text:
Talk:List of mathematics articles

Initial comments
−Very nice and useful list. The only strange thing are the names of mathematicians. I guess they should be excluded somehow or they should be in a separate list as they are already in list of mathematicians.

I think they should at least go to a separate list. They clutter the present list. There is the additional problem of their ordering: the first letter of the first name determines their classification: that makes it about useless. So Dirichlet is found under J as "Johann Peter Gustav Lejeune Dirichlet". A few minutes ago, it was under P as "Peter Gustav Lejeune Dirichlet". God knows where he will be tomorrow ;-) FvdP 23:01 Oct 8, 2002 (UTC)
 * Ha, ha. I guess he would end at P, because someone someday will short his name to Peter Dirichlet. --XJam 23:29 Oct 8, 2002 (UTC)

The mathematicians are here so that we can track all changes on pages remotely related to math with a single "Watch links" operation. This list is not primarily for public consumption, and the alphabetical ordering is unimportant. If you want a nicely organized list of mathematicians, you can go to a list of mathematicians, but please don't remove them from here. Thanks, AxelBoldt 03:42 Oct 9, 2002 (UTC)

 * A bit late, sorry for having pushed that move out... --FvdP

Names of theorems
It is OK to write Matiyasevich's theorem but not Dirichlet's theorem. Why is that so? Can you please decide how to name theorems? --XJam 09:50 Oct 14, 2002 (UTC)

 * Discussion moved to Wikipedia talk:Naming conventions (theorems)

Should redirects like poset also be listed ? --FvdP

Yes, for two reasons: some people will use this list to look up a certain term, and we shouldn't hide "poset" from them; also, sometimes a redirect is turned into a real article, and we want to monitor things like that with the "Related Changes" feature. AxelBoldt 01:24 Jan 9, 2003 (UTC)

What about deleting one of "regular expression" and "regular expressions"? They point to the same article and are definitely redundant in this list. I would delete "regular expression", because the plural form sounds nicer to my ears (just a feeling ...). What do you think out there? --zeno 07:12 Jan 14, 2003 (UTC)

 * I'd say it's a pretty common standard in the mathematics area to use the singular; that way you can write number of integers and get number of integers (the Wiki formatting automatically includes the "s" in the link). If only the plural form were only available, you'd have to write number of integers . The worse part is - without a standard, you'd always be guessing; is it the Sylow theorem or Sylow Theorems?. So I always use singular, as in real number, rational number, etc. Chas zzz brown 09:18 Jan 14, 2003 (UTC)

 * The main purpose of this list is to monitor changes in the math area by using the "Related Changes" feature in the sidebar. Since the article lives at regular expression and regular expressions is just a redirect, we need to keep the singular in the list for this monitoring to work. The plural could be deleted. As a general naming convention, singular terms are preferred in article titles, for the reasons Chas gave above. AxelBoldt 20:11 Jan 14, 2003 (UTC)

In view of the length of this page and the time it takes to load, I think it would be useful to have a page titled "Mathematical topics" on which one sees: A, B, C, D, ....., Z, and then clicking on any of those would take you to a page that lists mathematical topics with the corresponding initial letter. Michael Hardy 00:53 Feb 5, 2003 (UTC)

 * Yes very good idea Michael. The same thing would probably be with page List of astronomical topics and if someone would start others like List of physical topics, ... I guess AxelBoldt did not think this would be necessary some day. --XJamRastafire 01:04 Feb 5, 2003 (UTC)

The problem for me is, I have a shortcut which takes me to related changes for this page - if we broke it up into A, B, C, etc., then I'd have to check related changes for math with "A", then check related changes for math with "B", etc. I don't know if there's a workaround; but the main reason for this page to exist is that related changes function. Maybe a database function could be implemented which would make this easier somehow... Cheers Chas zzz brown 02:02 Feb 5, 2003 (UTC)

I agree with Chas: the original reason for this page was to enable "Related Changes" for a quick list of changes in the math area; it's not really meant for users to look up mathematical topics. They should just use the search engine. AxelBoldt 04:18 Feb 6, 2003 (UTC)
 * Yes Chas and Axel's arguments are just okay. But I understand also Michael's torments when he is opening this page. This problem still remains regardless of being just a function for related changes. His second function of being a certain mathematical index is also very useful. How to kill two flies with one shot would be fine to know. --XJamRastafire

If, for each link in the page, "Related changes" returned changes in both to the article and the talk page, then we could remove about half the current links (the talk: ones). That would probably make the page load a bit faster. Chas zzz brown 10:47 Feb 6, 2003 (UTC)

A related idea I've been thinking of... Many of the topics on this list might be better served by a List of physics topics. For some examples from recent changes in the last 2 days: temperature, charge, semiconductor, Electromagnetism, special relativity, evolution, diode. These are topics that I wager a lot of mathematicians know something about, but strictly speaking, they aren't mathematics proper.

Of course, a lot of physics these days is mathematical; and there's no particular reason some topics couldn't be on both lists; after all, this is primarily a maintenance page. But I see no particular reason to include "diode" for example. I can start on this process, but first - comments? Chas zzz brown 01:47 Feb 9, 2003 (UTC)

Sure, diode and evolution don't belong here for sure. Do you want to start List of physics topics? It's a lot of work though. AxelBoldt 03:23 Feb 9, 2003 (UTC)

Start with List of physics topics Looxix 00:34 Feb 10, 2003 (UTC)

 * Refactoring is sure needed but first can we break this up into several pieces? The article is extremely too long to edit. -- Taku 14:39 18 May 2003 (UTC)

What is the purpose of all the empty Talk: links? Don't they make the page unnecessarily large? -- Timwi 22:57 15 Jun 2003 (UTC)

 * They are there so that when you click "Related changes" (which is the main purpose of the page) you see recently modified Talk pages as well. --Zundark 19:12 16 Jun 2003 (UTC)

 * Aahh.... the software should really be doing that automatically :-p -- Timwi 21:39 16 Jun 2003 (UTC)

How about having two lists? One as an "index" of terms and the other as a list of top level categories. For example, the last list could simply have "Group theory" while the first has Lagrange's theorem, normal subgroup, group homomorphism, automorphism group, etc.. Phys 17:09, 20 Aug 2003 (UTC)

 * The top level topics should be (and I believe are) listed at mathematics. AxelBoldt 13:20, 12 Sep 2003 (UTC)

If I could just make a general comment. Currently the number of mathematical pages not linked to from this list must run well into three figures. That is, simply finding what is on the site and relevant is an uphill task. Fine-tuning would be welcome in all of the areas (a) organisation by topic (b) tutorial guidance (c) standardisation of article format to something stable and appropriate at a level.

If my previous wiki experience elsewhere is a reliable guide though, something has to be done first about the tide of stubby articles and 'opportunistic' edits. Not to speak of the demarcation questions on the physics and compsci and other fronts. Centralising lists are good for the simple reason that they find stuff.

Charles Matthews 08:37, 21 Aug 2003 (UTC)

Why are computer terms on here? I study math and work on computers and the two fields are very different. Some things are arguably pertinent to both (eg Cryptography), but FIPS, ENIAC? These did/do nothing for math.....

The answer to the question about ENIAC seems to be that it was added a long time ago (in terms of this page) when, for example, there were also many topics in physics and other mathematical sciences included.

Charles Matthews 13:17, 6 Sep 2003 (UTC)

What do you people think of the idea of creating a list of mathematical examples? It would list concrete examples; Cantor function would be a good candidate. Many articles probably already exist that would be appropriate. I may write one illustrating the use of Lebesgue's convergence theorems; it was that one that caused me to think of this. Would those who would contribute so indicate below? Michael Hardy 00:39, 6 Nov 2003 (UTC)

Lists are good. Would you want Petersen graph, just because it's a famous example? Sin(1/x) thingies? Counterexamples to symmetry of second derivative? Just saying 'example' is leaving it very broad.

Charles Matthews 09:36, 6 Nov 2003 (UTC)

The fact that it's broad would mean the list would be long -- maybe even half as long as the list of mathematical topics. I would include all of the above. I guess a certain concreteness would be a qualification for inclusion in the list. "Riemann integral" is not conrete enough, IMO. The Petersen graph definitely is. Proofs and theorems would not generally be included; mathematical objects would be. The outer automorphisms of S6 would be included if there's a Wikipedia article about them. (6 is the only value of n for which Sn has any outer automorphisms.) The non-Desarguean projective planes would be included if there's a Wikipedia article about them. Many concrete examples are very enlightening and should be objects of study in their own right. Michael Hardy 20:09, 6 Nov 2003 (UTC)

OK - sounds like a 'mathematical atlas'.

Charles Matthews 20:53, 6 Nov 2003 (UTC)

 * Good idea. And I'm eager to hear about the outer automorphisms of S6 (if there's anything deep underneath at least). --FvdP

On general stuff about these mathematical topics pages:

 * 1) there is now no consistency in the way they self-link;
 * 2) the links to each other are as they should be (??);
 * 3) I don't actually agree with the idea of links to (for example) Riemann as well as Bernhard Riemann now being in the list.

Charles Matthews 14:32, 26 Feb 2004 (UTC)

Reorganizing this list
I would like to suggest two changes to this list:

 * We stop listing mathematicians here. It's too easy to forget to add them here as well as to List of mathematicians.
 * We go through and remove the non-math topics listed, especially if they are already covered on another list of topics. I volunteer to do this.

 * I would suggest that in removing a topic on the grounds that it is a non-math topic, you make clear in your summary that that's the reason for removal, and state which topics were removed. That way those who might disagree are given notice. Michael Hardy 21:21, 11 Mar 2004 (UTC)

 * That is a reasonable request. -- Walt Pohl 21:52, 11 Mar 2004 (UTC)

I agree with the above suggestions. Here's another minor one: I'd have done this already, but I'm not sure if it will screw anything up. -- Fropuff 01:48, 2004 Mar 12 (UTC)
 * Move the A-C topics to another page and move the categorical sublists (currently on the L page) to here. That way when people come here they can easily choose to browse alphabetically or by category.

