text:
Talk:Lake Michigan

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Untitled
Lake Michigan flows into the Chicago River. The natural flow of the river was reversed in 1900 to prevent sewage from flowing into Lake Michigan.

What river(s) do Lake Michigan drain into? It would be nice to have that information in the article, and possibly the major rivers that feed into it.

Bull Sharks and connection with salt water
Just wondering if there should be mention of Bull Shark as a rare but possible inhabitant of the lake (please see the article for Bull Shark and the related reference) due to the connection of Lake Michigan to Salt water via the Illinois River->Mississippi River? It is fact that there have been bull shark sightings and even a verified shark attack near Chicago but not sure if it should be in the article or really even how to include, looking for community consensus. Thanks. —Preceding unsigned comment added by 4.224.0.41 (talk) 17:32, 18 May 2009 (UTC)

Chicagoland
I've removed the rather large footer with links to topics about greater Chicago, because it doesn't seem relevant to this article. That's a bit like having a navigation guide for Rio de Janeiro on an article about the Atlantic Ocean just because the Atlantic beach is a popular feature of the city. Lake Michigan may seem to be just a part of Chicagoland to Chicagoans, but it's a bit bigger than that. Tverbeek 01:07, 10 Apr 2005 (UTC)

Beaches
I really think that material about "singing sands", "exceptional" beauty, opinions about the steel mills and their supposed contribution to the sunsets, etc. belongs in a Dept or Tourism brochure, not Wikipedia. Tverbeek 19:29, 15 July 2005 (UTC)
 * Except that there are, in fact, steel mills dotting the Indiana shoreline that can be seen in both directions from the Indiana dunes (most popular public beach on the lake) and the sand is, in fact, called "singing sands". It's not just being lyrical.  The pollutants released by the steel mills, due to their higher indices of refraction than normal air, due cause more colorful sunsets.  If you think there is too much POV in there, please adjust it, but try not to stomp on factual information in the process. siafu 19:33, 15 July 2005 (UTC)
 * I'm trying to, but someone just stomped on my use of objective prose. I know that the steel mills are visible, but calling them "perhaps the only drawback" is not a fact, but an opinion.  (Some people find the tourists to be a drawback.  Or even the dune grass.)  The statement that the mills (and not other factors) are solely responsible for the "spectacular" sunsets is questionable.  I don't find the sand to be particularly "soft" and it's pretty far from white (I've seen far whiter).   Tverbeek 20:08, 15 July 2005 (UTC)
 * Then feel free to remove the quoted pieces. Your "use of objective prose" had previously removed far more than that. siafu 20:10, 15 July 2005 (UTC)
 * Then feel free to add the material back next time. Simply reverting a good-faith effort at abiding by Wikipedia's policies about NPOV and verifiaiblity is both rude and unproductive. Tverbeek 20:22, 15 July 2005 (UTC)
 * I did add it back, after you rv'ed a good faith contribution from an anon.
 * Pardon the interruption, but I did no such thing. Look at the edit history for that edit  or spanning the whole anon-editor's session, and you'll see that I took some stuff out and put other stuff in. That's not a revert. A revert is when there's no trace of the previous edit... such as what you did to my contribution . Tverbeek 02:17, 16 July 2005 (UTC)
 * To quote Avoiding common mistakes:

"Deleting useful content. A piece of content may be written poorly, yet still have a purpose. Consider what a sentence or paragraph tries to say. Clarify it instead of throwing it away."
 * Sorry if you're offended, but it wasn't very helpful to chop everything out on account of a few POV words and phrases. siafu 20:49, 15 July 2005 (UTC)
 * I had reasons for removing everything I removed (as I've already explained). They weren't poorly written; they were written beautifully.... but "what they were trying to say" was to express opinions, not facts.  You disagree with me on some of that, and I'm compromising. So stop trying to make me out as a Bad Guy here. Tverbeek 02:17, 16 July 2005 (UTC)

I removed the bit about sand replenishment pending some citation. There is simply way too much sand in the Chicago beaches to be anything but "natural". Yes the sand is "managed" within beaches by bulldozers but the wholesale trucking of sand is not done to my knowledge. Cite it and you can put it back. Wegerje (talk) 19:02, 9 June 2009 (UTC)

"Cold"
I don't think "cold" is the appropriate term for 55-70F lake water. Certainly compared to Lake Superior, southern Lake Michigan beach water is quite mild. Tverbeek 20:29, 15 July 2005 (UTC)
 * My POV says 70 degrees is cold. Compared to ice, Lake Michigan is warm, but that doesn't make it really warm. Just asking:Have you actually swum in 70 degree water? What objective measure could we use here?MPS 20:34, 15 July 2005 (UTC)
 * Since the subject is summertime lake water, how about we use that as a frame of reference? (I think most readers will grasp that we're not comparing it to the inside of a furnace or the surface of Pluto.)  Yes, I've been swimming in water that temperature.  I've been in Lake Superior, Lake Michigan, the Atlantic Ocean off Florida, the Pacific off Jalisco (Mexico), and countless small lakes.  Superior (40-50F isn't unusual) I'd call "cold".  Inland lakes that are shallow enough to heat up to 80F all the way down, I'd call "warm".  A typical August Lake Michigan beach falls somewhere in between, and I think "cool" reflects that better than "cold" does. If you think 70F is "cold"... you just don't know what cold water feels like. :) Tverbeek 02:17, 16 July 2005 (UTC)
 * Swimming in Lake Michigan tells me it's cold. Cool maybe, in August, but cold the other 11 months which to me justify the term "cold."
 * You all may have been swimming in different parts of the lake. I've added a ref. stating that in the summer, the water along the eastern shore is warmer. I would have said the lake water is somewhat "warm" in the summer - but my experience is based on swimming in the lake off southwestern Michigan. :) Zariane (talk) 15:31, 5 July 2008 (UTC)
 * During July and August southern Lake Michigan is swimable by many people and not just kids. That puts it in the cool to warm category. SE Lake Michigan often has water that you can loll in, that is just float around in comfortably without exercise. That to me puts it int the warm category. Wegerje (talk) 18:53, 9 June 2009 (UTC)
 * The water temperature reaches the low 80s on occassion. I've been to Grand Haven, Michigan in August and swam in 80 degree water. Phizzy [[Image:SimpleMichigan.svg|30x15px]] 19:57, 9 June 2009 (UTC)
 * Updated article to reflect the fact that temperatures reach 80 degrees. Several locations in Lake Michigan have already reached 75+ degrees, and it is barely summer. Phizzy [[Image:SimpleMichigan.svg|30x15px]]  03:25, 29 June 2009 (UTC)

Can we get any details on the average extent of ice cover on the lake in winter an d the months when it is present?--AssegaiAli (talk) 12:34, 23 January 2008 (UTC)

we could use the world's nuclear waste to heat the lake just a little bit. we need to put it somewhere, so why not put it to good use at the same time. 23:33, 3 March 2013 (UTC) Michael Christian — Preceding unsigned comment added by 76.23.224.120 (talk)

Lake Chicago
This article really should talk about the "precursur" to Lake Michigan, which geologists call Lake Chicago (some geologists even give it different names at different time periods -- talk about confusing).

check out:

http://www.encyclopedia.chicagohistory.org/pages/702.html http://www.emporia.edu/earthsci/student/damery1/gl_form.html

Traverse City
I removed the Traverse City entry in the Michigan cities section because this city does not exceed, or even approach, 30,000 in population. I would support rewording the section to include metro areas or other designations of significance, since Michigan certainly has more than two noteworthy towns on the big lake(i.e., Traverse City, Benton Harbor/St. Joseph, etc.), but they do not fit as the group currently exists.

