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Monoceros

Monoceros (Greek: Μονόκερως, "unicorn") is a faint constellation on the celestial equator. Its definition is attributed to the 17th-century cartographer Petrus Plancius. It is bordered by Orion to the west, Gemini to the north, Canis Major to the south, and Hydra to the east. Other bordering constellations include Canis Minor, Lepus, and Puppis.

Stars
Monoceros contains only a few fourth magnitude stars, making it difficult to see with the naked eye. Alpha Monocerotis has a visual magnitude of 3.93, while for Gamma Monocerotis it is 3.98.

Beta Monocerotis is a triple star system; the three stars form a fixed triangle. The visual magnitudes of the stars are 4.7, 5.2, and 6.1. William Herschel discovered it in 1781 and called it "one of the most beautiful sights in the heavens".

Epsilon Monocerotis is a fixed binary, with visual magnitudes of 4.5 and 6.5.

S Monocerotis, or 15 Monocerotis, is a bluish white variable star and is located at the center of NGC 2264. The variation in its magnitude is slight (4.2–4.6). It has a companion star of visual magnitude 8.

V838 Monocerotis, a variable red supergiant star, had an outburst starting on January 6, 2002; in February of that year, its brightness increased by a factor of 10,000 in one day. After the outburst was over, the Hubble Space Telescope was able to observe a light echo, which illuminated the dust surrounding the star.

Monoceros also contains Plaskett's Star, a massive binary system whose combined mass is estimated to be almost 100 solar masses.

Monoceros is the location of the binary system Scholz's Star, host to a red dwarf primary and brown dwarf secondary; the system performed a close flypast of the Solar System approximately 70,000 years ago, travelling within 120,000 astronomical units of the Sun within the Oort cloud.

One of the nearest known black holes to the Solar System is in this constellation. The binary star system A0620-00 in the constellation of Monoceros is at a distance of roughly 3,300 light-years (1,000 parsecs) away. The black hole is estimated to be 6.6 solar masses.

Planets
Monoceros contains two super-Earth exoplanets in one planetary system: CoRoT-7b was detected by the CoRoT satellite and CoRoT-7c was detected by the High Accuracy Radial Velocity Planet Searcher from ground-based telescopes. Until the announcement of Kepler-10b in January 2011, CoRoT-7b was the smallest exoplanet to have its diameter measured, at 1.58 times that of the Earth (which would give it a volume 3.95 times Earth's). Both planets in this system were discovered in 2009.

Deep-sky objects
Part of the galactic plane goes through Monoceros, so background galaxies are concealed by interstellar dust. Monoceros contains many clusters and nebulae; most notable among them are:
 * Messier 50, an open cluster
 * The Rosette Nebula (NGC 2237, 2238, 2239, and 2246) is a diffuse nebula in Monoceros. It has an overall magnitude of 6.0 and is 4900 light-years from Earth. The Rosette Nebula, over 100 light-years in diameter, has an associated star cluster and possesses many Bok globules in its dark areas. It was independently discovered in the 1880s by Lewis Swift (early 1880s) and Edward Emerson Barnard (1883) as they hunted for comets.
 * The Christmas Tree Cluster (NGC 2264) is another open cluster in Monoceros. Named for its resemblance to a Christmas tree, it is fairly bright at an overall magnitude of 3.9; it is 2400 light-years from Earth. The variable star S Monocerotis represents the tree's trunk, while the variable star V429 Monocerotis represents its top.
 * The Cone Nebula (NGC 2264), associated with the Christmas Tree Cluster, is a very dim nebula that contains a dark conic structure. It appears clearly in photographs, but is very elusive in a telescope. The nebula contains several Herbig–Haro objects, which are small irregularly variable nebulae. They are associated with protostars.
 * NGC 2254 is an open cluster with an overall magnitude of 9.7, 7100 light-years from Earth. It is a Shapley class f and Trumpler class I 2 p cluster, meaning that it appears to be a fairly rich cluster overall, though it has fewer than 50 stars. It appears distinct from the background star field and is very concentrated at its center; its stars range moderately in brightness.
 * Hubble's Variable Nebula (NGC 2261) is a nebula with an approximate magnitude of 10, 2500 light-years from Earth. It is named for Edwin Hubble, and was discovered in 1783 by Herschel. Hubble's Variable Nebula is illuminated by R Monocerotis, a young variable star embedded in the nebula; the star's unique interaction with the material in the nebula makes it both an emission nebula and a reflection nebula. One hypothesis regarding their interaction is that the nebula and its illuminating star are a very early stage planetary system.
 * IC 447, a reflection nebula.

