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Talk:Pure mathematics

Pure mathematics is not the opposite of applied math. Many results in "pure math" manage to find applications in other fields. Besides, results in "pure math" are often applied in other math fields and many fields in math are motivated by other fields. Critical

Yo
I recall that some mathematician/group or school of mathematicians was skeptical of the value of proof at all and instead desired to simply experiment with methods and find the best ones for physical modeling (and by this I do not mean the 18th century). If anybody knows anything about him/her/them/it, please add it before or after the entry on Hardy under "Purism" (which can be molded to fit the knowledge of those other persons). Diocles

About Users Critical and CStar
For the record, the user Critical ( talk,  contributions), who slapped the "disputed NPoV" sticker on this page, has made his or her first edits tonight (or today) and within less than two hours has attacked eight articles for PoV, including (ironically given the CStar example given on the Logical fallacy talk page), Physical law. These were the only "edits" (plus weak justifications on talk pages in the same vein as this one). I don't think the PoV claim has merit. We may ask if this series of attacks is to be taken seriously.

For the following reasons I am thinking that these pages has been the victim of a tiresome semi-sophisticated troll and the PoV sticker should be removed sooner rather than later, if not immediately. We may note that CStar ( talk,  contributions) after making edits, paused during the period user Critical made edits, and then CStar took up responding to these edits after the series of user Critical edits ends, as if there is only one user involved, and the user logged out, changed cookies and logged back in. Further, user CStar left a note on Charles Matthew's talk page,  Chalst's talk page, and   Angela's talk page pointing to a supposed PoV accusation placed on the Logical argument page, when in fact no such sticker has been placed. Perhaps the irony regarding the Physical law page is not so ironic. Hu 05:18, 2004 Dec 1 (UTC)

 * I have responded to this on the logical fallacy talk page, as well as on the pages of the above mentioned users. It does appear that these pages were as Hu suggests the victim of a tiresome semi-sophisticated troll.  But I wasn't the perpetrator.  This suggestion appears to have been an honest mistake, I consider the matter closed, and it appears that Hu does as well. CSTAR 01:36, 2 Dec 2004 (UTC)

 * Just because he hasn't been a registered user for very long doesn't mean he has no right to an opinion on the page. If you want to dispute his statement then do so, do not belittle his merit.
 * Having said that though, the article doesn't state that pure is the opposite of applied. And if it did, that is not POV, rather a simplification to the point of fallacy. Critical: Just change the wording next time.

A mathematician is walking through a carpark, late at night. Halfway to his car, he drops his keys. If he was an applied mathematician, he would drop to his knees and methodically search around his feet. If he was a pure mathematician, he would realise the probability of him finding his keys is greater in the lighted region 500m away, so he heads in that direction.

18/19th century
The introduction says the origin is in the 18th century, yet the history farther down begins at the 19th century. Which is it?

subfields of pure mathematics
The article says about number theory "It is perhaps the most accessible discipline in pure mathematics for the general public."

This is just wrong. If you are talking about statements of theorems, yes there are some hard theorems of number theory with elementary statements. But that is true in other subjects -- the isoperimetric inequality, the Poincare conjecture, can be stated in a way anyone can understand. But the real substance of the subject cannot be readily understood by the public ... things like factorization of ideals in a ring of algebraic integers, on to the Langlands program, or the Riemann hypothesis. 86.128.141.126 11:24, 4 March 2007 (UTC)

subjective?
The opening stagement "It is distinguished by its rigour, abstraction and beauty." seems to be a little subjective, what do people think?

Definitely. This should be removed; there's no way to prove it's something that's a matter of opinion, and if you wanted to prove that most people thought it beautiful, you'd need a citation. Verisimilarity (talk) 03:53, 1 December 2009 (UTC)

Mathematical logic
Perhaps mathematical logic should be listed as a subfield? --Quux0r 07:22, 16 April 2007 (UTC)

You also do probablity in Mathamatics its not only a little kid thing. Well there much other things that you can do with math that what you might of used in elementary school. SO GET USED TO IT. CUZ IT IS NOT FUNNY.