Door County
I agree with the above said, why is 30,000 important? Now I want to know why a county in Wisconsin (Door) that according to the statistics is under 30,000 is included? Oh yea and, it is a county not a city! I suggest get rid of the 30,000 rule and even city distinction, maybe important shoreline communities. I have not changed anything but I will remove Door if no one changes or removes! —The preceding unsigned comment was added by 67.186.114.73 (talk) 04:57, 7 May 2007 (UTC).
 * I agree and have removed the "30,000 rule" from the text. Zariane (talk) 15:34, 5 July 2008 (UTC)

Chicago River image
I removed the Chicago River image because (a) article was crowded with images, and (b) didn't really offer a view of the lake or any important content to the article. --mtz206 (talk) 14:53, 17 June 2006 (UTC)

Polar Bears
I think a section of "fun facts" or something like that could be added, where there could be a mention of the Polar Bear Club in Jacksonport, WI

fish?
No mention of fish, can someone add? —The preceding unsigned comment was added by 209.206.165.61 (talk) 09:48, 29 January 2007 (UTC).

i added a small section about fish but it would need more work on it and perhaps a link of data about stocking and such (i found much of the information on other pages mentioning the great lakes and from personal experiance) Huzzahmaster018 02:43, 17 August 2007

Coordinates
The coordinates need the following fixes:
 * Write here

216.163.33.178 (talk) 14:45, 10 June 2009 (UTC)

Coordinates in article are okay. BrainMarble (talk) 02:20, 10 December 2009 (UTC)

Lake Michigan and Lake Huron rankings
I think the problem on the ranking is that it is second in volume but third in area (before/after Lake Huron, so that the term "largest" creates an unintended ambiguity. 7&6=thirteen (talk) 15:49, 19 June 2009 (UTC) Stan
 * I would rank Lake Michigan third, as most people think of surface area when speaking of size of lakes. Lake Ontario has nearly 3 1/2 times the volume of Lake Erie, but most people think of them as roughly the same size. Phizzy [[Image:SimpleMichigan.svg|30x15px]]  19:34, 19 June 2009 (UTC)

Cities on the lake
I was just wondering what was the determining factor for which cities are listed? Because there are towns on the lake in other states that have much larger populations than some of the ones listed for Michigan. There is, for instance, a town listed for Michigan that has a population of less than 2,000 people. Tad Lincoln (talk) 03:23, 3 December 2009 (UTC)

Good article on Great Lakes levels
[http://detnews.com/article/20101108/METRO/11080360/Low-Great-Lakes-levels-prompt-new-call-for-action#ixzz14jknHuGQ Lynch, Jim, November 08. 2010 Low Great Lakes levels prompt new call for action: U.S., Canada look at options to slow flow out of Lake Huron] Detroit News. 7&6=thirteen (☎) 15:18, 17 April 2013 (UTC)

Michigan and Huron together form one single lake.
Michigan and Huron together form one single lake. both are merely larges bays of that lake.

i believe that a six-mile straight connects them, and they certainly rise and fall together.

so there are not really five great lakes, but instead only four.

Michigan is not the sole entirely US great lake because it is not a lake.

Lake Huron-Michigan is the largest great lake by surface area, and the second largest by volume.

people would come to recognize this if Wikipedia combined its articles on the two supposed lakes into one article and called them Huron-Michigan. Huron is the larger, and many Canadians would very likely feel offended or slighted if priority were given to the entirely US bay of the lake.

23:27, 3 March 2013 (UTC) Michael Christian

I do not claim to have come up with this argument. — Preceding unsigned comment added by 76.23.224.120 (talk) 23:27, 3 March 2013 (UTC)

 * Lake Michigan is indeed a LAKE and is entirely within the United States. How can that offend anyone? — Preceding unsigned comment added by 50.32.50.241 (talk) 12:44, 17 April 2013 (UTC)

 * For some people it doesn't take much. — Preceding unsigned comment added by 50.32.56.189 (talk) 17:35, 6 November 2013 (UTC)

Number of lakes in (or on) each great lake?
I was looking at a map of Lake Michigan while visiting Chicago recently, and noticed an interesting feature that most people probably never considered about that, or any of the great lakes. That feature is that the lake is so large, that it contains numerous islands that in themselves are large enough to contain bodies of water that are large enough to themselves be lakes.

So I thought that the following would be some interesting facts to add to the wiki articles about not only each of the great lakes, but also to the articles about all other lakes in the world that also contain lakes:

How many total lakes are in (or on) each of the great lakes? What islands are they located on? What are their names? 99.153.192.158 (talk) 15:32, 5 May 2013 (UTC)

There's the page Islands of the Great Lakes—there are very very many. Lake Manitou is fairly famous for being the world's largest lake on an island in a lake. Pfly (talk) 23:06, 5 May 2013 (UTC)

No map?
The article's lack of a modern map indicating the lake's geographical features (islands, bays, etc.) and surrounding cities is a curious omission. For that matter, there is not such a map accompanying any of the main articles for the five Great Lakes. Starling2001 (talk) 19:03, 26 June 2014 (UTC)

Michigan Triangle
I added a brief section on the Michigan Triangle. I'm not sure if it's noteworthy enough to be a standalone article, I'll let others be the judge of that. But, it has been covered by several local media outlets in both Wisconsin and Michigan, and has been covered by CNN, all over the span of several years, so I believe that it is an important section to include in the article on Lake Michigan. — Preceding unsigned comment added by Fredsteve3 (talk • contribs) 21:08, 13 March 2016 (UTC)

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Does anybody know what the nicknames for Lake Michigan are? — Preceding unsigned comment added by 91.125.157.220 (talk) 18:23, 20 September 2019 (UTC)

Ojibwe Language
I believe Lake Michigan is the Great Water and that is spelled Gichigami. It doesn't begin with a M. — Preceding unsigned comment added by Mmallonen (talk • contribs) 18:50, 8 June 2020 (UTC)

Environmental threats and damage
This article could arguably use a standalone section that digs more deeply into environmental damage to Lake Michigan -- including pollution, invasive species, overdevelopment, destruction of specific habitats, changes to fisheries, changes to drinkable water quality, etc. I see references scattered across other sections, but no standalone treatment. Not sure if there's a protocol for discussion of environmental issues that's already being used in similar articles that could be copied. Earnestmidwest (talk) 19:06, 25 May 2021 (UTC)

Minimum Width
The article lists the minimum width of the lake as 91 miles. I am confused about where this came from, as the lake at points is clearly less than 91 miles wide. This section, for example, is around 60 miles wide. https://i.imgur.com/E18fbUL.png WhiteWaterBottle (talk) 22:03, 24 July 2022 (UTC)

title: Talk:Lake Michigan


text:
Talk:Arabia (disambiguation)

==Make redirect to Arabian Peninsula==

Untitled
Given the number of pages that 'link here', I suggest this page be made a redirect to Arabian Peninsula, with a notice at the top directing readers to Arabia (disambiguation).--Pharos 21:22, 23 Feb 2005 (UTC)
 * As should be clear, I have now moved what was previously at Arabia here to Arabia (disambiguation), and made Arabia a redirect to Arabian Peninsula. And so, the above comment is no longer relevant.--Pharos 21:02, 10 Mar 2005 (UTC)

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

title: Talk:Arabia (disambiguation)


text:
Kerry South (Dáil constituency)

Kerry South was a parliamentary constituency represented in Dáil Éireann, the lower house of the Irish parliament or Oireachtas, from 1937 to 2016. The constituency elected 3 deputies (Teachtaí Dála, commonly known as TDs). The method of election was proportional representation by means of the single transferable vote (PR-STV).

History and boundaries
The constituency was located in the southern half of County Kerry taking in the Dingle and Iveragh peninsulas, including the towns of Killarney, Dingle, Cahirciveen, Killorglin and Kenmare.

It was established by the Electoral (Revision of Constituencies) Act 1935 when the former Kerry constituency was divided into the constituencies of Kerry North and Kerry South. It was first used at the 1937 general election electing 9th Dáil.

The Electoral (Amendment) Act 2009 defined the constituency as:

 * "The county of Kerry, except the part thereof which is comprised in the constituency of Kerry North–West Limerick."

It was abolished at the 2016 general election and replaced by the new Kerry constituency.

1966 by-election
Following the death of Fianna Fáil TD Honor Crowley, a by-election was held on 7 December 1966. The seat was won by the Fianna Fáil candidate John O'Leary.

1945 by-election
Following the death of Fianna Fáil TD Frederick Crowley, a by-election was held on 4 December 1945. The seat was won by the Fianna Fáil candidate Honor Crowley, widow of the deceased TD.

1944 by-election
Following the resignation of Fine Gael TD Fionán Lynch upon his appointment as a judge, a by-election was held on 10 November 1944. The seat was won by the Fianna Fáil candidate Donal O'Donoghue.

title: Kerry South (Dáil constituency)


text:
Iverson Award

The Iverson Award, more formally the Kenneth E. Iverson Award for Outstanding Contribution to APL, is presented by the Special Interest Group on APL (SIGAPL) of the Association for Computing Machinery (ACM). It is presented to a person who has made significant contributions to the APL programming language or to the APL community. These contributions may be Technical (i.e. new developments in the APL language itself) or Service (assistance or support to SIGAPL or the APL community generally). The award consists of a plaque and a certificate, and is accompanied by a cash prize and a lifetime membership in SIGAPL.

The award is named in honor of Kenneth E. Iverson, the creator of APL.