History

In Western astronomy, Monoceros is a relatively modern constellation, not one of Ptolemy's 48 in the Almagest. Its first certain appearance was on a globe created by the cartographer Petrus Plancius in 1612 or 1613 and it was later charted by German astronomer Jakob Bartsch as Unicornu on his star chart of 1624.

German astronomers Heinrich Wilhelm Olbers and Ludwig Ideler indicate (according to Richard Hinckley Allen's allegations) that the constellation may be older, quoting an astrological work from 1564 that mentioned "the second horse between the Twins and the Crab has many stars, but not very bright"; these references may ultimately be due to the 13th century Scotsman Michael Scot, but refer to a horse and not a unicorn, and its position does not quite match. Joseph Scaliger is reported to have found Monoceros on an ancient Persian sphere. French astronomer Camille Flammarion believed that a former constellation, Neper (the "Auger"), occupied the area of the sky now home to Monoceros and Microscopium, but this is disputed.

Chinese asterisms Sze Fūh, the Four Great Canals; Kwan Kew; and Wae Choo, the Outer Kitchen, all lay within the boundaries of Monoceros.

title: Monoceros


text:
User talk:Gene Poole

AfD SM Lifestyle Center
I'm baffled by your comment on this AfD. I looked in Mandarin and couldn't easily find reliable sources. Moreover, it's a small mall by SM standards: it turned out to be one-quarter of the originally estimated size, and their smallest mall in China. Was the language in my Merge comment confusing? Matt's talk 10:51, 3 November 2008 (UTC)
 * My comments supporting retention of a discrete article on the above subject refer to the prior comments of Blanchardb and Edison, which suggest that citable sources about the mall exist, and that the mall itself is the largest in the district in which it's located. --Gene_poole (talk) 18:40, 7 November 2008 (UTC)

Space music
Hi Gene, I think in dealing with this article we need only deal with the obvious outstanding content issues. If what you say about said editor is true, I would personally avoid engaging in any debate other than that which relates directly to policy, and the manner in which this article deviates from stated guidelines. I was threading softly becasue I realise the points I'm raising will seem contentious to some. I haven't looked at all the published sources cited, other that the 10 pages dedicated to 'space music' in Lanza (1994) but that was enough for me to see that there are some glaring omissions and many inaccuracies in the article. I wasn't aware of the HOS radio program before seeing the article but having looked up the website I now see it is a commercial operation, this automatically undermines all of the cited material taken from this site - it was already problematic insofar as it is self-published. I think a drastic cutting back of citations and removal of synthetic material is inevitable. I would suggest waiting for further responses to the tagging before taking action. Semitransgenic (talk) 20:37, 7 November 2008 (UTC)
 * OK well I can see this is a somewhat sensitive issue then. The way I see it, that is, relative to my understanding of how various genre definitions have evolved, inaccuracies exist in the article, the historical assessment is somewhat muddled, and I now understand the point you make about the HOS influence. This is going to be messy. Semitransgenic (talk) 22:27, 7 November 2008 (UTC)
 * Well I had never heard of this HOS show, but in the UK & Europe 'space music' is the English translation of 'kosmische musik' which is interchangeable with 'krautrock', I would refer to what HOS are doing as largely 'New Age music' at least judging by some of the music they are endorsing. Semitransgenic (talk) 01:09, 8 November 2008 (UTC)
 * Hi Gene, it seems your assessment was correct, my WP:GF efforts were wasted. Said user bluntly refuses to deal with the content dispute in a constructive fashion and seeks only to lower the tone of proceedings with juvenile taunts. Would you mind offering your opinion here so user:Will Beback can get an idea of the pattern of behavior on the 'space music' article. I suggest we move forward by posting on WP:NORN, WP:RSN and WP:RFC. Do you have any suggestions? Semitransgenic (talk) 04:19, 11 November 2008 (UTC)
 * Hi Gene, in an effort to try and move things forward, would you be prepared to put your differences with Milo aside so we can all try and tease out matters relating to the HOS source? I am suggesting the first step be a WP:RSN posting before editing continues. If we could begin some kind of civil discussion on the talk page that would be a positive step, how does that meet with you? Semitransgenic (talk) 22:01, 11 November 2008 (UTC)
 * OK thanks, lets see what comes of this, hopefully we can hammer something out that we are all be happy with. Cheers. Semitransgenic (talk) 00:09, 12 November 2008 (UTC)
 * PS. In the past, has there been any attempt at mediation or any posting on a content related notice board regarding the article? Semitransgenic (talk) 00:10, 12 November 2008 (UTC)

