text:
User talk:Morphh

Proposal to delete Federal taxation in the United States
I have tagged the article Federal taxation in the United States as proposed for deletion, as previously noted. Your prior discussions with User:Int21h indicate that most of the article was copied by him from Taxation in the United States. While I agree that the topic is of sufficient length and notability that it could be a separate article, I believe the needs of the community are better served with a single article. Further, trying to maintain two high level articles, one of which is merely a subset of the other, will impose too great an editing burden and lead to many errors and contradictions. I believe the Federal taxation article should be no more than a redirect to Taxation in the United States. Comments welcome on my talk page or the Federal tax article talk page. Thanks. Oldtaxguy (talk) 23:03, 2 January 2011 (UTC)

Invitation to join WikiProject United States
...only 4 years late......cheers, Casliber (talk · contribs) 08:19, 14 January 2011 (UTC)

Thanks
Much appreciated! Oldtaxguy (talk) 18:41, 2 March 2011 (UTC)

Linder pic caption suggestion
The Linder picture on the FairTax page, I believe, is from 2007 and shows Linder with the FairTax and the 2007 tax code, yet the caption says "current" tax code, ("Rep John Linder holding the 133 page Fair Tax Act in contrast to the current U.S. tax code.") making it dated and inaccurate.

I would suggest perhaps adjusting it to something like this: "Rep John Linder holding the 133 page Fair Tax Act in contrast to the then-current 2007 U.S. tax code." or "Rep John Linder in 2007 holding the 133 page Fair Tax Act in contrast to the annually growing U.S. tax code."

As you are someone so knowledgable on the article, I thought I'd throw that out to you because this is something that strikes me every time I look at it. Thanks! Pbgiv (talk) 19:16, 3 March 2011 (UTC)

 * Thanks, I updated taking a bit from each suggestion. I used then-current and added 2007 to the bill version Fair Tax Act of 2007, since I'm not sure if it is still 133 pages (they made a few tweaks in 2009 & 2011).   Morphh   (talk) 02:39, 4 March 2011 (UTC)

 * The Linder picture is very deceptive. The "then-current tax code" is the two maroon volumes on which Mr. Linder is resting the pages he's holding.  I don't know what the blue volumes beside him are, other than maybe an attempt to make the reader believe they are the current state of the law.  I strongly favor removing this photo as inherently very biased. Oldtaxguy (talk) 20:14, 2 May 2011 (UTC)
 * That would be the complete set of Title 26 of the US Code of Federal Regulations (that's the part written by the IRS), which make up twenty volumes. I'll adjust the caption.  Morphh   (talk) 23:34, 2 May 2011 (UTC)

Orphaned non-free image File:TaxFoundation.jpg
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Nomination as a United States Wikipedians' Collaboration of the Month candidate
The Hope Diamond has been nominated to be a future United States Wikipedians' Collaboration of the Month. All editors interested in improving this article are encouraged to participate. You can vote for this or other articles article of the Month here. --Kumioko (talk) 19:36, 30 June 2011 (UTC)

Article feedback
You might want to chime in at WP:VPP but I'm pessimistic about any chances of slowing this down until things start to go wrong, and even then who knows? Dougweller (talk) 06:12, 18 July 2011 (UTC)

A barnstar for you!

 * Thanks, always nice to get a barnstar. :) Morphh   (talk) 03:22, 12 August 2011 (UTC)

Possibly unfree File:Revenuereform.jpg
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Talkback
18:47, 1 September 2011 (UTC)

Nomination as a United States Wikipedians' Collaboration of the Month candidate
Greetings, as someone who has signed up to be a member of the United States Wikipedians' collaboration of the Month, I wanted to let you know that several articles have been nominated to be a future Collaboration of the Month article. All editors interested in voting for or improving these article are encouraged to participate. You can cast your vote here. --Kumioko (talk) 19:00, 9 December 2011 (UTC)

December 2011 Newsletter for WikiProject United States
--Kumioko (talk) 03:59, 12 December 2011 (UTC)

January 2012 Newsletter for WikiProject United States and supported projects
--Kumi-Taskbot (talk) 18:22, 16 January 2012 (UTC)

Nomination of Leon Panetta as a United States Wikipedians' Collaboration of the Month candidate
Greetings, as a member of the United States Wikipedians' collaboration of the Month, this notice was sent to let you know that the article, Leon Panetta, has been nominated to be a future Collaboration of the Month article. All editors interested in voting for or improving these article are encouraged to participate. You can cast your vote here. --Kumioko (talk) 16:29, 31 January 2012 (UTC)

MOTDs (This space for rent)
You may have noticed over the past few days that the MOTD that you link to on your user page has simply displayed a red link. This is due to the fact that not enough people are reviewing pending MOTDs here. Please help us keep the MOTD template alive and simply go and review a few of the MOTDs in the list. That way we can have a real MOTD in the future rather than re-using (This space for rent). Any help would be appreciated! –p joe f (talk • contribs) 12:05, 7 March 2012 (UTC)

WP:NOTFORUM - Forward!
You are, of course, quite correct. As a historian in Wisconsin (birthplace of the actual Republican Party (R.I.P.) I am simply amazed and annoyed at the pathetic efforts by the paid liars of the chattering classes to taint my state's motto as evidence of communism, as part of their effort to brand the mealy-mouthed Eisenhower Republicanism of the Obama administration as the work of Stalin's minions (with a side order of guilt-by-association with the Hitler Youth). Sadly, my annoyance leads me to attempt to actually teach them some history, undoubtedly a futile gesture. -- Orange Mike |  Talk  20:22, 4 May 2012 (UTC)
 * Indeed, it's certainly easy to get side tracked on such issues. I find the back and forth quite annoying and pathetic as well, but it is what it is I guess - politics as usual.   Morphh   (talk) 20:46, 4 May 2012 (UTC)

Obama Controversies Not Mentioned
If you want some points that have been getting kept out of the Obama article for years, controversies they don't want mentioned no matter how prominent, here are some examples.

 * Opposed medical care for newborn infants, was a major issue in both the 2004 and 2008 elections and brought up by Alan Keyes, Hillary Clinton, and John McCain. Newt Gingrich brought it up in 2012. I've written this page covering it, which includes 50 prominent sources. Some major sources include:
 * Disqualified all four opponents in first election, in 1996, so he could run unopposed. He used a team of lawyers to disqualify the petition signatures of opponents on technicalities after the filing deadline. I've written this section covering it. Some major sources include:
 * Struck a deal with Illinois Senate leader to get all legislation from other Illinois Senators directed to his desk in 2003, building his entire legislative record in one year, in preparation for the 2004 elections so he could become a U.S. Senator. I've written this page covering it. Some major sources include:

--98.220.198.49 (talk) 08:49, 14 May 2012 (UTC)
 * I can't say that I'm interested in getting involved with inserting contentious material into hot topic articles. I'm not looking to target inserting criticism.  I evaluate each piece of content on its own merits based on the encyclopedia's policy.  So I could just as easily argue against inserting such content depending on the arguments and sources presented in discussion.  It looks like you've done some work though, so I encourage you to create an account and present this on the appropriate article's talk page if you think it necessary content for an encyclopedia article.  Morphh   (talk) 12:47, 14 May 2012 (UTC)

Thanks for the input, Morphh. It may be stretching things to call those edits 'good faith', but your point is well taken.JoelWhy (talk) 19:56, 15 May 2012 (UTC)

RE
I replied to your comment on my talk page. I don't know how this works, whether you get a notification of my reply or not, therefore I am leaving this message. - 173.74.164.212 (talk) 06:40, 9 June 2012 (UTC)

Notice of Dispute resolution discussion
Hello. This message is being sent to inform you that there is currently a discussion at Dispute resolution noticeboard regarding an issue with which you may have been involved. The thread is "War on Women". Thank you. --CartoonDiablo (talk) 01:31, 18 July 2012 (UTC)

Notice of Neutral point of view noticeboard discussion
Hello, Morphh. This message is being sent to inform you that there currently is a discussion at Neutral point of view/Noticeboard regarding an issue with which you may have been involved. Thank you.

This is a courtesy heads-up for you. I'm adding everybody who worked on the article since I have.  Belch fire - TALK 02:28, 1 August 2012 (UTC)

Re: Tax chart
Moving this back to the other talk page to keep the discussion in one place...
 * I've replied further at User talk:Cupco. — Cup co  21:41, 20 September 2012 (UTC)

Re: Graphs
Which specific graphs do you think don't improve the articles? And what pattern are you talking about? I've been adding graphs in several different topics, none of which I have any COI or work interest in. — Cup co  19:55, 3 October 2012 (UTC)
 * Replied on User talk:Cupco's talk. Morphh   (talk) 21:16, 3 October 2012 (UTC)

Freedom of speech = New WikiProject
Hi there, I'm notifying you as I noticed your impressive work on the GA Quality article, Tax protester constitutional arguments. If you're interested, here are some easy things you can do: Thank you for your interest in Freedom of speech, — Cirt (talk) 22:21, 25 October 2012 (UTC)
 * WP:WikiProject Freedom of speech
 * 1) List yourself as a participant in the WikiProject, by adding your username here: WikiProject_Freedom_of_speech.
 * 2) Add userbox User Freedom of speech to your userpage, which lists you as a member of the WikiProject.
 * 3) Tag relevant talk pages of articles and other relevant pages using WikiProject Freedom of speech.
 * 4) Join in discussion at Wikipedia talk:WikiProject Freedom of speech.
 * 5) Notify others you think might be interested in Freedom of speech to join the WikiProject.

