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Talk:Think tank

He who pays the piper calls the tune
Something about sources of funding for think tanks would also be a useful addition. For example, comparing think tanks with clear sources of funding and those with opaque sources. Transparency campaigners consider that think tank funding sources could be clearer. Are there reliable sources which report which think tanks have clear sources of funding and which are opaque? I'm fairly sure there are organisations which specialise in identifying funding sources which are unclear in relation to lobbying about public policy. Philh-591 (talk) 21:57, 4 August 2023 (UTC)

Citing Organizations
Organizations which are listed should be considered to be cited with references to their pages themselves. Several paragraphs have organizations listed and asserted in different categories without any citations. For example, some organization have generic names and are not linked to another wiki article. Internet searching for this organizations yield several results that may or may not be the one referenced. Additionally, claiming an organization is a commercial think tank vs a government think tank; stating it is in the defense sector, etc. is not common knowledge and should be referenced. This is being noted since updated citations efforts were removed. Jackashiya (talk) 16:47, 2 July 2024 (UTC)

 * Wikipedia doesn't add external links to organizations own websites simply because those organizations are mentioned. The citations added did not actually support anything in the article - they were just a means of adding links. Wikipedia isn't a web directory, we're not concerned with helping internet searchers find a particular group's website. MrOllie (talk) 16:51, 2 July 2024 (UTC)

title: Talk:Think tank


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User:Russell Dovey

Russell Storm Dovey; writer, satirist, roleplayer, bookworm, computer nut, non-sequiturist and there's a bee on my shoe, this... human has a permanent residence at long last after leaping around the world from Samoa to Fiji to sharehouse to couch, as the goat leaps from tree to tree on the mighty Canadian main, fending off pirates and mounties with its hooves.

His family is scattered around the country, from his sister a few suburbs away to his old da' on the South Coast, from his brother in the exclusive rich bugger's enclave of Narrabundah College to his mum recently returned from the South Pacific island paradise of Samoa. Most of the rest are in Melbourne, poor sods.

His friends are likewise spread throughout these many lands, in Samoa, Melbourne (poor sods), and (luckily for him) in Canberra. They range (or derange) from roleplayers to ale-quaffers, expat Kiwis to stranded dreamers, graphic artists to martial artists, imagineers to poets, musicians to madmen.

Russell is a playful, iconoclastic, whimsical, antisocial, stubborn individual, so his friends tend to understand that just because he sometimes disappears for months, or forgets to ring them occasionally, or turns up on their doorstep at 7AM demanding coffee and bus money doesn't mean that he's a selfish, inconsiderate, weird, lazy, deliberately annoying bastard.

Russell is in the process of learning to program in C++, which is why he is procrastinating by farting around on Wikipedia, writing this potty biography.

If you want to contact Russell and distract him further from his work, which he may welcome desperately as a sort of Deus Ex Procrastina, use the following methods:

 * You can email him at antipaganda@gmail.com.
 * His mobile phone number is 0488 983 537.

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

title: User:Russell Dovey


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Credibility

Credibility comprises the objective and subjective components of the believability of a source or message. Credibility dates back to Aristotle theory of Rhetoric. Aristotle defines rhetoric as the ability to see what is possibly persuasive in every situation. He divided the means of persuasion into three categories, namely Ethos (the source's credibility), Pathos (the emotional or motivational appeals), and Logos (the logic used to support a claim), which he believed have the capacity to influence the receiver of a message. According to Aristotle, the term "Ethos" deals with the character of the speaker. The intent of the speaker is to appear credible. In fact, the speaker's ethos is a rhetorical strategy employed by an orator whose purpose is to "inspire trust in his audience". Credibility has two key components: trustworthiness and expertise, which both have objective and subjective components. Trustworthiness is based more on subjective factors, but can include objective measurements such as established reliability. Expertise can be similarly subjectively perceived, but also includes relatively objective characteristics of the source or message (e.g., credentials, certification or information quality). Secondary components of credibility include source dynamism (charisma) and physical attractiveness.

Credibility online has become an important topic since the mid-1990s. This is because the web has increasingly become an information resource. The Credibility and Digital Media Project @ UCSB highlights recent and ongoing work in this area, including recent consideration of digital media, youth, and credibility. In addition, the Persuasive Technology Lab at Stanford University has studied web credibility and proposed the principal components of online credibility and a general theory called Prominence-Interpretation Theory.

In journalism
According to the Society of Professional Journalists' code of ethics, professional integrity is the cornerstone of a journalist's credibility. A journalist's number one obligation is to be honest.

According to Gallup polls, Americans' confidence in the mass media has been consistently declining each year since 2007.

In 2013, a survey conducted by the Pew Research Center for the People & the Press found that credibility ratings for major news organizations are at or near their all-time lows.

"As audiences lose confidence in traditional news outlets, many see great promise in the Internet as a response to this crisis in journalism."

The widespread use of the internet has helped motivate journalists to become more credible. The reason for this is because the competition of providing news increased when consumers had the chance and ability to choose the media that they consume through online sources. The internet has provided a chance for anyone to report news. In order to increase credibility, and therefore increase readers of their articles, journalists should be objective, accurate, trustworthy, and reliable.

Three aspects of credibility: clarity (how easily the article can be understood), accuracy (how well documented the information is), and trustworthiness (how believable the information is).

In academia
Students' perception of instructors has great importance and possible consequences. Instructor credibility, which is defined as "the attitude of a receiver which references the degree to which a source is seen to be believable", consists of three dimensions-, competence, character, and caring. Competence focuses on his or her expertise or knowledge in a subject matter. Character refers to the "goodness" (i.e., honesty, trustworthiness) of an instructor. Caring focuses on whether the instructor shows concern or empathy for the students' welfare or situation. Although an instructor may show one or two of these qualities, the best and most respected exude all three qualities. A study done by Atkinson and Cooper revealed that students who are taught by an instructor they perceive as credible, results in extreme allegiance to those instructors.

Generally, instructors who are perceived to have credibility are associated with effective teaching skills. Instructors who demonstrate competence, character, and/or caring are perceived to engage in a variety of effective instructional communication behaviors such as argumentativeness, verbal and nonverbal immediacy, affinity seeking, and assertiveness and responsiveness. Moreover, credible instructors are perceived to be low in verbal aggressiveness and less likely to use behaviors that interfere with student learning.

Unlike instructor competence which centers on instructors' perceived expertise, instructor character and caring are rooted in students' perceptions of their instructors' interpersonal communication behaviors. Students can feel more connected to the material being taught and have the information stay in their mind, if the instructor sharing the information has credibility. According to studies, when instructors exemplify the qualities of character (i.e., kind, virtuous, good) and caring (i.e., empathetic, understanding, responsive), students report a greater likelihood of communicating with them.

Teachers who are concerned with whether students communicate with them, either in class or out of class, may want to reconsider the role their own in-class communication behaviors play in students' willingness or likelihood to communicate with them. Instructors who are interested in how students perceive their competence, character, and caring should examine how their in-class communication behaviors contribute to these perceptions. They can evaluate themselves, go back over their lectures, scores that students give them at the end of the semester, and seek advice and training from their peers. By doing so, instructors may find students are more willing, likely, or interested in communicating with them.

In science
Scientific credibility has been defined as the extent to which science in general is recognized as a source of reliable information about the world. The term has also been applied more narrowly, as an assessment of the credibility of the work of an individual scientist or a field of research. Here, the phrase refers to how closely the work in question adheres to scientific principles, such as the scientific method. The method most commonly used to assess the quality of science is peer review and then publication as part of the scientific literature. Other approaches include the collaborative assessment of a topic by a group of experts, this process can produce reviews such as those published by the Cochrane Collaboration, or the Intergovernmental Panel on Climate Change.

The general public can give a great deal of weight to perceptions of scientific authority in their decisions on controversial issues that involve scientific research, such as biotechnology. However, both the credibility and authority of science is questioned by groups with non-mainstream views, such as some advocates of alternative medicine, or those who dispute the scientific consensus on a topic, such as denialists of AIDS and of evolution.

In medicine
People rely on doctors' expertise to respond to issues relating to their health. Trust in a doctor's credibility is essential to a patient's health: depending on the patient's trust in the doctor they will be more or less willing to seek help, reveal sensitive information, submit to treatment, and follow the doctor's recommendations. According to numerous studies, done over 15 years we can conclude that we see a doctor's credibility as having five overlapping characteristics: Fidelity, which is caring and advocating for the patient's interests or welfare and avoiding conflicts of interest; competence, which is having good practice and interpersonal skills, making correct decisions, and avoiding mistakes; honesty, which is telling the truth and avoiding intentional falsehoods; confidentiality, which is proper use of sensitive information; and global trust, which is the irreducible "soul" of trust, or aspects that combine elements from some or all of the separate dimensions.