Hi .. can I spot my three cents worth in here somewhere.? re: space? (sound) or the continuim of all energy waves .. of accoustical enerrgy .. wherever that may actually 'sit' on the entire electromechanical spectrum of "sound" frequency. As Yes.. u see.. - I believe.. that GODS "kingdom" is - real.. it exists.. AND - that GODS 9plural) spoke truthfully to Mosses.. whom .. after a long and arduous (tiresome) climb BACK down the mountain .. just could NOT be bothered arguing with the silly scribes.. whom did NOT hear & see what moses SAW .. and was told.. by GODS .. upon the mountain top.. where "GODS" overall plan & message was extremely simple. LIGHT- I will shine a LIGHT -- and you will thus see MY MESSAGE (in your ears) And so too -- will you HEAR my noise -- in your eyes. You will feell me speak .. through the lowes frequencies of all -- as the earth moves for you.

All energy -- when two articles 9small particles) pass one another.. they react upon each & create a NOISE in pssing.. such that it may just be a lowest "reverb" of earth plates .. sliding past .. at a millimeter every ten thousand years.. ? Or .. it could be - the sound of air .. as it passes over a humans vocl chords.. or? maybe a fast flying piece of "atom.. that streakes across the sky -- and which ONLY makes a noise .. in the highest of frequencies 9that humans can still detect. LIGHT Or .. maybe -- it's even faster .. innto the tegabytes of frequencies.. that computors talk to each other with.? ALL SOUND.. exists.. even deep in space.. (where) ? space noise.. IS LIGHT. — Preceding unsigned comment added by QUIX4U (talk • contribs) 05:53, 19 September 2011 (UTC) OOpsies..? O forgot didn't i -- squiggles are needed. to day bye bye QUIX4U (talk) 05:56, 19 September 2011 (UTC) Oh & p.pspsp.sps? or whatever it's supossed to be) THAT -- is also - the actual reason why/? Why I have always used LIGHT -- with sound 9speakers) to see.. what the audio i doing.. Across many many different simultainiously runing spaeker chs .. so that I can "hear" the differences .. with my EYES.. as I fine tune .. any of my "analogue multiple ch surround sound systems.. having discovered HOW T .. do exactly that -- in 1965.. AND.. have "always" made -- spqacially different "accoustical resonances & harmonic "effects" of intermixed.. inversed reveersed -- orientationall y changes phase shifted .. 3Ddimensional sound feilds.. in ALL mjusic. Try some.. there's plaenty of mine "out ther" deep in Cyber space too. QUIX4U (talk) 06:04, 19 September 2011 (UTC) (via) Youtube, xanga, blogspot, wordpress, twitter, facebook ... ?can't find them .? Well u "probably' haven't really taken a good look yet (with Ur "ears" - eh.?) QUIX4U (talk) 06:04, 19 September 2011 (UTC)

Koyaanisqatsi
Cool commercial bumper in UT 734. Very creative. :) Viriditas (talk) 05:31, 20 November 2008 (UTC)

Space music MedCab
Hi there! You have been named as a participant in an informal mediation regarding the article Space music, which I am mediating. I would like you to drop by the case page and indicate whether or not you agree to participate in the case. Please know that participation in the case doesn't mean you've done anything wrong! It's just a way to take everyone involved in a dispute away from whatever has caused the dispute and discuss the issues with a third party helping to keep the conversation on track. I look forward to working with you to address the problems and resolve them. // roux   10:07, 23 November 2008 (UTC)

WP:V and Blue Mountains panther
Just as a reminder: and its subsection
 * WP:V: "Editors should provide a reliable source for quotations and for any material that is challenged or likely to be challenged, or the material may be removed."
 * WP:BURDEN: "The burden of evidence lies with the editor who adds or restores material. All quotations and any material challenged or likely to be challenged should be attributed to a reliable, published source using an inline citation."