Reynolds American
Hello. I have some basic factual edit suggestions for the Reynolds American article I posted on the article’s talk page. I am an employee of the company and I am therefore just suggesting edits due to my WP:COI. I saw you are a member of the North Carolina WikiProject and so I was wondering if you could take a look at the proposed edits and implement them if you deem them appropriate? Thanks. Velinflo (talk) 16:14, 12 November 2012 (UTC)
 * Please disregard; already handled by another editor. Thanks. Velinflo (talk) 20:29, 19 November 2012 (UTC)

question about dynamic scoring edits
Hi Morphh,

You contend that my edits to the dynamic scoring page present an incorrect premise. Can you please clarify? The premise I added (lower taxes increase economic growth and subsequently tax receipts) is exactly what conservative leaders are arguing for to restore the economy. Are they wrong?

I feel that this article lacks balance and is skewed to promote conservative fiscal ideology. I was attempting to add a little balance by providing historical and factual data refuting that philosophy.

best wishes,

trappem — Preceding unsigned comment added by Trappem (talk • contribs) 20:14, 4 December 2012 (UTC)
 * This article is not the article to debate supply-side economics and the effects of a particular policy choice. Dynamic scoring is simply considering the economic effects of policy when scoring the plan, be it good, bad, or otherwise.  Taxation has economic disturbance - dynamic scoring attempts to measure that disturbance.  The article states that conservatives promote dynamic scoring as common methodologies factor lower taxes return higher benefits in terms of GDP growth and provide revenue increases over static scoring - this is a true statement.  There is no need to include the premise, which is WP:OR as opinions differ depending on what conservative your talking about or liberal for that matter (as they too argue that tax increases hurt economic growth) and what income or policy your discussing (tax increases on the middle class, business owners, "the rich"?).  The second portion is also vague - increased revenue over what... static scoring or prior revenues?  And of course the rebuttal conclusion is extreme and very weakly supported by the sources.  All things equal, 75% marginal tax rates will not boost GDP - there is no causality in these historical figures and it goes against all empirical evidence (U.S. and Global).  I'm fine with trying to add balance, but let's not turn this article into a debate on tax policy and the vast opinions regarding it's effects.   Morphh   (talk) 21:24, 4 December 2012 (UTC)

Thanks for your explanation...t — Preceding unsigned comment added by Trappem (talk • contribs) 22:13, 4 December 2012 (UTC)

Nomination for deletion of Template:TaxationCOTM
Template:TaxationCOTM has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for discussion page. Kumioko (talk) 03:00, 5 June 2013 (UTC)

Help with Sales taxes in the United States article
Hi Morphh, I'm an employee of The Heritage Foundation and I'm looking for help with a request I posted a little while ago on the Sales taxes in the United States talk page. I'm looking to add a new section to this article about sales taxes on the Internet, but I would like other editors to review what I have written because I've mentioned some criticism from The Heritage Foundation (about the recent Marketplace Fairness Act) in the section. I see that you are a member of WikiProject Taxation and thought you might be interested in looking at this. If you'd like to help out, the request is on the article's talk page here. Thanks! Thurmant (talk) 21:19, 1 July 2013 (UTC)

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Off-topic
"99.9%" of people supporting criminalization of homosexuality in 1990 isn't quite on. By that point, states which still had sodomy laws on the books were in a minority. The USA is backward, but not apparently that backward. –Roscelese (talk ⋅ contribs) 19:45, 22 July 2013 (UTC)
 * Ya, I was being facetious in making a point. I don't have any statistic on it.  Morphh   (talk) 20:01, 22 July 2013 (UTC)
 * Yeah, I don't know what the opinion statistic would be either. I don't think the "lots of people supported criminalization back then" is relevant either way, since it's Card's support that is controversial, not anyone else's; I just took the off-topic discussion here since I wasn't sure you knew that most states had actually already repealed their sodomy laws before Lawrence. –Roscelese (talk ⋅ contribs) 20:18, 22 July 2013 (UTC)

Genealogy and Family History merger
Hi, this merger has been spotlighted on FamilySearch Blog: https://familysearch.org/blog/en/difference-genealogy-family-history/. Hope I did OK explaining it to the public. Murphynw (talk) 02:37, 10 August 2013 (UTC)

 * I agree with your comments. I don't understand the purpose of trying to parce differences between "genealogy" and "family history." It looks like picking one over the other is largely a regional difference in English. It looks like each country has it's own bizarre history of bouncing back between one or the other. If I've understand the comments correctly, in the UK, Australia, and New Zealand, “family history” is the preferred verbiage. In the United States, Mormons (members of The Church of Jesus Christ of Latter-day Saints) also prefer to call the endeavor “family history,” but people who are not Mormons prefer “genealogy.” But overall, it's clearly "genealogy" that is most recognizable according to the studies I've seen. LOL Murphynw (talk) 22:34, 11 August 2013 (UTC)

Thanks!
For the barnstar. I also really appreciate your efforts to meet me halfway and find solutions we can both agree on. –Roscelese (talk ⋅ contribs) 02:59, 5 September 2013 (UTC)

Advice
Walter Brooke in the movie The Graduate had one word of advice: "Plastics". – S. Rich (talk) 17:59, 16 October 2013 (UTC)
 * Thanks :) I needed that. Morphh   (talk) 18:14, 16 October 2013 (UTC)

Nrcprm2026 SPI
I think you need to revert your recent archival of this case. You do not appeared to have considered or evaluated the behavioural evidence at play, which I think needs to happen before the investigation can be closed (notwithstanding that I declined to provide technical evidence). This is unless you actually have looked at the behaviour of the two accounts, in which case you need to state this fact on the investigation, or unless I have missed something, in which case you need to WP:TROUT me :-). Thanks, AGK  [•] 22:39, 24 October 2013 (UTC)

Progressivism & education & taxes
While what you say has merit, I think omitting remarks about editor behavior is the best course of action. Perhaps an WP:RFC/U is in order. Thanks. – S. Rich (talk) 19:05, 18 January 2014 (UTC)
 * You're probably right - just frustrating. And yes, RFC/U or ANI (recommend topic ban as related to economic inequality) would be a good next step.  I'm not really familiar with starting either one though.  Morphh   (talk) 20:08, 18 January 2014 (UTC)

Perhaps we should have an RFC/U on editors who plan actions against others without informing them they are being discussed. EllenCT (talk) 23:22, 18 January 2014 (UTC)
 * I recall that you actually did file an ANI without notifying me. Me responding to a post on my talk page about another editor's behavior is not something that I think requires notification.    Morphh   (talk) 23:37, 19 January 2014 (UTC)

Morph, I appreciate your attempts on the article talk pages, but I don't think EllenCT is misunderstanding what's logically required. My suspicion is that she see this as her mission to provide a counterpoint to conservative perspectives and wants to push certain conclusions she has, even if there's no direct support for it. You've laid out the logical gap, but she ignores simple direct requests and refers to irrelevant sources as her justification. I'm at my end trying to reason with her tendentious editing.Mattnad (talk) 16:25, 19 January 2014 (UTC)

 * I agree that she should be fully aware of the issues and policy by now - it's a reoccurring theme. She's tried to create several straw men, so I just wanted to lay it out directly, maybe more for anyone else that reads the discussion later.  I didn't want others falling for the logical fallacy.  Morphh   (talk) 18:05, 19 January 2014 (UTC)

Replacement of "progressive" with "redistributive"
If I remember correctly, at least two times and likely more in the past week or two you have replaced text and links referring to "progressive" and similar terms with other terms referring to "redistributive", after having asked for the original terms to be included because, as you pointed out, progressive taxes don't increase income equality unless they are accompanied by progressive transfer payments. However, transfer payment redistributions can and do also occur from the poor to the rich, both through government fiscal policy, government monetary policy and private sector rent-seeking. Since "redistributive" policies can be regressive instead of progressive, would you please undo those edits? EllenCT (talk) 11:04, 20 January 2014 (UTC)

 * I think you mistaking me with someone else, as I don't recall saying that "progressive taxes don't increase income equality unless they are accompanied by progressive transfer payments". Ignoring dynamic effects, even if the government just burned the money, the taxation itself would reduce income inequality. No transfer payments are necessary, but I probably asked for inclusion of mentioning progressive spending because it's what is done.  Since many people might not be aware of what "progressive spending" is (it's sort of a neologism and not a common term to the general public) and perhaps confuse it with spending tied to a political philosophy and not a distribution method, I thought the term redistributive spending was a more familiar for readers that said essentially the same thing.  I agree that the term redistribution could go both ways, but given the context of the section and sentence "and social safety nets result" along with the common use of the term to the general public, rich to poor is implied/assumed.  It doesn't matter much to me though and I'll undo it on Progressive tax (not sure which other article you're thinking), I was just trying to clarify it for the average reader following WP:TECHNICAL, which says "Every reasonable attempt should be made to ensure that material is presented in the most widely understandable manner possible. If an article is written in a highly technical manner, but the material permits a more understandable explanation, then editors are strongly encouraged to rewrite it." Perhaps we could find a better wording like the phrasing we use on the income inequality article "in a more equal distribution of income across the board."  Morphh   (talk) 13:35, 20 January 2014 (UTC)
 * I noted the change on the Progressive tax article. In the context of that sentence, it's more than clear that redistribution means from wealthier to poorer households. However, Ellen's comment is something to be celebrated.  Here she acknowledges that progressive spending does not have to follow progressive taxation - something she would not consider in the RFC and related discussions about the graph that juxtaposed top marginal tax rates and economic growth. Mattnad (talk) 14:20, 20 January 2014 (UTC)

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Fair Tax
Thanks for addressing my request! Have there been any recent proposals regarding a flat tax? Cmckain (talk) 00:37, 7 February 2014 (UTC)
 * There are many organizations and politicians calling for various flat tax proposals in the United States, but here are a few bills that are in the 113th Congress:, , , . I believe HR1040 is the traditional Armey / Forbes Hall–Rabushka flat tax (aka Freedom Flat Tax, aka Freedom and Fairness Restoration Act).  I think HR1569 (New Fair Deal) is a new proposal, which I recall is being promoted by FreedomWorks.    Morphh   (talk) 15:16, 7 February 2014 (UTC)

Request for suggestion
Hi there,, I hope you're doing well !

