of citable support for the notion that apes have learned sign *language*, as well as citable works such as Anderson's (as well as any textbook for an Introduction to Linguistics class, which treats the topic of animal communication and why it cannot be considered to be language--works that represent the consensus within the linguistic community). Given that absence, it seems appropriate to omit any mention about attempts to teach signs to apes from the lede. I'm not saying eliminate it from the article entirely; the current treatment at the end of the article, with a reference to the other article where the subject is treated in more depth, is adequate. At this point, it is up to Jack Sebastian to provide citations of articles that support including any more information about ape use of sign language in this article. I'd submit that these should be recent citations, since 2000, rather than the old claims that are currently cited. AlbertBickford (talk) 04:08, 25 June 2016 (UTC)
 * On a related matter, I have been suspicious about some of the references cited in the article. In particular, the references that were cited about teaching sign languages to Bonobos (pygmy chimpanzees) do not support that claim. It was not ASL or even signs from ASL that were learned by pygmy chimpanzees, but an abstract symbol system represented by drawings on a symbol board. For example, in the article by Savage-Rumbaugh et al "Spontaneous Symbol Acquisition and Communicative Use by Pygmy Chimpanzees", there is no mention of ASL, sign language, or signs. Accordingly, I have removed all references to Bonobos from the article. (Now, admittedly, it is impressive that these bonobos learned the symbol system spontaneously, without being taught it--but that belongs in an article about Great Apes or Bonobos; it has nothing to do with sign language.) AlbertBickford (talk) 04:33, 25 June 2016 (UTC)
 * Here's one more thought on the significance of non-human use of sign languages to an article on sign languages. Suppose this was the article about English. It would not be notable that English was used to train dogs, that dogs could learn to respond to commands issued in English. It would not be notable that English was taught to any particular group of people in Afghanistan. It would not be notable that parrots can learn to speak English phrases. Indeed, some of the Bonobos who have learned an abstract symbol system also are claimed to understand English. All of those things are simply not important enough to an article about English to be mentioned in it. They might indeed be notable in articles about dogs, Afghanistan, parrots, or bonobos, but not in an article about English. It is the same situation here. The primary use of sign languages is by Deaf people and their friends and family. They are secondarily used by other groups of people under special circumstances. But, their use by a tiny handful of apes does not say anything of significance about sign languages. Those are facts about great apes, worth mentioning briefly in the article, but not in the lede. AlbertBickford (talk) 04:44, 25 June 2016 (UTC)
 * Oh, BTW, lest anyone misunderstand, my reference to Afghanistan was not meant in any way to demean people in that country. Their ability to learn English is far greater than the ability of the animals mentioned. The point is that just because a language is taught to someone or something, that doesn't make it a notable fact about that language. AlbertBickford (talk) 04:50, 25 June 2016 (UTC)

Looking back through talk pages, I found an earlier (and unfortunately much more contentious) discussion on this topic that may be worth reviewing, here. The conclusion seems to have been to include a brief mention of animals' use of sign language in the article, which is what we inherited when the current discussion began. AlbertBickford (talk) 05:26, 25 June 2016 (UTC)
 * Thanks . There is no consensus to include information about teaching signs to apes in the lead; in fact the weight of opinions at this point is in the opposite direction. Regarding the previous discussion from 2010, there was support for mentioning teaching of "signs" to apes, although not much support for teaching "language". Sundayclose (talk) 14:36, 25 June 2016 (UTC)

 * Thanks, Sundayclose, for spotting that issue about "sign language" vs. "signs". I agree, the sources currently cited support only the claim that apes have learned signs, not that they have learned sign language. Although I still favor removing the whole sentence from the lead, I'm content to leave it there for now until we can insert more recent citations that document the claim that consensus among linguists is a) what apes have learned is not language and b) the topic of apes learning signs is not important enough to be mentioned in the lede, at least not in the way it currently is. (Again, I've got the relevant books on order.)
 * But, here's a new idea, something that may help us move toward consensus on this issue. I've noticed that the last few subsections of the article concern use of communication systems that resemble sign languages in various ways, but aren't full languages--in other words, things that non-linguists often confuse with full, natural sign languages but which linguists generally agree are not (full) languages: baby sign, home sign, ape use of signs, etc. Also, the current major heading that they are under, "In society", seems very broad and not particularly helpful. Suppose we group these few sections together under a new major section head titled "Communication systems that resemble sign languages". Besides the ones we already have, we could include a short section on manual codes for spoken languages, a topic that (I think) is otherwise mentioned only in the hatnote. Another topic to mention might be sign systems like those used by sports umpires and scuba divers, which consist of a relatively small set of standardized vocabulary and perhaps rudimentary syntax, but a very limited semantic domain. Anyway, each topic (subsection) in this new section would include a short paragraph or two about the topic, consisting of a description, summary of the similarities and differences with natural sign languages, and a hatnote to the main article about the topic. If we do that, then the overall major section would be significant enough within the article that we could include a single sentence in the lede mentioning it, something like "Natural sign languages are distinguished from other systems that are derived from them or otherwise resemble them, such as manual codes for spoken languages, "baby signs", "body language", signs taught to non-human primates, and speculation about use of signs in the early evolution of language." That allows mention of the ape research in the lede, but in a context that keeps it in balance with other topics. Would that be acceptable to everyone? And, I think the article would be strengthened by making clear, in the lede, that not everything that the general population calls "sign language" is considered to be that by linguists. AlbertBickford (talk) 22:14, 25 June 2016 (UTC)
 * Thanks for your well thought-out suggested changes in the organization of the article, as well as your suggested sentence in the lead that incorporates various non-language systems that are derived from sign languages. I agree completely. I also agree that a brief section on manually coded systems that are based on sign languages is needed in the article. Sundayclose (talk) 23:34, 25 June 2016 (UTC)
 * Since there are no further comments, I'm going to go ahead and give it a shot now. Hold tight while I put the page through a series of changes. AlbertBickford (talk) 01:49, 6 July 2016 (UTC)
 * OK, I'm done. Take a look at what I've done so far. I also intend to go ahead and update the citations and wording in the section on primate use of sign languages, but before I do that, I want to see if people like this rearrangement of things. People who may be interested: Sundayclose, Jack Sebastian, Wugapodes, Mark viking. Thanks! AlbertBickford (talk) 02:02, 6 July 2016 (UTC)
 * I took a quick look and agree with the changes. There's a problem with a citation syntax in the home sign section that I can't figure out how to fix, so maybe someone else can take a look. Thanks. Sundayclose (talk) 02:44, 6 July 2016 (UTC)
 * I fixed the citation problem; it was one tag inside another. AlbertBickford (talk) 12:05, 6 July 2016 (UTC)

I have now completed the changes I had anticipated in my comments above. In the discussion of ape use of signs at the end of the article, I added a reference to Dr. Doolittle's Delusion and two other published works that represent linguists' perspective on signing apes, to balance the claims by primatologists (in previously-existing references). Someone may want to also insert these references into the main article: Great_ape_language, but I think I'll stop here. Thanks to everyone for a stimulating discussion, which finally prompted me to read the Doolittle book. AlbertBickford (talk) 02:15, 28 July 2016 (UTC)