He's crackin' —Preceding unsigned comment added by 92.112.13.41 (talk) 06:07, 18 January 2009 (UTC)

Bridging Pure Mathematics and Philosophy of Mind/Body (x_0)

 * Suppose {1 | continuum(x)}
 * {o | o <- object}
 * { x <- o }
 * Run forever

--Vektor-k (talk) 18:43, 6 August 2013 (UTC)

"intrinsic to nature"
(said about automorphic forms) What does this mean, if anything?

And if it does mean something (e.g. implying some relevance to "nature"), how does the rest of the sentence make any sense? It seems like this needs to be removed or clarified. 211.31.63.48 (talk) 09:10, 25 June 2015 (UTC)

Euclidean geometry is the the most accessible pure math
We live in a universe of curved Einsteinian space-time. Neither Euclidean geometry nor Newtonian mechanics actually exist anyplace in our universe. That makes them pure math by the definition in this article. Before you get to the example of the Banach–Tarski paradox given in the article, it's fair to point out that there are no real spheres, they are paradoxical, but if you had a paradoxical sphere then you could see the increased paradoxicality of the Banach-Tarski proof 74.65.224.183 (talk) 17:50, 26 October 2017 (UTC)

Edits of the lead
I have restored the last version of the lead before the recent edit war. Please do not edit the lead again without getting first a WP:consensus in this talk page. Without consensus, every edit will be reverted, and if a reverted edit is restored, administrators intervention will be required for either protecting the article and/or blocking edit-warriors.

My opinion is that the version that I have restored is not good, but the reverted edits make it worse. I'll discuss the different points in separate threads for making easier the discussions toward a consensus. D.Lazard (talk) 15:11, 24 November 2018 (UTC)

 * I agree with all of the above.Paul August ☎ 15:43, 24 November 2018 (UTC)

Fundamental mathematics
One of the edits in the recent edit-war was the introduction of "fundamental mathematics" as a synonymous for "pure mathematics". This is not true. The reference that has been added for supporting the claim is non-reliable source, as it is simply a course title, and does not establish any relationship between the two phrases. So the phrase "or fundamental mathematics" is original research (Wikipedia meaning), and its addition breaks Wikipedia policy WP:NOR.

The term "fundamental mathematics" is also confusing, because it seems to refer to foundations of mathematics, which is a completely different subject. D.Lazard (talk) 15:30, 24 November 2018 (UTC)

 * I removed "fundamental mathematics" as synonymous for "pure mathematics" (but was reverted), since I've never heard of that term being used this way. So even if it is used this way somewhere, I doubt that this use is common enough to be included here. Paul August ☎ 15:51, 24 November 2018 (UTC)

 * I've never heard "fundamental mathematics" used as a synonym for "pure mathematics", either. To me, "fundamental mathematics" might refer to foundational studies, or to the basic contents of a primary school curriculum, depending on whether a philosopher or a schoolteacher is speaking. I agree: it doesn't belong here. XOR'easter (talk) 15:58, 24 November 2018 (UTC)

Mathematics is not necessarily applied mathematics
Edit warriors removed "is not" from this sentence. The result is not grammatical. However the first sentence of this paragraph may be confusing, although the remainder of the paragraph is essentially correct. A more correct first sentence would be

In pure mathematics concepts are defined and studied independently of any application to the real word. However, these concepts may often be applied to the real world because, either they were introduced for modeling the real world (for example numbers and geometry), or after having been introduced independently of any application, they become widely used outside mathematics. An example is elliptic curves over a finite field, which are used for securing internet connexions (HTTPS protocol).

However, this is a definition of pure mathematics, which is better than the one that is given in the first paragraph. In fact it uses the concept of "entirely abstract concept", which is an oxymoron, as implying the existence of "partially abstract concepts".

So the lead deserves to be completely rewritten. I'll propose later a new version of the lead. D.Lazard (talk) 16:27, 24 November 2018 (UTC)
 * I agree that the current lead is terrible, even if better than than what it replaced. I am looking forward to D. Lazard's new version and if it is in line with the above snippet I will heartily approve it. A few suggestions. I think that "elliptic curves over a finite field" may be a bit too esoteric for the lead and doesn't sit well being juxtaposed with the other examples ("numbers" and "geometry"). I would suggest that it be replaced by number theory or even more pointedly "factoring large numbers". This would also entail replacing "numbers" in the earlier example for fear of confusion. Maybe with something like "networks" or probability. Also, I have a friend (a pure mathematician working in an applied mathematics department) who was fond of making the distinction between applicable mathematics and applied mathematics, the latter being a field of study and the former referring to the mathematics that possibly could be used in some application. This may be a useful turn of phrase in this article. --Bill Cherowitzo (talk) 20:22, 24 November 2018 (UTC)

