text:
Talk:A∴A∴

Neutrality?
The article makes this assertion: "The A∴A∴ is present in all societies and epochs, although not necessarily under that name"

That sounds more like wish-thinking on behalf of its fans rather than a factual statement. Surely that sentence alone should be amended? — Preceding unsigned comment added by 88.91.209.143 (talk) 15:07, 22 June 2014 (UTC)

From Talk A.'. A.'.
Copied from Talk:A.'.A.'.:

Cite please? Or is this simply based on the Illuminatus! books? -- The Anome 20:18, 26 Nov 2003 (UTC)

 * It is mentioned in Aleister Crowley's Book Of Lies if I remember correctly. -- DenisMoskowitz

--Iscariot 09:34, 26 Feb 2005 (UTC)
 * According to Do What Thou Wilt: A Life of Aleister Crowley by Lawrence Sutin, the A.'.A.'. was formed in 1906 by Crowley and Jones.

(Smerdis of Tlön 11:40, 3 Jun 2004 (UTC))

Some References
The A.'.A.'. is mentioned on the Ordo Templi Orientis's site as an associate of that organization. It also appears to have its own website at www.outcol.org. Although that site's main page initially appears to be for "Outer College Curriculum Resources", the A.'.A.'. is frequently mentioned in the sub-pages and at the bottom of the main page itself.

---Deleted "Motta via J. Daniel Gunther lineage" from the outercol.org link. There is no reference to Motta or Gunther on the site and it is doubtful that it has any connection at all with Motta.-27 Aug 2008

 * Is there any reason to keep the outcol.org link?jonathon (talk) 22:07, 27 August 2008 (UTC)
 * ---Why wouldn't it be kept? It is a valid page with contact information for the A.'.A.'. it is simply not through Motta.  The OTO page for A.'.A.'. links to it also.-28 August 2008

 * It makes no representations as having a historical lineage. Your only justification for leaving it in, is the Caliphate OTO connection, despite the previous listing of two other A∴A∴ branches that have Caliphate OTO connections. It'd be slightly different if this had a demonstrable Typhonian OTO connection.jonathon (talk) 22:48, 28 August 2008 (UTC)
 * The link on the OTO website http://www.oto-usa.org/aa.html establishes it as "the" contact "endorsed" by the (Caliphate) OTO and the fact that the outercol.org site states an address for "those who wish to establish contact with the Order" to contact by. The other A.'.A.'. "branches" with "Caliphate OTO connections" are not described as such by the OTO's site.  And of course it would be different if there were a demonstrable Typhonian connection, but this lineage has C-OTO connections, not Typhonian, as demonstrated by the link via the OTO Grand Lodge site and the matching address/site information in recent publications (see the contact page in Magick: Book 4 as published by the C-OTO, the current copyright holders for Crowley's Libri.  —Preceding unsigned comment added by 216.201.151.90 (talk) 15:13, 29 August 2008 (UTC)

Disputed
Anonymoyus user User:67.48.77.208 placed the disputed template on this article and made the following comment which I am moving here to talk:

According to "The Magick of Thelema: A Handbook of the Rituals of Aleister Crowley," by Lon Milo Duquette (Weiser 1993), A.'.A.'. does NOT stand for Argenteum Astrum. On p. 216, the author states that this is commonly believed, but that he has "been informed in no uncertain terms that this is not the case."

I have looked at the reference you refer to, which appears as a footnote. It would seem to me that Lon Milo Duquette is expressing personal opinion based on the idea that the A.'. A.'. has other secret meanings, which with Crowley is undoubtedly the case. This does however not change the fact that Crowley himself used the Silver Star reference and connected this name to the passage every man and every woman is a star in Liber AL. --Solar 13:53, 12 Dec 2004 (UTC)

The phrase "Argentium Astrum", used to refer to the third Order the "Silver Star", dates to the original Hermetic Order of the Golden Dawn. Crowley's innovation was to translate this phrase into Greek: "Astron Argon". The reason for this was that the phrase has the same numeric value (451) as the phrase "Konx Om Pax", or "Light in Extension". The source of this interpretation is "The Mystical and Magical System of the A.'. A.'." by James Eshelman, an Adept of the Soror Estai lineage of the A.'. A.'. See the third edition, pp. 22-24

All links to major, extant lineages of the A.'.A.'. have been removed. This makes no sense. susan holmes 19:07, 10 August 2007 (UTC)

 * I agree and have restored them (only six month late). Valtyr (talk) 18:45, 12 February 2008 (UTC)

I would like to see a source for the following statement made above — The phrase "Argentium Astrum", used to refer to the third Order the "Silver Star", dates to the original Hermetic Order of the Golden Dawn. PedroLamarao (talk) 17:36, 16 January 2014 (UTC)

Magickal puncktuation?
What's the significance of the three dots after each letter in these abbreviations? Is there a name for that kind of punctuation? Does it mean anything in particular? Is it used exculsively by Crowley and his followers, or is it a more general occult thing? Any information would be welcome.
 * Previous was by User:Pterodactyler
 * Generally ∴ is the mathematical symbol for "therefore". I imagine it had further occult symbolism to Crowley and gang, but what that was may be unknowable at this point.  I don't know of any previous groups using that punctuation, though I've seen later groups do it in imitation of the A∴A∴. --DenisMoskowitz 15:55, 2005 July 27 (UTC)
 * I've seen the latin magical mottos of colleges in original Crowley works abbreviated in such a way; such as Frater "V∴N∴", but also done like "Fra∴ Volo Noscere". Nagelfar 07:19, 17 November 2005 (UTC)
 * Masons use it as well. It denotes that something was left off, possibly due to secrecy, IIRC.

 * Test: Magickal puncktuation. Umh, doesn't exist yet. Perhaps a good idea for April 1 2007. --Pjacobi 09:09, 12 May 2006 (UTC)
 * I don't see why it would be left off due to secrecy, as it's used as an abbr. in the same context that it is also clearly stated many times. It could be as simple as indicating that it is a non-native-tongue abbreviation. Though it's always used in the context of an abbreviation. Nagelfar 18:10, 4 August 2007 (UTC)

 * It comes from Freemasonry and suggests the person or institution possesses the secretes of Freemasonry. This is why you see things like O∴S∴M∴ or A∴A∴ or Fra∴ F∴L∴. I don't, however, have a citable source for this, unless I can cite documents that I'm not allowed to show you. —Preceding unsigned comment added by 152.2.81.214 (talk) 18:31, 21 September 2007 (UTC)

 * Is “A∴A∴” pronounced as if it were “A. A.” (namely ”ey-ey”?) If so, it'd be nice if someone would copy this to after the headword: « » —Sburke (talk) 02:39, 25 February 2013 (UTC)
 * Exactly. Currently we have an article whose title the uninitiated cannot pronounce. Malick78 (talk) 22:39, 7 January 2017 (UTC)

wtf is &#127; ?
there's a bunch of references to &#127; - but that doesn't make any sense, since that corresponds to 'delete' in iso 8859-1 and unicode. what's the deal?

 * In my browser, it shows up as a little square. Like the shape displayed for an unknown character, only smaller. Is that how it is supposed to look? IPSOS (talk) 02:21, 13 April 2007 (UTC)

 * It is supposed to be a glyph that contains three dots, in the shape of a triangle. Unicode character 0x2234. ∴ jonathon 01:00, 12 July 2007 (UTC)

 * No, that's not the one being discussed. This one is used for the square degree sign in 5=6, etc. IPSOS (talk) 20:06, 4 August 2007 (UTC)

the grades (0°=0), (1°=10) ... through (10°=1) & ...?
I don't know if it is notable enough to warrant a place in the article, but Aleister Crowley gave a grade 'above' Ipsissimus on page 25 of his table of correspondences included with 777 and other qabalistic writings.., though he did not give it a name; he included it in the 3rd order (of the Silver Star) & gave it's grade as (0=0°) (as opposed to probationer (0°=0) and all the rest with "°" before "", here "°" is after "". Nagelfar 16:09, 13 August 2007 (UTC)

As Crowley nowhere, to my knowledge, discusses such a grade, and as a case could be made for identifying the Probationer within the system with 0 in the key scale, I wouldn't want to discount a strong likelihood that this is simply a typo. There are certainly many others in Liber 777 as published by Crowley. Anlala 00:56, 15 August 2007 (UTC)

 * It's not a typo because its put alongside the grade of probationer on the opposite end, check it out yourself. Nagelfar 01:11, 29 August 2007 (UTC)

 * Nothing rules out the possibility of a typo on one, but not the other. The very nature of typos is such. However, assuming for the sake of argument, that he did mean it to signify some sort of degree beyond Ipsissimus linking back to Probationer, it's actual significance is nil, unless some authentic secret tradition exists that has never been published. Until such time as some such tradition is published, it still doesn't warrant mention in the article, though its inclusion on the Talk Page is certainly appropriate. Anlala 05:56, 2 October 2007 (UTC)

 * Which one or other are you referring to? It is clearly added as additional information in the source cited. Nagelfar (talk) 06:37, 9 December 2007 (UTC)

Hello All, editing of (0=0 Neophyte): I inserted an "y" instead of the "u". Ancient Greek (which I studied for several years ) used the "y" in this instance. The letter looks a bit like the modern "u". Oops, forgot to sign: -- Greek logos 08:46, 17 October 2007 (UTC)

Now I remember! The 15th Aethyr in Liber 418 tells of AC's visionary initiation into the grade of Magister Templi, 8=3°:

''Above the altar is a veiled Figure, whose name is Pan. Those in the outer tier adore him as a Man; and in the next tier they adore him as a Goat; and in the next tier they adore him as a Ram; and in the next tier they adore him as a Crab; and in the next tier they adore him as an Ibis; and in the next tier they adore him as a Golden Hawk; and in the next tier they adore him not7.''

And the footnote reads: ''That is, in the lowest grade of the Second Order 5x = 6{square x}, "God" is worshipped under the form of a man (Tiphareth). In 6x = 5 {squarex}, he seems as a goat (Mendes Kahn). In 7x = 4{square x}, a ram (Amoun). In 8x = 3{square x}, a crab (connected with the star sponge vision). In 9x = 2{square x}, an ibis (Thoth). In 10x = 1 {square x} a golden hawk (Ra Hoor Khuit). Above this (Kether), He is the Negative only.''