Recipients of the award by year:
 * 2016 Morten Kromberg and Gitte Christensen
 * 2007 IBM APL2 Products and Services Team
 * 2001 Jon McGrew
 * 2000 Lynne Shaw
 * 1999 William Rutiser
 * 1998 Roy Sykes, Jr.
 * 1997 John C. McPherson
 * 1996 Roger Hui
 * 1995 Peter Donnelly and John Scholes
 * 1994 Donald B. McIntyre (geologist)
 * 1993 James A. Brown
 * 1991 Phil Abrams
 * 1990 Ray Polivka
 * 1989 Philip Van Cleave
 * 1988 Al Rose (Allen J. Rose)
 * 1987 Eugene McDonnell
 * 1986 Raymond Tisserand, Clark Wiedmann, and Alex Morrow
 * 1985 Dan Dyer and Ian Sharp
 * 1984 Garth Foster
 * 1983 Adin Falkoff

title: Iverson Award


text:
Talk:Brian Close

Gentlemen and players
What a great article. I think that the relationship between gentlemen and players ('Close replied with "Thank you, Billy". Yet in those days, that was a mistake') needs a brief explanation here. --Theo (Talk) 23:13, 25 Feb 2005 (UTC)

 * Thank you for your comments. I've added some words of explanation of Players and Gentlemen - though there's a whole article itself on that subject if anyone wants to give it a bash, jguk 10:59, 26 Feb 2005 (UTC)

Wow ! Brilliant stuff.

Tintin (Talk)

Jguk,

You may also find this interesting. It would also be nice to add the story that is referred there, of Close's reaction when someone was caught off Close's head.

Tintin  April 15, 2005

---

Richie Benaud at Old Trafford, 1961
Jguk,

The Close article contains this passage :

 * Then Ted Dexter and Peter May got out in quick succession to Benaud, who was pitching his leg spin googlies in the rough outside the right handers' off stump (that is, the part of the wicket furthest away from where the batsman is standing). This brought Close to the crease. It was the last day of the Test, and the captain, May, was still asking his players to go for the runs. The rough into which Benaud was pitching was on Close's legside, Close being a left-hander.

I am not sure about Close's case, but in the case of Dexter and May, Benaud was bowling from around the wicket and pitching the ball outside the leg stump. May was bowled round the legs trying to sweep one that pitched a long way outside the leg. Trueman received cricticism for 'creating' the rough patches that Benaud exploited.

Did Benaud use the roughs outside both the stumps or is this an oversight ?

There is a mention in the section about Close's captaincy that his 7/6/1/0 record is the best by someone who captained in more than two Tests. Lord Hawke has a perfect win record in the four Tests that he captained. That needs to be modified.

Tintin1107 20:42, 11 May 2005 (UTC)

 * I may have misremembered the details of Close's dismissal against Benaud and the events before it (which was written shortly after I read Close's comments on it in his autobiography). Please feel free to correct it as appropriate. On your second point, I think played 7 won 6 drawn 1 is better than played 4 won 4 - though I accept some may disagree, jguk 19:44, 12 May 2005 (UTC)

 * Thanks. But first we may have to confirm the specifics of Close's dismissal.

Re. captaincy, agree that it is a matter of opinion. My complaint was about the specific phrase "the best record of any England captain who has captained in more than 2 Tests." The two Tests looked like a reference to Walter Read's captaincy (2 matches, 2 wins) as was mentioned in 'History of Test Cricket 1890-1900)'. Maybe it is better to leave it slightly vague like 'arguably the finest captaincy record' or something, instead of qualifying with 'more than 2 tests'.

Tintin1107 20:02, 12 May 2005 (UTC)

 * mmm, thinking about it, I was probably forgetting about Lord Hawke when I wrote that bit. Also the Indian and Pakistani sides were pretty weak at the time - anything other than a comprehensive victory would have been bad - but they still needed beating, jguk 11:50, 13 May 2005 (UTC)

The age is buried
The interesting fact about him being the youngest is claimed at the openning but the facts are burried way down the body of information.

I recommend that this fact should detailed with prominence and not buried as a passing fact in the lower portion of this document.

As my journalism lecturer at University once said to me - "If it is good enough to get a mention at the top then it also deserves to be followed up at the top too".

Cheers

Phil

 * Please feel free to edit the article in the way you suggest. Kind regards, jguk 18:59, 12 May 2005 (UTC)

Decent grammar would put it that he WAS the youngest etc. Who do give a poo?

 * He IS still the youngest to play for England, jguk 11:48, 13 May 2005 (UTC)

Football Career
There needs to be a section devoted to his professional football career to ensure that Close isn't just remembered for Cricket only.

I'm not doing it - I don't know much about football!

--One Salient Oversight 11:23, 12 May 2005 (UTC)

 * Close's professional football career did not last long and he played just a handful of first team games. That's why it's not mentioned in too much detail. Kind regards, jguk 18:49, 12 May 2005 (UTC)

Close had a very dimented childhood He had a what?

UPDATE - Sentence added at top of story to include his age

Images
I have just tagged two of the images in this article. Image:Brian Close.jpg is certainly not a promotional photo according to the definitions on Template:Promophoto and Publicity photos, so I've marked it "No license". Image:Brian Close - Small pic.jpg is also probably not a promotional photo, but I couldn't find the source for it, so I marked it "No source". Both of these photos are now liable to be deleted in one week, unless someone can come up with a valid source and copyright for them.

Stephen Turner (Talk) 09:10, 1 April 2006 (UTC)

Ambidextrous?
I recall my father, an avid cricket fan, telling me when I was a kid that Brian Close could bat left and right handed and that as a golfer he played left handed, got his handicap down to scratch, then played right handed and got down to scratch that way too. Any of this verifiable? --ukexpat 18:37, 1 May 2007 (UTC)

Two bits of trivia
Close has the highest first-class runs aggregate of anyone who never scored a double century. He is the only man with a career highest score of 198. I don't know if these are worth putting in the article.Brianboulton (talk) 23:40, 8 January 2008 (UTC)

Football
Close played only a handful of league games as a footballer. He was signed by Arsenal but according to the Rothams Book, did not appear for the first team.JimBakken (talk) 14:57, 28 January 2008 (UTC)

Second XI
Close was captain of Yorkshire's Colts XI which played in the Yorkshire League. (see A Sidebottom's book for some anecdotes)Fieldgoalunit (talk) 22:16, 19 March 2008 (UTC)

What a pity - From featured article to (fact) tag ruined
I see that the article was a former featured article on 12 May 2005 yet in its current revision it is full to the brim with (fact) tags, which totally ruins the article. Can we do our best to put in a concerted effort to get rid of the (fact) tags? Add in references, verify that everything is right, and get it back to featured article status? The subject is obviously important enough to warrant such an effort. Myrrideon (talk) 15:01, 11 July 2008 (UTC)

I notice that the article's display was totally ruined during this edit by User:SGGH on 27 May 2008, who didn't even stop to make a comment in the talk page. Is there any reason why we should think that this article really does need the citations? It got to featured article status without them. I notice that the same user also added in notes at the top to make it look doubly ugly.

If the article was considered to be good enough to be a featured article, and stayed as a featured article for 3 years, why would we think that one person's addition of fact tags with no comment attached as to why they need it should be taken seriously? Can we not simply remove the fact tags and carry on? Myrrideon (talk) 15:16, 11 July 2008 (UTC)

I can compare its original application (successfully) to FA with its review and demotion. I can't say that I agree with User:SGGH's attack on this article, and I'd like to know why he/she chose to destroy what was a perfectly good article. But I will leave this with others. Myrrideon (talk) 15:24, 11 July 2008 (UTC)
 * It might not look pretty, but unfortunately the standards have changed since Brian Close first made FAC. It's now the norm for inline citations and all is needed is to replace those fact tags with some citations. Peanut4 (talk) 18:03, 11 July 2008 (UTC)

 * This article is an utter disgrace. Some of the statements needs sourcing, undoubtedly, but demanding sources for facts such as the score by which England won a test match is ludicrous. There was even a fact tag on a statement that is explained in the next sentence (and which is itself sourced). Jimmy Pitt   talk  14:31, 17 February 2011 (UTC)

Assessment comment
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title: Talk:Brian Close


text:
Descent direction

In optimization, a descent direction is a vector $$\mathbf{p}\in\mathbb R^n$$ that points towards a local minimum $$\mathbf{x}^*$$ of an objective function $$f:\mathbb R^n\to\mathbb R$$.

Computing $$\mathbf{x}^*$$ by an iterative method, such as line search defines a descent direction $$\mathbf{p}_k\in\mathbb R^n$$ at the $$k$$th iterate to be any $$\mathbf{p}_k$$ such that $$\langle\mathbf{p}_k,\nabla f(\mathbf{x}_k)\rangle < 0$$, where $$ \langle, \rangle $$ denotes the inner product. The motivation for such an approach is that small steps along $$\mathbf{p}_k$$ guarantee that $$\displaystyle f$$ is reduced, by Taylor's theorem.

Using this definition, the negative of a non-zero gradient is always a descent direction, as $$ \langle -\nabla f(\mathbf{x}_k), \nabla f(\mathbf{x}_k) \rangle = -\langle \nabla f(\mathbf{x}_k), \nabla f(\mathbf{x}_k) \rangle < 0 $$.

Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method.

More generally, if $$P$$ is a positive definite matrix, then $$p_k = -P \nabla f(x_k)$$ is a descent direction at $$x_k$$. This generality is used in preconditioned gradient descent methods.

title: Descent direction


text:
Wikipedia:Articles for deletion/Runzor

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was delete. Joyous 23:44, Mar 1, 2005 (UTC)

Runzor
Leet neologism that seems mostly unused. 30 displayed hits, most of which are usernames, not actual uses of the term. Niteowlneils 21:31, 23 Feb 2005 (UTC)

 * deletezor - It's already an example on Leet (should be unlinkedzor there, though), and that's sufficient. --grmwnr 22:54, 23 Feb 2005 (UTC)
 * Delete, do not redirectz0r. According to google, this neologism isn't even in use and should be stricken from the main leet page if mentioned.      Otherwise, we may as well just addz0r in every single English verb into that article!     GRider\talk 23:53, 23 Feb 2005 (UTC)
 * Delete --Sn0wflake 01:40, 24 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.

title: Wikipedia:Articles for deletion/Runzor


text:
Talk:Knightly Virtues

Untitled

 * This is the archived discussion of a redirected/merged talk page

.

 * Where ever this list came from on the source page, it's gone now. Furthermore, the source page doesn't look very authoritative.  It seems to be an incredible ugly and poorly formatted mix of tourist (trap?) information, realty listings, and who knows what else. I recommend a complete rewrite using http://www.chivalrytoday.com/Farrell/Knightly-Virtues.html as well as http://www.chivalrytoday.com/Farrell/Best-Of-CTW/Chaucers-Virtues.html as source material. Charles 21:31, 23 Feb 2005 (UTC)

 * I too would like to point out the fact that the Emblem of the Order of St. John, (an organization that can be traced back to the Knights templar) does have a meaning behind the symbol. The emblem of the Order is a white eight-pointed cross embellished in the four principal angles alternately with a lion passant guardant and a unicorn passant. The four arms of the cross signify the cardinal virtues: Prudence, Temperance, Justice and Fortitude. The eight points signify the beatitudes: Humility, Compassion, Courtesy, Devotion, Mercy, Purity, Peace and Endurance. --not sure if this link will work, but its on the Sja.ca website Exit2DOS2000   •T•C•  23:49, 6 October 2007 (UTC)

Merge proposal
Since neither of the sources cited are particularly authoritative (one may be a dubious plug of an external website), I'd suggest moving what can be salvaged of this article into the main Chivalry article.

Most of the authoritative sources on this topic historically are probably dead tree editions. Research into the modern orders (i.e. OBE) might get enough for a real article, but at this point I don't see much.Somedumbyankee (talk) 04:17, 26 May 2008 (UTC)

 * I dont think Knightly Virtues and Chivalry are the same thing, so I do not think such a merge would be a good idea. Exit2DOS2000   •T•C•  05:53, 26 May 2008 (UTC)

 * My problem with the page currently is that it appears to be a plug for this Farrell guy's web site. The Order of St. John information could probably be moved to Venerable Order of Saint John, and that leaves this page with no information?Somedumbyankee (talk) 06:35, 26 May 2008 (UTC)

 * Although I am not willing to remove Farrels info myself, I hope this edit alleviates your concerns. Exit2DOS2000   •T•C•  08:01, 26 May 2008 (UTC)

Nobility/Valour - incongruent link
Under the proposed list of virtues is "Nobility/Valour". Yet the link on the word "nobility" points to the Wikipedia page on the hereditary status of nobility - completely unrelated to the virtue of "Nobility/Valour". Is there another Wikipedia page that this could be linked to? Or should the link be removed, as there is not yet a Wikipedia page for the concept of "Nobility/Valour"? —Preceding unsigned comment added by 58.41.106.142 (talk) 22:35, 14 April 2010 (UTC)

Problem with citation
The reference to Altmann seems dubious; if you look up page 99 in The Court Reconvenes (which is an edited collection and not a book by author, by the way), there seems to be no reference to the list of knightly virtues - it is instead the first page of an article on didactic strategies in the Ritterspiegel of Johannes Rothe. --Nuwanda (talk) 22:07, 29 January 2011 (UTC)

title: Talk:Knightly Virtues


text:
Wikipedia:Peer review/Brian Close/archive1

Brian Close
So far it's just me that's been contributing to this article. I think it's a very interesting subject. Unfortunately a very famous picture of him beaten black and blue in 1963 is copyright, so I can't add that. However I would welcome comments before I make the final push to FA status, jguk 21:33, 23 Feb 2005 (UTC)
 * Great article. I have made some minor copy edits. I think that the relationship between gentlemen and players needs a brief explanation. --Theo (Talk) 23:13, 25 Feb 2005 (UTC)
 * Sorry, should have said: did some copyediting too. Otherwise, looks very good - WP:FAC soon, I expect. -- ALoan (Talk) 11:46, 28 Feb 2005 (UTC)


text:
Matrix chain multiplication

Matrix chain multiplication (or the matrix chain ordering problem ) is an optimization problem concerning the most efficient way to multiply a given sequence of matrices. The problem is not actually to perform the multiplications, but merely to decide the sequence of the matrix multiplications involved. The problem may be solved using dynamic programming.

There are many options because matrix multiplication is associative. In other words, no matter how the product is parenthesized, the result obtained will remain the same. For example, for four matrices A, B, C, and D, there are five possible options:

 * ((AB)C)D = (A(BC))D = (AB)(CD) = A((BC)D) = A(B(CD)).

Although it does not affect the product, the order in which the terms are parenthesized affects the number of simple arithmetic operations needed to compute the product, that is, the computational complexity. The straightforward multiplication of a matrix that is $X × Y$ by a matrix that is $Y × Z$ requires $XYZ$ ordinary multiplications and $X(Y − 1)Z$ ordinary additions. In this context, it is typical to use the number of ordinary multiplications as a measure of the runtime complexity.

If A is a 10 × 30 matrix, B is a 30 × 5 matrix, and C is a 5 × 60 matrix, then

 * computing (AB)C needs (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 operations, while
 * computing A(BC) needs (30×5×60) + (10×30×60) = 9000 + 18000 = 27000 operations.

Clearly the first method is more efficient. With this information, the problem statement can be refined as "how to determine the optimal parenthesization of a product of n matrices?" The number of possible parenthesizations is given by the (n–1)th Catalan number, which is O(4n / n3/2), so checking each possible parenthesization (brute force) would require a run-time that is exponential in the number of matrices, which is very slow and impractical for large n. A quicker solution to this problem can be achieved by breaking up the problem into a set of related subproblems.

A dynamic programming algorithm
To begin, let us assume that all we really want to know is the minimum cost, or minimum number of arithmetic operations needed to multiply out the matrices. If we are only multiplying two matrices, there is only one way to multiply them, so the minimum cost is the cost of doing this. In general, we can find the minimum cost using the following recursive algorithm:

 * Take the sequence of matrices and separate it into two subsequences.
 * Find the minimum cost of multiplying out each subsequence.
 * Add these costs together, and add in the cost of multiplying the two result matrices.
 * Do this for each possible position at which the sequence of matrices can be split, and take the minimum over all of them.

For example, if we have four matrices ABCD, we compute the cost required to find each of (A)(BCD), (AB)(CD), and (ABC)(D), making recursive calls to find the minimum cost to compute ABC, AB, CD, and BCD. We then choose the best one. Better still, this yields not only the minimum cost, but also demonstrates the best way of doing the multiplication: group it the way that yields the lowest total cost, and do the same for each factor.

However, this algorithm has exponential runtime complexity making it as inefficient as the naive approach of trying all permutations. The reason is that the algorithm does a lot of redundant work. For example, above we made a recursive call to find the best cost for computing both ABC and AB. But finding the best cost for computing ABC also requires finding the best cost for AB. As the recursion grows deeper, more and more of this type of unnecessary repetition occurs.

One simple solution is called memoization: each time we compute the minimum cost needed to multiply out a specific subsequence, we save it. If we are ever asked to compute it again, we simply give the saved answer, and do not recompute it. Since there are about n2/2 different subsequences, where n is the number of matrices, the space required to do this is reasonable. It can be shown that this simple trick brings the runtime down to O(n3) from O(2n), which is more than efficient enough for real applications. This is top-down dynamic programming.

The following bottom-up approach computes, for each 2 ≤ k ≤ n, the minimum costs of all subsequences of length k using the costs of smaller subsequences already computed. It has the same asymptotic runtime and requires no recursion.

Pseudocode:
 * Note : The first index for dims is 0 and the first index for m and s is 1.

A Python implementation using the memoization decorator from the standard library:

More efficient algorithms
There are algorithms that are more efficient than the O(n3) dynamic programming algorithm, though they are more complex.