In general, it is easy to see what patients are looking for when it comes to a trustworthy doctor and the best way they can have their needs satisfied. There does seem to be a growing discontent with the medical field, however, because of for-profit drug companies that are influencing money behind the medical field. In 2002 a doctor attended the hearings of a drug company that was on trial for the death of adolescents who committed suicide while taking their antidepressants. Before the hearing studies had been filed with the FDA under the Best Pharmaceuticals for Children Act of 2002. These studies reflected a congressional effort to motivate drug companies to study the effects of medications on children. Since children are a much smaller market for new drugs, the pharmaceutical industry was suspected to not study them as much. The Best Pharmaceuticals for Children Act of 2002 was meant to strengthen drug companies credibility by rewarding those that performed pediatric studies. The law, however, did not require these pediatric studies performed to be publicized or published

According to a New England Journal of Medicine study, 94% of American doctors have some relationship with a drug or medical device company, including payments but also drug samples and industry lunches, for example. Such alarming evidence is what has prompted a growing mistrust in medical professionals credibility. Despite the studies conducted intended on finding out how to increase doctors' credibility, the findings are inconclusive. It is a strong general consensus that increased visibility of the relationship between doctors and pharmaceutical companies is the first place to start.

We are seeing some progress towards transparency. The US Open Payments Act (Physician Payments Sunshine Act) has from October 2014 required drug companies to disclose payments to doctors, but it's still does not give total transparency. There is a long way to go in establishing trust and credibility behind what the doctors recommend to patients. Being honest and showing that they are acting off their expertise instead of motivated by incentives given by pharmaceutical companies.

In the Web
In case of the Web pages, vast majority of researchers identifies two key components of credibility:
 * Trustworthiness – related to well-intentioned, truthful, unbiased information and perceived goodness or morality of the source.
 * Expertise – connected with such terms as knowledgeable, experienced, competent and captures the perceived knowledge and skill of the source.

On the street
Street credibility or "street cred" (also referred to as "the word on the street") is the degree to which someone's word can be believed by a typical person, the "person on the street". Corporations have gone through their own ways of getting street credibility; however, it goes by a different name: branding. This is a process in which companies spend billions of dollars a year to convey information about a product, who is using it, and why others should also. They are targeting certain individuals as to increase their ability to grow their "street cred" so that the sales growth does not end. From clothing like running shoes and jeans to food and alcoholic beverages, branding is used to assist companies improve their street cred and better sell a product.

The CEO of the company is the face of what the public sees. A CEO helps illustrate the organization's internal and external shareholders. CEOs are spokesmen who are actively visible and shape the corporate image. The role of the CEO is to influence employees' attitudes, perceptions, and performances through example of leadership and support.

In business leadership
CEO credibility is made up of two factors: knowing what one is talking about, or expertise; and being able to be trusted, or trustworthiness. One of the ways that a CEO's expertise is measured is by the way his/her employees perceive them. If the CEO is seen as someone to whom the senior employees can go to for knowledge and help, this goes to show they have confidence that the CEO holds the skills necessary to help, and is thus valued in their position as such. The extent to which the employee gives their confidence to the CEO determines the CEO's trustworthiness. An employee may totally embrace or quietly set aside the message of the CEO, these results measure the degree of trustworthiness there is in the CEO. The whole reputation of the organization represented by the CEO is built mainly by the experience of the employees as time passes. This reputation is carefully built by many factors experienced by the employees such as the actual services or products sphere, social aspects related to work and the overall foresight and ability to lead in a successful manner.

There is a natural connection link between the CEO and the organization. A CEO's credibility affects how employees view the organization's image. Employees who perceive the CEO as more qualified, competent, knowledgeable, and possessing more expertise and skills tend to view the organizational reputation more positively. Employees who view the CEO as more honest and trustworthy tend to evaluate the organization in a positive manner.

The employees view of the organization completely intervenes the positive relationship between the CEO credibility and the employee's involvement of engagement. Although the CEO's credibility positively affects employee engagement, the actual impact is exercised by the employee's view of the organization's reputation.

In social media
Social media credibility is dependent on cues and heuristics. Cues used to assess credibility online are authority cues, identity cues, and bandwagon cues. Authority cues are the most influence source credibility. Authority cues are cues that let the viewer know that it is an expert source such as a university or government institution. Identity cues are peer information. Users trust information more if they can identify the person that published it the publisher is not anonymous. Users view information as more credible if a peer shared it than a stranger. Bandwagon cues triggers credibility processing based on the logic that "if others think it's good, so should I.

Two-phase model of credibility
Jürgen Habermas in his theory of communicative action developed four validity claims (truth, sincerity, appropriateness and understandability) leading to the concept of credibility.

In a different study researchers empirically validated the claims and derived a two-phase model of "reporting credibility", where first of all understandability needs to be reached. Only then the three other validity claims make a difference and may lead to credibility in the Habermasian sense.

title: Credibility


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Talk:Mont Ventoux

Part of the Alps?
I have heard elsewhere that Ventoux is "not part of the Alps", and I didn't believe it then, mostly because I've seen maps, showing convincingly that Ventoux is part of the Alps. It may be considered a peripheral part, but a real part nonetheless. I don't know who started the myth that it was separate from the Alps, but can we please abandon it here? --Stemonitis 15:09, 28 September 2005 (UTC)

 * The fact is that the Mont Ventoux is very much a stand-alone mountain, surrounded by plains. It is not part of the Alps per se, but may be considered as being located at the external limit of what is sometimes called "Pre-Alps". Maybe the following description from could be translated and inserted into the WIkipedia article" "Le Mont Ventoux est l'un des derniers contreforts sud-occidentaux des préalpes françaises". olivier 11:26, 30 September 2005 (UTC)

South route gradient?
The article here states that the last 16 kilometers of the climb are an average of 10% gradient. That would mean that 1600 meters of the 1606 total are climbed in that last 16 kilometers. I know from experience that riding or even driving such a distance at 10% grade is unusual and it seems like an error. More likely there are sections that are 10% or more but not an average over 16 clics. __

The last 16 kilometers have an average gradient of 8,9%, actually. 1387 meters are climbed in the last 15,6 kilometers exactly. There's a small error but 8,9% over 16 km is still tough. Changed on the page.

Petrarch
The following assortment of googled direct quotations on Petrarch and Mont Ventoux are from the  deprecated article, Birthday of alpinism. They should not be included as quotes (that's what Wikisource is for) but some of them may be useful citations for this article, or a future one on Petrarch's letter.

This is a pure dump; I would not have put Famous First Facts between Burckhardt and Mattingly. Septentrionalis PMAnderson 17:37, 30 June 2007 (UTC)

Quotes
In a letter dated April 26 of the year 1336 by the Italian poet Francesco Petrarch to Francesco Dionigi of Borgo San Sepolcro, a close friend of Petrarch's who was an Augustinian monk, he gives his account of the ascent. Petrarch was about 30 years of age when he did the ascent. This letter reads in part: "Today, I ascended the highest mountain in this region, which, not without cause, they call the Windy Peak. Nothing but the desire to see its conspicuous height was the reason for this undertaking." InThe Civilization of the Renaissance in Italy Jacob Burkhardt [sic Septentrionalis PMAnderson ]describes Petrarch's ascent as the first time mountain climbing had been undertaken just for the sport of it.
 * Mentioned here; will belong in article on letter. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)
 * Not what Burckhardt says; see link to translation; I presume the reference to Iphigenia auf Tauris can be sourced. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

Famous First Facts: International Edition credits the Italian poet Francesco Petrarch for writing of the first account of mountain climbing of importance, "In April 1336 'to see what so great an elevation had to ofer,' he climbed the peak of Mount Ventoux in Provence, France, which is 6,203 feet high (1,909 meters). In a letter to the Augustinian monk Dionisio da Borgo San Sep, he later wrote: 'I stood like one dazed, I beheld the clouds under our feet, and what I had read of Athos and Olympus seemed less incredible as I witnessed the same things from a mountain less famous.'
 * Tertiary source. Omit. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

Morris Bishop's book, Petrarch and His World, has a long chapter titled "The Ascent of Mont Ventoux" on the ascent Petrarch made to the top of Mont Ventoux. He says in this chapter,  "There is no clear record that anyone ever climbed a mountain for pleasure or mere curiosity from the time of King Philip of Macedonia to that of Petrarch. True, there is the case of King Peter of Aragon in the thirteenth century, who is said to have climbed Mount Canigou in the Pyrenees only to see what was on the summit. There he found a lake with monstrous hovering dragon, darkening the face of heaven with his breath.  I think we may rule this out.  We may rule out also the Alpine hermits, who sought their high retreats only to escape the world; and even Empedocles, who climbed Mount Etna in order to throw himself in the crater.  Of course there were hunters, pursuing game to the upper fast-nesses, and shepherds seeking stray sheep or goats.  However, Petrarch remains the first recorded Alpinist, the first to climb a mountain because it is there....Probably by design, for Petrarch had a great sense of anniversaries, he planned the ascent for April 26, 1336, exactly ten years from the day he and Gherardo had left Bologna." ''
 * Largely repetitious; but may belong in article on letter. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