 * The lead of baby sign language and ape sign language is out of place in this generic article about Sign Language. The article is about the language used by the Deaf. It is a diversion that does not highlight what the language using hands in conjunction of body and face is all about. Baby sign language and primate sign language deserve their own entries separate of sign language as used by humans, chiefly by Deaf people. They should not be co-mingled in an article. Sign Language of the Deaf is HUGE, more so than a spoken language!
 * Here I wish to comment about the use of signs by primates. As far I read the reports, the signed utterances of chimpanzees and a gorilla are no longer than two signs. One trained chimpanzee uttered creatively WATER BIRD for "swan" and CRY FRUIT for "onion". The researcher claims that it is language use, because of the use of metaphor. So he fused cognitive ability with linguistic ability. No later report of the chimpanzee's language output. The report about the longest work with a gorilla Koko (over 20 yeas) does not deliver longer strings of signs Koko produced nor described conversations between the caretaker and Koko.  By these evidences, animals cannot converse in language beyond the two-word stage. However, anecdotes about use of spoken words or signs with dogs or cats evidence their ability to understand human language more than what the trained primates produce.  Of course, the apes could understand the signs given by humans more than they can utter, more like a human infant.  Understanding and uttering of a linguistic string require different cognitive abilities.  74.104.144.152 (talk) 04:16, 25 June 2019 (UTC) Hartmut Teuber, 23 June 2019, 23:45

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Section To Add
According to U.S. Department of Health & Human Services, "No one form of sign language is universal. Different sign languages are used in different countries or regions". Since there is not one form of sign language, a section to be added identifying the sign language around the world, and how each region of the world affect each individual type of sign language. Also, how do each culture and religion view sign language? How would one come about in answering these questions, and is it even possible? — Preceding unsigned comment added by Toanndo (talk • contribs) 20:27, 5 December 2017 (UTC)

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Hi,

I read your wiki information and I want to talk about your “Acquisition” section. I think you should give more information about bilingualism and how it impacts deaf children’s acquisition of language. For example, the deaf children who are exposed to American Sign Language earlier as opposed to later in their life will have a better understanding of written English. Deaf children who learn ASL first before cochlear implantation will achieve more desirable progress with spoken languages. Teaching a child ASL first, preferably in early ages, will impact the child’s language development overall. There is an article titled, Spoken English Language Development Among Native Signing Children With Cochlear Implants, that might protect your wiki information with valuable credits.

I have a couple of questions to ask:

Can you explain how sign language does not have a traditional or formal written form? Additionally, the information presented in the article should mention several research studies to help prove the point. How does the research you collected show that sign language has significant transformative properties towards a child’s language development? Could you argue that a deaf person’s video-recorded or photo-recorded sign language could be viewed as a written language?

Thank you, Dnalves1990 (talk) 23:40, 3 February 2018 (UTC) David

Need for more citations and editing a possible biased portion
I'm currently looking through the article to see if anything needs any kind of improvement on. I've found a few areas that could be edited and would love to know if anyone agrees, disagrees, or has any other comments.

Under the Linguistics portion of the article, the last sentence in paragraph three that talks about the characteristics of human language needs citing. In paragraph four, the last sentence talks about how linguists refer to the word "classifiers" as different terms and I think there should be a few examples there and also a citation. Under the Relationships with spoken languages portion, the last sentence of the last paragraph should also have a citation.

Aside from citation, under the Iconicity portion of the article, the first paragraph has a sentence, "Frishberg (1975) wrote a very influential paper addressing the relationship between arbitrariness and iconicity in ASL." which I think is slightly biased. The "very influential paper" is subjective in my opinion. I feel like that should be changed to just "Frishberg (1975) wrote a paper addressing..." That portion of the paragraph (the last 3 sentences) could be rewritten to convey the subject a bit more clearly since it seems a bit redundant and drawn out. --Adrisheh (talk) 01:15, 5 February 2018 (UTC)

Suggestions
Hello!

I noticed in the "linguistics" (tongue is the instrument) or "handistics" (hand is the instrument) section of this article, signed languages are heavily compared to oral languages. Although it is very easy to make this connection since the majority of people are familiar only with oral languages, but it could be more beneficial to avoid this close comparison. Historically their is a stigma that oral languages are not real/complete languages. By relating signed languages back to oral languages, it is almost as if signed languages need to prove themselves to readers that they fit all of the criteria of language and that the only way to do so is to use oral languages as a guide.

In addition, the "'baby sign language' with hearing children" section, the statement "Babies can usually produce signs before they can speak." lacks a citation.

Best, --Brooke hayman (talk) 04:52, 6 February 2018 (UTC)

Sign language glove
We could really use a picture for Sign language glove. Anyone? Anna Frodesiak (talk) 18:47, 3 April 2019 (UTC)

Section on classifier constructions needed
Considering that classifier constructions are near-universal in sign languages, they should be described in more detail. Currently, information about classifier constructions is mentioned sporadically in two paragraphs, neither of which describe them particularly well. They're also confusingly linked to the article on measure words, which is a very different concept.

I'd say there should be a separate section devoted to classifier constructions explaining the four different types of classifiers (whole entity, handling/instrument, limb, extension/surface) and the types of movement (position, motion, manner and extension). Perhaps use some examples from ASL if possible. Additionally a quick mention that some village sign languages, like Adamorobe Sign Language, do not seem to have entity classifiers at all.--Megaman en m (talk) 16:39, 8 May 2019 (UTC)

ASL - What's the meaning of the message this person signs?
Thank you in advance. --Blutgretchen (talk) 15:37, 10 November 2019 (UTC)

Gloss: NAMESIGN(L-on-forehead) HIS SON DIE YOUNG, LEAVE WHAT? 100. LATER, [unintelligble], MOVE ILLIOIS. Approximate translation: L____'s son passed away when he was young. He left behind 100 [?] Later, [?] moved to Illinois.