 * Those are both really good ideas. The inclusion of A-C on the main page is so odd, though, that I had just assumed it was for strictly technical Wiki software reasons. :-) -- Walt Pohl 02:26, 12 Mar 2004 (UTC)

I hear some good ideas here. Perhaps the relatively simple moves should come first (lists to the 'main page', A-C to own page). Then a bit more policy discussion. For example, the charter is currently drawn up very broadly, and the content reflects that. Things move on, and I agree for example that mathematicians should be on their proper list. But it would be good to have proper consensus about that.

Charles Matthews 08:40, 12 Mar 2004 (UTC)

While we're at it, a couple of other policies to work out.

 * Red links - it seems to me that people should put these in the proper Requested Articles page now, rather than on the list. The RA turnover is quite good, while the math-lists have become unreadable.

 * Redirects. Is there a policy to make for inclusion, or just leave it to common sense?

Charles Matthews 16:18, 12 Mar 2004 (UTC)

Yes, the red links need to go. The RA page works much better for this purpose. I say just leave redirects to common sense. I include then unless they are just minor spelling differences. -- Fropuff 15:41, 2004 Mar 13 (UTC)

Do we want to add every current red link to RA?

 * It is clear to me that RA could be much expanded, if that were a good idea. Probably not a good idea, currently. So, I think red links from this list should be given priority for moving there: since people may have added them to the list thinking in good faith that they would attract attention, we should respect that. Some sorting may then be required. Charles Matthews 20:39, 13 Mar 2004 (UTC)

As for redirects, I think we should definitely include them for things that might have their own page someday, or things that are very common terms, like poset. -- Walt Pohl 17:12, 13 Mar 2004 (UTC)

If no one objects, in the next couple of days I'm going to do the following:

 * Move 0-9 and A-C to their own pages.
 * Move the big list of lists to its own page, List of mathematical topics (lists).
 * Replace the current navigation for the different pages by a MediaWiki namespace element that's included by transclusion. Something like this:
 * List of mathematical topics
 * 0-9, A-C, etc.
 * See also Lists of mathematical topics (lists) for lists organized by subtopic.

I'll save any other changes for a future day. -- Walt Pohl 17:12, 13 Mar 2004 (UTC)

Reasons for my recent edit
Someone has put a very conspicuous link to the mathematics category page on Wikipedia's main page. At this time, very few of the mathematics articles on Wikipedia are listed on that page. Therefore, I put a warning to that effect on the category page, with a link to list of mathematical topics. So suddenly, this page becomes much more conspicuous to the (non-Wikipedian) public. Since the "recent changes" links on this page appeared above the actual topics lists pages, they were more conspicuous than the links to the actual topics lists. The non-Wikipedian public should be directed first to the topics lists and only later to the "recent changes" lists. Michael Hardy 20:32, 30 Aug 2004 (UTC)

Sorting criteria for the List of mathematical topics
As a possible future project I am considering adding to the List of mathematical topics all the articles from the math categories. I would like to sometime have a community-wide discussion of this. For now, I have a question, which would need to be solved if one would ever attempt to update this list automatically. And that is, what are the sorting criteria for the articles?

So far, I assume the following rules:

(1) Order is alphabetical, with capital letters, lowercase letters, and accented letters treated the same.

(2) The space character takes precedence to numbers and letters, and numbers take precedence to letters. So,

 * Abel theorem

is before

 * Abelian

(please ignore the fact that Abel theorem is not grammatical).

Now the tricky part, as there are other characters involved. It looks to me, that the general rule in this list (not universally respected) is to treat:

(3) The apostrphes, quoting characters, commas, and the parantheses, as the empty character. That is,

 * Abel's theorem
 * Abels theorem
 * Abel's (theorem)
 * Abels, theorem

are considered equal when it comes to sorting (again, forget the grammar for the moment).

(4) The dash character is treated the same as the space character, so

 * Abel Rufini

and

 * Abel-Rufini

are treated as equal when it comes to sorting.

I wonder if this is acceptable, and if I missed something. Thanks, Oleg Alexandrov 01:16, 18 Apr 2005 (UTC)

 * Since the main reason now to have the lists is to use RelatedChanges - for which the order doesn't matter - I'd say any consistent system is good. Charles Matthews 07:34, 18 Apr 2005 (UTC)

 * Another problem is that many mathematicians are sorted on their last name. However, I agree with Charles that the ordering is not that important; even an unsorted list of all articles in Category:Mathematics and its subcategories and LoMT would be very useful. -- Jitse Niesen 09:33, 18 Apr 2005 (UTC)

 * Right, the mathematicians are sorted by the last name (I had forgotten to mention it, but been aware of the thing). This can be a problem when adding new people as software is too stupid to figure out which is the last name in certain cases (I will inspect every single entry individually, which will take more time, but will take care of this problem).

 * To me, the order does not matter absolutely at all either. What I mentioned above, is what I think the order is implicitely assumed from carefully inspecting the existing lists. I will soon ask for more community opinion onthe whole thing. Oleg Alexandrov 15:57, 18 Apr 2005 (UTC)

 * Actually, I would say that in a big revision the mathematicians should all be removed: list of mathematicians must anyway be big now, and the old reasons for having a single list of mathematics-related topics have gone. Charles Matthews 16:49, 18 Apr 2005 (UTC)

 * Fine with me either way. Oleg Alexandrov 17:52, 18 Apr 2005 (UTC)

Some statistics
Here I will write from time to time the number of articles we have in the list. So far, before removing the mathematicians, there were

 * 5067 articles.

(So, a ~ 3500 figure I gave a while ago is wrong, it was due to a bug in my code.)

After removing the mathematicians, we are left with

 * 4663 articles.

Just curious how many we will have after all the articles from math categories will be added. Oleg Alexandrov 03:22, 29 Apr 2005 (UTC)

 * I finished adding the articles from the math categories. There are now 6964 articles in List of mathematical topics A-Z, and, together with the articles in List of mathematical topics 0-9, gives us 7197. That's a lot of math articles!

 * There are still math-stubs to be categorized, and I was kind of conservative when deciding what a math category is. With the latter, I might need some help and suggestions, see list of mathematics categories. Oleg Alexandrov 04:54, 7 May 2005 (UTC)

Update
Today I started adding articles from the math categories. I caught some bugs in my code, and as result at some point I reverted the lists 0-9, and A to C. (And I learn again and again that the only way to make sure a bot does its job is to check every single edit. :) Oleg Alexandrov 04:33, 2 May 2005 (UTC)

List of mathematics categories
I started a new list, List of mathematics categories. I would appreciate it if more people have it on the watchlist and correct me if I add something wrong there. Oleg Alexandrov 01:39, 3 May 2005 (UTC)
 * The reason this list is important is because my bot daily fetches articles form the categories listed there and adds them to the list of mathematical topics. Oleg Alexandrov (talk) 23:58, 10 December 2005 (UTC)

Proposed renaming
This is a result of discussion over at List of lists of mathematical topics - most people wanted it renamed, and it was also suggested that this article (and related) be re-named List of mathematical articles or List of mathematics articles. I know it would be a lot of work to actually do, and I would be happy to help out where I could. What do people think? Tompw 23:30, 9 December 2005 (UTC)

Now the page violates WP:SELF
Topics are external to Wikipedia, as they exist in the real world. Wikipedia's articles exist solely within Wikipedia making reference to them a self-reference, and a departure from Wikipedia's Manual of Style. --The Transhumanist 11:06, 17 October 2006 (UTC)

Another point is that we're reinventing the wheel here. What is a "list of articles"? There are two types of such lists that come to mind: Tables of contents and indices. What you guys have created is a massive index system for the mathematics contents of Wikipedia! And since you've made the move to formality by the inclusion of the word "articles", you might as well go all the way by naming it Index of mathematics articles. --The Transhumanist 11:06, 17 October 2006 (UTC)

I think it may be time for a new namespace: Contents:. to be reserved for tables of contents (article lists) and indices of articles. --The Transhumanist 11:06, 17 October 2006 (UTC)

New namespace proposal
I've posted the above thougth at Village pump (proposals). --The Transhumanist 11:29, 17 October 2006 (UTC)

Self-references and suggested move
I just left this same note at User talk:Oleg Alexandrov. I think that a move to the Wikipedia namespace should be seriously considered. The problem with this page is that, except for the template, the entire page is written as if the reader is an editor of Wikipedia. If this text were reused for some reason in another form, it would not make sense. Khatru2 18:46, 11 December 2006 (UTC)
 * I think you should post the note of suggested move to Wikipedia talk:WikiProject Mathematics. Note that the move would be a lot of work (I did one such move earlier) and I would not agree with it, I think those lists look better in the main namespace. Oleg Alexandrov (talk) 03:49, 12 December 2006 (UTC)

 * Lists are an exception to the no self-references guideline. See the list guideline.  The Transhumanist  19:04, 5 November 2007 (UTC)

What's wrong with http://en.wikipedia.org/wiki/Category:Mathematics? 68.192.48.250 00:12, 4 February 2007 (UTC)

 * If you're suggesting it should replace this list, I'd say that's wrong on several counts. That category is not intended to contain all mathematics articles most of which are in subcategories, and categories are vastly inferior to topics lists. Michael Hardy 02:03, 4 February 2007 (UTC)

