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Dumb and Dumberer: When Harry Met Lloyd

Dumb and Dumberer: When Harry Met Lloyd is a 2003 American buddy comedy film directed by Troy Miller from a screenplay by Miller and Robert Brener. It is the second installment in the Dumb and Dumber franchise and a prequel to the 1994 film Dumb and Dumber. Depicting the original film's characters during their high school years, it stars Derek Richardson and Eric Christian Olsen in the title roles. The film was a moderate box office success, but was panned by critics, who compared it unfavorably with the original.

Plot
In 1986, Harry Dunne finally gets his chance to go to regular school. At the same time, Lloyd Christmas has been adopted and exchanged several times until he is finally accepted by the school janitor, Ray. Harry bumps into Lloyd on the way to school, in search of a treasure his mother asked him to find, and as if it were destiny, the two instantly became the best of friends. Lloyd introduces Harry to his "friend", Turk, the school bully whose main function in life appears to be making Lloyd's life miserable. After putting Lloyd in a trash can, he hoists the two friends up a flagpole.

Meanwhile, the corrupt Principal Collins is searching for a way to get a large amount of money to get a condominium in Waikiki, Hawaii for him and his girlfriend, Ms. Heller, the school's cafeteria lady. Seeing Harry and Lloyd getting hoisted on a flagpole, Principal Collins decides to establish a fake "special needs" class to swindle $100,000 from a former Special Needs student named Richard Moffit. Obviously, Harry and Lloyd are more than thrilled to help, unaware of the real reason, and thus find themselves signing up people who are "special" enough for the class. These include a reluctant Turk; a teen named Toby who broke his leg and arm in a skateboarding accident—and whom Lloyd believes is a "little crippled boy"; Toby's gorgeous girlfriend, Terri; geeky Lewis, whom Harry and Lloyd believe is a centaur after seeing him half-dressed in his horse mascot uniform; Cindy, also known as "Ching-Chong", a Chinese exchange student who later becomes Turk's girlfriend; and Carl, a badly injured football player obsessed with his sport. Ms. Heller becomes the teacher of the fake class and holds it in Ray's tool shed.

Jessica Matthews, a headstrong student and reporter for the school paper, is suspicious of Principal Collins' sudden contribution. Jessica invites Harry over to her house for dinner and asks Harry for information. Harry, who thinks that she is flirting with him, turns to Lloyd for courtship tips. A repulsive disaster involving Jessica's bathroom and a melted chocolate bar that looks like feces makes her father, Walter, freak out, inadvertently directing her attention to Lloyd. Soon, Harry and Lloyd get into a fight over Jessica, without her knowing it, which causes the duo to angrily break off their friendship. Inevitably, the two make amends when Harry and Lloyd realize that they were nothing without each other. They find Principal Collins' chest in his office which contains evidence of every scam he and Ms. Heller ever pulled, and that evidence could put them away for 20 years.

The next day, Principal Collins finds his evidence chest missing, and Ms. Heller falsely accuses Jessica of taking it. As a result, Principal Collins prank calls her parents and keeps her at his house overnight in an attempt to interrogate her. Meanwhile, the Special Needs class builds a float of George Washington for the Thanksgiving Parade. However, after Lloyd and Harry discover the evidence in the chest, they change the float to look like Principal Collins instead. After the class discovers his evidence, they agree to use him as the float instead. They also plan on having it pulled by the class's special bus. Before bringing out the float, they call the police. During the parade, the superintendent of the school district has a police detective pose as Richard Moffit, so Principal Collins would take the grant. Eventually, the Special Needs class brings out their float and proves Principal Collins and Ms. Heller as thieves by putting their recordings over loudspeakers, therefore exposing their plot. Before Principal Collins and Ms. Heller escape with the money, they are arrested by the police. Jessica is grateful for Harry and Lloyd and regards them as heroes, but just like in the original film, the duo's advances to Jessica are in vain, as it turns out that Jessica had a boyfriend. He commends Harry and Lloyd for exposing Collins' and Heller's plot and rides off with Jessica.

Harry and Lloyd vow never to fight and risk their friendship over a woman, but as they head home, they are approached by Fraida Felcher and her twin sister, Rita in a red Ferrari 308 GTS, who offer to take them to visit a new girls' college. After Harry and Lloyd get into another debate over which girl they want, Lloyd declines the offer to settle the debate, and Fraida and Rita furiously drive off, splattering Harry with mud in the process. Walter accidentally hits Harry with his Mercedes, resulting in Harry getting the windshield and hood covered with mud. Jessica's father recognizes Harry and as he frantically thinks his car is covered in feces, Harry and Lloyd casually walk away.

Cast

 * Derek Richardson as Harry Dunne
 * Lucas Gregory as young Harry Dunne
 * Eric Christian Olsen as Lloyd Christmas
 * Colin Ford as young Lloyd Christmas
 * Rachel Nichols as Jessica Matthews, Harry and Lloyd's crush.
 * Eugene Levy as Principal Collins
 * Mimi Rogers as Mrs. Dunne
 * Luis Guzman as Ray Christmas, the Janitor and Lloyd's dad.
 * Cheri Oteri as Ms. Heller
 * Bob Saget as Walter Matthews (Charlie)
 * Julia Duffy as Mrs. Matthews
 * Elden Henson as Turk "the school bully"
 * Shia LaBeouf as Lewis
 * William Lee Scott as Carl
 * Michelle Krusiec as Cindy "Ching-Chong"
 * Josh Braaten as Toby
 * Teal Redmann as Terri
 * Lin Shaye as Margie Neugeboren
 * Julie Costello as Fraida Felcher
 * Shawnie Costello as Rita Felcher
 * Timothy Stack as doctor
 * Brian Posehn as convenience store clerk Big "A"
 * Vahe Manoukian as security guard

Production
Much of the film was filmed in Atlanta. Many of the school scenes were filmed at Walton High School in Marietta and at the Atlanta International School in Fulton County. The Farrelly brothers, who co-wrote and directed the original Dumb and Dumber, had no involvement in this film whatsoever, nor did Jim Carrey or Jeff Daniels, who played Lloyd and Harry in the original film. Although Peter Farrelly has never seen the prequel, he went on record as saying that he holds no ill will against the film and wished the filmmakers well on it.

Following the success of South Park, co-creators Trey Parker and Matt Stone were originally slated to write the script for the film, but due to scheduling conflicts, by 2000 they opted out of the project and returned their salary to New Line Cinema. Adam Brody wanted to play the role of Lloyd Christmas.

Home media
Dumb and Dumberer: When Harry Met Lloyd was released on DVD and VHS on November 11, 2003 by New Line Home Entertainment.

Box office
In its opening weekend, the film grossed $10.8 million in 2,609 theaters in the United States and Canada, ranking in sixth place behind Finding Nemo, 2 Fast 2 Furious, Bruce Almighty, Rugrats Go Wild and Hollywood Homicide. By the end of its run, Dumb and Dumberer: When Harry Met Lloyd grossed $26.3 million domestically and $13 million internationally for a worldwide total of $39.3 million, against a $19 million budget.

Critical response
Dumb and Dumberer: When Harry Met Lloyd was panned by critics. Review aggregation website Rotten Tomatoes gives it a 10% rating based on reviews from 119 critics, with an average score of 2.8/10. The site's critical consensus states: "This lame prequel induces more groans than laughs. Rent the original instead". Metacritic gives the film a score of 19 out of 100, based on reviews from 28 critics, indicating "overwhelming dislike".

title: Dumb and Dumberer: When Harry Met Lloyd


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User talk:Michael Snow/Archive (Oct-Nov 2004)

A question on a logo
Michael, way back in February 2004, there was a graphic of the USFWS logo on Copyright problems. The consensus back then was that although not copyrighted (as a U.S. government graphic), it shouldn't be used in light of the statements at. I then found a public domain photo showing the badge with the logo on a USFWS officer's uniform, and we've used that image since then to avoid any problems. Now, somebody has again uploaded a graphics of the logo, claiming it was in the public domain. Since the only participants in the discussion back in February were Anthony DiPierro and myself, I'd appreciate it if you could give your opinion on the issue of such protected U.S. government service logos. (There may be more such protected logos. I remember having come across at least one other instance, but in that case, Wikipedia used a PD photo of a logo relief on some building. I only wish I could find that instance again!) Thanks, Lupo 07:25, 5 Oct 2004 (UTC)

 * Sorry to bother you so much, but I have two other questions on my mind that I haven't found an answer to, and since I don't know whom else I might ask them, I'll ask you:
 * Can "fair use" claims under U.S. law be made for non-U.S. items, such as images copied from, say, a French web server?
 * (Posted already on Wikipedia talk:Copyright problems, but ignored there) Can we use images under NATO copyright such as Image:B031007bc.jpg (from )? See NATO's copyright statement, especially at the bottom.
 * If you have the time, I'd appreciate knowing your view on these issues. Lupo 12:44, 5 Oct 2004 (UTC)

 * Actually, my comment at the time was that both images were essentially equal. Whether it's the logo itself or a photo of the logo on some guys shirt, the law still applies (though perhaps a slightly better case for fair use can be made depending on the presentation).  If I remember correctly, rather than reach consensus, I just left the discussion.  anthony 警告 12:19, 26 Oct 2004 (UTC)

Response
I've responded to your message on my talk page. anthony (see warning) 00:38, 6 Oct 2004 (UTC)

Request for Page protection
Please protect the following articles from anon vandalism. They have been reverted to the originals over a dozen times in the past 24 hours.