I noticed you reverted another user's edits to the article I brought to WP:GA quality, Beck v. Eiland-Hall.

Perhaps you could suggest alternate wording to describe the argumentation style of the commentator, which would be to your satisfaction?

Perhaps something like, "asks guests to disprove an imagined assertion", or something like that?

Or maybe we should just leave the lede intro sect as it is right now, in its present WP:GA quality version?

Thank you for your interest helping to further improve the quality of this WP:GA rated article,

— Cirt (talk) 19:07, 7 February 2014 (UTC)

 * , I'll try to think about how to reword it, but it may be difficult for the lead and perhaps best to leave it out. It would need to be both brief and neutral, and using a short out-of-context sound bite would be difficult.  In addition, there would need to be proper phrasing that the example represents a point of view regarding the argument style.    Morphh   (talk) 19:42, 7 February 2014 (UTC)
 * If you could suggest some sample text to maybe use to add to lede, that'd be appreciated, otherwise, I'm fine leaving the current lede intro text as is now. — Cirt (talk) 19:43, 7 February 2014 (UTC)
 * Ok, I added a bit that I think addresses the point trying to be made (helping define the commentary style) without getting into the issue of context regarding any specific example. Hope that helps.   Morphh   (talk) 20:11, 7 February 2014 (UTC)
 * Thank you! Agreed. This looks much better. I also like the edit adding the wikilink to Russell's teapot, most fascinating! — Cirt (talk) 03:13, 8 February 2014 (UTC)

Thanks for the note, and respect to you as well
Thanks for the note. Yes, I also didn't mean to imply that you were assuming bad faith or anything like that. I like conversations like ours. I probably seem really manic writing as much as I have—this is just one article after all—but the underlying issues do interest me. I probably can't add much more to what I've said, and I'll have to admit that there is no dominating reason to support my principles over yours. Obviously we both agree that we should reflect the current state of scholarship (where it exists), but we don't agree on how best to do that. I have some favoured principles, and, if I'm understanding correctly, you favour a more intuitive, common sense survey of the reliable sources: We can divide up claims into "subjective" vs. "objective" by use of our common sense. I saw your recent question on the NPOV talk page. I think if you go through the discussions in the archives (say from 2010 onwards to the end of 2012), you can see that our debate has taken various guises: Most editors have this sense of what it means for something to be subjective vs. objective (sometimes they use other terms for this as well), and many of these think that this is very useful for determining how we assert statements. But then many others disagree. I guess ours is just another chapter in this unsettled matter. I completely respect your manner of discussion and your fundamental positions. -- Atethnekos (Discussion, Contributions) 21:26, 12 February 2014 (UTC)

Others comments
Hi, I have no objection to the way you tweaked my comment at the Neutralzone, and I'm not miffed just passing on an FYI.... it probably should have run it by me first. As I said, I'm not mad and the change is fine (I officially approve), just don't want you to step on procedural landmine when tweaking someone else's remarks. NewsAndEventsGuy (talk) 18:23, 27 March 2014 (UTC)

 * User talk:NewsAndEventsGuy, I'm not understanding. If I tweaked any of your comments, I'm not aware of it - it was not intentional (perhaps an edit conflict).  Could you point me to what you're talking about?  Morphh   (talk) 18:32, 27 March 2014 (UTC)
 * I should have mentioned it was probably just an oversight. Anyway see https://en.wikipedia.org/w/index.php?title=Wikipedia_talk%3ANeutral_point_of_view&diff=601451635&oldid=601426930 this series of edits].  Like I said, it was a helpful change &  I wish I had thought of it myself, so no harm done! NewsAndEventsGuy (talk) 19:19, 27 March 2014 (UTC)
 * Oh ya, understanding you now. Thanks - good point.  I thought it would be better to improve the existing quotebox than write it again. :)   Morphh   (talk) 19:29, 27 March 2014 (UTC)

IP block exempt
I have granted your account an exemption from IP blocking. This will allow you to edit through full blocks affecting your IP address when you are logged in.

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Note in particular that you are not permitted to use this newly-granted right to edit Wikipedia via anonymous proxies, or disruptively. If you do, or there is a serious concern of abuse, then the right may be removed by any administrator.

Appropriate usage and compliance with the policy may be checked periodically, due to the nature of block exemption, and block exemption will be removed when no longer needed (for example, when the block it is related to expires).

I hope this will enhance your editing, and allow you to edit successfully and without disruption. Please advise me when your course has ended so I can remove the flag. Spartaz Humbug! 22:16, 5 April 2014 (UTC)
 * Thanks - will do. If you can set the expiration now, I will no longer require the exemption after May 2014, so 1 June 2014 would be fine.   Morphh   (talk) 22:34, 5 April 2014 (UTC)
 * No time setting here and I'kll forget si just drop me a note. Spartaz Humbug! 23:19, 5 April 2014 (UTC)

Replaceable fair use File:Adam smith note.jpg
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Secondary source identification
There is currently a discussion at Administrators' noticeboard/Incidents regarding an issue with which you may have been involved. Thank you. See Administrators' noticeboard/Incidents please. EllenCT (talk) 21:56, 7 April 2014 (UTC)

EllenCT suggests you be banned until you understand Wikipedia
So perhaps we should get studying. There may be a test later. Capitalismojo (talk) 00:05, 8 April 2014 (UTC)
 * Thanks for the laugh; Iselilja (talk) 01:51, 8 April 2014 (UTC)
 * Yup - though I should know them pretty good by now, being that I've been here for almost 9 years and I help write some of them. Still writing some of them..   Morphh   (talk) 02:02, 8 April 2014 (UTC)
 * I'm a bit new to Wikipedia myself, at 8 years. I think I need some schoolin' Mattnad (talk) 03:38, 8 April 2014 (UTC)
 * Yes, clearly. I too have begun a period of intense study and reflection. Thank heavens for the wonderful guidance with which we have been blessed! Whatever did we do before this? Trapped in the false consciousness of right-deviationism no doubt. Capitalismojo (talk) 03:57, 8 April 2014 (UTC)

Motto of the Day Help Request April 2014
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Georgism
There is an RfC at Talk:Georgism concerning scope of the article. This is a neutral notification. Collect (talk) 15:39, 30 May 2014 (UTC)

Wrong article
Thanks for that. I get lost in all of the POV pushing that's been going on. Updated comment.Mattnad (talk) 15:29, 3 June 2014 (UTC)

Orphaned non-free image File:Taxanalysts.png
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Your revert
I implemented the July 2014 consensus. The fact that a current active discussion wants to review that consensus, is a contra-indication to apply reverts either way. --Francis Schonken (talk) 15:08, 22 October 2014 (UTC)

 * The prior version represented a long established consensus of a policy (see WP:CONLEVEL), which typically requires higher standard of participation and consensus for changes. The July 2014 link did not contain such participation or discussion on the merits of the change.  Not saying you did anything wrong with adding it, but now that an objection has been raised, it would be better to fall back to the long established consensus while this new addition is considered (now that it has participation and discussions on the merits).    Morphh   (talk) 16:27, 22 October 2014 (UTC)

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Talkback
Stefan2 (talk) 15:28, 30 October 2014 (UTC)

Please contact
Would like to email you, but your email isn't registered here. If you get a chance, please email me here. Thanks, Scott P. (talk) 17:24, 31 October 2014 (UTC)

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ArbCom elections are now open!
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Taxation in Singapore listed at Redirects for discussion
An editor has asked for a discussion to address the redirect Taxation in Singapore. Since you had some involvement with the Taxation in Singapore redirect, you might want to participate in the redirect discussion if you have not already done so. Piotr Konieczny aka Prokonsul Piotrus| reply here 07:21, 25 April 2016 (UTC)

Sorry
I just wanted to say sorry for this edit. It was entirely unintentional. Another editor was kind enough to restore your edit. Deli nk (talk) 19:45, 14 December 2016 (UTC)
 * Thanks for the note. No problem - I expected it was an unintentional.    Morphh   (talk) 19:49, 14 December 2016 (UTC)

Abuse of Wikipedia for advertsing
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Payroll taxes
Payroll taxes don't come out of your paycheck; they come out of your employer as a tax wedge. They're basically like raising the wages your employer pays, but not giving that to you.

If Social Security's payroll FICA was 100% directed at payrolls for those earning over $1M, the *consumer* would pay for it. It actually raises the basic cost of labor regardless of revenue (unlike taxes on corporate profits), thus must be diffused into price.John Moser (talk) 03:31, 5 July 2019 (UTC)

 * One could argue that all taxes are born by the end consumer while another that the worker bears the entire burden via lower wages, but that is a matter of tax incidence. Wherever the ultimate burden falls, the payroll tax is widely described as a tax on wages that is split between employer and worker. A 12.4% Social Security tax (each pay 6.2%) and a 2.9% Medicare tax (each pay 1.45%).  FICA is clearly visible as a tax coming out of the American's paycheck on each pay stub.  Morphh   (talk) 13:44, 10 July 2019 (UTC)

2019 US Banknote Contest
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Message from Project North Carolina
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Your access to AWB may be temporarily removed
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Is MyHeritage a reliable source?
Good evening Morphh,

I hope you're having a fantastic Friday today!

I'm sorry for taking a few minutes out of your time, but I will start off by mentioning we've never worked together on any projects in the past. I've noticed recently you've previously commented on the Talk:MyHeritage page before, and my question is would you consider MyHeritage a reliable source?

I was looking at the site and noticed there was a document on the site (I can't see access it, but I must imagine I could use it to good use for a page), which I was planning to use it for the Carlos Felipe de Habsburgo page under the family heading of the page. Here's the MyHeritage website I was looking at.