It is clearly up to you to do the citing if you wish that material in the article. I am asking you to either undue your edit returning improperly sourced material, or for you to properly source the materisl. And also be aware of : WP:3RR. -- The Red Pen of Doom  13:47, 29 November 2008 (UTC)
 * I do believe that you are not interpreting our policies correctly. Removing unsourced and improperly sourced material is not vandalism. But returning unsourced and improperly sourced material is. -- The Red Pen of Doom  15:18, 29 November 2008 (UTC)
 * Please read WP:CITE - simply making a bunch of claims and then stating that one of thise many links here at the bottom should verify that claim, is not proper sourcing. Each claim in the article must be verifiable by noting which reliable source supports that particular claim. and repeating our policy: the editor who adds or restores material is responsible for providing the proper inline citation to support the claims. --  The Red Pen of Doom  15:26, 29 November 2008 (UTC)

 * Your statement "There is no WP policy which states that it is appropriate to delete links to as-yet uncited sources then immediately blank article content, without either prior talk page discussion or appropriate tagging" is wrong. WP:V: "Editors should provide a reliable source for quotations and for any material that is challenged or likely to be challenged, or the material may be removed." - without a source, material in an article can be removed with no tagging and no discussion. -- The Red Pen of Doom  02:49, 30 November 2008 (UTC)

Grand Duchy of Westarctica and deletion nominations
There seems to be no problems with the categories, however there is a deletion nomination. - Onecanadasquarebishopsgate  21:25, 20 December 2008 (UTC)

After two days I am seeing yet again a repetition of arguments. We need a page within the WikiProject, an FAQ for example, so that in the inevitable event of another deletion nomination, we can simply say Keep - [add link to FAQ here]. - Onecanadasquarebishopsgate  21:29, 22 December 2008 (UTC)

Happy Holidays!
Hi Gene, thanks for your efforts to save good articles. I hope after the holidays you'll come back refreshed and renewed. I'd like to see you back here less frustrated and having more fun. Take care. ChildofMidnight (talk) 17:16, 23 December 2008 (UTC)

Kings of Redonda
I concur with your diagnosis of the section of this article which is about "King William Leo Timlin" as a hoax. Invertzoo (talk) 01:15, 24 January 2009 (UTC)

A centralised discussion which may interest you
Hi. You may be interested in a centralised discussion on the subject of "lists of unusual things" to be found here. SP-KP (talk) 17:36, 27 January 2009 (UTC)

Please don't piss where you live
GP; I've undone the blanking of your userpage, some else unblanked your talk. I'll be approaching the blocking admin as per his request. Can I request that in the interim you don't kakn your nest in the interim? brenneman 05:32, 28 January 2009 (UTC)
 * And again. Slow connection is making me bugger everything up, but in the event that the real Gene Poole (please stand up) wants to sign in and ask, I'll happily re-re-blank. -  brenneman  05:38, 28 January 2009 (UTC)

AfD nomination of Independent State of Aramoana
I have nominated Independent State of Aramoana, an article that you created, for deletion. I do not think that this article satisfies Wikipedia's criteria for inclusion, and have explained why at Articles for deletion/Independent State of Aramoana. Your opinions on the matter are welcome at that same discussion page; also, you are welcome to edit the article to address these concerns. Thank you for your time.Please contact me if you're unsure why you received this message. Rob (talk) 06:05, 21 February 2009 (UTC)

Orphaned non-free media (File:Arms Aramoana.GIF)
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Orphaned non-free media (File:Aramoana stamps 01.jpg)
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Welcome Back
I saw that you will be unblocked soon. Sorry that you got blocked in the first place. Welcome back and better luck this time. -- Micromaster  (talk)   (contributions)  02:02, 17 March 2009 (UTC)
 * Seconded. ChildofMidnight (talk) 05:37, 17 March 2009 (UTC)