It reminds me of the later admission into the company of "atheists", 5th Aethyr. Dan (talk) 05:29, 19 January 2008 (UTC)

List of known members
What is the criterion for inclusion on this list, a documentation from Crowley of one's membership? a documentation from some other A∴A∴ claimant? or a self-identification? Grady McMurtry is included on the list, though I don't know of any documentation of his membership by Crowley or another, except McMurtry's own claim to be a Magister Templi. Phyllis Seckler said that McMurtry wasn't even a Neophyte of the A∴A∴ (which does leave open the possibility that he was recognized by her as a Probationer). Could anyone include themselves on the list by claiming to be a member? Anlala 05:00, 27 August 2007 (UTC)

- I don't personally trust the "Known Members" list. It definitely needs a citation, or removal. As far as I know, Regardie was never a member of the A.'.A.'. He joined the Stella Matutina around 6 years or so after parting ways with Crowely. What's more, in the "Introduction to the Third Edition" of "The Tree of Life - An Illustrated Study in Magic" (Edited and Annoted by Chic Cicero and Sandra Tabitha Cicero), it is stated that Crowely himself never formally trained Regardie as the latter had wished (I am paraphrasing this). And finally, as far as my research shows, Blavatsky was never a member of the A.'.A.'. either. I'll just remove that portion.71.53.129.111 (talk) 02:03, 14 January 2009 (UTC)

 * I have to agree with it needing either reputable citations or deletions. If there isn't some documentation, then that section should be wiped as it can't be proven. (A lot of these people are DEAD. Good luck finding the truth). Also, forgive me if I'm wrong...but I thought the names of A.'.A.'. members weren't supposed to be made public in the first place. FUTURI (talk) 16:44, 5 August 2011 (UTC)

FUTURI, where did you get the idea that the names of A∴A∴ members were not supposed to be made public? In Crowley's Class D publication of the Tasks of every grade from Probationer to Dominus Liminis he clearly states that "He [that is, the A∴A∴ member] shall everywhere proclaim openly his connection with the A∴A∴ and speak of IT and Its principles ..." Anlala (talk) 01:29, 24 August 2011 (UTC)

Name of the A∴A∴
It currently reads "The A∴A∴ (Arcanum Arcanorum)", though this is arguable, which should be put into the article itself. It should have the previously added "Latin: Argenteum Astrum or Greek: Αστρον Αργον, "Astron Argon", literally; "Silver star" in addition also.

Both are, according to wikipedia standards, attestable and note worthy, and all have been used in the literature surrounding the A∴A∴, to omit any well known attestable variation as such is going against the fiber of wikipedia. It seems on articles like this, pseudo-intellectual, secretive and self-interested types edit mercilessly to the detriment of the purpose behind the wikipedia project; to dispense information on the topic rather than instead monopolize or make exclusive some socially engineered view. Nagelfar (talk) 06:43, 9 December 2007 (UTC)

 * I'm yet again being bold in this matter before a counter-argument or consensus, but I really do not understand the difficulty besides the demographic here on the subject matter relating to the addition of this information. Nagelfar (talk) 06:56, 9 December 2007 (UTC)

 * Is it improper to point out that "astron argon" doesn't mean "silver star" in Greek? Silver would be "arguron." "Argon" means "shining."Antaios632 (talk) 19:49, 23 January 2008 (UTC)
 * That certainly sounds like a fact we should add. But we'd want a source, perhaps a Greek dictionary of some kind. Google just gives "lazy" or "inactive". Dan (talk) 21:01, 25 January 2008 (UTC)

Where does Angel and Abyss" come from? The citation (8) says "Nowhere in Crowley's writings does it say what A.'.A.'. stands for." The rest are common speculations and have good sources, but I have never heard Angel and Abyss and the citation isn't useful at all. Maybe this should be removed as original research? 70.181.242.86 (talk) 07:01, 7 November 2010 (UTC)
 * Agreed 209.134.115.80 (talk) 04:59, 10 February 2011 (UTC)
 * Just found a reference to it and added. I know it's not by Crowley, but neither are some of the others. 209.134.115.80 (talk) 22:58, 10 February 2011 (UTC)

The very-most veritableness
Ipsissimus doesn't quite mean anything to do with "self", which in Latin is rather "Sui-", but is in-fact much more subtle and unqualified in meaning than such, as per how "Ipsissima verba" means "the very words", not the "very identity of the words" or "the very entity of those words" et cetra... (However an Ipsissimus is an Iussuissimus, or law/ius- unto self/sui-, of the utmost possibility to be.) 67.171.248.22 (talk) 00:07, 9 September 2010 (UTC)

Seal?
Anyone else think it would make sense to use the seal of A.'.A.'. as the image on this page? 70.181.242.86 (talk) 06:59, 7 November 2010 (UTC)

 * Seems logical, Captain. FUTURI (talk) 00:55, 27 July 2011 (UTC)
 * I added it. FUTURI (talk) 01:20, 27 July 2011 (UTC)

Lineages
Stealthepiscopalian has been waging a low grade edit war on these pages - removing legitimate external links to A.'.A.'. lineages. I suggest that he immediately cease and try and seek consensus.

The existence of other lineages such as the Bennett lineage or the Charles Stansfeld Jones is factual and common knowledge. The fact that no-one has yet thought to write about them in a book is not relevant as the fact of their existence is not in question nor controversial. — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 19:50, 14 January 2014 (UTC)

 * 'common knowledge' is insufficient as a standard for Wikipedia data.-- self-ref (nagasiva yronwode) (talk) 23:09, 14 January 2014 (UTC)

Does anyone else think that it is unacceptable for one lineage of the AA to "own" a Wikipedia article? There are plenty of books (including Book 4) that mention various people other than Jane Wolf as students of Aleister Crowley. Why is Stealthepiscopalian being allowed to vandalize this page by removing links to existing groups of people working towards the goals of the order? I suggest that every AA lineage should be allowed to list its link. — Preceding unsigned comment added by SororSvetlonos (talk • contribs) 04:29, 15 May 2014 (UTC)

"Lineages" and there are a number on this page require, by Wikipedia's standards, to be verified by secondary sources. See above for a discussion of this matter. Simply including a claimant without any kind of outside evidence is a direct violation of Wikipedia policy on any kind of information. The link you provided doesn't even provide its own bona fides, and is not cited by any independent source. Therefore it is not something that is acceptable. ~ChoronzonClub~ — Preceding unsigned comment added by Choronzonclub (talk • contribs) 22:25, 15 May 2014 (UTC)

The A.'.A.'. and the Seven Palaces of the Merkabah Mystics.
"The holy book of the order is Liber AL vel Legis (in English, The Book of the Law). This book and many others issued by the A.'.A.'. contains encrypted material derived from the Seven Palaces of Merkabah mysticism, rather than the Kabbalistic Tree of Life used by the O.T.O."

The fact that A.'.A.'. issued texts that are encrypted should not be controversial. Again - it's common knowledge, not in dispute, and therefore not in need of citation although we could cite Crowley umpteen times on this matter.

I am an initiate of the A.'.A.'. and the Golden Dawn. If anyone would like to challenge the factual basis of my claim that the System of the A.'.A.'. is based on the Merkabah Seven Palaces rather than the Kabbalistic Tree of Life, then please provide your reasons for doing so before demanding book citations be produced for initiated and previously secret knowledge. Prove the A.'.A.'. is based on the Tree of Life or be Silent.

If you don't know that .'. means the holder (whether an organisation or an individual) is in possession of the Lost Word - now you do. Ask any Master Mason. In this case it is the A.'.A.'. which is in possession of the Lost Word. The A.'.A.'. has no name other than the two Alephs extracted from the Lost Word since names do not apply above the Abyss.

The Lost Word has always been associated with the Merkabah rather than the Kabbalah. It is the 'secret doctrine' talked of by Waite. If it surprises anyone that the Inner Order system of the A.'.A.'. is based on the Merkabah rather than the Tree of Life then they should read Liber Al vel Legis again - "Thus ye have star & star, system & system; let not one know well the other!"

Think carefully before being pedantic on this issue. Review the matter and look at the page - considering how much I could be pedantic about on this and other pages if I was of the mind...

Thank you. A .'. 93 93/93. — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 20:26, 14 January 2014 (UTC)

 * original research is insufficient support for data addition to Wikipedia.-- self-ref (nagasiva yronwode) (talk) 23:10, 14 January 2014 (UTC)

"Think carefully before being pedantic on this issue. Review the matter and look at the page - considering how much I could be pedantic about on this and other pages if I was of the mind..."

Is this some kind of veiled threat? This user signed up today and began violating Wikipedia policies, without clearly having read them. Most of this: original research, lineages links, numerological justifications, and the lost word have been hashed out before in talk here. If the person calling themselves Alrah had bothered to read the Wikipedia policies and the history of this article she might have known that. These are suspiciously like another batch of edits by another Alrah about six months ago that were similarly motivated by original ideas not supported by secondary or even primary sources. https://en.wikipedia.org/w/index.php?limit=50&tagfilter=&title=Special%3AContributions&contribs=user&target=Dara+Allarah&namespace=&tagfilter=&year=2014&month=-1

comment added by User:Stealthepiscopalian —Preceding undated comment added 01:18, 15 January 2014 (UTC)

Alrah I am going to give you the benefit of the doubt, but your comments and reactions are quite similar to the Dara Allarah that Stealthepisopalian is referring to. Wikipedia is an encyclopedia and is therefore necessarily pedantic and conservative by nature, expecting sources and being free from original research as obvious as its conclusions might seem to you. I am curious though how you are labeling this Merkavah and how you are even bringing the Seven Palaces into it. Your conclusions seem completely alien to such common sources for Merkavah like III Enoch, Giktala or Rabbi Akiva. There are no paths for instance and the Seven Palaces are a later cabalistic construct unrelated directly to Merkavah. It is true that the second ascension of the Merkavah begins with aleph aleph followed by aleph bet, aleph gimel etc. but what this could possibly have to do with the initials of the Order A.'.A.'. when Crowley clearly states in numerous places they are the initials for actual words is confusing to me. Likewise your assertion about the Lost Word; it is simply false. For instance The Great Architect of the Universe is commonly rendered in Freemasonry as G.'.A.'.O.'.T.'.U.'. (see Pike and Mackey) and it is a title of God, not an order at all. The Lost Word, in any case, is a Masonic trope, lost in the Master Mason degree so that it can be recovered in the Royal Arch. It really isn't lost at all, and certainly O.T.O. claims to have it, so your comparison is false on its face. Etc. etc. which is why your original research just doesn't meet Wikipedia standards. It's just that: original, not substantiated, not peer reviewed and clearly wrong in some cases about which your aren't an expert. I do invite you to be as pedantic as you will in your own edits though, please cull anything that cannot be substantiated, that is what Wikipedia edits are for and certainly add anything you can back up from secondary, esp. academic source. comment added by User:choronzonclub —Preceding undated comment added 02:54, 15 January 2014 (UTC)