Hu & Shing
An algorithm published by T. C. Hu and M.-T. Shing achieves O(n log n) computational complexity. They showed how the matrix chain multiplication problem can be transformed (or reduced) into the problem of triangulation of a regular polygon. The polygon is oriented such that there is a horizontal bottom side, called the base, which represents the final result. The other n sides of the polygon, in the clockwise direction, represent the matrices. The vertices on each end of a side are the dimensions of the matrix represented by that side. With n matrices in the multiplication chain there are n−1 binary operations and Cn−1 ways of placing parentheses, where Cn−1 is the (n−1)-th Catalan number. The algorithm exploits that there are also Cn−1 possible triangulations of a polygon with n+1 sides.

This image illustrates possible triangulations of a regular hexagon. These correspond to the different ways that parentheses can be placed to order the multiplications for a product of 5 matrices.

For the example below, there are four sides: A, B, C and the final result ABC. A is a 10×30 matrix, B is a 30×5 matrix, C is a 5×60 matrix, and the final result is a 10×60 matrix. The regular polygon for this example is a 4-gon, i.e. a square:

The matrix product AB is a 10x5 matrix and BC is a 30x60 matrix. The two possible triangulations in this example are:

The cost of a single triangle in terms of the number of multiplications needed is the product of its vertices. The total cost of a particular triangulation of the polygon is the sum of the costs of all its triangles:

 * (AB)C: (10×30×5) + (10×5×60) = 1500 + 3000 = 4500 multiplications
 * A(BC): (30×5×60) + (10×30×60) = 9000 + 18000 = 27000 multiplications

Hu & Shing developed an algorithm that finds an optimum solution for the minimum cost partition problem in O(n log n) time. Their proof of correctness of the algorithm relies on "Lemma 1" proved in a 1981 technical report and omitted from the published paper. The technical report's proof of the lemma is incorrect, but Shing has presented a corrected proof.

Other O(n log n) algorithms
Wang, Zhu and Tian have published a simplified O(n log m) algorithm, where n is the number of matrices in the chain and m is the number of local minimums in the dimension sequence of the given matrix chain.

Nimbark, Gohel, and Doshi have published a greedy O(n log n) algorithm, but their proof of optimality is incorrect and their algorithm fails to produce the most efficient parentheses assignment for some matrix chains.

Chin-Hu-Shing approximate solution
An algorithm created independently by Chin and Hu & Shing runs in O(n) and produces a parenthesization which is at most 15.47% worse than the optimal choice. In most cases the algorithm yields the optimal solution or a solution which is only 1-2 percent worse than the optimal one.

The algorithm starts by translating the problem to the polygon partitioning problem. To each vertex V of the polygon is associated a weight w. Suppose we have three consecutive vertices $$V_{i-1}, V_i, V_{i+1}$$, and that $$V_{\min}$$ is the vertex with minimum weight $$w_{\min}$$. We look at the quadrilateral with vertices $$V_{\min}, V_{i-1}, V_i, V_{i+1}$$ (in clockwise order). We can triangulate it in two ways:
 * $$(V_{\min}, V_{i-1}, V_i)$$ and $$(V_{\min}, V_{i+1}, V_i)$$, with cost $$w_{\min}w_{i-1}w_i+w_{\min}w_{i+1}w_i$$
 * $$(V_{\min}, V_{i-1}, V_{i+1})$$ and $$(V_{i-1}, V_i, V_{i+1})$$ with cost $$w_{\min}w_{i-1}w_{i+1}+w_{i-1}w_{i}w_{i+1}$$.

Therefore, if

 * $$w_{\min}w_{i-1}w_{i+1}+w_{i-1}w_{i}w_{i+1}<w_{\min}w_{i-1}w_i+w_{\min}w_{i+1}w_i $$

or equivalently

 * $$\frac{1}{w_i}+\frac{1}{w_{\min}}<\frac{1}{w_{i+1}}+\frac{1}{w_{i-1}} $$

we remove the vertex $$V_i$$ from the polygon and add the side $$(V_{i-1}, V_{i+1})$$ to the triangulation. We repeat this process until no $$V_i$$ satisfies the condition above. For all the remaining vertices $$V_n$$, we add the side $$(V_{\min}, V_n)$$ to the triangulation. This gives us a nearly optimal triangulation.

Generalizations
The matrix chain multiplication problem generalizes to solving a more abstract problem: given a linear sequence of objects, an associative binary operation on those objects, and a way to compute the cost of performing that operation on any two given objects (as well as all partial results), compute the minimum cost way to group the objects to apply the operation over the sequence. One somewhat contrived special case of this is string concatenation of a list of strings. In C, for example, the cost of concatenating two strings of length m and n using strcat is O(m + n), since we need O(m) time to find the end of the first string and O(n) time to copy the second string onto the end of it. Using this cost function, we can write a dynamic programming algorithm to find the fastest way to concatenate a sequence of strings. However, this optimization is rather useless because we can straightforwardly concatenate the strings in time proportional to the sum of their lengths. A similar problem exists for singly linked lists.

Another generalization is to solve the problem when parallel processors are available. In this case, instead of adding the costs of computing each factor of a matrix product, we take the maximum because we can do them simultaneously. This can drastically affect both the minimum cost and the final optimal grouping; more "balanced" groupings that keep all the processors busy are favored. There are even more sophisticated approaches.

title: Matrix chain multiplication


text:
Talk:Emma Smith

Emma's knowledge of Joseph's plural marriages
Given the flat denials of Emma regarding plural marriage, how are we able to say with any certainty what Emma knew and didn't know? I guess the bottom line of my question is whether we should be hedging statements about what she knew. It of course implies serious character defect on Joseph's part (not that that is unusual) to say Emma knew nothing of plural marriage for 10 years. I just want to know we are stating the unbiased facts. Tom Haws 21:40, Feb 23, 2005 (UTC)

The article doesn't have much to do with facts. It is rumor and mistakes. If Emma wrote and said what she knew, shouldn't we regard that as fact instead of what the author is trying to make it appear to be?

 * I think this area is hard to know anything with certainty because people on all sides of the issue were trying to frame the issues in relation to the Succession crisis etc. I think the reason people say she knew was she was present for some of the ceremonies, but I think she could deny she knew because she didn't want to believe the implications etc. I was reading the Dialog special issue on Joseph Smith a couple months ago - I'll look through it because it has some well researched comments on this issue Trödel| talk 22:42, 23 Feb 2005 (UTC)

Where are the fact relating to her presence at any such event? Where is this evidence? Apparently this is once again rumor.

These passages should be ironclad or hedged a bit: "Joseph had continued to practice plural marriage in secret, taking additional polygamous wives without Emma's knowledge. In Nauvoo, he began to privately teach other men in the church the doctrine." "It was also in Kirtland, however, the Emma's husband began to teach and practice the doctrine of "plural marriage"—although at this stage he kept all of these relationships secret from Emma." Tom Haws 23:26, Feb 23, 2005 (UTC)

Where again is the fact in this supposed knowledge? History says he did not practice polygamy and many writings, etc., point to the lack of evidence and the Mormon's even admit this is speculation rather than fact.

 * I think if you want to hedge the text more or rephrase it, that's fine. However, I think we can say with a good deal of certainty that Emma knew about some of the "marriages."  The records are pretty clear.  I think Emma's denials should be viewed no differently than Joseph (Jr.)'s denials.  Publically, Joseph Jr. repeatedly condemned polygamy and repeatedly denied his involvement in polygamy.  However, despite these statements, it is clear he was involved in it.  Emma's policy of public denial --- like Joseph III's --- can be seen as a continuation of Joseph Jr.'s policy, honoring the apparent wishes of the deceased prophet.  --John Hamer 23:58, 23 Feb 2005 (UTC)

So basically what you're saying is, you have a secret way of knowing what a person who lived many years ago said in private. And that means that all of her statements, every single one of her statements and all the supporting documents are to be thrown out for a bunch of rumors. Interesting - I thought this was supposed to be about facts.

