text:
Talk:Raging Bull

References to use

 * Please add to the list references that can be used for the film article.

Script anecdote
Source of the script anecdote is Stephen Bach's memoir, "Final Cut".

Removing Link
I'm removing the link to the poster site. It's akin to an advertisement, and the brief synopsis it gives is redundant.--Pewpewlazers 03:29, 6 November 2006 (UTC)

Plot
Needs extensive revision, picks up on miniscule details whilst ignoring much more significant plot details (e.g. the fights with Sugar Ray). Several mistakes ("second glitch of Vickie") and totally omits the end of the film. —Preceding unsigned comment added by 212.219.116.67 (talk) 08:50, 4 September 2008 (UTC)

i know i'm getting that sorted out but you are going to have to be patient. i will take your advice into account so thank you anyway Kilnburn (talk) 00:53, 21 September 2008 (UTC)

i have since cut down much of the plot and it is now at a managable size. i'm really pleased with it and thanks for those who did those neccesary changes Kilnburn (talk) 10:05, 8 October 2008 (UTC)

Trivia
This film is extensively studied in a lot of academic circles, especially film schools, most notably for the sound design. Is any of this wikipedia worthy? I'm talking about how certain sound effects are used, such as the sound of breaking glass for camera flashes and the like. Also, is the fact that Joe Pesci's ribs were broken in real life during one of the sparring scenes notable for addition here? (just as long as the source is cited?)Toquinha 18:57, 22 December 2006 (UTC)

 * Also wanted to add that the trivia-esque comment, "DeNiro gained 60 pounds to prepare for his role, more than any other actor has gained or lost for a role" is untrue and has been appropriately deleted. Jjmckool (talk) 20:28, 29 March 2008 (UTC)

Analysis
The topic of analysis on this page is profane, biased, and hardly relevant. Please change it.

Agreed. I haven't seen it, I was just passing by as a fan of some other Scorsese films. Wikipedia should hold a neutral opinion, and that said stuff like "it's an extremely thematic film", and the comparisons didn't seem relevant at all. It may be that those who do most, dream most. (talk) 22:41, 24 January 2008 (UTC)

After removing it, I think it's fair to say that it's a start, not B class quality. It may be that those who do most, dream most. (talk) 23:37, 24 January 2008 (UTC)

As well it says DeNiro supported Jake LaMotta even though he is suing us, it was Joey LaMotta NOT Jake in the speech —Preceding unsigned comment added by 66.131.25.183 (talk) 21:01, 27 October 2008 (UTC)

B Class?
I have not seen the film. In turn I have not read the plot description. Criticize me if you will for taking concern in a film I haven't seen, but this seems far from "B Class", especially after I deleted the slightly irrelevant "Analysis" section. I put this up for reassesment, and would feel it appropriate if it were changed to "Start". P.S. I'm sure it's an amazing film and all, but the article had some POV issues. It may be that those who do most, dream most. (talk) 23:59, 24 January 2008 (UTC)

It's been reassessed, and it's still B Class. Perhaps the plot summary is well written (I don't know), but the other sections are meager. It may be that those who do most, dream most. (talk) 21:41, 26 January 2008 (UTC)

In the course of time, I think it's fair to note that I've seen it now and may take it on as a project. I still strongly object to it being B Class. Of all the sections, If find production to be the only one that's engaging. The person who reassessed it gave no clear reason as to why it should remain in this state. MwNNrules (talk) 13:21, 5 April 2008 (UTC)

it's start class material in my opinion, along with the fact there are no pictures (exception of the movie poster on the info box) and few sources making this a rather poor article. some of the content of the article also looks strangely familiar as it has maybe been copied from a book word-by-word. ihave seen the film about 7-8 times (a favourite of mine) and have got this in my work to do, it needs to be sorted out. Kilnburn (talk) 08:53, 26 August 2008 (UTC)

Myspace Poll
I don't see how the opinions of sixteen year olds are relevant —Preceding unsigned comment added by 24.182.235.0 (talk) 14:33, 30 January 2008 (UTC)

For an article on a landmark film, this one has an appalling number of ungrammatical and even incoherent sentences. I've made a few changes, but the article still needs a great deal of work. A plea to potential contributors: please don't rely on others to fix up your sloppy writing. The fact that Wikipedia is an open source encyclopedia is no excuse for carelessness and unprofessionalism. —Preceding unsigned comment added by 24.37.24.9 (talk) 07:40, 31 January 2009 (UTC)

Sloppy writing
The writing is very sloppy, confusing, and in many cases downright misleading. In particular, it's full of ambiguous referents and statements that seem very much out of place. 80.235.59.103 (talk) 21:19, 12 July 2009 (UTC)

This Title shouldnt be used
it's the name of a ride in six flags. so it has to be changed! —Preceding unsigned comment added by 67.167.12.238 (talk) 16:45, 6 December 2009 (UTC)

references to book The Making of Raging Bull
I have no idea who wrote these references, or who wrote the book, but currently, there are four different authors' names cited for 'The Making of Raging Bull', and surely only one (or at most two) of them could be right.

That book also apparently includes some erroneous information, as cited in the Wikipedia article: "However, when it was revealed that John Hinckley, Jr.'s assassination attempt of the then president Ronald Reagan had been influenced by his love for Taxi Driver, this hurt the chances for [Raging Bull] to pick up the Oscar."

That isn't possible. Reagan was shot March 30, 1981 -- the very day the Oscars were to be held. (The ceremony was postponed until the next day.) The Oscar ballots had already been submitted and tabulated. People may have been upset with Scorsese, but it was far too late for Oscar voters to take it out on "Raging Bull." —Preceding unsigned comment added by 71.38.151.239 (talk) 02:46, 27 June 2010 (UTC)

Themes
The recently-added "themes" section is a travesty; there are no proper citations, only book titles, and there are no quotes from the book, only interpretation by an editor who has a habit of offering his own opinion as though it were fact. This article could have a themes section, but only if it actually quotes sources that are then properly cited. --- The Old Jacobite The '45  12:04, 27 August 2013 (UTC)

 * There are three citations in this fully researched section which are fully documented and available at many libraries. Previously Editor has apparently not read the section or read any of the three books which are clearly referenced. AutoMamet (talk) 05:53, 28 August 2013 (UTC)

 * You do not get it. Whether I have the read the books or not is irrelevant.  If you are arguing that these books support these ideas, you need to quote the books with specific page numbers.  The rambling content of this section reads like your interpretation. --- The Old Jacobite The '45  12:33, 28 August 2013 (UTC)

You appear to state "Whether I have read the books...is irrelevant." If you have not read the books and citations in this fully cited edit, please refrain from editing it. AutoMamet (talk) 05:12, 29 August 2013 (UTC)

 * Your comment indicates a complete failure to understand how Wikipedia operates. I suggest you stop editing until such point that you understand the policies and guidelines.  All of your actions up to this point indicate that you do not. --- The Old Jacobite The '45  11:27, 29 August 2013 (UTC)

 * AutoMamet, your Themes section is simply a personal essay you have written. It doesn't belong in Wikipedia. Wikipedia is an encyclopedia, and requires sourced independent third-party reliable sources. What you have been doing is reading and compiling original-source material and adding your own opinions and interpretations about it. That would be great for a personal blog; however Wikipedia is not a personal blog, it's an encyclopedia of verifiable information, not personal interpretations and observations. I hope that makes sense. It's great that you have an interest in film and want to add your observations and analysis about films somewhere, but Wikipedia is not the proper venue. The only way for a section like this to work is to source/cite every single statement/sentence, not from original-source materials (e.g., not the film itself nor from autobiographies themselves), but from critics and reviewers and commentators, or direct statments by the filmmakers. Preferably the substantiating material should be readable online -- in other words, if it's from a review or article, post the link to the article; if it's from a book, cite the exact page number and a link to that exact page viewable on GoogleBooks or Amazon. Cite every single sentence, and every statement within each sentence, from a secondary or third-party source, and if the source is a (non-original-source) book, give the exact page number, and if it is not viewable online, include an exact quote in your footnote. Do not draw conclusions on your own or make your own observations. This isn't a place for personal film reviews. For reference on how a Themes section should read and be referenced, see E.T. the Extra-Terrestrial. --Softlavender (talk) 03:25, 2 September 2013 (UTC)
 * AutoMamet has been asking for my advise regarding some of the events that have occurred here and at The Departed. While I have expressed to AutoMamet some concerns about her/his approach, I do have to say that some of the requests above go significantly beyond Wikipedia policy. Encyclopedia articles are not literary criticism: they do not require quotations and references for every single sentence. Quotations, in fact, are only really required on talk pages (except in special cases, like really strong claims or BLP issues), and you should only require quotations if you actually believe the editor has falsified information or is incorrectly interpretting it. The section does require some more detailed information, so I do think that if AutoMamet wants to include that, we need some more specificity to the references (definitely page numbers, definitely more parts of the text cited); I share the concern that this section may be crossing over into WP:OR (or, it's sub-problem, WP:SYNTH). But I also think that it wouldn't have been horrible to tag the section rather than outright delete it; there was clearly a good faith effort to provide useful information, and sources were provided, even if they were not complete. We even have templates that specifically mark something as needing a page number or quotation. Furthermore, TheOldJacobite should not have edit warred to keep the information out (nor should AutoMamet have edit warred to keep it in).
 * At this point, I've suggested that AutoMamet draft a new version, with more specific sources and more in-line citations. Probably the easiest way is to do that in a sandbox, and then that could be brought here for discussion. Qwyrxian (talk) 02:35, 3 September 2013 (UTC)
 * I agree with that. The reason I personally suggested quotations in footnotes for pages that were not specifically linked and readable online (and I'm guessing he probably does not even know how to find and link the viewable pages on GoogleBooks and Amazon), is that the editor has shown tendencies to interpret, opinionate, and write personal essays, and so even if he were to provide page numbers of all his citations, if he provides no way for other more experienced editors to view the sources, given his extreme lack of experience on Wikipedia and his tendencies to post personal essays rather than encyclopedic content, we could be simply dealing with more interpretation at best. Softlavender (talk) 02:53, 3 September 2013 (UTC)