Garrett Mattingly, a professor of European history at Columbia University, writes of Petrarch's ascent on Mount Ventoux much in his book Renaissance Profiles (co-author John H. Plumb) and refers to him as being the "Father of Alpinism." Morris Bishop also calls Petrarch "the first alpinist" because of his ascent of Mount Ventoux in 1336.
 * Reference inexact; nor does Garrett Mattingly need to be idenrified to a literate audience. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

In another article of December 2006 Quadrant Magazine says, "One small episode in late medieval history is often singled out for special mention by historians, especially those with an interest in environmental history. This concerns the ascent of Mt Ventoux in France by Petrarch in 1336. Kenneth Clark, the noted art historian, supposes that Petrarch "was, as everybody knows, the first to climb a mountain for its own sake, and to enjoy the view from the top" (Landscape into Art, 1949). Many other historians quote this same event as providing the earliest example of the new humanistic, Renaissance spirit where nature was enjoyed for its own sake. I have come across this assertion in several history books and commentaries on the man-in-nature question."
 * Another tertiary source. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

Bruce MacLennan identifies in his article '"Some Remarks of Hillman on Renaissance Neoplatonism and Archetypal Psychology" the rediscovery of soul and its paradoxical nature in Petrarch's descent from Mont Ventoux: "James Hillman, one of the founders of modern archetypal psychology, which is a further development of Jung's ideas, has written about the roots of archetypal psychology in Renaissance Neoplatonism. He makes the argument that what enabled the Renaissance was not (as is commonly supposed) the rediscovery of humanity or nature, but the rediscovery of soul and its paradoxical nature, for while it is in us, we are also in it. That is, the imaginative world of the soul has an objective existence independent of our individual egos. He identifies Petrarch's descent from Mont Ventoux as the turning point because, as you will recall, it was there that he consulted Augustine's Confessions at random and, from what he read, realized that the world inside is just as large and real (just as given) as the world outside. In that passage Augustine described his imagination as 'a large and boundless chamber,' both a power of his and a part of his nature, yet beyond his comprehension. 'Therefore is the mind too strait to contain itself.'"
 * May belong to article on letter, but see WP:UNDUE. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

A classical historian would put the ascent of Mount Ventoux by Petrarch and his comrades as a symbolic act marking the beginning of the new humanistic "Renaissance" spirit. The ascent of Mount Ventoux in the spring of 1336 by Petrarch correlates directly with humanism, personal growth and self-knowledge. Pope Innocent III in his classic non-humanistic work Misery of the Human Condition asked the same question of why people climb mountains. He came up with the same answer as Petrarch: "the need to see the vista." This event of Petrarch's ascent to the top of Mount Ventoux just to see the view of the landscape is in the cultural history of Europe regarded iconographically as "the beginning of a conscious perception of landscape." Petrarch is known for being the father of Italian Renaissance humanism. Greek ideals were taken up then when he wrote of the philosophical concepts found in the birth of alpinism event. Of Petrarch's Epistolae familiares none provide a vision quite so stunning as that offered by the description of the ascent of Mont Ventoux. Petrarch has the ability to evoke, through narrative powerful images of the world, his own inner life as is expressed in his letter The Ascent of Mount Ventoux.
 * OR. The first sentence is "sourced" to Petrarch himself. Septentrionalis PMAnderson 18:00, 30 June 2007 (UTC)

The Church Fathers taught in the Dark Ages that mountains were considered sacred and that no person should trespass upon them. Petrarch broke away from this tradition by ascending Mont Ventoux for the beginning of the birth of Alpinism. He was later filled with secret shame upon his descent that he had had the boldness to trespass upon such sacred ground.
 * From Rudolf Steiner. Nonsense, as may be expected. Inclusion, even as Steiner's view, may be undue weight. Septentrionalis PMAnderson 17:58, 30 June 2007 (UTC)

Summary
I see no reason why any of this randomly googled pother belongs in this article, or any other. Septentrionalis PMAnderson 21:32, 1 July 2007 (UTC)
 * It doesn't belong here, but if someone were to write an article about Petrarch's letter (not the actual climb, but its literary representation), then some of these links/sources might be useful. --Akhilleus (talk) 02:21, 2 July 2007 (UTC)
 * Granted; I must be in a bad mood reading this indiscriminate heap of information Especially since the Kimmelmann article above denies the factual assertion that Petrarch was first:
 * Petrarch was not the first man in his day to climb a mountain for the sake of the climb aGerman writers in the 10th and 11th centuries described various ascents, and Jean Buridan, a Parisian, left an account of climbing Ventoux early in the 14th century, just before Petrarch. But Petrarch wrote more extensively and better about the experience than anyone before him. His account is full of esthetic gratification. Hence he is regarded by mountain climbers today as proto-modern, though a closer reading of his work compels a more nuanced interpretation: at the moment of his deepest satisfaction, on top of Ventoux, he is overcome by doubt. As he tells it, he picks up his copy of Augustine's Confessions, which he has taken along, and by chance, he says, his eyes fall on a passage chastising people who wonder at the heights of mountains'' when they should recognize God's presence in humbler circumstances.

Holm Oak is not deciduous.
The holm oak is an evergreen not a deciduous tree. The correct term in the context is hardwood and I will edit to correct.MidlandLinda (talk) 15:19, 25 July 2009 (UTC)

Gaulish
The ancient names given in the introduction are really questionable. While Vintur is still just plausible as Latin or Gaulish, Ven-Top looks nothing like either Gaulish nor Latin; -p at the end of a noun is extremely atypical for Latin if not impossible, and in Gaulish would only appear after the disappearance of a final vowel (perhaps in Late Gaulish) – but the spelling still looks really strange and un-ancient. Other language versions of Wikipedia (and Wiktionary) mention forms like Vinturi, but only French Wikipedia really explains the issue in any detail: the attested form in Latin, in the 2nd century AD, is VENTVRI or VINTVRI, which is apparently a dative presupposing a Latin nominative Vintur with two short vowels. However, the "Gaulish god of the summits" appears to be baseless speculation.

*Ven-topp, on the other hand, is merely a reconstructed form – on which basis remains unclear –, that, with its double -pp at the end of the word, looks even less than Latin or Gaulish, and, I'd say, is plain impossible according to the phonotactic rules of either language (certainly in the 2nd century AD or earlier). Rather, it looks like (West) Germanic from about the 4th century AD on, which is supported by the given meaning 'snowy peak' – see Wiktionary.

Or rather, like a compound of a word from an entirely unattested and speculative late form of Gaulish, (certainly significantly later than the 2nd century AD!) *ven, from Proto-Celtic *windos, with West Germanic *topp. Had such a compound been formed and attested in a Latinised form in the 2nd century AD, the expected form would be *Vindotoppus, compare Vindobona and Vindolanda.

This would be conceivable in principle, although there do not seem to have been any Germanic speakers anywhere near the region at the time (only significantly further to the north, on the lower Rhine and the upper Main). And of course, *Ventopp is incompatible with this. It's a purely speculative, arbitrary reconstruct (i. e., not even a plausible hypothetical reconstruction) that is plain incompatible with what we know of Gaulish, Latin and even Germanic in the 2nd century AD – let alone earlier.

At French Wikipedia, doubts about this reconstruction are also noted, especially its inability to explain the attested form Vinturi, whose stem ends in -r rather than -p(p), i. e., a completely different consonant (there's no plausible way /p/ could have changed into /r/). And finally, looking at the references in French Wikipedia, a certain Paul Peyre (apparently a serious Provençal linguist and etymologist) is cited and Encyclopédie Ventoux, which may be ''Le mont Ventoux. Encyclopédie d'une montagne provençale (2007), though the ultimate source given (in Peyre's work, apparently) is Bullet, 1784''! It's not even clear what Peyre says about it – perhaps he merely mentions it in the context of a review on historical attempts to etymologise the name and makes the observation found in French Wikipedia itself: that it is a completely implausible, amateurish, scientifically untenable attempt to explain the name.

If Ven-topp is really an 18th-century concoction (which I strongly suspect: I've seen "Celtic" words on Wikipedia several times before in attempts to explain toponyms etymology, curious words that were no more Celtic than Elvish is, and at least in one case I was able to trace it back to a similarly old book still set in blackletter; keep in mind that Celtology has made incredible strides in the 20th century, while ancient Celtic languages were barely known before, and are still obscure to non-linguists and most amateur etymologists), we can safely dismiss it. While there were a few pioneering brave souls working on historical linguistics using methodically rigorous principles already in the 17th and 18th centuries, in the wake of the Scientific Revolution, their work appears to have been largely isolated and the comparative method did not become more mainstream before the 19th century.