Thanks again for taking the time to read into my thread and I hope to hear back!

Sincerely, JayzBox (talk) 15:24, 9 April 2021 (UTC)

 * It depends on what the source goes to. MyHeritage can be a reliable source for MyHeritage, if supporting a statement regarding their company.  So it would be fine to find them sourced in the MyHeritage article for example, or one of their partners or services to reference something about the company.  It could also probably be a reliable source if referencing a document on the site.  Both of these instances would be primary sources though, so not preferred, if a reliable secondary source is available.  If the link to MyHeritage is to an online tree or what looks like in your example, a search query, then no, I would not consider that a reliable source.  MyHeritage is has documents, census, birth records, death records, etc, that could be reliable primary sources, but it also includes user generated family trees.  These would not be reliable sources to support the genealogy of a person.   Morphh   (talk) 21:52, 10 April 2021 (UTC)

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title: User talk:Morphh


text:
Talk:Monitor (synchronization)

Mesa vs. Hoare semantics
Hi guys, I added the bit about Mesa vs. Hoare semantics, but was logged in anonymously. Just wanted to put a name to the edit. I'm not sure if it's really the most elegant way to display the information; does anyone have any suggestions? --Voorhies 22:22, 7 March 2007 (UTC)

Java monitor
Hi, I was just wondering, is there some way that this page can appear when one searches for "java monitor"? Currently the Javan Rhinocerous gets a higher relevancy then "concurrent programming languages" when using that search term, and this page doesn't appear at all. Thanks! Nekonobaka

"Modern"
A good overview article, but the paragraph "In most modern implementations,..." is a bit misleading to my mind. This "modern" monitor way is the sematics of Java Programming Language. For some reason (perhaps speed which is a bad argument in safety critical systems) they did not follow monitor semantics defined in 70's but made their own. This causes much confusion (in this very page the queue examples do not work correctly if they are to be implemented in java).

Perhaps this page should tell that there are three semantics in use for monitors: hoare (signal-and-wait), mesa (signal-and-continue) and Java (the "modern").

 * I don't think that "modern" is a standard term for either signal-and-continue (as the article stands now) or for Java semantics (as proposed). I'd suggest dropping that word. Also there are a few other semantics that could be mentioned. Theodore.norvell (talk) 14:40, 26 August 2008 (UTC)

C#
"C# does not have monitors as a feature of the language". We-ell. C# has a "lock" mechanism which is directly analagous to Java's synchronized mechanism; it happens that it's implemented using the Framework's Monitor class internally (see http://research.microsoft.com/~birrell/papers/ThreadsCSharp.pdf ), but any hypothetical "free-standing" C# implementation (i.e. one not tied to Rotor, .NET FX, Mono, DotGNU, etc.) would have to have an equivalent mechanism. As such it seems to me that C# probably does have built-in monitors, at least to the same extent as Java does. DrPizza 18:07, 9 October 2005 (UTC)

Monitor implemented using semaphores
I believe the implementation given here is incorrect. If a thread calls wait after signal has been called it may be stuck indefinitely, since signal increments the semaphore only enough times for threads already waiting. — Preceding unsigned comment added by 2601:647:5100:4C2:34BB:EEAA:46DD:66AD (talk) 21:54, 8 March 2016 (UTC)

 * No, it's correct because  is supposed to only wake up threads that are currently waiting. However, this implementation has another problem regarding the wait operation's atomicity, which is described in Andrew D. Birrell's paper. Tcpp (talk) 13:34, 18 May 2021 (UTC)

Condition variable
I think that 'Condition variables' can live without a monitor. If that is right, why Condition variable redirects here?

 * You're mistaken. Condition variables were developed specifically for monitors, and I've never heard of anyone recommending their use outside that context. Gazpacho 04:30, 14 April 2006 (UTC)

 * condition variables are used all over the place. even with java, for example, every object has a condition variable built in with the wait, signal, and signalAll methods supported at the Object class. 68.83.85.175 00:25, 6 November 2006 (UTC)

 * Condition variables were introduced for use with monitors, but they are definitely useful in and of themselves. By way of reference, none of the pthread condition variable man pages mention the word "monitor".  The key behavior of condition variables, allowing a single thread to signal multiple waiting threads, is not monitor-specific.  I don't know if that means a condition variable is worthy of its own article, but they are perfectly okay to use outside monitors.  ScotS (talk) 23:42, 12 December 2007 (UTC)

 * In pthreads, the mutex takes the role of the monitor. Condition variables are associated with some other lock: In pthreads it is a mutex, in monitors it is the monitor lock Theodore.norvell (talk) 14:40, 26 August 2008 (UTC)

I think the key thing that is missing here is the notion that a condition variable is (or ought to be) associated with some boolean expression. This is what makes programming with monitors effective. When I have time, I'd like to add that and also make the use of invariants clearer. Any objections? Theodore.norvell (talk) 14:40, 26 August 2008 (UTC)

Monitors and condition variables are different concepts. The PThread condition variables are not monitors, because it is for example possible to use multiple cvars with the same mutex lock. Also, in a monitor, every operation is mutually exclusive, which rules out typical cvar operations such as signal_all. Condition variables make perfect sense without a monitor. A monitor is implemented using mutexes and condition variables, that is the relationship. I think it would be better to have an own article for conditation variables. --95.91.236.185 (talk) 11:37, 8 June 2010 (UTC)

Room_synchronization
Someone queried the difference between this article and Room_synchronization, can someone who knows more than I take a quick look at that page? 212.44.19.62 13:27, 21 April 2006 (UTC)

 * Room synchronization is quite different from monitors. With monitors there is only one room and only one process may be in it at a time. With room synchronization, there are a number of rooms and all processes that are in any room must be in the same room, but there is no limit on how many processes can be in that room. You could use a monitor to implement room synchronization.  —Preceding unsigned comment added by Theodore.norvell (talk • contribs) 20:30, 15 December 2008 (UTC)

Condition Variable example ?
I think the example is wrong: when doing wait, the queueSize is increased, but never decreased. I think there should be a queueSize-- following the waiting.up. -- Marc —The preceding unsigned comment was added by 193.49.124.107 (talk) 11:17, 15 May 2007 (UTC). Marc, you must be right, decreasing it that way is safe as it's protected, and else you would always have signal>0 once this is true once, therefore i correct the algorithm... Cédric —Preceding unsigned comment added by Gonnet (talk • contribs) 01:35, August 27, 2007 (UTC)

 * I have another question about the CV example code. Consider thread A running , after releasing   but before pending on  .  Thread A is pre-empted by thread B which does  , which runs to completion, leaving   "up" and   unlocked, meaning a possible lucky thread C could   and run straight through, bypassing the poor original thread A, even though C arrived at   after   ran and should therefore have had to wait until the next call to  .  The fact that A didn't get signalled isn't the end of the world, since it will catch the signal intended for C the next time and A's   hadn't returned anyway, so A didn't really expect to catch the first   -- the possible problem is C getting to skip a  . I may be missing something, perhaps specific to the monitor use case of CV's or to the assumed semantics of  , that makes this okay. Can you clarify what I'm missing? ScotS (talk) 23:55, 12 December 2007 (UTC)

Proposed rewrite
While I think the page is pretty good as it stands, I think it is missing a few things, in particular mention of Hoare's rules for using signal and wait. As a result I rewrote the article. The proposed rewrite is at http://en.wikipedia.org/wiki/User:Theodore.norvell/monitor. Please leave comments on it there. If there aren't too many negative comments that can't be easily responded to, I'll put it up here in a few weeks. Theodore.norvell (talk) 12:43, 31 December 2008 (UTC)

 * There were no negative comments, so I've gone ahead with the rewrite. Theodore.norvell (talk) 21:17, 3 February 2009 (UTC)

 * The rewrite is very good. TiagoCogumbreiro (talk) 16:28, 21 April 2009 (UTC)

According to Per Brinch Hansen, he didn't invent monitors
Not to cast flys into everyones drink, Per Brinch Hansen wrote in his books and notes that E. W. Dijkstra invented monitors. In turn, E. W. Dijkstra himself credits Per Brinch Hansen. You can of course simply ascribe this to the modesty of the authors, but take into account that these two men were good friends and close collaborators working on the same subject at the same time. I would say there is a good case for co-invention here, despite the common assertion that professor Hansen was the sole inventor. —Preceding unsigned comment added by 71.198.201.162 (talk) 20:03, 25 January 2009 (UTC)

 * I've changed it to credit Hoare and Brinch Hansen equally. I also mention that they were basing the concept of earlier ideas of Dijkstra as well as  themselves.  In Hansen's "Monitors and concurrent Pascal: a personal history", I didn't find any direct credit to Dijkstra.
 * If you read Dijkstra's "Hierarchical Ordering of Sequential Processes" you will find: "A secretary presents itself primarily as a bunch of non-reentrant routines with a common state space. But as far as the activity of the main program is concerned there is a difference between the routine of a secretary and a normal subroutine." It sounds a lot like a monitor. However, the way that a secretary puts processes to sleep or wakes them up it a bit different from the "wait" and "signal" of monitors. Theodore.norvell (talk) 21:32, 3 February 2009 (UTC)

It is not correct that Brinch Hansen credited Dijkstra for monitors. Brinch Hansen credited Dijkstra with being one of the original sources (along with Tony Hoare and himself) of the ideas that evolved into the monitor concept. It was Brinch Hansen and Hoare that actually developed the concept. I have updated the article to more accurate reflect the details of such. Jsg68x (talk) 21:18, 15 December 2015 (UTC)

Occupy a Monitor
I think we should be using the original usage of "inside" and "outside" of a monitor instead of using "occupy" and "unoccupying" monitors. TiagoCogumbreiro (talk) 16:28, 21 April 2009 (UTC)