 * I agree with Michael. Categories are vastly inferior to topics lists. The entries of a topics list are centralized, that is, they reside on the topics list itself and can be edited directly; categories are autogenerated, with their entries on the pages of the entries rather than on the category pages, which makes the direct editing of categories impossible.  This makes categories cumbersome to create and maintain.  Because they are decentralized, categories are much harder to edit, requiring a tool like AutoWikiBrowser, which most editors do not know how to use, and force a time-consuming save operation after the addition or removal of any change in a category, which slows edits down to 2 to 6 edits per minute.  By comparison, in topics lists you can add, delete, or move hundreds or even thousands of links at a time without having to edit the pages represented by the links being moved. Lists take a fraction of the time to build and maintain, and therefore a single list editor can maintain many times more list items than the category items a  category maintainer can handle. Topics lists are also easier to monitor and defend against vandalism and inappropriate changes because they have edit histories, while the edit histories of category pages do not track changes to the categories themselves -- and because of this, entries can be removed from a category and not be noticed by anyone else.    Because of the reasons just given, lists with dedicated maintainers are much more comprehensive, while the corresponding categories are typically sparse or filled with holes.  Topics lists are more useful: they support scrolling, while categories only display 200 items at a time, but force most topics to be presented in subcategories -- therefore, accessing topics in the category system is more time consuming, and its small segmentation and formatting hinders copy/paste operations.  Topic lists support Related changes better, because more items can be presented on each page -- this is useful for spotting vandalism and inappropriate changes to the articles represented by the links on the list, making the lists a powerful tracking tool.  They also support redlinks, which are useful for tracking topics that do not yet have articles, and for spotting articles that have been deleted, allowing a new gap in the coverage of a list to be addressed and corrected.  Categories do not support redlinks - deleted pages simply disappear from categories.  Topics lists can be formatted, structured with subheadings, supported by images and templates, and aren't forced to be alphabetized -- entries can be presented in whatever order is most appropriate or useful in serving the purposes of the list.  Lists rock.  Categories suck.  Relatively speaking.  :-)  The Transhumanist  18:43, 5 November 2007 (UTC)

Updating this page
I have made a couple of edits to this article in order to: There are a couple of other changes I would like to make: Comments? Geometry guy 12:42, 29 April 2007 (UTC)
 * draw attention to the list of mathematics categories and its relation to this list;
 * clarify the purpose of the topical lists;
 * make this article look more like a mainspace article in an attempt at compromise with those who think it should be moved to Wikipedia (I am neutral on this point, but understand that it would be a lot of work).
 * 1) incorporate the recent changes lists into the  template, so that they are less dominant;
 * 2) replace the final section with a See also section pointing to these links with briefer descriptions in a more appropriate tone.

I've now partially carried out these last two suggestions. I wasn't able to incorporate the recent changes for mathematicians into the template, because there is no page where these are all linked any more. I also didn't introduce much tonal change in the See also section. Geometry guy 18:42, 29 April 2007 (UTC)

Wikipedia talk:Verifiability
There's a discussion on what the reference requirements for lists like this one. The Transhumanist (talk) 01:10, 12 January 2008 (UTC)
 * Archived at Wikipedia_talk:Verifiability/Archive_23. -- Quiddity (talk) 01:29, 25 August 2010 (UTC)

Removed LaTeX
I removed LaTeX and LaTeX2HTML from this list. Does anyone know why they were added? The categories that they are in don't even seem mathematical. Cheers, — sligocki (talk) 08:34, 25 October 2009 (UTC)

Linkfarm
Is this list a notable topic, or is it a WP:LINKFARM? Join in the discussion at WT:NOT. --Gavin Collins (talk|contribs) 22:31, 24 August 2010 (UTC)

Proposed move / reorganization
A move was requested to rename this article to Lists of mathematics articles, a page which currently redirects to Lists of mathematics topics. It seems to me that this page is meant to be the top-level of a general list of all mathematics articles, so that the pages it links to are subpages of it in some sense. On the other hand there is always some confusion between "List of mathematics articles" and "Lists of mathematics topics". I think it would make more sense to make "Lists of mathematics articles" into a dab page that lets readers go to either of those, since it is not clear which one they would mean if they went to it directly. What do other people think? Is there some better way to organize these? — Carl (CBM · talk) 17:48, 4 March 2012 (UTC)
 * This page should be split, the content as is can be moved to Wikiepdia: namespace, since its content is mainly links to WP:, the mainspace content can be kept in mainspace, if it isn't already duplicated here. Rich Farmbrough, 00:42, 8 March 2012 (UTC).

Redirect to Lists of mathematics topics
This hasn't been a list in many years and now is merely a call to a template. I suggest redirecting this page to Lists of mathematics topics Illia Connell (talk) 22:46, 25 December 2012 (UTC)
 * Tentatively agree. –Quiddity (talk) 00:39, 30 December 2012 (UTC)
 * Absent any further comment for a week or so, I have made the change Illia Connell (talk) 07:20, 11 January 2013 (UTC)

title: Talk:List of mathematics articles


text:
Nirṛti

Nirṛti (निर्ऋति) sometimes spelled Nirruti or Nirriti, is a Hindu deity, personifying death, decay, and sorrow. In early Hindu scriptures, Nirṛti is a goddess who is lives in the kingdom of the dead. In later Hinduism, Nirṛti and Nirṛta is also a male god, who is regarded as a dikapala ("guardian of the directions") of the southwest.

Etymology
The Sanskrit word Nirṛti means 'decay' and is derived from nirṛ (lit. 'to separate'). It can be interpreted as meaning "devoid of ṛta/i", a state of disorder or chaos.

The name  has the meaning of "absence of ṛta", meaning 'disorder', or 'lawlessness', specifically the guardian to the absence of divine or cosmic disorder.

This term was used in Vedic texts to indicate a realm of non-existence and absolute darkness, which threatened to consume those who failed in their duties to sacrifice and procreate. In nirṛti, there was no light, no food, and no children: none of the necessary elements of Vedic life and ritual

Goddess
Nirṛti is mentioned in the hymns of the Rigveda, mostly to seek protection from her or imploring for her during a possible departure. In one hymn (X.59), she is mentioned several times. This hymn, after summing up her nature, also asks for her in departure from the sacrificial site. In the Atharvaveda (V.7.9), she is described as having golden locks. In the Taittiriya Brahmana (I.6.1.4), Nirṛtī is described as dark, dressed in dark clothes and her sacrificial shares are dark husks. In the sacred Shatapatha Brahmana (X.1.2.9), she is associated with the southwest quarter as her region. But elsewhere in the same text (V.2.3.3.) she is mentioned as living in the kingdom of the dead.

In later Hindu texts, Nirṛti was re-conceptualized as a deity. According to some texts, she is the wife of Adharma (not-dharma) that signifies an important component of Prakriti (nature) for the Purusha (human -beings) who dwell in forests and the mother of three rakshasas—Mrityu (death), Bhaya (fear) and Mahabhaya (terror)—who were collectively referred to as Nairrita. Other texts portray her as the daughter of Adharma and Himsa (violence, the opposite of Ahimsa); she married her brother—Arita (not ṛta) and became the mother of Naraka (personification of the hell) and Bhaya. In the Bhagavata Purana, he is presented as Aprajaḥ (one without children) who takes Adharma and Mṛṣā (untruth), two of Brahma's sons or creations, as adopted sons. Some texts identify Nirṛti with other inauspicious goddess, Jyeshtha or Alakshmi. In this context, she is described to have emerged from the Samudra Manthana (the churning of the ocean).

Dikpala
According to some scholars and authors, the goddess Nirṛti transformed into a male in later Hindu mythology and became a dikpala. Nirṛti is regarded as the guardian of the southwest direction.

Nirṛti is sometimes included as one of the rudras and described as the son of Sthanu. Varying descriptions of the god Nirṛti are found in different scriptures. According to the Agamas, Nirrti is dark-skinned with a large body and draped in yellow garments. His vahana is either a man or a lion. The Vishnudharmottara Purana states that Nirṛti has a terrific appearance with ill-looking eyes, gaping mouth, and exposed teeth. The same scripture also gives a varying account that Nirṛti's vahana is a donkey and he holds a danda in his hands. The Vishnudharmottara Purana also mentions that Nirṛti has four consorts named Devi, Krishnangi, Krishavandana and Krishnapasha. According to the scripture Devi-Bhagavata Purana, Nirṛti resides in a city named Krishnajana, which is located in the southwestern part of Mount Meru. The city is said to have an area of 2500 yojanas.

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

title: Nirṛti


text:
Wilhelm Weber

Wilhelm Weber may refer to:

 * Wilhelm Eduard Weber (1804–1891), German physicist
 * Wilhelm Weber (gymnast) (1880–1963), German Olympic gymnast
 * Wilhelm Weber (SS officer) (1918–1980), Waffen-SS officer
 * Willi Weber (Wilhelm Friedrich Weber, born 1942), motorsport manager

title: Wilhelm Weber


text:
Ashlesha (nakshatra)

Ashlesha (Sanskrit: आश्लेषा or Āśleṣā) (Tibetan: སྐར་མ་སྐག), also known as Ayilyam in Tamil and Malayalam (Tamil: ஆயில்யம், Malayalam: ആയില്യം, Āyilyaṃ), is the 9th of the 27 nakshatras in Hindu astrology. Ashlesha is also known as the Clinging Star or Nāga. It is known as the Hydra. It extends from 16:40 to 30:00 Cancer.

The planetary lord is Mercury or Budha. Its presiding deities are the Nāgas. The nakshatra's symbol is a coiled serpent. It is a trikshna or sharp nakshatra. Its animal symbol is the male cat.

title: Ashlesha (nakshatra)


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A. Baldwin Wood

Albert Baldwin Wood (December 1, 1879 – May 10, 1956) was an inventor and engineer from New Orleans, Louisiana. He graduated from Tulane University with a Bachelor of Science in Engineering in 1899.

Wood was hired by the Sewerage & Water Board of New Orleans in 1899, to try to improve the flood-prone city's drainage, Wood invented "flapgates" and other hydraulic devices, most notably his efficient low-maintenance, high-volume pumps including the Wood Screw Pump (1913) and the Wood Trash Pump (1915). He spearheaded swampland reclamation and development of much of the land now occupied by the city.

While he spent most of his career in New Orleans, Wood also consulted and designed the drainage, pumping, and sewage systems for other cities including Chicago, Milwaukee, Baltimore, and San Francisco, as well as projects in Canada, Egypt, China, and India. His work was especially helpful in the Zuiderzee Works, which reclaimed large areas of land from the Zuider Zee in the Netherlands.

Some of Wood's pumps have been in almost continuous use in New Orleans for over 80 years without need of repairs, and new ones continue to be built from his designs.