I have seen outdated scholarship naively cited at face value in Wikipedia before, but rarely a case this extreme; I suspect it (or similar cases) comes from a work (perhaps an encyclopedia) that was uncritically used because it was in the public domain – and thus handy for the editor as it was easily available on the Internet: a cardinal mistake. It's as if, in biology, a Wikipedia article passed off an 18th-century taxonomic scheme, perhaps by Linné himself, as current, or presented the steam engine as an exciting new invention. Etymology as done by actual 21st-century scholars, however, like historical linguistics in general, is just as much a science as biology or physics is, and we've come a long way since Voltaire's (alleged/apocryphal) dismissive quip about etymology. --Florian Blaschke (talk) 22:31, 15 November 2020 (UTC)

title: Talk:Mont Ventoux


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Photoemission spectroscopy

Photoemission spectroscopy (PES), also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in the substance. The term refers to various techniques, depending on whether the ionization energy is provided by X-ray, XUV or UV photons. Regardless of the incident photon beam, however, all photoelectron spectroscopy revolves around the general theme of surface analysis by measuring the ejected electrons.

Types
X-ray photoelectron spectroscopy (XPS) was developed by Kai Siegbahn starting in 1957 and is used to study the energy levels of atomic core electrons, primarily in solids. Siegbahn referred to the technique as "electron spectroscopy for chemical analysis" (ESCA), since the core levels have small chemical shifts depending on the chemical environment of the atom that is ionized, allowing chemical structure to be determined. Siegbahn was awarded the Nobel Prize in 1981 for this work. XPS is sometimes referred to as PESIS (photoelectron spectroscopy for inner shells), whereas the lower-energy radiation of UV light is referred to as PESOS (outer shells) because it cannot excite core electrons.

Ultraviolet photoelectron spectroscopy (UPS) is used to study valence energy levels and chemical bonding, especially the bonding character of molecular orbitals. The method was developed originally for gas-phase molecules in 1961 by Feodor I. Vilesov and in 1962 by David W. Turner, and other early workers included David C. Frost, J. H. D. Eland and K. Kimura. Later, Richard Smalley modified the technique and used a UV laser to excite the sample, in order to measure the binding energy of electrons in gaseous molecular clusters.

Angle-resolved photoemission spectroscopy (ARPES) has become the most prevalent electron spectroscopy in condensed matter physics after recent advances in energy and momentum resolution, and widespread availability of synchrotron light sources. The technique is used to map the band structure of crystalline solids, to study quasiparticle dynamics in highly correlated materials, and to measure electron spin polarization.

Two-photon photoelectron spectroscopy (2PPE) extends the technique to optically excited electronic states through the introduction of a pump-and-probe scheme.

Extreme-ultraviolet photoelectron spectroscopy (EUPS) lies in between XPS and UPS. It is typically used to assess the valence band structure. Compared to XPS, it gives better energy resolution, and compared to UPS, the ejected electrons are faster, resulting in less space charge and mitigated final state effects.

Physical principle
The physics behind the PES technique is an application of the photoelectric effect. The sample is exposed to a beam of UV or XUV light inducing photoelectric ionization. The energies of the emitted photoelectrons are characteristic of their original electronic states, and depend also on vibrational state and rotational level. For solids, photoelectrons can escape only from a depth on the order of nanometers, so that it is the surface layer which is analyzed.

Because of the high frequency of the light, and the substantial charge and energy of emitted electrons, photoemission is one of the most sensitive and accurate techniques for measuring the energies and shapes of electronic states and molecular and atomic orbitals. Photoemission is also among the most sensitive methods of detecting substances in trace concentrations, provided the sample is compatible with ultra-high vacuum and the analyte can be distinguished from background.

Typical PES (UPS) instruments use helium gas sources of UV light, with photon energy up to 52 eV (corresponding to wavelength 23.7 nm). The photoelectrons that actually escaped into the vacuum are collected, slightly retarded, energy resolved, and counted. This results in a spectrum of electron intensity as a function of the measured kinetic energy. Because binding energy values are more readily applied and understood, the kinetic energy values, which are source dependent, are converted into binding energy values, which are source independent. This is achieved by applying Einstein's relation $$E_k=h\nu-E_B$$. The $$h\nu$$ term of this equation is the energy of the UV light quanta that are used for photoexcitation. Photoemission spectra are also measured using tunable synchrotron radiation sources.

The binding energies of the measured electrons are characteristic of the chemical structure and molecular bonding of the material. By adding a source monochromator and increasing the energy resolution of the electron analyzer, peaks appear with full width at half maximum (FWHM) less than 5–8 meV.

title: Photoemission spectroscopy


text:
Curvature of Riemannian manifolds

In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous way to define curvature for these manifolds, now known as the Riemann curvature tensor. Similar notions have found applications everywhere in differential geometry of surfaces and other objects. The curvature of a pseudo-Riemannian manifold can be expressed in the same way with only slight modifications.

The Riemann curvature tensor
The curvature of a Riemannian manifold can be described in various ways; the most standard one is the curvature tensor, given in terms of a Levi-Civita connection (or covariant differentiation) $$\nabla$$ and Lie bracket $$[\cdot,\cdot]$$ by the following formula:

 * $$R(u,v)w=\nabla_u\nabla_v w - \nabla_v \nabla_u w -\nabla_{[u,v]} w .$$

Here $$R(u,v)$$ is a linear transformation of the tangent space of the manifold; it is linear in each argument. If $$u=\partial/\partial x_i$$ and $$v=\partial/\partial x_j$$ are coordinate vector fields then $$[u,v]=0$$ and therefore the formula simplifies to

 * $$R(u,v)w=\nabla_u\nabla_v w - \nabla_v \nabla_u w $$

i.e. the curvature tensor measures noncommutativity of the covariant derivative.

The linear transformation $$w\mapsto R(u,v)w$$ is also called the curvature transformation or endomorphism.

N.B. There are a few books where the curvature tensor is defined with opposite sign.

Symmetries and identities
The curvature tensor has the following symmetries:

 * $$R(u,v)=-R(v,u)^{}_{}$$

 * $$\langle R(u,v)w,z \rangle=-\langle R(u,v)z,w \rangle^{}_{}$$

 * $$R(u,v)w+R(v,w)u+R(w,u)v=0 ^{}_{}$$

The last identity was discovered by Ricci, but is often called the first Bianchi identity, just because it looks similar to the Bianchi identity below. The first two should be addressed as antisymmetry and Lie algebra property respectively, since the second means that the R(u, v) for all u, v are elements of the pseudo-orthogonal Lie algebra. All three together should be named pseudo-orthogonal curvature structure. They give rise to a tensor only by identifications with objects of the tensor algebra - but likewise there are identifications with concepts in the Clifford-algebra. Let us note that these three axioms of a curvature structure give rise to a well-developed structure theory, formulated in terms of projectors (a Weyl projector, giving rise to Weyl curvature and an Einstein projector, needed for the setup of the Einsteinian gravitational equations). This structure theory is compatible with the action of the pseudo-orthogonal groups plus dilations. It has strong ties with the theory of Lie groups and algebras, Lie triples and Jordan algebras. See the references given in the discussion.

The three identities form a complete list of symmetries of the curvature tensor, i.e. given any tensor which satisfies the identities above, one could find a Riemannian manifold with such a curvature tensor at some point. Simple calculations show that such a tensor has $$n^2(n^2-1)/12$$ independent components. Yet another useful identity follows from these three:

 * $$\langle R(u,v)w,z \rangle=\langle R(w,z)u,v \rangle^{}_{}$$

The Bianchi identity (often the second Bianchi identity) involves the covariant derivatives:

 * $$\nabla_uR(v,w)+\nabla_vR(w,u)+\nabla_w R(u,v)=0$$

Sectional curvature
Sectional curvature is a further, equivalent but more geometrical, description of the curvature of Riemannian manifolds. It is a function $$K(\sigma)$$ which depends on a section $$\sigma$$ (i.e. a 2-plane in the tangent spaces). It is the Gauss curvature of the $$\sigma $$-section at p; here $$\sigma $$-section is a locally defined piece of surface which has the plane $$\sigma $$ as a tangent plane at p, obtained from geodesics which start at p in the directions of the image of $$\sigma $$ under the exponential map at p.

If $$v,u$$ are two linearly independent vectors in $$\sigma$$ then

 * $$K(\sigma)= K(u,v)/|u\wedge v|^2\text{ where }K(u,v)=\langle R(u,v)v,u \rangle$$

The following formula indicates that sectional curvature describes the curvature tensor completely:

 * $$6\langle R(u,v)w,z \rangle =^{}_{}$$
 * $$[K(u+z,v+w)-K(u+z,v)-K(u+z,w)-K(u,v+w)-K(z,v+w)+K(u,w)+K(v,z)]-^{}_{}$$
 * $$[K(u+w,v+z)-K(u+w,v)-K(u+w,z)-K(u,v+z)-K(w,v+z)+K(v,w)+K(u,z)].^{}_{} $$

Or in a simpler formula:

$$\langle R(u,v)w,z\rangle=\frac 16 \left.\frac{\partial^2}{\partial s\partial t} \left(K(u+sz,v+tw)-K(u+sw,v+tz)\right)\right|_{(s,t)=(0,0)}$$

Curvature form
The connection form gives an alternative way to describe curvature. It is used more for general vector bundles, and for principal bundles, but it works just as well for the tangent bundle with the Levi-Civita connection. The curvature of an n-dimensional Riemannian manifold is given by an antisymmetric n×n matrix $$\Omega^{}_{}=\Omega^i_{\ j}$$ of 2-forms (or equivalently a 2-form with values in $$\operatorname{so}(n)$$, the Lie algebra of the orthogonal group $$\operatorname{O}(n)$$, which is the structure group of the tangent bundle of a Riemannian manifold).