 * I can answer all of your enquiries on Crowley's use of the Lost Word and the Merkabah, CC but is this the proper place? I invite you to join the FB A.'.A.'. group to discuss these matters if you will.  The Lost Word or true Name of God isn't just a Masonic thing.  Actually they have used substitute words for the MM and the Royal Arch for years so this shouldn't affect them.  The true name of God was hidden by the Jewish mystics.  It appears on the palaces of the Merkabah when you decrypt the Zohar.  It's the EL & Hadad pantheon of course, and the Palaces & paths are derived from ancient Babylonia - originally they were the 14 path of Inanna.  Hekhalot, is a loan word from Akkadian ekallu, "palace."  If you are interested I have a short article on the Zohar & Liber Al decryptions here:  http://www.paganspace.net/forum/topics/the-temple-of-solomon-the-lost-word-and-the-key-of-it-all  and I've keyed some of Crowley's texts to the Merkabah too on the 'Let it Fill me' FB page.  Just scroll down below the Tom Schuler lectures on the Tree of Life for them.  https://www.facebook.com/pages/Let-it-fill-me/253134744759426?fref=ts .  Crowley took the Merkabah and used it as a basis for his A.'.A.'. system but he's changed it for the New Aeon.  Best,  Alrah.  93 93/93.       Alrah Fraser (talk) 07:52, 15 January 2014 (UTC)

I'm really glad that you all feel so strongly about having good citations in an article, but I'm puzzled by the fact that you've left uncited material on the page since May 2013 and in some cases 2008! With so much work to do citing your own stuff I'm surprised you can be bothered to object to mine and instantly delete it. That smacks of something.... well... :-)

I'll be back in 3 days to delete the rest of the material without citations on the page as by your own pedantic criteria - it's obviously not up to standard. Is it? A .'. 93 93/93 — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 04:25, 15 January 2014 (UTC)

clearly Alrah is not only threatening the integrity of Wikipedia but conducting a campaign of vandalism. — Preceding unsigned comment added by Stealthepiscopalian (talk • contribs) 05:37, 15 January 2014 (UTC)

Vandalism by Alrah
Can someone please revert to good faith edits before user Alrah Fraser vandalized this article. — Preceding unsigned comment added by 75.170.4.196 (talk) 05:24, 15 January 2014 (UTC)

I've deleted material that was uncited since May 2013 and in some cases 2008 as well as someone that presented their own argument (counts as original research). This isn't vandalism. It's a much needed clean up. — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 05:41, 15 January 2014 (UTC)

Please stop vandalizing this page.
Please Alrah, stop using this page as your personal catbox. Mvmontgomery (talk) 05:51, 15 January 2014 (UTC)

I haven't vandalised the page and I resent the allegation. I've deleted material that has lack citation for years! I've also corrected when I could and placed appropriate refs. I also changed an entry unsupported by the reference.

For instance: " While the A ∴A∴ is not part of Ordo Templi Orientis, O.T.O. does consider the A∴A∴ to be a close ally." - This was cited from 1909 while it spoke in the present tense.

In Ipsissimus section someone started debating the topic and presenting their own original research!

You don't like uncited material and original research so you should all be patting me on the back right now and saying 'well done Alrah' for doing a much needed clean up of the page. I should get a barnstar for this not your complaints. Alrah Fraser (talk)

Alrah is capriciously vandalizing these pages.
This is not the place for your independent "research", nor is it your place to make wholesale changes on the page. You do not speak for everyone in the A A and I find what you are doing extremely offensive, as is your crowing on FB about it. Don't worry, I already saved the thread. Mvmontgomery (talk) 06:12, 15 January 2014 (UTC)

The page was largely unsourced for years. I've deleted the uncited material. I'm well within Wiki guidelines on good practise by doing so and I don't give a flying fig if you're offended by that. There isn't one set of rules for you and another set for me you know. You can scream vandalism all you like but it's actually a clean up and an impartial wiki editor would thank me for it. I suggest that you work on adding material to the page that can be cited - and with more than primary sources too - rather than wasting your time complaining about a perfectly good clean up. — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 06:32, 15 January 2014 (UTC)

"Aleister Crowley's Secret Temple. Posted by Dara Allarah on October 3, 2012 at 4:30pm in Religious Mysticism" so you are the Dara Allarah that was involved in numerous edit wars. I suspected as much. It claimed to be a he and back in the alt.magick on usenet days Jason Scott Dean. Interesting level of dishonesty you perpetrate. Choronzonclub — Preceding unsigned comment added by Choronzonclub (talk • contribs) 23:08, 15 January 2014 (UTC)

 * Exaggeration and ad hominem attacks?  That's a sign of a weak position.  I was briefly involved in ONE edit war, but I suspect you are a regularly perp.  I have no idea who Jason Scott Dean is; I have never used sock puppets; nor did I ever pretend to be a 'he'.  But if all you can do is slander me and pull bizarre fantasies about me out of your ass instead of concentrating on the debate then you're just trolling wiki and you need to retire from this conversation.  — Preceding unsigned comment added by Alrah Fraser (talk • contribs) 05:05, 16 January 2014 (UTC)

Not a Religious Order
Wikipedia's page on "Religious order" states that: "A religious order is a lineage of communities and organizations of people who live in some way set apart from society in accordance with their specific religious devotion."

The A∴ A∴ and it's members do not conform to this definition.

Wikipedia's page on "Fraternity" states that: "A fraternity (or fraternal organization) is an organized society of men associated together in an environment of companionship and brotherhood; dedicated to the intellectual, physical, and social development of its members."

The A∴ A∴ is clearly a "Fraternal organization".

I intend to change the article to reflect this. PedroLamarao (talk) 14:47, 16 January 2014 (UTC)

Or perhaps a "Secret society", though it is not meant to be secret. PedroLamarao (talk) 14:54, 16 January 2014 (UTC)

I agree the present phrasing is both imprecise and unfortunate. 'Fraternity' has general implications that don't really apply to A∴ A∴ either. It doesn't meet in groups like say the Odd Fellows, a Martial Arts studio, an Athenian Symposium etc. I like the phrase Teaching Order https://en.wikipedia.org/wiki/Teaching_order but it has extremely Roman Catholic overtones. Stealthepiscopalian Stealthepiscopalian  — Preceding unsigned comment added by Stealthepiscopalian (talk • contribs) 20:17, 16 January 2014 (UTC)

There's isn't a good 'social first' label for the A.'.A.'. - It's an open access system which is either followed by lineages descending from Crowley and his primary pupils or is worked through by independent persons. Therefore it's not primarily defined by external social organisation but by the internal initiation of individuals. — Preceding unsigned comment added by 188.30.197.47 (talk) 21:14, 16 January 2014 (UTC)

I agree there is no excellent choice. But "Religious organization" is less than good, it is actually bad. I agree also that the expression "Teaching order" has the best literal meaning, but, as pointed, it 's encyclopaedic definition is still religious. "Fraternal organization" is the most neuter name, and the corresponding article makes clear how broad in meaning in the term. One option is to link to the diambiguation page: Fraternity_(disambiguation) Can we change this? PedroLamarao (talk) 20:03, 22 January 2014 (UTC)

History of the Order
I am working on an expanded section on the History of the Order. My objective is to increase the amount of time covered to match the History Lection. My work in progress is here: User:PedroLamarao/History_of_A⸫_A⸫. Please, feel free to comment and criticize. (I am sorry for the unusual glyph in that page's name. That is the ONE DOT OVER TWO DOTS PUNCTIATION character. I am used to writing the abbreviated name of the Order with it, by all my systems have additional fonts installed. I wasn't thinking when I started that page. ) PedroLamarao (talk) 21:04, 27 January 2014 (UTC)

Name section and POV
Is the Name section of this article perhaps a bit POV? It seems like the vast bulk of the table is based entirely on Eschelman's writings. Is he the only source aside from Crowley (and, barely, de Camp) for public discussion of the meaning of the name? --Geoff Capp (talk) 23:29, 11 September 2014 (UTC)

Frater Sabazius X°: O.T.O. and A∴A∴
Would it be of note and relevant for the article that Fra. Sabazius has established the Gunther line from London as the single recognized administration of A∴A∴ as far as it concerns the purposes of O.T.O.? http://www.invisiblebasilica.blogspot.co.uk/2015/07/oto-and-aa.html viciarg ᚨ 12:18, 2 December 2015 (UTC)

I think that recognition would be relevant if the whole passage or at least the provisos are quoted as well. Just stating it will imply that the recognition is blanket and it is clearly not. The conclusion: "It is not the place of the O.T.O. to judge the spiritual merits or ultimate “validity" of these various claimants, but it is also not the case that O.T.O. can have a “close alliance” and working relationship with a multiplicity of A∴A∴ administrations." is critically important to understanding the 'administrative' recognition, as opposed to the absolute recognition. Stealthepiscopalian 19:38, 7 January 2016 (UTC)Stealthepiscopalian

External links modified
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title: Talk:A∴A∴


text:
User talk:Serge K. Keller

Welcome
Hello Serge, welcome to Wikipedia.

You might find these links helpful in editing pages or creating new ones: How to edit a page, Tutorial, Naming conventions, Manual of Style. You should probably read our policies at some point too.

But don't feel you have to read every policy document before you do anything. Dive in, be bold in editing, and if you do anything wrong, someone will be quick to correct it and let you know (hopefully, politely!)

If you have any questions, see the help pages, add a question to the village pump or ask me on my talk page. I hope you enjoy editing here and being a Wikipedian!

You may have already noticed that you can sign your name using three tildes, like this:. If you use four, you can add a datestamp too, as I've done below. This is mostly useful, and is considered good wikiquette, on talk pages. But be aware that the actual wikipedia articles should never be signed - they belong to the community, rather than the individual who created them.

Again, welcome! --   ALargeElk | Talk 11:40, 3 Jun 2004 (UTC)

User categorisation
You were listed on the Wikipedians/Switzerland page as living in or being associated with Switzerland. As part of the User categorisation project, these lists are being replaced with user categories. If you would like to add yourself to the category that is replacing the page, please visit Category:Wikipedians in Switzerland for instructions. --Army1987 12:31, 2 September 2005 (UTC)

Translation of Rodovid.org
Hi there, I find your user page using Wikipedians/Translators. I am working on the project proposal Rodovid.org and want to have it translated into as many languages as posible. If you could help with translation, add your name to Rodovid.org/translation and please, go ahead, translate the page. I would greatly appreciate your help.--Bjw e bb (talk) 14:49, 27 March 2006 (UTC)

Translation
Hello! A while ago you signed up to help translate articles from other Wikipedias at Translators available.