 * I feel unqualified, especially with true experts present, to make the changes. From your summary above, it sounds like the two sentences I marked should be corrected though.  Would you do it so it is right? Tom Haws 17:59, Feb 24, 2005 (UTC)

I believe from some of my own research (which should NOT be used as primary reference material) that Emma knew about most if not all of the marriages. However, like many in the early church made a covenant not to discuss it, and to deny it at all costs. It wasn't until 1852 that it was officially endorsed as a practice and doctrine of the LDS church, so until then (even though it was publicly known leaders practiced) it was vehemently denied. Even Young offered to marry Emma

Wives of Joseph Smith Category
I don't understand why placing Emma Smith under the categories of Joseph Smith's wives in insulting. She was his wife, and as you said the most important one. Also, removing a factual tag because it's "insulting" is POV. -FlyingToaster (talk) 05:33, 25 September 2008 (UTC)
 * Excuse me, but you just reverted three edits, which is vandalism. I am a frequent editor of all LDS Movement articles, so if you have a particular cited challenge to any of my edits, go ahead. RE: the new category of 'wives of JSJR.' created by Descartes1979, this was a very contentious set-up, which did not happen without some controversy. Smith herself denied throughout all records any knowledge or involvement, regardless of whatever secondary sources now claim; factual is one thing, allegations another. In the meantime, I've reverted your rollback of several unconnected edits as unjustified. Best, A Sniper (talk) 05:38, 25 September 2008 (UTC)

RE: my revert
I reverted the most recent edit as it implied the RLDS as being a 'new organization' without allowing the facts to speak for themselves. The RLDS narrative is that they were a reorganization as opposed to a 'new' one. Best, A Sniper (talk) 02:48, 16 March 2009 (UTC)

Emma Smith: My Story
Should there be some mention of the 2008 film: 'Emma Smith: My Story'; [official site: http://www.emmasmithmovie.com/] -- Perhaps in the External links section? ~Eric F 184.76.225.106 (talk) 01:33, 16 March 2012 (UTC)
 * Only if it is qualified to be a pro-LDS piece made by the Mormon members of the Joseph Smith Jr. family organization (run by Michael Kennedy of Salt Lake). Best, A Sniper (talk) 02:16, 16 March 2012 (UTC)

Name of the church in 1839
An editor has made a good faith edit claiming that the name of the church in 1838 was The Church of Jesus Christ of Latter-day Saints. I have corrected this to point out that the name was Church of Jesus Christ of Latter Day Saints, and to mention in the edit summary that the church in Utah did not add 'The' to the name and being using 'Latter-day' until several years later. Best, A Sniper (talk) 00:39, 22 March 2013 (UTC)

Emma Smith: Polygamy - Note referencing Journal of Mormon History, Spring 2005, Volume 31, p. 70.
Note 17 under the section on Polygamy references a page in an article on the Kinderhook plates. Surely this reference is incorrect? "Over the years, many RLDS Church historians attempted to prove that the practice had originated with Brigham Young.[17]" 17 = Journal of Mormon History, Spring 2005, Volume 31, p. 70.

http://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=2383&context=facpub — Preceding unsigned comment added by 97.121.59.118 (talk) 21:03, 17 March 2017 (UTC)

Introduction
I cleaned up the photo, that is several months old David Hyrum Smith born in November, citation added. I gave Emma a nationality in the introduction and made her ID independent from "the wife of ..." Plus, controversial or not, if Joseph Smith had multiple wives, Emma was his first. ~ Fimbriata (talk) 16:05, 11 August 2022 (UTC)

title: Talk:Emma Smith


text:
Georges Erasmus

Georges Henry Erasmus, OC (born August 8, 1948 in Behchoko, Northwest Territories) is a Canadian politician. He was the national chief of the Assembly of First Nations from 1985 to 1991.

Erasmus was born in a Dene community of the Northwest Territories to a family of 12 children. He attended high school in Yellowknife. In 1967, he was a volunteer with the Company of Young Canadians.

He became president of the Dene Nation in 1974 and while president fought against the proposed Mackenzie Valley Pipeline.

He was the federal New Democratic Party candidate in 1979 for Western Arctic riding.

Erasmus was national chief of the Assembly of First Nations during the Oka Crisis. After serving two terms as national chief he co-chaired the Royal Commission on Aboriginal Peoples.

Erasmus has been honoured for his work many times. He was appointed to the Order of Canada as a member in 1987, and was promoted to officer in 1999. He has also been awarded honorary doctorates by seven Canadian universities, including the University of Toronto, Queen's University, and the University of Manitoba. He was awarded an honorary doctorate by the University of Western Ontario in June 2006. In 2009 he was awarded the Governor General's Northern Medal.

Intellectual Contribution to Indigenous Rights
Georges Erasmus is a committed advocate, political leader, and well-respected spokesperson for Indigenous peoples in Canada. In 1976, Erasmus presented to the Berger Inquiry the Dene’s position to the proposed pipeline. This presentation, "We the Dene" gives some initial insight into the intellectual thinking of Erasmus. However, it is important to stress that Erasmus speaks from his location as a member of the Dene and his intellectual thoughts would be influenced by his relationships with his elders and his position within his community. Speaking as one of the Dene, Erasmus outlined the Dene’s assertion of sovereignty.

As a distinct Dene nation, Erasmus pointed out that they sought to enter into the confederation of Canada as a "recognized entity" with their own self-government over a specific land base. Erasmus points out in this presentation that the Treaties 8 and 11 were agreements entered into on the understanding that they recognized the right of the Dene to govern themselves and from which the Dene nation could live separately but in peaceful coexistence with the non Dene people. Erasmus states, "Clearly these agreements have been broken. Instead of recognition of our national right to self-determination, we have been subjected to over fifty years of colonization, of forced assimilation." In representing his people on the public stage, Erasmus has pursued the need for negotiation, new agreements, and recognition of Indigenous rights from the Canadian government. At times his frustration towards a noncommittal federal government has shown, and he has had to forewarn the government of potential conflict.

At an early point in his intellectual and political life, Erasmus began to highlight the importance of de-colonization and how this must be based on collective action. In taking this approach he attempted to highlight the collective capacity of resistance, and challenged the power relations embedded within the language and practice of paternalism, asserting his people’s right to define themselves, and their own needs. Beginning with the Dene declaration, the model of nations coexisting together in an ethical relationship while retaining sovereignty, is highlighted as a central tenet of his people’s position. This was carried on throughout his public interviews and is presented in the Royal Commission on Aboriginal Peoples.

In a speech given by Erasmus in 2002, he continued to call for conversation "nation to nation," as the means upon which to build a "common future". Importantly, Erasmus proposed that the contemporary focus should move from an emphasis on "Aboriginal Rights to relationship between peoples; from crying needs to vigorous capacity; from individual citizenship to nations within the nation state." He suggests that the pursuit of seeking recognition of Aboriginal Rights through the Canadian courts should change because "Litigation is no way to build a community." Erasmus reasserts instead, the importance of treaty making as a way forward to build renewed relationships built on "mutual trust" and a bond "like that of brothers who might have different gifts and follow different paths, but who could be counted on to render assistance to one another in times of need."

title: Georges Erasmus


text:
Talk:Nabuur

This page was voted on for deletion at Votes for deletion/Nabuur. The consensus was to keep it. dbenbenn | talk 21:45, 23 Feb 2005 (UTC)

title: Talk:Nabuur


text:
User:Jun-Dai

Main page: m:User:Jun-Dai

Me:
 * Jun-Dai's homepage

User pages:

title: User:Jun-Dai


text: User talk:82.43.197.111

title: User talk:82.43.197.111


text:
Talk:WKB approximation

Untitled
I just removed the long paragraph on WKB's relationship to Feynman diagrams because it was rather unclear (I'm a physics grad student and couldn't tell what it was trying to say) and also seemed to belong more to the article on One-loop Feynman diagrams rather than this page. Laura Scudder 21:48, 23 Feb 2005 (UTC)

Shouldn't the equation be

 * $$\psi(x)\approx \frac{1}{\sqrt{2m[E-V(x)]}}\exp\left(\pm \frac{i}{\hbar} \int_{-\infty}^x dx' 2m(E-V(x))\right)$$

rather than

 * $$\psi(x)\approx \frac{1}{\sqrt{2m[E-V(x)]}}\exp\left(\pm \frac{i}{\hbar} \int_{-\infty}^x dx' \sqrt{2m(E-V(x))}\right)$$

?

See, e.g., http://webpages.ursinus.edu/lriley/courses/p212/lectures/node37.html

 * That page agrees with the current version of this article. See this equation, which says

 * $$ k(x) = \sqrt{2 m [E - V(x)]} / \hbar $$

 * and then three equations lower (7.66)

 * $$\psi (x, t) = A_0 \sqrt{\frac{k_0}{k(x)}} \exp \left( i \int_{x_0}^{x} k(x) dx - \omega t \right)$$

 * so the square root in the exponential is correct, but it should be a 1/4 power in the denominator out front, which I just confirmed in Sakurai. --Laura Scudder | Talk 20:31, 7 May 2005 (UTC)

One loop diagram
The link to one loop diagrams should be explained. It isn't clear to me at all. The WKB approximation typically yields nonperturbative results. Take e.g. the hydrogen atom in an electrical field. The tunneling rate to the ionized state is proportional to Exp[-constant/|eE|], which is nonperturbative in the coupling (the charge e). To obtain this result from perturbation theory you must perform a resummaton over an infinite number of terms. So, perhaps by 'one loop effect' a summation over all one loop diagram is meant?Count Iblis 22:35, 2 September 2005 (UTC)

Demonstration
The demonstration given is not conclusive at all.