Let $$e_i$$ be a local section of orthonormal bases. Then one can define the connection form, an antisymmetric matrix of 1-forms $$\omega=\omega^i_{\ j}$$ which satisfy from the following identity

 * $$\omega^k_{\ j}(e_i)=\langle \nabla_{e_i}e_j,e_k\rangle$$

Then the curvature form $$\Omega=\Omega^i_{\ j}$$ is defined by

 * $$\Omega=d\omega +\omega\wedge\omega$$.

Note that the expression "$$\omega\wedge\omega$$" is shorthand for $$ \omega^i_{\ j}\wedge\omega^j_{\ k}$$ and hence does not necessarily vanish. The following describes relation between curvature form and curvature tensor:

 * $$R(u,v)w=\Omega(u\wedge v)w. $$

This approach builds in all symmetries of curvature tensor except the first Bianchi identity, which takes form

 * $$\Omega\wedge\theta=0$$

where $$\theta=\theta^i$$ is an n-vector of 1-forms defined by $$\theta^i(v)=\langle e_i,v\rangle$$. The second Bianchi identity takes form

 * $$D\Omega=0$$

D denotes the exterior covariant derivative

The curvature operator
It is sometimes convenient to think about curvature as an operator $$Q$$ on tangent bivectors (elements of $$\Lambda^2(T)$$), which is uniquely defined by the following identity:
 * $$\langle Q (u\wedge v),w\wedge z\rangle=\langle R(u,v)z,w \rangle.$$

It is possible to do this precisely because of the symmetries of the curvature tensor (namely antisymmetry in the first and last pairs of indices, and block-symmetry of those pairs).

Further curvature tensors
In general the following tensors and functions do not describe the curvature tensor completely, however they play an important role.

Scalar curvature
Scalar curvature is a function on any Riemannian manifold, denoted variously by $$S, R$$ or $$\text{Sc}$$. It is the full trace of the curvature tensor; given an orthonormal basis $$\{e_i\}$$ in the tangent space at a point

we have

 * $$S =\sum_{i,j}\langle R(e_i,e_j)e_j,e_i\rangle=\sum_{i}\langle \text{Ric}(e_i),e_i\rangle, $$

where $$\text{Ric}$$ denotes the Ricci tensor. The result does not depend on the choice of orthonormal basis. Starting with dimension 3, scalar curvature does not describe the curvature tensor completely.

Ricci curvature
Ricci curvature is a linear operator on tangent space at a point, usually denoted by $$\text{Ric}$$. Given an orthonormal basis $$\{e_i\}$$ in the tangent space at p we have

 * $$\text{Ric}(u)=\sum_{i} R(u,e_i)e_i.^{}_{} $$

The result does not depend on the choice of orthonormal basis. With four or more dimensions, Ricci curvature does not describe the curvature tensor completely.

Explicit expressions for the Ricci tensor in terms of the Levi-Civita connection is given in the article on Christoffel symbols.

Weyl curvature tensor
The Weyl curvature tensor has the same symmetries as the Riemann curvature tensor, but with one extra constraint: its trace (as used to define the Ricci curvature) must vanish.

The Weyl tensor is invariant with respect to a conformal change of metric: if two metrics are related as $$\tilde{g} = f g$$ for some positive scalar function $$f$$, then $$\tilde{W} = W$$.

In dimensions 2 and 3 the Weyl tensor vanishes, but in 4 or more dimensions the Weyl tensor can be non-zero. For a manifold of constant curvature, the Weyl tensor is zero. Moreover, $$W = 0$$ if and only if the metric is locally conformal to the Euclidean metric.

Ricci decomposition
Although individually, the Weyl tensor and Ricci tensor do not in general determine the full curvature tensor, the Riemann curvature tensor can be decomposed into a Weyl part and a Ricci part. This decomposition is known as the Ricci decomposition, and plays an important role in the conformal geometry of Riemannian manifolds. In particular, it can be used to show that if the metric is rescaled by a conformal factor of $$e^{2f}$$, then the Riemann curvature tensor changes to (seen as a (0, 4)-tensor):

 * $$e^{2f}\left(R+\left(\text{Hess}(f)-df\otimes df+\frac{1}{2}\|\text{grad}(f)\|^2 g\right) {~\wedge\!\!\!\!\!\!\!\!\;\bigcirc~} g\right)$$

where $${~\wedge\!\!\!\!\!\!\!\!\;\bigcirc~}$$ denotes the Kulkarni–Nomizu product and Hess is the Hessian.

Calculation of curvature
For calculation of curvature

 * of hypersurfaces and submanifolds see second fundamental form,
 * in coordinates see the list of formulas in Riemannian geometry or covariant derivative,
 * by moving frames see Cartan connection and curvature form.
 * the Jacobi equation can help if one knows something about the behavior of geodesics.

title: Curvature of Riemannian manifolds


text: User talk:218.185.69.66

title: User talk:218.185.69.66


text:
Talk:Riemann curvature tensor

Old comments
I started new page Curvature of Riemannian manifold, I think it is bit better than this one, I plan to remove from this page everything except things directly connected with curvature tensor and link it to page above. Tosha 04:09, 13 May 2004 (UTC)

But please write Lie ... with a capital L, because Lie refers to the norwegian mathematician Sophus Lie. Hannes Tilgner

 * It will be hard for me, but I will try

Tosha 05:40, 15 May 2004 (UTC)

If you remove this article OK, but still I doubt that you catch the most general aspect of curvature in the sense of Nomizu, Kulkarni and other modern writers. Look at the reference http://www.EarningCharts.NET/ipm/ipmWaves.htm where you find more references. In the references there (look also at that one in Lecture Notes in Mathematics) you find a decomposition of the space of all curvature structures in terms of Lie and Jordan algebras. And you find how elegantly electrodynamics and gravitational waves fit into the curvature play, look at the basic work of Lichnerowics. As an ,algebraiker' I like to write the curvature structure in the following triple form, generalizing the concept of Lie triples (the book on Symmetric Spaces of Otmar Loos is a nice generalization of Lie theory): [x,y,z]=R(x,y)z. This concept generalizes the notion of a Lie triple to that one of a curvature triple, where only the Jacobiidentity is missing, but a reference to the bilinear form <,> is added in such a way, that R(x,y) is an element of the pseudoorthogonal Lie algebra. Note that the complete work of Ricci, Einstein and Weyl can be summarized as a decomposition of the space of curvature structures of Levi type (for Lie algebras). All this shows, that we do not yet understand this curvature space completely. Especially the gravitational wave aspect needs clarification. Hannes Tilgner

 * It seems that you want to include some basic identites with curvature plus Pseudo-Riemannian case (is it?) I think it is a good idea.

Tosha 05:40, 15 May 2004 (UTC)

Yes, I'm considering the following: Instead of writing a full publication in some mathematical journal (I have done that too often, it didn't pay out), use the Wikipedia for publication. By the rules of the scientific world, everything written down here, is published. Actually you can start with an outline of the idea, putting it step by step into a full scientific article. This cannot be done with a scientific journal. Writing an scientific article is time consuming. In this way everybody can see how - and immediately comment. The (my)problem is time - since I work hard on my webpage, mentioned above. Hannes Tilgner

Please have a look at No original research. This is a good place for 'survey articles'; but not for new results. Charles Matthews 08:02, 17 May 2004 (UTC)

A new comment :) it would be a grave mistake to mistake Riemannian curvature for the curvature of a Riemann manifold, because Riemannian curvature does not require a Riemannian metric, it only requires a connection. 95.181.46.66 (talk) 16:58, 16 November 2010 (UTC)

the "typo"
Hey, I just reverted an edit. It was a subtle point (but perhaps worth writing down) but

 * $$[\nabla_u,\nabla_v] \ne \nabla_{[u,v]}$$

and so the original formula was correct as written by Geometry guy. Cheers, Wesino 21:47, 14 April 2007 (UTC)

Merge proposal
The articles Riemann curvature tensor and Curvature of Riemannian manifolds cover much the same sort of material. I propose merging them. Does anyone have any objections? Silly rabbit 20:15, 21 May 2007 (UTC)
 * I agree to merge those two articles. But how about the opposite way? Currently, it is proposed to merge Curvature of Riemannian manifolds to Riemann curvature tensor. However, as Riemann curvature tensor is only one of the ways to define curvature on Riemannian manifold, I think Riemann curvature tensor should be a part of the other article. --Acepectif 08:43, 24 August 2007 (UTC)
 * Actually, I don't think we need to have each article for every kind of curvatures. For example, Weyl tensor article should better be a part of this article. --Acepectif 08:46, 24 August 2007 (UTC)

 * I think that it is valuable to have separate articles on the various types of curvatures (e.g., Weyl tensor). A great deal can be said about the Weyl tensor vis-a-vis conformal geometry, for example, that would be decidedly out of place in a general article on the curvature of Riemannian manifolds.  The same sort of remark applies to the Ricci tensor, where people study things like the positivity of the eigenvalues (although in my field it's mostly the Weyl-Schouten tensor that is of interest).  Again, much can be said which is not relevant here.