 * Here's the reason that I changed it from "inside"/"outside" to "occupying"/"unoccupying". To me the word "inside" suggests that a thread is executing code that is "inside" of an object (or module). That is, in OO terms, a thread is "inside" whatever object is currently "this", and in, nonOO terms, it is "inside" whatever module is associated with its program counter. Say a thread calls a monitor's public method but then, before it returns, it calls a method in another object.  At this point the thread is inside the other object.  Is it still "inside" the original monitor?  Well maybe and maybe not.  Conversely if a thread calls a monitor and then calls "wait" is it "inside" the monitor?  Another reason I like "occupy" is that it then lets me talk about the module's "occupant". Theodore.norvell (talk) 10:03, 14 May 2009 (UTC)

Monitors as objects
Monitors are not necessarily objects. Although they are used in object-oriented programming languages like Java, a monitor is infact introduced by Hoare as a module. The reader does not need to know what an object in order to grasp the concept of a monitor. Understanding what a module is is easier than an object. TiagoCogumbreiro (talk) 16:28, 21 April 2009 (UTC)

 * You are quite right. (By the way, I learned monitors while using Concurrent Euclid, which was a modular language.) My thinking was that very few people these days would be familiar with the term "module" as used in Concurrent Euclid and Modula 2. And those who are would probably be familar with OO concepts as well. It would probably be a good idea to add a mention that in nonOO languages, monitors can be modules. By the way, in Concurrent Pascal, monitors were "classes" and could have multiple instances. Theodore.norvell (talk) 10:03, 14 May 2009 (UTC)

assertion? Or predicate?
Since this major rewrite, this article uses the word assertion several times, e.g. At least when it comes to the usage of the word assertion as defined within Wikipedia, is it correct speak of assertions throughout this monitor article? An assertion is a predicate that a developer expects to always be true. I would have expected predicate within the monitor article wherever assertion is used (also see conditional (programming)). --Abdull (talk) 18:30, 13 September 2010 (UTC)
 * "Threads attempting an operation may need to wait until some assertion P holds true."

 * I think this is a point worth considering. My first reaction was that Abdull is right, but that the word condition might be preferable to predicate. (Another possibility is boolean expression.)  However, I looked back at the literature and found that the main sources agree on assertion. For example from [Hoare 74] we have "With each condition variable b the programmer may associate an assertion B which describes the condition under which a program waiting on b wishes to be resumed." Hoare also uses the term condition at one point. From [Burh et al. 1995] we have "When programming with monitors, it is common to associate with each condition variable an assertion about the state of the monitor".  Admittedly, Burh et al. also use the term predicate.  Lampson and Redell [1980] use predicate. Theodore.norvell (talk) 15:38, 6 December 2010 (UTC)

 * I have to quibble with one thing that Abdull says. He says "an assertion is a predicate that a developer expects to always be true". I think what he meant is that an assertion is a predicate that a developer expects to be true at a specified place in the program. (As the wikipedia article Assertion (computing) currently says.) This fits with the current use of assertion in the monitor article, as the assertion associated with a condition variable is expected to be true after a wait and prior to a signal. The point is that the use of boolean expressions in monitors fits in the tradition of assertional reasoning that started with Hoare's 1969 An Axiomatic Basis for Programming paper. For me, preconditions, postconditions, and object invariants are all just varieties of assertions. Theodore.norvell (talk) 15:38, 6 December 2010 (UTC)

 * After taking another look, I agree that the article did use the word assertion in places that where it was probably not appropriate. I've changed these occurrences to condition. Theodore.norvell (talk) 17:17, 6 December 2010 (UTC)

Error in Monitor (synchronization)-Mesa.png
See the file's talk page. - Craig Pemberton 06:54, 1 March 2011 (UTC)
 * Fixed. Thanks Craig. Theodore.norvell (talk) 22:29, 11 May 2011 (UTC)

Small change in "Waiting and signaling"
I added some other (crappy) solutions to the busy waiting problem, just to expand a bit on the issue and how monitors are a great solution. Should I expand my explanation or remove it? It's my first wiki edit so I'm not sure on the policies.. — Preceding unsigned comment added by Mtzguido (talk • contribs) 18:09, 9 April 2013 (UTC)

Code typo
Thank you for catching and fixing my accidental errors with "isEmpty"/"isFull" in the pseudocode samples. I think you're correct; it probably was from copying and pasting and not proofreading enough. I'm glad people are checking. --Wykypydya (talk) 22:36, 1 November 2013 (UTC)

wording problem
> the next program counter to be executed

That makes no sense. The program counter cannot be executed. It points to code to be executed.

That sounds like an "edito" from thinking of saying "the program counter points to" and thinking of saying "the next program location to be executed" and mis-fusing the two. — Preceding unsigned comment added by 2620:0:1000:1501:1260:4BFF:FE68:1974 (talk) 22:58, 4 November 2013 (UTC)

Harmful Link
Hey guys, I never used to Edit something here, but i found a "bad" link down at the end of the Article. "Tutorial multiprocessing traps" <- this one directs you to one of the "MAKE XXXXX CASH IN 10 MINUTES!!!". I just dont wanna Edit and delete it, because I dont know if it would be okay. — Preceding unsigned comment added by 194.45.13.131 (talk) 15:17, 11 November 2013 (UTC)
 * Deleted. Theodore.norvell (talk) 00:03, 16 March 2014 (UTC)

New introduction
An edit in October 2013 substantially changed the introductory paragraphs. For example it added this sentence. "In essence, a monitor M = (m, c) is a pair of a mutex (lock) object m and a condition variable c." To me this doesn't look right. Since the start (i.e. Hoare's paper and Brinch Hansen's work) monitors have allowed an arbitrarily large set of condition variables. The restriction to one variable (as in Java) is one variation on the monitor concept. 142.134.201.203 (talk) 12:16, 16 March 2014 (UTC)
 * Thanks for pointing that out! I changed it. If you think anything else was better before the October 2013 edit feel free to restore it. Inverse Hypercube  (talk) 02:57, 6 April 2014 (UTC)

New sections
Several new subsections have been added to section 2, Condition variables. These are currently "2.2. Case study: classic bounded producer/consumer problem", "2.3 Condition variables", "2.4 Monitor usage", "2.5 synchronization primitives", and "2.6 Semaphore". There are some good ideas here, but I think that they mostly serve to make an already long and complex article longer and more complex. They also move the article more toward's a "how to", as noted by the warning "This article contains instructions, advice, or how-to content. The purpose of Wikipedia is to present facts, not to train. " that now sits in front of the article. My suggestion is to revert the article back to its earlier structure, while keeping only what is most useful from the added material. Maybe the new material can be moved elsewhere: e.g. wikibooks Theodore.norvell (talk) 13:21, 16 March 2014 (UTC)

please truncate the article
this article is very lengthy. it should be shrunk and summarized.

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title: Talk:Monitor (synchronization)


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Virgin of Montserrat

Our Lady of Montserrat or the Virgin of Montserrat (Mare de Déu de Montserrat) is a Marian title associated with a statue of the Madonna and Child venerated at the Santa Maria de Montserrat monastery on Montserrat mountain in Catalonia, Spain. She is the patroness saint of Catalonia, an honour she shares with Saint George (Sant Jordi in Catalan). Miracles have been attributed to the statue. Pope Leo XIII granted the image a canonical coronation on 11 September 1881. The image is one of the Black Madonnas of Europe, hence its familiar Catalan name, La Moreneta ("the little dark-skinned one" or "the little dark one"). Believed by some to have been carved in Jerusalem in the early days of the Church, it is more likely a Romanesque sculpture in wood from the late 12th century.

An 18th-century polychromed statue of the same image is also displayed in Saint Peter's basilica, previously stored in the Vatican Museums, which was gifted by President of Brazil João Goulart on the papal election of Pope Paul VI in 1963. The image has been on display for papal masses since the pontificate of Pope Benedict XVI.

History
The mountain of Montserrat has been of religious significance since pre-Christian times, when the Romans built a temple to honor the Roman goddess Venus.

By one account, the image of the Madonna was moved to Montserrat in 718, to avoid the danger posed by invading Saracens.

Legend has it that the Benedictine monks could not move the statue to construct their monastery, choosing to instead build around it. The statue's sanctuary is located at the rear of the chapel, where an altar of gold surrounds the icon, and is now a site of pilgrimage.

Description
The 95-cm (38-inch) wooden statue shows evidence of Byzantine conventional and stylized form, and is painted in polychrome. The reliquary statue of Sainte-Foy in Conques (southern France) may have been a model. The art-historical designation for this type of pose is called "Throne of Wisdom". The body is thin, the face elongated. She holds an orb of the earth in her right hand. The Child's hand is raised in a formalized and traditional Eastern blessing.

In 2001, renovators working for the government observed that the black hands and face of La Moreneta had over the centuries undergone a change in colour. They attribute the change—from a lighter tone to black—either to prolonged exposure to candle smoke or a chemical reaction caused by a varnish used as a paint sealant. The statue was repainted black by successive generations of restorers. A series of tests, including X-rays, revealed the statue's original colour and also showed that the last repainting took place at the turn of the 18th century.

Veneration
After making a pilgrimage to Our Lady of Montserrat around 1203, Peter Nolasco went to Barcelona where he began to practice various works of charity. Nolasco became concerned with the plight of Christians captured in Moorish raids and decided to establish the Merecedarians, a religious order to succor these unfortunates.

Upon his recovery from battle wounds, Ignatius of Loyola visited the Benedictine monastery of Montserrat (on 25 March 1522), where he laid down his military accoutrements before the image. He then led a period of asceticism before later founding the Society of Jesus.

The hymn to the Virgin of Montserrat, known as "el Virolai" and sung at noon each day by the Escolania de Montserrat boys' choir, begins with the words: "Rosa d’abril, Morena de la serra..." (Rose of April, dark-skinned lady of the mountain...). Therefore, this virgin is sometimes also known as the "Rosa d'abril". Her feast is kept on April 27.