 * Protest Warrior History
 * East Germany History
 * Hugo Chávez History
 * Great Purge History
 * Human rights in Cuba History
 * Poland's betrayal by the Western Allies History
 * Chilean coup of 1973 History]
 * U.S. invasion of Afghanistan History
 * Consensus democracy History
 * Useful idiot History

I realize that this is 'ALOT to ask for, but of you go through the histories of these articles, you will see just how persisitent this vandal is and that abnning his IP will not stop him. I would also ask that if you do protect, that you protect the last non anon version. TDC 20:26, Oct 8, 2004 (UTC)

Thanks! TDC 21:04, Oct 8, 2004 (UTC)

 * Why is Chilean coup of 1973 protected in the state left by a lone anonymous individual rather than the state consistently defended by two experienced participants of quite different politics? (BTW, from what I can see, the person is not a vandal in the usual sense, just over-persistent in insisting on his/her versions of articles. On some pages, I think he/she has actually improved the article, but not on this one.) -- Jmabel 21:36, Oct 8, 2004 (UTC)

 * Thanks for fixing. This one is clear-cut. Heck, I think any time VeryVerily and I can agree on something politically charged, that's pretty clear-cut! -- Jmabel 22:03, Oct 8, 2004 (UTC)

I understand the concerns about protecting the "wrong version", but this is simple vandalism, not a content dispute, and so I don't believe this applies. Look at some of Turrican's (anonymous) reverts:. He reverts any edits by TDC and me (a fact overlooked by Fred Bauder when he singles out a "reasonable edit"). Refer if you haven't been keeping tabs on this situation to the arbitration request and his statements that he intends to revert all my edits and later that he is carrying out this threat. Just as I think it would be inapproriate to protect a page on the version that says "Bush is a monkey", I think the handful that are on the "wrong version" should be corrected (put aside the q of whether protection is needed at all - this is an attack on users not articles). Otherwise we send the message that vandalism will be rewarded. Well, let me know what you think. Very Verily 22:38, 8 Oct 2004 (UTC)

 * The edits are vandalism because of their intent not their content. Reverting housekeeping edits because of the editor counts, e.g., reverting the bypass of miscapitalized redirects (Poland) and the fixing of spelling ("assymetric" on consensus), which should be no-brainers.  Is there any possible alternative explanation for the anon reverts?  The fact that said person has been involved in other acts of vandalism such as my user page should remove remaining doubt.  It would really help if the ArbCom would get off their elbows and issue an injunction on Turrican, but a vandal is a vandal is a vandal.  If you examine the edit history (I'm not suggesting you do this, you could take my word for it), there really isn't reasonable doubt that they are all one and the same person.  (Also, some are id'able proxies.)   None of this has anything to do with issues as to whether it is acceptable to remove content.  It's about abusing Wikipedia to prosecute a vendetta, which should not be tolerated.  The approach of haggling on every petty revert is a good way to waste everyone's time (including yours, since TDC pulled you into this) and feed the trolls.

 * Well I'm busted; I don't actually know what with(out) prejudice means. It could be something like I could care less which is "technically" wrong but in common use.  Or not.  Oh well, I sometimes fail words. Very Verily  00:24, 9 Oct 2004 (UTC)

 * Maybe I do sound frustrated. It just seems to me that you do not perceive that there is no "dispute over capitalization", which is how you describe it; there is a vandal who is reverting all my edits, which is a very different situation (i.e., not a content dispute).  If someone did something like this to, say, RickK or Hephaestos, all of the IPs would have been immediately blocked and the pages reverted and protected.  This makes your take not seem like "persistent pursuit of impartiality".  Perhaps you wouldn't approve of the other approach, but is there really any doubt about this person's intent?  The IPs which actually vandalized my user page were (save one) not even blocked. Very Verily  23:20, 9 Oct 2004 (UTC)

 * Well, it is as I described. But whatever the trolls will be a little happy for a little bit.  Anyway, sorry you got dragged into this.  Somehow you keep winding up involved in issues relating to me. Very Verily  06:07, 10 Oct 2004 (UTC)

Tip of the day
I've noticed (by going over the history of that page) that you're recently in charge - inasmuch as you're the one doing it, which is all that matters - of adding new tips to Template:Tip of the day. I suppose you've got a list of your own, but I just thought I'd suggest Magic Button as a possible tip. -- Itai 23:53, 11 Oct 2004 (UTC)

My nomination for adminship
Thank you for supporting my nomination for adminship. I will do my best to serve Wikipedia. --Slowking Man 00:02, Oct 13, 2004 (UTC)

Library meetings
I'm sure you've got it watchlisted, but as an additional flag, I thought I'd note here that I've left you a comment at Wikipedia talk:Meetup/Seattle -- I think we do need to consider more seriously where we'll go from the cafe, given current numbers (which are excitingly high -- I had no idea we'd be planning for this many!). Jwrosenzweig 22:29, 13 Oct 2004 (UTC)

Admin nomination
Thanks for support my nominating for admin! - Ta bu shi da yu 02:36, 15 Oct 2004 (UTC)

External search engines
Hi Michael. I reverted your redirect at External search engines because the questions there are frequently asked on the Help desk and it is useful to point people to those previous answers and discussion. I had to use rollback since going to the revision as of 00:17, Sep 3, 2004 brought up an empty page claiming it was last edited in 1969! I've moved the page to the talk namespace to make it clearer what it is though. Angela. 19:56, Oct 22, 2004 (UTC)

Thank you for your interference. Arminius 00:40, 23 Oct 2004 (UTC)

Did you get my email, by any chance? Have you seen how broad the area of inquiry is for the case that the AC has accepted against me (the AC is allowing Sam Spade to cherry-pick anything out of ~15,000 edits and two years despite the lack of a basis of an ongoing conflict)? I know that we've had our differences, but I'm hoping that you will respond; given all the work that you've put into the AC process, I doubt that you'll want to see the system corrupted to this extent. 172 21:33, 23 Oct 2004 (UTC)

Thank you for responding. But I think that you are overlooking something important regarding this "revert parole." Regardless of its practical effect, you overlook the fact that it also strips an editor of his legitimacy. After the amount of time that I have contributed to this site-- for which I could've been paid for some of the very same work-- I will not suffer the humiliation of editing under these restrictions... Nor would I even be able to edit under these restrictions. I think that you know very well that Sam Spade, among others under no set of restrictions, would just go through my user history each day-- as Sam Spade already does-- and revert everything that I write. I'm not going to waste my time editing under these restrictions... Moreover, it's disgusting how the very same user spearheading this case is not sanctioned for provoking more unnecessary disruption than just about any other user. 172 00:14, 24 Oct 2004 (UTC)

I don't think being on revert parole has much affected Cantus' legitimacy as an editor, though he's gotten blocked a few times for violating the parole, which I trust you wouldn't do. You think that it is alright for me to be put in the same league as Cantus, compared to what he has contributed and compared to what I have contributed? Thank you for taking the time to respond, but the response is reaffirming my doubts about even wasting a minute of time working on this site to begin with... Or maybe Wiki was a better cause in the past... The people who used to write good articles hardly seem in control of the process any longer; lately this site seems to be under the control of an increasingly legalistic cabal interested more in process as opposed to product. 172 08:50, 24 Oct 2004 (UTC)

Thanks
Thank you very much for your vote for my adminship. I greatly appreciate your support. ffirehorse 23:46, 24 Oct 2004 (UTC)

Plebisite Project
I think you were a bit hasty with your deletion of Plebisite Project. User:Oldsoul listed it on VfU. Without discussing whether or not your deletion was proper, which I agree is disputable, can I request that you at least contact a user explaining your deletion when you do this sort of thing? After reviewing the situation this seems to have been made by a new user acting in good faith. anthony 警告 12:09, 26 Oct 2004 (UTC) Michael, I think you did exactly the right thing. It was a vanity page. I suggested to the OP that he might rewrite the entry when his project is more established and pointed him to the undeletion policy in the hope that he would feel it was not his contribution that was unwelcome as such.Dr Zen 12:18, 26 Oct 2004 (UTC)

Father nomination
Dear Michael: Hi! I just wanted to know why are you agains me nominating my father for administrationship? If he was someone who acted like he doesnt care about Wikipedia, Id be the first one to tell him so. On the other hand, I know he is very dedicated to this site, he spends about 6 or 7 hours each day researching, looking for informantion before he writes about his subjects, and then he also looks out for vandals and does other things to make sure the site remains respectable. Thats why I nominated him twice. Because I am witness that he spends most of his non-working or sleeping hours here every day.

I want you to know that I have the deepest respect towards you, as a great wikipedian that you are, part of the "hood". I just have that question..why can't I nominate my father?

Sincerely yours, "Antonio Spinning Machine Martin"

Dear Michael: Thanks for clarifying. Now I understand your view.

Thanks and God bless you!

Sincerely yours, "Antonio Degeneration M Martin"

User page unprotection
Hi Michael, out of curiosity - where did UninvitedCompany request that my userinfo page be unprotected? Thanks. ^^ -- Schnee 22:44, 29 Oct 2004 (UTC)

 * Requests for page protection. uc 00:41, 30 Oct 2004 (UTC)

Page Protections and Disputes
Howdy, Michael. Would it be possible to impose upon you to review the Protected Page situation with Winter Soldier Investigation? I've been involved in an edit war with TDC over this article. TDC managed to talk Uncle Ed into protecting the page, thus locking it into a POV version that is over a week old. Uncle Ed has suggested that I contact other Admins regarding this situation, as he will be gone for the weekend. Unfortunately, this is one of those politically charged articles that is of particular relevance during these next 4 days. I am requesting that the current protection be lifted so that the article may be returned to it's NPOV state, and additional accurate content added.

In support of my request, please note:

TDC has refused attempts to rationally discuss his edit issues, despite numerous requests on the Discussion pages and in Edit Summaries. See Talk:Winter Soldier Investigation TDC has threatened endless Revert Wars without citing his reasoning. See related article Talk:Vietnam Veterans Against the War See also Admin talk pages for Cecropia and Uncle Ed for the past 48 hours of history on this matter.