File:Flag Araucania.gif listed for deletion
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Orphaned non-free media (File:Rose Island Arms.JPG)
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Fair use rationale for File:Arms Aramoana.GIF
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 * NOTE: I added a fair use rationale for this logo here I hope it is kept. I'm afraid all fair use images must have rationales today. This poster is one image with an excellent fair use rationale: With kind Regards, --Leoboudv (talk) 00:08, 3 July 2009 (UTC)

Orphaned non-free image (File:Rose Island pennant.JPG)
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Welcome back Gene!
It's always good to see you. Viriditas (talk) 02:53, 12 September 2009 (UTC)

 * Welcome back also from me. Sorry about the slow response. I haven't been editing as much as I used to, but if there's somethign I can help with I will certainly try to do so. :) The list of article seemed to do okay, so I think that's a good sign. ChildofMidnight (talk) 15:40, 17 September 2009 (UTC)
 * Also, I replied to your comment (finally). The website looks good to me! Take care. ChildofMidnight (talk) 20:05, 17 September 2009 (UTC)

Re: Quick question
Viriditas (talk) 08:18, 12 September 2009 (UTC)

Hello
I'm glad you're editing again. Welcome back! -- Micromaster  (talk)   (contributions)  16:19, 13 September 2009 (UTC)

Micronations
Bravo, I support your decisiond about the External Link.-- Coldplay   Expert  10:02, 14 September 2009 (UTC)

External link
Before you propose it, it would probably help if the site itself clearly indicated somewhere on it who the own and webmaster are, as questions on that topic often come up in such discussions. John Carter (talk) 15:39, 14 September 2009 (UTC)
 * I might also add, Gene, that it might help your case if you outline how it meets the EL guideline. That way you won't have to work too much at defending it. Viriditas (talk) 03:03, 16 September 2009 (UTC)

File:Aramoana stamps 01.jpg listed for deletion
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 * As your stamp image was tagged as being unacceptable, you might like to offer an opinion about changing their guidelines for stamps such as yours which would be considered commemorative stamps. Any opinions on this issue could be very helpful: It's discussed here.]--Wikiwatcher1 (talk) 04:21, 7 October 2009 (UTC)

File source problem with File:Nan Tien Temple 01a.JPG
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February 2011
Please do not attack other editors, as you did at User talk:VirtualSteve. Comment on content, not on contributors. Personal attacks damage the community and deter users. Please stay cool and keep this in mind while editing. Thank you. ''Given the notice at the top of your talk page "Personal attacks, harrassment, trolling, incivility, threats and all other forms of abuse will be removed from this page without comment", this comment here is interesting. I guess everyone else has to follow your rules, but you are free to be as incivil as you like. WP:NPA applies to everyone, even you.'' Mattinbgn (talk) 02:46, 3 February 2011 (UTC)

 * After more than five years as a valued contributor to the WP project I ceased being a part of the community on 16 September 2009, when User:VirtualSteve applied a 3 month block to my account on wildly spurious, entirely manufactured grounds, which were concocted by he and small group of other similarly malevolent admins. As such, WP policies are no longer of any concern to me. However, for his systemic misapplication of WP policy and general abuse of admin authority, Virtual Steve deserves every bit of the contempt with which I have today elected to greet his long-overdue resignation from the project. Have a nice day. --Gene_poole (talk) 03:42, 3 February 2011 (UTC)

 * For the record: --Gene_poole (talk) 03:52, 3 February 2011 (UTC)

Please do not attack other editors. If you continue, you may be blocked from editing Wikipedia. ''Note that while you continue to post here you remain part of this community and still are required to follow the basic behavioral rules that everyone else does. If you do not want to follow those rules and don't consider yourself part of the community, then don't post here. There are many other venues where you can attack others to your hearts content. Continued personal attacks will see your editing privileges removed. You have been warned.'' Mattinbgn (talk) 04:32, 3 February 2011 (UTC)

Nomination of Interactions between micronations for deletion
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Draft Beer Party
Back in 2005, you contributed to the deletion discussion of this article at Articles for deletion/Draft Beer Party. I believe consensus has changed since then and this article is no longer notable by our guidelines. I have renominated the article for deletion, and your comments are welcome at Articles for deletion/Draft Beer Party (2nd nomination). Robofish (talk) 23:33, 25 September 2011 (UTC)