When Wood died, he left a bequest to Tulane University on the condition that it preserve and display his sailboat, the Nydia, for 99 years. Until 2003, the boat was housed in a specially constructed glass-fronted display area located between the University Center and Fogelman Arena. It was moved to make room for the renovation and expansion of University Center. Because Tulane did not fully adhere to the terms of the will, Wood's heirs recovered possession of the boat. The Nydia is on display at the Maritime and Seafood Industry Museum in Biloxi, Mississippi, not far from where the boat was originally constructed at the Johnson Shipyard.

title: A. Baldwin Wood


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Astomi

In Greek and Roman mythology, the Astomi, also known as the Gangines, are an ancient legendary race of people who had no need to eat or drink anything at all. They survived by smelling apples and flowers and perfumes that they sprayed on their victims.

Megasthenes and Pliny the Elder (quoting Megasthenes) mentioned these people in his Indica. Megasthenes located them at the mouth of the river Ganges. In his description, they had rough and hairy bodies and no mouths. When traveling, they would carry roots, flowers and apples to smell. They could die by smelling a strong, unpleasant smell.

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Asvayujau

In Hinduism, Asvayujau is a goddess of fortune, good luck, joy and other names is Svasti wife of Vayu according to the Devi Bhagavata Purana.

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Atharvan

Atharvan (अथर्वन्, '; an n-stem with nominative singular अथर्वा ') is a legendary Vedic sage (rishi) of Hinduism, who along with Angiras, is supposed to have authored ("heard") the Atharvaveda. He is also said to have first instituted the fire-sacrifice or yajña. Sometimes he is also reckoned among the seven seers, the Saptarishi. His clan is known as the Atharvanas. Atharvan married Shanti, daughter of Prajapati Kardama, and had a great sage Dadhichi as a son. He is referred to as a member of the Bhrigu clan.

According to the Mundaka Upanishad and other texts, he was the eldest son and (Manasaputra) born from mind of the creator deity, Brahma.

Etymology
Vedic atharvan is cognate with Avestan āθrauuan / aθaurun, "priest", but the etymology of the term is not yet conclusively established. It was once thought to be etymologically related to the Avestan ātar, but that is now considered unlikely (Boyce, 2002:16). It has been suggested by scholars that the Vedic and Avestan terms are not of Indo-European origin, and are derived from the BMAC substrate.

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Talk:Coprime integers

Awkward wording (a.k.a., "Huh?!" )
From the text:

"...As specific examples, 14 and 25 are coprime, being commonly divisible only by 1, while 14 and 21 are not coprime, because they are both divisible by 7..."

Huh?!?! If you're trying to say that "14 and 25 are coprime, sharing no factors in common between them except 1," then for God's sake, please say that! I puzzled over that text uncomprehendingly for a good two minutes, trying to decipher the odd phrase commonly divisible, which I recall seeing nowhere else; it was only when I stopped ruminating on the first example long enough to take in the second, counterexample, that understanding finally came. Good grief! The Grand Rascal (talk) 08:31, 28 September 2020 (UTC)
 * , I agree. "Commonly divisible" is not a common phrase for saying "having a common divisor". I have fixed it. D.Lazard (talk) 08:51, 28 September 2020 (UTC)
 * [a] By chance, I read that a few days ago and found it perfectly understandable. The "proposed" version is also ok. [b] commonly divisible seems to be used: see (https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-prime-factorization-prealg/v/common-divisibility-examples). LMSchmitt 09:33, 28 September 2020 (UTC)
 * Indeed, that's because it's a completely standard English language construction -- there's nothing jargony or obscure at all about it. --JBL (talk) 11:32, 28 September 2020 (UTC)
 * , it is grammatically correct, but semantically confusing. In mathematics, one must always take care when words have a mathematical meaning that differ from their common (usual) meaning. In the case of "common divisor", "common" refers to "common to two integers". In "commonly divisible", "commonly" is not used in its common meaning, but is used in place of "simultaneously divisible". So the formulation is confusing. By the way Khan Academy is not a reliable source for attesting a common use of "commonly divisible" D.Lazard (talk) 14:35, 28 September 2020 (UTC)
 * To be clear: this is just forum-y chatting, I am not trying to get anyone to change the article. The most common meaning of "common" is probably "widespread; public". The second-most common meaning of "common" is "shared; joint".  Both of these can be turned into an adverb: "commonly" meaning "frequently; often; usually" and "commonly" meaning "in common; jointly".  The phrase "greatest common divisor" uses the second meaning of the adjective "common", and the phrase "commonly divisible" uses the corresponding adverbial form.  Anyone who understands the phrase "greatest common divisor" should, by applying standard rules of English, be able to convert it to the corresponding adverbial form, and vice-versa.  P.S. I feel like it is strangely common (at least, this is not the first time) for you, a PhD mathematician who writes English well but not fluently, to lecture me, a PhD mathematician who writes English fluently, on basic points of English grammar and its use in mathematics.  I promise that I will never attempt to lecture you on fine points of French usage or grammar! --JBL (talk) 12:51, 29 September 2020 (UTC)

Well. It may not be my recommended wording, but at least it's a lot clearer than it was! Thanks. 😊 The Grand Rascal (talk) 09:13, 28 September 2020 (UTC)

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Nbecker1.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 18:27, 16 January 2022 (UTC)

Clarity in the lead
The lead can be difficult for someone first coming to this concept, even though the concept is not complicated. I suggest that a sentence like the one Dan Harkless suggested be used, but with changes to avoid objections about 'coprime' not being a noon. Another clarification would be to expand on the example of 8 and 9 by naming the prime factors of each (2 and 3). 2600:6C67:1C00:5F7E:6DF1:CD52:7E5F:D359 (talk) 15:25, 9 July 2022 (UTC)

Maths
What is co prime number 103.66.81.7 (talk) 17:04, 10 July 2022 (UTC)

 * The answer is in the article. D.Lazard (talk) 18:06, 10 July 2022 (UTC)

Cases for three integers
When three different random integers are selected, there are five different cases of the three numbers having a common divisor or being coprime to one another:

1. All three integers have a common divisor greater than 1.

Example: 4, 6, 8; 4, 6, and 8 are all divisible by 2.

2. Exactly one pair of the three integers have a common divisor greater than 1 and the other integer is relatively prime to both the other two integers.

Example: 3, 4, 10; 4 and 10 are divisible by 2, 3 is relatively prime to both 4 and 10.

3. Exactly two pairs of the three integers have a common divisor greater than 1 and one pair of integers is relatively prime.

Example: 4, 6, 9; 4 and 6 are both divisible by 2, 6 and 9 are both divisible by 3, and 4 and 9 are relatively prime.

4. All three pairs of the three integers have a common divisor greater than 1 but the greatest common divisor of all three numbers is 1.

Example: 6, 10, 15; 6 and 10 are both divisible by 2, 6 and 15 are both divisible by 3, 10 and 15 are both divisible by 5, but the greatest common divisor of 6, 10, and 15 is 1.

5. No two integers have a common divisor greater than 1 (pairwise coprime).

Example: 3, 4, 5; 3, 4, and 5 are all relatively prime to one another.

What is the probability that each of the five cases will occur when choosing three random integers? Ar Colorado (talk) 16:02, 2 December 2022 (UTC)

 * This depends on the probability law that is chosen, and, except for the case 4 (setwise coprimality), it should be an exercise of probability theory to deduce the probability from the case of the probability of pairwise coprimality. In any case, per WP:VERIFIABILITY, a reliable source is needed for mentioning the result in this article, D.Lazard (talk) 16:39, 2 December 2022 (UTC)

title: Talk:Coprime integers


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Ātman (Hinduism)

Ātman (आत्मन्) is a Sanskrit word for the true or eternal Self or the self-existent essence or impersonal witness-consciousness within each individual. Atman is conceptually different from Jīvātman, which persists across multiple bodies and lifetimes. Some schools of Indian philosophy regard the Ātman as distinct from the material or mortal ego (Ahamkara), the emotional aspect of the mind (Citta), and existence in an embodied form (Prakṛti). The term is often translated as soul, but is better translated as "Self", as it solely refers to pure consciousness or witness-consciousness, beyond identification with phenomena. In order to attain moksha (liberation), a human being must acquire self-knowledge (Atma Gyaan or Brahmajnana).

Ātman is a central concept in the various schools of Indian philosophy, which have different views on the relation between Atman, individual Self (Jīvātman), supreme Self (Paramātmā) and, the Ultimate Reality (Brahman), stating that they are: completely identical (Advaita, Non-Dualist), completely different (Dvaita, Dualist), or simultaneously non-different and different (Bhedabheda, Non-Dualist + Dualist).

The six orthodox schools of Hinduism believe that there is Ātman in every living being (jiva), which is distinct from the body-mind complex. This is a major point of difference with the Buddhist doctrine of Anatta, which holds that in essence there is no unchanging essence or Self to be found in the empirical constituents of a living being, staying silent on what it is that is liberated.

Etymology
Ātman (Atma, आत्मा, आत्मन्) is a Sanskrit word that refers to "essence, breath." It is derived from the Proto-Indo-European word  (a root meaning "breath" similar to Ancient Greek ἀτμός along with Germanic cognates: Dutch adem, Afrikaans asem, Old High German atum "breath," Modern German atmen "to breathe" and Atem "respiration, breath", Modern English ethem, and Old English ǽþm and eþian).

Ātman, sometimes spelled without a diacritic as atman in scholarly literature, means "real Self" of the individual, "innermost essence." While often translated as "soul", it is better translated as "self."

Meaning
In Hinduism, Atman refers to the self-existent essence of human beings, the observing pure consciousness or witness-consciousness as exemplified by the Purusha of Samkhya. It is distinct from the ever-evolving embodied individual being (jivanatman) embedded in material reality, exemplified by the prakriti of Samkhya, and characterized by Ahamkara (ego, non-spiritual psychological I-ness Me-ness), mind (citta, manas), and all the defiling kleshas (habits, prejudices, desires, impulses, delusions, fads, behaviors, pleasures, sufferings and fears). Embodied personality and Ahamkara shift, evolve or change with time, while Atman doesn't. It is "pure, undifferentiated, self-shining consciousness."

As such, it is different from non-Hindu notions of soul, which includes consciousness but also the mental abilities of a living being, such as reason, character, feeling, consciousness, memory, perception and thinking. In Hinduism, these are all included in embodied reality, the counterpart of Atman.