I apologize for the lack of a logged-in User ID at the moment. Any help you can provide would be appreciated. -Rob

 * If there's an ongoing edit war, as certainly seems to be the case, then it may well be that neither version is NPOV. Please discuss the issues on the talk page and come to a resolution. If it would help to have more people involved, you can try listing the article on requests for comment. Somebody is bound to complain that articles are protected on The Wrong Version. In this case, it looks like Vietnam Veterans Against the War is protected on your version, and Winter Soldier Investigation is protected on TDC's version, which seems pretty fair to me. --Michael Snow 04:22, 30 Oct 2004 (UTC)
 * There isn't an ongoing edit war -- it's a revert war, and therein lies the problem. TDC simply selects a version that is over a week old (and MANY edits old) and does a revert, without stating why -- other than claiming NPOV.  This results in more than a third of the content being deleted, including spelling corrections, formatting, links, etc.  When asked to discuss what he has issues with, he says "everything" and then clams up -- stating in his revert summaries that he refuses to discuss the matter.  Regarding the Winter Soldier Investigation specifically, he hasn't even entered the talk page, and my request for an explanation from him still remains there unanswered (since BEFORE the protection, no less).

 * You suggest that I discuss the issues on the talk page. Please tell me how long I should discuss the issues with myself before the protection can be lifted?  Cecropia suggested that I have an uninvolved Admin remove the protection after verifying that TDC is not discussing his reverts.  That is why I contacted you.  You are correct, by the way, in noting that the VVAW article is indeed protected in an acceptable format to me, but I fail to see how that fact makes the locking of the WSI article into a POV format without possibility of discussion somehow "fair." -Rob

 * It's "fair" because your POV temporarily prevails on one page, and his POV temporarily prevails on the other. Edit war and revert war effectively mean the same thing. Almost all of the discussion I see is with SEWilco, and this dispute apparently has only one very short post relating to it. In other words, hardly more effort on your part than TDC's. Since I realize one-sided discussion is difficult, that's why I suggested requests for comment. --Michael Snow 05:25, 30 Oct 2004 (UTC)

 * Michael, I beg to differ - on several of your comments. First, I don't see the VVAW page as "my POV."  Like most editors, I strive for an NPOV article, and until suspected POV issues are raised and verified, I must conclude it is presently NPOV.  Wholesale reverts with an edit summary that does nothing more than call the article "trash" not withstanding.  Scot (SEWilco) and I have been at these articles for months, and I dare say there is more of his original content in them than mine.  As I am sure you have noted, SEWilco and I are often of opposing viewpoints, sometimes heatedly so, yet we still beat the various issues to death until we arrive at a mutually acceptable NPOV.  TDC will not even raise an issue - he simply reverts.  Regarding this dispute, you see only a "very short" post relating to it?  You do not see several paragraphs on the Talk pages of other Admins?  You do not see TDC's stated refusal to discuss issues on the VVAW discussion page, or in the Edit Summaries of his dozens of reverts?  I am petitioning you at the urging of Cecropia and Uncle Ed, because they said an uninvolved Admin could remove the protection if it can be verified that TDC is not participating in discussions.  By the tone of your recent comment, it appears you have indeed verified TDC's refusal to participate.  RfC is an avenue that I will inevitably persue regardless, but this particular request is about a Page Protection.  -Rob

 * I saw the talk pages you referred me to, but it's mostly about the question of protection again, rather than anybody discussing issues with the content of the page (and the proper place to discuss that is the article's talk page anyway). And I can't make judgments on protecting/unprotecting based on which version I prefer or believe is more NPOV. If I unprotect right now, my best guess is that the revert war will simply restart. So I'm not inclined to do it. --Michael Snow 06:22, 30 Oct 2004 (UTC)
 * I'm not asking you to evaluate the NPOV of the article, although you are more than welcome to dive in (and the RfC formally exists now, by the way). The request was (as prompted by 2 other Admins) that you evaluate TDCs "good faith intentions" to follow Wiki protocol and enter into discussions to support his reverts.  I assert TDC has no intention of entering into rational discussions, and I've pointed out ample proof of that - not the least of which is his very POV quote: "I am not going to argue this with an Anon user who is trying to stuff this garbage into an article."  Meanwhile, TDCs intent of keeping the page locked in a POV format during the very critical remaining 4 days of the U.S. political campaigns is being carried out. -Rob

 * Evaluating good faith is a very tricky thing, especially when people have established a strong mutual hostility. I prefer to assume it as much as possible, and you certainly haven't disproven it. You've reminded me that he is predisposed to think of you as inferior and a likely vandal because you edit without a username, which I already knew about, and is an attitude I consider entirely inappropriate. Still, it hardly follows that he does not in good faith believe that his edits are improving the content of the article. Only time can show whether protection and RfC will promote constructive discussion toward a consensus, neutral form of the article.
 * And with respect to the question of time, even though this is the internet it's unreasonable to expect to achieve any particular result instantly, and I don't think this is more urgent than any other dispute. The next four days may be critical for many political candidates, but this article is not critical to their campaigns. Elections may hang on small things sometimes, but to believe that they will hang on the state of a minor Wikipedia article (with two prominent warnings that the content is disputable) that will reach relatively few eyeballs and change even fewer minds, is beyond my credulity. --Michael Snow 07:04, 30 Oct 2004 (UTC)

 * I am not sure I follow your logic regarding a "strong mutual hostility." I believe you are assuming that TDC and I can not or do not communicate.  That is a false premise, as evidenced by our discussions elsewhere. Here for example, and you'll also note that such discussions have taken place during and AFTER the most recent page protection disputes.  Ability to discuss is certainly not the problem, nor is mutual hostility.  The problem is getting him to discuss any of his reverts on the two currently protected pages (VVAW and WSI).  This he simply will not do, and he has stated as much.  Granted, he has misleadingly posed as willing to enter discussions, when it served his purpose in requesting a Page Protection (see Uncle Ed's talk page) - but posing is all it was.  In two days worth of polite requests to discuss with me the issues he alleges are POV, the closest thing I get to a response is: Gee, I dont know, everything. TDC 20:02, Oct 29, 2004 (UTC) -- and not a word more, regarding those 2 articles anyway.  What exactly does it take to "disprove" good faith?
 * As for the question of time, candidates and the importance of Wiki articles - I must again disagree with your assessment. During the past week when Sinclair's intent to broadcast anti-Kerry material on their TV stations was all over the news, no fewer than 34 blogs cited one or both of those presently protected wiki articles.  I would imagine much of the hoopla has since died down, but certainly not all of it.  As for number of eyeballs viewing, and numbers of minds changing, I'd wager the importance of these numbers this particular year is greater than either of us might guess. Or... I could be totally wrong.  Regardless, the fact remains that an article is locked in POV form, and the requestor has not entered discussions as to why. -Rob

Hi. Like I told Mr Company several months ago when he unprotected my user page, he is incorrect both in his interpretation of the wikipedia guidelines and in his assertion that my page has never been vandalised. It has, twice, by Faedra, and I choose that it remain protected. Deb 16:51, 30 Oct 2004 (UTC)

 * Salve, Michael Snow! Read your message re my comment on Wikipedia talk:Page protection. First, I will state I have not gone over the manual on the proper criteria for restricting pages, I only have looked at the arguments on the aforementioned page.  That said, I understand the difficulty you cite of restricting pages when the user is not himself an admin, which is why I support the suggestion by User:Improv to alter the program so nobody but the creator can edit a user page.  I think that a worthy change that should be investigated.  Ave!  PedanticallySpeaking 20:04, Nov 2, 2004 (UTC)

A Question on Deleting Keith Anthonisz
I noticed that you were involved in deleting my article on myself (Keith Anthonisz) and my involvement in Australian music as an Australian musician. Given that on the talk page, I noted that the content was mine and that the content had been used with my permission on other web pages, can you explain to me why I was deleted?

Images by Cheung1303
Hi, I noticed that you (and multiple other admins) have complained on User:Cheung1303's talk page about his uploading of images without sources. He is, unfortunately, still doing it (most recently for an the image at .) —Steven G. Johnson 21:02, Nov 4, 2004 (UTC)

 * Something very much needs to be done about this user. He is now adding copyright tags seemingly at random to the images he uploads . Is it time for a request for comment from the wider community? - SimonP 02:01, Nov 5, 2004 (UTC)

What to do?
Hello. I noticed you've taken care of an item on Copyright problems recently so I'm hoping you can guide me through what I need to do. Saint Vasilije (listed on 05 AUG) is a bit of a mess. The article had the copyvio tag added to the text instead of replacing the text. The copyvio version has had edits since, but a good non-copyvio stub exists on the temp page as well. I would be willing to merge the modifications into the temp version, as they are good changes, but that would destroy the authorship history when the main (copyvio) page is deleted. What should one do in this case? Thank you. SWAdair | Talk 05:59, 5 Nov 2004 (UTC)

Question About Deletion
Salve, Michael Snow! While checking the page of what links to Dawson's Creek--a page I patrol--I found this: Colour Moving and Still. It's a nice page and all, well done, but are we going to create a page for every album ever? I was reading a discussion about creating pages for episodes of television series--where I don't recall, otherwise I'd link it here--and the point was correctly made that our servers would runneth over if we followed such a policy. (Dawson's Creek alone has 128 episodes, Buffy the Vampire Slayer 144, Gunsmoke over 600. I looked through the deletion criteria and didn't see anything truly applicable to this album article.  Rather than list it as a candidate for deletion myself, I thought I'd ask someone with more (I hope) experience in these matters.  Is this a candidate for deletion?  Ave!  PedanticallySpeaking 19:20, Nov 5, 2004 (UTC)

Adminship
Hi, Michael, I saw your question about adminship for me on Geogre's page, I just wanted to thank you for bringing it up. As Geogre told you, I don't really want to be an admin, for several reasons, but I love having it suggested! It's a great compliment, and it's only happened once before, not three times as Geogre thought, so I'm anything but blasée about it. Your question made me feel like a million bucks, thanks very much.--[[User:Bishonen|Bishonen (talk)]] 15:39, 6 Nov 2004 (UTC)