Update: Agreement with Admin above. There are 3 separate paragraphs in this theme section, each of which represents a different level of research and a different level of citation and reference material required to justify the edit. Any comments/critiques made of this edit should specify which one of the paragraphs is being discussed or criticized. Of the 3 separately edited paragraphs, paragraph 1 and paragraph 3 represent and require only material from LaMotta's own autobiography to establish them as legitimate for the discussion of their influence on Scorsese's selection of themes used for the making of this film. Paragraph 2 is the most elaborate paragraph and would require the most effort to rewrite to the standards mentioned above. It is therefore suggested in this new edit, that only paragraphs 1 and paragraph 3 from the original edit be used, which establish the parts of LaMotta's biography's which were applied by Scorsese in selecting the themes which he would come to portray in his actual film. The second paragraph would not be included in this newly re-edited version of the section. AutoMamet (talk) 02:55, 13 September 2013 (UTC)
 * Go ahead and make a draft of your suggestion in a sandbox in your user space. If you don't know how to do that, I will create one for you. Then come here and provide a link. Do not add it to the article until you first get consensus for the addition. Qwyrxian (talk) 03:58, 13 September 2013 (UTC)

User:Qwyrxian, message received, and thanks for your oversight here. It is almost the only voice-of-reason comments I have seen since posting this edit. The short history for the abridged re-write draft I am posting here is that Robert De Niro brought a copy of LaMotta's autobiography to Scorsese who was at first reluctant. Scorsese then decided to hire LaMotta himself to consult after Scorsese decided he was only interested in the last half of the autobiography and what happened After the autobiography ended. This info supplement was provided verbally to Scorsese by LaMotta for the movie, and after the completion of the film, LaMotta then wrote another autobiography with the details included in the film but not in his first autobiography. These were all already documented in the original edit here but the contentious edit at The Departed Talk page has apparently sensitized everyone unduly. Since the edit is so short I am posting it here as I did with the similar re-write on The Departed Talk page discussion. This is the new version summarizing the above:

Draft:

(Themes section) Scorsese in his 1981 interview with Michael Henry indicated that he became interested only in some of the themes covered in Jake La Motta's autobiography when De Niro brought him a copy of the La Motta autobiography. The film revisits at least three of the five themes introduced in the original book version titled Raging Bull: My Story which was a 1970 memoir by middleweight boxer Jake La Motta. The five themes of the book (a facsimile of the Table of Contents taken from the autobiography itself is presented) are about Jake La Motta's life as (i) a young teenage criminal, (ii) his reformation in prison, (iii) his boxing years, (iv) his struggle with the mafia who kept the title out of reach, and (v) his jealous obsession with his wife Vickie. The film concentrates on the latter three themes introduced in the original biography, as well as partially moving into his post-retirement years. Scorsese has stated that his wanting to delete Jake's youth was done because, "In removing La Motta's youth ... he became more opaque (to the audience and more mysterious)." The final theme covered by Scorsese, which was not covered in the original book but only in the autobiographical book sequel, examines the ambiguous attempt which Jake tries to make, after his boxing career has ended, to rehabilitate his personal and social life. Virtually all of his friends and family have effectively gone their own ways, now largely separated from the influence which Jake once had upon their lives, and thematically no particular prospects appear open or promising to him as the film ends (see Sequel section below).

This is the new re-write version of the section for mark-up with citation templates as needed and as requested. AutoMamet (talk) 12:27, 14 September 2013 (UTC)

RfC: Discussion of Inclusion of a new Theme section for Raging Bull
RfC: Discussion of Inclusion of a new Themes section with rudimentary comments on LaMotta's Autobiography as the primary source of the film's main themes.

Two week old discussion between multiple editors is at a standstill concerning if a Themes section should be included on this wikipage. Rudimentary start version should mention what themes and parts of LaMotta's autobiography were used in the making of Raging Bull. Section edit is included on Talk page entry immediately above. AutoMamet (talk) 02:34, 18 September 2013 (UTC)

Survey
— | Gareth Griffith-Jones | The Welsh Buzzard | —  19:06, 18 September 2013 (UTC)
 * Support Academy Awards for film scripts are divided into two categories and two separate awards; Those for Adapted Film Scripts and those for Original Film Scripts. In the case of Raging Bull, both the director (Scorsese) and the lead actor (DeNiro) have indicated that the LaMotta autobiography was the source adapted for the film. Credit where credit is due. LaMotta wrote the book that made the movie about his life! AutoMamet (talk) 02:08, 19 September 2013 (UTC)
 * Oppose This article is about the film, which was an interpretation of LaMotta's life, this is not a biography article about LaMotta. --- The Old Jacobite The '45  13:56, 18 September 2013 (UTC)
 * Oppose Most emphatically. Could be the subject of or in another article, but certainly not this.
 * Note: While a survey or RfC isn't a vote, per se, it's not appropriate for AutoMamet to make it look (probably unintentionally), like there are 2 editors supporting inclusion of this text. So I just made a slight formatting adjustment so that both of AM's points lie in the same bullet point. Qwyrxian (talk) 02:49, 19 September 2013 (UTC)
 * I deleted the two contradictory votes, since AutoMamet said they were intended as examples or "banners". Binksternet (talk) 15:02, 25 September 2013 (UTC)
 * Note: In posting the RfC, the original pair of Support-Oppose headings were not listed for the purpose of posting a comment but only for the purpose of providing banners for the two categories so that participants could begin to list and append their comments. When I posted the two banners I was not making any statement of my own comment and nor did I in any way mean to suggest that I Oppose the inclusion of the autobiography edit being recommended even though I signed it following the format instructions for starting an RfC. The initial post of the pair was as banners pro and contra to which participants would then append their own comments. Two days later, I posted the sole position of Support next to the banner to date, and my reason for it. The two-banner format is the standard one recommended on the RfC start-up page for all editors. AutoMamet (talk) 03:55, 20 September 2013 (UTC)
 * That's fair; I didn't think that you were deliberately trying to be deceptive. I've never actually seen a set-up like you had; I think the "two-banner format" you're talking about means that people often put three level three headings (3 equal signs); one for support, one for oppose, and one for threaded discussion. They don't generally put a "null" bulleted point. But everything is good as long as we know what was actually intended. Qwyrxian (talk) 06:51, 20 September 2013 (UTC)

 * Oppose for a variety of reasons. (1) Sources must be about the film, and must not be primary sources such as the source (biography, memoir, novel, etc.) the film was taken from. (2) This editor has an extensive history of WP:OR and WP:SYNTHESIS and is replicating that here. (3) This editor has a history of repeated and varied disruptive editing and refusal to listen to or comprehend repeated efforts to explain Wikipedia policy to him. (4) This editor also has an extensive history of misrepresenting the facts, and therefore in my opinion cannot even be trusted to accurately represent even a quote from a book or article unless it is directly linked and viewable online (or a scanned page copy is provided). (5) But most of all, to repeat, this article is about the film, not about Jake LaMotta or his memoir(s); therefore all sources and commentary must be about and from sources about the film, not sources about Jake LaMotta. Softlavender (talk) 04:44, 23 September 2013 (UTC)

Update for User:Qwyrxian: It appears sufficiently clear to me that after five days that a thirty year old film (Raging Bull) is not likely to receive much more comment or review. My request is that, if all are agreed, to request a possible recommendation be made regarding the quality of the edit in the presence of all of the above comments. Since you are more than familiar with all of this matter and its history, and that you are twice as experienced as anyone else on this Talk page exchange, I am acknowledging that I would fully accept your evaluation as sufficiently neutral and unbiased in any way for either posting the proposed edit, posting the edit with mods, or any other evaluation which you might place. In the absence of any objection, that you may do so anytime after midnight tomorrow, on the 23rd, providing no other comments are posted.

Post-script. Although I understand the intention in your posting your previous comments on the RfC survey above, the other editors have taken it upon themselves to make multiple copy-pastes of it on The Departed Talk page as well, as a continuing criticism of me by you in spite of your explanation of it. It was copied four times throughout the Talk page on The Departed, and on the edit history log of The Departed Talk page, also in the form of a harsh reprimand against me. Is there anything I can do to try to ameliorate the Talk page on The Departed wikipage after so much copy-paste of your statement above by the other editors? With appreciation for any attention you can give this. AutoMamet (talk) 02:46, 23 September 2013 (UTC)
 * RfCs generally run for 30 days, so just leave this open. We have a bot that automatically notifies random people who've signed up, so it is not unusual to have comments trickle in slowly over time. Of course, if the RfC were to close with no more change, the consensus would be obvious: not to include the suggested section. I'll take a look at the Departed talk page. Qwyrxian (talk) 03:24, 23 September 2013 (UTC)

 * Regarding AutoMamet's "Post-script": I just have to point this out as yet another blatant and massive misrepresentation of the truth. "[O]ther editors have taken it upon themselves to make multiple copy-pastes of it on The Departed Talk page .... It was copied four times throughout the Talk page on The Departed" No, Gareth Griffith-Jones made ONE single verbatim copy of it when he fixed the format following Qwyrxian's lead. "[A]s a continuing criticism of me by you in spite of your explanation of it." No, it was never presented as a criticism (just a page cleanup and clarification), much less as one by Qwyrxian; it was acknowledged as being, as the edit summary distinctly indicates, "probably unintentional". "[A]lso in the form of a harsh reprimand against me." Nowhere at all in the remediation of your formatting has there been any "harsh reprimand" of you. In fact, quite the reverse: It has been acknowledged over and over that your misleading formatting was "probably unintentional", "understandable", and "inadvertent". We don't expect people who are creating their first RfC to get it perfect, but it was best for the editing to be normalized for the reasons given by Qwyrxian (and by the way, Qwyrxian's exact words were used). Softlavender (talk) 05:43, 23 September 2013 (UTC)