Atman, in Hinduism, is considered as eternal, imperishable, beyond time, "not the same as body or mind or consciousness, but... something beyond which permeates all these". Atman is the unchanging, eternal, innermost radiant Self that is unaffected by personality, unaffected by ego; Atman is that which is ever-free, never-bound, the realized purpose, meaning, liberation in life. As Puchalski states, "the ultimate goal of Hindu religious life is to transcend individuality, to realize one's own true nature", the inner essence of oneself, which is divine and pure.

Vedas
The earliest use of the word Ātman in Indian texts is found in the Rig Veda (RV X.97.11). Yāska, the ancient Indian grammarian, commenting on this Rigvedic verse, accepts the following meanings of Ātman: the pervading principle, the organism in which other elements are united and the ultimate sentient principle.

Other hymns of Rig Veda where the word Ātman appears include I.115.1, VII.87.2, VII.101.6, VIII.3.24, IX.2.10, IX.6.8, and X.168.4.

Upanishads
Ātman is a central topic in all of the Upanishads, and "know your Ātman" is one of their thematic foci. The Upanishads say that Atman denotes "the ultimate essence of the universe" as well as "the vital breath in human beings", which is "imperishable Divine within" that is neither born nor does it die. Cosmology and psychology are indistinguishable, and these texts state that the core of every person's Self is not the body, nor the mind, nor the ego, but Ātman. The Upanishads express two distinct, somewhat divergent themes on the relation between Atman and Brahman. Some teach that Brahman (highest reality; universal principle; being-consciousness-bliss) is identical with Ātman, while others teach that Ātman is part of Brahman but not identical to it. This ancient debate flowered into various dual and non-dual theories in Hinduism. The Brahmasutra by Badarayana (~100 BCE) synthesized and unified these somewhat conflicting theories, stating that Atman and Brahman are different in some respects, particularly during the state of ignorance, but at the deepest level and in the state of self-realization, Atman and Brahman are identical, non-different (advaita). According to Koller, this synthesis countered the dualistic tradition of Samkhya-Yoga schools and realism-driven traditions of Nyaya-Vaiseshika schools, enabling it to become the foundation of Vedanta as Hinduism's most influential spiritual tradition.

Brihadaranyaka Upanishad
The Brihadaranyaka Upanishad (800-600 BCE ) describes Atman as that in which everything exists, which is of the highest value, which permeates everything, which is the essence of all, bliss and beyond description. In hymn 4.4.5, Brihadaranyaka Upanishad describes Atman as Brahman, and associates it with everything one is, everything one can be, one's free will, one's desire, what one does, what one doesn't do, the good in oneself, the bad in oneself. "That Atman (self, soul) is indeed Brahman. It [Ātman] is also identified with the intellect, the Manas (mind), and the vital breath, with the eyes and ears, with earth, water, air, and ākāśa (sky), with fire and with what is other than fire, with desire and the absence of desire, with anger and the absence of anger, with righteousness and unrighteousness, with everything — it is identified, as is well known, with this (what is perceived) and with that (what is inferred).

As it [Ātman] does and acts, so it becomes: by doing good it becomes good, and by doing evil it becomes evil. It becomes virtuous through good acts, and vicious through evil acts. Others, however, say, 'The self is identified with desire alone. What it desires, so it resolves; what it resolves, so is its deed; and what deed it does, so it reaps."

This theme of Ātman, that the essence and Self of every person and being is the same as Brahman, is extensively repeated in Brihadāranyaka Upanishad. The Upanishad asserts that this knowledge of "I am Brahman", and that there is no difference between "I" and "you", or "I" and "him" is a source of liberation, and not even gods can prevail over such a liberated man. For example, in hymn 1.4.10, "Brahman was this before; therefore it knew even the Ātma (soul, himself). I am Brahman, therefore it became all. And whoever among the gods had this enlightenment, also became That. It is the same with the sages, the same with men. Whoever knows the self as 'I am Brahman,' becomes all this universe. Even the gods cannot prevail against him, for he becomes their Ātma. Now, if a man worships another god, thinking: 'He is one and I am another,' he does not know. He is like an animal to the gods. As many animals serve a man, so does each man serve the gods. Even if one animal is taken away, it causes anguish; how much more so when many are taken away? Therefore it is not pleasing to the gods that men should know this."

Chandogya Upanishad
The Chandogya Upanishad (7th-6th c. BCE) explains Ātman as that which appears to be separate between two living beings but isn't, that essence and innermost, true, radiant self of all individuals which connects and unifies all. Hymn 6.10 explains it with the example of rivers, some of which flow to the east and some to the west, but ultimately all merge into the ocean and become one. In the same way, the individual souls are pure being, states the Chandogya Upanishad; an individual soul is pure truth, and an individual soul is a manifestation of the ocean of one universal soul.

Katha Upanishad
Along with the Brihadāranyaka, all the earliest and middle Upanishads discuss Ātman as they build their theories to answer how man can achieve liberation, freedom and bliss. The Katha Upanishad (5th to 1st century BCE) explains Atman as the imminent and transcendent innermost essence of each human being and living creature, that this is one, even though the external forms of living creatures manifest in different forms. Hymn 2.2.9 states: "As the one fire, after it has entered the world, though one, takes different forms according to whatever it burns, so does the internal Ātman of all living beings, though one, takes a form according to whatever He enters and is outside all forms."

Katha Upanishad, in Book 1, hymns 3.3-3.4, describes the widely cited proto-Samkhya analogy of chariot for the relation of "Soul, Self" to body, mind and senses. Stephen Kaplan translates these hymns as, "Know the Self as the rider in a chariot, and the body as simply the chariot. Know the intellect as the charioteer, and the mind as the reins. The senses, they say are the horses, and sense objects are the paths around them". The Katha Upanishad then declares that "when the Self [Ātman] understands this and is unified, integrated with body, senses and mind, is virtuous, mindful and pure, he reaches bliss, freedom and liberation".

Bhagavad Gita
In Bhagavad Gita verses 10-30 of the second chapter, Krishna urges Arjuna to understand the indestructible nature of the atman, emphasizing that it transcends the finite body it inhabits. The atman neither kills nor can be killed, as it is eternal and unaffected by birth or death. The analogy of changing clothes is used to illustrate how the soul discards old bodies for new ones. Krishna emphasizes the eternal existence of the soul by explaining that even as it undergoes various life stages and changes bodies it remains unaffected. It is imperceptible, inconceivable, and unchanging.

Orthodox schools
Atman is a metaphysical and spiritual concept for Hindus, often discussed in their scriptures with the concept of Brahman. All major orthodox schools of Hinduism – Samkhya, Yoga, Nyaya, Vaisesika, Mimamsa, and Vedanta – accept the foundational premise of the Vedas and Upanishads that "Ātman exists." In Hindu philosophy, especially in the Vedanta school of Hinduism, Ātman is the first principle. Jainism too accepts this premise, although it has its own idea of what that means. In contrast, both Buddhism and the Charvakas deny that there is anything called "Ātman/soul/self".

Samkhya

In Samkhya, the oldest school of Hinduism, Puruṣa, the witness-consciousness, is Atman. It is absolute, independent, free, imperceptible, unknowable through other agencies, above any experience by mind or senses and beyond any words or explanations. It remains pure, "nonattributive consciousness". Puruṣa is neither produced nor does it produce. No appellations can qualify purusha, nor can it substantialized or objectified. It "cannot be reduced, can't be 'settled'." Any designation of purusha comes from prakriti, and is a limitation. Unlike Advaita Vedanta, and like Purva-Mīmāṃsā, Samkhya believes in plurality of the puruṣas.

Samkhya considers ego (asmita, ahamkara) to be the cause of pleasure and pain. Self-knowledge is the means to attain kaivalya, the separation of Atman from the body-mind complex.

Yoga philosophy
The Yogasutra of Patanjali, the foundational text of Yoga school of Hinduism, mentions Atma in multiple verses, and particularly in its last book, where Samadhi is described as the path to self-knowledge and kaivalya. Some earlier mentions of Atman in Yogasutra include verse 2.5, where evidence of ignorance includes "confusing what is not Atman as Atman".

"अनित्याशुचिदुःखानात्मसु नित्यशुचिसुखात्मख्यातिरविद्या

Avidya (अविद्या, ignorance) is regarding the transient as eternal, the impure as pure, the pain-giving as joy-giving, and the non-Atman as Atman."

In verses 2.19-2.20, Yogasutra declares that pure ideas are the domain of Atman, the perceivable universe exists to enlighten Atman, but while Atman is pure, it may be deceived by complexities of perception or mind. These verses also set the purpose of all experience as a means to self-knowledge.

"द्रष्टा दृशिमात्रः शुद्धोऽपि प्रत्ययानुपश्यः तदर्थ एव दृश्यस्यात्मा

The seer is the absolute knower. Though pure, modifications are witnessed by him by coloring of intellect. The spectacle exists only to serve the purpose of the Atman."

In Book 4, Yogasutra states spiritual liberation as the stage where the yogin achieves distinguishing self-knowledge, he no longer confuses his mind as Atman, the mind is no longer affected by afflictions or worries of any kind, ignorance vanishes, and "pure consciousness settles in its own pure nature".

The Yoga school is similar to the Samkhya school in its conceptual foundations of Ātman. It is the self that is discovered and realized in the Kaivalya state, in both schools. Like Samkhya, this is not a single universal Ātman. It is one of the many individual selves where each "pure consciousness settles in its own pure nature", as a unique distinct soul/self. However, Yoga school's methodology was widely influential on other schools of Hindu philosophy. Vedanta monism, for example, adopted Yoga as a means to reach Jivanmukti – self-realization in this life – as conceptualized in Advaita Vedanta. Yoga and Samkhya define Ātman as an "unrelated, attributeless, self-luminous, omnipresent entity", which is identical with consciousness.