This page has since become obsolete and has been replaced by two userbox templates.

If you are still interested in translating, you may sign up again by using one of the following userboxes on your userpage :

'''

We hope to see you soon on Translation!

Hi, I need a native translation of a sentence, into French

 * 1) The sentence is: "Welcome to the first stage, of the fourth international program of MAL's method, the internatinal training course of MAL, 2021"
 * 2) By "program" I mean, like in: "governmental program", or "educational program", and the like.
 * 3) By "stage" I mean: phase/part/step (Actually the "program" consists of a few stages).
 * 4) I know to use GoogleTranslate, but I need a native translation.
 * 5) Additionally, I would like to know how to pronounce the whole translated sentence (including "2021"), so please add also the transcription in IPA (or in Latin letters, as close to the original pronunciation as possible - if you are not familiar with IPA). Please mark also the stress, e.g. by adding an apostrophe before the stressed syllable (or by typing the stressed vowel in a capital letter).

185.24.76.178 (talk) 18:33, 9 December 2021 (UTC)

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

title: User talk:Serge K. Keller


text:
Nek Chand

Nek Chand Saini (15 December 1924 – 12 June 2015) was a self-taught Indian artist, known for building the Rock Garden of Chandigarh, an eighteen-acre sculpture garden in the city of Chandigarh.

Early life and background
Nek Chand hailed from Shakargarh tehsil. Shakargarh was previously in Gurdaspur district in British India, but now falls in district Narowal in Pakistan. His family moved to India in 1947 during the Partition. They moved to Chandigarh in 1955. At the time, the city was being redesigned as a modern utopia by the Swiss/French architect Le Corbusier. It was to be the first planned city in India, and Chand found work there as a roads inspector for the Public Works Department in 1951.

He was awarded the Padma Shri by Government of India in 1984. He died in 2015.

The Rock Garden is one of the most famous sites in India. Chand, its creator, died in 2015, but it is still visited by millions of people every year.

In his spare time, Nek Chand began collecting materials from demolition sites around the city. He recycled these materials into his own vision of the divine kingdom of Sukrani, New Delhi choosing a gorge in a forest near Sukhna Lake for his work. The gorge had been designated as a land conservancy, a forest buffer established in 1902 that nothing could be built on. Chand's work was illegal, but he was able to hide it for eighteen years before it was discovered by the authorities in 1975. By this time, it had grown into a 13 acre complex of interlinked courtyards, each filled with hundreds of pottery-covered concrete sculptures of dancers, musicians, and animals. Chand built up the mass with a cement and sand mix made from recycled materials before adding a final coating of smoothly burnished pure cement combined with waste materials such as broken glass, bangles, crockery, mosaic, and iron-foundry slag. His work was in serious danger of being demolished, but he was able to get public opinion on his side, and in 1986 the park was inaugurated as a public space. Chand was given a salary, a title ("Sub-Divisional Engineer, Rock Garden"), and a workforce of 50 laborers so that he could concentrate full-time on his work. It even appeared on an Indian stamp in 1983. The Rock Garden is still made out of recycled materials; and with the government's help, Chand was able to set up collection centers around the city for waste, especially rags and broken ceramics.

When Chand left the country on a lecture tour in 1996, the city withdrew its funding, and vandals attacked the park. The Rock Garden Society took over the administration and upkeep of this unique visionary environment. The garden is visited by over five thousand people daily, the second most popular location in India (after the Taj Mahal) with a total of more than twelve million visitors.

Exhibitions
Chand's statues have found their way into museums across the world, including an environment at the Capitol Children's Museum in Washington, D.C., the American Folk Art Museum in New York City and the main entrance to the Collection de l'art brut in Lausanne, Switzerland. The John Michael Kohler Arts Center in Wisconsin, USA owns the largest collection of Chand's work outside of Chandigarh. The pieces were on exhibition there from June 2007 to January 2008 as part of the museum's focus on artist environment builders, or outsider artists.

An exhibition of Chand's work also took place at the Royal Institute of British Architects (RIBA) gallery in Liverpool, England from 16 April to 11 May 2007. The exhibition displayed survey drawings of the garden's architecture and landscaping, and plans to be a travelling exhibition.

Numerous Nek Chand sculptures are also displayed in the gardens and on the walkways of the campus of the American Embassy School in New Delhi.

There is a Nek Chand Foundation in London founded to raise funds for the garden.

title: Nek Chand


text:
Talk:Lita (wrestler)

Breast augmentation in article
Other then Michael Jackson does anyone ever mention a man's plastic surgery in their bio? Who cares about her boob job and why is it notable? 184.175.47.208 (talk) 07:14, 8 February 2023 (UTC)

Lita's ethnicity
I notice that in the article someone said that Lita is Mexican and Puerto Rican descent. The references they used does not mention her descent other than her parents' names and where she was born. Lita's last name Dumas is French. I am not denying that she isn't Mexican or Puerto Rican too. Her skin is white and is American but there are Mexicans/Puetro Ricans that are white too coming from Spain. Maybe her ancestors were born in France and moved to Spain before coming to Florida and Latin America. It's important to have citations for her descents. Somebody maybe was fooling around and decided to use the Mexcian-Puerto Rican descent for Lita's wrestling background. Please, please before putting someone ethnicites have citations to prove that it's true.Kingzwest (talk) 16:13, 3 October 2023 (UTC)(talk)

title: Talk:Lita (wrestler)


text:
Doolin

Doolin is a coastal village in County Clare, Ireland, on the Atlantic coast. It is southwest of the spa town of Lisdoonvarna and 4 miles from the Cliffs of Moher. It is a noted centre of traditional Irish music, which is played nightly in its pubs, making it a popular tourist destination. There are numerous nearby archaeological sites, many dating to the Iron Age and earlier. Doonagore Castle and Ballinalacken Castle are also in the area. The area was officially classified as part of the West Clare Gaeltacht (an Irish-speaking community) prior to the 1950s, and maintains a connection with Irish-speaking areas - including via its maritime connection with the Aran Islands.

Layout
The village of Doolin does not have a defined centre, comprising a number of "scattered" sections:
 * "The Harbour" is the departing point for boat trips to the Aran Islands and the Cliffs of Moher. There is also a campsite nearby
 * "Fisher Street" has O'Connor's Pub and several shops and hostels.
 * "Fitz's Cross" has a hostel, campsite, two new hotels and another pub which opened in 2006
 * "Roadford" has McGann's and McDermott's pubs, four restaurants, two hostels and a number of B&Bs. Trips to Doolin Cave are also run from here.

The Aille River runs from the hills of the Burren down past Doolin to meet the sea. The small Crab Island is a short distance out from Doolin Harbour, barren except for the remains of an early 19th-century stone constabulary outpost.

Doolin Cave
The Great Stalactite, measuring 7.3 metres, was discovered in 1952. According to the Doolin Cave website, it is the largest stalactite in the Northern hemisphere. Owing to environmental protection measures, concurrent visitor numbers are limited to 20 per tour.

Surfing
Doolin is a noted surfing destination. A break which generates Ireland's biggest wave, 'Aill na Searrach', is just off the Cliffs of Moher. The wave features in the movie Waveriders. Crab Island is also a local surfing spot.

Rock climbing
As well as serving as an accommodation centre for visitors to the major limestone rock climbing area of Ailladie (most climbs at or above E1 5b), a short 8 km drive away, Doolin has its own less-popular sea-cliff rock-climbing area, with several routes recorded. Like Ailladie, the cliffs are single-pitch steep limestone; however the rock is not of a high quality, the cliffs are tidal, and access is not as easy. There are also several smaller inland crags scattered throughout the Burren region (e.g. Ballyryan, Murroughkilly, Aill na Cronain and Oughtdarra), and some good bouldering to be found along the coast, most notably at Lackglass, which was first bouldered in April, 2005.

Pubs
Pubs in Doolin include Fitzpatricks, Gus O'Connor's, McDermott's, and McGann's. The Micho Russell Festival Weekend is held each year after the last Friday in February.

Dining
The restaurant Homestead Cottage received a Michelin star in 2023.

Ferry
Doolin is one of three places (Galway and the village of Rossaveal on the northwest shore of Galway Bay are the others) with ferry services to the Aran Islands, which are visible from the town. A ferry service also brings tourists to the base of the Cliffs of Moher from Doolin Pier. There is also an Irish Coast Guard station at Doolin Pier.

Bus
As Doolin is close to the Cliffs of Moher, a bus service between Galway and Ennis calls at both Doolin and the cliffs in each direction. Bus Éireann route 350 links Doolin to Ennis, Ennistymon, Cliffs of Moher, Lisdoonvarna, Fanore, Kinvara and Galway. There are a number of journeys each way daily. Onward rail and bus connections are available at Ennis and Galway.

Road
Two regional roads serve the village. The R479 connects the village both with coastal areas to the north and with Lisdoonvarna to the east. The R459 connects the village to the Cliffs of Moher, the Burren Way and the Inisheer ferry port.

People
Musicians associated with Doolin, who have lived there or played in its pubs, include Micho Russell and his brothers Packie and Gussie, Sharon Shannon, Davy Spillane, and Steve Wickham of The Waterboys.

Popular culture
Doolin is the main setting for the 2007 PlayStation 3 game Folklore. According to the game's storyline, the Netherworld, the world of the dead is a realm that can only be accessed from one place in the world, the sea-side village of Doolin.