 * Point taken about merging the opposite way. Obviously this is a "slow merge". Silly rabbit (talk) 02:02, 23 February 2008 (UTC)

I don't think a merge is a really good idea. The articles do cover much of the same material but Curvature of Riemannian manifolds is meant to be an overview of the various ways of understanding curvature in the Riemannian setting. The Riemann curvature tensor is one way, but it is not the only one. Sectional curvature is an equivalent method. There are many other inequivalent methods. I think having a separate overview article (written in summary style) is helpful. -- Fropuff (talk) 06:03, 23 February 2008 (UTC)

 * You know, I am beginning to have the same feeling. However, the both articles could probably use some refocusing and trimming, with summary style in mind. Silly rabbit (talk) 14:03, 23 February 2008 (UTC)

I strongly disagree with the merge: you can define Riemannian curvature on any smooth manifold with a connection, but you obviously need a Riemannian metric for Riemannian manifold :) —Preceding unsigned comment added by 95.181.46.66 (talk) 17:00, 16 November 2010 (UTC)

Riemann
What is difference between a vector & a tensor?118.95.114.159 (talk) 13:06, 10 October 2008 (UTC)

 * If you do not know that, this article is much too advanced for you. Try reading Tensor first. As it says, "A tensor is an object which extends the notion of scalar, vector, and matrix.".
 * Thus at each event in our four dimensional space-time: A scalar (just a real number) is a rank 0 tensor; it has 40 = 1 component. A vector is a rank 1 tensor; it has 41 = 4 components. A square matrix is a rank 2 tensor; it has 42 = 16 components. There are tensors of higher rank such as the one which is the subject of this article — the Riemann-Christoffel tensor is a rank 4 tensor. The Riemann-Christoffel tensor at each event is an array of 44 = 256 real numbers. JRSpriggs (talk) 15:07, 10 October 2008 (UTC)

Deleted sentence
I removed the following sentence; it makes sense to experts, but is not sufficiently well-explained:

The transformation of a vector $$\,V^\mu$$ after circling an infinitesimal rectangle $$\,dx^\nu dx^\sigma$$ is: $$\delta V^\mu = R^\mu_{\nu\sigma\tau} dx^\nu dx^\sigma V^\tau$$.

Geometrical Meaning
I made a fix to this section a while back, but it has been reverted, perhaps for good reason. However, the reverter not only deleted the section I added to this page, but also did not make any record of what he did or why. Nor did he eliminate the original problems, which I will now attempt to explain.

First, the definition of the tau mapping can be a little mysterious if the tau of your font doesn't look like the Greek tau you get in the math-brackets of the equations that use tau. This was a problem for me in particular because I use the Times New Roman font, which I think is a standard font, at least it is not one that I remember ever having changed for my firefox browser. So, I put the definition of the mapping on its own line using a math-bracket for clarity.

Second, the tau symbol is used incorrectly (per the definition) except in the first equation that uses it. The subsequent two equations are incompatible with the definition. Therefore, we need a new definition or something else has to change. In the definition, the subscript of tau is the index to a point along the curve of transport. After the first equation, however, it is a designator of a side of a parallelogram.

My definition modified the original definition to use a curve-designator similar to the use of xt by the original author (I guess), who, I admit, uses it ambiguously as a point and as a curve-designator. Since the side of a parallelogram is a curve designator, that change rendered the uses consistent with the definition.

The t parameter is often used for time in physics. So, as it reads now, it looks like we have tau sometimes indexed by time and sometimes by a path.

I'll fix this whole thing properly in a new and improved way in a few days unless I get a response, preferably one that doesn't just wipe out my edits here.

I don't want to get into a reversion war, but I do want the problem to be fixed. I'll take it up through complaint channels if my changes are reverted again without comment or the fixes are still needed.

I have added my name to the WikiProject Physics table, in case its absence had anything to do with the reversion. Thinkor (talk) 13:21, 6 February 2010 (UTC)

 * I don't see any indication that you have ever added a section to the page. Rather the only edit I see you ever having made to this page is this one.  This edit is problematic for two reasons.  First of all, it changes from a well-established notation for the parallel transport (which is exactly that used by the very authoritative text of Kobayashi and Nomizu) to a misleading notation that seems to suggest that the parallel transport map depends only on the endpoint.  (Parallel transport depends only on the endpoint if and only if the connection is flat.)  Secondly, the formatting changes violate the manual of style for mathematics, specifically the section that discourages inline LaTeX formulas that render as PNG images (for a litany of reasons).   Sławomir Biały  (talk) 16:36, 10 February 2010 (UTC)

 * Okay. My main interest is in having the text rendered more understandable.  I was unaware of the discouragement of inline LaTeX formulas.  If the original mystifying (to me) notation was consistent with Kobayashi and Nomizu, there should be a reference somewhere to what that notation is.  I'm interested in this subject, but I'm not an expert.  I think the articles should be written with non-experts at least somewhat in mind.  My idea, perhaps naive, is that if I want to find out about GR, I should be able to go to the main article, read everything it references, etc., right down to the bottom of the hierarchy, and eventually understand GR.

Thinkor (talk) 00:54, 15 February 2010 (UTC)

Bianchi identity
The following subject of a recent edit war is a good addition to the encyclopedia, but it seems terribly out of place in this article:

"[The Bianchi identity] may be written concisely:

 * $d^\nabla R=0. $

Here $ R $ is regarded as an alternating map on pairs of vector fields, taking values in endomorphisms of vector fields. Thus $ d^\nabla R $ is an alternating map on triples of vector fields, so the Bianchi identity may be written out:

 * $(d^\nabla R)(u,v,w)=$

 * $ \nabla_u(R(v,w))+\nabla_v(R(w,u))+\nabla_w

(R(u,v))-R([u,v],w)-R([v,w],u)-R([w,u],v) = 0.$

Returning to the case of a torsion free connection on a tangent bundle (such as the Levi-Civita connection), we may regard $ R $ as a trilinear map from triples of vector fields to vector fields. In this case the Bianchi identiy takes the form:"

There is already the article curvature form that addresses more general kinds of curvature forms (and their associated Bianchi identities to some extent), as well as a few other articles (such as connection (vector bundle) and exterior covariant derivative) that might benefit from a more thorough general discussion of Bianchi identities. This article, however, is about the Riemann tensor (associated to the Levi-Civita connection), not about connection forms and more general sorts of Bianchi identities. It seems that we should keep the notation as familiar as possible without getting side-tracked with discussion of tensor-valued forms and exterior covariant derivatives. Sławomir Biały (talk) 01:11, 5 August 2011 (UTC)

Thanks for resolving that edit war (even if I lost it!). I agree with what you are saying but it is extremely confusing if you are looking up the Bianchi identity and Google or Bing take you to this page and you get something which claims to be the Bianchi identity but isn't.

Perhaps the best way to resolve it is to qualify in this article that this is the Bianchi identity for the Levi-Cevita connection:

`On a Riemanninan manifold the Bianchi identity (often called the second Bianchi identity or differential Bianchi identity) involves the covariant derivative:'

Then the word `Bianchi identity' could link to one of the other articles you mention and the co-ordinate free definition (above) could be included in that article.

W

 * More or less off-topic, but why is there no Bianchi identity? Various formulations of the identity (in local coordinates, for instance) seem to fit to that article. (I guess maybe it should be called Bianchi identities.) -- Taku (talk) 15:57, 5 August 2011 (UTC)

 * Someone who is merely trying to learn about general relativity would be confused by references to torsion which does not exist in the real world and is not a function of the metric tensor. JRSpriggs (talk) 12:04, 6 August 2011 (UTC)

 * Would anyone mind if I made the following edit. It is very little different to the current sentence, but avoids confusing anyone who is not from a GR background:

On a Riemannian manifold one has the covariant derivative $$ \nabla_u R $$ and the Bianchi identity (often called the second Bianchi identity or differential Bianchi identity) takes the form: — Preceding unsigned comment added by 2.124.32.5 (talk) 15:04, 6 August 2011 (UTC)

Historical comment.
The curvature tensor was invented by Riemann in his 1854 Habilitationvortrag "Ueber die Hypothesen, welche der Geometrie zu Grunde liegen".

As Marcel Berger wrote at page 214 of his book "A Panoramic View of Riemannian Geometry":

Enthusiast of mathematical history will note that Riemann made a small mistake in his Habilitationschrift (sic) of 1854, in characterizing flat manifolds; see a detailed historical account in Di Scala 2001.'

