Wikipedia:Featured article candidates/Introduction to general relativity


 * The following is an archived discussion of a featured article nomination. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.

The article was promoted 01:59, 24 July 2007.

Introduction to general relativity
This article has evolved quite a lot over the past months, and it has recently undergone a thorough peer review here. Having checked the FA criteria, I'm confident it's now a promising candidate for featured status. The topic is certainly important - general relativity is one of the fundamental theories of modern physics; on the other hand, the main article general relativity is necessarily quite technical. This article is meant to fill the gap and provide an accessible introduction that is suitable for a general audience. As I have contributed to the article's recent overhaul, this is a self-nomination. Markus Poessel 13:46, 9 July 2007 (UTC)


 * Strong support and thank you so much. I've been trying to get my head around 'the' big theory of the 20th century for years, to no avail. This article, for some reason, actually makes sense! Nicely illustrated. The only comments I'd make is 1. "the gravitational deflection of light:" - isn't this effect observed when massive bodies pass in front of stars making them appear to move slightly to the observer - Is this observed during eclipses? perhaps a mention. 2. I did once read an analogy of curved spacetime as like a gridded sheet of rubber stretched flat onto which heavy (massive) spheres were placed. Objects moving along the sheet were then deflected in their paths by the resultant curvatures. I've no idea how accurate the analogy is, but it made for a useful graphic. Thanks again. --Joopercoopers 15:05, 10 July 2007 (UTC)


 * You're welcome - and thanks for your support! Gravitational deflection of light is indeed observed as you describe, and I have now included a sentence about eclipses – thanks for the suggestion! I would like to keep the rubber sheet out of this, though. In my opinion (and in the opinion of all relativists to whom I have talked about this), it creates more problems than it solves.  It has a number of confusing aspects (e.g. if gravity is the distortion of the rubber sheet, what makes the heavy sphere sink into the rubber sheet?) and is somewhat misleading in its main physics message (in fact, the deflection of objects that are forced to orbit around the sun is due almost exclusively to time distortions - the rubber sheet image suggests [wrongly] that space distortions are to blame). Markus Poessel 16:54, 10 July 2007 (UTC)
 * I'm all for keeping rubber sheets out of most discussions! :-) --Joopercoopers 15:08, 11 July 2007 (UTC)


 * Oppose Comment (see below). This piece strikes a wonderful balance between theoretical literacy and accessibility. While I can image the pitched battles that must have occurred on general relativity with regard to striking such a balance, Wikipedia is not a textbook — information on the same topic shouldn't be mirrored across several pages. I would, however, suggest introducing this page to Simple English wikipedia. Madcoverboy 05:03, 11 July 2007 (UTC)
 * The creation of introductory articles is explicitly recommended by Make technical articles accessible. Since the example given on that page is Introduction to special relativity, it would be difficult to argue that Introduction to general relativity does not meet the same criteria. That style guideline, by the way, is not in conflict with Wikipedia is not a textbook, which only tells us that an article should not read like a textbook – it shouldn't be written in textbook style, with leading questions, step-by-step problem solutions, and so on. Markus Poessel 07:49, 11 July 2007 (UTC)
 * Rather than being "explicitly recommended" the page reads "it may be appropriate...(depending on the topic and the amount of interest in it)." I do not believe it is appropriate when it seems that little has been done to improve the primary page before forking the content. The general relativity page, while thorough, is not as readable as this intro article and lacks examples that this article has. A similar situation applies to the special relativity page and the other "introduction" pages I reviewed. I don't understand how the content in both the "primary" and "introduction" pages couldn't be merged and with judicious use of summary style with regard to both technical formulae as well as explanations/examples to make one excellent page providing an overview on the topic.Madcoverboy 14:46, 11 July 2007 (UTC)
 * Come on chaps, this is a mindbendingly difficult subject for the lay reader and a good case for WP:IAR - the rules that apply to articles about computer games shouldn't be applied here. I'm the last to suggest we dumb down wikipedia but; 1. The general relativity article isn't here for consideration, it's the introduction. 2. This is a very important subject which most people don't have a grasp of. 3. to have a concise, accessible text for the lay reader is 'an example of our best work'. --Joopercoopers 15:18, 11 July 2007 (UTC)
 * Especially since I don't think we are ignoring the rules. The guideline lists Introduction to special relativity as its example for a case where a "trampoline" page is appropriate. It's hard to see why general relativity should be treated differently. Markus Poessel 18:20, 11 July 2007 (UTC)
 * Having done more research and searching, its apparent that this phenomena of "Introduction to x" is more prevalent than I thought. Per WP:WIAFA, an "introduction" article should fail 1(b) because it is necessarily non-comprehensive if it is just an introduction. In other words, if it is an introduction, why not put it into the introduction of the primary article? I continue to take issue with the content fork and consensus-cum-resignation resignation-cum-consensus (see WP:BIAS) to leaving the primary articles of important scientific concepts as bastions of impenetrable mathematics and technical jargon while developing excellent articles like this that should be included on the primary article in the first place. However, FAC is not the appropriate forum to debate this apparent consensus on content forks, so I withdraw my opposition.Madcoverboy 19:43, 11 July 2007 (UTC)
 * Thanks. In this particular case, I hope that consensus-cum-resignation will not be an issue, anyway. Trying to improve the main article general relativity is next on my to-do-list after this FA candidacy is finished. --Markus Poessel 20:02, 11 July 2007 (UTC)


 * Support. Bravo. – Outriggr § 04:54, 12 July 2007 (UTC)
 * Oppose on principle since it is an introductory article and in fact nominate for deletion/merge into main article. I have no complaint with the article content other than that it is an "introduction to" article for another article. I do not believe there should be two articles on every topic, one and introduction and one the full article - instead the one article should be made readable and useful to the average person. Science is no harder to explain to the layman than artistic or architectural movements, it simply needs to be done correctly. In any area of expertise there are conventions, terminologies and ideas that are unfamiliar to the lay reader. A good encyclopedia article discusses the subject anyway and makes it live. A good scientist is no more intelligent and able to grasp ideas than a good artist, mathematician, linguist, historian, whatever, and it is scientific conceit to suppose otherwise. General relativity may not have been trivial to figure out from first principles, but it is trivial to understand when explained properly. If an article is difficult to understand, fix the article, don't create a dumbed-down version of it. The problem here is that the main article on this topic is written by scientists for scientists, rather than for the layman. Each wikipedia article should make no preconceptions of the reader and if the reader cannot follow the article, then that is the article's fault, not the reader's. Give an eloquent enough writer the article Schwarzschild metric to work on and they could make it live for the reader. I am in absolute opposition to any article reaching FA that is effectively a dumbed-down version of another article. I can't understand why this wasn't addressed at the article's outset rather than on its FA candidacy- PocklingtonDan (talk) 20:45, 12 July 2007 (UTC)
 * I should also point out that a lot of the hard science that it is argued must be included in the article could more properly be included in daughter articles or "proof of general realtivity" or "development of the theory of general relativity" or suchlike - an encyclopedia article should be about the phenomenon itself primarily, not about the work that went into inventing/discovering/proposing it. For example, I would expect an article on the Roman Empire, to be about the Roman empire primarily, not about the history of thought and archaeology that has built our modern view of it. By all means, again, put this is a "history of the development of the theory of general relativity" or similar, but the primary article out to be about what general relativity is, and what general relativity is can and shoudl be able to be explained simply in the main article without recourse to "dumbed down" and "science members only" versions - PocklingtonDan (talk) 20:51, 12 July 2007 (UTC)

rest of discussion moved to talk, please continue discussing there, as the discussion has moved beyond the scope of this particular FAC Spamsara 04:09, 14 July 2007 (UTC)


 * Oppose Comment I have to agree with Dan. It's indicative of a problem if an article needs an introductory article. To quote Charles Van Doren, "The ideal reader of an encyclopedia should be primarily the curious average man. He should only secondarily be the specialist and/or the high school student." Atropos 00:45, 14 July 2007 (UTC)
 * Yet this article is exactly what is required for the "curious average man"... – Outriggr § 01:02, 14 July 2007 (UTC)
 * Which is why it should be found at general relativity. Atropos 03:23, 22 July 2007 (UTC)
 * Since you agree with Dan, would you consider also changing your vote to "Oppose on principle"? After all, you are not objecting to anything that can be addressed by improving this particular article - only complete withdrawal of the nomination will do. The discussion about "Introduction to...", yes or no, has now moved to the discussion page, so I'll be replying there. --Markus Poessel 06:47, 14 July 2007 (UTC)
 * I've changed it to comment. The (in my opinion, very poor) way the science-inclined are handling their wing of the encyclopedia should not effect the question of whether this content is among our best. Atropos 03:23, 22 July 2007 (UTC)