The Celtic band Gaelic Storm has a fiddle tune which references the town called "The Devil Went Down to Doolin" (presumably a play on the popular song The Devil Went Down to Georgia) on their album Herding Cats.

title: Doolin


text:
Yul

Yul or YUL may refer to:

 * Yul (name), including a list of people with the name
 * YUL, the IATA airport code of Montréal–Pierre Elliott Trudeau International Airport
 * YUL Condos, a residential high-rise in downtown Montreal
 * Yul, a fictional kingdom from the Korean novel Hong Gildong jeon
 * Yul Kwon, an American television host and former Survivor contestant
 * Yuen Long station, Hong Kong, MTR station code

title: Yul


text:
Operation Phoenix

Operation Phoenix or Phenix may refer to:

Military

 * Phoenix Program, CIA military, intelligence, and internal security program during the Vietnam War
 * Vela incident, alleged 1979 Israeli-South African nuclear test that was supposedly codenamed "Operation Phenix"
 * Project Phoenix (South Africa), SANDF project to revitialise the Reserve Force
 * Operation Phoenix (South Africa), South African response to mass SWAPO infiltration of South-West Africa
 * 2008 Colombian raid into Ecuador, codenamed Operación Fénix (Operation Phoenix)
 * Operation Phoenix (1966), Vietnam War military operation, February 1966 in Biên Hòa Province
 * Operation Phoenix (1995), Croatian Army defence of Slavonia during Operation Storm

Other

 * Operation Phoenix (railway), Victorian Railways post-war rebuilding project commenced in 1950
 * Operation Phoenix (album), album by Good Riddance
 * Operation Phoenix (game expansion), a game add-on for Counter-Strike: Global Offensive

title: Operation Phoenix


text:
Dusty Hare

William Henry "Dusty" Hare (born 29 November 1952) is a former international  rugby union footballer who played fullback.

Hare holds the world record for points scored in a first-class rugby career, with 7,337 points.

He was born in Newark-on-Trent, Nottinghamshire and attended the Magnus Grammar School (now Magnus Church of England School).

Rugby career
Hare played for Newark RUFC & Nottingham R.F.C. before joining Leicester Tigers and playing nearly 400 games for them.

He made his England debut 16 March 1974 in a match against Wales, and played his final game ten years later on, having gained 25 caps. He toured with the British Lions to New Zealand in 1983.

He retired from club rugby after the 1989 cup final loss to Bath, and is now the chief scout at Northampton Saints. Previous to this job, Hare was a farmer in South Clifton, Nottinghamshire and had been since a young man carrying on the family business. However, Hare sold the farm in 2001 to take a full-time job at Leicester Tigers working for the academy and latterly as head scout.

In January 2010 it was announced that he was to join Northampton Saints. He returned to Tigers in 2017

Cricket career
Hare was also a good cricketer, and he played ten first-class and seven List A matches for Nottinghamshire between 1971 and 1977. He played regularly for the Nottinghamshire Second XI and Under-25s between 1969 and 1978.

title: Dusty Hare


text:
Ásmundur Sveinsson

Ásmundur Sveinsson (20 May 1893 – 9 December 1982) was an Icelandic sculptor, whose works include “Thor's gavel”, the ornate gavel used by the President of United Nations General Assembly.

Early years
Ásmundur Sveinsson was born in Kolsstadir in West Iceland on 20 May 1893. In 1915 he moved to Reykjavík where he enrolled in the Technical College of Iceland and apprenticed with sculptor Ríkarður Jónsson for four years. In 1919 he relocated to Copenhagen, Denmark, and from there to Stockholm, Sweden, where he enrolled in the Academy of Fine Arts where he remained for six years, much of it spent studying with sculptor Carl Milles. In 1924 he married sculptor Gunnfríður Jónsdóttir. He and Gunnfríður divorced several years later. After graduating from the Academy, Ásmundur moved to Paris, France where he continued his study, here under the sculptor Charles Despiau.

Work
Ásmundur returned to Iceland in 1929 and began producing a series of abstracted figurative works. His themes were often men and women at work and included such pieces as, The Blacksmith, The Washer Women, and The Water Carrier. During the 1940s Ásmundur's work moved even farther away from the human and animal form that had been his mainstay until then and by the 1950s he was producing work that was almost entirely abstract.

Like many Icelandic artists, he drew upon the traditions of his native country when seeking subjects to inspire him. In 1939, for example, Ásmundur's sculpture of Guðríðr Þorbjarnardóttir and her son Snorri was displayed at the New York World's Fair. Casts of his original smaller scuplture of the pair were later installed in Iceland, at both Glaumbær and Laugarbrekka, and gifted to the Canadian government and the Vatican. Other works of Ásmundur's drawing on Icelandic traditions include Trollwoman (1948), Head Ransom (1948), based on a poem that Egil Skallagrimsson purportedly composed to save his own head, and Hel-Ride (1944) taken from the Prose Edda of Snorri Sturlusson. His Sæmundur and the Seal, also in this vein, is situated in front of the main building of the University of Iceland in Reykjavík.

Generally, the artist believed in placing works of art not only in the hands of a small elite, but also in making them accessible to the public. Other works of Ásmundur Sveinsson are to be found on the hill Öskjuhlíð near Perlan in Reykjavík or at the farm of Borg á Mýrum near Borgarnes. The abstract sculpture here represents the saga hero Egill having his dead son in his arms. The title Sonartorrek is referring to a poem which Egill Skallagrimsson wrote about this scene. Ásmundur died in Reykjavík on 9 December 1982. In 2015, his statue of poet Einar Benediktsson was moved to a spot near Höfði house in Reykjavik, where the poet had lived.

Ásmundarsafn
The former house of the artist in Laugardalur, Reykjavík, has been installed as a museum, called Ásmundarsafn. The house was constructed from 1942 until ca. 1958 in three parts, based on designs drawn by the artist who was a fan of the Bauhaus style. He lived there through most of his life with his second wife, Ingrid Sveinsson. The house is slightly reminiscent of Le Corbusier and his chapel of Ronchamp. The sculpture garden nearby is open to public.

title: Ásmundur Sveinsson


text:
User:MrJones/vptest

'''STOP! Read the following to find out where to post:'''

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title: User:MrJones/vptest


text:
Carlos Orta

Carlos Orta (1944–2004) was a dancer, choreographer and teacher with the José Limón Dance Company in New York since 1979. Mr. Orta was born in Caracas, Venezuela, and trained at the Scola Cantorum in Paris. He also later studied with Pina Bausch at Germany's Folkwang Hochschule.

He was the founder and director of the Corearte Dance Company of Venezuela, a dance troupe which performed his original moves, often based on Venezuelan folk dances.

He won the International Academy of Dance's choreography award in Cologne, Germany, and Venezuela's Prize of Dance. Orta also taught at Long Island University and Manhattanville College.

title: Carlos Orta


text:
CatB

CatB may refer to:

 * The Cathedral and the Bazaar, an essay, and later a book, by Eric S. Raymond on software engineering methods
 * Catb.org, the website of Eric S. Raymond
 * Cathepsin B, an enzymatic protein
 * Catfish and the Bottlemen, a British indie rock band

title: CatB


text:
User talk:Bakra~enwiki

Hi there, welcome to Wikipedia, Bakra!

This image is okay on Wikipedia... its deemed "fair use" being essentially free promotion for the show, and being a screen-shot of the program. See fair use.

Anyway, welcome, user:zanimum

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Bakra. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Bakra~enwiki that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name. If you think you might own all of the accounts with this name and this message is in error, please visit Special:MergeAccount to check and attach all of your accounts to prevent them from being renamed.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 22:22, 19 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 10:52, 22 April 2015 (UTC)

title: User talk:Bakra~enwiki


text:
User:APH

 * I plan to work any topic that I will find interesting.
 * The science pearls project is my favorite.
 * Please, join and help.

title: User:APH


text:
Fletcher's checksum

The Fletcher checksum is an algorithm for computing a position-dependent checksum devised by John G. Fletcher (1934–2012) at Lawrence Livermore Labs in the late 1970s. The objective of the Fletcher checksum was to provide error-detection properties approaching those of a cyclic redundancy check but with the lower computational effort associated with summation techniques.

Review of simple checksums
As with simpler checksum algorithms, the Fletcher checksum involves dividing the binary data word to be protected from errors into short "blocks" of bits and computing the modular sum of those blocks. (Note that the terminology used in this domain can be confusing. The data to be protected, in its entirety, is referred to as a "word", and the pieces into which it is divided are referred to as "blocks".)

As an example, the data may be a message to be transmitted consisting of 136 characters, each stored as an 8-bit byte, making a data word of 1088 bits in total. A convenient block size would be 8 bits, although this is not required. Similarly, a convenient modulus would be 255, although, again, others could be chosen. So, the simple checksum is computed by adding together all the 8-bit bytes of the message, dividing by 255 and keeping only the remainder. (In practice, the modulo operation is performed during the summation to control the size of the result.) The checksum value is transmitted with the message, increasing its length to 137 bytes, or 1096 bits. The receiver of the message can re-compute the checksum and compare it to the value received to determine whether the message has been altered by the transmission process.

Weaknesses of simple checksums
The first weakness of the simple checksum is that it is insensitive to the order of the blocks (bytes) in the data word (message). If the order is changed, the checksum value will be the same and the change will not be detected. The second weakness is that the universe of checksum values is small, being equal to the chosen modulus. In our example, there are only 255 possible checksum values, so it is easy to see that even random data has about a 0.4% probability of having the same checksum as our message.

The Fletcher checksum
Fletcher addresses both of these weaknesses by computing a second value along with the simple checksum. This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum. Both sums start with the value zero (or some other known value). At the end of the data word, the modulus operator is applied and the two values are combined to form the Fletcher checksum value.

Sensitivity to the order of blocks is introduced because once a block is added to the first sum, it is then repeatedly added to the second sum along with every block after it. If, for example, two adjacent blocks become exchanged, the one that was originally first will be added to the second sum one fewer times and the one that was originally second will be added to the second sum one more time. The final value of the first sum will be the same, but the second sum will be different, detecting the change to the message.

The universe of possible checksum values is now the square of the value for the simple checksum. In our example, the two sums, each with 255 possible values, result in 65025 possible values for the combined checksum.

Overview of the different algorithm parameters
While there is an infinity of parameters, the original paper only studies the case K=8 (word length) with modulus 255 and 256.

The 16 and 32 bits versions (Fletcher-32 and -64) have been derived from the original case and studied in subsequent specifications or papers.

Fletcher-16
When the data word is divided into 8-bit blocks, as in the example above, two 8-bit sums result and are combined into a 16-bit Fletcher checksum. Usually, the second sum will be multiplied by 256 and added to the simple checksum, effectively stacking the sums side-by-side in a 16-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-16 checksum. The use of the modulus 28−1=255 is also generally implied.

Fletcher-32
When the data word is divided into 16-bit blocks, two 16-bit sums result and are combined into a 32-bit Fletcher checksum. Usually, the second sum will be multiplied by 216 and added to the simple checksum, effectively stacking the sums side-by-side in a 32-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-32 checksum. The use of the modulus 216−1=65,535 is also generally implied. The rationale for this choice is the same as for Fletcher-16.