Patronage
The statue has always been considered one of the most celebrated images in Spain. "La Moreneta" is one of Catalonia's two patron saints, together with Sant Jordi (Saint George).

Given name
The name Montserrat, traditionally abbreviated to Serrat, Rat, Rateta, Tat or Tóna, and also to Montse in recent years, is a popular girl's name in Catalonia.

title: Virgin of Montserrat


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1934 in Norwegian football

Results from Norwegian football in 1934. See also 1933 in Norwegian football and 1935 in Norwegian football

Class A of local association leagues
Class A of local association leagues (kretsserier) is the predecessor of a national league competition.

 * 1In the following season, Lofoten og Vesterålen local association split into Salten and Lofoten og Vesterålen.

National team
June 10: Norway – Austria 4-0, friendly

July 1: Sweden – Norway 3-3, friendly

September 2: Norway – Finland 4-2, friendly

September 23: Norway – Denmark 3-1, friendly

title: 1934 in Norwegian football


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USS Jeannette

Two ships of the United States Navy have borne the name USS Jeannette:

 * USS Jeannette (1878), was formerly a Royal Navy gunboat HMS Pandora, launched in 1861, purchased by the US Navy in 1878 for an expedition to the North Pole, and sunk in 1881 in the Arctic Ocean
 * USS Jeannette (SP-149), was launched in 1905, acquired by the US Navy in 1917 for service as a patrol craft during World War I, and sold in 1920

title: USS Jeannette


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Henrhyd Falls

Henrhyd Falls (Welsh: Sgwd Henrhyd) in the Brecon Beacons National Park, Wales, is the tallest waterfall in southern Wales with a drop of 90 ft. It lies on National Trust land, in the traditional county of Brecknockshire (administered as part of the unitary authority of Powys). The nearest settlement to it is Coelbren, on the road between Glynneath and Abercraf. Though not in the core of the area, it is considered by many to constitute a part of Wales' celebrated Waterfall Country.

Geology
The falls occur where the small river, the Nant Llech drops over the faulted edge of a hard sandstone known as the Farewell Rock which forms the top half of the rock face and which forms the base of the South Wales Coal Measures. Beneath this, and forming much of the recessed portion of the drop, is the Subcrenatum Sandstone separated from the Farewell Rock above by the Subcrenatum marine band. Both the marine band and sandstone are part of the Bishopston Mudstone Formation included within the Marros Group, the modern name in South Wales for the assemblage of strata that was traditionally known as the Millstone Grit series. A stream gully between the descent path and the falls marks the line of the Henrhyd Fault which is responsible for the falls' presence.

One of the area's most famous visitors was Sir William Edmond Logan (later head of the Geological Survey of Canada). In 1833 he carried out detailed geological survey work in the area, discovering a mile (1.5 km) down the valley from the foot of the falls the fossil trees which now stand in the garden at Swansea Museum. They are 'Object 1' in their 'History of Swansea in 20 Objects'.

Access
The waterfall is reached after a steep walk down into the valley from the car park established by the National Trust, and is a popular spot to visit. A further footpath leads steeply down to the falls via the opposite side of the valley, accessed from Dol Henrhyd, the road that goes to Coelbren village.

authors: غیر معمولی معمول

title: Henrhyd Falls


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Geodesics in general relativity

In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational forces is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting a star is the projection of a geodesic of the curved four-dimensional (4-D) spacetime geometry around the star onto three-dimensional (3-D) space.

Mathematical expression
The full geodesic equation is $$ {d^2 x^\mu \over ds^2}+\Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}=0\ $$ where s is a scalar parameter of motion (e.g. the proper time), and $$ \Gamma^\mu {}_{\alpha \beta}$$ are Christoffel symbols (sometimes called the affine connection coefficients or Levi-Civita connection coefficients) symmetric in the two lower indices. Greek indices may take the values: 0, 1, 2, 3 and the summation convention is used for repeated indices $$\alpha$$ and $$\beta$$. The quantity on the left-hand-side of this equation is the acceleration of a particle, so this equation is analogous to Newton's laws of motion, which likewise provide formulae for the acceleration of a particle. The Christoffel symbols are functions of the four spacetime coordinates and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation.

Equivalent mathematical expression using coordinate time as parameter
So far the geodesic equation of motion has been written in terms of a scalar parameter s. It can alternatively be written in terms of the time coordinate, $$t \equiv x^0$$ (here we have used the triple bar to signify a definition). The geodesic equation of motion then becomes: $$ {d^2 x^\mu \over dt^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over dt}{d x^\beta \over dt}+ \Gamma^0 {}_{\alpha \beta}{d x^\alpha \over dt}{d x^\beta \over dt}{d x^\mu \over dt}\ .$$

This formulation of the geodesic equation of motion can be useful for computer calculations and to compare General Relativity with Newtonian Gravity. It is straightforward to derive this form of the geodesic equation of motion from the form which uses proper time as a parameter using the chain rule. Notice that both sides of this last equation vanish when the mu index is set to zero. If the particle's velocity is small enough, then the geodesic equation reduces to this: $$ {d^2 x^n \over dt^2} =- \Gamma^n {}_{00}.$$

Here the Latin index n takes the values [1,2,3]. This equation simply means that all test particles at a particular place and time will have the same acceleration, which is a well-known feature of Newtonian gravity. For example, everything floating around in the International Space Station will undergo roughly the same acceleration due to gravity.

Derivation directly from the equivalence principle
Physicist Steven Weinberg has presented a derivation of the geodesic equation of motion directly from the equivalence principle. The first step in such a derivation is to suppose that a free falling particle does not accelerate in the neighborhood of a point-event with respect to a freely falling coordinate system ($$X^\mu$$). Setting $$T \equiv X^0$$, we have the following equation that is locally applicable in free fall: $$ {d^2 X^\mu \over dT^2} = 0 .$$ The next step is to employ the multi-dimensional chain rule. We have: $$ {d X^\mu \over dT}={d x^\nu \over dT} {\partial X^\mu \over \partial x^\nu} $$ Differentiating once more with respect to the time, we have: $$ {d^2 X^\mu \over dT^2}={d^2 x^\nu \over dT^2} {\partial X^\mu \over \partial x^\nu} + {d x^\nu \over dT} {d x^\alpha \over dT} {\partial^2 X^\mu \over \partial x^\nu\partial x^\alpha}$$ We have already said that the left-hand-side of this last equation must vanish because of the Equivalence Principle. Therefore: $$ {d^2 x^\nu \over dT^2} {\partial X^\mu \over \partial x^\nu} =- {d x^\nu \over dT} {d x^\alpha \over dT} {\partial^2 X^\mu \over \partial x^\nu\partial x^\alpha}$$ Multiply both sides of this last equation by the following quantity: $$ {\partial x^\lambda \over \partial X^\mu}$$ Consequently, we have this: $$ {d^2 x^\lambda \over dT^2} = - {d x^\nu \over dT} {d x^\alpha \over dT} \left[{\partial^2 X^\mu \over \partial x^\nu\partial x^\alpha} {\partial x^\lambda \over \partial X^\mu}\right] .$$

Weinberg defines the affine connection as follows: $$\Gamma^\lambda {}_{\nu \alpha} = \left[{\partial^2 X^\mu \over \partial x^\nu\partial x^\alpha} {\partial x^\lambda \over \partial X^\mu}\right]$$ which leads to this formula: $$ {d^2 x^\lambda \over dT^2} = - \Gamma^{\lambda}_{\nu \alpha} {d x^\nu \over dT} {d x^\alpha \over dT} .$$

Notice that, if we had used the proper time “s” as the parameter of motion, instead of using the locally inertial time coordinate “T”, then our derivation of the geodesic equation of motion would be complete. In any event, let us continue by applying the one-dimensional chain rule: $$ {d^2 x^\lambda \over d t^2} \left( \frac{d t}{d T} \right)^2 + {d x^\lambda \over d t} \frac{d^2 t}{d T^2} = - \Gamma^{\lambda}_{\nu \alpha} {d x^\nu \over d t} {d x^\alpha \over d t} \left( \frac{d t}{d T} \right)^2 .$$ $$ {d^2 x^\lambda \over d t^2} + {d x^\lambda \over d t} \frac{d^2 t}{d T^2} \left( \frac{d T}{d t} \right)^2 = - \Gamma^{\lambda}_{\nu \alpha} {d x^\nu \over d t} {d x^\alpha \over d t} .$$

As before, we can set $$t \equiv x^0$$. Then the first derivative of x0 with respect to t is one and the second derivative is zero. Replacing λ with zero gives: $$ \frac{d^2 t}{d T^2} \left( \frac{d T}{d t} \right)^2 = - \Gamma^{0}_{\nu \alpha} {d x^\nu \over d t} {d x^\alpha \over d t} .$$

Subtracting d xλ / d t times this from the previous equation gives: $$ {d^2 x^\lambda \over dt^2} = - \Gamma^{\lambda}_{\nu \alpha} {d x^\nu \over dt} {d x^\alpha \over dt} + \Gamma^{0}_{\nu \alpha} {d x^\nu \over dt} {d x^\alpha \over dt}{d x^\lambda \over dt} $$ which is a form of the geodesic equation of motion (using the coordinate time as parameter).

The geodesic equation of motion can alternatively be derived using the concept of parallel transport.

Deriving the geodesic equation via an action
We can (and this is the most common technique) derive the geodesic equation via the action principle. Consider the case of trying to find a geodesic between two timelike-separated events.