 * Support, with qualifications I think the authors have done a good job on this article, although perhaps not yet FAC level. Here are some major gaps that I see immediately, even as a beginner to GR:
 * I would argue that most (not all) of what you note below is not about gaps (let alone major gaps), but about how much detail there should be on topics for which other, more thorough, dedicated articles exist. In the current version of "Intro to GR", I have deliberately tried to keep matters as brief as possible - have a look at the article's talk page; brevity was being called for by the other editors.  My personal preference would be to indeed include some more information on the topics you mention, so I will take your comments as an excuse to follow my inclinations a valuable suggestion to be followed. In consequence (and in reaction to your more specific comments, below) I have now expanded that section, and all the major astrophysics themes have gotten their own subsections. --Markus Poessel 10:48, 15 July 2007 (UTC)
 * No significant treatment of the cosmological constant; this is an egregious omission, especially given that it's oft quoted ("my greatest blunder") and recent observations that it is not zero. Bonus points for discussing connection to wormholes! :)
 * You are right; the cosmological constant should, indeed, be mentioned. Fixed. --Markus Poessel 10:48, 15 July 2007 (UTC)
 * Cosmology deserves its own section, separate from "Astrophysical applications". The lengths scales involved (1 stellar radius vs. billions of light-years) between black hole formation and the shape/origin of the universe suggest that these concepts do not belong in the same section.  The average lay-person may also care more about the "Big Bang" than about black holes.
 * As they're both clearly part of astrophysics, as long as there is a section on astrophysics, that is where they belong, no?  And remember that there are even subjects like "astro-particle physics" where the length-scales are as disparate as it gets.  However, I hope the compromise solution that is now implemented is acceptable to you: All the major astrophysics subjects get their own subsections (and a somewhat more detailed description), so that the black holes are not lumped together with the expanding universes as closely as before. --Markus Poessel 10:48, 15 July 2007 (UTC)
 * Strictly speaking, light deflection and the consequent gravitational lensing did not originate with GR, although GR got its magnitude correct.
 * I will address this later, in reply to comments to that effect made below by another reviewer. --Markus Poessel 10:48, 15 July 2007 (UTC)
 * Frame-dragging and geodetic effects deserve some kind of mention, given the recent Gravity probe B results.
 * Sure. But they do get mentioned in the current version, do they not?  Including  GPB (with link and reference) and the dates of the preliminary/final results?  I do agree it should be mentioned, but I would hesitate to give it broader coverage (it is a rather special topic). --Markus Poessel 10:48, 15 July 2007 (UTC)
 * Perhaps a separate section for black holes and the "no hair" theorem? The public is curious about them.  A passing references to the Schwarzschild metric, Kerr metric, etc. would be nice, perhaps as a See also header.
 * Again, a passing references to Schwarzschild is present in the current version. I have added a reference to Kerr. Also, having now given black holes a subsection of their own under "Astrophysical applications", I have worked in the "no hair" theorem as part of that. --Markus Poessel 10:48, 15 July 2007 (UTC)
 * Contrary to some of the "Opposes" aboves, I think this article is essential. We would do our readers a disservice by trying cram too much into the General relativity article.  Anyone who understands this subject realizes how difficult it is to explain, and why a stepwise approach is essential.  One of Wikipedia's strengths is its (effectively) unlimited space, which I think we should harness for explaining difficult subjects such as general relativity. Willow 03:36, 14 July 2007 (UTC)
 * Contrary to all of the current "Opposed". So far, no-one has opposed other than on principle, and I'm proud of that :-) --Markus Poessel 10:48, 15 July 2007 (UTC)
 * PS. I included some introductory material at Kepler problem in general relativity; please take whatever might be useful to you! :) Willow 03:45, 14 July 2007 (UTC)


 * Many thanks for your comments – it's a refreshing change to find someone making suggestions that can actually be addressed by improving the article in question. I'll address them over the coming days; for today I have (frustratingly) spent my Wikipedia time on warding of Wiki-Unitarianism ("there can only be one!"). --Markus Poessel 10:11, 14 July 2007 (UTC)


 * Support I cannot believe what I am reading here. Wikipedia is a new kind of encyclopedia and can invent its own style. Because wikipedia is not paper, it has the luxury of being able to address more groups of readers than a traditional encyclopedia. We should embrace that, not reject it. As Jimbo Wales has said, "Imagine a world in which every single person on the planet is given free access to the sum of all human knowledge. That’s what we’re doing." The "sum of all human knowledge" includes a real page on general relativity (with all of the math that I never studied) and a general-relativity-lite page for readers like myself. I, for one, am extremely grateful to the editors for all of the work they have put into this excellent article and am startled that others see only problems here. Awadewit | talk  06:47, 14 July 2007 (UTC)


 * PocklingtonDan writes, "general relativity may not have been trivial to figure out from first principles, but it is trivial to understand when explained properly". I do not think that this is true. As I understand it, if one graduates with a BS in physics, one still does not understand general relativity very well (if at all); it is a course taken only by graduate students who need it for their subfield. Not all physics professors could teach it; general relativity is not the pulleys and levers of classical mechanics. Awadewit | talk  06:47, 14 July 2007 (UTC)


 * Atroops quotes Charles Van Doren (in what context, we don't know): "The ideal reader of an encyclopedia should be primarily the curious average man. He should only secondarily be the specialist and/or the high school student." - The "curious average man" is an impossible construct; it also leaves out half of the population. I would like to point out to Atroops that the editors of this page have very carefully considered their audience. It was discussed at the peer review. I was struck with how thoughtful the editor's comments were on that topic; few editors stop to consider their readership so carefully. Perhaps Atroops has neglected to read the peer review? Awadewit | talk  06:47, 14 July 2007 (UTC)

Let us look at the WP:FACR:
 * 1. "It is well written, comprehensive, factually accurate, neutral and stable."
 * (a) This article is exceptionally well-written for a wikipedia article.
 * (b) I cannot comment on the article's comprehensiveness, not being a physicist myself, but Willow has provided us with that assessment.
 * (c) The article is properly sourced to academic works and even provides references for the curious non-expert. I wish all wikipedia editors were so considerate.
 * (d) I believe the article to be neutral; no far-flung theories of relativity seem to be here, but Willow can speak to that better than I can.
 * (e) The article is stable; only minor changes, such as dashes, have been made to the page in the last week or so.
 * 2. "It complies with the manual of style and relevant WikiProjects."
 * (a) It has an excellent lead.
 * (b) It has a clear and helpful organizational structure.
 * (c) Its TOC does not dominate the page.
 * (d) It has consistent citations.
 * 3. "It has images and other media where they are appropriate to the subject, with succinct captions and acceptable copyright status."
 * This article has exceptionally helpful images, all of which are in the public domain.
 * 4. "It is of appropriate length, staying focused on the main topic without going into unnecessary detail (see summary style)."
 * For an introduction, this article does an excellent job of balancing detail with summary. I have read many explanations of general relativity for the layman (in popular science books such as The Elegant Universe). This is one of the best I have ever read. Awadewit | talk  06:47, 14 July 2007 (UTC)


 * I would also like to quote from the explanation of "supporting and objecting" on WP:FAC itself: "If you oppose a nomination, write *Object or *Oppose followed by the reason(s). Each objection must provide a specific rationale that can be addressed. If nothing can be done in principle to address the objection, the FA Director may ignore it."
 * I would like to suggest that Raul ignore the opposes that do not do this. Objections based on principle do not belong at FAC. You cannot oppose an article because you do not like the idea of it. That way lies censorship. Awadewit | talk  06:47, 14 July 2007 (UTC)
 * You are wrong - there is something that can be done to address the objection, which is to merge the two articles into one single article ont he same topic, which is exactly what I proposed in my initial comment. Just because you are unwilling to address this issue doesn't mean that it cannot be addressed - PocklingtonDan (talk) 07:06, 14 July 2007 (UTC)
 * I addressed this issue in my opening comments. See WP:MP if you want to propose a merger. This is not the forum for such a discussion. Awadewit | talk  08:16, 14 July 2007 (UTC)
 * I could be wrong (and would certainly welcome correction) but I doubt that any previous article having reached FA-status so easily submitted to being merged into a lesser article and thus losing the status. Once (if?) this reaches FA and I nominate it to be merged with General relativity in good faith, would these talented editors so easily amputate their accomplishment? We would be having the same conversation, only now perhaps there is more participation and better chance of reaching a consensus (Linus's Law) on whether this is the type of article that should be held as an example for all others to strive for. In my opinion, it is not because we shouldn't encourage spinout topics targeting different audiences (although, different levels of detail, per summary style, is obviously acceptable). Madcoverboy 17:13, 14 July 2007 (UTC)
 * I do agree that the "excellent work [smack], now do it again" aspect of an immediate merger proposal would probably move me to oppose merger, even in the absence of other arguments (which I have laid out on the discussion page). I would ask you to be patient for a few weeks (possibly months); as I said, one of my next goals is to improve the main article general relativity, hopefully to the point of FA status.  Once we're there (whether this introduction makes FA or gets shot down on principle, never mind the guidelines), at least the hurdle of merging articles in different stages of development would be removed, and a merger discussion could indeed concentrate on the more fundamental question of "Introduction to...". --Markus Poessel 10:48, 15 July 2007 (UTC)