Dicussion about an article's deletion you have contributed to
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Sydney edit-a-thon invitation
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Sydney meetup invitation: January 2013
Hi there! You are cordially invited to attend a meetup being held on Thursday 10 January 2013. Details an attendee list are at Meetup/Sydney/January 2013. Hope you can make it! John Vandenberg 09:38, 27 December 2012 (UTC)

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Sydney September 2013 edit-a-thon invite
Hi there! You are cordially invited to an edit-a-thon this Saturday (21 September) in Sydney at the State Library of New South Wales (SLNSW), where you can collaborate with other Wikipedians throughout the day. Andy Carr, a senior librarian at SLNSW will also be helping out. The theme of the edit-a-thon is paralympics sports, but you are free to come along to meet other wiki contributors, and edit other topics.

If you are unable to attend in person, we will also be collaborating online. Details and an attendee list are at Meetup/Sydney/September 2013. Hope you can make it! John Vandenberg 09:15, 19 September 2013 (UTC)

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Invitation
There is a backstage pass coming up to be followed by an editathon in the State Library of New South Wales on 23 November. This is the first time that an Australian cultural institution has opened its doors to us in this way and will be a special opportunity because the Library is providing: one of its best rooms; its expert curators (along with their expertise and their white gloves); a newly launched website (containing new resources); and of course, items from its collection (including rare and usually unavailable material) which we can look at, learn from, and use, to improve WP articles. For example, on the chosen topic (Australia and WWI), the Library holds many diaries and manuscripts from the period.

As you can see from the Library's project page, they have connected this editathon with their own work. They have already set out a wide range of resources to make things easier for us. Please sign up on the editathon project page if you can participate either online or in person with other Wikipedians. Hope to see you there! Lankiveil (speak to me) 12:10, 3 November 2013 (UTC)

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ArbCom elections are now open!
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Speedy deletion nomination of Blue Mountains panther

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Your draft article, User:JRG/Flags of micronations

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Thanks for your submission to Wikipedia, and happy editing. 10Eleventeen 03:02, 15 May 2018 (UTC)

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title: User talk:Gene Poole


text:
Herbes de Provence

Herbes de Provence (èrbas de Provença) is a mixture of dried herbs considered typical of the Provence region of southeastern France. Formerly simply a descriptive term, commercial blends started to be sold under this name in the 1970s. These blends often contain savory, marjoram, rosemary, thyme, and oregano. Lavender leaves are also sometimes included, especially in North American formulations. The herb mixture is typically used with grilled foods and stews.

History
Provençal cuisine has traditionally used many herbs which were often characterized collectively as herbes de Provence, but not in specific combinations, and not sold as a mixture. It was in the 1970s that homogenised mixtures were formulated by spice wholesalers, including Ducros in France, which is now part of McCormick & Company.

Origin
The commercial name herbes de Provence has no Protected Geographical Status or other legal definition. Indeed, only 10% of herbes de Provence sold in France are produced in France; 95% come from Central European (especially Poland) and Eastern European (notably Albania) countries, the Maghreb, or China. Herbes de Provence are often sold in larger bags than other herbs, and the price in Provence is considerably lower than for other herbs.

Herbs used
These mixtures typically contain savory, marjoram, rosemary, thyme, oregano, and other herbs. In the North American market, lavender leaves are also typically included, though lavender does not appear in the recipes in Jean-Baptiste Reboul's 1910 compendium of Provençal cooking. The Label Rouge definition is 19% thyme, 27% rosemary, 27% savory, and 27% oregano.

Uses
Herbes de Provence are used to flavour grilled foods such as fish and meat, as well as vegetable stews. The mixture can be added to foods before, during, or after cooking or mixed with cooking oil prior to cooking so as to infuse the flavour into the cooked food. They can also be sprinkled on raw foods such as vinaigrettes, salads or fresh cheese.

title: Herbes de Provence


text:
Necessity and sufficiency

In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If $P$ then $Q$", $Q$ is necessary for $P$, because the truth of $Q$ is guaranteed by the truth of $P$. (Equivalently, it is impossible to have $P$ without $Q$, or the falsity of $Q$ ensures the falsity of $P$.) Similarly, $P$ is sufficient for $Q$, because $P$ being true always implies that $Q$ is true, but $P$ not being true does not always imply that $Q$ is not true.