Update for User:Qwyrxian: The comments by User:SoftL are false and look delusional. I continue to be the only one of the users among the participants who has actually read the referenced books and this is sitting badly for some reason with the other editors. User:Hearfourmewesique has tried to explain to User:SoftL with more patience than I thought was humanly possible that her/his understanding of the Scorsese quotes on The Departed Page is deeply flawed and in error. User:SoftL had apparently taken this very badly and appeared to leave the discussion for several days. Now there appears to be a monomania, a fixation on User hounding which is uncivil and looks like outright slander. The copy-paste of your RfC comments without your permission appeared four (4) times as a reprimand to me without your approval on The Departed page. It was first (1) reposted as a straight reprimand about me on The Departed page, second, (2) my comment field was then re-edited as a second reprimand to me on The Departed page, (3) The Edit history page separately repeated the reprimand a third time about me, and (4) when my own comment was re-edited it appeared another time as a full line reprimand to me on the Edit history log for The Departed Talk page again. I then brought this to your attention and asked for you to look at this yesterday. Is there a wiki policy for curtailing fixated and disturbed users like SoftL who have no sense of civility and are fixated on hounding the only participant in this discussion who has actually read the books which are being discussed? I believe I have followed all of the rules in posting this RfC. How do I report User:SoftL for uncivil conduct which appears like a deviant fixation? AutoMamet (talk) 01:01, 24 September 2013 (UTC)
 * I have attempted to counsel Softlavender, and asked that s/he removed points 2-4 above, but s/he refused. If you wish to pursue sanctions, the correct place would be at WP:ANI. However, I do have to point out that you also have some problems above--specifically, I don't think any possible reading of Softlavender's actions, even though wrong, could be called a "deviant fixation"; also, there is no requirement that anyone get my permission to copy my words--the CC-BY-SA license, in fact, means anyone is always free to do that with anything you or I write, here or anywhere else on WP. But, overall, I do feel that you bringing this matter to RfC (and at the other page) was the correct move on your part, and not in any way disruptive. Qwyrxian (talk) 03:22, 24 September 2013 (UTC)

 * Oppose. A themes section should be based on critical consideration of the film, not on LaMotta's life and career. The danger lies in synthesis and original research of LaMotta material to achieve a novel conclusion about the film. We should let film scholars provide the conclusions here. (Note that I have fixed the initial confusion created by the OP in which it appeared as if he was voting three times.) Binksternet (talk) 22:11, 24 September 2013 (UTC)

Update to User:Qwyrxian, thank you for trying to counsel with user:SoftL. For the present, your indication that user:SoftL was wrong in his/her comments should be clear with no immediate follow-up on my part needed there. Also, your indication that the thirty day period should be allowed to continue for this RfC was appreciated. Your other comment previously was that if the comments/opinions do not change substantially regarding opposition, that this would be a self-determined conclusion on the basis of this survey here. I have a specific question. The standard for Academy Awards committees, the world-wide authority, is that film scripts are awarded this prize on the basis of being either an Original Film Script or an Adapted Film Script (two separate awards) and that adapted film scripts need to identify their source of adaptation. My question in this specific context then would state that even if 10 or 20 or 100 wikipedians do not like this decision by the Academy Award committees, that then general "band-wagoning" of opinion here should still not mediate against what the Academy Awards committee has designated as their policy of recognition independently of wiki. My understanding is that in such cases that it is up to Admin to decide what the best thing is for wiki at the end of the day. In this case, no matter what wikipedians may like to form as an opinion, by band-wagoning or otherwise, it is up to Admin to decide if the bandwagoning represents something good for wiki in general or not. It is the Academy Awards committee that has designated the category of Best Adapted Film Script and its standards of recognition, not me, and in this case only Admin would appear to be able to avoid the obvious direction that band-wagoning of opinion would lead this Talk page discussion towards under normal circumstances. If the role of Admin is different from what I have described here then possibly you could post something to inform this situation of when only the mere bandwagoning of comments leads in directions not good for wiki in the larger picture. AutoMamet (talk) 12:47, 25 September 2013 (UTC)
 * Your perception is, only partially correct. First of all, admins don't close most RfCs--only those that are very complex, have lots of discussion, have potential to have a wide effect, and/or are very close. None of those is the case here. Second, an admin would never weigh in the rules of an outside body, as that's not relevant. Third, even if they did, that wouldn't be relevant here, as the question isn't really about whether the material goes in at all, but rather whether the extent that you wish to include it is appropriate. While this is a policy-based question (WP:UNDUE and WP:OR play in here), it's certainly not a cut-and-dried case where policy obviously favors your interpretation. Admins cannot super-vote; they may discount comments/arguments that are not based in policy, but, at least at first glance, I don't see any arguments like that here. Finally, I recommend that you not impugn other editors comments by calling them bandwagoning, as quite a number of them appear to have well-thought out reasons; those reasons may ultimately be incorrect, and ultimately not be consensus, but that doesn't mean that they aren't considered decisions made based upon other people's interpretation of policy. Qwyrxian (talk) 13:23, 25 September 2013 (UTC)

For User:Qwyrxian. From my threaded discussion on The Departed Talk page, i have noticed that there has been no objection and no opposition to the edit as i have presented it there for the new "Infernal Affairs" subsection, which is a recognized source for the making of The Departed. Since there is no objection there, it is my understanding that it may be presented as a valid edit for the wiki community. Short of any opposition being posted over the next day, it is my intention to post it there as a valid edit for the regular wiki community editing process. AutoMamet (talk) 12:54, 1 October 2013 (UTC)
 * That discussion has nothing to do with this page; please don't cross discussions like this; I'll make a comment over there. Qwyrxian (talk) 21:38, 1 October 2013 (UTC)

For User:Qwyrxian. Not crossing discussion lines but there is a note for you on The Departed page from a day or two ago. Also, someone there appears to be belligerent on a one word correction i am trying to place correcting the "film TRILOGY Infernal Affairs" in the LEDE which someone is displeased about. The film TRILOGY status is confirmed by a one-click wikilink to the Lead section of "Infernal Affairs" or "Infernal Affairs III". Your previous comment to me was never to exceed three reverts after posting a new edit. Could you look at this. AutoMamet (talk) 01:11, 4 October 2013 (UTC)
 * Your edit is just plain wrong. This film is not based on the trilogy, it is based on the first film.  You have been revered multiple times because you are factually incorrect. --- The Old Jacobite The '45  01:41, 4 October 2013 (UTC)

Most well-informed reviewers disagree with you. Correct version posted on The Departed new thread. AutoMamet (talk) 04:12, 4 October 2013 (UTC)

Threaded discussion

 * Are there concerns for the civility of this discussion, and, for assessing the need to study the Autobiography by LaMotta to make effective recommendations. AutoMamet (talk) 02:34, 18 September 2013 (UTC)
 * What kind of concerns? AutoMamet (talk) 02:34, 18 September 2013 (UTC)

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Sugar Ray Robinson / Johnny Barnes
Just enjoyed the movie again. Seen it countless times.

Question: Has anyone considered writing a WP article for actor Johnny Barnes? There's a nice 2005 article from the NY Times  Considering his authenticity and important role in the film, isn't it worth a stub? Gprobins (talk) 15:30, 12 March 2019 (UTC)

Biskind, Peter, Easy Riders, Raging Bulls
1998 or 1999. Which is it? We have both in the article. Or are we citing two different editions. If so, why, is one a revised one or a mere reprint? Renard Migrant (talk) 18:00, 7 January 2020 (UTC)

title: Talk:Raging Bull


text:
Zvenigorod

Zvenigorod (Звени́город) is a town in the Moscow Oblast of western Russia. In 2010 it had a population of about 16,000.

History
The town's name is based either on a personal name (cf. Zvenislav, Zvenimir) or on a hydronym (cf. the Zvinech, Zvinyaka, Zveniga Rivers); the derivation from "town of ringing (bells)" is a folk etymology.

The community has existed since the 12th century, although its first written mention is dated around 1339, in the last will of Grand Duke of Moscow Ivan I Daniilovich Kalita, in which he says: "Thus, I pass on to my son Ivan: Zvenigorod, Kremchina, Ruza..." In the historical records, or annals (лéтопись [letopis'] in Russian), Zvenigorod is first mentioned around 1382, soon after khan Tokhtamysh burnt down Moscow, and destroyed a number of towns on the way, including Zvenigorod.

Zvenigorod rose to prominence in the late 14th century after it was bequeathed by Dmitry Donskoy to his second son Yuri, who founded his residence on the steep bank of the Moskva River. The local kremlin, called Gorodok, contains the only fully preserved example of 14th-century Muscovite architecture, the Dormition Cathedral (1399). The cathedral's interior features frescoes attributed to Andrei Rublev.

Zvenigorod is primarily remembered for internecine wars waged by Yuri's sons for control of Moscow during the reign of their cousin Vasily II (1425–1462). After their party was defeated, the town was incorporated into the Grand Duchy of Moscow.

Zvenigorod was granted town rights in 1784. By the late 19th century, the town gained popularity among the intelligentsia as a fashionable banlieue of Moscow. Many extravagant dachas were built in the neighbourhood. Some of these house museums of Sergey Taneyev, Anton Chekhov, and Isaac Levitan.

During World War II Zvenigorod was near, or on the frontline in the 1941-2 Battle of Moscow.

Savvino-Storozhevsky Monastery
The Storozhi Monastery near Zvenigorod was established in 1398 by St. Savva, one of the first disciples of Sergius of Radonezh. The oldest church is the katholikon completed in 1405 and dedicated to the feast of the Nativity of the Theotokos. In 1650, the monastery was chosen by Tsar Alexis as his suburban residence. In five years, they constructed a white-stone royal palace and a festive chamber for tsaritsa. The compound was encircled with stone walls and towers, patterned after those of the Trinity Lavra of St. Sergius. Particularly noteworthy is a large belfry, erected in four bays in 1650 and crowned with three tents and a clocktower. A church over the holy gates was consecrated to the Holy Trinity in 1652.

After the death of Feodor III, who spent most of his time there, the monastery declined. In May 1918, when the Bolsheviks tried to seize the relics of St. Savva, several persons were shot dead. In 1985, the cloister was assigned to the Danilov Monastery in Moscow. St. Savva's relics were returned to the monastery in 1998.

Administrative and municipal status
Within the framework of administrative divisions, it is incorporated as Zvenigorod Town Under Oblast Jurisdiction—an administrative unit with the status equal to that of the districts. As a municipal division, Zvenigorod Town Under Oblast Jurisdiction is incorporated as Zvenigorod Urban Okrug.

Sport
The city has a woman's handball team Zvezda Zvenigorod, which won the Women's EHF Champions League in the 2007–08 season.