 * I would like to suggest that opposers of this article seriously consider what they are doing. There are many FAC's that need reviewing. Do they really believe that this page is so detrimental to wikipedia that it should not exist and thus merits this extensive discussion? I cannot see that having two pages on general relativity (one of the most important scientific discoveries of the twentieth century) is really such a problem. Those who want to read a layperson's introduction can read this and those who want a more advanced understanding can read the mathematical article. Who cares that they are not the same article (which would be huge if they were)? Why does this matter so much? If you don't want a technical article, don't read that one. Having both only enhances wikipedia. Please articulate a cogent argument for the harm done with these two articles. I don't see it. Awadewit | talk  08:16, 14 July 2007 (UTC)
 * It is exactly because there are two pages on the same topic, each pandering to a specific audience that is a problem. As I said before, there is a resignation-cum-consensus (maybe I had that causation reversed in an earlier comment?) on wikipedia owing to systematic bias that it's "ok" to have impenetrable and contextless pages on mathematical and technical minutae, even on the most fundamental topics like this that leads us to the current situation wherein we are writing second articles within an encyclopedia simply to describe the first page of an encyclopedia. It's madness! Madcoverboy 17:13, 14 July 2007 (UTC)
 * If you believe that the problem is "impenetrable and contextless pages on mathematical and technical minutae", you should support this page and suggest that general relativity be deleted (if you achieve its deletion, this one will be renamed "general relativity"). There is no reason to complain about the more accessible article, is there? Awadewit | talk  22:09, 14 July 2007 (UTC)


 * I quote from one of the commenters: "This piece strikes a wonderful balance between theoretical literacy and accessibility." I cannot believe that someone who wrote this would want to stand in the way of the article becoming an FA or discourage the writing of other such articles. Awadewit | talk  08:16, 14 July 2007 (UTC)
 * I still continue to oppose the article on principle because content forking inevitably leads to fiefdoms and incompatibility/contradiction. If the current "General Relativity" page was instead "Mathematics of general relativity" or "Theoretical constructs of general relativity" or some such technical subject and this "Introduction" page was instead the primary "General Relativity" article, I would have absolutely no opposition. I will respond to Markus' comprehensive response in due time on the talk page, but we should absolutely discourage the writing of other such introduction articles and instead focus on improving the original articles. Madcoverboy 17:41, 14 July 2007 (UTC)
 * This is a semantic game with no real point. Awadewit | talk  22:09, 14 July 2007 (UTC)
 * Adding evidence for my claims above: Here is a link to MIT's introduction to general relativity class. It is a graduate class; there is no "introduction to general relativity" class for undergraduates, only an "introduction to special relativity". Here is some of the knowledge required to take the class: "The course   catalog lists 18.03 (differential equations), 18.06 (linear    algebra), and 8.07 (electricity and magnetism) as prerequisites.    Students should also be familiar with Lagrangians and action    principles, Green's functions, and numerical analysis (some    homework assignments will require the numerical solution of systems    of differential equations)." Awadewit |  talk  09:10, 14 July 2007 (UTC)
 * I don't understand what argument is being expounded with this evidence, but having been an undergraduate at MIT, allow me to address this hearsay. I can say with certainty that general and special relativity were covered in an introductory manner in 8.01 and 8.02 (intro physics classes required of all MIT undergraduates) and were developed more in 8.03 (Optics & Waves) and 8.033 (Relativity) which are the introductory classes for Physics majors. Likewise, there is an evening seminar for undergraduates entitled 8.224 Exploring Black Holes: General Relativity and Astrophysics. The prerequisites for these classes are Calculus and differential equations, and despite the arcane names, Lagrangians, Green's functions, and numerical analysis are likewise covered in any calc-based physics and DiffyQ class worth its weight. So no, general relativity isn't so complex that even MIT undergraduates couldn't possibly grasp the mathematics. Madcoverboy 17:13, 14 July 2007 (UTC)
 * Quoting myself from above: "As I understand it, if one graduates with a BS in physics, one still does not understand general relativity very well (if at all); it is a course taken only by graduate students who need it for their subfield." - This is the claim being supported. I recognize that relativity in general is covered in a fleeting manner in 8.01 (I'm watching the lectures as we write) and 8.033, but again please read the statement. My point is that no "introduction to general relativity" class can be taught to undergraduates and the level of mathematics required for it goes beyond the "average curious reader". An entire class on "Introduction to special relativity" can be taught to undergraduates. Are you a physics major, by the way? I would like your opinion on whether or not undergraduate physics majors really understand general relativity - I have repeatedly heard it stated that they do not. Awadewit | talk  22:04, 14 July 2007 (UTC)


 * While I do not want to pass judgment on what MIT undergraduates can and cannot possibly grasp, I certainly welcome the support for my claim that an article on gr that meets the needs of beginning undergraduates (one of the sections of Wikipedia's readership) does require technical material (namely calculus and differential equations) that is not accessible to a general audience (the other important section of readership we are talking about here). --Markus Poessel 20:56, 14 July 2007 (UTC)

This whole argument about MIT course materials seems extremely pointless to me. What MIT instructors decide to teach their students should not influence editorial decisions in Wikipedia. And basic calculus is not exactly a specialised field of mathematics. Anyone who studied math in high-school knows what differential equations are, if not special techniques to solve them. What this article needs is more respect for the average readers intellect. The aricle Introduction to special relativity ends at the doorstep of general relativity, by mentioning that the Minowski metric is globally valid only for flat spacetime and that this is extended in GTR by the field equation which can be solved to find the metric tensor (a term that has been intuitively explained earlier in the article as a distance formula, an extension of the Pythagorean theorem) in the space surrounding a given mass distribution. This is quite accessible (once you have read the whole article) and manages to explain something concrete to the reader about GTR in just one line: a perfect starting point for an introduction to general relativity. It allows the reader to leave with an understanding, not simply facts. I don't know the math of GTR, or I'll have tried something similar for this article. Loom91 15:43, 16 July 2007 (UTC)
 * Well, I'm afraid that the majority of the population in the United States, anyway, does not know basic calculus (see my examples below). My high school, for example, offered a single course which very few people took. I didn't go to one of those fancy-schmancy suburban high schools with a plethora of mathematics and science courses. Nor do most students, I think. I would like to think that all this article needs is "more respect for the average reader's intellect" (inserting apostrophe), but part of the problem is simply the knowledge you need to begin this article. Many readers will not be able to understand this article (that would include almost all of the freshmen I have ever taught). Might you describe the reader who you think is going to read this page? Awadewit | talk  01:59, 17 July 2007 (UTC)
 * How strange! I know that the American education system is more... elementary than most others, but I didn't think that you could get through without ever touching calculus! In India (and in most other countries I'm aware of) calculus of functions of a single real variable (including an introduction to differential equations) is compulsory for all mathematics students in the country. Students of physics additionally have to study some basic vector calculus to deal with electrodynamics. Students of statistics have to study optimisation of functions of several real variables. This means that undergraduate math courses (I'm speaking from the first-year IIT syllabus) start calculus from somewhere close to Taylor expansions.
 * Here, course material does not vary from school to school. There are many eeducational boards (differing ostly in details of curriculum and standard of examination), but under any one the syllabus is the same in all schools. In addition, students aspiring for one of the more advanced engineering entrance examinations have likely learned more advanced calculus (say at the level of Apostol). Perhaps my perspective is biased and the global situation is not like this, but as far as I know IB students also have to compulsorily study calculus. Loom91 20:48, 18 July 2007 (UTC)


 * Support and remind FA director that oppositions "on principle" should be ignored because they can not be resolved by edits to the article. BenB4 16:33, 14 July 2007 (UTC)
 * Comment (was initially a support, then withdrawn, now supporting under a new section Carcharoth 22:14, 16 July 2007 (UTC)) - [support] on principle (does that mean this can be ignored?). Seriously, I read it, I liked it, it was good. Wikipedia shouldn't get too technical, but it should sometimes offer a range of choices for readers. Not a suitable way to treat every subject, but it seems to work well here. Carcharoth 18:36, 14 July 2007 (UTC)
 * And about the summary style concerns. I see this article as a spin-off from the main article and part of a series on the topic. See Template:General_relativity. This way of structuring the article series fits and it works. No need to fix it if it isn't broken. Carcharoth 18:40, 14 July 2007 (UTC)
 * I am mildly concerned though that the description of Eddington's experiment is dumbed down too much. The paragraph links to Tests of general relativity, but the summary in the introduction article fails to say or make clear enough the following: (a) Newton's theories also predict a deflection (half the value predicted in Einsteinian physics); (b) the doubt surrounding Eddington's results; (c) how Eddington's 'results' made the front page of many newspapers and made Einstein and general relativity world-famous; (d) the date and location of Eddington's eclipse observations (29 May 1919), though Tests of general relativity also fails to mention that the observations took place in 1919. Is the rest of the article like this? Withdrawing support for now. Carcharoth 18:53, 14 July 2007 (UTC)
 * I suppose much of what you are missing in the article has been left out in an effort to try to keep matters as brief as is possible while still conveying the essentials. I'm open to compromise – I have added the Newtonian prediction (it is also mentioned, although not under that name, in a footnote to an earlier section); I have added a cautionary remark that Eddington's results were not that accurate (but accurate enough), plus a reference (Hartl) that gives all the details about how the results were arrived at; I have added the year (and done the same for Pound-Rebka, to keep things balanced), but I have so far refrained from adding the day, month, and the two locations - details at that level are not included for any of the other tests that have been mentioned, and should, in my opinion, be left to the more detailed articles dealing with those tests.  I don't know what exactly your ominous question about the rest of the article means – the rest of the article is also kept brief (for better accessibility), and hopefully not dumbed down (although some details are given only in the footnotes, again for better accessibility). If you have any specific concerns, I'll do my best to address them. -- Markus Poessel 17:24, 15 July 2007 (UTC)
 * My "ominous question"? It was merely reminding myself to check the rest of the article for things like this. :-) See my more detailed comments below. Carcharoth 11:30, 16 July 2007 (UTC)
 * Certainly "ominous" then, in the original sense - an omen of much more input to come. Many thanks for your detailed comments, which I will now address in more detail. --Markus Poessel 16:10, 16 July 2007 (UTC)