Meetup
Michael--Great to meet you today. It was a pleasure to see all you. I appreciated your comments about licensing. They were very insightful. I put some pictures up at Meetup/Seattle, including one of you. P.S. Quiz was fantastic. -- Matt Decumanus 09:06, 2004 Nov 7 (UTC)
 * I second Matt's comments -- it was very good to meet everyone in person. I feel I know my friends a little better, and some people I've never interacted with before will now be sought out by me as intelligent and reasonable voices.  Maybe there's more sanity here than I am able to see in my more despairing moments. :-)  Thanks for doing the work of getting us all together -- it was a real success.  I look forward to seeing you and chatting with you again in the near future.  Best wishes, James R. 20:49, 7 Nov 2004 (UTC)

Dore Gold
The current edit war being waged by Blankfaze and Alberuni is in violation of at least five policies, including NPOV, Wikipedia is not a soapbox, Stay_on_topic, Guidelines for controversial articles, and Three revert rule. The dispute in question has been resolved by Mustafaa, Jayjg, Josiah, and myself. The four of us are in agreement about a specific quote being used on the page. Unfortunately, Alberuni and Blankfaze continue to revert this quote, against our best wishes. Blankfaze won't even participate in the discussion on the Talk page. Both Alberuni and Blankfaze insist that the page is about Israel, but we have repeatedly and patiently reminded them that the page is about Dore Gold. We have also repeatedly explained to them the reasons for our decision, but they continue to revert the version agreed upon by the four of us. Why have you protected a version of the page that is not agreed upon by the majority of editors on Talk:Dore Gold? I couldn't help notice that you protected the page approximately four minutes after Blankfaze reverted the article, contrary to the consensus of the editors on the Talk page. --Viriditas 12:52, 7 Nov 2004 (UTC)
 * Well, first of all, I don't think any sort of "consensus" has been reached. Secondly, I have attempted to participate in discussions but have become frustrated with the blatant POV-pushing going on, especially concerning User:Jayjg.  It's hard to debate with people who are hell-bent on installing certain points-of-view.  Regardless, however, I have surrendered and precluded myself from further involvemnt in the edit war; so, Michael, feel free to revert to their supposed "consensus" version. BLANKFAZE | (что??) 21:59, 7 Nov 2004 (UTC)
 * I don't think it's fair to use Mr. Snow's Talk page to discuss this topic (bring your comments to the article's talk page and link here) but I will briefly reply to your comment. A rough consensus has been reached.  You have not actively participated in the discussion, instead you have logrolled for Alberuni, a  POV-pusher of the highest order (see his edit history, including the POV article titles he has created) who happens to be pushing an anti-Israel POV on a page that has nothing to do with Israel.  It's ironic that you should accuse others of your own misdeeds in this matter, but I said I would be brief, so I will leave this rest of this discussion (which I encourage you to continue since you have shown an interest in this subject) to the Talk:Dore Gold page.  You may be surprised to learn that your opinion of myself and Jayjg are entirely without merit.  We are both willing to work with multiple POV's, and in fact, we actively encourage it, as our edit histories demonstrate.  Again, I am asking you to join the discussion and explain your position when you have time.  Thank you. --Viriditas 04:01, 8 Nov 2004 (UTC)
 * I agree with Viriditas--Josiah 02:37, 8 Nov 2004 (UTC)
 * I fully agree with Viriditas. IZAK 06:25, 9 Nov 2004 (UTC)

Quizz
I had a good laugh when I learned I was part of the quizz :-) Hope you all had a good day :-) SweetLittleFluffyThing

Yeah ?

Okay, my guess was ... say 45. The picture makes you look like... say 30. Which is nearer ? :-) SweetLittleFluffyThing

Nearer 30... funny. Well, perhaps I felt you more mature than 30... or perhaps than now that I am well over 30, I can only see 30 as a very tender age ? Who knows ? Well, at least, your virtual self fit with the actual self (figure, hair color...). Not so bad :-)

Scars
My scars were twitching tonight. Really. Especially the big one across my forehead that allows me to win bar fights by default just by combing my hair. I don't know what exactly makes them twitch. Must be the weather, or maybe just too much sun. They say scars are like tattoos, only with better stories. I have no tattoos, so I would not know. In any case, this has nothing to do with protection of user pages. At least, I don't think it does. I will re-run that query one of these days. 02:23, 8 Nov 2004 (UTC)

Atheism
I noticed you unprotected this page. I think that was a bit pre-mature, please have a look at the talk page. Sam [Spade] 21:11, 8 Nov 2004 (UTC)

When you protected this page again, what was your plan for getting it unprotected again? Who is it protected from? When are you planning to unprotect it? BM 18:40, 2 Dec 2004 (UTC)

Arbitration
Copy from my talk:

Many thanks for your contribution to the evidence on Gzornenplatz. Does it remind you of anyone in particular? --Michael Snow 18:00, 9 Nov 2004 (UTC)
 * I see I'm not the only one. Some notes are available at User:Mirv/gzp if you've seen anything worth adding to them. —No-One Jones (m) 18:58, 9 Nov 2004 (UTC)

Undeletion of American World University
Would you mind looking at this undeletion entry? The consensus currently seems to be 2:1 in favor of undeltion, but I am worried that the admis who are currently involved are unwilling to take action in this matter due to the fact that this has become entangeld with their personal conflict with anthony. (Evidence of this is here.) Thanks for your assistance. --L33tminion | (talk) 00:20, Nov 12, 2004 (UTC)

If you want to add to Votes for deletion/American World University, please do so, but don't delete the historical archive. RickK 00:58, Nov 12, 2004 (UTC)

Thanks for the heads up. I saw that yesterday, I don't have a problem with it since it's a rewrite, I just don't like Anthony's attitude. RickK 20:32, Nov 12, 2004 (UTC)

ArbCom FYI
Your user name was mentioned in the arbitration case against Gzornenplatz, Kevin Baas, Shorne, and VeryVerily, so I'm informing you of the below temporary order against the users named in this arbitration.

1) Gzornenplatz and VeryVerily are banned from editing any article having to do with German or Polish subjects whilst Arbitration is on-going. Sysops may use their discretion in determining what falls into these areas, and are hereby authorised to enact 24 hour blocks for violations of this.

2) Gzornenplatz, Kevin Baas, Shorne, and VeryVerily are banned from reverting any article more than twice in one 24 hour period whilst Arbitration is on-going. Sysops are hereby authorised to enact 24 blocks for violations of this.

See Requests for arbitration/Gzornenplatz, Kevin Baas, Shorne, VeryVerily. --mav 12:00, 15 Nov 2004 (UTC)

Hope you're happy. Very Verily 12:56, 15 Nov 2004 (UTC)

Jeremiah Duggan page
Michael, thank you for your edit of the Jeremiah Duggan page, where I had Princess Diana allegedly being killed by M16. :-) Slim user:SlimVirgin 06:27, 16 Nov 2004

Arbitration / Mediation
Aside from the fact that I'm not terribly upset about the whole situation anymore, I don't share mav's opinion that it was your job to tell me. My question on RfA was clearly directed at the ArbCom who's job it was to let me know if the mediation was trumped by any arbitration matter. Furthermore, it would have been the ArbCom's job (as I interpret it) to explore whether the proper path of dispute resolution had occurred. This exploration would have (with at least a modicum of thoroughness) uncovered the mediation I was proctoring. Again, not your fault. I didn't expect you to do anything, I expected the ArbCom to a) answer my question and b) notify me of the arbitration and solicit my input. In any event, it's all, as they say, "water under the bridge". Let me know if you need anything from my end in the current matter and I'll assist as best I can given my role. --Dante Alighieri | Talk 08:18, Nov 17, 2004 (UTC)

Jean-Jacques Goldman
I created this page, but when I search for it, it can't be found. Ksnow 15:26, 17 Nov 2004 (UTC)ksnow

I made a redirect from "Goldman", but that is currently the only way I can access it, other than typing in the URL or accessing it from a link in a category.

Thanks for the note, Michael, it's appreciated. I was probably in a rather touchy mood at the time I wrote my response and might have overreacted a bit. You are right, of course, that something needs to change with the arbitration committee: either its structure or duties need to be changed to reduce the load on individual arbitrators, or it needs to be stuffed with people who are prepared to commit buckets of time to it (practically speaking, I think the first is rather more likely). --Camembert

FYI: New temporary ArbCom order
New temporary order:

3) Shorne and VeryVerily are banned from editing any article having to do with the Cold War or communism whilst Arbitration is on-going. Sysops may use their discretion in determining what falls into these areas, and are hereby authorized to enact 24 hour blocks for violations of this.

--mav 20:48, 17 Nov 2004 (UTC)

Goldman
Nope, it still doesn't work, just through the redirect under Goldman or from links. The lookup seem s to be looking for jean+jacques+goldman, instead of jean-jacques_goldman.

Eequor
I may have been too harsh in my comments to you, though I stand by the sentiment. I got upset over the beating she was receiving for what struck me as little more than care-free quirkiness. To her further credit, she handled it all with remarkable good grace. Anyway, the whole TINC thing is stupid. There is neither clearly a cabal nor clearly not one; rather, there is a complex social hierarchy which, like most, has a handful who dominate. Perhaps your sense of your own position in it is what caused you to lash out, although that's mere speculation. Very Verily 00:22, 19 Nov 2004 (UTC)

endorsements
Since you're moving these, and I don't want to trip you up with an edit conflict, please send mine to User:Mirv/Arbitration election, where I originally placed them. —No-One Jones (m) 08:12, 19 Nov 2004 (UTC)

Thanks. —No-One Jones (m) 09:04, 19 Nov 2004 (UTC)

Michael, I don't appreciate your unilateral decision to bury my endorsements and opposition on an obscure subpage under my user page, where no one will ever read them, especially before asking me if it was OK. What is your motivation for wanting to hide my comments about the candidates?