Twin towns — Sister cities
Zvenigorod is twinned with:

 * 🇧🇾 Mogilev, Belarus (2006)
 * 🇮🇹 Tropea, Italy (2013)
 * 🇨🇳 Bijie, China (2016)

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

title: Zvenigorod


text:
Glass cockpit

A glass cockpit is an aircraft cockpit that features an array of electronic (digital) flight instrument displays, typically large LCD screens, rather than traditional analog dials and gauges. While a traditional cockpit relies on numerous mechanical gauges (nicknamed "steam gauges") to display information, a glass cockpit uses several multi-function displays and a primary flight display driven by flight management systems, that can be adjusted to show flight information as needed. This simplifies aircraft operation and navigation and allows pilots to focus only on the most pertinent information. They are also popular with airline companies as they usually eliminate the need for a flight engineer, saving costs. In recent years the technology has also become widely available in small aircraft.

As aircraft displays have modernized, the sensors that feed them have modernized as well. Traditional gyroscopic flight instruments have been replaced by electronic attitude and heading reference systems (AHRS) and air data computers (ADCs), improving reliability and reducing cost and maintenance. GPS receivers are usually integrated into glass cockpits.

Early glass cockpits, found in the McDonnell Douglas MD-80, Boeing 737 Classic, ATR 42, ATR 72 and in the Airbus A300-600 and A310, used electronic flight instrument systems (EFIS) to display attitude and navigational information only, with traditional mechanical gauges retained for airspeed, altitude, vertical speed, and engine performance. The Boeing 757 and 767-200/-300 introduced an electronic engine-indicating and crew-alerting system (EICAS) for monitoring engine performance while retaining mechanical gauges for airspeed, altitude and vertical speed.

Later glass cockpits, found in the Boeing 737NG, 747-400, 767-400, 777, Airbus A320, later Airbuses, Ilyushin Il-96 and Tupolev Tu-204 have completely replaced the mechanical gauges and warning lights in previous generations of aircraft. While glass cockpit-equipped aircraft throughout the late 20th century still retained analog altimeters, attitude, and airspeed indicators as standby instruments in case the EFIS displays failed, more modern aircraft have increasingly been using digital standby instruments as well, such as the integrated standby instrument system.

History
Glass cockpits originated in military aircraft in the late 1960s and early 1970s; an early example is the Mark II avionics of the F-111D (first ordered in 1967, delivered from 1970 to 1973), which featured a multi-function display.

Prior to the 1970s, air transport operations were not considered sufficiently demanding to require advanced equipment like electronic flight displays. Also, computer technology was not at a level where sufficiently light and powerful electronics were available. The increasing complexity of transport aircraft, the advent of digital systems and the growing air traffic congestion around airports began to change that.

The Boeing 2707 was one of the earliest commercial aircraft designed with a glass cockpit. Most cockpit instruments were still analog, but cathode ray tube (CRT) displays were to be used for the attitude indicator and horizontal situation indicator (HSI). However, the 2707 was cancelled in 1971 after insurmountable technical difficulties and ultimately the end of project funding by the US government.

The average transport aircraft in the mid-1970s had more than one hundred cockpit instruments and controls, and the primary flight instruments were already crowded with indicators, crossbars, and symbols, and the growing number of cockpit elements were competing for cockpit space and pilot attention. As a result, NASA conducted research on displays that could process the raw aircraft system and flight data into an integrated, easily understood picture of the flight situation, culminating in a series of flights demonstrating a full glass cockpit system.

The success of the NASA-led glass cockpit work is reflected in the total acceptance of electronic flight displays. The safety and efficiency of flights have been increased with improved pilot understanding of the aircraft's situation relative to its environment (or "situational awareness").

By the end of the 1990s, liquid-crystal display (LCD) panels were increasingly favored among aircraft manufacturers because of their efficiency, reliability and legibility. Earlier LCD panels suffered from poor legibility at some viewing angles and poor response times, making them unsuitable for aviation. Modern aircraft such as the Boeing 737 Next Generation, 777, 717, 747-400ER, 747-8F 767-400ER, 747-8, and 787, Airbus A320 family (later versions), A330 (later versions), A340-500/600, A340-300 (later versions), A380 and A350 are fitted with glass cockpits consisting of LCD units.

The glass cockpit has become standard equipment in airliners, business jets, and military aircraft. It was fitted into NASA's Space Shuttle orbiters Atlantis, Columbia, Discovery, and Endeavour, and the Russian Soyuz TMA model spacecraft that were launched for the first time in 2002. By the end of the century glass cockpits began appearing in general aviation aircraft as well. In 2003, Cirrus Design's SR20 and SR22 became the first light aircraft equipped with glass cockpits, which they made standard on all Cirrus aircraft. By 2005, even basic trainers like the Piper Cherokee and Cessna 172 were shipping with glass cockpits as options (which nearly all customers chose), as well as many modern utility aircraft such as the Diamond DA42. The Lockheed Martin F-35 Lightning II features a "panoramic cockpit display" touchscreen that replaces most of the switches and toggles found in an aircraft cockpit. The civilian Cirrus Vision SF50 has the same, which they call a "Perspective Touch" glass cockpit.

Commercial aviation

Unlike the previous era of glass cockpits—where designers merely copied the look and feel of conventional electromechanical instruments onto cathode ray tubes—the new displays represent a true departure. They look and behave very similarly to other computers, with windows and data that can be manipulated with point-and-click devices. They also add terrain, approach charts, weather, vertical displays, and 3D navigation images.

The improved concepts enable aircraft makers to customize cockpits to a greater degree than previously. All of the manufacturers involved have chosen to do so in one way or another—such as using a trackball, thumb pad or joystick as a pilot-input device in a computer-style environment. Many of the modifications offered by the aircraft manufacturers improve situational awareness and customize the human-machine interface to increase safety.

Modern glass cockpits might include synthetic vision systems (SVS) or enhanced flight vision systems (EFVS). Synthetic vision systems display a realistic 3D depiction of the outside world (similar to a flight simulator), based on a database of terrain and geophysical features in conjunction with the attitude and position information gathered from the aircraft navigational systems. Enhanced flight vision systems add real-time information from external sensors, such as an infrared camera.

All new airliners such as the Airbus A380, Boeing 787 and private jets such as Bombardier Global Express and Learjet use glass cockpits.

General aviation

Many modern general aviation aircraft are available with glass cockpits. Systems such as the Garmin G1000 are now available on many new GA aircraft, including the classic Cessna 172. Many small aircraft can also be modified post-production to replace analogue instruments.

Glass cockpits are also popular as a retrofit for older private jets and turboprops such as Dassault Falcons, Raytheon Hawkers, Bombardier Challengers, Cessna Citations, Gulfstreams, King Airs, Learjets, Astras, and many others. Aviation service companies work closely with equipment manufacturers to address the needs of the owners of these aircraft.

Consumer, research, hobby & recreational aviation
Today, smartphones and tablets use mini-applications, or "apps", to remotely control complex devices, by WiFi radio interface. They demonstrate how the "glass cockpit" idea is being applied to consumer devices. Applications include toy-grade UAVs which use the display and touch screen of a tablet or smartphone to employ every aspect of the "glass cockpit" for instrument display, and fly-by-wire for aircraft control.

Spaceflight

The glass cockpit idea made news in 1980s trade magazines, like Aviation Week & Space Technology, when NASA announced that it would be replacing most of the electro-mechanical flight instruments in the space shuttles with glass cockpit components. The articles mentioned how glass cockpit components had the added benefit of being a few hundred pounds lighter than the original flight instruments and support systems used in the Space Shuttles. The was the first orbiter to be retrofitted with a glass cockpit in 2000 with the launch of STS-101. Columbia was the second orbiter with a glass cockpit on STS-109 in 2002, followed by Discovery in 2005 with STS-114, and Endeavour in 2007 with STS-118.

NASA's Orion spacecraft will use glass cockpits derived from Boeing 787 Dreamliner.

Safety
As aircraft operation depends on glass cockpit systems, flight crews must be trained to deal with failures. The Airbus A320 family has seen fifty incidents where several flight displays were lost.

On 25 January 2008, United Airlines Flight 731 experienced a serious glass-cockpit blackout, losing half of the Electronic Centralised Aircraft Monitor (ECAM) displays as well as all radios, transponders, Traffic Collision Avoidance System (TCAS), and attitude indicators. The pilots were able to land at Newark Airport without radio contact in good weather and daylight conditions.

Airbus has offered an optional fix, which the US National Transportation Safety Board (NTSB) has suggested to the US Federal Aviation Administration (FAA) as mandatory, but the FAA has yet to make it a requirement. A preliminary NTSB factsheet is available. Due to the possibility of a blackout, glass cockpit aircraft also have an integrated standby instrument system that includes (at a minimum) an artificial horizon, altimeter and airspeed indicator. It is electronically separate from the main instruments and can run for several hours on a backup battery.

In 2010, the NTSB published a study done on 8,000 general aviation light aircraft. The study found that, although aircraft equipped with glass cockpits had a lower overall accident rate, they also had a larger chance of being involved in a fatal accident. The NTSB Chairman said in response to the study:

"Training is clearly one of the key components to reducing the accident rate of light planes equipped with glass cockpits, and this study clearly demonstrates the life and death importance of appropriate training on these complex systems... While the technological innovations and flight management tools that glass cockpit-equipped airplanes bring to the general aviation community should reduce the number of fatal accidents, we have not—unfortunately—seen that happen."

title: Glass cockpit


text:
Ilam, Iran

Ilam is a Kurdish city in the Central District of Ilam County, Ilam province, Iran, serving as capital of the province, the county, and the district. The Kabir Kuh mountain range lies east of the city. To the west, it borders Iraq.

Demographics
At the 2006 National Census, Ilam's population was 155,289 in 34,549 households. The following census in 2011 counted 172,213 people in 42,613 households. The latest census in 2016 showed the population had risen to 194,030 people in 53,581 households.

Language composition:

Architecture
Like many other regions of Iran the architecture in Ilam includes traditional and contemporary periods. Although easy access to fossil fuels and electricity may have aided the transition in Iranian architecture in other regions of Iran from its traditional to modern styles, in Ilam the increasing population has also played a role.