Comments - I like to see proper historical context being provided. It is easy to add little things like this, and it is easy for readers to understand the history - it helps offset the sometimes heavy science explanation bits. Once that's been done, I'll almost certainly support, as the science explanation side of things is fairly good. Here are some more examples of 'missing years', plus some other concerns:
 * You give GR date as 1916, but fail to say when Newton published his theory. 1687 would be the equivalent publication date for Newton, I suppose. More generally, it is probably worth emphasizing just how long Newton's theory had been around for, and how many centuries of science Einstein was overthrowing (well, overthrowing is overstating it somewhat). It is also worth emphasizing that for everyday situations, Newton's theory is still perfectly adequate.
 * The reason I did not give the Newton date was that this is, well, an article about general relativity.  I was trying to keep the lead as succinct as possible (and still am, in fact). I agree that it might be an improvement so say more about Newton; I have now inserted some information about this into the sections where I think that it fits in well: The beginning paragraph of "From sr to gr", and the beginning of "Observations". --Markus Poessel 16:10, 16 July 2007 (UTC)


 * I like to see lead sections, and articles, ending with a few dated statements, allowing the reader to see how up-to-date (or how out-of-date) the article is. If there is a "2007" in there, then the reader knows when the article was written. If it says "2005", then the reader knows that they may need to find out somewhere else what has happened in the last two years.
 * OK, that seems a good idea. I have inserted a parenthesis into the final paragraph of the lead which shows the observational tests spanning from 1859 to 2006. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * "a non-technical introduction to this theory can be found in the article Introduction to special relativity" - I feel there should be a better way to write this, though the self-reference may be unavoidable. This also falls foul of my concern above, that you are shunting people off to read about special relativity, and then expecting them to come back and start again at the point "Soon after, he began to think about how to incorporate gravity into his new relativistic framework." - the reader who has not gone and read the article on special relativity (or its introduction) will wonder what this "relativistic framework" is. Surely it is worth a few sentences to lay the groundwork here for later explanations? If it is not actually necessary to understand special relativity in order to understand general relativity, then don't encourage readers to go and read that article.
 * This was something that was explicitly suggested in the peer review, but I agree that the result is not optimal in terms of smoothly flowing text. I think it is not necessary to understand special relativity at the level given in Introduction to special relativity to follow this text, beyond what is explicitly said later on (Minkowski and so on).  I do not want to leave the link out altogether, but I have moved it to the top of the "See also" section now. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * "the privileged ("inertial") observers" - again, you send readers scrabbling for another article (or for chapter 2 of Wheeler), trying to work out what you mean here.
 * That is a good idea. I was hoping to keep readers from hurrying away by mentioning "inertial" only in quotation marks, but I have now added a few sentences of explanation. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * "the second observer's clocks are running faster" - I've always been uncomfortable with this analogy. It implies a technical reason for the clocks running at different speeds. In fact, the clocks are identical and running at the same speed, but time is different for one compared to the other. When someone says "clocks are running faster", someone can easily misunderstand this to mean that if you swap the clocks round, the one running faster is still running faster. In other words, it is not the clocks that are different, but the environment.
 * In a sense they are running at the same speed, in another sense they are not. Stationary spacetimes have a privileged way of defining coordinate time, and with respect to that time the two clocks are definitely running at different speed; in another sense, they are both running at the same speed "relative to local (proper) time", of course. I've tried to make clearer what is meant here. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * Dates reappear in the "From acceleration to geometry" section. "1907", "early nineteenth century", "1850s" and "late 1915". What would be helpful here is saying when Einstein first started working on general relativity. You say "it took Einstein three years", but three years from when? Also "With the help of Riemannian geometry, Einstein formulated a geometric description of gravity" - when was this? Admittedly, the books you are referring to, which are explaining the physics of this, probably don't give dates, so you will need to go to a history book instead, but some of the many biographies of Einstein out there should give these details. The Pais biography (Subtle is the Lord) will probably tell you what you need to know. Incidentially, how do you feel about linking authors in the references when they have Wikipedia articles? John Wheeler and Abraham Pais, for example?
 * I agree that the current version could use some more concrete dates, and I have added them. From Pais, I gather that Einstein really started about incorporating gravity in 1907 (p. 178), so I will make the "Soon after, he began to think about..." more precise. I've also added some explanation in the footnote; after all, we cannot see inside Einstein's mind. Riemannian geometry: Fixed (the date is now there, but before the elementary geometry; right where it says that Einstein started his search). Reference to Pais has been added as well. As for linking authors in the reference section, what would you liked changed? As far as I can see, both Wheeler and Pais have been wikilinked from quite some time now. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * "Paraphrasing the doyen of American relativity research, John Wheeler" - this seems a bit over the top to me. Wheeler is well-known enough that you don't need to call him a doyen. Just leave a link to his article for people who want to know more about him, and call him a "US theoretical physicist" or something.
 * This was in direct response to a point raised in the peer review: Who is John Wheeler, and why should we care what he says?  "US theoretical physicist" would answer the first, but not really the second.  As far as I can see, it's not over the top, either - Wheeler basically brought general relativity research to the prominence it has now, and going by the PhD genealogies, he really is the granddaddy of American gr.  Also, as far as I can tell (and I've talked to quite a number of American relativists as they visited AEI), he is the most respected US relativist in the community, so "doyen" does sound no more than descriptive. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * You use the phrase "probing the gravitational field" without explaining what you mean by this. If you mean "test" or "measure" or something more complicated, it would be best to explain this.
 * You're right; I've changed the first sentence a bit, hopefully it's clearer now. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * At the end of the section "Einstein's equations" you give dates for some of the theories, but not all. Ideally you would put: Einstein's equations (date), then give solutions: Minkowski spacetime (date); Schwarzschild solution (1916); Kerr solution (1963); and Friedmann-Lemaître-Robertson-Walker solution (1922-1935). OK, that last one looks a bit strange, but some form of historical context is needed. The reader may assume that you have given these solutions in chronological order, but you need to tell them as well.
 * Einstein's equations have already been dated in an earlier section; so has Minkowski spacetime – I have left out the dates for now (since Einstein's equations are not a solution, I am reluctant to insert a year; Minkowski would be redundant, but in line with the other solutions) and I have tried to find a more elegant way of dating FLRW. The dates should definitely make clear now that the order is not chronological. --Markus Poessel 16:10, 16 July 2007 (UTC)


 * The "observations" section could still do with more dates. When were the radio telescope measurements of Mercury done? When were the measurements of Sirius B performed? When was Gravity Probe A launched? When were the quasar measurements (Eddington section) carried out?
 * Added dates for Mercury, Sirius B, Gravity Probe A, and the quasar measurements. --Markus Poessel 16:37, 16 July 2007 (UTC)


 * I disagree with your sentence on Eddington's results. See Predictive_power. That has been marked as unreferenced, but the last I heard there was still enough controversy over this that you can't say Eddington's results were "sufficient to distinguish between the Newtonian and Einsteinian predictions".
 * Could you be a bit more concrete? I've read the references that I gave, and I have read Eddington's own description, and I have vague collections of some other articles about this.  If you can give me a reference that takes into account all that is reliably known about the measurements, but still comes to the conclusion that the result quoted by Eddington was obtained by arbitrary "cherry picking", I will mention that (although it probably belongs in a footnote). --Markus Poessel 16:10, 16 July 2007 (UTC)


 * "most recently by the Cassini space probe" - using phrases like "most recently" will date the article horribly in a few years time. Better to give the date when it carried out the experiment.
 * Well, I do hope to be around here for some time to make little updates. :-) And even if I weren't, someone would hopefully revisit this article whenever there are major developments. Anyway, I have added a year, as well. --Markus Poessel 16:42, 16 July 2007 (UTC)


 * You mention atomic clocks again. What would be useful here is to mention the very first atomic clock tests of general relativity. When did they take place? I'm thinking here of the ones in high-altitude aeroplanes.
 * Added names and date. --Markus Poessel 16:50, 16 July 2007 (UTC)


 * In the section on the cosomological constant you say "From the late 1990s on". A phrase like this would be useful if you want to summarise the historical context of the various experimental tests of general relativity, rather than painstakingly date all of them.
 * OK, now that I've painstakingly dated so many at your behest, I've changed this, too. --Markus Poessel 16:50, 16 July 2007 (UTC)