If this election is to be free and fair, then in the "public square" that the candidate discussion page represents, everyone should be allowed to make their opinions known. Please restore my comments to the public discussion page where potential voters can read them without having to click on dozens of links before a potential voter can see what I have to say. Thank you. --DV 00:02, 20 Nov 2004 (UTC)

Follow up
Your comment about only requiring a click on one link is dishonest, and I think you are smart enough to know that. Potential voters will have to click on dozens of links above mine, or below mine, (depending on the order they are going through the other user's endorsements) before they get to mine. Most users will become impatient and stop clicking long before they get to my endorsements. Hence why I posted on the central discussion in the first place - so my comments would be read!.

Excerpts from other pages get read much more frequently than links. (Many popular news sites and blogs illustrate this every day, by excerpting what they link to in order to entice the reader to bother clicking on the link.)

Also, I made endorsements of Neutrality and blankfaze, and they do not appear on the candidate subpages where you moved other user's endorsements/opposition. Since you weren't super careful about moving this material around without losing some of it, those two candidates lost some endorsements that they would otherwise have.

Your "consensus" on redistributing comments on a single page into many subpages seems weak. And who appointed you the "boss" of the candidate endorsements discussion page in the first place? Your statements that you will continue your actions despite the wishes of others doesn't seem very wiki-like. --DV 00:18, 20 Nov 2004 (UTC)

 * Michael, I have taken your creative suggestion, and "piped" my endorsements into my link. I disagree with your assessment of linking vs. a central page (for the reasons I gave above), but if this is as far as you are willing to compromise, so be it. --DV 00:40, 20 Nov 2004 (UTC)

 * Hmm. How does consensus work if other users run around doing whatever they like? User VeryVerily unilaterally reverted my change to my link text on sight, without a word on the talk page. I asked him to take up his objections on the talk page if he disagrees with my use of your "piping" suggestion.

 * If VeryVerily persists in removing my contributions without discusssion, please consider blocking him, as I refuse to participate in a revert-war.

 * I have compromised and chosen to participate according to your suggestions, so isn't it unfair that VeryVerily, who is standing as a candidate in this election, can run roughshod over me?

 * As a voter offering endorsements and opposition, it is only fair for me to be able to offer my opinions in close proximity to the self-endorsements of the candidates themselves. If my endorsements and opposition are artifically kept out of sight and out of mind for the vast majority of the electorate, then I might as well have never offered them at all.

 * In any case, I appreciate your attempts to work out a compromise from your own initial position. --DV 06:01, 20 Nov 2004 (UTC)

Stylebook Proposal
Salve, Michael Snow! Where should a proposal to amend the stylebook go? I would like to clarify the policy about spelling out numbers that is at Manual_of_Style_%28dates_and_numbers%29 and wonder if there's someplace other than the talk page for this sort of thing. Ave atque vale! PedanticallySpeaking 16:07, Nov 19, 2004 (UTC)

My adminship request
Thanks for the support and the kind words. --jpgordon{gab} 04:17, 20 Nov 2004 (UTC)

I can't not be amused by your little "run-in" with Shorne and Wik Gzornenplatz on Vandalism in progress. A tiny taste of what I've been up against? Very Verily 04:48, 20 Nov 2004 (UTC)

Lobbying vs Spamming
Is there a policy on Wikipedia concerning how strong the pre-existing affiliation must be in order for lobbying not to qualify as "spamming"?

Obviously, I would likely be called out if I set a 'bot lose, posting messages on the user talk pages of everyone who contributed to Wikipedia within the past 30 days, asking them to vote on this survey.

On the other hand, how about if I lobby everyone I have worked on an article with since I started contributing as an editor?

How strong does the pre-existing affiliation need to be before lobbying crosses the threshold into spamming? I looked in the policy pages and had little luck finding any guidance on this issue. I believe that a policy must be quickly agreed upon, if there isn't one already, for effective, but not overly disruptive, lobbying to be allowed on Wikipedia during campaign cycles.

Your thoughts? --DV 07:11, 20 Nov 2004 (UTC)

 * This same question applies to the general election as well. How strong does the pre-existing affiliation with a potential voter have to be, to insure that the administration of Wikipedia will not consider such lobbying as spam? --DV 09:15, 20 Nov 2004 (UTC)

 * As I am looking for guidance from any user who cares to comment, I have posted a more generalized version of this question on the Endorsements talk page, and on the Election talk page. If you choose to reply, please do so on one of those pages. Thanks. --DV 09:52, 20 Nov 2004 (UTC)

Arbcom proposed decision
Well, do you like what you see? Very Verily 09:07, 20 Nov 2004 (UTC)

endorsement page
Hi Michael, I read your message, read the page and the discussion and talked to danny about it - we decided that we want to talk to uninvited company first to find a solution for this problem. I'm currently in frankfurt organizing wikimania. when I'll be back home sunday evening, I'll look at it with more time at hands. --Elian 23:53, 20 Nov 2004 (UTC)

Subpages and endorsements
Just a note: I would have preferred for you not to have moved things to one of my user subpages without you having told me or discussing this on the relevant arbcom endorsement talk page. Never mind (I'll be moving the content to my talk page, if that's ok.) Thanks Dysprosia 04:24, 22 Nov 2004 (UTC)
 * I'm sorry, I must have missed it somehow. Dysprosia 04:28, 22 Nov 2004 (UTC)

Proposal for change in style policy
I would like to propose a change in style policy. As a professional editor/tech writer, my exprience has been that generally other character styles (especially italics) are not applied when the word is a link. I would like to see this adopted by Wikipedia as their style.

Voting should be a civic duty of all Wikipedians
It's not that big of an obligation in return for all the benefits this site provides. But please hear me out, as I reply to your comments. --DV 03:08, 23 Nov 2004 (UTC)

 * Not that voting should be mandatory.

 * But voting should be thought of as a duty of any good Wikipedia citizen, and those who don't vote should have received at least one message about an election - enough to feel that they are missing out on something that is good and right if they don't vote. --DV 03:11, 23 Nov 2004 (UTC)

Your opinion please
What do you think I should do about this Should i revert or leave the page as it is? Theresa Knott (Tart, knees hot) 00:12, 24 Nov 2004 (UTC)

RfC comments
Thanks for moving my comments. Will use the appropriate pages henceforth. (darned learning curves...) - Amgine

Election Dates
I will correct the image this evening. I'm at the office right now so I don't have access to the source file. Cheers, --DV 03:51, 24 Nov 2004 (UTC)

 * I just uploaded a new version with the corrected dates. After the upload, I noticed that I had to purge the page in my cache and then refresh to get the new image to appear. --DV 06:01, 24 Nov 2004 (UTC)

A quick note to say thanks

I just wanted to drop you a quick note to thank you for your support in my request for adminship. It was certainly a wild ride, and I really appreciate you taking some time out to contribute. ClockworkSoul 16:31, 24 Nov 2004 (UTC)

how do I...
How does Alphabetical index get built/maintained? I'd like to do the same on my personal wiki, and haven't figured it out. - Amgine 20:42, 25 Nov 2004 (UTC)

 * Thanks for the information; 'bout what I figured, but not what I was hoping for . - Amgine

Inserting pictures
Lew has given me permisson to lift anything I want from his website. How do I insert a picture in his article? Ksnow 11:44, 26 Nov 2004 (UTC)ksnow

I have uploaded the JPEG, and it shows up in the image list, but not on the page. Ksnow 12:16, 26 Nov 2004 (UTC)ksnow

Merci mille fois! Ksnow 19:16, 26 Nov 2004 (UTC)ksnow

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


text:
Wikipedia:Articles for deletion/Binary Cell

Binary Cell
A fresh invention; looks like non-notable kookery. Mikkalai 03:39, 3 Dec 2004 (UTC)
 * Delete vanity, original research. Gazpacho 09:17, 3 Dec 2004 (UTC)
 * Delete. Original Research. utcursch 12:06, Dec 3, 2004 (UTC)
 * Delete self advertising Mozzerati 19:19, 2004 Dec 4 (UTC)
 * Delete. Original research, as indicated by the line "These rough drafts were sent to the Ministry of Science and Technology of Spain in the 2002." [[User:Dpbsmith|Dpbsmith (talk)]] 23:46, 4 Dec 2004 (UTC)


text:
Bellman equation

A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices. This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes. The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used.

The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory; though the basic concepts of dynamic programming are prefigured in John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior and Abraham Wald's sequential analysis. The term 'Bellman equation' usually refers to the dynamic programming equation (DPE) associated with discrete-time optimization problems. In continuous-time optimization problems, the analogous equation is a partial differential equation that is called the Hamilton–Jacobi–Bellman equation.

In discrete time any multi-stage optimization problem can be solved by analyzing the appropriate Bellman equation. The appropriate Bellman equation can be found by introducing new state variables (state augmentation). However, the resulting augmented-state multi-stage optimization problem has a higher dimensional state space than the original multi-stage optimization problem - an issue that can potentially render the augmented problem intractable due to the “curse of dimensionality”. Alternatively, it has been shown that if the cost function of the multi-stage optimization problem satisfies a "backward separable" structure, then the appropriate Bellman equation can be found without state augmentation.

Analytical concepts in dynamic programming
To understand the Bellman equation, several underlying concepts must be understood. First, any optimization problem has some objective: minimizing travel time, minimizing cost, maximizing profits, maximizing utility, etc. The mathematical function that describes this objective is called the objective function.

Dynamic programming breaks a multi-period planning problem into simpler steps at different points in time. Therefore, it requires keeping track of how the decision situation is evolving over time. The information about the current situation that is needed to make a correct decision is called the "state". For example, to decide how much to consume and spend at each point in time, people would need to know (among other things) their initial wealth. Therefore, wealth $$(W)$$ would be one of their state variables, but there would probably be others.