In general, a necessary condition is one (possibly one of multiple conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary and sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.

In ordinary English (also natural language) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a male is a necessary condition for being a brother, but it is not sufficient—while being a male sibling is a necessary and sufficient condition for being a brother. Any conditional statement consists of at least one sufficient condition and at least one necessary condition.

In data analytics, necessity and sufficiency can refer to different causal logics, where necessary condition analysis and qualitative comparative analysis can be used as analytical techniques for examining necessity and sufficiency of conditions for a particular outcome of interest.

Definitions
In the conditional statement, "if S, then N", the expression represented by S is called the antecedent, and the expression represented by N is called the consequent. This conditional statement may be written in several equivalent ways, such as "N if S", "S only if N", "S implies N", "N is implied by S", $S → N$, $S ⇒ N$ and "N whenever S".

In the above situation of "N whenever S," N is said to be a necessary condition for S. In common language, this is equivalent to saying that if the conditional statement is a true statement, then the consequent N must be true—if S is to be true (see third column of "truth table" immediately below). In other words, the antecedent S cannot be true without N being true. For example, in order for someone to be called Socrates, it is necessary for that someone to be Named. Similarly, in order for human beings to live, it is necessary that they have air.

One can also say S is a sufficient condition for N (refer again to the third column of the truth table immediately below). If the conditional statement is true, then if S is true, N must be true; whereas if the conditional statement is true and N is true, then S may be true or be false. In common terms, "the truth of S guarantees the truth of N". For example, carrying on from the previous example, one can say that knowing that someone is called Socrates is sufficient to know that someone has a Name.

A necessary and sufficient condition requires that both of the implications $$S \Rightarrow N$$ and $$N \Rightarrow S$$ (the latter of which can also be written as $$S \Leftarrow N$$) hold. The first implication suggests that S is a sufficient condition for N, while the second implication suggests that S is a necessary condition for N. This is expressed as "S is necessary and sufficient for N ", "S if and only if N ", or $$S \Leftrightarrow N$$.

Necessity

The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". By contraposition, this is the same thing as "whenever P is true, so is Q".

The logical relation between P and Q is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q). It may also be expressed as any of "P only if Q", "Q, if P", "Q whenever P", and "Q when P". One often finds, in mathematical prose for instance, several necessary conditions that, taken together, constitute a sufficient condition (i.e., individually necessary and jointly sufficient ), as shown in Example 5.

 * Example 1: For it to be true that "John is a bachelor", it is necessary that it be also true that he is
 * unmarried,
 * male,
 * adult,
 * since to state "John is a bachelor" implies John has each of those three additional predicates.

 * Example 2: For the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime.

 * Example 3:Consider thunder, the sound caused by lightning. One says that thunder is necessary for lightning, since lightning never occurs without thunder. Whenever there is lightning, there is thunder. The thunder does not cause the lightning (since lightning causes thunder), but because lightning always comes with thunder, we say that thunder is necessary for lightning. (That is, in its formal sense, necessity doesn't imply causality.)

 * Example 4:Being at least 30 years old is necessary for serving in the U.S. Senate. If you are under 30 years old, then it is impossible for you to be a senator. That is, if you are a senator, it follows that you must be at least 30 years old.

 * Example 5:In algebra, for some set S together with an operation $$\star$$ to form a group, it is necessary that $$\star$$ be associative. It is also necessary that S include a special element e such that for every x in S, it is the case that e $$\star$$ x and x $$\star$$ e both equal x. It is also necessary that for every x in S there exist a corresponding element x″, such that both x $$\star$$ x″ and x″ $$\star$$ x equal the special element e.  None of these three necessary conditions by itself is sufficient, but the conjunction of the three is.

Sufficiency

If P is sufficient for Q, then knowing P to be true is adequate grounds to conclude that Q is true; however, knowing P to be false does not meet a minimal need to conclude that Q is false.

The logical relation is, as before, expressed as "if P, then Q" or "P ⇒ Q". This can also be expressed as "P only if Q", "P implies Q" or several other variants. It may be the case that several sufficient conditions, when taken together, constitute a single necessary condition (i.e., individually sufficient and jointly necessary), as illustrated in example 5.

 * Example 1:"John is a king" implies that John is male. So knowing that John is a king is sufficient to knowing that he is a male.