 * "Other attempts to modify general relativity have been made" - do you have any dates for these? Are they recent or do they date all the way back to the 1920s?
 * Much more recent. I've added dates. --Markus Poessel 17:07, 16 July 2007 (UTC)


 * On another point, I sometimes disagree on the dividing line over when to send the reader off to read another article, and when to explain things in this article. I'll point out a few cases in the lead where you link to an article instead of providing a brief explanation in this article: gravitation, space and time. These are examples of articles that a reader should possibly read before this article, though I tend towards the best practice of keeping articles self-contained, and providing links for background information and further reading (astrophysics is a good example of something that doesn't need explaining in this article). To my mind, it is annoying when a reader has to keep reading other articles while trying to read this one, but at the end of the day, you often have to do this with such a complex topic.
 * I would have hoped that, in those cases, a reader should be able to read on and still understand the arguments set out in the text. I have added a parenthesis for gravitation, but I think the common vague understanding of what space and time are should be sufficient. --Markus Poessel 17:07, 16 July 2007 (UTC)


 * The ending of the article: you end with the Pioneer anomaly. I think a better ending would be to bring the article as close to the present-day as possible and say what the very latest research and theories are.
 * OK, I'll change the title of that section and at least add a paragraph indicating what the hot topics are. --Markus Poessel 17:12, 16 July 2007 (UTC)

Hope that was helpful! Carcharoth 11:30, 16 July 2007 (UTC)
 * Eminently so! Proof that there can never be enough sets of carefully scrutinizing eyes.  Thanks! --Markus Poessel 17:12, 16 July 2007 (UTC)
 * Looking good. I'll try and dig out the Eddington refs later this evening, after which I should be ready to support. Thanks for finding all those dates. Only one problem... This article is now better than History of general relativity! I've also bee reading Golden age of general relativity, which has a fascinating timeline. Maybe something to consider when doing an overhaul of all the relativity related material. Carcharoth 17:38, 16 July 2007 (UTC)


 * Support - following the discussion above, but without prejudice to a later merge to an FA-standard non-mathematical article at general relativity. Eddington point taken to the article's talk page. Carcharoth 22:14, 16 July 2007 (UTC)
 * Support on principle, the principle being that an article that fully meets the featured article criteria deserves the label. The writing is excellent, with a tone and pacing just right to demystify this topic at an accessible level for an interested, intelligent reader.  Furthermore, the article retains exceptional accuracy without resorting to technical digressions.  The logical flow in the article may serve as a model to improve and arrange other relativity-related material in the encyclopedia, which frankly, is in some disarray.  Tim Shuba 15:44, 15 July 2007 (UTC)
 * Withdrawing support. Article is not stable and politics of FAC nomination have markedly reduced the quality of the writing.  Tim Shuba 21:09, 17 July 2007 (UTC)
 * Sorry we lost your support - I hope we can get it back. As for stability, I don't think we have an ongoing edit war, and remember that "improvements based on reviewers' suggestions do not apply"!  As for markedly reduced quality of writing, I'm optimistic that we're on our way to a version that has at least the quality of the original - please check back a bit later and reconsider! --Markus Poessel 07:32, 18 July 2007 (UTC)
 * I agree that edits to the article in response to the FAC are explicitly excluded from the stability criteria. I include my own edits among these: I could have complained here first and then fixed my complaints, but I regard this as pointless, and so I simply fixed the issues directly. Geometry guy 20:06, 19 July 2007 (UTC)
 * While I was a bit daunted at first, I find it marvellous that this FAC review has led to the cooperation currently going on on the article's talk page. So far, the discussion is just the opposite of an edit war, it is a steady progression of presenting different viewpoints, reaching consensus, and moving on to the next issue.  I can understand if Tim Shuba were to withhold support until the ongoing work there is completed, and I hope (in fact, am confident) that in the end, the quality of writing will be in fact better than when this  discussion started.  I can also understand if the FAC director chooses not to close this review before the editing over there is completed (although we are closer to consensus here now than I had hoped for). FAC review is meant to make an article better; this review, including the discussion on the article talk page, seems to me to be an excellent example of the kind of improvement you can hope for; I am at a loss to understand how this could possibly be held against the article. --Markus Poessel 20:38, 20 July 2007 (UTC)
 * Support Excellent. Very relaxing read. I would encourage Markus to write more such introductions if it suits him. This article reminds me of a recommendation at Citizendium.Org that their articles should aim to have lucid highly readable introductions to topics rather than lists of information. This is primarily important when it comes to articles on the hard sciences which are difficult enough to understand as it is.-BillDeanCarter 12:06, 16 July 2007 (UTC)
 *  Oppose Comment. A good article, but I didn't find it very illuminating. A page of solid text without one single equation, not even the field equation! It may be very readable, but ultimately it tells the reader very little concrete about general relativity. It drones on, giving out a lot of pre-digested information (in fact, too much facts for an introduction) without ever trying to explore even superficially the connection between the principles and the results. It makes GTR appear to be a collection of facts, not emphasising understanding enough. Most importantly, it never excites the reader, never makes him gasp as understanding suddenly hit him, never leaves him wondering at the beauty of the universe and physics. I think it could benefit from a dash of the accessible but analytical and explanatory (as opposed to factual) approach employed by Introduction to special relativity. Loom91 12:57, 16 July 2007 (UTC)
 * Also, you attribute the principle of equivalence to Einstine, when he was simply restating what Galileo had said in a more primitive form. In fact, the principle is often called Galilean equivalence. Very strange really, when you consider that the principle of relativity in its original form had also been stated by Galileo. Loom91 13:03, 16 July 2007 (UTC)
 * "Einsteine"? Is that a foreign language spelling? I notice that Introduction to special relativity has this spelling of Einstein in many places - could someone do a search-and-replace? Carcharoth 14:56, 16 July 2007 (UTC)
 * Those typos and others now fixed. Carcharoth 22:11, 16 July 2007 (UTC)
 * As for the equivalence principle, please note that there are several of those around. In line with all the literature I'm aware of, I am attributing what is nowadays called the Einstein equivalence principle to Einstein, while you are probably talking about the weak equivalence principle. I'm not sure what you mean by "restating what Galileo had said in a more primitive form" - the Einstein equivalence principle, encompassing as it does all of physics (hence its use in embedding other physical theories, not just mechanics, in general relativit), is much more general than the weak equivalence principle. --Markus Poessel 18:32, 16 July 2007 (UTC)
 * Galileo showed that all bodies fall at the same rate in a gravitational field. This directly leads to the equivalence of inertial and gravitational mass. Einstein phrased this in the more sophisticated, but basically equivalent, form that a constant gravitational field is equivalent to a uniformly accelerated reference frame. I've seen the principle, even in its modern form, called the principle of Galilean equivalence (can't remember where, perhaps something by Penrose). If the literature attributes the prrinciple to Einstein, that's all right then. Loom91 20:48, 18 July 2007 (UTC)
 * If we were talking about inertial=gravitational mass (or the universality of free fall), that would indeed be wrong to attribute to Einstein. My point is that the  Einstein equivalence principle goes much further (and that is important for gr): it includes all laws of physics; otherwise, you couldn't really make any statements about light propagation by using sr, for instance.  And you wouldn't get to the heuristic, but quite general "take the laws of sr, replace partial by covariant derivatives" recipe for formulating physical laws in general relativity. --Markus Poessel 22:46, 19 July 2007 (UTC)


 * The Einstein equation is now in the text, and I have added some explanation of its meaning which attempts to provide some understanding that the theory is not arbitrary. Geometry guy 20:06, 19 July 2007 (UTC)
 * On a more general note, I think you and Markus both have valid points, but seem to be taking different approaches to introductory articles. Should introductory articles be a collection of links to other articles (essentially saying to the reader - read this article and those articles to get an idea of what this is all about), or should they be an expanded explanation of existing articles, linking to the articles but also explaining (with diagrams) what is meant? That, to me, seems to be at the heart of your two different approaches. For what it is worth, I did find Introduction to special relativity easier to read, but it did feel more like a textbook than an encyclopedia. Carcharoth 14:56, 16 July 2007 (UTC)
 * Hi Loom91; it would be much easier to address your objections if you could tell us a bit more what your pronouncements are based on. For instance, as far as I can see, the section "From special to general relativity", makes a coherent argument leading from the universality of free fall via the equivalence of gravity and acceleration, the problem of tidal forces and its resolution via the analogy to the geometry of curved surfaces to Einstein's geometric theory of gravity.  Given this, I find it hard to understand how you come by your claim that the article, as it stands, makes GTR to be merely "a collection of facts".