The Governor Castle, Falahaty Mansion and The Mirgholam Castle are examples of some surviving traditional buildings in Ilam. The courtyard dwelling is the main type of the buildings of this period. This type of building was accepted as the main building type over all Iran for both climatic and cultural reasons. Brick is the main constructional material in these buildings. The passive thermal techniques indicated for the Iranian traditional buildings are commonly used in these buildings.

The Governor Castle of Ilam was built in type of courtyard. Adding shade and moisture by using green landscape, high trees and a pond, were the main passive techniques used in this building to reduce the temperature in summer. The Mirgholam Castle of Ilam presents a classic Iranian courtyard. The garden and the pound were the main elements of this type of buildings. The Falahaty Mansion used a pitched roof as it was regular beside the flat roofs in the traditional buildings in Ilam earlier.

Climate
Ilam is situated in the cold mountainous region of Iran at a height of 1319 m above mean sea level. It is located in the west of Iran at a latitude of 33° 38´ north and longitude of 46° 26´ east. Although this city is surrounded by mountains, its climate is also affected by deserts from the west and the south. This region presents a highly variable annual weather profile. Heavy showers or snow in the winter and dusty, brutally hot, dry weather in the summer are normal for this region. Monthly rainfalls have been as high as 352.1 mm in March 1974, whilst daily rainfalls have reached 86 mm on 26 February 1991. Temperatures have ranged from a high of 47.0 C on 20 August 1975 to a low of −15.0 C on 5 February 1974.

Ilam's climate is classed under the Köppen climate classification as a Mediterranean climate (Csa) with continental influences.

Colleges and universities
Ilam contains the following universities:
 * Ilam University of Medical Sciences
 * University of Ilam
 * Islamic Azad University of Ilam
 * Safir Danesh
 * Farhangian University, Shahid Modares Campus of Ilam (Men) and Imam Jafar -e- Sadiqh Campus of Ilam (Women)

title: Ilam, Iran


text:
Stuart Hall

Stuart Hall may refer to:

People

 * Stuart Hall (presenter) (born 1929), British television and radio presenter
 * Stuart Hall (cultural theorist) (1932–2014), Jamaican cultural theorist in Britain and first editor of the New Left Review
 * Stuart Hall (boxer) (born 1980), British bantamweight champion in 2010
 * Stuart Hall (racing driver) (born 1984), British racing driver

Other uses

 * Stuart Hall Building, Kansas City, Missouri
 * Stuart Hall High School, boys' school in San Francisco, California
 * Stuart Hall School, private girls' boarding/co-ed day student school in Staunton, Virginia
 * Stuart Hall, County Tyrone, a townland in County Tyrone, Northern Ireland

title: Stuart Hall


text:
Robert C. Craig

Robert Charles Craig (March 9, 1921 – March 25, 1990) was a professor in the department of Counseling, Educational Psychology, and Special Education at Michigan State University from 1966–1989.

Craig also worked at Washington State University, American Institute of Research, Marquee University, and the University of Pittsburgh.

Craig published three books: The Psychology of Learning in the Classroom, Contemporary Educational Psychology, and Contemporary Issues in Educational Psychology.

title: Robert C. Craig


text:
Gush Etzion

Gush Etzion (גּוּשׁ עֶצְיוֹן, lit. Etzion Bloc) is a cluster of Israeli settlements located in the Judaean Mountains, directly south of Jerusalem and Bethlehem in the West Bank. The core group includes four Jewish agricultural villages that were founded in 1943–1947, and destroyed by the Arab Legion before the outbreak of the 1948 Arab–Israeli War, in the Kfar Etzion massacre. The area was left outside of Israel with the 1949 armistice lines. These settlements were rebuilt after the 1967 Six-Day War, along with new communities that have expanded the area of the Etzion Bloc. , Gush Etzion consisted of 22 settlements with a population of 70,000.

The international community considers Israeli settlements in the West Bank illegal under international law, but the Israeli and US governments dispute this.

History

The four core original settlements of Gush Etzion were Kfar Etzion (founded in 1943), Massu'ot Yitzhak (1945), Ein Tzurim (1946) and Revadim (1947); the land area of all four were located within the village boundaries of Khirbet Beit Zakariyyah. From November 29, 1947, Kfar Etzion was under siege and cut off from Jerusalem. On May 13, 1948, when the village surrendered, 127 Jewish inhabitants were massacred by local village irregulars, with the possible involvement of the Arab Legion. The other villages surrendered the next day. The inhabitants were taken prisoner and the homes were plundered and burned.

The establishment, defense and fall of Gush Etzion have been described as "one of the major episodes of the State of Israel-in-the-making", playing a significant role in Israeli collective memory. The motivation for resettling the region is not so much ideological, political or security-related as symbolic, linked in the Israeli psyche to the massive loss of life (1% of its total population) in the 1947–1949 Palestine war.

Settlements in Mandatory Palestine

In 1927, a group of religious Yemenite Jews founded an agricultural village they named Migdal Eder (מִגְדַּל עֵדֶר), based on a biblical quotation. The land had been purchased in 1925 by Zikhron David, a private Jewish land holding company at a site between Bethlehem and Hebron that fell between the zones of influence of the local Arab clans. This early community did not flourish, mainly due to economic hardships and escalating tension with neighboring Arab communities. Two years later, during the 1929 Palestine riots and recurring hostilities, Migdal Eder was attacked and destroyed. Residents of the neighboring Palestinian village of Beit Ummar sheltered the farmers, but they could not return to their land.

In 1932, a Jewish businessman of German extraction, Shmuel Yosef Holtzmann, provided financial backing for another attempt at resettling the area, through a company named El HaHar ("To the Mountain"). The kibbutz established there in 1935 was named Kfar Etzion, in his honor (the German word Holz means "wood", which is etz עץ in Hebrew). The 1936–1939 Arab revolt made life intolerable for the residents, who returned to Jerusalem in 1937. The Jewish National Fund organized a third attempt at settlement in 1943 with the refounding of Kfar Etzion by members of a religious group called Kvutzat Avraham. Despite the rocky soil, shortage of potable water, harsh winters, and constant threat of attack, this group managed to succeed.

Their isolation was somewhat relieved by the establishment in 1945 of Masu'ot Yitzhak and Ein Tzurim, populated by members of the religious Bnei Akiva movement and Religious Kibbutz Movement. Against the backdrop of an impending struggle for Israeli independence, the secular Hashomer Hatzair movement founded a fourth kibbutz, Revadim. A religious center, Neve Ovadia, was also founded by the bloc's members. By the start of the 1948 Arab–Israeli War, the Etzion bloc numbered 450 residents and stretched over an area of 20000 dunam.

Civil war and Arab–Israeli War

On November 29, 1947, the United Nations approved the Partition Plan. The bloc fell within the area allotted to a proposed Arab state. The Haganah command decided not to leave the bloc. Arab hostilities began almost immediately, and travel to Jerusalem became exceedingly difficult. For five months the bloc was besieged, first by Arab irregulars, and then by the Jordanian Arab Legion. Throughout the winter hostilities intensified and several relief convoys from the Haganah in Jerusalem were destroyed in ambushes. For 47 days the armed conflict was intense. In January, the women and children were evacuated with British assistance. An emergency reinforcement convoy put together by the Haganah and attempting to get to Gush Etzion under cover of darkness was discovered; all 35 members were massacred. Despite some resupply flights by Piper Cubs out of Tel Aviv landing onto an improvised airfield, adequate supplies were not getting in.

On March 27, land communication with the Yishuv was severed completely when the Nabi Daniel Convoy was ambushed on its return journey to Jerusalem. In the following months, Arab irregular forces continued small-scale attacks against the bloc, which the Haganah was able to effectively withstand. At times, the Haganah forces, commanded by Uzi Narkiss, ambushed Arab military convoys—and, according to Morris, also Arab civilian traffic and British military convoys —on the road between Jerusalem and Hebron. The defenders of Gush Etzion and the central command in Jerusalem mulled evacuation, but, although they had very few arms, a decision was made to hold out due to their strategic location as the only Jewish-held position on Jerusalem's southern approach from Hebron.

Gush Etzion massacre
On May 12, the commander of Kfar Etzion requested from the Central Command in Jerusalem permission to evacuate the kibbutz, but was told to stay. Later in the day, the Arabs captured the Russian Orthodox monastery, which the Haganah used as a perimeter fortress for the Kfar Etzion area, killing twenty-four of its thirty-two defenders. On May 13, a massive attack began, involving parts of two Arab Legion infantry companies, light artillery and local irregular support, attacking from four directions. The kibbutz fell within a day; the Arab forces massacred 127 of the 133 surrendering defenders. The total number of dead during the final assault, including those killed in the massacre and those who committed suicide, was estimated to be between 75 and 250. Only three men and one woman survived. The following day, the day Israel declared its independence, the three other kibbutzim surrendered. The Arab Legion took 320 persons as prisoners of war and held them in Jordan for a year before releasing them.

Interim period (1949–1967)

In May 1948, the women and children evacuated from the bloc before the battle were taken to the Ratisbonne Monastery in Jerusalem. In June 1948, when the road to Jerusalem was opened, they were moved to Petah Tikva for two months. The refugees lived at the Netzah Yisrael school until the school year began, later resettling in Giv'at Aliyah, a neighborhood in Jaffa organized like a kibbutz.

Four years later, the returning prisoners of war of the bloc founded Nir Etzion in the Mount Carmel area near Haifa. Nir Etzion sought to accept the majority of the bloc's children into it, but despite wishing to unite in a new place of residence, the issue of joining Nir Etzion was a matter of debate among the children, many of whom joined the Nahal military unit. The survivors of Masu'ot Yitzhak, Ein Tzurim, and Revadim founded their communities anew in Israel proper.

The interim period saw the rise of two movements designed to commemorate the fall of Gush Etzion, through songs, poetry, prose and cultural activities. Both the land of the bloc, and the events that transpired there in the war of 1948, became sacred to the descendants of the original participants. Some compared the story of the yearning to return to the bloc to the story of the Jews yearning to return to the Land of Israel. For 19 years, some survivors would gather on the Israel–Jordan frontier and gaze at the giant oak tree there in remembrance of what was. This became an annual gathering following the Independence Day ceremony (independence day was one day after the bloc had fallen). Poems and stories were written that humanized the lone tree. This was criticized by the novelist Haim Be'er, who called the bloc's settlement movements a "fervent cult" and compared them to the Canaanites.