Fletcher-64
When the data word is divided into 32-bit blocks, two 32-bit sums result and are combined into a 64-bit Fletcher checksum. Usually, the second sum will be multiplied by 232 and added to the simple checksum, effectively stacking the sums side-by-side in a 64-bit word with the simple checksum at the least significant end. This algorithm is then called the Fletcher-64 checksum. The use of the modulus 232−1=4,294,967,295 is also generally implied. The rationale for this choice is the same as for Fletcher-16 and Fletcher-32.

Comparison with the Adler checksum
The Adler-32 checksum is a specialization of the Fletcher-32 checksum devised by Mark Adler. The modulus selected (for both sums) is the prime number 65,521 (65,535 is divisible by 3, 5, 17 and 257). The first sum also begins with the value 1. The selection of a prime modulus results in improved "mixing" (error patterns are detected with more uniform probability, improving the probability that the least detectable patterns will be detected, which tends to dominate overall performance). However, the reduction in size of the universe of possible checksum values acts against this and reduces performance slightly. One study showed that Fletcher-32 outperforms Adler-32 in both performance and in its ability to detect errors. As modulo-65,535 addition is considerably simpler and faster to implement than modulo-65,521 addition, the Fletcher-32 checksum is generally a faster algorithm.

Caution on modulus
A modulus of 255 is used above and in examples below for Fletcher-16, however some real-world implementations use 256. The TCP protocol's alternate checksum has Fletcher-16 with a 256 modulus, as do the checksums of UBX-* messages from a U-blox GPS. Which modulus is used is dependent on the implementation.

Example calculation of the Fletcher-16 checksum
As an example, a Fletcher-16 checksum shall be calculated and verified for a byte stream of 0x01 0x02.
 * C0_initial = 0
 * C1_initial = 0

The checksum is therefore 0x0403. It could be transmitted with the byte stream and be verified as such on the receiving end. Another option is to compute in a second step a pair of check bytes, which can be appended to the byte stream so that the resulting stream has a global Fletcher-16 checksum value of 0.

The values of the checkbytes are computed as follows: where C0 and C1 are the result of the last step in the Fletcher-16 computation.
 * CB0 = 255 − ((C0 + C1) mod 255),
 * CB1 = 255 − ((C0 + CB0) mod 255),

In our case the checksum bytes are CB0 = 0xF8 and CB1 = 0x04. The transmitted byte stream is 0x01 0x02 0xF8 0x04. The receiver runs the checksum on all four bytes and calculates a passing checksum of 0x00 0x00, as illustrated below:

Weaknesses
The Fletcher checksum cannot distinguish between blocks of all 0 bits and blocks of all 1 bits. For example, if a 16-bit block in the data word changes from 0x0000 to 0xFFFF, the Fletcher-32 checksum remains the same. This also means a sequence of all 00 bytes has the same checksum as a sequence (of the same size) of all FF bytes.

Implementation
These examples assume two's complement arithmetic, as Fletcher's algorithm will be incorrect on ones' complement machines.

Straightforward
The below is a treatment on how to calculate the checksum including the check bytes; i.e., the final result should equal 0, given properly-calculated check bytes. The code by itself, however, will not calculate the check bytes.

An inefficient but straightforward implementation of a C language function to compute the Fletcher-16 checksum of an array of 8-bit data elements follows:

On lines 3 and 4, the sums are 16-bit variables so that the additions on lines 9 and 10 will not overflow. The modulo operation is applied to the first sum on line 9 and to the second sum on line 10. Here, this is done after each addition, so that at the end of the for loop the sums are always reduced to 8 bits. At the end of the input data, the two sums are combined into the 16-bit Fletcher checksum value and returned by the function on line 13.

Each sum is computed modulo 255 and thus remains less than 0xFF at all times. This implementation will thus never produce the checksum results 0x??FF, 0xFF?? or 0xFFFF (i.e., 511 out of the total 65536 possible 16-bit values are never used). It can produce the checksum result 0x0000, which may not be desirable in some circumstances (e.g. when this value has been reserved to mean "no checksum has been computed").

Check bytes
Example source code for calculating the check bytes, using the above function, is as follows. The check bytes may be appended to the end of the data stream, with the c0 coming before the c1.

Optimizations
In a 1988 paper, Anastase Nakassis discussed and compared different ways to optimize the algorithm. The most important optimization consists in using larger accumulators and delaying the relatively costly modulo operation for as long as it can be proven that no overflow will occur. Further benefit can be derived from replacing the modulo operator with an equivalent function tailored to this specific case—for instance, a simple compare-and-subtract, since the quotient never exceeds 1.

Here is a C implementation that applies the first but not the second optimization:

The second optimization is not used because the "never exceeds 1" assumption only applies when the modulo is calculated naively; applying the first optimization would break it. On the other hand, modulo Mersenne numbers like 255 and 65535 is a quick operation on computers anyway, as tricks are available to do them without the costly division operation.

Test vectors
8-bit implementation (16-bit checksum) "abcde" -> 51440 (0xC8F0) "abcdef" -> 8279 (0x2057) "abcdefgh" -> 1575 (0x0627)

16-bit implementation (32-bit checksum), with 8-bit ASCII values of the input word assembled into 16-bit blocks in little-endian order, the word padded with zeros as necessary to the next whole block, using modulus 65535 and with the result presented as the sum-of-sums shifted left by 16 bits (multiplied by 65536) plus the simple sum "abcde" -> 4031760169 (0xF04FC729) "abcdef" -> 1448095018 (0x56502D2A) "abcdefgh" -> 3957429649 (0xEBE19591)

32-bit implementation (64-bit checksum) "abcde" -> 14467467625952928454 (0xC8C6C527646362C6) "abcdef" -> 14467579776138987718 (0xC8C72B276463C8C6) "abcdefgh" -> 3543817411021686982 (0x312E2B28CCCAC8C6)

Bit and byte ordering (endianness / network order)
As with any calculation that divides a binary data word into short blocks and treats the blocks as numbers, any two systems expecting to get the same result should preserve the ordering of bits in the data word. In this respect, the Fletcher checksum is not different from other checksum and CRC algorithms and needs no special explanation.

An ordering problem that is easy to envision occurs when the data word is transferred byte-by-byte between a big-endian system and a  little-endian system and the Fletcher-32 checksum is computed. If blocks are extracted from the data word in memory by a simple read of a 16-bit unsigned integer, then the values of the blocks will be different in the two systems, due to the reversal of the byte order of 16-bit data elements in memory, and the checksum result will be different as a consequence. The implementation examples, above, do not address ordering issues so as not to obscure the checksum algorithm. Because the Fletcher-16 checksum uses 8-bit blocks, it is not affected by byte endianness.

title: Fletcher's checksum


text:
User talk:Illyrianka

Welcome to the Wikipedia
Here are some links I find useful

 * Policy Library
 * Cite your sources
 * Verifiability
 * Wikiquette
 * Conflict resolution
 * Brilliant prose
 * Neutral point of view
 * Pages needing attention
 * Peer review
 * Bad jokes and other deleted nonsense
 * Village pump
 * Boilerplate text

Feel free to ask me anything the links and talk pages don't answer. You can sign your name by typing 4 tildes, likes this: ~.

Cheers, Sam [Spade] 12:24, 3 Jun 2004 (UTC)

title: User talk:Illyrianka


text:
Talk:Bishop (artillery)

Untitiled
Considering that the title has (artillery) in it, I hardly think anyone would get this confused with another reference to the word/name Bishop or look it up while trying to find something else. Best to leave the disambiguation notice on Bishop only. Oberiko 12:25, 3 Jun 2004 (UTC)

Designation

 * Anyone got a credible source on where that designation has came from, because my source says different. King nothing 13:57, 27 May 2006 (UTC)

 * You mean Ordnance QF 25-pdr on Carrier Valentine 25-pdr Mk 1 ? AFAIR from Henry, Fuller - The 25-pounder Field Gun 1939-72. Bukvoed 14:13, 27 May 2006 (UTC)

I checked... the aforementioned book says the designation was 25-pounder Mk I on Carrier, Valentine, 25-pdr, Mk I. Is it what your source says ? Bukvoed 06:08, 29 May 2006 (UTC)

 * Carrier, Valentine, 25pdr gun Mk I, Bishop King nothing 14:01, 2 June 2006 (UTC)

Copyright issue
Looks like Afrikakorps.org is copying Wikipedia and puts its copyright on it... Chaoborus (talk) 05:13, 30 March 2008 (UTC)

Clarification Needed
From the article:

It was replaced in service by the M7 Priest (105 mm) and Sexton (25-pounder) when those became available in sufficient numbers, and surviving Bishops were diverted for artillery use

It's not clear what diverted for artillery use means, when the Bishop was already a self-propelled artillery piece. Catsmeat (talk) 09:41, 19 April 2012 (UTC)

title: Talk:Bishop (artillery)


text:
Karl Kruszelnicki

Karl Sven Woytek Sas Konkovitch Matthew Kruszelnicki (born 1948), often referred to as "Dr Karl", is an Australian science communicator and populariser, who is known as an author and a science commentator on Australian radio, television, and podcasts.

Kruszelnicki is the Julius Sumner Miller Fellow in the Science Foundation for Physics at the School of Physics, University of Sydney.

Early life
Kruszelnicki was born in Helsingborg, Sweden, to Polish parents, Rina and Ludwik. Kruszelnicki's background was hidden from him for a long time, with his mother having told him that she was Swedish and a Lutheran but she was, in fact, Polish and Jewish. Both his parents were Holocaust survivors. His father Ludwik, a Polish Gentile, was turned in to the Gestapo for smuggling Jews out of Poland and was imprisoned at Sachsenhausen, a concentration camp used mainly for political prisoners. As the end of World War II approached, Ludwik avoided execution by swapping identities with a dead person. Rina escaped the Auschwitz concentration camp when the Nazis ran out of Zyklon B that was used to gas prisoners. They separately fled to Sweden, where they met, and where Karl was born.

When Kruszelnicki was two years old, his parents became concerned about the risk of Sweden being overrun by Russia and decided to flee the country. Before boarding a boat bound for America, Karl became ill with fever following a smallpox vaccination. Worried for his health, his parents decided not to board the boat. "Luck has it that the next ship went to Australia, so that is where we ended up. It is amazing how fate can take you in unexpected directions."

On arrival in Australia, the family were tenanted at the migrant camp in Bonegilla, Victoria. They remained there for three years before settling in the city of Wollongong, New South Wales. Kruszelnicki said his childhood as a refugee in Wollongong was difficult, and he was bullied at school; he said "anybody who was not an Irish Catholic was considered an outsider". He found an escape in the Wollongong Library, where he became interested in science fiction.