Matthall.research (talk) 21:03, 5 March 2021 (UTC)

Sign language interpreters in public life
They are quite common now e.g. when politicians are speaking. It wasn't always like this. When, how, and why did the change take place? Mporter (talk) 07:36, 8 June 2020 (UTC)
 * I don't have any reliable sources immediately available, but it has been a slow progression over decades. A major step forward was with William Stokoe's seminal research in the 1960s and 1970s that clearly confirmed that ASL is a legitimate language. Beginning in the 1970s there have been a number of legal and social changes that made availability of interpreters more common (and in many cases required legally) in educational, employment, and other settings; this was in the USA, I'm not familiar with other countries. This led to the development of interpreter training programs. Disability rights groups became more prominent and politically effective. Like most social change, it evolved slowly but with a few leaps from time to time. Sundayclose (talk) 16:20, 8 June 2020 (UTC)

"Influence from the surrounding spoken languages [on sign language word order] is not improbable."
This statement in this section is a little strange, because most of the languages given as examples given immediately before that in the paragraph differ from the surrounding spoken languages in their word order. Japanese is SOV, but Japanese Sign Language is SVO. Hindi, Urdu, Punjabi, Pashto, and Sindhi are all SOV, but Indo-Pakistani Sign Language is SVO. English is SVO, but American Sign Langauge is SOV. The statement is also apparently uncited. — Preceding unsigned comment added by VIVIT-r (talk • contribs) 00:33, 27 February 2021 (UTC)

 * Not to mention pretty weaselly: "influence is not improbable" doesn't exactly nail it down. Regulov (talk) 09:39, 12 June 2022 (UTC)

independance from spoken languages
The introduction should make it more clear that sign languages are completely independent from spoken languages. For example, that ASL is not just some non-spoken form of (spoken) American english. --217.149.171.189 (talk) 21:50, 2 January 2022 (UTC)
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. There are many sign languages. To include such a statement in this generic article would require a reliable source that it's true for all sign languages. That's impractical. Such information really belongs in the articles for specific sign languages. It's stated in the lead for American Sign Language, although it doesn't necessarily have to be in the WP:LEAD because the lead has limited information. Sundayclose (talk) 23:21, 2 January 2022 (UTC)

Awkward phrasing
From the lead:

"Linguists consider both spoken and signed communication to be types of natural language, meaning that both emerged through an abstract, protracted aging process and evolved over time without meticulous planning."

The phrase "an abstract, protracted aging process" needs improvement. It makes sign language sound like a cheese. "Aging process" is simply inappropriate here; I don't like either "abstract" or "protracted", either. Substitute "continuous" for "protracted"? I think the whole sentence needs to be rebuilt from the ground up. The key point is that sign languages are not constructed languages, no? It might be clearer to just say that.

"Sign languages are not constructed languages. Like spoken languages, they are undirected, unplanned emergent phenomena."

Or:

"Linguists consider both spoken and signed communication to be types of natural language. Sign language, like spoken language, emerges from its users' behaviour without central management or direction."

Something like that? Just thinking out loud, here. I really don't think "abstract, protracted aging process" is what is called for. Regulov (talk) 09:54, 12 June 2022 (UTC)

I need to learn sign language
I need to learn sign language to understand my sister 50.101.197.154 (talk) 03:20, 19 June 2022 (UTC)

Adding a sign language section to the mutual intelligibility article
Can someone add a section about the mutual intelligibility (or lack there of) of sign languages to the mutual intelligibility article? Treetoes023 (talk) 01:29, 12 November 2022 (UTC)

Sign Launguage
How do I do sign language Bugs the bunny13 (talk) 18:06, 6 March 2023 (UTC)
 * This talk page is not for general discussion of the topic. You might be interested in discussing at the reference desk. Sundayclose (talk) 18:30, 6 March 2023 (UTC)
 * ok Bugs the bunny13 (talk) 17:02, 9 March 2023 (UTC)

Wiki Education assignment: Linguistics in the Digital Age
— Assignment last updated by Fedfed2 (talk) 00:53, 9 December 2023 (UTC)

title: Talk:Sign language


text:
Hamamelidales

Hamamelidales is an order of flowering plants formerly accepted in a number of systems of plant taxonomy, including the Cronquist system published in 1968 and 1988. The order is not currently accepted in the Angiosperm Phylogeny Group III system of plant taxonomy, the most widely accepted system as molecular systematic studies have suggested that these families are not closely related to each other. The APG II system (2003) assigns them to several different orders: Hamamelidaceae and Cercidiphyllaceae to Saxifragales, Eupteleaceae to Ranunculales, Platanaceae to Proteales, and Myrothamnaceae to Gunnerales. Additional studies of the chloroplast genome have since confirmed that the families moved into the Saxifragales are closely related.

The Cronquist system (1981) included the order in subclass Hamamelidae with the circumscription:

 * order Hamamelidales
 * family Hamamelidaceae, now in order Saxifragales
 * family Cercidiphyllaceae, now in order Saxifragales
 * family Eupteleaceae, now in order Ranunculales
 * family Platanaceae, now in order Proteales
 * family Myrothamnaceae, now in order Gunnerales

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Hamamelidales


text:
Nymphaeales

The Nymphaeales are an order of flowering plants, consisting of three families of aquatic plants, the Hydatellaceae, the Cabombaceae, and the Nymphaeaceae (water lilies). It is one of the three orders of basal angiosperms, an early-diverging grade of flowering plants. At least 10 morphological characters unite the Nymphaeales. One of the traits is the absence of a vascular cambium, which is required to produce both xylem (wood) and phloem, which therefore are missing. Molecular synapomorphies are also known.

The Plant List, created by the Royal Botanic Gardens, Kew and Missouri Botanical Garden recognizes about 70 species in 11 genera within the order, but a phylogenetic study of the genus Nymphaea implies that the number of species could be more than 90. The difference in species numbers is due almost entirely to the difficulty of delineating species in the genus Nymphaea.

All of the species are rhizomatous aquatic herbs with a broad leaf base and large, showy flowers.

Fossils
The fossil record consists especially of seeds, but also pollen, stems, leaves, and flowers. It extends back to the Cretaceous. The crown group of the Nymphaeales has been estimated to be about 112 million years old. Some have suggested that this age might be too old.

A basal member of Nymphaeales, Monetianthus, is known from Early Cretaceous Portugal. A fossil member of the Nympheaceae is Jaguariba from the Early Cretaceous of Brazil. Several Cretaceous-age Cabombaceae genera are also known, including Scutifolium from Jordan, Pluricarpellatia from Brazil, and Brasenites from Kansas. The fossil genus Notonuphar, thought to be a close relative of the modern Nuphar, is known from Eocene-aged sediments from Seymour Island, Antarctica. The aquatic plant fossil Archaefructus from the Early Cretaceous of Liaoning, China possibly also belongs to this group.

Classification
The Nymphaeales currently include three families and about 70 to 90 species.

This order was not part of the APG II system's 2003 plant classification (unchanged from the APG system of 1998), which instead had a broadly circumscribed family Nymphaeaceae (including Cabombaceae) unplaced in any order. The APG III system did separate the Cabombaceae from the Nymphaeaceae and placed them in the order Nymphaeales together with the Hydatellaceae. The family Hydatellaceae was placed among the monocots in previous systems, but a 2007 study found that the family belongs to the Nymphaeales. In the APG IV system, Hydatellaceae, Cabombaceae and Nymphaeaceae are the three families included in the Nymphaeales.

Some earlier systems, such as Cronquist's system of 1981, often included the Ceratophyllaceae and Nelumbonaceae in the Nymphaeales. Although, the Takhtajan system of 1980 separated the Nelumbonales, the new order was retained alongside the Nymphaeales in the superorder Nymphaeanae.

The Cronquist system placed the Nymphaeales in subclass Magnoliidae, in class Magnoliopsida [=dicotyledons]. In addition, Cronquist included the Ceratophyllaceae and split the family Barclayaceae from the Nymphaeaceae. Under the APG II system, the family Cabombaceae was included within the Nymphaeaceae, but could optionally be recognized separately. As of APG III, the two families are recognized separately.