Re-establishment
As a result of the 1967 Six-Day War, Israel controlled the area of the former Etzion Bloc. A loose organisation of Bnei Akiva activists, who later coalesced into Gush Emunim, led by Hanan Porat, whose parents had been evacuated, petitioned Israeli prime minister Levi Eshkol to allow the reestablishment of Kfar Etzion. Among the supporters were Ra'anan Weitz, head of the settlement department in the Jewish Agency; minister of internal affairs Haim-Moshe Shapira; and Michael Hazani of the national religious movement. Supporters of the Allon Plan in the government were also in favor of settling the bloc. Eshkol was finally persuaded to give a green light to the plan. He was not decisive however, and the settlement movement did not immediately begin to build in the entire bloc, but only on the location of Kfar Etzion. Construction began in September, 1967. Since the government initially decided not to establish civilian settlements in the captured territories, the settlement was falsely portrayed as a Nahal outpost. According to Ra'anan Weitz's plan, Kfar Etzion was meant to be one of three settlements in the new bloc, which also included Aviezer. A new middle village would be established on Jewish National Fund land purchased in the 1940s.

Weitz's plan of creating a line of settlements based on territorial continuity, however, had a number of opponents: the descendants of the original residents of the bloc, the settlers on the ground, the Religious Kibbutz Movement, and the Israel Defense Forces. The IDF surveyed the land and decided that, "Kfar Etzion B should be founded near the existing Kfar Etzion, and not near the former Green Line". This eventually was supported by defense minister Moshe Dayan, who envisioned five settlement points in the West Bank, one of them being the Etzion bloc. On September 30, 1968, the government gave permission to create a regional center and Hesder Yeshiva in Kfar Etzion, a major demand of the settlers and the final departure from the continuity plan.

In the same decision, the government appointed a committee for planning the settlement of the bloc. In accordance with the committee's recommendations, Revadim and the settlement of Rosh Tzurim were founded on the former site of Ein Tzurim in July 1969, and Alon Shvut in June 1970. Many other settlements and two municipalities (Efrat and Beitar Illit) have been founded in the area of the historic Etzion bloc, and its name was taken for the greater Gush Etzion Regional Council.

Today there is a museum about the history of Gush Etzion.

Today
Here is a list of communities in modern Gush Etzion.

Gush Etzion Junction
The entrance to the Gush Etzion bloc is the Gush Etzion Junction, which is located just west of the intersection of Route 60 and Route 367. The junction is located between Efrat and Alon Shvut and very close to Migdal Oz. It is the site of the Gush Etzion visitors' center, a gas station, an automotive repair shop, a Rami Levy discount supermarket, an electronics store, the Gush Etzion Winery (one minute towards Alon Shvut on the north side of the road), a bakery, natural foods store, eyeglass shop, clothing store and pizza / felafel / shawarma stands. Across the street are a nursery and car dealership. The junction is a popular hitchhiking post, both south to Hebron / Be'er Sheva and north to Jerusalem, as well as west towards Bet Shemesh and the coast) which has frequently been the site of attacks by Palestinians against Israeli citizens.

2014 "State land" classifications
On 6 April and 25 August 2014, the Israeli Civil Administration declared 1,000 and 3,799 dunums of land respectively in the Bethlehem Governorate within the boundaries of Surif, Nahalin, Husan, Jab'a and Wadi Fukin villages as "state land". According to Peace Now, it was the largest confiscation of Palestinian land in three decades.

The United States responded to the announcement by rebuking Israel for taking measures that were 'counter-productive' to the two-state solution in peace talks. The expropriation was also condemned by the United Nations, the United Kingdom, Egypt, France, Spain, Russia, the European Union, Turkey, Norway, Japan and Amnesty International.

As of September 2014, eight years after approving the 45 km stretch of barrier enclosing Gush Etzion, no progress had been made on it. The reclassified land would be on the Palestinian side of the barrier. On 21 September 2014, the government voted to not reauthorize the barrier in the Gush Etzion area.

title: Gush Etzion


text:
Tetration

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though Knuth's up arrow notation $$\uparrow \uparrow$$ and the left-exponent xb are common.

Under the definition as repeated exponentiation, $${^{n}a}$$ means $${a^{a^{\cdot^{\cdot^{a}}}}}$$, where $n$ copies of $a$ are iterated via exponentiation, right-to-left, i.e. the application of exponentiation $$n-1$$ times. $n$ is called the "height" of the function, while $a$ is called the "base," analogous to exponentiation. It would be read as "the $n$th tetration of $a$".

It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.

Tetration is also defined recursively as
 * $${a \uparrow \uparrow n} := \begin{cases} 1 &\text{if }n=0, \\ a^{a \uparrow\uparrow (n-1)} &\text{if }n>0, \end{cases}$$

allowing for attempts to extend tetration to non-natural numbers such as real, complex, and ordinal numbers.

The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions. None of the three functions are elementary.

Tetration is used for the notation of very large numbers.

Introduction
The first four hyperoperations are shown here, with tetration being considered the fourth in the series. The unary operation succession, defined as $$a' = a + 1$$, is considered to be the zeroth operation.

 * 1) Addition $$a + n = a + \underbrace{1 + 1 + \cdots + 1}_n$$ $n$ copies of 1 added to $a$ combined by succession.
 * 2) Multiplication $$a \times n = \underbrace{a + a + \cdots + a}_n$$ $n$ copies of $a$ combined by addition.
 * 3) Exponentiation $$a^n = \underbrace{a \times a \times \cdots \times a}_n$$ $n$ copies of $a$ combined by multiplication.
 * 4) Tetration $${^{n}a} = \underbrace{a^{a^{\cdot^{\cdot^{a}}}}}_n$$ $n$ copies of $a$ combined by exponentiation, right-to-left.

Importantly, nested exponents are interpreted from the top down: $a^{b^c}$ means $a^{\left(b^c \right)}$ and not $\left(a^b \right)^c.$

Succession, $$a_{n+1} = a_n + 1$$, is the most basic operation; while addition ($$a + n$$) is a primary operation, for addition of natural numbers it can be thought of as a chained succession of $$n$$ successors of $$a$$; multiplication ($$a \times n$$) is also a primary operation, though for natural numbers it can analogously be thought of as a chained addition involving $$n$$ numbers of $$a$$. Exponentiation can be thought of as a chained multiplication involving $$n$$ numbers of $$a$$ and tetration ($$^{n}a$$) as a chained power involving $$n$$ numbers $$a$$. Each of the operations above are defined by iterating the previous one; however, unlike the operations before it, tetration is not an elementary function.

The parameter $$a$$ is referred to as the base, while the parameter $$n$$ may be referred to as the height. In the original definition of tetration, the height parameter must be a natural number; for instance, it would be illogical to say "three raised to itself negative five times" or "four raised to itself one half of a time." However, just as addition, multiplication, and exponentiation can be defined in ways that allow for extensions to real and complex numbers, several attempts have been made to generalize tetration to negative numbers, real numbers, and complex numbers. One such way for doing so is using a recursive definition for tetration; for any positive real $$a > 0$$ and non-negative integer $$n \ge 0$$, we can define $$\,\! {^{n}a}$$ recursively as:
 * $${^{n}a} := \begin{cases} 1 &\text{if }n=0 \\ a^{\left(^{(n-1)}a\right)} &\text{if }n>0 \end{cases}$$

The recursive definition is equivalent to repeated exponentiation for natural heights; however, this definition allows for extensions to the other heights such as $$^{0}a$$, $$^{-1}a$$, and $$^{i}a$$ as well – many of these extensions are areas of active research.

Terminology
There are many terms for tetration, each of which has some logic behind it, but some have not become commonly used for one reason or another. Here is a comparison of each term with its rationale and counter-rationale.

 * The term tetration, introduced by Goodstein in his 1947 paper Transfinite Ordinals in Recursive Number Theory (generalizing the recursive base-representation used in Goodstein's theorem to use higher operations), has gained dominance. It was also popularized in Rudy Rucker's Infinity and the Mind.
 * The term superexponentiation was published by Bromer in his paper Superexponentiation in 1987. It was used earlier by Ed Nelson in his book Predicative Arithmetic, Princeton University Press, 1986.
 * The term hyperpower is a natural combination of hyper and power, which aptly describes tetration. The problem lies in the meaning of hyper with respect to the hyperoperation sequence. When considering hyperoperations, the term hyper refers to all ranks, and the term super refers to rank 4, or tetration. So under these considerations hyperpower is misleading, since it is only referring to tetration.
 * The term power tower is occasionally used, in the form "the power tower of order $n$" for $${\ \atop {\ }} {{\underbrace{a^{a^{\cdot^{\cdot^{a}}}}}} \atop n}$$. Exponentiation is easily misconstrued: note that the operation of raising to a power is right-associative (see below). Tetration is iterated exponentiation (call this right-associative operation ^), starting from the top right side of the expression with an instance a^a (call this value c). Exponentiating the next leftward a (call this the 'next base' b), is to work leftward after obtaining the new value b^c. Working to the left, use the next a to the left, as the base b, and evaluate the new b^c. 'Descend down the tower' in turn, with the new value for c on the next downward step.

Owing in part to some shared terminology and similar notational symbolism, tetration is often confused with closely related functions and expressions. Here are a few related terms:

In the first two expressions $a$ is the base, and the number of times $a$ appears is the height (add one for $x$). In the third expression, $n$ is the height, but each of the bases is different.

Care must be taken when referring to iterated exponentials, as it is common to call expressions of this form iterated exponentiation, which is ambiguous, as this can either mean iterated powers or iterated exponentials.

Notation
There are many different notation styles that can be used to express tetration. Some notations can also be used to describe other hyperoperations, while some are limited to tetration and have no immediate extension.

One notation above uses iterated exponential notation; this is defined in general as follows:

 * $$\exp_a^n(x) = a^{a^{\cdot^{\cdot^{a^x}}}}$$ with $n$ $a$s.