The variables chosen at any given point in time are often called the control variables. For instance, given their current wealth, people might decide how much to consume now. Choosing the control variables now may be equivalent to choosing the next state; more generally, the next state is affected by other factors in addition to the current control. For example, in the simplest case, today's wealth (the state) and consumption (the control) might exactly determine tomorrow's wealth (the new state), though typically other factors will affect tomorrow's wealth too.

The dynamic programming approach describes the optimal plan by finding a rule that tells what the controls should be, given any possible value of the state. For example, if consumption (c) depends only on wealth (W), we would seek a rule $$c(W)$$ that gives consumption as a function of wealth. Such a rule, determining the controls as a function of the states, is called a policy function.

Finally, by definition, the optimal decision rule is the one that achieves the best possible value of the objective. For example, if someone chooses consumption, given wealth, in order to maximize happiness (assuming happiness H can be represented by a mathematical function, such as a utility function and is something defined by wealth), then each level of wealth will be associated with some highest possible level of happiness, $$H(W)$$. The best possible value of the objective, written as a function of the state, is called the value function.

Bellman showed that a dynamic optimization problem in discrete time can be stated in a recursive, step-by-step form known as backward induction by writing down the relationship between the value function in one period and the value function in the next period. The relationship between these two value functions is called the "Bellman equation". In this approach, the optimal policy in the last time period is specified in advance as a function of the state variable's value at that time, and the resulting optimal value of the objective function is thus expressed in terms of that value of the state variable. Next, the next-to-last period's optimization involves maximizing the sum of that period's period-specific objective function and the optimal value of the future objective function, giving that period's optimal policy contingent upon the value of the state variable as of the next-to-last period decision. This logic continues recursively back in time, until the first period decision rule is derived, as a function of the initial state variable value, by optimizing the sum of the first-period-specific objective function and the value of the second period's value function, which gives the value for all the future periods. Thus, each period's decision is made by explicitly acknowledging that all future decisions will be optimally made.

A dynamic decision problem
Let $$x_t$$ be the state at time $$t$$. For a decision that begins at time 0, we take as given the initial state $$x_0$$. At any time, the set of possible actions depends on the current state; we express this as $$ a_{t} \in \Gamma (x_t)$$, where a particular action $$a_t$$ represents particular values for one or more control variables, and $$\Gamma (x_t)$$ is the set of actions available to be taken at state $$x_t$$. We also assume that the state changes from $$x$$ to a new state $$T(x,a)$$ when action $$a$$ is taken, and that the current payoff from taking action $$a$$ in state $$x$$ is $$F(x,a)$$. Finally, we assume impatience, represented by a discount factor $$0<\beta<1$$.

Under these assumptions, an infinite-horizon decision problem takes the following form:

 * $$ V(x_0) \; = \; \max_{ \left \{ a_{t} \right \}_{t=0}^{\infty} } \sum_{t=0}^{\infty} \beta^t F(x_t,a_{t}), $$

subject to the constraints

 * $$ a_{t} \in \Gamma (x_t), \; x_{t+1}=T(x_t,a_t), \; \forall t = 0, 1, 2, \dots $$

Notice that we have defined notation $$V(x_0)$$ to denote the optimal value that can be obtained by maximizing this objective function subject to the assumed constraints. This function is the value function. It is a function of the initial state variable $$x_0$$, since the best value obtainable depends on the initial situation.

Bellman's principle of optimality
The dynamic programming method breaks this decision problem into smaller subproblems. Bellman's principle of optimality describes how to do this:"Principle of Optimality: An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision. (See Bellman, 1957, Chap. III.3.)" In computer science, a problem that can be broken apart like this is said to have optimal substructure. In the context of dynamic game theory, this principle is analogous to the concept of subgame perfect equilibrium, although what constitutes an optimal policy in this case is conditioned on the decision-maker's opponents choosing similarly optimal policies from their points of view.

As suggested by the principle of optimality, we will consider the first decision separately, setting aside all future decisions (we will start afresh from time 1 with the new state $$x_1 $$). Collecting the future decisions in brackets on the right, the above infinite-horizon decision problem is equivalent to:

 * $$ \max_{ a_0 } \left \{ F(x_0,a_0)

+ \beta \left[ \max_{ \left \{ a_{t} \right \}_{t=1}^{\infty} } \sum_{t=1}^{\infty} \beta^{t-1} F(x_t,a_{t}): a_{t} \in \Gamma (x_t), \; x_{t+1}=T(x_t,a_t), \; \forall t \geq 1 \right] \right \}$$

subject to the constraints

 * $$ a_0 \in \Gamma (x_0), \; x_1=T(x_0,a_0). $$

Here we are choosing $$a_0$$, knowing that our choice will cause the time 1 state to be $$x_1=T(x_0,a_0)$$. That new state will then affect the decision problem from time 1 on. The whole future decision problem appears inside the square brackets on the right.

The Bellman equation
So far it seems we have only made the problem uglier by separating today's decision from future decisions. But we can simplify by noticing that what is inside the square brackets on the right is the value of the time 1 decision problem, starting from state $$x_1=T(x_0,a_0)$$.

Therefore, we can rewrite the problem as a recursive definition of the value function:

 * $$V(x_0) = \max_{ a_0 } \{ F(x_0,a_0) + \beta V(x_1) \} $$, subject to the constraints: $$ a_0 \in \Gamma (x_0), \; x_1=T(x_0,a_0). $$

This is the Bellman equation. It can be simplified even further if we drop time subscripts and plug in the value of the next state:

 * $$V(x) = \max_{a \in \Gamma (x) } \{ F(x,a) + \beta V(T(x,a)) \}.$$

The Bellman equation is classified as a functional equation, because solving it means finding the unknown function $$V$$, which is the value function. Recall that the value function describes the best possible value of the objective, as a function of the state $$x$$. By calculating the value function, we will also find the function $$a(x)$$ that describes the optimal action as a function of the state; this is called the policy function.

In a stochastic problem
In the deterministic setting, other techniques besides dynamic programming can be used to tackle the above optimal control problem. However, the Bellman Equation is often the most convenient method of solving stochastic optimal control problems.

For a specific example from economics, consider an infinitely-lived consumer with initial wealth endowment $${\color{Red}a_0}$$ at period $$0$$. They have an instantaneous utility function $$u(c)$$ where $$c$$ denotes consumption and discounts the next period utility at a rate of $$0< \beta<1 $$. Assume that what is not consumed in period $$t$$ carries over to the next period with interest rate $$r$$. Then the consumer's utility maximization problem is to choose a consumption plan $$\{{\color{OliveGreen}c_t}\}$$ that solves

 * $$\max \sum_{t=0} ^{\infty} \beta^t u ({\color{OliveGreen}c_t})$$

subject to

 * $${\color{Red}a_{t+1}} = (1 + r) ({\color{Red}a_t} - {\color{OliveGreen}c_t}), \; {\color{OliveGreen}c_t} \geq 0,$$

and

 * $$\lim_{t \rightarrow \infty} {\color{Red}a_t} \geq 0.$$

The first constraint is the capital accumulation/law of motion specified by the problem, while the second constraint is a transversality condition that the consumer does not carry debt at the end of their life. The Bellman equation is

 * $$V(a) = \max_{ 0 \leq c \leq a } \{ u(c) + \beta V((1+r) (a - c)) \},$$

Alternatively, one can treat the sequence problem directly using, for example, the Hamiltonian equations.

Now, if the interest rate varies from period to period, the consumer is faced with a stochastic optimization problem. Let the interest r follow a Markov process with probability transition function $$Q(r, d\mu_r)$$ where $$d\mu_r$$ denotes the probability measure governing the distribution of interest rate next period if current interest rate is $$r$$. In this model the consumer decides their current period consumption after the current period interest rate is announced.

Rather than simply choosing a single sequence $$\{{\color{OliveGreen}c_t}\}$$, the consumer now must choose a sequence $$\{{\color{OliveGreen}c_t}\}$$ for each possible realization of a $$\{r_t\}$$ in such a way that their lifetime expected utility is maximized:

 * $$\max_{ \left \{ c_{t} \right \}_{t=0}^{\infty} } \mathbb{E}\bigg( \sum_{t=0} ^{\infty} \beta^t u ({\color{OliveGreen}c_t})  \bigg).$$

The expectation $$\mathbb{E}$$ is taken with respect to the appropriate probability measure given by Q on the sequences of r's. Because r is governed by a Markov process, dynamic programming simplifies the problem significantly. Then the Bellman equation is simply:

 * $$V(a, r) = \max_{ 0 \leq c \leq a } \{ u(c) + \beta \int V((1+r) (a - c), r') Q(r, d\mu_r) \} .$$

Under some reasonable assumption, the resulting optimal policy function g(a,r) is measurable.

For a general stochastic sequential optimization problem with Markovian shocks and where the agent is faced with their decision ex-post, the Bellman equation takes a very similar form

 * $$V(x, z) = \max_{c \in \Gamma(x,z)} \{F(x, c, z) + \beta \int V( T(x,c), z') d\mu_z(z')\}. $$

Solution methods

 * The method of undetermined coefficients, also known as 'guess and verify', can be used to solve some infinite-horizon, autonomous Bellman equations.
 * The Bellman equation can be solved by backwards induction, either analytically in a few special cases, or numerically on a computer. Numerical backwards induction is applicable to a wide variety of problems, but may be infeasible when there are many state variables, due to the curse of dimensionality. Approximate dynamic programming has been introduced by D. P. Bertsekas and J. N. Tsitsiklis with the use of artificial neural networks (multilayer perceptrons) for approximating the Bellman function. This is an effective mitigation strategy for reducing the impact of dimensionality by replacing the memorization of the complete function mapping for the whole space domain with the memorization of the sole neural network parameters. In particular, for continuous-time systems, an approximate dynamic programming approach that combines both policy iterations with neural networks was introduced. In discrete-time, an approach to solve the HJB equation combining value iterations and neural networks was introduced.
 * By calculating the first-order conditions associated with the Bellman equation, and then using the envelope theorem to eliminate the derivatives of the value function, it is possible to obtain a system of difference equations or differential equations called the 'Euler equations'. Standard techniques for the solution of difference or differential equations can then be used to calculate the dynamics of the state variables and the control variables of the optimization problem.