Let the action be $$S = \int ds$$ where $$ds=\sqrt{-g_{\mu\nu}(x) \, dx^\mu \, dx^\nu}$$ is the line element. There is a negative sign inside the square root because the curve must be timelike. To get the geodesic equation we must vary this action. To do this let us parameterize this action with respect to a parameter $$\lambda$$. Doing this we get: $$S=\int\sqrt{-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}} \, d\lambda$$

We can now go ahead and vary this action with respect to the curve $$x^{\mu}$$. By the principle of least action we get: $$0=\delta S=\int\delta\left(\sqrt{-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}}\right) \, d\lambda =\int\frac{\delta\left(-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}\right)}{2\sqrt{-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}}}d\lambda$$

Using the product rule we get: $$0=\int\left(\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\tau}\delta g_{\mu\nu}+g_{\mu\nu}\frac{d\delta x^\mu}{d\lambda}\frac{dx^\nu}{d\tau} + g_{\mu\nu} \frac{dx^\mu}{d\tau} \frac{d\delta x^\nu}{d\lambda}\right) \, d\lambda = \int\left(\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\tau} \partial_\alpha g_{\mu\nu} \delta x^\alpha +2g_{\mu\nu}\frac{d\delta x^\mu}{d\lambda}\frac{dx^\nu}{d\tau}\right) \, d\lambda $$ where $$ \frac{d\tau}{d\lambda} = \sqrt{-g_{\mu\nu}\frac{dx^\mu}{d\lambda}\frac{dx^\nu}{d\lambda}} $$

Integrating by-parts the last term and dropping the total derivative (which equals to zero at the boundaries) we get that: $$0=\int \left(\frac{dx^\mu}{d\tau}\frac{dx^\nu}{d\tau}\partial_\alpha g_{\mu\nu}\delta x^\alpha-2\delta x^\mu\frac{d}{d\tau} \left(g_{\mu\nu} \frac{dx^\nu}{d\tau}\right)\right) \, d\tau = \int \left(\frac{dx^{\mu}}{d\tau}\frac{dx^\nu}{d\tau} \partial_\alpha g_{\mu\nu}\delta x^\alpha-2\delta x^\mu \partial_\alpha g_{\mu\nu}\frac{dx^\alpha}{d\tau}\frac{dx^\nu}{d\tau}-2\delta x^\mu g_{\mu\nu}\frac{d^2 x^\nu}{d\tau^2}\right) \, d\tau $$

Simplifying a bit we see that: $$0=\int \left(-2g_{\mu\nu}\frac{d^2 x^\nu}{d\tau^2}+\frac{dx^\alpha}{d\tau}\frac{dx^\nu}{d\tau} \partial_\mu g_{\alpha\nu} - 2\frac{dx^\alpha}{d\tau} \frac{dx^\nu}{d\tau} \partial_\alpha g_{\mu\nu}\right) \delta x^\mu d\tau $$ so, $$0=\int \left(-2g_{\mu\nu}\frac{d^2 x^\nu}{d\tau^2}+\frac{dx^\alpha}{d\tau}\frac{dx^\nu}{d\tau}\partial_\mu g_{\alpha\nu}-\frac{dx^\alpha}{d\tau}\frac{dx^\nu}{d\tau}\partial_\alpha g_{\mu\nu}-\frac{dx^\nu}{d\tau} \frac{dx^\alpha}{d\tau} \partial_\nu g_{\mu\alpha}\right) \delta x^\mu \, d\tau $$ multiplying this equation by $-\frac{1}{2}$ we get: $$0=\int \left(g_{\mu\nu}\frac{d^2 x^\nu}{d\tau^2}+\frac{1}{2} \frac{dx^\alpha}{d\tau}\frac{dx^\nu}{d\tau}\left(\partial_\alpha g_{\mu\nu} + \partial_\nu g_{\mu\alpha}-\partial_\mu g_{\alpha\nu}\right)\right) \delta x^\mu \, d\tau $$

So by Hamilton's principle we find that the Euler–Lagrange equation is $$g_{\mu\nu}\frac{d^{2}x^{\nu}}{d\tau^{2}}+\frac{1}{2}\frac{dx^{\alpha}}{d\tau}\frac{dx^{\nu}}{d\tau}\left(\partial_{\alpha}g_{\mu\nu}+\partial_{\nu}g_{\mu\alpha}-\partial_{\mu}g_{\alpha\nu}\right)=0$$

Multiplying by the inverse metric tensor $$g^{\mu\beta}$$ we get that $$\frac{d^{2}x^{\beta}}{d\tau^{2}}+\frac{1}{2}g^{\mu\beta}\left(\partial_{\alpha}g_{\mu\nu}+\partial_{\nu}g_{\mu\alpha}-\partial_{\mu}g_{\alpha\nu}\right)\frac{dx^{\alpha}}{d\tau}\frac{dx^{\nu}}{d\tau}=0$$

Thus we get the geodesic equation: $$\frac{d^{2}x^{\beta}}{d\tau^{2}}+\Gamma^{\beta}{}_{\alpha\nu}\frac{dx^{\alpha}}{d\tau}\frac{dx^{\nu}}{d\tau} = 0$$ with the Christoffel symbol defined in terms of the metric tensor as $$\Gamma^{\beta}{}_{\alpha\nu}=\frac{1}{2}g^{\mu\beta}\left(\partial_{\alpha}g_{\mu\nu}+\partial_{\nu}g_{\mu\alpha}-\partial_{\mu}g_{\alpha\nu}\right)$$

(Note: Similar derivations, with minor amendments, can be used to produce analogous results for geodesics between light-like or space-like separated pairs of points.)

Equation of motion may follow from the field equations for empty space
Albert Einstein believed that the geodesic equation of motion can be derived from the field equations for empty space, i.e. from the fact that the Ricci curvature vanishes. He wrote: "It has been shown that this law of motion — generalized to the case of arbitrarily large gravitating masses — can be derived from the field equations of empty space alone. According to this derivation the law of motion is implied by the condition that the field be singular nowhere outside its generating mass points." and One of the imperfections of the original relativistic theory of gravitation was that as a field theory it was not complete; it introduced the independent postulate that the law of motion of a particle is given by the equation of the geodesic. A complete field theory knows only fields and not the concepts of particle and motion. For these must not exist independently from the field but are to be treated as part of it. On the basis of the description of a particle without singularity, one has the possibility of a logically more satisfactory treatment of the combined problem: The problem of the field and that of the motion coincide. Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from the field equations to describe the motion of a gravitational singularity, but this claim remains disputed. According to David Malament, “Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein’s equation (or the conservation principle) alone. Other assumptions are needed to derive the theorems in question.” Less controversial is the notion that the field equations determine the motion of a fluid or dust, as distinguished from the motion of a point-singularity.

Extension to the case of a charged particle
In deriving the geodesic equation from the equivalence principle, it was assumed that particles in a local inertial coordinate system are not accelerating. However, in real life, the particles may be charged, and therefore may be accelerating locally in accordance with the Lorentz force. That is: $$ {d^2 X^\mu \over ds^2} = {q \over m} {F^{\mu \beta}} {d X^\alpha \over ds}{\eta_{\alpha \beta}}.$$ with $$ {\eta_{\alpha \beta}}{d X^\alpha \over ds}{d X^\beta \over ds}=-1.$$

The Minkowski tensor $$\eta_{\alpha \beta}$$ is given by: $$\eta_{\alpha \beta} = \begin{pmatrix}-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}$$

These last three equations can be used as the starting point for the derivation of an equation of motion in General Relativity, instead of assuming that acceleration is zero in free fall. Because the Minkowski tensor is involved here, it becomes necessary to introduce something called the metric tensor in General Relativity. The metric tensor g is symmetric, and locally reduces to the Minkowski tensor in free fall. The resulting equation of motion is as follows: $$ {d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}\ +{q \over m} {F^{\mu \beta}} {d x^\alpha \over ds}{g_{\alpha \beta}}.$$ with $$ {g_{\alpha \beta}}{d x^\alpha \over ds}{d x^\beta \over ds}=-1.$$

This last equation signifies that the particle is moving along a timelike geodesic; massless particles like the photon instead follow null geodesics (replace −1 with zero on the right-hand side of the last equation). It is important that the last two equations are consistent with each other, when the latter is differentiated with respect to proper time, and the following formula for the Christoffel symbols ensures that consistency: $$\Gamma^{\lambda}{}_{\alpha\beta}=\frac{1}{2}g^{\lambda \tau} \left(\frac{\partial g_{\tau\alpha}}{\partial x^\beta} + \frac{\partial g_{\tau\beta}}{\partial x^{\alpha}} - \frac{\partial g_{\alpha\beta}}{\partial x^{\tau}} \right) $$ This last equation does not involve the electromagnetic fields, and it is applicable even in the limit as the electromagnetic fields vanish. The letter g with superscripts refers to the inverse of the metric tensor. In General Relativity, indices of tensors are lowered and raised by contraction with the metric tensor or its inverse, respectively.

Geodesics as curves of stationary interval
A geodesic between two events can also be described as the curve joining those two events which has a stationary interval (4-dimensional "length"). Stationary here is used in the sense in which that term is used in the calculus of variations, namely, that the interval along the curve varies minimally among curves that are nearby to the geodesic.

In Minkowski space there is only one geodesic that connects any given pair of events, and for a time-like geodesic, this is the curve with the longest proper time between the two events. In curved spacetime, it is possible for a pair of widely separated events to have more than one time-like geodesic between them. In such instances, the proper times along several geodesics will not in general be the same. For some geodesics in such instances, it is possible for a curve that connects the two events and is nearby to the geodesic to have either a longer or a shorter proper time than the geodesic.

For a space-like geodesic through two events, there are always nearby curves which go through the two events that have either a longer or a shorter proper length than the geodesic, even in Minkowski space. In Minkowski space, the geodesic will be a straight line. Any curve that differs from the geodesic purely spatially (i.e. does not change the time coordinate) in any inertial frame of reference will have a longer proper length than the geodesic, but a curve that differs from the geodesic purely temporally (i.e. does not change the space coordinates) in such a frame of reference will have a shorter proper length.