Kruszelnicki attended Edmund Rice Christian Brothers College in Wollongong, New South Wales. After high school, he attended the University of Wollongong, completing a Bachelor of Science degree majoring in physics in 1968. In 1980, Kruszelnicki was awarded a Master of Biomedical Engineering degree at the University of New South Wales. He completed his Bachelor of Medicine and Bachelor of Surgery degrees at Sydney University in 1986.

After primary school, Kruszelnicki's first job was ditch digger in the Wollongong suburb of Dapto. He also worked as a filmmaker, car mechanic, TV weatherman and as roadie for Slim Dusty, Bo Diddley and Chuck Berry. While working as a taxi driver in Sydney, he was beaten unconscious after picking up a passenger trying to escape a group of men.

Science career
After graduating from university at age 19, Kruszelnicki took a job as a physicist working for a steel works in his home town of Wollongong. He designed a machine to test the strength of steel made for use in Melbourne's West Gate Bridge, which was under construction at the time. After he was asked to fake the results of his tests, he resigned.

In the early 1980s, Kruszelnicki worked for ophthalmologist Fred Hollows. His Master of Biomedical Engineering degree allowed him to design and build a machine to pick up electrical signals off the human retina to diagnose certain eye diseases.

Kruszelnicki commenced his degree in medicine at the University of Sydney at the age of 32, graduating in 1986. From here he began work at a number of hospitals around Sydney, including the Children's Hospital in Camperdown. He talks fondly of his time as a children's doctor, though he left this profession after witnessing the first child die from whooping cough in twenty years. This came about, he says, after a television program tried to create controversy by presenting the efficacy of vaccinations with a false balance. This caused a drop in herd immunity, and eventually the death of this child. "That very strongly influenced me to go into the media, because I felt like I could do more good there (convincing people to vaccinate). And as a result, I gave up the best job of my life, which was being a doctor in a kids' hospital, so I could do more good in the community."

Television
Kruszelnicki presented the first series of Quantum (replaced by Catalyst) in 1985. As a science communicator and presenter, he appears on the Seven Network's Weekend Sunrise and on ABC TV. From early 2008 to 2010 he co-hosted a TV series called Sleek Geeks with Adam Spencer.

Journalism, radio and podcasts

Kruszelnicki does a number of weekly radio shows and podcasts. His hour-long show on ABC radio station Triple J has been going on in one form or another since 1981; this weekly science talkback show, Science with Dr Karl, is broadcast on Thursday mornings from 11:00 am to midday and attracts up to 300,000 listeners; it is also available as a podcast.

Kruszelnicki also often helps with other science and education Triple J promotions such as the Sleek Geek Week roadshow with Adam Spencer and Caroline Pegram. He and Adam Spencer released the Sleek Geeks podcast regularly until December 2015. Also, Since 2016, he has hosted the podcast Shirtloads of Science.

For many years, until March 2020, Kruszelnicki appeared on a live weekly late-night link-up on BBC Radio 5 Live's Up All Night, usually with Rhod Sharp, answering science questions. In 2017, he hosted Dr. Karl's Outrageous Acts of Science on Discovery Channel (Australia).

Kruszelnicki writes a regular column for Australian Geographic magazine, called 'Need to Know', which is republished as a blog on the magazine's website. He has also written for the Sydney Morning Herald Good Weekend magazine.

Politics
Kruszelnicki was an unsuccessful candidate for the Australian Senate in the 2007 Australian federal election. He was placed number two on the Climate Change Coalition ticket in New South Wales.

In 2015, Kruszelnicki appeared in an Australian Government advertising campaign for the recently published intergenerational report. He had previously agreed to do the campaign, believing it would be a "non-political, bipartisan, independent report." After its publication, however, he backed away from the campaign, describing it as "flawed". "How can you possibly have a report that looks at the next 40 years and doesn't mention climate change? It should have acknowledged that climate change is real and we cause it and it will be messy."

Personal life
Kruszelnicki met his wife Mary in his first year of medical school. They have three children together: Karl, Alice, and Lola.

Kruszelnicki has prosopagnosia, meaning he lacks the ability to recognise faces. To help him recognise co-workers, he has been known to carry a seating map of familiar office spaces. He puts the cause of his condition down to having an unhappy, lonely childhood, saying that it impeded the development of the part of his brain responsible for remembering faces.

Recognition and awards
In 2000, the Australian Financial Review Internet Awards awarded Kruszelnicki the Best Science and Technology Website.

In the 2001 honours list, he was awarded the Centenary Medal "for major service in raising public awareness of the importance of science and technology".

One of Kruszelnicki's more notable undertakings was his part in a research project on belly button fluff, for which he received the tongue-in-cheek Ig Nobel Prize in 2002.

He received the Australian Father of the Year award in 2003.

In the 2006 honours list, he was made a Member of the Order of Australia.

In 2006, the Australian Skeptics recognised him as the Australian Skeptic Of The Year.

In 2012, Kruszelnicki was named as a National Living Treasure by the National Trust of Australia (NSW).

In 2012, Main-belt asteroid 18412 Kruszelnicki was named in his honour.

In 2014, Reader's Digest readers voted Kruszelnicki as the ninth-most-trusted person in Australia

In 2016, he received an honorary doctorate from the University of the Sunshine Coast.

Kruszelnicki won UNESCO's 2019 Kalinga Prize for science communication.

Selected publications

 * Books
 * Spacescape, Harcourt Brace Jovanovich, (Australia), 1992, ISBN 0-7295-1100-6.
 * Absolutely Fabulous Moments in Science, Australian Broadcasting Corporation Enterprises, Sydney, Australia, 1994, ISBN 0-7333-0407-9.
 * Sensational Moments in Science, Australian Broadcasting Corporation Enterprises, Sydney, Australia, 1995, ISBN 0-7333-0456-7.
 * Pigeon Poo the Universe & Car Paint – and other awesome science moments, HarperCollins Publishers Pty Ltd, Australia, 1996, ISBN 0-7322-5723-9.
 * Flying Lasers, Robofish and Cities of Slime – and other brain-bending science moments, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-7322-5874-X.
 * Dr Karl's Collection of Great Australian Facts & Firsts
 * 1. Ears, Gears and Gadgets, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-207-19610-9.
 * 2. Forests, Fleece & Prickly Pears, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-207-19611-7.
 * 3. Flight, Food & Thingummygigs, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-207-19612-5.
 * 2. Forests, Fleece & Prickly Pears, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-207-19611-7.
 * 3. Flight, Food & Thingummygigs, HarperCollins Publishers Pty Ltd, Australia, 1997, ISBN 0-207-19612-5.

 * Munching Maggots, Noah's Flood and TV Heart Attacks and other cataclysmic science moments, HarperCollins Publishers Pty Ltd, Australia, 1998, ISBN 0-7322-5858-8.
 * Fidgeting Fat, Exploding Meat & Gobbling Whirly Birds – and other delicious science moments - New Moments in science 4, 1999.
 * Q&A With Dr. K – Why It Is So. Headless Chickens, Bathroom Queues and Belly Button Blues, HarperCollins Publishers Pty Ltd, Australia, 2001, ISBN 0-7322-5855-3.
 * Dr. Karl's Collection of Great Australian Facts & Firsts, HarperCollins Publishers Pty Ltd, Australia, 2002, ISBN 0-207-19860-8.
 * Bumbreath, Botox and Bubbles and other Fully Sick Science Moments, HarperCollins Publishers Pty Ltd, Australia, 2003, ISBN 0-7322-6715-3.
 * Great Mythconceptions – Cellulite, Camel Humps and Chocolate Zits, HarperCollins Publishers Pty Ltd, Australia, 2004, ISBN 0-7322-8062-1.
 * Dis Information and Other Wikkid Myths: More Great Myths In Science, HarperCollins Publishers Pty Ltd, Australia, 2005, ISBN 0-7322-8060-5.
 * It Ain't Necessarily So Bro, HarperCollins Publishers Pty Ltd, Australia, 2006, ISBN 0-7322-8061-3.
 * Please Explain, HarperCollins Publishers Pty Ltd, Australia, 2007, ISBN 0-7322-8535-6.
 * Science Is Golden, HarperCollins Publishers Pty Ltd, Australia 2008 ISBN 978-0-732-28536-4
 * Never Mind the Bullocks, Here's the Science, HarperCollins Publishers Pty Ltd, Australia, 2009, ISBN 0-7322-8537-2.
 * Dinosaurs Aren't Dead, Pan Macmillan Pty Limited, Australia, 2010 ISBN 978-0-330-42579-7
 * Curious and Curiouser, Pan Macmillan Pty Limited, Australia, 2010 ISBN 978-1-742-61170-9
 * Brain Food, Pan Macmillan Pty Limited, Australia, 2011 ISBN 978-1-742-61039-9
 * 50 Shades of Grey Matter, Pan Macmillan Pty Limited, Australia, 2012 ISBN 978-1-742-61138-9
 * Game of Knowns, Pan Macmillan Pty Limited, Australia, 2013 ISBN 978-1-742-61334-5
 * Dr Karl's Big Book of Science Stuff and Nonsense, Pan Macmillan Pty Limited, Australia, 2013 ISBN 978-1-742-61368-0
 * House of Karls, Pan Macmillan Pty Limited, Australia, 2014 ISBN 978-1-743-51951-6
 * Dr Karl's Short Back & Science, Pan Macmillan Pty Limited, Australia, 2015 ISBN 978-1-743-53334-5
 * The Doctor, Pan Macmillan Pty Limited, Australia, 2016 ISBN 978-1-743-54742-7
 * Karl, The Universe and Everything, Pan Macmillan Pty Limited, Australia, 2017 ISBN 978-1-925-48132-7
 * Vital Science, Pan Macmillan Australia Pty Limited, Australia, 2018 ISBN 978-1-760-78122-4
 * Dr Karl's Random Road Trip Through Science, HarperCollins Publishers Australia Pty Limited, Australia, 2019 ISBN 978-0-7333-4032-1
 * Dr Karl's Surfing Safari Through Science, HarperCollins Publishers Australia Pty Limited, Australia, 2020 ISBN 978-0-7333-4033-8
 * Dr Karl's Little Book of Climate Change Science, HarperCollins Publishers Australia Pty Limited, Australia, 2021 ISBN 978-0-7333-4129-8
 * Journal articles

title: Karl Kruszelnicki


text:
Albert Victor Bäcklund

Albert Victor Bäcklund (11 January 1845 – 23 February 1922) was a Swedish mathematician and physicist. He was a professor at Lund University and its rector from 1907 to 1909.