The Dahlgren system placed the Nymphaeales with the Piperales in superorder Nymphaeanae, within subclass Magnoliideae (dicotyledons). Thorne's 1992 system (and 2000 revision) placed the Nymphaeales as the sole order in the superorder Nymphaeanae within subclass Magnoliideae (=dicotyledons).

title: Nymphaeales


text:
User talk:G from B

Hello there, welcome to the 'pedia! I hope you like the place and decide to stay. If you need any questions answered about the project then check out Help or drop me a line. Cheers! --maveric149

RE your comment on my talk page: You're welcome and don't worry. We all have made mistakes in the past and will all continue to make mistakes in the future-- such is being human. I made plenty in my early days in wikiland and still make mistakes now -- even big ones once in a while. If and when you make mistakes others will fix them if you don't first. Such is the wikiway. Just keep on having good intentions and check out our policies and guidelines especialy naming conventions and neutral point of view and don't forget to have fun! --maveric149

Dear Guy: re your entries on days that never existed in the calendar changeover -- I thought that different countries changed over in different years. Could you specify the countries referred to? Thanks! The Anome

 * That's how it works on Wikipedia. We learn new stuff all the time.  Welcome to the club. -- Derek Ross

 * So it does. Guy -- I forgot to say: Welcome to Wikipedia! The Anome

Als je eens twee minuten tijd hebt dan zouden we je op WikiNL ook graag verwelkomen. Er is nog heeel veel werk en we zijn met bitter weinig. User:giskart

A great contact for WikiProject protected areas would be User:ClaudeMuncey who has contributed a framework for National Parks. I just can't find where it is right now. --mav

 * I found it: Talk:National park --mav

Why did you redirect National parks (Australia) to Protected areas of Australia? I thought National Parks were called just that in Australia. I'm not opposed to the name change per se, but this type of name change needs to be discussed before being done unilaterally. I suggest Wikipedia talk:Naming conventions. Your title, or something similar, may just bring order to the chaos of naming these type of index pages (since this would be a more inclusive and consistant name) -- might even become a naming convention. --mav 15:24 Aug 8, 2002 (PDT)

 * First I want to apologise for the redirect without discussing it first. The reasons for it were:

 * 1) To create a test article for the WikiProject Protected Areas. Since the basic information already existed on the page National parks of Australia (which was already a redirect from National parks (Australia) I took that information, put it on the page Protected areas of Australia and redirected the two national park pages. I admit that it probably would have been better to create the new page without the redirects...
 * 2) An area called a national park obviously is just that, though the meaning of it can vary in different countries. However, on the said page there were only 6 national parks out of a total of 37 protected areas (14 of which -the Historic Shipwrecks- I included more than two months ago). While doing the redirect I included 8 more protected areas. That makes 6 national parks out of a total of 45. IMO it's not a very good idea to call a page something that covers only 13 percent of its contents.
 * 3) I used the name "protected area" because, as you said, it is more inclusive and it can be used for any existing (and possibly future) type of protected area. Moreover, it is the term used by The World Conservation Union (IUCN) and other national and international organisations. For more information, see this link. Even if a particular country only has one protected area type, I am for using "protected area" as a general page title. The precise names can then be used on the page itself.
 * As you suggested I will put your question and my answer on Wikipedia talk:Naming conventions (protected areas). I'll wait for a consensus before doing any more changes. -- Guy 04:42 Aug 9, 2002 (PDT)

re: the table. You're welcome! Glad I could help. --Bth

Goede Morgen, Guy! Thanks for telling me about the Protected Areas page(s). I'm just doing something similar, writing pages about SSSIs, SACs, etc. Your page(s) would have to be part of the "conservation portal". I'm glad someone else apart from me is interested in these things and attaches some importance to them! By the way, I live in the Peak District National Park :-)) User:Renata

Hi Guy, have a look at Protected area! User:Renata

Hi again, I've replied to your latest comments on my Talk page. User:Renata

Good evening, Guy! When you have time, would you like to have a look at WikiProject Conservation worldwide and in Countries A-Z click on United Kingdom/Conservation? There are things you could add to Australia/Conservation, I'm sure. Thanks! User:Renata October 13, 2002

Hello Guy, have a look at Biosphere Reserves in Australia. Do you fancy working on it? User:Renata
 * Why not - it looks interesting. I'll see what info I can come up with. I don't know when that will be, though. The coming week I have quite a few things scheduled (other than Wikipedia, that is...) Guy 09:25 Oct 21, 2002 (UTC)

Dutch Wikipedia symposium in Rotterdam (27/11/2004)
Hi,

As a personal initiative I want to mention to you http://nl.wikipedia.org/wiki/Wikipedia:Symposium/Najaar_2004

There have been some voices that Dutch-speaking Belgian wikipedians might be underrepresented at that venue, so I took the liberty to post this message on the talk page of all people I found on Wikipedians/Belgium.

If this doesn't apply to you (e.g. while French-speaking, or not interested in Dutch wikipedia,...) simply ignore this message.

--Francis Schonken 09:25, 22 Sep 2004 (UTC)

Article Licensing
Hi, I've started a drive to get users to multi-license all of their contributions that they've made to either (1) all U.S. state, county, and city articles or (2) all articles, using the Creative Commons Attribution-Share Alike (CC-by-sa) v1.0 and v2.0 Licenses or into the public domain if they prefer. The CC-by-sa license is a true free documentation license that is similar to Wikipedia's license, the GFDL, but it allows other projects, such as WikiTravel, to use our articles. Since you are among the top 1000 Wikipedians by edits, I was wondering if you would be willing to multi-license all of your contributions or at minimum those on the geographic articles. Over 90% of people asked have agreed. For More Information:
 * Multi-Licensing FAQ - Lots of questions answered
 * Multi-Licensing Guide
 * Free the Rambot Articles Project

To allow us to track those users who muli-license their contributions, many users copy and paste the " " template into their user page, but there are other options at Template messages/User namespace. The following examples could also copied and pasted into your user page:

 * Option 1
 * I agree to multi-license all my contributions, with the exception of my user pages, as described below:

OR
 * Option 2
 * I agree to multi-license all my contributions to any U.S. state, county, or city article as described below:

Or if you wanted to place your work into the public domain, you could replace " " with "  ". If you only prefer using the GFDL, I would like to know that too. Please let me know what you think at my talk page. It's important to know either way so no one keeps asking. -- Ram-Man (comment| talk)

World Heritage template
Hi! I created a template for World Heritage Sites: Infobox World Heritage Site. Since many of the protected areas are also recognized as World Heritage Sites, I thought that it will be appropriate to forward this template here, and hopefully, for the community to help improve the template. Someone mentioned that the footnotes are unclear (i.e. why the need to emphasize "official" there). It's because the official name (or the name as inscribed on the List) is different from what we usually know. And the Region also has footnote to tackle specifically the classification of those regions which may fall ambiguously between two continents (e.g. those in Russia, Turkey, Cyprus, etc.). In addition, I think that the info provided in the template is much like a jargon for most readers since it box is more of use for internal references in the World Heritage program. I hope that the community will help improve the template and make it more relevant to the readers of wikipedia in general. Thanks. Joey80 13:41, 20 March 2007 (UTC)