Nyaya
Early atheistic Nyaya scholars, and later theistic Nyaya scholars, both made substantial contributions to the systematic study of Ātman. They posited that even though "self" is intimately related to the knower, it can still be the subject of knowledge. John Plott states that the Nyaya scholars developed a theory of negation that far exceeds Hegel's theory of negation, while their epistemological theories refined to "know the knower" at least equals Aristotle's sophistication. Nyaya methodology influenced all major schools of Hinduism.

The Nyaya scholars defined Ātman as an imperceptible substance that is the substrate of human consciousness, manifesting itself with or without qualities such as desires, feelings, perception, knowledge, understanding, errors, insights, sufferings, bliss, and others. Nyaya school not only developed its theory of Atman, it contributed to Hindu philosophy in a number of ways. To the Hindu theory of Ātman, the contributions of Nyaya scholars were twofold. One, they went beyond holding it as "self evident" and offered rational proofs, consistent with their epistemology, in their debates with Buddhists, that "Atman exists". Second, they developed theories on what "Atman is and is not". As proofs for the proposition 'self exists', for example, Nyaya scholars argued that personal recollections and memories of the form "I did this so many years ago" implicitly presume that there is a self that is substantial, continuing, unchanged, and existent.

Nyayasutra, a 2nd-century CE foundational text of Nyaya school of Hinduism, states that Atma is a proper object of human knowledge. It also states that Atman is a real substance that can be inferred from certain signs, objectively perceivable attributes. For example, in book 1, chapter 1, verses 9 and 10, Nyayasutra states "Ātman, body, senses, objects of senses, intellect, mind, activity, error, pretyabhava (after life), fruit, suffering and bliss are the objects of right knowledge. Desire, aversion, effort, happiness, suffering and cognition are the Linga (लिङ्ग, mark, sign) of the Ātman."

Book 2, chapter 1, verses 1 to 23, of the Nyayasutras posits that the sensory act of looking is different from perception and cognition–that perception and knowledge arise from the seekings and actions of Ātman. The Naiyayikas emphasize that Ātman has qualities, but is different from its qualities. For example, desire is one of many qualities of Ātman, but Ātman does not always have desire, and in the state of liberation, for instance, the Ātman is without desire.

Vaiśeṣika
The Vaisheshika school of Hinduism, using its non-theistic theories of atomistic naturalism, posits that Ātman is one of the four eternal non-physical substances without attributes, the other three being kala (time), dik (space) and manas (mind). Time and space, stated Vaiśeṣika scholars, are eka (one), nitya (eternal) and vibhu (all pervading). Time and space are indivisible reality, but human mind prefers to divide them to comprehend past, present, future, relative place of other substances and beings, direction and its own coordinates in the universe. In contrast to these characteristics of time and space, Vaiśeṣika scholars considered Ātman to be many, eternal, independent and spiritual substances that cannot be reduced or inferred from other three non-physical and five physical dravya (substances). Mind and sensory organs are instruments, while consciousness is the domain of "atman, soul, self".

The knowledge of Ātman, to Vaiśeṣika Hindus, is another knowledge without any "bliss" or "consciousness" moksha state that Vedanta and Yoga school describe.

Mimamsa
Ātman, in the ritualism-based Mīmāṃsā school of Hinduism, is an eternal, omnipresent, inherently active essence that is identified as I-consciousness. Unlike all other schools of Hinduism, Mimamsaka scholars considered ego and Atman as the same. Within Mimamsa school, there was divergence of beliefs. Kumārila, for example, believed that Atman is the object of I-consciousness, whereas Prabhakara believed that Atman is the subject of I-consciousness. Mimamsaka Hindus believed that what matters is virtuous actions and rituals completed with perfection, and it is this that creates merit and imprints knowledge on Atman, whether one is aware or not aware of Atman. Their foremost emphasis was formulation and understanding of laws/duties/virtuous life (dharma) and consequent perfect execution of kriyas (actions). The Upanishadic discussion of Atman, to them, was of secondary importance. While other schools disagreed and discarded the Atma theory of Mimamsa, they incorporated Mimamsa theories on ethics, self-discipline, action, and dharma as necessary in one's journey toward knowing one's Atman.

Advaita Vedanta
Advaita Vedanta (non-dualism) sees the "spirit/soul/self" within each living entity as being fully identical with Brahman. The Advaita school believes that there is one soul that connects and exists in all living beings, regardless of their shapes or forms, and there is no distinction, no superior, no inferior, no separate devotee soul (Atman), no separate god soul (Brahman). The oneness unifies all beings, there is divine in every being, and that all existence is a single reality, state the Advaita Vedanta Hindus. In contrast, devotional sub-schools of Vedanta such as Dvaita (dualism) differentiate between the individual Atma in living beings, and the supreme Atma (Paramatma) as being separate.

Advaita Vedanta philosophy considers Atman as Sat-cit-ānanda, self-existent awareness, limitless and non-dual. To Advaitins, the Atman is the Brahman, the Brahman is the Atman, each self is non-different from the infinite. Atman is the universal principle, one eternal undifferentiated self-luminous consciousness, the truth asserts Advaita Hinduism. Human beings, in a state of unawareness of this universal self, see their "I-ness" as different from the being in others, then act out of impulse, fears, cravings, malice, division, confusion, anxiety, passions, and a sense of distinctiveness. To Advaitins, Atman-knowledge is the state of full awareness, liberation, and freedom that overcomes dualities at all levels, realizing the divine within oneself, the divine in others, and in all living beings; the non-dual oneness, that God is in everything, and everything is God. This identification of individual living beings/souls, or jiva-atmas, with the 'one Atman' is the non-dualistic Advaita Vedanta position.

Dvaita Vedanta
The monist, non-dual conception of existence in Advaita Vedanta is not accepted by the dualistic/theistic Dvaita Vedanta. Dvaita Vedanta calls the Atman of a supreme being as Paramatman, and holds it to be different from individual Atman. Dvaita scholars assert that God is the ultimate, complete, perfect, but distinct soul, one that is separate from incomplete, imperfect jivas (individual souls). The Advaita sub-school believes that self-knowledge leads to liberation in this life, while the Dvaita sub-school believes that liberation is only possible in after-life as communion with God, and only through the grace of God (if not, then one's Atman is reborn). God created individual souls, state Dvaita Vedantins, but the individual soul never was and never will become one with God; the best it can do is to experience bliss by getting infinitely close to God. The Dvaita school, therefore, in contrast to the monistic position of Advaita, advocates a version of monotheism wherein Brahman is made synonymous with Vishnu (or Narayana), distinct from numerous individual Atmans.

Buddhism
Applying the disidentification of 'no-self' to the logical end, Buddhism does not assert an unchanging essence, any "eternal, essential and absolute something called a soul, self or atman," According to Jayatilleke, the Upanishadic inquiry fails to find an empirical correlate of the assumed Atman, but nevertheless assumes its existence, and, states Mackenzie, Advaitins "reify consciousness as an eternal self." In contrast, the Buddhist inquiry "is satisfied with the empirical investigation which shows that no such Atman exists because there is no evidence" states Jayatilleke.

While Nirvana is liberation from the kleshas and the disturbances of the mind-body complex, Buddhism eludes a definition of what it is that is liberated. According to Johannes Bronkhorst, "it is possible that original Buddhism did not deny the existence of soul," but did not want to talk about it, as they could not say that "the soul is essentially not involved in action, as their opponents did." While the skandhas are regarded is impermanent (anatman) and sorrowfull (dukkha), the existence of a permanent, joyful and unchanging self is neither acknowledged nor explicitly denied. Liberation is not attained by knowledge of such a self, but by " turning away from what might erroneously be regarded as the self."

According to Harvey, in Buddhism the negation of temporal existents is applied even more rigorously than in the Upanishads: "While the Upanishads recognized many things as being not-Self, they felt that a real, true Self could be found. They held that when it was found, and known to be identical to Brahman, the basis of everything, this would bring liberation. In the Buddhist Suttas, though, literally everything is seen is non-Self, even Nirvana. When this is known, then liberation – Nirvana – is attained by total non-attachment. Thus both the Upanishads and the Buddhist Suttas see many things as not-Self, but the Suttas apply it, indeed non-Self, to everything."

Nevertheless, Atman-like notions can also be found in Buddhist texts chronologically placed in the 1st millennium of the Common Era, such as the Mahayana tradition's Tathāgatagarbha sūtras suggest self-like concepts, variously called Tathagatagarbha or Buddha nature. In the Theravada tradition, the Dhammakaya Movement in Thailand teaches that it is erroneous to subsume nirvana under the rubric of anatta (non-self); instead, nirvana is taught to be the "true self" or dhammakaya. Similar interpretations have been put forth by the then Thai Sangharaja in 1939. According to Williams, the Sangharaja's interpretation echoes the tathāgatagarbha sutras.

The notion of Buddha-nature is controversial, and "eternal self" concepts have been vigorously attacked. These "self-like" concepts are neither self nor sentient being, nor soul, nor personality. Some scholars posit that the Tathagatagarbha Sutras were written to promote Buddhism to non-Buddhists. The Dhammakaya Movement teaching that nirvana is atta (atman) has been criticized as heretical in Buddhism by Prayudh Payutto, a well-known scholar monk, who added that 'Buddha taught nibbana as being non-self". This dispute on the nature of teachings about 'self' and 'non-self' in Buddhism has led to arrest warrants, attacks and threats.

Influence of Atman-concept on Hindu ethics
The Atman theory in Upanishads had a profound impact on ancient ethical theories and dharma traditions now known as Hinduism. The earliest Dharmasutras of Hindus recite Atman theory from the Vedic texts and Upanishads, and on its foundation build precepts of dharma, laws and ethics. Atman theory, particularly the Advaita Vedanta and Yoga versions, influenced the emergence of the theory of Ahimsa (non-violence against all creatures), culture of vegetarianism, and other theories of ethical, dharmic life.