 * You have told us that the article "drones on" and "never excites the reader": if it were so, it is a grievous fault. Yet more than thrice, earlier reviewers have read the article and have been so kind as to highly praise it, in tones kind enough to suggest that there was something akin to excitement there. Does this sound like an article that never excites "the reader", in general?  Yet you say it never excites the reader, and I am, of course, assuming good faith.  I write not to disprove what you wrote, but I write what I do know, namely that at least on some readers the article has had the desired effect.  Could it  that your pronouncement, in this case, is more an expression of your personal dislike, rather than a sentiment that, given the data available, can be attributed sweepingly to "the reader"?  Bear with me; my mind is still over there with the article itself and I just remembered I wanted to fix another reference; I will pause and then come back and address the last part of your objection. --Markus Poessel 18:32, 16 July 2007 (UTC)
 * Talking about a generalised abstract hypothetical reader is an unfortunate by-product of writing literary reviews :-) I was talking about my personal opinions, just like a movie reviewer might talk of the viewer feeling distinctly unsatisfied at the end of the film. Loom91 20:48, 18 July 2007 (UTC)
 * I thought as much; just couldn't help pointing it out. My question is: Would you see yourself more as the reader of the "Introduction to..." article, or do you think you might head straight for the main article?  It's hard to tell, since we're currently revamping it, but I think that the result would be much more what you're thinking about for your proposed introduction. --Markus Poessel 22:46, 19 July 2007 (UTC)


 * Coming back, I have now added Einstein's equation, and I think it is an improvement - thanks! As for making the article more like Introduction to special relativity, I think there is a fundamental problem.  Special relativity can be formulated (relatively) rigorously using only high-school mathematics (not even calculus).  General relativity needs mathematics that is so advanced that even Einstein had to get help (Marcel Grossmann) when developing it, and that a "quick course" in the relevant mathematics is provided as a standard service by general relativity textbook.  You can earn a PhD in physics without ever encountering the relevant mathematics in your studies.  Given this, I would argue that there is no direct analogy; the mere fact that it works (sort of; cf. textbook character remark) for the present version of Introduction to special relativity should not be taken to mean that general relativity can be presented at the same relative level.  If you are basing your faith that such a presentation is possible on anything other than that analogy, I would like to hear your reasons. That said, I am sure that one could add some more mathematics - say, a generalization of Pythagoras theorem to show what "metric components" are.  But I do not see that this would tell the reader that much more about the physics of general relativity.  On the other hand, I think you gravely underestimate the amount of math that the average reader has at their fingertips (braintips).  In my experience, even Pythagoras' theorem will make many people switch off and lose interest.  Why are books like those of Brian Greene so popular, while the valuable book of Schutz (2003), which does attempt something like you have in mind (but takes 400 pages to make it work, and even then does merely skim the edges of the real mathematical formalism) doesn't get rave reviews in the popular press? In my opinion, that is indicative of the fact that most people will find a presentation that goes easy on the math more accessible than one that requires them to unearth formulae they have never thought about after high school.  I am not making a value judgment – it's the same reason that so few people read French or Spanish books in their original language, even though, in reading English language editions, they can be sure that a number of subtleties will have gotten lost in translation.  I would be happy if those reviewers that were satisfied with the present version could give is information about how much more math they think could have been added without compromising accessibility. --Markus Poessel 19:11, 16 July 2007 (UTC)
 * Since GTR is a geometric theory of spacetime, couldn't just a little bit of the math explained in intuitive visual terms? I'm thinking about metric tensors here, though I hope a few other parts could be given the same treatment. Math != equations. Saying matter curves spacetime -> sloppy pop science writing that gives the reader a false sense of understanding without saying anything concrete. Saying the field equations can be solved to give a quantitative measure of how the presence of mass distorts the way we measure in distance in flat space (explain briefly the evolution Pythagoras -> Minowski -> GTR) and what straight lines actually mean -> intelligent, accessible writing that may take two instead of one reading but is actually saying something. Note that I'm not saying the example of sloppy writing is the one being used in the article, only that it could do with a little more leaning towards the second.
 * I realise that I'm not being very concrete here, that's a disability. I wouldn't object if Raul disregarded my oppose. As for your statement about Pytahgoras's theorem, I find that hard to believe. Where I live, a person would probably be laughed at if he couldn't say the theorem. That's almost as basic as you can get. Even if it's true in USA (which seems to be a land of mathophobics), we need to ask ourselves: when writing about an undeniably mathematical and difficult topic like GTR, do we really want to cater to an audience that won't understand Pythagoras''s theorem? That section on from SR to GTR seems like a section the article should be based on, instead of looking like one of those sideboxes "containing more advanced material for interested students".
 * Implementing what I'm thinking of may require a fundamental restructuring though. Suddenly, the ridiculous suggestion of two different introductory articles is not looking that ridiuclous anymore. What's the disadvantage in letting readers choose and pick what works best for them? Loom91 20:48, 18 July 2007 (UTC)
 * If you look more closely, there is more math (in terms of non-equations) there than in many popular science books. While it doesn't go as far as Pythagoras (I think you're still too optimistic about that), it does try to explain the metric by using the simple image of a sphere, and the fact that 30 degrees different in longitude do not always mean the same distance.  As for the two different introductory articles, as I said above, I think the main article might head a bit more in the direction you're looking for than this "Introduction to...".  It's currently being reworked; once it's done, there might not be the need for another introductory article like you're envisioning (but I'm sure there still will be the need for the introductory article we're currently discussing).
 * As for the audience, it's always encouraging to hear about math-friendly countries, but what you say about "do we really want to cater to...." - yes, I think we should! Those people's money is paying for a lot of research on the subject; there *are* aspects of general relativity that can be fascinating (sadly not to you, but that's may be because you have too much previous knowledge) without all but a basic notion of pictorial geometry, and even people who shudder when they think about high school math can be interested in cosmology and the question of where it all came from, in black holes and some of the most energetic phenomena in the universe, and, by implication, in the theory that made all that possible - general relativity. I can understand if you say the resulting article is not for you, but I'd like to ask you to take a step back and try to take a look through a different set of eyes.  You're not a literary critic on this, you're part of a peer review process that is based on certain, specific criteria: Is the prose professional (we certainly don't want poor grammar, or articles that read like bad middle school essays)?  Is the article reasonably comprehensive (and please don't read too much about this - leaving out Pythagoras is a matter of the level of presentation; leaving out the metric altogether might still be debatable; leaving out black holes would be unforgivable)?  Reliable sources?  Stable?  Manual of style compliant (after all the hours spent on chasing the right kind of dashes, it better be)? Images? Proper length?  This isn't about inspiration and about whether the article touches your soul (though that would be nice, and I am sad to hear of anyone - like you - who finds it  boring and side-bar-ish; I hoped that readers with previous knowledge would at least appreciate how the article deals with many things that, in dumbed-down texts, are often not quite right - the relation of the bending of light to the equivalence principle, stuff like that). This is more about craftsmanship, albeit on a very high level.  If, leaving aside your personal gut feeling and your inner literary critic, you think that the article shows bad craftsmanship, then by all means oppose.  If not, even though you have a vague feeling of disappointment, I would ask you to consider changing "Oppose" to "Comment"; your different philosophy for writing an article like this would be noted, but the craftsmanship aspects acknowledged. And I'd certainly like to invite you to head over to the main article general relativity and join the bunch of us who have started re-working it.  This is where I think the kind of basic-math-based explanation (such as the metric with generalized Pythagoras) might well find a proper place. --Markus Poessel 22:46, 19 July 2007 (UTC)

As you say, a personal feeling of disappointment and disagreement over target audience is probably not sufficient grounds to oppose. I change to comment. That leaves you with inanimous support (except Opposes on principle). Good job! My knowledge of GTR is severely limited, so I fear I could contribute little to the article, particularly since specialists in the subject must surely be working there. I will try to help out with accessibility issues. But won't the main article be the place to discuss differential topology, pseudo-Riemannian manifolds and other such esoteric what-nots rather than provide the basic, intuitive mathematical description I was proposing? Loom91 12:20, 20 July 2007 (UTC)
 * Thank you for changing to "comment"! I am not sure how the main article will develop; the current consensus is that it should go easy on the more complicated formulae (there is an additional article "Mathematics of general relativity" for that), but it is, of course, going mention the more advanced concepts (and the necessary technical terms - comprehensiveness!); my hope is that at least some of what you were proposing (e.g. an image explaining generalized Pythagoras to motivate talk about the metric) can fit in there.  It would still not be a systematic introduction at that level like Introduction to special relativity (and for general relativity, as I said, I'd think that kind of introduction is simply not possible - unless you go book-length, perhaps).  We'll have to see how it works out - at the moment, my main concern is to get some sections written and well-referenced, but afterwards there will surely come a phase where your input on accessibility would be greatly appreciated. --Markus Poessel 12:47, 20 July 2007 (UTC)