AfD nomination of Mount Colosseum National Park
I have nominated Mount Colosseum National Park, an article you created, for deletion. I do not feel that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Articles for deletion/Mount Colosseum National Park. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time. Bananaqueen (talk) 00:11, 14 March 2008 (UTC)

ArbCom elections are now open!
MediaWiki message delivery (talk) 08:52, 23 November 2015 (UTC)

title: User talk:G from B


text:
Partition function

Partition function may refer to:
 * Rotational partition function
 * Vibrational partition function
 * Partition function (number theory)
 * Partition function (mathematics), which generalizes its use in statistical mechanics and quantum field theory:
 * Partition function (statistical mechanics)
 * Partition function (quantum field theory)

title: Partition function


text:
Floor and ceiling functions

In mathematics, the floor function is the function that takes as input a real number $x$, and gives as output the greatest integer less than or equal to $x$, denoted $⌊x⌋$ or $floor(x)$. Similarly, the ceiling function maps $x$ to the smallest integer greater than or equal to $x$, denoted $⌈x⌉$ or $ceil(x)$.

For example, for floor: $⌊2.4⌋ = 2$, $⌊−2.4⌋ = −3$, and for ceiling: $⌈2.4⌉ = 3$, and $⌈−2.4⌉ = −2$.

The floor of $x$ is also called the integral part, integer part, greatest integer, or entier of $x$, and was historically denoted $[x]$ (among other notations). However, the same term, integer part, is also used for truncation towards zero, which differs from the floor function for negative numbers.

For $n$ an integer, $⌊n⌋ = ⌈n⌉ = n$.

Although $floor(x+1)$ and $ceil(x)$ produce graphs that appear exactly alike, they are not the same when the value of x is an exact integer. For example, when $x$=2.0001; $⌊2.0001+1⌋ = ⌈2.0001⌉ = 3$. However, if $x$=2, then $⌊2+1⌋ = 3$, while $⌈2⌉ = 2$.

Notation
The integral part or integer part of a number (partie entière in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula.

Carl Friedrich Gauss introduced the square bracket notation $⌊x⌋$ in his third proof of quadratic reciprocity (1808). This remained the standard in mathematics until Kenneth E. Iverson introduced, in his 1962 book A Programming Language, the names "floor" and "ceiling" and the corresponding notations $⌈x⌉$ and ${x}$. (Iverson used square brackets for a different purpose, the Iverson bracket notation.) Both notations are now used in mathematics, although Iverson's notation will be followed in this article.

In some sources, boldface or double brackets $[x]$ are used for floor, and reversed brackets $⌊x⌋$ or $⌈x⌉$ for ceiling.

The fractional part is the sawtooth function, denoted by $⟦x⟧$ for real $x$ and defined by the formula

For all x,

These characters are provided in Unicode:

In the LaTeX typesetting system, these symbols can be specified with the  and   commands in math mode, and extended in size using   and   as needed.

Definition and properties
Given real numbers x and y, integers m and n and the set of integers $$\mathbb{Z}$$, floor and ceiling may be defined by the equations

 * $$ \lfloor x \rfloor=\max \{m\in\mathbb{Z}\mid m\le x\},$$

 * $$ \lceil x \rceil=\min \{n\in\mathbb{Z}\mid n\ge x\}.$$

Since there is exactly one integer in a half-open interval of length one, for any real number x, there are unique integers m and n satisfying the equation
 * $$x-1<m\le x \le n <x+1.$$

where $$\lfloor x \rfloor = m$$ and $$\lceil x \rceil = n$$ may also be taken as the definition of floor and ceiling.

Equivalences
These formulas can be used to simplify expressions involving floors and ceilings.

\begin{alignat}{3} \lfloor x \rfloor &= m \ \ &&\mbox{ if and only if } &m &\le x < m+1,\\ \lceil x \rceil &= n    &&\mbox{ if and only if } &\ \ n -1 &< x \le n,\\

\lfloor x \rfloor &= m  &&\mbox{ if and only if } &x-1 &< m \le x,\\ \lceil x \rceil &= n   &&\mbox{ if and only if }  &x &\le n < x+1. \end{alignat} $$

In the language of order theory, the floor function is a residuated mapping, that is, part of a Galois connection: it is the upper adjoint of the function that embeds the integers into the reals.

\begin{align} x<n &\;\;\mbox{ if and only if } &\lfloor x \rfloor &< n, \\ n<x &\;\;\mbox{ if and only if } &n &< \lceil x \rceil, \\ x\le n &\;\;\mbox{ if and only if } &\lceil x \rceil &\le n, \\ n\le x &\;\;\mbox{ if and only if } &n &\le \lfloor x \rfloor. \end{align} $$

These formulas show how adding an integer $n$ to the arguments affects the functions:

\begin{align} \lfloor x+n \rfloor &= \lfloor x \rfloor+n,\\ \lceil x+n \rceil &= \lceil x \rceil+n,\\ \{ x+n \} &= \{ x \}. \end{align} $$

The above are never true if $n$ is not an integer; however, for every $x$ and $y$, the following inequalities hold:

 * $$\begin{align}

\lfloor x \rfloor + \lfloor y \rfloor &\leq \lfloor x + y \rfloor \leq \lfloor x \rfloor + \lfloor y \rfloor + 1,\\[3mu] \lceil x \rceil + \lceil y \rceil -1 &\leq \lceil x + y \rceil \leq \lceil x \rceil + \lceil y \rceil. \end{align}$$

Monotonicity
Both floor and ceiling functions are monotonically non-decreasing functions:

\begin{align} x_{1} \le x_{2} &\Rightarrow \lfloor x_{1} \rfloor \le \lfloor x_{2} \rfloor, \\ x_{1} \le x_{2} &\Rightarrow \lceil x_{1} \rceil  \le \lceil  x_{2} \rceil. \end{align} $$

Relations among the functions
It is clear from the definitions that
 * $$\lfloor x \rfloor \le \lceil x \rceil,$$  with equality if and only if x is an integer, i.e.
 * $$\lceil x \rceil - \lfloor x \rfloor = \begin{cases}

0&\mbox{ if } x\in \mathbb{Z}\\ 1&\mbox{ if } x\not\in \mathbb{Z} \end{cases}$$

In fact, for integers n, both floor and ceiling functions are the identity:
 * $$\lfloor n \rfloor = \lceil n \rceil = n.$$

Negating the argument switches floor and ceiling and changes the sign:
 * $$ \begin{align}

\lfloor x \rfloor +\lceil -x \rceil &= 0 \\ -\lfloor x \rfloor &= \lceil -x \rceil \\ -\lceil x \rceil  &= \lfloor -x \rfloor \end{align} $$

and:
 * $$\lfloor x \rfloor + \lfloor -x \rfloor = \begin{cases}

0&\text{if } x\in \mathbb{Z}\\ -1&\text{if } x\not\in \mathbb{Z}, \end{cases}$$

 * $$\lceil x \rceil + \lceil -x \rceil = \begin{cases}

0&\text{if } x\in \mathbb{Z}\\ 1&\text{if } x\not\in \mathbb{Z}. \end{cases}$$

Negating the argument complements the fractional part:

 * $$\{ x \} + \{ -x \} = \begin{cases}

0&\text{if } x\in \mathbb{Z}\\ 1&\text{if } x\not\in \mathbb{Z}. \end{cases}$$

The floor, ceiling, and fractional part functions are idempotent:

\begin{align} \big\lfloor \lfloor x \rfloor \big\rfloor &= \lfloor x \rfloor, \\ \big\lceil \lceil x \rceil \big\rceil &= \lceil x \rceil, \\ \big\{ \{ x \} \big\} &= \{ x \}. \end{align} $$

The result of nested floor or ceiling functions is the innermost function:

\begin{align} \big\lfloor \lceil x \rceil \big\rfloor &= \lceil x \rceil, \\ \big\lceil \lfloor x \rfloor \big\rceil &= \lfloor x \rfloor \end{align} $$ due to the identity property for integers.

Quotients
If m and n are integers and n ≠ 0,
 * $$0 \le \left\{ \frac{m}{n} \right\} \le 1-\frac{1}{|n|}.$$

If n is a positive integer
 * $$\left\lfloor\frac{x+m}{n}\right\rfloor = \left\lfloor\frac{\lfloor x\rfloor +m}{n}\right\rfloor,

$$

 * $$\left\lceil\frac{x+m}{n}\right\rceil = \left\lceil\frac{\lceil x\rceil +m}{n}\right\rceil.

$$

If m is positive

 * $$n=\left\lceil\frac{n\vphantom1}{m}\right\rceil + \left\lceil\frac{n-1}{m}\right\rceil +\dots+\left\lceil\frac{n-m+1}{m}\right\rceil,

$$

 * $$n=\left\lfloor\frac{n\vphantom1}{m}\right\rfloor + \left\lfloor\frac{n+1}{m}\right\rfloor +\dots+\left\lfloor\frac{n+m-1}{m}\right\rfloor.

$$

For m = 2 these imply

 * $$n= \left\lfloor \frac{n\vphantom1}{2}\right \rfloor + \left\lceil\frac{n\vphantom1}{2}\right \rceil.$$

More generally, for positive m (See Hermite's identity)

 * $$\lceil mx \rceil =\left\lceil x\right\rceil + \left\lceil x-\frac{1}{m}\right\rceil +\dots+\left\lceil x-\frac{m-1}{m}\right\rceil,

$$

 * $$\lfloor mx \rfloor=\left\lfloor x\right\rfloor + \left\lfloor x+\frac{1}{m}\right\rfloor +\dots+\left\lfloor x+\frac{m-1}{m}\right\rfloor.

$$

The following can be used to convert floors to ceilings and vice versa (m positive)

 * $$\left\lceil \frac{n\vphantom1}{m} \right\rceil = \left\lfloor \frac{n+m-1}{m} \right\rfloor = \left\lfloor \frac{n - 1}{m} \right\rfloor + 1, $$

 * $$\left\lfloor \frac{n\vphantom1}{m} \right\rfloor = \left\lceil \frac{n-m+1}{m} \right\rceil = \left\lceil \frac{n + 1}{m} \right\rceil - 1, $$

For all m and n strictly positive integers:

 * $$\sum_{k = 1}^{n - 1} \left\lfloor \frac{k m}{n} \right\rfloor = \frac{(m - 1)(n - 1)+\gcd(m,n)-1}2,$$

which, for positive and coprime m and n, reduces to

 * $$\sum_{k=1}^{n-1} \left\lfloor \frac{km}{n} \right\rfloor = \tfrac{1}{2}(m - 1)(n - 1) ,$$

and similarly for the ceiling and fractional part functions (still for positive and coprime m and n),

 * $$\sum_{k=1}^{n-1} \left\lceil \frac{km}{n} \right\rceil = \tfrac{1}{2}(m + 1)(n - 1),$$

 * $$\sum_{k=1}^{n-1} \left\{ \frac{km}{n} \right\} = \tfrac{1}{2}(n - 1).$$

Since the right-hand side of the general case is symmetrical in m and n, this implies that

 * $$\left\lfloor \frac{m\vphantom1}{n} \right \rfloor + \left\lfloor \frac{2m}{n} \right \rfloor + \dots + \left\lfloor \frac{(n-1)m}{n} \right \rfloor =

\left\lfloor \frac{n\vphantom1}{m} \right \rfloor + \left\lfloor \frac{2n}{m} \right \rfloor + \dots + \left\lfloor \frac{(m-1)n}{m} \right \rfloor. $$

More generally, if m and n are positive,

 * $$\begin{align}

&\left\lfloor \frac{x\vphantom1}{n} \right \rfloor + \left\lfloor \frac{m+x}{n} \right \rfloor + \left\lfloor \frac{2m+x}{n} \right \rfloor + \dots + \left\lfloor \frac{(n-1)m+x}{n} \right \rfloor\\[5mu] = &\left\lfloor \frac{x\vphantom1}{m} \right \rfloor + \left\lfloor \frac{n+x}{m} \right \rfloor + \left\lfloor \frac{2n+x}{m} \right \rfloor + \cdots + \left\lfloor \frac{(m-1)n+x}{m} \right \rfloor. \end{align} $$

This is sometimes called a reciprocity law.

Division by positive integers gives rise to an interesting and sometimes useful property. Assuming $$m,n >0$$,

 * $$ m \leq \left\lfloor \frac{x}{n} \right \rfloor \iff n \leq \left\lfloor \frac{x}{m} \right \rfloor \iff n \leq  \frac{ \lfloor x \rfloor }{m}. $$

Similarly,

 * $$ m \geq \left\lceil \frac{x}{n} \right \rceil \iff n \geq \left\lceil \frac{x}{m} \right \rceil \iff n \geq  \frac{ \lceil x \rceil }{m}. $$

Indeed,

 * $$ m \leq \left\lfloor \frac{x}{n} \right \rfloor \implies m \leq \frac{x}{n} \implies n \leq \frac{x}{m}

\implies n \leq \left \lfloor \frac{x}{m}\right \rfloor \implies \ldots \implies m \leq \left\lfloor \frac{x}{n} \right \rfloor,$$ keeping in mind that $ \lfloor x/n \rfloor = \bigl\lfloor \lfloor x \rfloor / n \bigr\rfloor.$ The second equivalence involving the ceiling function can be proved similarly.