There are not as many notations for iterated exponentials, but here are a few:

Examples
Because of the extremely fast growth of tetration, most values in the following table are too large to write in scientific notation. In these cases, iterated exponential notation is used to express them in base 10. The values containing a decimal point are approximate.

Remark: If x does not differ from 10 by orders of magnitude, then for all $$k \ge3,~ ^mx =\exp_{10}^k z,~z>1 ~\Rightarrow~^{m+1}x = \exp_{10}^{k+1} z' \text{ with }z' \approx z$$. For example, $$z - z' < 1.5\cdot 10^{-15} \text{ for } x = 3 = k,~ m = 4$$ in the above table, and the difference is even smaller for the following rows.

Extensions
Tetration can be extended in two different ways; in the equation $$^na\!$$, both the base $2$ and the height $4$ can be generalized using the definition and properties of tetration. Although the base and the height can be extended beyond the non-negative integers to different domains, including $${^n 0}$$, complex functions such as $${}^{n}i$$, and heights of infinite $16$, the more limited properties of tetration reduce the ability to extend tetration.

Base zero
The exponential $$0^0$$ is not consistently defined. Thus, the tetrations $$\,{^{n}0}$$ are not clearly defined by the formula given earlier. However, $$\lim_{x\rightarrow0} {}^{n}x$$ is well defined, and exists:
 * $$\lim_{x\rightarrow0} {}^{n}x = \begin{cases}

1, & n \text{ even} \\ 0, & n \text{ odd} \end{cases}$$

Thus we could consistently define $${}^{n}0 = \lim_{x\rightarrow 0} {}^{n}x$$. This is analogous to defining $$0^0 = 1$$.

Under this extension, $${}^{0}0 = 1$$, so the rule $${^{0}a} = 1$$ from the original definition still holds.

Complex bases

Since complex numbers can be raised to powers, tetration can be applied to bases of the form $n = 2, 3, 4, ...$ (where $19,728$ and $6.03123×1019,727$ are real). For example, in $z = a + bi$ with $nz$, tetration is achieved by using the principal branch of the natural logarithm; using Euler's formula we get the relation:

 * $$i^{a+bi} = e^{\frac{1}{2}{\pi i} (a + bi)} = e^{-\frac{1}{2}{\pi b}} \left(\cos{\frac{\pi a}{2}} + i \sin{\frac{\pi a}{2}}\right)$$

This suggests a recursive definition for $z = i$ given any $n+1i = a′ + b′i$:
 * $$\begin{align}

a' &= e^{-\frac{1}{2}{\pi b}} \cos{\frac{\pi a}{2}} \\[2pt] b' &= e^{-\frac{1}{2}{\pi b}} \sin{\frac{\pi a}{2}} \end{align}$$

The following approximate values can be derived:

Solving the inverse relation, as in the previous section, yields the expected $ni = a + bi$ and $i$, with negative values of $106.03123×1019,727$ giving infinite results on the imaginary axis. Plotted in the complex plane, the entire sequence spirals to the limit $0.2079$, which could be interpreted as the value where $3$ is infinite.

Such tetration sequences have been studied since the time of Euler, but are poorly understood due to their chaotic behavior. Most published research historically has focused on the convergence of the infinitely iterated exponential function. Current research has greatly benefited by the advent of powerful computers with fractal and symbolic mathematics software. Much of what is known about tetration comes from general knowledge of complex dynamics and specific research of the exponential map.

Infinite heights

Tetration can be extended to infinite heights; i.e., for certain $27$ and $3,638,334,640,024$ values in $${}^{n}a$$, there exists a well defined result for an infinite $4$. This is because for bases within a certain interval, tetration converges to a finite value as the height tends to infinity. For example, $$\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\cdot^{\cdot^{\cdot}}}}}$$ converges to 2, and can therefore be said to be equal to 2. The trend towards 2 can be seen by evaluating a small finite tower:

 * $$\begin{align}

\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{1.414}}}}} &\approx \sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{1.63}}}} \\ &\approx \sqrt{2}^{\sqrt{2}^{\sqrt{2}^{1.76}}} \\ &\approx \sqrt{2}^{\sqrt{2}^{1.84}} \\ &\approx \sqrt{2}^{1.89} \\ &\approx 1.93 \end{align}$$

In general, the infinitely iterated exponential $$x^{x^{\cdot^{\cdot^{\cdot}}}}\!\!$$, defined as the limit of $${}^{n}x$$ as $154$ goes to infinity, converges for $0.9472 + 0.3208i$, roughly the interval from 0.066 to 1.44, a result shown by Leonhard Euler. The limit, should it exist, is a positive real solution of the equation $0.0501 + 0.6021i$. Thus, $0.3872 + 0.0305i$. The limit defining the infinite exponential of $256$ does not exist when $0.7823 + 0.5446i$ because the maximum of $0.1426 + 0.4005i$ is $0.5198 + 0.1184i$. The limit also fails to exist when $0.5686 + 0.6051i$.

This may be extended to complex numbers $8.0723×10153$ with the definition:
 * $${}^{\infty}z = z^{z^{\cdot^{\cdot^{\cdot}}}} = \frac{\mathrm{W}(-\ln{z})}{-\ln{z}} ~,$$

where $0i = 1$ represents Lambert's W function.

As the limit $−1i = 0$ (if existent on the positive real line, i.e. for $0.4383 + 0.3606i$) must satisfy $e−e ≤ x ≤ e1/e$ we see that $y = xy$ is (the lower branch of) the inverse function of $x = y1/y$.

Negative heights
We can use the recursive rule for tetration,
 * $${^{k+1}a} = a^{\left({^{k}a}\right)},$$

to prove $${}^{-1}a$$:
 * $$^{k}a = \log_a \left(^{k+1}a\right);$$

Substituting −1 for $5$ gives
 * $${}^{-1}a = \log_{a} \left({}^0 a\right) = \log_a 1 = 0$$.

Smaller negative values cannot be well defined in this way. Substituting −2 for $2,184$ in the same equation gives
 * $${}^{-2}a = \log_{a} \left( {}^{-1}a \right) = \log_a 0 = -\infty$$

which is not well defined. They can, however, sometimes be considered sets.

For $$n = 1$$, any definition of $$\,\! {^{-1}1}$$ is consistent with the rule because
 * $${^{0}1} = 1 = 1^n$$ for any $$\,\! n = {^{-1}1}$$.

Real heights
At this time there is no commonly accepted solution to the general problem of extending tetration to the real or complex values of $3,125$. There have, however, been multiple approaches towards the issue, and different approaches are outlined below.

In general, the problem is finding — for any real $x > e1/e$ — a super-exponential function $$\,f(x) = {}^{x}a$$ over real $y1/y$ that satisfies
 * $$\,{}^{-1}a = 0$$
 * $$\,{}^{0}a = 1$$
 * $$\,{}^{x}a = a^{\left({}^{x-1}a\right)}$$for all real $$x > -1.$$

To find a more natural extension, one or more extra requirements are usually required. This is usually some collection of the following:
 * A continuity requirement (usually just that $${}^{x}a$$ is continuous in both variables for $$x > 0$$).
 * A differentiability requirement (can be once, twice, $1.33574×102,184$ times, or infinitely differentiable in $6$).
 * A regularity requirement (implying twice differentiable in $36,305$) that:
 * $$\left( \frac{d^2}{dx^2}f(x) > 0\right)$$ for all $$x > 0$$

The fourth requirement differs from author to author, and between approaches. There are two main approaches to extending tetration to real heights; one is based on the regularity requirement, and one is based on the differentiability requirement. These two approaches seem to be so different that they may not be reconciled, as they produce results inconsistent with each other.

When $$\,{}^{x}a$$ is defined for an interval of length one, the whole function easily follows for all $e1/e$.

Linear approximation for real heights
A linear approximation (solution to the continuity requirement, approximation to the differentiability requirement) is given by:
 * $${}^{x}a \approx \begin{cases}

\log_a\left(^{x+1}a\right) & x \le -1 \\ 1 + x & -1 < x \le 0 \\ a^{\left(^{x-1}a\right)} & 0 < x \end{cases}$$

hence:

and so on. However, it is only piecewise differentiable; at integer values of $46,656$ the derivative is multiplied by $$\ln{a}$$. It is continuously differentiable for $$x > -2$$ if and only if $$a = e$$. For example, using these methods $${}^\frac{\pi}{2}e \approx 5.868...$$ and $${}^{-4.3}0.5 \approx 4.03335...$$

A main theorem in Hooshmand's paper states: Let $$0 < a \neq 1$$. If $$f:(-2, +\infty)\rightarrow \mathbb{R}$$ is continuous and satisfies the conditions:

 * $$f(x) = a^{f(x-1)} \;\; \text{for all} \;\; x > -1, \; f(0) = 1,$$
 * $$f$$ is differentiable on $2.0692×1036,305$,
 * $$f^\prime$$ is a nondecreasing or nonincreasing function on $7$,
 * $$f^\prime \left(0^+\right) = (\ln a) f^\prime \left(0^-\right) \text{ or } f^\prime \left(-1^+\right) = f^\prime \left(0^-\right).$$

then $$f$$ is uniquely determined through the equation
 * $$f(x) = \exp^{[x]}_a \left(a^{(x)}\right) = \exp^{[x+1]}_a((x)) \quad \text{for all} \; \; x > -2,$$

where $$(x) = x - [x]$$ denotes the fractional part of $695,974$ and $$\exp^{[x]}_a$$ is the $$[x]$$-iterated function of the function $$\exp_a$$.

The proof is that the second through fourth conditions trivially imply that $695,974$ is a linear function on $8$.

The linear approximation to natural tetration function $${}^xe$$ is continuously differentiable, but its second derivative does not exist at integer values of its argument. Hooshmand derived another uniqueness theorem for it which states:

If $$ f: (-2, +\infty)\rightarrow \mathbb{R}$$ is a continuous function that satisfies:

 * $$f(x) = e^{f(x-1)} \;\; \text{for all} \;\; x > -1, \; f(0) = 1,$$
 * $$f$$ is convex on $15,151,335$,
 * $$f^\prime \left(0^-\right) \leq f^\prime \left(0^+\right).$$

then $$f = \text{uxp}$$. [Here $$f = \text{uxp}$$ is Hooshmand's name for the linear approximation to the natural tetration function.]