Dharma-sutras
The Dharmasutras and Dharmasastras integrate the teachings of Atman theory. Apastamba Dharmasutra, the oldest known Indian text on dharma, for example, titles Chapters 1.8.22 and 1.8.23 as "Knowledge of the Atman" and then recites,

"There is no higher object than the attainment of the knowledge of Atman. We shall quote the verses from the Veda which refer to the attainment of the knowledge of the Atman. All living creatures are the dwelling of him who lies enveloped in matter, who is immortal, who is spotless. A wise man shall strive after the knowledge of the Atman. It is he [Self] who is the eternal part in all creatures, whose essence is wisdom, who is immortal, unchangeable, pure; he is the universe, he is the highest goal. – 1.8.22.2-7

Freedom from anger, from excitement, from rage, from greed, from perplexity, from hypocrisy, from hurtfulness (from injury to others); Speaking the truth, moderate eating, refraining from calumny and envy, sharing with others, avoiding accepting gifts, uprightness, forgiveness, gentleness, tranquility, temperance, amity with all living creatures, yoga, honorable conduct, benevolence and contentedness – These virtues have been agreed upon for all the ashramas; he who, according to the precepts of the sacred law, practices these, becomes united with the Universal Self. – 1.8.23.6"

Ahimsa
The ethical prohibition against harming any human beings or other living creatures (Ahimsa, अहिंसा), in Hindu traditions, can be traced to the Atman theory. This precept against injuring any living being appears together with Atman theory in hymn 8.15.1 of Chandogya Upanishad (ca. 8th century BCE), then becomes central in the texts of Hindu philosophy, entering the dharma codes of ancient Dharmasutras and later era Manu-Smriti. Ahimsa theory is a natural corollary and consequence of "Atman is universal oneness, present in all living beings. Atman connects and prevades in everyone. Hurting or injuring another being is hurting the Atman, and thus one's self that exists in another body". This conceptual connection between one's Atman, the universal, and Ahimsa starts in Isha Upanishad, develops in the theories of the ancient scholar Yajnavalkya, and one which inspired Gandhi as he led non-violent movement against colonialism in early 20th century.

"यस्तु सर्वाणि भूतान्यात्मन्येवानुपश्यति । सर्वभूतेषु चात्मानं ततो न विजुगुप्सते ॥६॥ यस्मिन्सर्वाणि भूतान्यात्मैवाभूद्विजानतः । तत्र को मोहः कः शोक एकत्वमनुपश्यतः ॥७॥   स पर्यगाच्छुक्रमकायमव्रणम् अस्नाविरँ शुद्धमपापविद्धम् । कविर्मनीषी परिभूः स्वयम्भूःयाथातथ्यतोऽर्थान् व्यदधाच्छाश्वतीभ्यः समाभ्यः ॥८॥

And he who sees everything in his atman, and his atman in everything, does not seek to hide himself from that. In whom all beings have become one with his own atman, what perplexity, what sorrow, is there when he sees this oneness? He [the self] prevades all, resplendent, bodiless, woundless, without muscles, pure, untouched by evil; far-seeing, transcendent, self-being, disposing ends through perpetual ages."

title: Ātman (Hinduism)


text:
Atri

Atri or Attri is a Vedic sage, who is credited with composing numerous hymns to Agni, Indra, and other Vedic deities of Hinduism. Atri is one of the Saptarishi (seven great Vedic sages) in the Hindu tradition, and the one most mentioned in its scripture Rigveda.

The fifth Mandala (Book 5) of the Rigveda is called the Atri Mandala in his honour, and the eighty seven hymns in it are attributed to him and his descendants.

Atri is also mentioned in the Puranas and the Hindu epics of the Ramayana and the Mahabharata.

Legend
Atri is one of the seven great Rishis or Saptarshi along with Marichi, Angiras, Pulaha, Kratu, Pulastya and Vashistha. According to the legends of the Vedic era, sage Atri was married to Anasuya Devi. They had three sons, Dattatreya, Durvasa and Chandra. As per divine account, he is the last among the seven Saptarishis and is believed to have originated from the tongue. The wife of Atri was Anasuya, who is considered one of the seven female pativratas. When instructed by divine voice to do tapas, Atri readily agreed and did severe tapas. Pleased by his devotion and prayers, the Hindu trinity, namely, Brahma, Vishnu, and Shiva appeared before him and offered him boons. He sought all the three to be born to him. Another version of the legend states that Anasuya, by the powers of her chastity, rescued the three gods and in return, they were born as children to her. Brahma was born to her as Chandra, Vishnu as Dattatreya and Shiva in some part as Durvasa. The mention of Atri is found in various scriptures, with the notable being in Rig Veda. He is also associated with various ages, the notable being in Treta Yuga during Ramayana, when he and Anasuya advised Rama and his wife Sita. The pair is also attributed to bringing river Ganga down to earth, the mention of which is found in the Shiva Purana.

He is said to be a resident of the south in Valmiki Ramayana. The same is supported by Puranic tradition.

Seer of Rig Veda
He is the seer of the fifth Mandala (Book 5) of the Rigveda. Atri had many sons and disciples who have also contributed in the compilation of the Rig Veda and other Vedic texts. Mandala 5 comprises 87 hymns, mainly to Agni and Indra, but also to the Visvedevas ("all the gods'), the Maruts, the twin-deity Mitra-Varuna and the Asvins. Two hymns each are dedicated to Ushas (the dawn) and to Savitr. Most hymns in this book are attributed to the Atri clan composers, called the Atreyas.

The Atri hymns of the Rigveda are significant for their melodic structure as well as for featuring spiritual ideas in the form of riddles. These hymns include lexical, syntactic, morphological and verb play utilizing the flexibility of the Sanskrit language. The hymn 5.44 of the Rigveda in Atri Mandala is considered by scholars such as Geldner to be the most difficult riddle hymn in all of the Rigveda. The verses are also known for their elegant presentation of natural phenomenon through divinely inspired poems, such as poetically presenting dawn as a cheerful woman in hymn 5.80.

While the fifth mandala is attributed to Atri and his associates, sage Atri is mentioned or credited with numerous other verses of the Rigveda in other Mandalas, such as 10.137.4.

Ramayana
In the Ramayana, Rama, Sita and Lakshmana visit Atri and Anasuya in their hermitage. Atri's hut is described to be in Chitrakuta, near a lake with divine music and songs, the water loaded with flowers, green water leaves, with many "cranes, fisherbirds, floating tortoises, swans, frogs and pink geese".

Puranas
A number of sages named Atri are mentioned in the various medieval era Puranas. The legends therein about Atri are diverse and inconsistent. It is unclear if these refer to the same person, or to different Rishis who had the same name.

Cultural influence
The Vaikhanasas sub-tradition within Vaishnavism found in South India near Tirupati, credit their theology to four Rishis (sages), namely Atri, Marichi, Bhrigu and Kashyapa. One of the ancient texts of this tradition is Atri Samhita, which survives in highly inconsistent fragments of manuscripts. The text are rules of conduct aimed at Brahmins of the Vaikhanasas tradition. The surviving parts of the Atri Samhita suggest that the text discussed, among other things, yoga, and ethics of living, with precepts such as:

"Self restraint: Charity: Compassion:
 * If material or spiritual pain is created by others, and one is not offended and does not wreak revenge, it is called Dama.
 * Even with limited income, something should be given away daily with care and liberal spirit. This is called Dana.
 * One should behave like his own self, towards others, his own relations and friends, him who envies him, and even his enemy. This is called Daya."

- Atri Samhita

The Vaikhanasas continue to be a significant community in South India, and they adhere to their Vedic heritage.

title: Atri


text:
Pacific Maritime Association

The Pacific Maritime Association (PMA) is a non-profit organization based in San Francisco, California that represents employers of the shipping industry on the Pacific coast.

Background
The Pacific Maritime Association was founded in 1949 as a non-profit corporation. It represented a merger of the Waterfront Employers Association (WEA) and the American Shipowners Association (ASA). Its principal business is to negotiate and administer labor agreements with the International Longshore and Warehouse Union (ILWU). PMA's 72 members are cargo carriers, terminal operators, and stevedores that operate along the U.S. West Coast.

In 1960, it negotiated the Mechanization and Modernization Agreement.

As of December 2012, PMA members employed nearly 14,000 registered longshore, clerk and foreman workers at 29 west coast ports in California, Oregon, and Washington, and thousands more “casual” workers, who typically work part-time. Since the 2002 agreement that brought the widespread use of technology to the West Coast, the registered workforce has increased by 32 percent.

In 2015, it negotiated a five-year contract with the ILWU.

title: Pacific Maritime Association


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Ayyappan

Ayyappan, also known as Dharmasastha and Manikandan, is the Hindu deity of truth and righteousness. His worship is more prevalant in South India. Although devotion to Ayyappan has been prevalent earlier, his popularity rose in the late 20th century. According to Hindu theology, he is the son of Vishnu in the form of Mohini and Shiva thus representing a bridge between Shaivism and Vaishnavism. Ayyappan is depicted as a youthful man, riding or near a Bengal tiger, carrying a bow and arrow. Most iconography of Ayyappan depict him in a yogapattasana, a seated position. His abode is in Sabarimala which is located in the forests of the Western Ghats on the banks of river Pamba, and is a major pilgrimage destination, attracting millions annually.

Names and etymology
Ayyappan is literally derived from "Ayyan" and "Appan" both meaning "father" and the root names might denote Mohini (the female form of Vishnu) and Shiva, respectively. An alternate theory links it to the Malayalam word acchan and Tamil word appa both meaning "father", with Ayyappan connoting as "Lord-father". The proposal is supported by the alternate name for Ayyappan being Sasta, a Vedic term that also means teacher or guide. However, the word Ayyappan is not found in the medieval era Puranas, while the words Sastha and Dharmasastha in the sense of a Hindu god are mentioned in the Puranas. Ayyappan is also known as Hariharasudhan, meaning the "son of Harihara" or a fusion deity of Hari and Hara, the names given to Vishnu and Shiva, respectively. He is also called Manikanda with Mani meaning bell and Kanda meaning neck in Sanskrit, translating to the wearer of a bell on the neck.