Applications in economics
The first known application of a Bellman equation in economics is due to Martin Beckmann and Richard Muth. Martin Beckmann also wrote extensively on consumption theory using the Bellman equation in 1959. His work influenced Edmund S. Phelps, among others.

A celebrated economic application of a Bellman equation is Robert C. Merton's seminal 1973 article on the intertemporal capital asset pricing model. (See also Merton's portfolio problem).The solution to Merton's theoretical model, one in which investors chose between income today and future income or capital gains, is a form of Bellman's equation. Because economic applications of dynamic programming usually result in a Bellman equation that is a difference equation, economists refer to dynamic programming as a "recursive method" and a subfield of recursive economics is now recognized within economics.

Nancy Stokey, Robert E. Lucas, and Edward Prescott describe stochastic and nonstochastic dynamic programming in considerable detail, and develop theorems for the existence of solutions to problems meeting certain conditions. They also describe many examples of modeling theoretical problems in economics using recursive methods. This book led to dynamic programming being employed to solve a wide range of theoretical problems in economics, including optimal economic growth, resource extraction, principal–agent problems, public finance, business investment, asset pricing, factor supply, and industrial organization. Lars Ljungqvist and Thomas Sargent apply dynamic programming to study a variety of theoretical questions in monetary policy, fiscal policy, taxation, economic growth, search theory, and labor economics. Avinash Dixit and Robert Pindyck showed the value of the method for thinking about capital budgeting. Anderson adapted the technique to business valuation, including privately held businesses.

Using dynamic programming to solve concrete problems is complicated by informational difficulties, such as choosing the unobservable discount rate. There are also computational issues, the main one being the curse of dimensionality arising from the vast number of possible actions and potential state variables that must be considered before an optimal strategy can be selected. For an extensive discussion of computational issues, see Miranda and Fackler, and Meyn 2007.

Example
In Markov decision processes, a Bellman equation is a recursion for expected rewards. For example, the expected reward for being in a particular state s and following some fixed policy $$\pi$$ has the Bellman equation:

 * $$ V^\pi(s)= R(s,\pi(s)) + \gamma \sum_{s'} P(s'|s,\pi(s)) V^\pi(s').\ $$

This equation describes the expected reward for taking the action prescribed by some policy $$\pi$$.

The equation for the optimal policy is referred to as the Bellman optimality equation:

 * $$ V^{\pi*}(s)= \max_a \left\{ {R(s,a) + \gamma \sum_{s'} P(s'|s,a) V^{\pi*}(s')} \right\}.\ $$

where $${\pi*}$$ is the optimal policy and $$V^{\pi*}$$ refers to the value function of the optimal policy. The equation above describes the reward for taking the action giving the highest expected return.

title: Bellman equation


text:
Elizabeth Resolutes

The Elizabeth Resolutes were a 19th-century professional baseball team based in Elizabeth, New Jersey. They were a member of the National Association of Professional Base Ball Players for the 1873 season, and played their home games at Waverly Fairgrounds. Though based in the vicinity of Elizabeth, they were usually listed in game reports as simply "Resolute" or "the Resolutes", per the style of the day. "Elizabeth Resolutes" is modern nomenclature.

The Resolutes were an amateur team dating back to the mid-1860s, and became one of a number of teams to try their hand at professional ball. The club played just 23 games during its lone professional season, finishing with two victories against 21 defeats, and losing all eight of their home games. Hugh Campbell was the pitcher of record for both wins and 16 of the losses. The Resolutes' leading hitter was Art Allison, who batted .323, his best season, while playing all 23 games, mostly in the outfield.

Although Philadelphia and New York City teams occasionally played games in New Jersey to circumvent blue laws that forbid professional baseball on Sundays, the Resolutes and the 1915 Newark Peppers of the Federal League are the only "major league" teams to be based in New Jersey.

title: Elizabeth Resolutes


text:
User:Ic0n0

I've been using Wikipedia for quite sometime although i never found the desire to submit content until recently. The Rash of Page vandalism has made me more aware of the necessity to have members willing to revert pages back to correct and current information. I have no desire other then to maintain fairness as well as resolve conflicts that may arise.

title: User:Ic0n0


text:
Colorado Air and Space Port

Colorado Air and Space Port, formerly known as Front Range Airport, is a public airport located in unincorporated Adams County, Colorado, in the United States, adjacent to Aurora and 6 mi southeast of Denver International Airport. Colorado Air and Space Port serves the Denver-Aurora-Lakewood, CO Metropolitan Statistical Area. The postal designation of Watkins, a nearby unincorporated community, is used in the airport's mailing address.

Colorado Air and Space Port ICAO/FAA identifiers are KCFO/CFO. The airport has no IATA designation.

Colorado Air and Space Port is a small general aviation airport, although increased demand has warranted several expansion programs in recent years. Currently, the airport serves as the base of a few flying schools, flight clubs, maintenance services, and air rescue training facilities. Due to its location on the flat plains of eastern Colorado, as well as generally cheaper aircraft rental rates, it is a very popular airport for both flight training and recreational flights. It is also popular among owners and pilots of kit-built aircraft, and the Experimental Aircraft Association (EAA) has a very strong presence at Colorado Air and Space Port, which frequently hosts the EAA Young Eagles Rallies.

In 2011, the State of Colorado applied to the FAA to certify Colorado Air and Space Port as a spaceport. The application was approved on August 17, 2018, and announced on August 20, 2018.

History
Front Range Airport opened in 1984 when the now demolished Stapleton International Airport  was the major air hub for the Denver metropolitan area. Until 2005, it was a non-towered airport without air traffic control (ATC) services when the tallest general aviation control tower in the United States (191 ft) was opened along with full ATC services. After 19 years as airport director, Dennis Heap and the airport board parted ways in August 2013. Heap was replaced in the late spring of 2014 by Dave Ruppel. The airport was originally owned by the Front Range Airport Authority (FRAA), continuing until January 1, 2014, when the FRAA was dissolved and the airport and all employees were folded into Adams County government as a department. Since then, the airport has seen a marked improvement in general aviation, air-taxi, military traffic as well as other air-based businesses, such as the helicopter-based businesses of Air Methods.

Facilities and aircraft
Colorado Air and Space Port covers an area of 3,349 acre which contains two asphalt paved runways, 8/26 is 8,002 ft x 100 ft (2,439 x 30 m) and 17/35, measuring 8000 by.

For the 12-month ending December 31, 2019, the airport had 75,647 aircraft operations, an average of 207 per day: 98.5% general aviation, <1% air taxi and 1.4% military. There was at the time 292 aircraft based at this airport: 247 single-engine, 38 multi-engine, 4 helicopters, 1 ultralight, and 2 jet aircraft.

The airport also hosts an armory belonging to the Colorado Army National Guard. HHC, 5th Battalion, 19th Special Forces Group is based there. There are no military aircraft based at the airport.

Spaceport proposal
In October 2011, the Governor of Colorado, John Hickenlooper, formally requested that the federal government designate Colorado a "spaceport state" and that the airport be designated a spaceport for suborbital horizontal takeoff flights (HTVL and HTHL). Spaceport designation would allow a facility offering suborbital tourism, travel, and cargo transport from one point to another on Earth. The Denver Post reported that "No vertical launches are planned at the Front Range, unlike most of the other eight certified U.S. spaceports. Instead, space planes — an emerging technology — will use regular runways and jet engines to take off and land, switching to rocket power above 50,000 feet."

Media sources in 2012 suggested that the Sierra Nevada Dream Chaser spaceplane might be used for suborbital spaceflights and that Colorado Air and Space Port might prove to be the preferred location, over Spaceport America in New Mexico. News reports indicated that the Colorado Air and Space Port proposal was gaining traction with political interests at the state and federal levels as well as with industry participants. One of those commercial interests was XCOR Aerospace, which was considering Spaceport Colorado as a candidate for HTHL operations with their Lynx rocketplane. However, XCOR announced in July 2012 that they would be moving their company headquarters and research and development activities to Texas, in part due to a significant set of financial incentives (US$10000000 ) offered to XCOR by the Midland Development Corporation (MDC) and the Midland City Council.

, Colorado state law "grants limited liability to spaceflight companies, allowing spaceflight participants who sign waiver forms to sue only if they are injured or killed as a result of a firm’s 'willful or wanton disregard' for safety."

Spanish architect Luis Vidal produced an architectural concept for the new airport in 2013.

In December 2017, British aerospace company Reaction Engines began construction of a test facility at Colorado Air and Space Port for the development of its SABRE air-breathing rocket engine.

The spaceport designation was approved in 2018.

In December 2020, Japanese aerospace company PD AeroSpace signed an agreement with the Air and Space Port that paves the way toward test flights of high-altitude planes above the plains east of Aurora.

In October 2022 plans for Port Colorado, an industrial mixed-use development spanning 6,500 acres adjacent to Colorado Air and Space Port, were reported.

title: Colorado Air and Space Port


text:
Talk:Holme-on-Spalding-Moor

Untitled
This "little" village is notable for in the past being listed in the Guinness Book of Records as the longest village in Britain. I live nearby and it does take an awful long time to drive through, but I have no direct proof whether this record still stands or is still listed in the book. X2qat 13:59, 9 August 2006 (UTC)

I heard that it is the longest village and I also live in the Village and it can take up to 5 minutes to travel through. Although would you call it a little village?

Removed the comment:

"Its most infamous inhabitant is a reclusive writer with a Canadian obsession."

as not particularly encyclopedic and needlessly cryptic.