He was born in Malmöhus County, now Skåne County, in southern Sweden and became a student at the nearby University of Lund in 1861. In 1864 he started to work for the observatory, and received his Ph.D. in 1868 working on methods to obtain the latitude of a place by astronomical observations. He was awarded the title of associate professor in Mechanics and Mathematical Physics in 1878, and elected Fellow of the Swedish Academy of Science in 1888. In 1897 he became a full professor.

In 1874 he was awarded a travel grant to study abroad for six months. He went to the universities at Leipzig and Erlangen to work with Felix Klein and Ferdinand von Lindemann.

His most important work was in the field of transformations pioneered by Sophus Lie. He improved greatly the understanding of contact transformations and introduced a new second class transformation, now known as auto-Bäcklund transformation.

title: Albert Victor Bäcklund


text:
Luigi Bianchi

Luigi Bianchi (18 January 1856 – 6 June 1928) was an Italian mathematician. He was born in Parma, Emilia-Romagna, and died in Pisa. He was a leading member of the vigorous geometric school which flourished in Italy during the later years of the 19th century and the early years of the twentieth century.

Biography
Like his friend and colleague Gregorio Ricci-Curbastro, Bianchi studied at the Scuola Normale Superiore in Pisa under Enrico Betti, a leading differential geometer who is today best remembered for his seminal contributions to topology, and Ulisse Dini, a leading expert on function theory. Bianchi was also greatly influenced by the geometrical ideas of Bernhard Riemann and by the work on transformation groups of Sophus Lie and Felix Klein. Bianchi became a professor at the Scuola Normale Superiore in Pisa in 1896, where he spent the remainder of his career. At Pisa, his colleagues included the talented Ricci. In 1890, Bianchi and Dini supervised the dissertation of the noted analyst and geometer Guido Fubini.

In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.

Through the influence of Luther P. Eisenhart and Abraham Haskel Taub, Bianchi's classification later came to play an important role in the development of the theory of general relativity. Bianchi's list of nine isometry classes, which can be regarded as Lie algebras, Lie groups, or as three dimensional homogeneous (possibly nonisotropic) Riemannian manifolds, are now often called collectively the Bianchi groups.

In 1902, Bianchi rediscovered what are now called the Bianchi identities for the Riemann tensor, which play an even more important role in general relativity. (They are essential for understanding the Einstein field equation.) According to Tullio Levi-Civita, these identities had first been discovered by Ricci in about 1889, but Ricci apparently forgot all about the matter, which led to Bianchi's rediscovery. However, the contracted Bianchi identities, which are sufficient for the proof that the divergence of the Einstein tensor always vanishes, had been published by Aurel Voss in 1880.

Books

 * Lezioni sulla teoria dei gruppi di sostituzioni e delle equazioni algebriche secondo Galois, Pisa 1899
 * Lezioni sulla teoria delle funzioni di variabile complessa e delle funzioni ellittiche 1916
 * Lezioni sulla teoria dei numeri algebrici e principi d'aritmetica analitica, 1921
 * Lezioni sulla teoria delle funzioni di variabile complessa e delle funzioni ellittiche 1916
 * Lezioni sulla teoria dei numeri algebrici e principi d'aritmetica analitica, 1921
 * Lezioni sulla teoria dei numeri algebrici e principi d'aritmetica analitica, 1921

title: Luigi Bianchi


text:
Grove Oak, Alabama

Grove Oak is a small unincorporated community in DeKalb County, Alabama, United States. It is located atop Sand Mountain in northeastern Alabama.

Grove Oak has one store, and is surrounded by forests and farmland. There are two Baptist churches. There is a small Masonic lodge and a now-closed junior high school. It also has a restaurant that has been in and out of business several times.

Until about the mid-1970s, it was the center of a farming community and had its own cotton gin. Today, farming is not so much the focus, and most working members of the Grove Oak community drive to factories or other jobs in the larger towns nearby. Limited farming, cattle, and poultry raising takes place in and around the town.

Geography
Grove Oak is located at 34.43806°N, -86.0525°W. Its average elevation is 1175 ft above sea level.

Notable person

 * Albert Rains, U.S. Representative from 1945 to 1965

title: Grove Oak, Alabama


text:
MHD

MHD may refer to:

 * MHD (rapper), a French rapper from the 19th arrondissement of Paris
 * MHD (album), the rapper's 2016 debut album
 * MHD, former name of the HDTV network for MTV, VH1, Palladia, and CMT now known as MTV Live
 * Mashhad International Airport's IATA code
 * Magnetohydrodynamics, the study of the magnetic properties and behaviour of electrically conducting fluids
 * Magnetohydrodynamics (journal)
 * Malteser International, an aid agency
 * Menstrual Hygiene Day, a day to raise awareness about menstrual hygiene management issues
 * Military history detachment, a unit of United States Army
 * Mindesthaltbarkeitsdatum, the German term for shelf life, printed on imported German food or medical products
 * Doctor of Marine Histories (DMH, formerly Marine Histories Doctorate or MHD), such as issued by Sea Research Society's College of Marine Arts
 * GNU libmicrohttpd, an embeddable HTTP server
 * Airline code for CAAC Airlines
 * Městská hromadná doprava (Czech) or mestská hromadná doprava (Slovak), public transport systems in Czech and Slovak cities
 * Marblehead, a historic town located in Massachusetts

authors: Мария Магдалина

title: MHD


text:
Talk:Berry

Semi-protected edit request on 26 December 2022
Strawberries are not a berry and need to be removed from the list. Isabelladangelo (talk) 23:12, 26 December 2022 (UTC)
 * Red information icon with gradient background.svg Not done: please provide reliable sources that support the change you want to be made. - FlightTime  ( open channel ) 23:17, 26 December 2022 (UTC)

Semi-protected edit request on 23 May 2023
A raspberry is NOT a berry. Axel Rivas Perez (talk) 21:33, 23 May 2023 (UTC)
 * This is not the page for the botanical terminology Hyphenation Expert (talk) 22:50, 23 May 2023 (UTC)

Semi-protected edit request on 25 November 2023
The picture of blackberries should be removed from the example pictures in the summary.

The text of the article states specifically that Blackberry is NOT a berry and yet the example pictures in the top right have a picture of blackberries. Jakespeedorg (talk) 07:35, 25 November 2023 (UTC)
 * This is not the page for the botanical terminology Hyphenation Expert (talk) 10:10, 25 November 2023 (UTC)

title: Talk:Berry


text:
Bäcklund transform

In mathematics, Bäcklund transforms or Bäcklund transformations (named after the Swedish mathematician Albert Victor Bäcklund) relate partial differential equations and their solutions. They are an important tool in soliton theory and integrable systems. A Bäcklund transform is typically a system of first order partial differential equations relating two functions, and often depending on an additional parameter. It implies that the two functions separately satisfy partial differential equations, and each of the two functions is then said to be a Bäcklund transformation of the other.

A Bäcklund transform which relates solutions of the same equation is called an invariant Bäcklund transform or auto-Bäcklund transform. If such a transform can be found, much can be deduced about the solutions of the equation especially if the Bäcklund transform contains a parameter. However, no systematic way of finding Bäcklund transforms is known.

History
Bäcklund transforms have their origins in differential geometry: the first nontrivial example is the transformation of pseudospherical surfaces introduced by L. Bianchi and A.V. Bäcklund in the 1880s. This is a geometrical construction of a new pseudospherical surface from an initial such surface using a solution of a linear differential equation. Pseudospherical surfaces can be described as solutions of the sine-Gordon equation, and hence the Bäcklund transformation of surfaces can be viewed as a transformation of solutions of the sine-Gordon equation.

The Cauchy–Riemann equations
The prototypical example of a Bäcklund transform is the Cauchy–Riemann system

 * $$u_x=v_y, \quad u_y=-v_x,\,$$

which relates the real and imaginary parts $$u$$ and $$v$$ of a holomorphic function. This first order system of partial differential equations has the following properties.

$$u_{xx} + u_{yy} = 0$$ (i.e., a harmonic function), and so is $$v$$. This follows straightforwardly by differentiating the equations with respect to $$x$$ and $$y$$ and using the fact that $$u_{xy}=u_{yx}, \quad v_{xy}=v_{yx}.\,$$ Thus, in this case, a Bäcklund transformation of a harmonic function is just a conjugate harmonic function. The above properties mean, more precisely, that Laplace's equation for $$u$$ and Laplace's equation for $$v$$ are the integrability conditions for solving the Cauchy–Riemann equations.
 * 1) If $$u$$ and $$v$$ are solutions of the Cauchy–Riemann equations, then $$u$$ is a solution of the Laplace equation
 * 1) Conversely if $$u$$ is a solution of Laplace's equation, then there exist functions $$v$$ which solve the Cauchy–Riemann equations together with $$u$$.

These are the characteristic features of a Bäcklund transform. If we have a partial differential equation in $$u$$, and a Bäcklund transform from $$u$$ to $$v$$, we can deduce a partial differential equation satisfied by $$v$$.

This example is rather trivial, because all three equations (the equation for $$u$$, the equation for $$v$$ and the Bäcklund transform relating them) are linear. Bäcklund transforms are most interesting when just one of the three equations is linear.

The sine-Gordon equation
Suppose that u is a solution of the sine-Gordon equation
 * $$ u_{xy} = \sin u.\,$$

Then the system
 * $$\begin{align}

v_x & = u_x + 2a \sin \Bigl( \frac{v+u}{2} \Bigr) \\ v_y & = -u_y + \frac{2}{a} \sin \Bigl( \frac{v-u}{2} \Bigr) \end{align} \,\!$$ where a is an arbitrary parameter, is solvable for a function v which will also satisfy the sine-Gordon equation. This is an example of an auto-Bäcklund transform.

By using a matrix system, it is also possible to find a linear Bäcklund transform for solutions of sine-Gordon equation.

The Liouville equation
A Bäcklund transform can turn a non-linear partial differential equation into a simpler, linear, partial differential equation.

For example, if u and v are related via the Bäcklund transform

 * $$\begin{align}

v_x & = u_x + 2a \exp \Bigl( \frac{u+v}{2} \Bigr) \\ v_y & = -u_y - \frac{1}{a} \exp \Bigl( \frac{u-v}{2} \Bigr) \end{align} \,\!$$ where a is an arbitrary parameter, and if u is a solution of the Liouville equation

$$u_{xy}=\exp u \,\!$$

then v is a solution of the much simpler equation, $$v_{xy}=0$$, and vice versa.

We can then solve the (non-linear) Liouville equation by working with a much simpler linear equation.

title: Bäcklund transform