Iconography and depictions
Ayyappan is a warrior deity and is revered for his ascetic devotion to Dharma, the ethical and right way of living, to deploy his military genius and daring yogic war abilities to destroy those who are powerful but unethical, abusive and arbitrary. He is usually represented as a celibate young man with a bow and arrow, riding a bengal tiger. In some representations, he is seen holding an upraised bow in his left hand, while holding either an arrow or sword in his right hand placed diagonally across his left thigh. Other iconography of Ayyappan, generally shows him in a yogic posture wearing a bell around his neck. In some representations, such as in Sri Lanka, he is shown riding an Indian elephant or a horse.

Theology and historical development
The legend and mythology of Ayyappa varies across regions, reflecting a tradition that evolved over time. According to Sribhutanatha Purana, Ayyappan is mentioned as an incarnation of Hariharaputra, the son of Shiva and Mohini. While this interaction between Shiva and Mohini is mentioned in the Bhagavata Purana, Ayyappan is not mentioned by name.

According to Malayalam folk songs, Ayyappan is presented as a warrior prince of Pandala kingdom. As the royal family was childless, the king of Pandalam found a baby boy in a forest. The king named the boy Manikantha and raised him his own son, on the advice of an ascetic. When Manikantha was 12 years old, the king wanted to formally anoit him as the heir. However, the queen objected to it, favoring her younger biological child. The queen feigned an illness, asking for the milk of a tiger to cure her illness and demanded that Manikantha be sent to obtain the same. Manikantha volunteers and goes into the forest, where he confronts the demoness Mahishi, whom he kills and returns back riding a tigress. The king realizing Manikantha's special ability recognizes him to be a divine being and resolves to make a shrine for him. Manikantha transforms into Ayyappan and shoots an arrow to denote the place for the shrine. There are minor variations in the story in certain versions with Ayyappan renouncing the kingdom and becoming an ascetic yogi in a forested mountain. In some versions, he was raised by a childless royal couple Rajashekara Pandian and Koperundevi, and grew up as a warrior yogi.

In the later years, the stories of Ayyappan expanded. One such version has roots between the 1st and 3rd century CE, where Ayyappan evolves to be a deity who also protects traders and merchants from enemies such as robbers and plundering outlaws. His temple and tradition inspired Hindu yogi mercenaries who protected the trade routes in South India from criminals and looters, restoring Dharmic trading practices. In another version, Ayyappan is portrayed as a child of a priest whose father was murdered by a fearsome outlaw. The outlaw kidnaps a princess and Ayyappan makes a daring rescue, while killing the outlaw in the process. In a variation of the story, Ayyappan forms an alliance with the Muslim warrior Vavar against the outlaw Udayanan, which forms the basis for worshiping both in a mosque and then in the Hindu temple before starting a pilgrimage to Ayyappan shrine.

According to Paul Younger, supplementary legends appeared in the late medieval times that linked other Hindu deities and mythologies to Ayyappan heritage. The divine beings Datta and Leela came to earth as humans. Datta wanted to return to the divine realm, but Leela enjoyed her life on earth and wanted to stay on earth. Datta became angry and cursed her to become a Mahishi, or water buffalo demoness. Leela in turn cursed him to become a Mahishi, or water buffalo demon. They both plundered the earth with their evil acts. Mahishasura was later killed by goddess Durga, while Mahishi was killed by Ayyapan, ending the terror of evil and liberating Leela who was previously cursed. These legends, states Younger, syncretically link and combine various Hindu traditions around Shaivism, Vaishnavism and Shaktism. According to Eliza Kent, the legends in the Ayyappa tradition seem to be "artificially mixed and assembled into a kind of collage". Ruth Vanita suggests that Ayyappan probably emerged from the fusion of a Dravidian god of tribal provenance and the Puranic story of Shiva and Mohini's interaction. In some regions, Ayyappa and Tamil folk deity Ayyanar are considered to be the same with similar characteristics, a reason for his large following amongst Tamils.

Worship
Although devotion to Ayyappan has been prevalent earlier, his popularity rose in the late 20th century. While there are many temples in South India whose presiding deity is Ayyappan, the most prominent Ayyappan shrine is at Sabarimala, nestled in the hills of Western Ghats on the banks of river Pamba in Kerala. It is a major pilgrimage center, attracting millions of Hindus every year. The temple is open only on select days of a year.

Pilgrims begin preparations weeks in advance by leading a simpler life, remaining celibate, eating a vegetarian diet or partially fasting and wearing a black or blue dress. These weeks of rituals are termed as Vrutham which is signified by wearing a Tulsi or Rudraksha. The pilgrims do not recognize any form of social or economic discrimination and form a fraternity treating each other as equals. The pilgrims call each other by the same name Swami meaning "God". The pilgrims bath in the Pamba river and embark on a trek to the top of the hill on barefoot while carrying an irumudi (a bag with two compartments containing offerings) on the head. Then they climb the 18 steps in front of the shrine, each representing a dharmic value. The shrine priests and devotees bring flowers and scatter them near the shrine, all the while chanting shlokas. As Ayyappan is believed to be a celibate deity, women in their fertile age are not allowed to enter the shrine. The most significant festival linked to him is the Makaravilakku, observed around the winter solstice. Harivarasanam is a Manipravalam ashtakam composed in praise of Shiva but sung as a lullaby for Ayyappan.

Other temples include Kulathupuzha Sastha Temple, Aryankavu Sastha Temple, Achankovil Sastha Temple, Erumely Sree Dharmasastha Temple and Ponnambalamedu temple. While Ayyappan temples typically show him as a celibate yogi, a few temples such as the one at Achankovil Sastha Temple depict him as a married man with two wives Poorna and Pushkala, as well as a son Satyaka. Some of Ayyappan temples are believed to have been established by Parashurama.

Ayyappan remains one of the few deities in Hindu tradition, who is respected by other religious communities, including Muslims and Christians. He is also revered by Muslims in Kerala due to his friendship with Vavar. In this mythology, Ayyappan confronts the plunder-driven pirate robber Vavar in the jungle with Ayyappan defeating Vavar, who then becomes Ayyappan's trusted lieutenant helping fight other pirates and robbers. In another version, Vavar is stated to be a Muslim saint from Arabia, who works with Ayyappan. A mosque dedicated to Vavar stands next to the Kadutha swami shrine at the foot of the pilgrimage path, both as a form of guardian deities. Pilgrims offer a prayer to both, before beginning the trek towards Sabarimala. According to Kent, the mosque does not contain mortal remains of Vavar though the mosque near Sabarimala includes a grave, and no one can date Vavar nor provide when and where he lived, so he may be a myth. The Vavar legend and palli shrines may reflect the Hindu approach to accepting and co-opting legendary figures or saints of other religions within its fold.

Popular culture
A number of Indian films have been made about Ayyappan. These include: Sabarimala Ayyappan (1961) by S. M. Sriramulu Naidu, Swami Ayyappan (1975) by P. Subramaniam, Saranam Ayyappa (1980) by Dasarathan, Arul Tharum Ayyappan (1987) by Dasarathan, Shiv Putra Swami Ayappa (1990) by P.S. Mani, Sabarimala Sri Ayyappan (1990) by Renuka Sharma, Engal Swamy Ayyappan (1990) by Dasarathan, Ayyappa Swamy Mahatyam (1991), Ayyappa Deeksha Mahimalu (1992) by Guda Rama Krishna, Swami Ayappa Shabarimalai (1993) by K. Shankar, Jai Hari Hara Putra Ayyappa (1995), Bhagwaan Ayyappa (2007) by Irajaral Bhakhta and V. Swaminathan, Swami Ayyappan (2012) by Chetan Sharma and Mahesh Vettiyar, Om Sharanam Ayyappa (2015) by K. Sharath, Sri Omkara Ayyappane (2016) by Sai Prakash, Ayyappa Kataksham (2019) by Rudrapatla Venugopal and Malikappuram (2023) by Vishnu Mohan.

Asianet launched a Malayalam series named Swami Ayyappan in 2006. Other series include Swami Ayyappan Saram (2010), Sabarimala Shri Dharmashasta (2012), Sabarimala Swami Ayappan (2019) and Malikappuram: Apathbandhavan Ayyappan (2023). The story of Ayyappa is dictated by Parvati to Ganesha in the Indian TV show Vighnaharta Ganesh. The story of Ayyappan was adapted as a comic in the 673rd issue of the Indian comic book series, Amar Chitra Katha.

title: Ayyappan


text:
Luxembourg (disambiguation)

Luxembourg, officially the Grand Duchy of Luxembourg, is a sovereign country in western Europe.

Luxembourg or Luxemburg may also refer to:

Luxembourg

 * Luxembourg City, the capital city
 * Luxembourg District, one of the three districts of Luxembourg
 * Luxembourg (canton), one subdivision of Luxembourg district
 * County of Luxemburg, a state of the Holy Roman Empire
 * Duchy of Luxemburg, a state of the Holy Roman Empire
 * Luxembourg (European Parliament constituency), a constituency in the European Parliament

Belgium

 * Luxembourg (Belgium), a province of Wallonia, Belgium
 * Place du Luxembourg, a square in Brussels

France

 * Luxembourg Garden, in Paris
 * Luxembourg Palace, located inside the Luxembourg Garden
 * Musée du Luxembourg, in Paris
 * Luxembourg station (Paris), on RER line B

United States

 * Luxemburg, Iowa
 * Luxemburg, Wisconsin
 * Luxemburg Township, Stearns County, Minnesota

People

 * Christoph Luxenberg, a pseudonymous author
 * François-Henri de Montmorency, duc de Luxembourg, a Marshal of France
 * Rosa Luxemburg (born Rosalia Luxemburg; 1871–1919), a Polish-German Marxist revolutionary
 * Vladimir Lyuksemburg (1888–1971), a Russian Communist, member of the first Bolshevik government of Ukraine
 * Rut Blees Luxemburg (born 1967), German photographer
 * Wilhelmus Luxemburg (1929–2018), American mathematician
 * House of Luxembourg, a medieval German royal family

Music

 * Luxembourg (album), an album by the English band The Bluetones
 * Luxembourg (band), a British five-piece indie band
 * "Luxembourg", a song by Elvis Costello on his album Trust

Other

 * Luxembourg (horse), Thoroughbred racehorse
 * House of Luxembourg, a royal family within the Holy Roman Empire

title: Luxembourg (disambiguation)