That said I'm curious who this reclusive writer is and, should anyone know his or her secret identity and wish to restore the comment with further elaboration, well, I think that would be just swell. Thehappysmith 03:43, 3 Dec 2004 (UTC)

Is this really a stub? I mean, is there anything more to say about this little village? Thehappysmith 14:38, 28 Dec 2004 (UTC)

Assessment comment
Substituted at 18:10, 29 April 2016 (UTC)

External links modified
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title: Talk:Holme-on-Spalding-Moor


text:
Flat Hat Club

The Flat Hat Club is the popular name of a collegiate secret society and honor fraternity founded in 1750 at the College of William and Mary in Williamsburg, Virginia. The fraternity, formally named the "F.H.C. Society", was founded at the College on November 11, 1750. The society maintains relationships with societies at the University of St. Andrews and Amherst College.

The F.H.C. Society is the first recorded collegiate secret society in the United States. Early in the 21st century, the Education section of The New York Times profiled America's oldest university clubs and societies and included a letter, now housed in the archives at Swem Library, which Thomas Jefferson wrote to Thomas McAuley, mentioning Jefferson's membership of the F.H.C.

Original society
The initials of the F.H.C. Society stand for a secret Latin phrase, likely "Fraternitas, Humanitas, et Cognitio" or "Fraternitas Humanitas Cognitioque" (two renderings of "brotherhood, humanity, and knowledge"). The "brothers" of the original F.H.C. devised and employed a secret handshake, wore a silver membership medal, issued certificates of membership, and met regularly for discussion and fellowship, especially at the Raleigh Tavern. The group became publicly known by the backronym "Flat Hat Club" in probable allusion to the mortarboard caps then commonly worn by all students at the College (now worn at graduation by students at most American universities).

William & Mary alumnus and third American president Thomas Jefferson may be the most famous member of the Flat Hat Club. Other notable members of the original group included Colonel James Innes, St. George Tucker, and George Wythe. Late in life, Jefferson wrote that, "[w]hen I was a student of Wm. & Mary College of this state, there existed a society called the F.H.C. society, confined to the number of six students only, of which I was a member. Still, it had no useful object, nor do I know whether it now exists."

A second Latin-letter fraternity, the P.D.A. Society (publicly known as "Please Don't Ask"), was founded at William and Mary in March 1773, in imitation of the F.H.C. Society. John Heath, a student at William and Mary who in 1776 sought but was refused admission to the P.D.A., later established the first Greek-letter fraternity, the Phi Beta Kappa Society.

The student members of the F.H.C. suspended the group's activities in 1781, probably due to the suspension of academic exercises at the university as the contending armies of the American Revolution approached Williamsburg during the Yorktown campaign.

"The memory of this fraternity had entirely died out at William and Mary, but [after 1909, there was a] discovery of certain manuscript material in the correspondence of St. George Tucker, who was a student of the College in 1772. . . . These manuscripts consist of (1) a letter of Mr. Jefferson, written to John D. Taylor, of Maryland, giving some account of the club at the College, stating that he was a member . . . [;] (2) a list of the books described as compiled for the club's library, in 1772, by Rev. Thomas Gwatkin, Professor of Mathematics; (3) the credentials of Robert Baylor as a member in abbreviated Latin." Therefore, we know the society existed for some years and possessed a small library.

Subsequent society
The name of the group was revived in the twentieth century by application to a select group of twelve undergraduate men and four professors which had been founded in 1916 as the Spotswood Club (it thus differed markedly from the original society, a fraternity of six undergraduate men with alumnus members in urbe -- that is, "in town", having graduated from the university). This society operated largely as a collegiate honorary society. It suspended its activities in 1943 as the number of men enrolled at the College steeply declined because of American involvement in World War II.

The modern F.H.C. Society was revived in May 1972. It remains an all-male society, consisting of twelve undergraduate men and alumni in urbe. In recent years, an additional six members were added. Most of its activities remain comparatively secret within the university. Members receive medals of distinction upon graduation from William and Mary, showing their membership. Contrary to the practice of some similar societies, alumni may disclose their membership after graduation.

title: Flat Hat Club


text:
Chlorite group

The chlorites are the group of phyllosilicate minerals common in low-grade metamorphic rocks and in altered igneous rocks. Greenschist, formed by metamorphism of basalt or other low-silica volcanic rock, typically contains significant amounts of chlorite.

Chlorite minerals show a wide variety of compositions, in which magnesium, iron, aluminium, and silicon substitute for each other in the crystal structure. A complete solid solution series exists between the two most common end members, magnesium-rich clinochlore and iron-rich chamosite. In addition, manganese, zinc, lithium, and calcium species are known. The great range in composition results in considerable variation in physical, optical, and X-ray properties. Similarly, the range of chemical composition allows chlorite group minerals to exist over a wide range of temperature and pressure conditions. For this reason chlorite minerals are ubiquitous minerals within low and medium temperature metamorphic rocks, some igneous rocks, hydrothermal rocks and deeply buried sediments.

The name chlorite is from the Greek chloros (χλωρός), meaning "green", in reference to its color. Chlorite minerals do not contain the element chlorine, also named from the same Greek root.

Properties
Chlorite forms blue-green crystals resembling mica. However, while the plates are flexible, they are not elastic like mica, and are less easily pulled apart. Talc is much softer and feels soapy between the fingers.

The typical general formula for chlorite is (Mg,Fe)3(Si,Al)4O10(OH)2*(Mg,Fe)3(OH)6. This formula emphasizes the structure of the group, which is described as TOT-O and consists of alternating TOT layers and O layers. The TOT layer (Tetrahedral-Octahedral-Tetrahedral = T-O-T) is often referred to as a talc layer, since talc is composed entirely of stacked TOT layers. The TOT layers of talc are electrically neutral and are bound only by relatively weak van der Waals forces. By contrast, the TOT layers of chlorite contain some aluminium in place of silicon, which gives the layers an overall negative charge. These TOT layers are bound together by positively charged O layers, sometimes called brucite layers. Mica is also composed of aluminium-rich, negatively charged TOT layers, but these are bonded together by individual cations (such as potassium, sodium, or calcium ions) rather than a positively charged brucite layer.

Chlorite is considered a clay mineral. It is a nonswelling clay mineral, since water is not adsorbed in the interlayer spaces, and it has a relatively low cation exchange capacity.

Occurrence
Chlorite is a common mineral, found in metamorphic, igneous, and sedimentary rocks. It is an important rock-forming mineral in low- to medium-grade metamorphic rock formed by metamorphism of mafic or pelitic rock. It is also common in igneous rocks, usually as a secondary mineral, formed by alteration of mafic minerals such as biotite, hornblende, pyroxene, or garnet. The glassy rims of pillow basalt on the ocean floor is often altered to pure chlorite, in part by exchange of chemicals with seawater. The green color of many igneous rocks, slates, and schists is due to fine particles of chlorite disseminated throughout the rock. Chlorite is a common weathering product and is widespread in clay and in sedimentary rock containing clay minerals. Chlorite is found in pelites along with quartz, albite, sericite, and garnet, and is also found in associate with actinolite and epidote.

In his pioneering work on metamorphic facies in the Scottish Highlands, G.M. Barrow identified the chlorite zone as the zone of mildest metamorphism. In modern petrology, chlorite is the diagnostic mineral of the greenschist facies. This facies is characterized by temperatures near 450 C and pressures near 5 kbar. At higher temperatures, much of the chlorite is destroyed by reactions with either potassium feldspar or phengite mica which produce biotite, muscovite, and quartz. At still higher temperatures, other reactions destroy the remaining chlorite, often with release of water vapor.

Chlorite is one of the most common minerals produced by propylitic alteration by hydrothermal systems, where it occurs in the "green rock" environment with epidote, actinolite, albite, hematite, and calcite.

Experiments indicate that chlorite can be stable in peridotite of the Earth's mantle above the ocean lithosphere carried down by subduction, and chlorite may even be present in the mantle volume from which island arc magmas are generated.

Members of the chlorite group

 * {| class="wikitable"

! Baileychlore ! IMA1986-056 ! Borocookeite ! IMA2000-013 ! Chamosite ! year: 1820 ! Clinochlore ! year: 1851 ! Cookeite ! year: 1866 ! Donbassite ! year: 1940 ! Gonyerite ! year: 1955 ! Nimite ! year: 1968 ! Pennantite ! year: 1946 ! Ripidolite ! chlinochlore var. ! Sudoite ! IMA1966-027
 * (Zn,Fe(2+),Al,Mg)6(Al,Si)4O10(O,OH)8
 * LiAl4(Si3B)O10(OH)8
 * (Fe,Mg)5Al(Si3Al)O10(OH)8
 * (Mg,Fe(2+))5Al(Si3Al)O10(OH)8
 * LiAl4(Si3Al)O10(OH)8
 * Al2[Al2.33][Si3AlO10](OH)8
 * (Mn,Mg)5(Fe(3+))2Si3O10(OH)8
 * (Ni,Mg,Al)6(Si,Al)4O10(OH)8
 * (Mn5Al)(Si3Al)O10(OH)8
 * (Mg,Fe,Al)6(Al,Si)4O10(OH)8
 * Mg2(Al,Fe)3Si3AlO10(OH)8
 * }

Clinochlore, pennantite, and chamosite are the most common varieties. Several other sub-varieties have been described. A massive compact variety of clinochlore used as a decorative carving stone is referred to by the trade name seraphinite. It occurs in the Korshunovskoye iron skarn deposit in the Irkutsk Oblast of Eastern Siberia.

Uses
Chlorite does not have any specific industrial uses of any importance. Some rock types containing chlorite, such as chlorite schist, have minor decorative uses or as construction stone. However, chlorite is a common mineral in clay, which has a vast number of uses.

Chlorite schist has been used as roofing granules, the mineral granules adhered to asphalt composition shingles due to the green color. It was quarried near Ely, Minnesota, US, until superseded by synthetic materials.

title: Chlorite group