 * Addressable oppose. Great work, guys, but the image in the lede is unintelligible without explanation and saying that it is a "simulation based on the equations of general relativity" doesn't help much. The legend on the picture is just about too small to read and what's that tiny squiggly graph supposed to tell me? If we want a picture that really explains something to the reader this needs to be addressed. If we want an eye-candy picture then others would be better - for example the one in the lede of General relativity. Haukur 15:10, 16 July 2007 (UTC)
 * I explained the picture using the caption at the image page. Carcharoth 15:28, 16 July 2007 (UTC)
 * Thank you, that was quick and indeed an improvement. I still feel the image is a bit small, but okay. Haukur 15:57, 16 July 2007 (UTC)
 * How about this new version? Following an off-the-record I received about the image possibly being a bit overwhelming, and taking my cue from Madcoverboy's proposed merged version, I've now taken the Cassini picture as a lead (and put Gravity Probe B where Cassini used to be).  Is this better? --Markus Poessel 15:28, 17 July 2007 (UTC)
 * (As you might guess, I'm trying to gently persuade you to change your struck-out addressable oppose to a "Support"! --Markus Poessel 15:32, 17 July 2007 (UTC))
 * I like the Cassini image. I still haven't read the article all the way through so I don't feel comfortable writing a "Support"! :) Haukur 21:40, 18 July 2007 (UTC)
 * Comment on Edit 1 I have tried my hand at merging the two articles at User:Madcoverboy/Sandbox/General relativity General relativity (BE BOLD!). I also put merge tags on both pages. I don't purport to be an expert, merely an educated user/reader/editor. I believe this version retains the technical literacy of the current general relativity page with the readability of the introduction. Obviously it could use a copy and fact check by an expert, but this is meant as a proof of concept that the main article can still be accessible without having to employ condescending/didactic assumptions about the reader requiring a second article to explain the first.Madcoverboy 18:28, 16 July 2007 (UTC)
 * I think the basic flaw in your thinking is assuming that general relativity was already as it should be, as a higher-level main article. It isn't, and that's why your gesture might be bold, but it's not a proof of principle.  I indicated earlier in this discussion that I was willing to put work into bringing it to the stage where a fair comparison (namely of a good introduction and a good main artice) should be possible, intended to do so, and that it should make matters clearer.  You didn't bother to reply, and forged ahead. As also indicated in the discussion, there are "Introduction to..." + main article pairs where the comparison is less skewed, for instance Evolution and Introduction to Evolution, where the more technical of the two articles is in very good and the less technical one in good shape. You did not choose to make an example of those; instead, you chose the less suitable example. I know I should assume good faith, but it's getting hard.  Let go of your anger!  Tempting the dark side is. --Markus Poessel 20:00, 16 July 2007 (UTC)
 * Although it may seem like "I have it out for this FAC (or you)" I am acting in the utmost good faith that the consensus "force" that is with me. I continue to assert that by electing Introduction to general relativity to FA-status, we are setting the precedent for electing future "introduction" articles when myself and other editors have expressed well-founded doubts about the merits of content forks (defining the audience, codifying the "introductory" style, selecting appropriate analogies/examples, cross-checking claims, grappling with verifiability/citations between articles). I certainly don't mean to sound alarmist, but I see these good-faith "Introduction" articles as the first step down a slippery slope whereby important/essential wikipedia content becomes ghettoized with some articles intended for some audiences and exclusive of others WP:BIAS. Although I didn't quite have the time in the last 2 days to change every single "introduction to" article, I was bold in editing this one since I was already so immersed in the material. Moreover, if GR was not already as it "should be" why is/was it rated an A-class article by two separate projects? I continue to believe that the primary pages can be written to appeal to the non-specialist/generalist while still retaining value as a scientific reference by judicious use of summary-style and linking to sub-articles as is already done (EFE, mathematics of general relativity, various solutions of EFE, etc). The reason, I believe, we are at loggerheads is because you would have the "Introduction" article be the first article read by a generally educated reader whereas I see no reason why "GR" couldn't be the same. Madcoverboy 20:54, 16 July 2007 (UTC)
 * Madcoverboy, do you think you could maybe look at Genetics and Introduction to genetics? That is a better candidate for merging than this one. Maybe you could even undo your merger and let Markus see if he can achieve his aim for General relativity and Introduction to general relativity? Carcharoth 21:57, 16 July 2007 (UTC)


 * I have no clear idea of how project-rating works - is it a single editor's decision? If yes, you should ask him or her. Reverse question: If all was as it should be, why did it fail its last FA candidacy? That certainly indicates a consensus for the need for improvement. Why does it have an impressive to-do list?  I know that Introduction to general relativity was also rated A by the Math project, and that I then spent a sizeable amount of time and effort to bring it to its current state. As for the consensus being with you, don't forget that you are opposing on personal principle something that is allowed by a guideline, which has by definition been developed "through the consensus of many editors".  It's frustrating enough seeing this article in danger of being shot down on principle – just as many others here, I joined since I enjoy creating content; I was aware that there were also guidelines to be followed; while I believe that content quality should always be more important than formal considerations (WP:IAR tells me I'm not alone), I was (and am) more than willing to follow these guidelines, and to make improvements in response to helpful suggestions. I didn't expect that someone would choose this article to make a steadfast last stand on some supremely important general principle, and that I would suddenly find myself in a classic Catch-22 situation where the only way to address an oppose would be to withdraw the candidacy.  I was certainly not prepared (and OK, may be that was naive on my part) for being sucked into discussions where the article's content suddenly became completely irrelevant (and half hating myself for rising to the bait — as I'm doing now, come to think of it).  All of the above would have been bad enough if it had been happening to demand compliance with a principle laid down somewhere in the guidelines or policies, clearly and unambiguously, or even almost clearly and more unambiguously than not. Talk about irony: all of this for a principle that is in direct opposition to an agreed-upon guideline? — OK, enough whining on my part.  As I wrote on the talk page of that article, I'd like to see this as an opportunity to bring the main article general relativity to FA status; once that is done, we can have a look back and see whether we do need an "Introduction to..." or not. --Markus Poessel


 * I understand your frustration Markus and I would be similarly miffed if I was in your position. Since you are committed to both improving the GR article as well as revisiting this Intro article when (if?) GR hits FA, I'll relent. Per the discussion on Talk:General relativity, let's focus on bringing the main GR page to FA, and re-evaluating the need for this article to be merged then. In the meantime, this exclusionist Grinch will go off and kill all the other intro articles. ;) Madcoverboy 00:25, 17 July 2007 (UTC)


 * Thank you, and I apologize for casting ever-so-slight aspersions on your good faith. I hope your skeptical "if?" is too pessimistic. --Markus Poessel 08:16, 17 July 2007 (UTC)

Comment Those editors who believe that a general introduction to general relativity for the layperson can easily be blended with a sophisticated, mathematical article would do well to look at this survey. The National Science Foundation does a "scientific literacy" survey each year (these results are then compared with Europe in the study). These are the most recent results (I believe). One interesting fact: fewer than half of the Americans surveyed knew that an electron was smaller than an atom. This kind of information should help keep us grounded, I believe, and keep us from assuming too much about the reader. Obviously, a self-selecting readership will come to this article, presumably one that is a bit more educated than this survey, but it is a good benchmark to start a conversation with. Other interesting results to look at are the math scores of high school and college students on standardized tests. Anyone who has seen those will know why books like The Elegant Universe don't use much, if any, mathematics. Awadewit | talk
 * Actually, the more I think about this, the more I think that the main article on general relativity should avoid mathematics, with all the mathematics shunted to a daughter article. I strongly oppose the idea that the main article on general relativity should go into any substantive detail about the mathematics. Carcharoth 22:21, 16 July 2007 (UTC)
 * That is absurd; any article on general relativity without the mathematics is castrated. As I am repeatedly told by friends and books, mathematics is central to physics. I quote from a lay introduction to the Standard Model, Bruce A. Schumm's Deep Down Things: "To be deeply interested, however, does not mean to be steeped in the formal content, mathematically or scientifically, of physics. In particular, I presume little in the way of mathematical background--just some very basic notions of algebra and the concept of orders of magnitude. It is impossible, though, to elicit the critical notions of the theory of particle physics without an involved discussion of the mathematics that underlies it. The beautiful connection between the worlds of the mathematician and the physical scientist is one of the most interesting threads we'll follow and one for which there is precious little material available to non-professionals. That the abstractions of higher mathematics bear some relation to the physical world--in fact, seem to lie at the very heart of its order and operation--is one of the most profound revelations of the modern era." (2-3) There is no reason why we cannot have one article that loses "one of the most profound revelations of the modern era" by necessity ("Introduction") but also one that retains it ("General relativity"). Let us not pretend that an article on general relativity denuded of its mathematics would explain much at all; such an article should be titled "Introduction to general relativity" since that is what it is. Awadewit | talk  22:42, 16 July 2007 (UTC)
 * So what is the purpose of Mathematics of general relativity and Introduction to mathematics of general relativity? Are you saying that general relativity = mathematics? Where does that leave History of general relativity and Golden age of general relativity and Tests of general relativity? Not to mention all the articles in Template:General relativity. All of the articles I've mentioned can be written about with a minimum of mathematics. Would you include those in an article on general relativity, reducing the mathematical content to a small section, and if so, why not make that small section a summary of Mathematics of general relativity? Carcharoth 23:07, 16 July 2007 (UTC)
 * Yes, I am saying that you cannot understand general relativity without mathematics. This has been stated in numerous "popular" books that I have read. Ask a physicist. I'm sure that they will agree with me. Awadewit | talk  23:57, 16 July 2007 (UTC)