"The demonstration given is not conclusive at all."

If by that you mean that the derivation is incomplete, then I concur.--Paul 03:22, 26 October 2005 (UTC)

Much nicer now, thanks !

Missing a bunch of stuff
Ok so long story short, I just spent 30 minutes writing out the WKB method for the tunneling article and, stupid me, I don't think to see if it is already done. However. This article is missing well over half of the solution. I am going to take what I just wrote and fill in all of the missing parts. —Preceding unsigned comment added by C h fleming (talk • contribs) 08:11, 27 October 2005

Action and classical EM
I'd like to add some discussion on the relationship between the WKB method and action, but I'm not sure to what extent this would clutter the article. I at least alluded to such a connection. Also, if memory serves, there was a similiar method to the WKB method used in classical EM, but I know nothing of this. Can anyone expand on this or at least verify? Threepounds 05:52, 27 November 2005 (UTC)

 * I have never seen the WKB method used with a Lagrangian, but I have seen other semiclassical approximations. Possibly you mean to talk about the action variable and the early pre-schroedinger equation classical-quantum mechanics that quantized the action variable Int p dq . In the first order of the semiclassical limit, the action variable with classical trajectories is correct. All of these things are related. But that is perhaps more a feature of semiclassical QM in general than the WKB method.
 * And yes the WKB method did exist before quantum mechanics. It can be used in many PDE's including the Hamilton Jacobi equation. (CHF 13:12, 1 December 2005 (UTC))
 * Yes, that's essentially what I was trying to get at. I think I agree with your point that that is more an artifact of semiclassical physics then the WKB method itself, so perhaps a bit out of scope.  Threepounds 04:31, 2 December 2005 (UTC)
 * In classical EM you probably mean the Eikonal equation. 130.20.125.39 (talk) 06:16, 11 November 2023 (UTC)

The instanton method in QFT is analogous to the WKB method. See e.g. here. Count Iblis 14:01, 3 December 2005 (UTC)

 * True. But the instanton method has it's own page. And WKB predates the instanton method. So I think isn't it really for the instanton method's page to mention this and explain it? There seems to be some kind of heirarchy to conserve here? CHF 22:14, 11 December 2005 (UTC)

Equation numbers?
I'd like to refer to an equation here from another article. The reference would be simpler if there were equation numbers, but perhaps we aren't doing equation numbers in WP? Alison Chaiken 18:35, 21 January 2006 (UTC)

 * Equation numbers and references/citations have to be put in by hand. In case of references you can use the pair of commands and a matching  command, but this doesn't work if you want to refer to a Ref. twice. Perhaps we need to talk to some of the administrators here, because making small edits to articles with a lot of numbered references like this one can be time consuming.Count Iblis 23:23, 21 January 2006 (UTC)

 * What I ended up doing was putting in this:  .    Maybe that's not exactly the right thing to do but it's the best I could figure out from Help:Anchors.    I don't quite know what you mean by "  and a matching  " since the only help pages I find that use "" are about templates.    As far as I can tell, there's no way to search within the "WP:Help" subspace.   Alison Chaiken 01:17, 22 January 2006 (UTC)

 * I used the in the article digital physics. You get automatically numbered references that act as links to the citations, but it doesn't work if you refer to the same citation more than once. I didn't previously know about the Anchor command you have used, though!Count Iblis 13:52, 22 January 2006 (UTC)

Missing Info
Shouldn't this article include a mention of the cases where the WKB approximation gives the exact solution? I don't remember them all off hand, but maybe I'll add them later. Or some else can doesn't matter to me. 24.59.193.0 04:01, 8 March 2006 (UTC)

Connection formula
It seems that there's an error in the connection formula expressed in terms of Bessel functions. The dimension of the parameter $$U_1$$ should be $$[x]^{-3}$$ judging from the simplified differential equation near the turning point $$x_1$$. The term ($$\frac{2}{3} \sqrt{U_1} (x-x_1)^{1/3}$$) inside the Bessel functions is supposed to be dimensionless but it's not. Could someone check this point? By the way, this DE can be cast into the form $$y''(x) = x*y(x)$$, the Airy DE. So, the solution can also be expressed by a linear combination of the two Airy functions: $$\psi(x) = C_1*AiryAi(U_1^{1/3}(x-x_1)) + C_2*AiryBi(U_1^{1/3}(x-x_1))$$. —Preceding unsigned comment added by 24.59.193.0 (talk • contribs) 04:01, 8 March 2006

Non-QM approach
While WKB was invented to solve Schrodingers equation, its widely used to solve other wave problems of the form
 * $$\frac{d^2\phi}{dx^2} + k^2(x) \phi = 0$$

where k varies slowly on the scale of a one wavelength.

This should be mentioned somewhere, and the derivation of the solution, with
 * $$\phi\sim k^{-1/2} \exp(\frac{1}{\epsilon}\int k(X)dX), \quad X = \epsilon x$$ —Preceding unsigned comment added by Jim McElwaine  (talk • contribs) 16:53, 27 April 2006

Non-QM
I think the page need to be rewritten along the lines of the Non-QM comment at the bottom. The mathematics of the method is very general and obscured by the extra notation h, E V etc. This would make the method easy to understand and to apply to particular cases. The connection to tunneling should be put in a separate page. There is no need to mention Bessel functions at all. The solution is neater in Airy functions and the Airy function page can link to Bessel functions. I am happy to rewrite the page, I'm an applied mathematician at Cambridge, but do not want to make any changes until other people have given their opinions. Jim McElwaine 16:53, 27 April 2006 (UTC)

 * I've started rewriting it at User:Gareth_Owen/WKB_approximation, but haven't had chance to do more than half. Please complete my job, and we'll present it here when its done. -- GWO

 * Makes sense. It was developed first independently to solve non-QM problems.  — Laura Scudder ☎ 18:36, 27 April 2006 (UTC)

 * I agree, and I have just come across the page as I am teaching the subject later this autumn. Unless anyone objects I will have a go at implementing the above suggestion when I get around to itBilllion (talk) 08:50, 5 September 2008 (UTC)

 * As far as I can see, the above already has been implemented, by 140.247.248.31 in November 2007. -- Crowsnest (talk) 09:31, 5 September 2008 (UTC)

 * The example section is appropriate, but the application to Schrodinger equation seems to me inappropriate. Perhaps it should be moved to a wikibook? Also, contrary to the introduction which states WKB is applicable to linear PDEs, the method section implies the method is applicable to linear homogeneous ODEs. All this, and it seems to me at after an hour's pondering, that the method has a good chance of helping one solve any DE where the highest order derivative dominates the lower order derivatives... I wish this idea had been in the first line of the article. 169.237.31.150 (talk) 02:49, 28 January 2012 (UTC)

wrong equation ?!
Psi=exp(phi) and Psi'=A+iB, but then the following statement below is not true, cause the DERIVATIVE of Psi equals A+iB and not Psi directly:

The amplitude of the wavefunction is then exp[A(x)] while the phase is B(x).

Better remove it completely?62.218.164.30 17:54, 17 November 2006 (UTC)

Wrong equation!
The derivative of Psi equals (A'+iB')Psi! The equations for the functions A and B are wrong. Plugging in the Ansatz

 * $$\Psi(x) = e^{\Phi(x)}$$

 * $$\Phi'(x) = A(x) + i B(x)$$

into the Schrödinger equation leads to

 * $$A'' + A'^2 - B'^2 = \frac{2m}{\hbar^2}(V-E)$$

 * $$B'' +2A' B' = 0$$

. —The preceding unsigned comment was added by Matrix1329 (talk • contribs) 11:06, 6 January 2007 (UTC).

Matrix1329 11:09, 6 January 2007 (UTC)

 * You seem to working with $$\phi(x) = A(x) + i B(x)$$ rather than the stated $$\phi ' (x) = A(x) + i B(x)$$. That's why you have second derivatives of A and B running around.  — Laura Scudder ☎ 14:36, 1 December 2007 (UTC)

Lacking basics
This page provides a lot of maths, suited more to a physics textbook and not an encyclopedia. I'm not saying anything should be removed, but simpler descriptions of the concepts should ideally be provided to those not of a physics-related background. LaudanumCoda 14:50, 10 May 2007 (UTC)

This is a topic which one would meet in the final year of a physics undergrad degree. Might be difficult to clearly give a good idea. 82.16.99.131 (talk) 10:12, 4 November 2008 (UTC)

Higher Dimension?
I think it should be added the WKB formulation for more than one dimension when SE ain't separable, for example whenever you have the potential $$ V(x,y,z) $$ in 3-D of the form V=xyz so you need to evaluate the solution using WKB approach, i think Einstein and others estudied this problem but not sure --85.85.100.144 11:31, 26 June 2007 (UTC)

Added specifics
I added some details of the WKB method and an example from Bender and Orszag. I can be contacted at [redacted] (at) gmail if you think the article still lacks clarity. (Or if you want to thank me for enabling you to do your Applied Math 201 problem set. I'm talking to you, Harvard students.)