The interval of a curve in spacetime is $$ l = \int \sqrt{\left|g_{\mu \nu} \dot x^\mu \dot x^\nu \right|} \, ds\ .$$

Then, the Euler–Lagrange equation, $$ {d \over ds} {\partial \over \partial \dot x^\alpha} \sqrt{\left| g_{\mu \nu} \dot x^\mu \dot x^\nu \right|} = {\partial \over \partial x^\alpha} \sqrt{\left| g_{\mu \nu} \dot x^\mu \dot x^\nu \right|} \ ,$$ becomes, after some calculation, $$ 2\left(\Gamma^\lambda {}_{\mu \nu} \dot x^\mu \dot x^\nu + \ddot x^\lambda\right) = U^\lambda {d \over ds} \ln |U_\nu U^\nu| \ ,$$ where $$ U^\mu = \dot x^\mu .$$

The goal being to find a curve for which the value of $$ l = \int d\tau = \int {d\tau \over d\phi} \, d\phi = \int \sqrt \, d\phi = \int \sqrt \, d\phi = \int f \, d\phi$$ is stationary, where $$ f = \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu} $$ such goal can be accomplished by calculating the Euler–Lagrange equation for f, which is $$ {d \over d\tau} {\partial f \over \partial \dot x^\lambda} = {\partial f \over \partial x^\lambda} .$$

Substituting the expression of f into the Euler–Lagrange equation (which makes the value of the integral l stationary), gives $$ {d \over d\tau} {\partial \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu} \over \partial \dot x^\lambda} = {\partial \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu} \over \partial x^\lambda} $$

Now calculate the derivatives: $$\begin{align} {d \over d\tau} \left( {-g_{\mu \nu} {\partial \dot x^\mu \over \partial \dot x^\lambda} \dot x^\nu - g_{\mu \nu} \dot x^\mu {\partial \dot x^\nu \over \partial \dot x^\lambda} \over 2 \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} \right) &= {-g_{\mu \nu, \lambda} \dot x^\mu \dot x^\nu \over 2 \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} && (1) \\[1ex] {d \over d\tau} \left( {g_{\mu \nu} \delta^\mu {}_\lambda \dot x^\nu + g_{\mu \nu} \dot x^\mu \delta^\nu {}_\lambda \over 2 \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} \right) &= {g_{\mu \nu, \lambda} \dot x^\mu \dot x^\nu \over 2 \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} && (2) \\[1ex] {d \over d\tau} \left( {g_{\lambda \nu} \dot x^\nu + g_{\mu \lambda} \dot x^\mu \over \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} \right) &= {g_{\mu \nu, \lambda} \dot x^\mu \dot x^\nu \over \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} && (3) \\[1ex] {\sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu} {d \over d\tau} (g_{\lambda \nu} \dot x^\nu + g_{\mu \lambda} \dot x^\mu) - (g_{\lambda \nu} \dot x^\nu + g_{\mu \lambda} \dot x^\mu) {d \over d\tau} \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu} \over -g_{\mu \nu} \dot x^\mu \dot x^\nu} &= {g_{\mu \nu, \lambda} \dot x^\mu \dot x^\nu \over \sqrt{-g_{\mu \nu} \dot x^\mu \dot x^\nu}} && (4) \\[1ex] {(-g_{\mu \nu} \dot x^\mu \dot x^\nu) {d \over d\tau} (g_{\lambda \nu} \dot x^\nu + g_{\mu \lambda} \dot x^\mu) + {1 \over 2} (g_{\lambda \nu} \dot x^\nu + g_{\mu \lambda} \dot x^\mu) {d \over d\tau} (g_{\mu \nu} \dot x^\mu \dot x^\nu) \over -g_{\mu \nu} \dot x^\mu \dot x^\nu} &= g_{\mu \nu ,\lambda} \dot x^\mu \dot x^\nu && (5) \end{align} $$ $$\begin{align} & (g_{\mu \nu} \dot x^\mu \dot x^\nu) (g_{\lambda \nu ,\mu} \dot x^\nu \dot x^\mu + g_{\mu \lambda ,\nu} \dot x^\mu \dot x^\nu + g_{\lambda \nu} \ddot x^\nu + g_{\lambda \mu} \ddot x^\mu) \\ & = (g_{\mu \nu ,\lambda} \dot x^\mu \dot x^\nu) (g_{\alpha \beta} \dot x^\alpha \dot x^\beta) + {1 \over 2} (g_{\lambda \nu} \dot x^\nu + g_{\lambda \mu} \dot x^\mu) {d \over d\tau} (g_{\mu \nu} \dot x^\mu \dot x^\nu) \qquad \qquad (6) \end{align} $$ $$ g_{\lambda \nu ,\mu} \dot x^\mu \dot x^\nu + g_{\lambda \mu ,\nu} \dot x^\mu \dot x^\nu - g_{\mu \nu ,\lambda} \dot x^\mu \dot x^\nu + 2 g_{\lambda \mu} \ddot x^\mu = {\dot x_\lambda {d \over d\tau} (g_{\mu \nu} \dot x^\mu \dot x^\nu) \over g_{\alpha \beta} \dot x^\alpha \dot x^\beta} \qquad \qquad (7) $$ $$ 2(\Gamma_{\lambda \mu \nu} \dot x^\mu \dot x^\nu + \ddot x_\lambda) = {\dot x_\lambda {d \over d\tau} (\dot x_\nu \dot x^\nu) \over \dot x_\beta \dot x^\beta} = {U_\lambda {d \over d\tau} (U_\nu U^\nu) \over U_\beta U^\beta} = U_\lambda {d \over d\tau} \ln |U_\nu U^\nu| \qquad \qquad (8) $$

This is just one step away from the geodesic equation.

If the parameter s is chosen to be affine, then the right side of the above equation vanishes (because $$U_\nu U^\nu$$ is constant). Finally, we have the geodesic equation $$ \Gamma^\lambda {}_{\mu \nu} \dot x^\mu \dot x^\nu + \ddot x^\lambda = 0\ .$$

Derivation using autoparallel transport
The geodesic equation can be alternatively derived from the autoparallel transport of curves. The derivation is based on the lectures given by Frederic P. Schuller at the We-Heraeus International Winter School on Gravity & Light.

Let $$ (M,O,A,\nabla)$$ be a smooth manifold with connection and $$\gamma $$ be a curve on the manifold. The curve is said to be autoparallely transported if and only if $$\nabla_{v_{\gamma}}v_{\gamma}=0 $$.

In order to derive the geodesic equation, we have to choose a chart $$(U,x) \in A$$: $$ \nabla_{\dot \gamma^i \frac{\partial}{\partial x^i}} \left( \dot \gamma^m \frac{\partial}{\partial x^m} \right)=0 $$ Using the $$ C^{\infty} $$ linearity and the Leibniz rule: $$ \dot \gamma^i \left( \nabla_{\frac{\partial}{\partial x^i}} \dot \gamma^m \right) \frac{\partial}{\partial x^m}+\dot \gamma^i \dot \gamma^m \nabla_{\frac{\partial}{\partial x^i}}\left( \frac{\partial}{\partial x^m} \right) = 0 $$

Using how the connection acts on functions ($$\dot \gamma^m $$) and expanding the second term with the help of the connection coefficient functions: $$ \dot \gamma^i \frac{ \partial \dot \gamma^m}{\partial x^i} \frac{\partial}{\partial x^m}+\dot \gamma^i \dot \gamma^m \Gamma^{q}_{im} \frac{\partial}{\partial x^q}=0 $$

The first term can be simplified to $$\ddot \gamma^m \frac{\partial}{\partial x^m} $$. Renaming the dummy indices: $$ \ddot \gamma^q \frac{\partial}{\partial x^q}+\dot \gamma^i \dot \gamma^m \Gamma^{q}_{im} \frac{\partial}{\partial x^q}=0 $$

We finally arrive to the geodesic equation: $$ \ddot \gamma^q +\dot \gamma^i \dot \gamma^m \Gamma^{q}_{im}=0 $$

title: Geodesics in general relativity


text:
Wikipedia:Articles for deletion/Jerry Hamilton

 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. Golbez 03:14, Jun 19, 2005 (UTC)

Jerry Hamilton
Vanity. --W(t) 16:51, 2005 Jun 13 (UTC)

 * Delete Vanity. Unless the Mason's come to get me. Will nobody help the widow's son? Leithp 18:40, 13 Jun 2005 (UTC)
 * Delete it! Brighterorange 18:43, 13 Jun 2005 (UTC)
 * (sigh) It's possible that he was involved in some historically significant rulings or events, but this is one of those local history bits. Essentially, this article boils down to "Some dude with a nice house who really liked being a Mason."  Not encyclopedic. Delete. Geogre 19:01, 13 Jun 2005 (UTC)
 * Delete nn vanity. --Etacar11 23:58, 13 Jun 2005 (UTC)
 * Delete vanity. JamesBurns 06:56, 14 Jun 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 .


text:
Wikipedia:Peer review/Éamon de Valera/archive1

Eamon de Valera
One of the most important Irish politicians of all time, critical in the foundation of the Republic of Ireland. Talrias (t | e | c) 16:51, 13 Jun 2005 (UTC)
 * It's a great article. The only thing I'm thinking is that perhaps the article strays a bit from deV's biography and goes into such detail on the historical background that we begin to lose the focus a bit. I'm thinking here especially of "Neutrality in WWII" which is good and very interesting, but maybe should be in a History of Ireland article. I'd also echo the note from the FAC that maybe there might be a better way to structure the TOC. PRiis 20:49, 14 Jun 2005 (UTC)
 * Oops, forgot to mention--the article should list its sources, too. PRiis 20:57, 14 Jun 2005 (UTC)