 * The separate articles are clearly more specialized; I would not expect them to be as accessible and I see no reason to merge them. And, by the way, what do you mean "a minimum of mathematics"? That "introduction to mathematics of general relativity" is a joke; that may be "introductory" to a minute portion of the population, but it isn't to even the "average, educated, curious reader," in my opinion. I think that I speak for many humanities people (the world is divided in half, isn't it?) when I say that the last time we did any significant math was in high school. Thus, the extent of my mathematical knowledge is theoretically early calculus, although I only vaguely remember that. With such a dim memory of high school mathematics, it is impossible for me to understand these articles without learning material that might take me months or perhaps years (I have another life, too). I am not going to do that to read one article. I am interested in science, but I haven't yet taken the plunge to learn the math necessary to really understand it. Also, I think that you greatly underestimate the fear of math, at least among students in the United States. It begins early: elementary school teachers spend less time on math than any other subject, because they don't like it and don't really understand it. I demand that my freshmen composition students figure their own grades (if I give them a 35 out of 50 on an assignment, for example, I won't tell them what percentage it is) - they cannot do those basic functions. I, who know nothing about teaching math, have had to teach students how to do this. I even taught area once, to a group of students studying for their "scary" midterm in some obviously remedial math class. Many people are frightened by math and including any equations at all in an article will scare people away from the page. This is true even of people who read popular science books - they want something easy to understand, to read on the airplane, say. I doubt that readers coming to wikipedia for an "introduction to general relativity" are going to spend hours decoding the page if it contains equations. It is already getting to be a mite technical and long. Awadewit | talk  23:57, 16 July 2007 (UTC)

Carcharoth, the answer to your question ("general relativity = math?") is basically yes, with only a few qualifications. Someone once said physics is a subject locally isomorphic to mathematics. To Awadewit, I find it frankly unbelievable that undergraduate students can't calculate percentage. Surely you are exaggerating? Even if that was true (my mind boggles even at the possibility, I can safely bet that I would be extremely hard pressed to find an adult who couldn't calculate the percentage of 35 out of 50 in their mind), should we really be aiming at that population? I think readers like you should be the standard (that is, we should set a dim knowledge of calculus as the minimum prerequisite). The concept of tensors can be introduced using vectors and matrices as the basis, and the elementary concepts of tensor calculus built up by restricting ourselves to a particular coordinate system and defining differentiation component by component. The concept of metric tensor can be derived from Pythagoras's theorem (which is actually a metric tensor itself). Curvature can be explained by starting from a bell-shaped curve and then generalising to 4 dimensions. Anyone with the inclination to really understand and a grounding in high-school math (as opposed to the man who only wants to flatter his ego and boast to his friends by reading some cheap pop sci book) could make it through such a treatment without suffering nervous breakdown. Loom91 11:05, 19 July 2007 (UTC)
 * Note: I am not exaggerating about the percentage thing - it has happened numerous times, unbelievably enough (one person asked me what 90 out of 100 was). I swear on my wikipedia user account. :) I have seen even worse, though, sadly. Two stunners: a student who didn't know the difference between "throne" and "thrown" and a student who thought slavery ended one generation ago (and I don't mean metaphorical slavery of any kind, I mean the enslavement of blacks in the U.S.). I could go on and on in this vein, and so could anyone who teaches college students, I think; my experiences are not atypical, as far as I know (I am at a major state university in the US). Like I said in one of my postings, obviously the readers of this article are going to be self-selecting to an extent, but even so, we need to determine just how much those special readers are going to know. Grasping the "average" knowledge of a regular old person (such as in that NSF survey) gives us a place to start. I mean, I thought 99.99% of the people surveyed would at least know that the earth went around the sun. Not so - only around 70%, I believe. I'm afraid that under your system, I would not qualify as a reader for this article. My memory of high school calculus is so dim, that I don't think I could use it (imagine a language you learned in high school and never used again - that is what calculus is like for me - a shady memory - things look familiar, but I don't remember what to do with them anymore). I have been working on understanding vectors for several days now, but I have not come very far. The thing is, you cannot pile so many new concepts on readers at once. In the space of 30 to 60 minutes (let's say I took that much time to read this article - a staggeringly long time, by the way), under your outline, I would have to learn what a vector is, what a metric is, what a tensor is, and try to comprehend four dimensions (along with all of the other stuff in the article). That is a lot of work; while some people would be willing to do it, far more, I think, will give up. Which is better - to have more readers make it through the article with less understanding or to have a few of them gain a more precise understanding? I can see why you would vote for "fewer readers" and "more understanding", but as wikipedia is trying to convey knowledge to everyone, I vote for less understanding and less frustration; we are not a textbook. :) I think that it is useful to note that all of the popular science books I own (many, I don't know the exact number) stop at algebra or maybe a little trigonometry. I think that the same people who buy The Elegant Universe are going to be interested in this page. Apparently, most of the authors of those books think calculus is too advanced or not well-known enough to use it in their books. (Roger Penrose is the exception, but I don't really believe that his book is meant for lay people, even though he says it is.) Loom91, I share your desire to educate the reader and your desire to "raise the bar" as it were, and I attempt to do so in my classroom every day, but it is possible to raise the bar too high and have everyone come crashing down with you. I have horrible visions now of trying to explain a section of J. S. Mill's On Liberty to a class of freshmen - it haunts my dreams. Awadewit | talk  12:08, 19 July 2007 (UTC)
 * How sad! As a sidenote: it is not meaningful to say that the Earth goes around the Sun. You could just as easily say the Sun goes around the Earth. I also don't think Penrose is for the laymen, it's frighteningly dense to anyone who is not consulting references as he reads. Coming to the point, the dilemma you refer to is one faced by high-school physics teachers here. As they face a new batch of students who have just reached the eleventh grade, they need concepts of basic differential calculus right form the start, but the students are not going to reach that stage in math for a few more months. The solution they usually adopt is to forget the math teacher and teach calculus themselves. That takes time though (article space in case of WP) and is probably inaapropriate for WP. What if we defined the term derivative as the rate of change? That sounds tame enough. Loom91 12:27, 19 July 2007 (UTC)
 * Sidenote: I believe that the survey respondents thought we lived in an Earth-centered galaxy. The point there is, what is most important to know - that it doesn't really matter from which reference you discuss orbits, or that the ancients were wrong and Copernicus/Galileo were right? I would go with, again, best to know that the Earth isn't at the center of the galaxy. :) Moving on, I thought that all physics taught math alongside itself? All of my roommate's physics books begin with some sort of review, most often of mathematical subjects necessary for the book (I was just perusing the description of vectors and tensors in his classical mechanics book). "Rate of change" sounds fine, but I would really need to see it context. Awadewit | talk  12:35, 19 July 2007 (UTC)


 * Strong support. Not only does it satisfies all the FA criteria, I believe it is a prime example of what is meant by well-written as "engaging, even brilliant, and of a professional standard."  Rather than discourage people from writing articles like this, we should be encouraging and so elevate the article to FA status.  I don't see any problem with stability.  In any case, it's a shame that some of the discussion here has led to actions like a merge request, which was obviously going to be rejected (and has been), and led to perceived stability issues and one subsequent withdrawal of support.  --C S (Talk) 22:04, 17 July 2007 (UTC)


 * Ready to support plus comments. Like many others here, I have been surprised by the objections to this FAC on the grounds that it is an "Introduction" article. Let me offer a few of my own observations.
 * I find it helpful to view Wikipedia not as a monolithic encyclopedia, but as a family of nested and overlapping encyclopedias: if WP is to become the "sum of all human knowledge", it must be this way, since general encyclopedias certainly are not. A general encyclopedia and (say) an encyclopedia of physics will contain different levels of detail. Sometimes WP can reconcile these differences, through summary articles, but sometimes introductions are needed. We can (and have to) be flexible about this.
 * Take a look at Category:General relativity, which has 12 subcategories and at least 10 further significant subsubcategories: this is a vast field. General relativity is the main article for this category, and must survey the field in order to be broad in its coverage. It is currently 60kB long, despite being written in summary style, with (I counted) fourteen subarticles. The article must be mathematically technical in one or two places for completeness reasons (as discussed previously, this is a very mathematical subject), but this is not the main reason that it will overwhelm the lay reader: it is overwhelming because the topic is so vast. To suggest merging an introduction into this vast overview is ridiculous; this is exactly the kind of topic where a separate introduction, which focuses on the key points, is essential.
 * Not all knowledge is easy to understand. There are some who object to technical FAs, or even technical articles in general. I accept there is a debate to be had about whether, or how often, technically difficult FAs should appear on the main page, but if WP is to fulfil its mission, then there is no question in my mind that it will include top quality articles of a technically difficult nature (and it already does). Instead the goal should be to make every article as accessible as possible, given the content. "Introduction" articles are no excuse for not making "main" articles as accessible as possible. This does not imply that "Introduction" articles should not exist where they are needed.
 * There have been suggestions that this article cannot be broad in its coverage because it is an "Introduction". Let me remind them that the title determines the coverage: this article needs to be cover everything that a good "Introduction to general relativity" would cover.
 * I read through the article entirely and found it remarkably thorough. I had some criticisms, but rather than complain about them, I have fixed them myself. The edits coming out of this FA candidacy are now being assimilated into the article. Once they are, I am confident I will be able to give it my full support. Geometry guy 20:15, 20 July 2007 (UTC)
 * The above discussion is preserved as an archive. Please do not modify it. Subsequent comments should be made on the article's talk page or in Wikipedia talk:Featured article candidates. No further edits should be made to this page.