Nested divisions
For positive integer n, and arbitrary real numbers m,x:

 * $$ \left\lfloor \frac{\lfloor x/m\rfloor}{n} \right\rfloor = \left\lfloor \frac{x}{mn} \right\rfloor $$

 * $$ \left\lceil \frac{\lceil x/m\rceil}{n} \right\rceil = \left\lceil \frac{x}{mn} \right\rceil. $$

Continuity and series expansions
None of the functions discussed in this article are continuous, but all are piecewise linear: the functions $$\lfloor x \rfloor$$, $$\lceil x \rceil$$, and $$\{ x\}$$ have discontinuities at the integers.

$$\lfloor x \rfloor$$ is upper semi-continuous and  $$\lceil x \rceil$$  and $$\{ x\}$$  are lower semi-continuous.

Since none of the functions discussed in this article are continuous, none of them have a power series expansion. Since floor and ceiling are not periodic, they do not have uniformly convergent Fourier series expansions. The fractional part function has Fourier series expansion $$ \{x\}= \frac{1}{2} - \frac{1}{\pi} \sum_{k=1}^\infty \frac{\sin(2 \pi k x)} {k} $$ for $x$ not an integer.

At points of discontinuity, a Fourier series converges to a value that is the average of its limits on the left and the right, unlike the floor, ceiling and fractional part functions: for y fixed and x a multiple of y the Fourier series given converges to y/2, rather than to x mod y = 0. At points of continuity the series converges to the true value.

Using the formula $$\lfloor x\rfloor = x - \{x\}$$ gives $$ \lfloor x\rfloor = x - \frac{1}{2} + \frac{1}{\pi} \sum_{k=1}^\infty \frac{\sin(2 \pi k x)}{k} $$ for $x$ not an integer.

Mod operator
For an integer x and a positive integer y, the modulo operation, denoted by x mod y, gives the value of the remainder when x is divided by y. This definition can be extended to real x and y, y ≠ 0, by the formula

 * $$x \bmod y = x-y\left\lfloor \frac{x}{y}\right\rfloor.$$

Then it follows from the definition of floor function that this extended operation satisfies many natural properties. Notably, x mod y is always between 0 and y, i.e.,

if y is positive,
 * $$0 \le x \bmod y y.$$

Quadratic reciprocity
Gauss's third proof of quadratic reciprocity, as modified by Eisenstein, has two basic steps.

Let p and q be distinct positive odd prime numbers, and let $$m = \tfrac12(p - 1),$$ $$n = \tfrac12(q - 1).$$

First, Gauss's lemma is used to show that the Legendre symbols are given by

 * $$\begin{align}

\left(\frac{q}{p}\right) &= (-1)^{\left\lfloor\frac{q}{p}\right\rfloor + \left\lfloor\frac{2q}{p}\right\rfloor + \dots + \left\lfloor\frac{mq}{p}\right\rfloor }, \\[5mu] \left(\frac{p}{q}\right) &= (-1)^{\left\lfloor\frac{p}{q}\right\rfloor + \left\lfloor\frac{2p}{q}\right\rfloor + \dots + \left\lfloor\frac{np}{q}\right\rfloor }. \end{align}$$

The second step is to use a geometric argument to show that

 * $$\left\lfloor\frac{q}{p}\right\rfloor +\left\lfloor\frac{2q}{p}\right\rfloor +\dots +\left\lfloor\frac{mq}{p}\right\rfloor

+\left\lfloor\frac{p}{q}\right\rfloor +\left\lfloor\frac{2p}{q}\right\rfloor +\dots +\left\lfloor\frac{np}{q}\right\rfloor

= mn. $$

Combining these formulas gives quadratic reciprocity in the form

 * $$\left(\frac{p}{q}\right) \left(\frac{q}{p}\right) = (-1)^{mn}=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}.$$

There are formulas that use floor to express the quadratic character of small numbers mod odd primes p:
 * $$\begin{align}

\left(\frac{2}{p}\right) &= (-1)^{\left\lfloor\frac{p+1}{4}\right\rfloor}, \\[5mu] \left(\frac{3}{p}\right) &= (-1)^{\left\lfloor\frac{p+1}{6}\right\rfloor}. \end{align}$$

Rounding
For an arbitrary real number $$x$$, rounding $$x$$ to the nearest integer with tie breaking towards positive infinity is given by $$\text{rpi}(x)=\left\lfloor x+\tfrac{1}{2}\right\rfloor = \left\lceil \tfrac12\lfloor 2x \rfloor \right\rceil$$; rounding towards negative infinity is given as $$\text{rni}(x)=\left\lceil x-\tfrac{1}{2}\right\rceil = \left\lfloor \tfrac12 \lceil 2x \rceil \right\rfloor$$.

If tie-breaking is away from 0, then the rounding function is $$\text{ri}(x) = \sgn(x)\left\lfloor|x|+\tfrac{1}{2}\right\rfloor$$ (see sign function), and rounding towards even can be expressed with the more cumbersome $$\lfloor x\rceil=\left\lfloor x+\tfrac{1}{2}\right\rfloor+\bigl\lceil\tfrac14(2x-1)\bigr\rceil-\bigl\lfloor\tfrac14(2x-1)\bigr\rfloor-1$$, which is the above expression for rounding towards positive infinity $$\text{rpi}(x)$$ minus an integrality indicator for $$\tfrac14(2x-1)$$.

Rounding a real number $$x$$ to the nearest integer value forms a very basic type of quantizer – a uniform one. A typical (mid-tread) uniform quantizer with a quantization step size equal to some value $$\Delta$$ can be expressed as

 * $$Q(x) = \Delta \cdot \left\lfloor \frac{x}{\Delta} + \frac{1}{2} \right\rfloor$$,

Number of digits
The number of digits in base b of a positive integer k is
 * $$\lfloor \log_{b}{k} \rfloor + 1 = \lceil \log_{b}{(k+1)} \rceil .$$

Number of strings without repeated characters
The number of possible strings of arbitrary length that doesn't use any character twice is given by

 * $$(n)_0 + \cdots + (n)_n = \lfloor e n! \rfloor$$

where:

 * $⟧x⟦$ > 0 is the number of letters in the alphabet (e.g., 26 in English)
 * the falling factorial $$(n)_k = n(n-1)\cdots(n-k+1)$$ denotes the number of strings of length $]x[$ that don't use any character twice.
 * ${x}$! denotes the factorial of ${x} = x − ⌊x⌋$
 * $0 ≤ {x} < 1$ = 2.718... is Euler's number

For $n$ = 26, this comes out to 1096259850353149530222034277.

Factors of factorials
Let n be a positive integer and p a positive prime number. The exponent of the highest power of p that divides n! is given by a version of Legendre's formula

 * $$\left\lfloor\frac{n}{p}\right\rfloor + \left\lfloor\frac{n}{p^2}\right\rfloor + \left\lfloor\frac{n}{p^3}\right\rfloor + \dots = \frac{n-\sum_{k}a_k}{p-1}$$

where $n = \sum_{k}a_kp^k$ is the way of writing n in base p. This is a finite sum, since the floors are zero when pk > n.

Beatty sequence
The Beatty sequence shows how every positive irrational number gives rise to a partition of the natural numbers into two sequences via the floor function.

Euler's constant (γ)
There are formulas for Euler's constant γ = 0.57721 56649 ... that involve the floor and ceiling, e.g.