The proof is much the same as before; the recursion equation ensures that $$f^\prime (-1^+) = f^\prime (0^+),$$ and then the convexity condition implies that $$f$$ is linear on $15,151,335$.

Therefore, the linear approximation to natural tetration is the only solution of the equation $$f(x) = e^{f(x-1)} \;\; (x > -1)$$ and $$f(0) = 1$$ which is convex on $9$. All other sufficiently-differentiable solutions must have an inflection point on the interval $369,693,099$.

Higher order approximations for real heights
Beyond linear approximations, a quadratic approximation (to the differentiability requirement) is given by:
 * $${}^{x}a \approx \begin{cases}

\log_a\left({}^{x+1}a\right) & x \le -1 \\ 1 + \frac{2\ln(a)}{1 \;+\; \ln(a)}x - \frac{1 \;-\; \ln(a)}{1 \;+\; \ln(a)}x^2 & -1 < x \le 0 \\ a^{\left({}^{x-1}a\right)} & x >0 \end{cases}$$

which is differentiable for all $$x > 0$$, but not twice differentiable. For example, $${}^\frac{1}{2}2 \approx 1.45933...$$ If $$a = e$$ this is the same as the linear approximation.

Because of the way it is calculated, this function does not "cancel out", contrary to exponents, where $$\left(a^\frac{1}{n}\right)^n = a$$. Namely,

{}^n\left({}^\frac{1}{n} a\right) = \underbrace{ \left({}^\frac{1}{n}a\right)^{ \left({}^\frac{1}{n}a\right)^{ \cdot^{\cdot^{\cdot^{\cdot^{ \left({}^\frac{1}{n}a\right) }}}}       }      }    }_n \neq a $$.

Just as there is a quadratic approximation, cubic approximations and methods for generalizing to approximations of degree $369,693,099$ also exist, although they are much more unwieldy.

Complex heights

In 2017, it was proven that there exists a unique function $10$ which is a solution of the equation $0 < x < e−e$ and satisfies the additional conditions that $W$ and $y = ∞x$ approaches the fixed points of the logarithm (roughly $e−e ≤ x ≤ e1/e$) as $10,000,000,000$ approaches $xy = y$ and that $10,000,000,000$ is holomorphic in the whole complex $a$-plane, except the part of the real axis at $x ↦ y = ∞x$. This proof confirms a previous conjecture. The construction of such a function was originally demonstrated by Kneser in 1950. The complex map of this function is shown in the figure at right. The proof also works for other bases besides e, as long as the base is greater than $$e^\frac{1}{e} \approx 1.445$$. Subsequent work extended the construction to all complex bases.

The requirement of the tetration being holomorphic is important for its uniqueness. Many functions $n$ can be constructed as
 * $$S(z) = F\!\left(~z~

+ \sum_{n=1}^{\infty} \sin(2\pi nz)~ \alpha_n + \sum_{n=1}^{\infty} \Big(1 - \cos(2\pi nz)\Big) ~\beta_n \right) $$

where $n$ and $a$ are real sequences which decay fast enough to provide the convergence of the series, at least at moderate values of $y ↦ x = y1/y$.

The function $b$ satisfies the tetration equations $a > 0$, $x > −2$, and if $x > −2$ and $−1 < x < 0$ approach 0 fast enough it will be analytic on a neighborhood of the positive real axis. However, if some elements of $0 < x < 1$ or $1 < x < 2$ are not zero, then function $n$ has multitudes of additional singularities and cutlines in the complex plane, due to the exponential growth of sin and cos along the imaginary axis; the smaller the coefficients $x = −2$ and $x = 2$ are, the further away these singularities are from the real axis.

The extension of tetration into the complex plane is thus essential for the uniqueness; the real-analytic tetration is not unique.

Ordinal tetration
Tetration can be defined for ordinal numbers via transfinite induction. For all $F(z + 1) = exp(F(z))$ and all $F(0) = 1$: $${}^0\alpha = 1$$ $${}^\beta\alpha = \sup(\{\alpha^{{}^\gamma\alpha} : \gamma < \beta\})\,.$$

Non-elementary recursiveness
Tetration (restricted to $$\mathbb{N}^2$$) is not an elementary recursive function. One can prove by induction that for every elementary recursive function $n$, there is a constant $a$ such that
 * $$f(x) \leq \underbrace{2^{2^{\cdot^{\cdot^{x}}}}}_c.$$

We denote the right hand side by $$g(c, x)$$. Suppose on the contrary that tetration is elementary recursive. $$g(x, x)+1$$ is also elementary recursive. By the above inequality, there is a constant $n$ such that $$g(x,x) +1 \leq g(c, x)$$. By letting $$x=c$$, we have that $$g(c,c) + 1 \leq g(c, c)$$, a contradiction.

Inverse operations
Exponentiation has two inverse operations; roots and logarithms. Analogously, the inverses of tetration are often called the super-root, and the super-logarithm (In fact, all hyperoperations greater than or equal to 3 have analogous inverses); e.g., in the function $${^3}y=x$$, the two inverses are the cube super-root of $n$ and the super-logarithm base $n$ of $x$.

Super-root
The super-root is the inverse operation of tetration with respect to the base: if $$^n y = x$$, then $z$ is an $k$th super-root of $k$ ($$\sqrt[n]{x}_s$$ or $$\sqrt[4]{x}_s$$).

For example,
 * $$^4 2 = 2^{2^{2^{2}}} = 65{,}536$$

so 2 is the 4th super-root of 65,536.

Square super-root
The 2nd-order super-root, square super-root, or super square root has two equivalent notations, $$\mathrm{ssrt}(x)$$ and $$\sqrt{x}_s$$. It is the inverse of $$^2 x = x^x$$ and can be represented with the Lambert W function:

 * $$\mathrm{ssrt}(x)=e^{W(\ln x)}=\frac{\ln x}{W(\ln x)}$$

The function also illustrates the reflective nature of the root and logarithm functions as the equation below only holds true when $$y = \mathrm{ssrt}(x)$$:

 * $$\sqrt[y]{x} = \log_y x$$

Like square roots, the square super-root of $n$ may not have a single solution. Unlike square roots, determining the number of square super-roots of $k$ may be difficult. In general, if $$e^{-1/e} 1$$, then $x$ has one positive square super-root greater than 1. If $x$ is positive and less than $$e^{-1/e}$$ it does not have any real square super-roots, but the formula given above yields countably infinitely many complex ones for any finite $(−1, 0)$ not equal to 1. The function has been used to determine the size of data clusters.

At $$ x = 1 $$: $ \mathrm{ssrt}(x) = 1 + (x-1) -(x-1)^2 + \frac{3}{2} (x-1)^3 - \frac{17}{6} (x-1)^4 + \frac{37}{6}(x-1)^5 - \frac{1759}{120}(x-1)^6 + \frac{13279}{360} (x-1)^7 + \mathcal O {\left((x-1)^8 \right)} $

Other super-roots
For each integer $F(z)$, the function $0.318 ± 1.337i$ is defined and increasing for $±i∞$, and $z ≤ −2$, so that the $(−1, 0)$th super-root of $x$, $$\sqrt[n]{x}_s$$, exists for $Im z$.

One of the simpler and faster formulas for a third-degree super-root is the recursive formula, if: $S(z + 1) = exp(S(z))$, and next $S(0) = 1$, for example $α_{n}$.

However, if the linear approximation above is used, then $$ ^y x = y + 1$$ if $β_{n}$, so $$ ^y \sqrt{y + 1}_s $$ cannot exist.

In the same way as the square super-root, terminology for other super-roots can be based on the normal roots: "cube super-roots" can be expressed as $$\sqrt[3]{x}_s$$; the "4th super-root" can be expressed as $$\sqrt[4]{x}_s$$; and the "$f$th super-root" is $$\sqrt[n]{x}_s$$. Note that $$\sqrt[n]{x}_s$$ may not be uniquely defined, because there may be more than one $[−1, 0]$$(−1, 0)$ root. For example, $(−1, 0)$ has a single (real) super-root if $(−1, +∞)$ is odd, and up to two if $(−1, 0)$ is even.

Just as with the extension of tetration to infinite heights, the super-root can be extended to ${α}$, being well-defined if ${β}$. Note that $$ x = {^\infty y} = y^{\left[^\infty y\right]} = y^x,$$ and thus that $$ y = x^{1/x} $$. Therefore, when it is well defined, $$ \sqrt[\infty]{x}_s = x^{1/x} $$ and, unlike normal tetration, is an elementary function. For example, $$\sqrt[\infty]{2}_s = 2^{1/2} = \sqrt{2}$$.

It follows from the Gelfond–Schneider theorem that super-root $$\sqrt{n}_s$$ for any positive integer $n$ is either integer or transcendental, and $$\sqrt[3]{n}_s$$ is either integer or irrational. It is still an open question whether irrational super-roots are transcendental in the latter case.

Super-logarithm
Once a continuous increasing (in $F$) definition of tetration, ${α}$, is selected, the corresponding super-logarithm $$\operatorname{slog}_ax$$ or $$\log^4_ax$$ is defined for all real numbers $z$, and ${β}$.

The function $α$ satisfies:
 * $$\begin{align}

\operatorname{slog}_a {^x a} &= x \\ \operatorname{slog}_a a^x &= 1 + \operatorname{slog}_a x \\ \operatorname{slog}_a x &= 1 + \operatorname{slog}_a \log_a x \\ \operatorname{slog}_a x &\geq -2 \end{align} $$

Open questions
Other than the problems with the extensions of tetration, there are several open questions concerning tetration, particularly when concerning the relations between number systems such as integers and irrational numbers:
 * It is not known whether there is a positive integer $F$ for which $β > 0$ or $n > 2$ is an integer. In particular, it is not known whether either of $nx$ or $x ≥ 1$ is an integer.
 * It is not known whether $n1 = 1$ is rational for any positive integer $z$ and positive non-integer rational $S$. For example, it is not known whether the positive root of the equation $x ≥ 1$ is a rational number.
 * It is not known whether $x^{x^{x}} = a|undefined$ or $x (n + 1) = exp (W (W (x (n) ln (a))))$ are rationals or not.

title: Tetration