 * Example 2:A number's being divisible by 4 is sufficient (but not necessary) for it to be even, but being divisible by 2 is both sufficient and necessary for it to be even.

 * Example 3: An occurrence of thunder is a sufficient condition for the occurrence of lightning in the sense that hearing thunder, and unambiguously recognizing it as such, justifies concluding that there has been a lightning bolt.

 * Example 4:If the U.S. Congress passes a bill, the president's signing of the bill is sufficient to make it law. Note that the case whereby the president did not sign the bill, e.g. through exercising a presidential veto, does not mean that the bill has not become a law (for example, it could still have become a law through a congressional override).

 * Example 5:That the center of a playing card should be marked with a single large spade (♠) is sufficient for the card to be an ace. Three other sufficient conditions are that the center of the card be marked with a single diamond (♦), heart (♥), or club (♣). None of these conditions is necessary to the card's being an ace, but their disjunction is, since no card can be an ace without fulfilling at least (in fact, exactly) one of these conditions.

Relationship between necessity and sufficiency

A condition can be either necessary or sufficient without being the other. For instance, being a mammal (N) is necessary but not sufficient to being human (S), and that a number $$x$$ is rational (S) is sufficient but not necessary to $$x$$ being a real number (N) (since there are real numbers that are not rational).

A condition can be both necessary and sufficient. For example, at present, "today is the Fourth of July" is a necessary and sufficient condition for "today is Independence Day in the United States". Similarly, a necessary and sufficient condition for invertibility of a matrix M is that M has a nonzero determinant.

Mathematically speaking, necessity and sufficiency are dual to one another. For any statements S and N, the assertion that "N is necessary for S" is equivalent to the assertion that "S is sufficient for N". Another facet of this duality is that, as illustrated above, conjunctions (using "and") of necessary conditions may achieve sufficiency, while disjunctions (using "or") of sufficient conditions may achieve necessity. For a third facet, identify every mathematical predicate N with the set T(N) of objects, events, or statements for which N holds true; then asserting the necessity of N for S is equivalent to claiming that T(N) is a superset of T(S), while asserting the sufficiency of S for N is equivalent to claiming that T(S) is a subset of T(N).

Psychologically speaking, necessity and sufficiency are both key aspects of the classical view of concepts. Under the classical theory of concepts, how human minds represent a category X, gives rise to a set of individually necessary conditions that define X. Together, these individually necessary conditions are sufficient to be X. This contrasts with the probabilistic theory of concepts which states that no defining feature is necessary or sufficient, rather that categories resemble a family tree structure.

Simultaneous necessity and sufficiency
To say that P is necessary and sufficient for Q is to say two things:
 * 1) that P is necessary for Q,  $$P \Leftarrow Q$$, and that P is sufficient for Q, $$P \Rightarrow Q$$.
 * 2) equivalently, it may be understood to say that P and Q is necessary for the other, $$P \Rightarrow Q \land Q \Rightarrow P$$, which can also be stated as each is sufficient for or implies the other.

One may summarize any, and thus all, of these cases by the statement "P if and only if Q", which is denoted by $$P \Leftrightarrow Q$$, whereas cases tell us that $$P \Leftrightarrow Q$$ is identical to $$P \Rightarrow Q \land Q \Rightarrow P$$.

For example, in graph theory a graph G is called bipartite if it is possible to assign to each of its vertices the color black or white in such a way that every edge of G has one endpoint of each color. And for any graph to be bipartite, it is a necessary and sufficient condition that it contain no odd-length cycles. Thus, discovering whether a graph has any odd cycles tells one whether it is bipartite and conversely. A philosopher might characterize this state of affairs thus: "Although the concepts of bipartiteness and absence of odd cycles differ in intension, they have identical extension.

In mathematics, theorems are often stated in the form "P is true if and only if Q is true".

Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. $$P \Leftarrow Q$$ is equivalent to $$Q \Rightarrow P$$, if P is necessary and sufficient for Q, then Q is necessary and sufficient for P. We can write $$P \Leftrightarrow Q \equiv Q \Leftrightarrow P$$ and say that the statements "P is true if and only if Q, is true" and "Q is true if and only if P is true" are equivalent.

title: Necessity and sufficiency