 * $$\gamma =\int_1^\infty\left({1\over\lfloor x\rfloor}-{1\over x}\right)\,dx,$$

 * $$\gamma = \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^n \left( \left \lceil \frac{n}{k} \right \rceil - \frac{n}{k} \right),$$

and

\gamma = \sum_{k=2}^\infty (-1)^k \frac{ \left \lfloor \log_2 k \right \rfloor}{k} = \tfrac12-\tfrac13 + 2\left(\tfrac14 - \tfrac15 + \tfrac16 - \tfrac17\right) + 3\left(\tfrac18 - \cdots - \tfrac1{15}\right) + \cdots $$

Riemann zeta function (ζ)
The fractional part function also shows up in integral representations of the Riemann zeta function. It is straightforward to prove (using integration by parts) that if $$\varphi(x)$$ is any function with a continuous derivative in the closed interval [a, b],

 * $$\sum_{a<n\le b}\varphi(n) =

\int_a^b\varphi(x) \, dx + \int_a^b\left(\{x\}-\tfrac12\right)\varphi'(x) \, dx + \left(\{a\}-\tfrac12\right)\varphi(a) - \left(\{b\}-\tfrac12\right)\varphi(b). $$

Letting $$\varphi(n) = n^{-s}$$ for real part of s greater than 1 and letting a and b be integers, and letting b approach infinity gives

 * $$\zeta(s) = s\int_1^\infty\frac{\frac12-\{x\}}{x^{s+1}}\,dx + \frac{1}{s-1} + \frac 1 2.$$

This formula is valid for all s with real part greater than −1, (except s = 1, where there is a pole) and combined with the Fourier expansion for {x} can be used to extend the zeta function to the entire complex plane and to prove its functional equation.

For s = σ + it in the critical strip 0 < σ < 1,

 * $$\zeta(s)=s\int_{-\infty}^\infty e^{-\sigma\omega}(\lfloor e^\omega\rfloor - e^\omega)e^{-it\omega}\,d\omega.$$

In 1947 van der Pol used this representation to construct an analogue computer for finding roots of the zeta function.

Formulas for prime numbers
The floor function appears in several formulas characterizing prime numbers. For example, since $\bigl\lfloor\frac{n}{m} \bigr\rfloor -\bigl\lfloor\frac{n-1}{m}\bigr\rfloor$ is equal to 1 if m divides n, and to 0 otherwise, it follows that a positive integer n is a prime if and only if

 * $$\sum_{m=1}^\infty \left(\biggl\lfloor\frac{n}{m}\biggr\rfloor-\biggl\lfloor\frac{n-1}{m}\biggr\rfloor\right) = 2.$$

One may also give formulas for producing the prime numbers. For example, let pn be the n-th prime, and for any integer r > 1, define the real number α by the sum

 * $$\alpha = \sum_{m=1}^\infty p_m r^{-m^2}.$$

Then

 * $$p_n = \left\lfloor r^{n^2}\alpha \right\rfloor - r^{2n-1}\left\lfloor r^{(n-1)^2}\alpha\right\rfloor.$$

A similar result is that there is a number θ = 1.3064... (Mills' constant) with the property that

 * $$\left\lfloor \theta^3 \right\rfloor, \left\lfloor \theta^9 \right\rfloor, \left\lfloor \theta^{27} \right\rfloor, \dots$$

are all prime.

There is also a number ω = 1.9287800... with the property that

 * $$\left\lfloor 2^\omega\right\rfloor, \left\lfloor 2^{2^\omega} \right\rfloor, \left\lfloor 2^{2^{2^\omega}} \right\rfloor, \dots$$

are all prime.

Let $\pi$(x) be the number of primes less than or equal to x. It is a straightforward deduction from Wilson's theorem that

 * $$\pi(n) = \sum_{j=2}^n\Biggl\lfloor\frac{(j-1)!+1}{j} - \left\lfloor\frac{(j-1)!}{j}\right\rfloor\Biggr\rfloor.$$

Also, if n ≥ 2,

 * $$\pi(n) = \sum_{j=2}^n \Biggl\lfloor 1\, \bigg/\ {\sum_{k=2}^j\left\lfloor\left\lfloor\frac{j}{k}\right\rfloor\frac{k}{j} \right\rfloor} \Biggr\rfloor.$$

None of the formulas in this section are of any practical use.

Solved problems
Ramanujan submitted these problems to the Journal of the Indian Mathematical Society.

If n is a positive integer, prove that  $$\left\lfloor\tfrac{n}{3}\right\rfloor + \left\lfloor\tfrac{n+2}{6}\right\rfloor + \left\lfloor\tfrac{n+4}{6}\right\rfloor = \left\lfloor\tfrac{n}{2}\right\rfloor + \left\lfloor\tfrac{n+3}{6}\right\rfloor,$$

 $$\left\lfloor\tfrac12 + \sqrt{n+\tfrac12}\right\rfloor = \left\lfloor\tfrac12 + \sqrt{n+\tfrac14}\right\rfloor,$$

 $$\left\lfloor\sqrt{n}+ \sqrt{n+1}\right\rfloor = \left\lfloor \sqrt{4n+2}\right\rfloor.$$ Some generalizations to the above floor function identities have been proven.

Unsolved problem
The study of Waring's problem has led to an unsolved problem:

Are there any positive integers k ≥ 6 such that

 * $$3^k-2^k\Bigl\lfloor \bigl(\tfrac 3 2\bigr)^k \Bigr\rfloor > 2^k-\Bigl\lfloor \bigl(\tfrac 3 2\bigr)^k \Bigr\rfloor -2 \ ?$$

Mahler has proved there can only be a finite number of such k; none are known.

Computer implementations
In most programming languages, the simplest method to convert a floating point number to an integer does not do floor or ceiling, but truncation. The reason for this is historical, as the first machines used ones' complement and truncation was simpler to implement (floor is simpler in two's complement). FORTRAN was defined to require this behavior and thus almost all processors implement conversion this way. Some consider this to be an unfortunate historical design decision that has led to bugs handling negative offsets and graphics on the negative side of the origin.

An arithmetic right-shift of a signed integer $$x$$ by $$n$$ is the same as $$\left\lfloor x / 2^n \right\rfloor$$. Division by a power of 2 is often written as a right-shift, not for optimization as might be assumed, but because the floor of negative results is required. Assuming such shifts are "premature optimization" and replacing them with division can break software.

Many programming languages (including C, C++, C#,   Java,  PHP,  R, and Python ) provide standard functions for floor and ceiling, usually called   and , or less commonly. The language APL uses  for floor. The J Programming Language, a follow-on to APL that is designed to use standard keyboard symbols, uses  for floor and   for ceiling. ALGOL uses for floor.

In Microsoft Excel the funtion  rounds down rather than toward zero, while   rounds toward zero, the opposite of what "int" and "floor" do in other languages. Since 2010  has been changed to error if the number is negative. The OpenDocument file format, as used by OpenOffice.org, Libreoffice and others, and   both do floor, and   has a third argument to reproduce Excel's earlier behavior.

title: Floor and ceiling functions