More precisely, Riemann claimed that if the sectional curvature vanish at n(n-1)/2 independent 2-planes at each point of the manifold then the manifold is flat. Several counterexamples are provided in:

A.J. Di Scala, On an assertion in Riemann's Habilitationsvortrag,l'Enseignement Mathematique 47, p. 57-63, (2001). — Preceding unsigned comment added by Holonomia (talk • contribs) 08:14, 18 March 2012 (UTC)

Parallel transport and covariant derivative: sign error?
To me it seems as though the equation after "The parallel transport maps are related to the covariant derivative by" needs a minus sign to conform to http://en.wikipedia.org/wiki/Parallel_transport#Recovering_the_connection_from_the_parallel_transport The vector at x0 should be subtracted, not be subtracted from.

Calculation in the Geometric meaning section
There was a calculation mistake in the previous edit. I give the detailed reasoning as follows. Let
 * $$W=\tau_{sX}^{-1}\tau_{tY}^{-1}\tau_{sX}\tau_{tY}.$$

Then
 * $$\tau_{tY}\tau_{sX}WZ = \tau_{sX}\tau_{tY}Z.$$

Thus
 * $$(\frac{d}{ds}\frac{d}{dt}\tau_{tY}\tau_{sX})WZ + \tau_{tY}\tau_{sX}(\frac{d}{ds}\frac{d}{dt}WZ) + \tau_{tY}\frac{d}{ds}\tau_{sX}(\frac{d}{dt}WZ) + \frac{d}{dt}\tau_{tY}\tau_{sX}(\frac{d}{ds}WZ) = \frac{d}{ds}\frac{d}{dt}\tau_{sX}\tau_{tY}Z.$$

Since s=t=0,
 * $$(\frac{d}{ds}\frac{d}{dt}\tau_{tY}\tau_{sX})Z + \frac{d}{ds}\frac{d}{dt}WZ = \frac{d}{ds}\frac{d}{dt}\tau_{sX}\tau_{tY}Z.$$

We have
 * $$\frac{d}{ds}\frac{d}{dt}WZ|_{s=t=0}=(\frac{d}{ds}\frac{d}{dt}\tau_{sX}\tau_{tY}Z - \frac{d}{ds}\frac{d}{dt}\tau_{tY}\tau_{sX}Z)|_{s=t=0}$$
 * $$=((\frac{d}{ds}\tau_{sX}\frac{d}{dt}\tau_{tY}Z + \frac{d}{ds}\tau_{s\frac{d}{dt}\tau_{tY}X}Z) - (\frac{d}{dt}\tau_{tY}\frac{d}{ds}\tau_{sX}Z + \frac{d}{dt}\tau_{t\frac{d}{ds}\tau_{sX}Y}Z))|_{s=t=0}$$
 * $$=(\frac{d}{ds}\tau_{sX}\frac{d}{dt}\tau_{tY}Z - \frac{d}{dt}\tau_{tY}\frac{d}{ds}\tau_{sX}Z - (\frac{d}{dt}\tau_{t\frac{d}{ds}\tau_{sX}Y} - \frac{d}{ds}\tau_{s\frac{d}{dt}\tau_{tY}X})Z)|_{s=t=0}$$
 * $$=(\nabla_X\nabla_Y-\nabla_Y\nabla_X-(\nabla_{\nabla_XY}-\nabla_{\nabla_YX}))Z$$
 * $$=(\nabla_X\nabla_Y-\nabla_Y\nabla_X-\nabla_{[X,Y]})Z.$$

--IkamusumeFan (talk) 09:33, 9 October 2014 (UTC)

 * The section assumes that X and Y commute, so [X,Y]=0.  Sławomir Biały  (talk) 11:35, 9 October 2014 (UTC)

 * I notice the assumption. Hence it was not a mistake. Thanks for reminding.

One may consider removing the commuting assumption, since the general case admits the quadrilateral construction. --IkamusumeFan (talk) 17:01, 9 October 2014 (UTC)

 * I agree overall with the edit. I don't think there is much to be gained by assuming commutativity, and the risk of confusion is very real.  But if we do decide to omit the assumption, then we should justify where the extra term comes from, possibly by adding some version of your derivation in the article.   Sławomir Biały  (talk) 17:23, 9 October 2014 (UTC)

 * I made the calculation clearer. I tried to make it as short as possible, but it is still quite lengthy. So I do not know whether the derivation fits the Wiki style. Maybe assuming the commutativity is just fine. Thanks.--IkamusumeFan (talk) 19:00, 9 October 2014 (UTC)

Link to empty page
The link ("second covariant derivative") in the sentence "The curvature formula can also be expressed in terms of the second covariant derivative defined as" links to an empty topic. Is the empty page in work, or does it need to link somewhere else? Thanks. BornRightTheFirstTime (talk) 19:02, 22 November 2014 (UTC)

 * See Red link for an explanation of the value of red-links.
 * If you know of an existing article which would be an appropriate target for this, please feel free to change the link. JRSpriggs (talk) 11:03, 23 November 2014 (UTC)

Symmetries and identities - undefined bracket operation
In the section symmetries and identities a bracket operation of the following syntax appears:
 * $$ $$

which is not defined or referenced anywhere in the article (where T is apparently a (0,2) tensor, and w a (0,1) tensor - or maybe w is a scalar field? this is also never specified in the article). Please add a definition or external reference to clarify what this bracket operation is supposed to mean. Thank you! — Preceding unsigned comment added by 138.16.124.81 (talk • contribs) 21:00, 28 November 2014 (UTC)

 * The only places where I see the "bracket operation" used in the article, it is the inner product of two contravariant vector fields using the metric. So
 * $$ \langle x, y \rangle = g_{\alpha \beta} \, x^{\alpha} \, y^{\beta} \,.$$
 * JRSpriggs (talk) 22:16, 28 November 2014 (UTC)

Informally-
Bravo to writers of this section! Terrific. Electricmic (talk) 17:16, 31 December 2019 (UTC)

Metric signature
It may be worth adding a comment on how there are two options for sign conventions in GR, which affects, say, the formula for Riemann in terms of the covariant derivatives.

About the authorship of Bianchi identities
In the  symmetries section there is a claim that Ricci came up with the algebraic identity while Bianchi came up with the second. I've found no evidence of this claim, which by the way is repeated in Curvature_of_Riemannian_manifolds (actually I think it was first written there, but I don't understand very well the revision history). Well, in any case, there is no evidence provided for the claim, and in this mathoverflow link there seems to be evidence that it's the other way around. For the moment I left the "citation needed" tag. Might come later to check. If you know something, please share the sources.

I also rolled back the 17:17, 17 December 2021 edit by Theodornak. The Bianchi identities should indeed involve antisimmetrization, not simmetrization. The expressions with simmetrization are also zero (trivially), but that is not related to the Bianchi identities. --JackozeeHakkiuz(talk) 05:32, 28 March 2022 (UTC)

Examples needed
Many visitors to this page will be students trying to acquaint themselves with the mathematics needed for problems involving general relativity. As such as student (self-study), this page appears to me to be admirably clear but situated on a plane a bit too high for my reach. It needs concrete examples with numbers, vectors, results, and definitions of all symbols. Without that connection to palpable entities, the symbols just float in some ethereal space where their meaning can be perceived only by the literati. Gpalmernc (talk) 00:43, 30 April 2024 (UTC)

title: Talk:Riemann curvature tensor


text:
Precocious puberty

In medicine, precocious puberty is puberty occurring at an unusually early age. In most cases, the process is normal in every aspect except the unusually early age and simply represents a variation of normal development. There is early development of secondary sex characters and gametogenesis also starts earlier. Precocious puberty is of two types: true precocious puberty and pseudoprecocious puberty. In a minority of children with precocious puberty, the early development is triggered by a disease such as a tumor or injury of the brain.

Even when there is no disease, unusually early puberty can have adverse effects on social behavior and psychological development (have a more mature knowledge than one's age, feel inadequate, try to attend and establish friendships with older people, depression), can reduce adult height potential, and may shift some lifelong health risks. Central precocious puberty can be treated by suppressing the pituitary hormones that induce sex steroid production. The opposite condition is delayed puberty.

The term is used with several slightly different meanings that are usually apparent from the context. In its broadest sense, and often simplified as early puberty, "precocious puberty" sometimes refers to any physical sex hormone effect, due to any cause, occurring earlier than the usual age, especially when it is being considered as a medical problem. Stricter definitions of "precocity" may refer only to central puberty starting before a statistically specified age based on percentile in the population (e.g., 2.5 standard deviations below the population mean), on expert recommendations of ages at which there is more than a negligible chance of discovering an abnormal cause, or based on opinion as to the age at which early puberty may have adverse effects. A common definition for medical purposes is onset before 8 years in girls or 9 years in boys.

Causes
Early pubic hair, breast, or genital development may result from natural early maturation or from several other conditions.