--140.247.248.31 (talk) 17:53, 26 November 2007 (UTC)

History
In:, p.228, there is an account on the history of the WKBJ method. References therein are: Liouville (1837) and Green (1837) are credited by Olver as the ones who developed the method. Further, in the same historical account by Olver, he cites Jeffreys (1953), who refers to Gans (1915) and (to a lesser extend) Lord Rayleigh (1912) as earlier accounts of the method. -- Kraaiennest (talk) 02:10, 25 January 2008 (UTC)
 * Francesco Carlini (1817). "Richerche sulla convergenza della serie che serva aal soluzione del problema di Keplero". Milano.
 * Joseph Liouville (1837). "Sur le développement des foncttions et séries ...". Journal de Mathématiques Pures et Appliquées 1:16-35.
 * George Green (1837). "On the motion of waves in a variable canal of small depth and width". Transactions of the Cambridge Philosophical Society 6:457-462.
 * Lord Rayleigh (1912). "On the propagation of waves through a stratified medium, with special reference to the question of reflection". Proceedings of the royal Society London, Series A 86:207-226.
 * Richard Gans (1915). "Fortplantzung des Lichts durch ein inhomogenes Medium". Annalen der Physik [4] 47:709-736.

Abbreviation alternatives
The abbreviation JWKB has been introduced, to replace WKBJ. I did a Google Scholar search to get an indication on the use of the various forms: WKB is by far the most used expression for the method, while JWKB and WKBJ are both quite often used. To my opinion, this should be reflected somehow in the article. -- Crowsnest (talk) 08:43, 18 March 2009 (UTC)
 * "WKB approximation": 15500 hits
 * "JWKB approximation": 1030
 * "WKBJ approximation" : 834
 * "WBK approximation" : 57
 * "BWK approximation" : 33
 * "BWKJ approximation" : none, but Google books finds one
 * "Wentzel-Kramers-Brillouin approximation" : 529
 * "Jeffreys-Wentzel-Kramers-Brillouin approximation" : 12
 * "Wentzel-Kramers-Brillouin-Jeffreys approximation" : 7

link to reference
https://archive.org/stream/ComptesRendusAcademieDesSciences0183/ComptesRendusAcadmieDesSciences-Tome183-Juillet-dcembre1926#page/n23/mode/2up --217.226.78.134 (talk) 17:29, 14 January 2016 (UTC)

Regarding recent changes
Hello. I originally intended to append 'validity of WKB' to the article but ended up rewriting and changing variables to match with the rest of the article. Although, I retained as much of the original article as possible and don't think I left out any detail, my apologies to any prior contributors who find this process disruptive.

Please consider sharing your criticism here first before choosing to revert article for any reason. I recommend we also give it a little time for others to share their views. Constructive feedback is always appreciated. Thank you!

For reference, this was the state of article before and then after. EditingPencil (talk) 12:00, 21 November 2023 (UTC)

title: Talk:WKB approximation


text:
Synchromism

Synchromism was an art movement founded in 1912 by American artists Stanton Macdonald-Wright (1890–1973) and Morgan Russell (1886–1953). Their abstract "synchromies," based on an approach to painting that analogized color to music, were among the first abstract paintings in American art. Though it was short-lived and did not attract many adherents, Synchromism became the first American avant-garde art movement to receive international attention. One of the difficulties inherent in describing Synchromism as a coherent style is connected to the fact that some Synchromist works are purely abstract while others include representational imagery.

Theory and style
Synchromism is based on the idea that color and sound are similar phenomena and that the colors in a painting can be orchestrated in the same harmonious way that a composer arranges notes in a symphony. Macdonald-Wright and Russell believed that, by painting in color scales, their visual work could evoke the same complex sensations as music. As Macdonald-Wright said,"Synchromism simply means 'with color' as symphony means 'with sound.'" The phenomenon of "hearing" a color or the pairing of two or more senses--synesthesia—was also central to the work of Wassily Kandinsky, who was developing his own synesthetic paintings, or "compositions," in Europe at approximately the same time.

The abstract "synchromies" are based on color scales, using rhythmic color forms with advancing and reducing hues. They typically have a central vortex and explode in complex color harmonies. The Synchromists avoided using atmospheric perspective or line, relying solely on color and shape to express form. Macdonald-Wright and Russell were among a number of avant-garde artists at work in the period immediately before World War I who believed that realism in the visual arts had long since reached a point of exhaustion and that, to be meaningful in the modern world, painting needed to sever any ties to older ideas about perspective and to literary or anecdotal content.

The earliest Synchromist works were similar to Fauvist paintings. The multi-colored shapes of Synchromist paintings also loosely resembled those found in the Orphism of Robert and Sonia Delaunay. Macdonald-Wright insisted, however, that Synchromism was a unique art form and "has nothing to do with Orphism and anybody who has read the first catalogue of Synchromism ... would realize that we poked fun at Orphism." The Synchromists' debts to Orphism remain a source of debate among art historians. Their approach more clearly owed something to Cubism. The Synchromists made use of the broken planes of the Cubists, but their lavishly colored areas of paint sometimes looked, as the art historian Abraham Davidson has described them, like "eddies of mist, the droplets of which collect to form parts of a straining torso....To find anything like this in American painting one has to wait for the color-field canvases of Jules Olitski in the 1960s."

History
Synchromism was developed by Stanton Macdonald-Wright and Morgan Russell while they were studying in Paris during the early 1910s. In 1907, Stanton Macdonald-Wright studied the ideas of optical scientists such as Michel-Eugene Chevreul, Hermann von Helmholtz, and Ogden Rood in order to further develop color theory influenced by musical harmonies. Then from 1911 to 1913, they both studied under the Canadian painter Percyval Tudor-Hart, whose color theory connected qualities of color to qualities of music, such as tone to hue and intensity to saturation. Also influential upon Macdonald-Wright and Russell were the Impressionists, Cézanne and Matisse with their emphasis of color over drawing. In addition to the Cubists and Impressionists, Macdonald-Wright and Russell were also inspired by artists such as Émile Bernard, who was a Cloisonnist, and the Synthetist Paul Gauguin for their unique explorations of the properties and effects of color. Russell coined the term "Synchromism" in 1912, in an express attempt to convey the linkage of painting and music.

The first Synchromist painting, Russell's Synchromy in Green, exhibited at the Paris Salon des Indépendants in 1913. Later that year, the first Synchromist exhibition by Macdonald-Wright and Russell was shown in Munich. Exhibitions followed in Paris in October 1913 and in New York in March 1914. Macdonald-Wright moved back to the United States in 1914, but he and Russell continued separately to paint abstract synchromies. Synchromism remained influential among artists well into the 1920s, though its purely abstract period was relatively brief. Many synchromies of the late 1910s and 1920s contain representational elements. At no time, though, did Macdonald-Wright or Russell achieve the level of critical or commercial success they had hoped for when they introduced Synchromism to the United States. It was not until after Russell's death and late in Macdonald-Wright's life that extensive museum and scholarly attention was paid to their highly original achievements. Other American painters who experimented with Synchromism include Thomas Hart Benton (1889–1975), Andrew Dasburg (1887–1979), Patrick Henry Bruce (1880–1936), and Albert Henry Krehbiel (1873–1945).

The earliest extended discussion of Synchromism appeared in the book Modern Painting: Its Tendency and Meaning (1915) by Willard Huntington Wright. Wright was a literary editor and art critic and the brother of Stanton Macdonald-Wright, and the book was secretly co-authored by Stanton. It surveyed the major modern art movements from Manet to Cubism, praised the work of Cézanne (at the time relatively unknown in the United States), denigrated "lesser Moderns" such as Kandinsky and the Futurists (and, of course, the Orphists), and predicted a coming age in which color abstraction would supplant representational art. Synchromism is presented in the book as the culminating point in the evolution of modernism. Willard Huntington Wright never acknowledged that he was writing about his own brother's work.

Three other extended treatments of Synchromism can be found in the catalogue by Gail Levin that accompanied a major traveling exhibition organized the Whitney Museum of American Art in 1978, Synchromism and American Color Abstraction, 1910–1925, in Marilyn Kushner's catalogue for a 1990 Morgan Russell retrospective at the Montclair Museum, and in Color, Myth, and Music: Stanton Macdonald-Wright and Synchromism by Will South, a catalogue-biography published in conjunction with a three-museum exhibition of the artist's work in 2001. Levin and South are the two art historians most responsible for attracting scholarly and public attention to Synchromism, a movement that has often occupied a minor place in twentieth-century art-history textbooks.

title: Synchromism