Central
If the cause can be traced to the hypothalamus or pituitary, the cause is considered central. Other names for this type are complete or true precocious puberty.

Causes of central precocious puberty can include:
 * hypothalamic hamartoma produces pulsatile gonadotropin-releasing hormone (GnRH)
 * Langerhans cell histiocytosis
 * McCune–Albright syndrome

Central precocious puberty can also be caused by brain tumors, infection (most commonly tuberculous meningitis, especially in developing countries), trauma, hydrocephalus, and Angelman syndrome. Precocious puberty is associated with advancement in bone age, which leads to early fusion of epiphyses, thus resulting in reduced final height and short stature.

Adrenocortical oncocytomas are rare with mostly benign and nonfunctioning tumors. There have been only three cases of functioning adrenocortical oncocytoma that have been reported up until 2013. Children with adrenocortical oncocytomas will present with "premature pubarche, clitoromegaly, and increased serum dehydroepiandrosterone sulfate and testosterone" which are some of the presentations associated with precocious puberty.

Precocious puberty in girls begins before the age of 8. The youngest mother on record is Lina Medina, who gave birth at the age of either 5 years, 7 months and 17 days or 6 years 5 months as mentioned in another report.

"Central precocious puberty (CPP) was reported in some patients with suprasellar arachnoid cysts (SAC), and SCFE (slipped capital femoral epiphysis) occurs in patients with CPP because of rapid growth and changes of growth hormone secretion."

If no cause can be identified, it is considered idiopathic or constitutional.

Peripheral
Secondary sexual development induced by sex steroids from other abnormal sources is referred to as peripheral precocious puberty or precocious pseudopuberty. It typically presents as a severe form of disease with children. Symptoms are usually as a sequelae from adrenal hyperplasia (because of 21-hydroxylase deficiency or 11-beta hydroxylase deficiency, the former being more common), which includes but is not limited to hypertension, hypotension, electrolyte abnormalities, ambiguous genitalia in females, signs of virilization in females. Blood tests will typically reveal high level of androgens with low levels of cortisol.

Causes can include:
 * Endogenous sources
 * Gonadal tumors (such as arrhenoblastoma)
 * Adrenal tumors
 * Germ cell tumor
 * Congenital adrenal hyperplasia
 * McCune–Albright syndrome
 * Silver–Russell syndrome
 * Familial male-limited precocious puberty (testotoxicosis)
 * Exogenous hormones
 * Environmental exogenous hormones
 * As treatment for another condition

Isosexual and heterosexual
Generally, patients with precocious puberty develop phenotypically appropriate secondary sexual characteristics. This is called isosexual precocity.

In some cases, a patient may develop characteristics of the opposite sex. For example, a male may develop breasts and other feminine characteristics, while a female may develop a deepened voice and facial hair. This is called heterosexual or contrasexual precocity. It is very rare in comparison to isosexual precocity and is usually the result of unusual circumstances. As an example, children with a very rare genetic condition called aromatase excess syndrome – in which exceptionally high circulating levels of estrogen are present – usually develop precocious puberty. Males and females are hyper-feminized by the syndrome. The "opposite" case would be the hyper-masculinisation of both male and female patients with congenital adrenal hyperplasia (CAH) due to 21-hydroxylase deficiency, in which there is an excess of androgens. Thus, in the aromatase excess syndrome the precocious puberty is isosexual in females and heterosexual in males, whilst in the CAH it is isosexual in males and heterosexual in females.

Research
Although the causes of early puberty are still somewhat unclear, girls who have a high-fat diet and are not physically active or are obese are more likely to physically mature earlier. "Obese girls, defined as at least 10 kilograms (22 pounds) overweight, had an 80 percent chance of developing breasts before their ninth birthday and starting menstruation before age 12 – the western average for menstruation is about 12.7 years." In addition to diet and exercise habits, exposure to chemicals that mimic estrogen (known as xenoestrogens) is another possible cause of early puberty in girls. Bisphenol A, a xenoestrogen found in hard plastics, has been shown to affect sexual development. "Factors other than obesity, however, perhaps genetic and/or environmental ones, are needed to explain the higher prevalence of early puberty in black versus white girls." While more girls are increasingly entering puberty at younger ages, new research indicates that some boys are actually starting later (delayed puberty). "Increasing rates of obese and overweight children in the United States may be contributing to a later onset of puberty in boys, say researchers at the University of Michigan Health System."

High levels of beta-hCG in serum and cerebrospinal fluid observed in a 9-year-old boy suggest a pineal gland tumor. The tumor is called a chorionic gonadotropin secreting pineal tumor. Radiotherapy and chemotherapy reduced tumor and beta-hCG levels normalized.

In a study using neonatal melatonin on rats, results suggest that elevated melatonin could be responsible for some cases of early puberty.

Familial cases of idiopathic central precocious puberty (ICPP) have been reported, leading researchers to believe there are specific genetic modulators of ICPP. Mutations in genes such as LIN28, and LEP and LEPR, which encode leptin and the leptin receptor, have been associated with precocious puberty. The association between LIN28 and puberty timing was validated experimentally in vivo, when it was found that mice with ectopic over-expression of LIN28 show an extended period of pre-pubertal growth and a significant delay in puberty onset.

Mutations in the kisspeptin (KISS1) and its receptor, KISS1R (also known as GPR54), involved in GnRH secretion and puberty onset, are also thought to be the cause for ICPP However, this is still a controversial area of research, and some investigators found no association of mutations in the LIN28 and KISS1/KISS1R genes to be the common cause underlying ICPP.

The gene MKRN3, which is a maternally imprinted gene, was first cloned by Jong et al. in 1999. MKRN3 was originally named Zinc finger protein 127. It is located on human chromosome 15 on the long arm in the Prader-Willi syndrome critical region2, and has since been identified as a cause of premature sexual development or CPP. The identification of mutations in MKRN3 leading to sporadic cases of CPP has been a significant contribution to better understanding the mechanism of puberty. MKRN3 appears to act as a "brake" on the central hypothalamic-pituitary access. Thus, loss of function mutations of the protein allow early activation of the GnRH pathway and cause phenotypic CPP. Patients with a MKRN3 mutation all display the classic signs of CCP including early breast and testes development, increased bone aging and elevated hormone levels of GnRH and LH.

Diagnosis
Studies indicate that breast development in girls and the appearance of pubic hair in both girls and boys are starting earlier than in previous generations. As a result, "early puberty" in children as young as 8 and 9 is no longer considered abnormal, particularly with girls. Although it is not considered as abnormal, it may be upsetting to parents and can be harmful to children who mature physically at a time when they are immature mentally.

No age reliably separates normal from abnormal processes in children, but the following age thresholds for evaluation are thought to minimize the risk of missing a significant medical problem:
 * Breast development in boys before appearance of pubic hair or testicular enlargement
 * Pubic hair or genital enlargement (gonadarche) in boys with onset before 9 years
 * Pubic hair (pubarche) before 8 or breast development (thelarche) in girls with onset before 7 years
 * Menstruation (menarche) in girls before 10 years

Medical evaluation is sometimes necessary to recognize the few children with serious conditions from the majority who have entered puberty early but are still medically normal. Early sexual development warrants evaluation because it may:
 * induce early bone maturation and reduce eventual adult height
 * indicate the presence of a tumour or other serious problem
 * cause the child, particularly a girl, to become an object of adult sexual interest.

Treatment
One possible treatment is with anastrozole. GnRH agonists, including histrelin, triptorelin, or leuprorelin, are other possible treatments. Non-continuous use of GnRH agonists stimulates the pituitary gland to release follicle stimulating hormone (FSH) and luteinizing hormone (LH). Triptorelin depot is widely used to treat central precocious puberty (CPP) in children.

Prognosis
Early puberty is posited to put girls at higher risk of sexual abuse; however, a causal relationship is, as yet, inconclusive. Early puberty also puts girls at a higher risk for teasing or bullying, mental health disorders and short stature as adults. Girls as young as 8 are increasingly starting to menstruate, develop breasts and grow pubic and underarm hair; these "biological milestones" typically occurred only at 13 or older in the past. African-American girls are especially prone to early puberty.

Though boys face fewer problems from early puberty than girls do, early puberty is not always positive for boys. Early sexual maturation in boys can be accompanied by increased aggressiveness due to the surge of pubertal hormones. Because they appear older than their peers, pubescent boys may face increased social pressure to conform to adult norms; society may view them as more emotionally advanced, although their cognitive and social development may lag behind their physical development. Studies have shown that early-maturing boys are more likely to be sexually active and are more likely to participate in risky behaviors.

History
Pubertas praecox is the Latin term used by physicians from the 1790s onward. Various hypotheses and inferences on pubertal (menstrual, procreative) timing are attested since ancient times, which, well into early modernity were explained on the basis of temperamental, humoral and Jungian "complexional" causes, or general or local "plethora" (blood excess). Endocrinological (hormonal) theories and discoveries are a twentieth-century development.

title: Precocious puberty