Draft for a new lead
I suggest the following for the lead. Feel free to improve the grammar and the style. However, this is a major modification of the lead. So we must base discussion on a rather stable version. Therefore I recommend that non-minor modifications should be discussed separately, before being incorporated in this draft. Also I have created subsections for distinguishing the discussions for improving the draft from the discussion on the choice between it and the present lead. These sections appear after a section (still not written) in which I'll explain and comment my choices. D.Lazard (talk) 11:31, 25 November 2018 (UTC)

 * The sentence "In particular, it is not uncommon that some members of a department of applied mathematics qualify themselves as pure mathematicians." is honestly bizarre and I removed it from the lead. It's not about what a mathematician identifies themselves as, it's about the particular fields, concepts, or ideas that are grouped as pure or applied mathematics.
 * Sidenote: I'm an undergraduate mathematics major. JohnAdams1800 (talk) 03:31, 4 January 2024 (UTC)

Original synthesis?
Both the draft and the present lead are WP:original synthesis. This seems unavoidable in such an article. In fact it always difficult to define an area of mathematics (and even mathematics them selves). But here, we are faced to the lack of consensus among mathematicians, not only on what should be understood as "pure mathematics", but also whether it is an area of mathematics. As we must keep this article, and it seems impossible to avoid original synthesis, we must find a consensus among editors, and then apply WP:IAR

Nevertheless, I have tried to keep a minima my personal opinions, and to support them with facts that cannot be disputed.

Here are two personal anecdotes illustrating the difficulties.

Around 1968 (I do not remember whether it was before of after), I participated to a working group, leaded by Pierre Samuel about Mathematics and society. At one of the sessions we discussed on what is applied mathematics, and, by contrast, what is pure mathematics. We has a long discussion, where it appeared that measure theory was a part of probability theory, and Sobolev spaces space belonged to numerical analysis. As, at least in France, probabilities and numerical analysis were considered as applied mathematics, and measure theory and Sobolev spaces are clearly pure mathematics, we had long discussion, which was concluded by one of us (a probabilist, I believe), who said that the only workable definition of applied mathematics is to define them as the mathematics that Bourbaki don't know of.

At the same period, Roger Godement claimed that he chosen to work on modular functions because they cannot be used for military purpose. Alas, a few years later, they become used in nuclear studies.

Body of the article
If my draft is accepted, all the body of the article must be rewritten for supporting it.

In particular, sections "Generality and abstraction" and "Subfields" should probably be suppressed as unsourced WP:OR.

Section "History" should be adapted for given more details on the "mathematical revolution" of the end of 19th century that I have sketched in the draft, and its influence on the view

The section "Purism" is mainly focused on Hardy's opinion, which is 78 years old. Even at that time, this opinion was not a consensus among mathematicians. It should thus be adapted for reflecting other opinions and giving more modern point of views. Probably, one could find one in Cedric Villani writings, as the results (of pure mathematics) for which he got the Fields Medal were related to some problems of physics, and this relation was a part of his inspiration. His book about his discovery is probably a source of quotations on the relationship between pure mathematics and applications. D.Lazard (talk) 17:31, 25 November 2018 (UTC)

Discussion for improving the daft
I have qualms about the proposed definition of pure mathematics. More later, maybe.... Michael Hardy (talk) 17:57, 25 November 2018 (UTC)
 * Overall I am quite happy with this draft. I have made some minor grammatical changes directly in the draft and I am sure that there will be some tweaks suggested by various editors (myself included), but I think the tone is correct and it says what should be said about pure mathematics. As it is the lead, I am not very concerned about the OR issue as long as the points are reliably justified in the body of the article. As to my tweaks, there are only two. In the first paragraph it is stated that pure mathematicians do not care about applications. I am a pure mathematician and I do not care about applications, but that statement seems a bit harsh and doesn't really capture the situation. The fact is that I do care about applications, but they do not dictate what or why I study what I do. Applications are useful to communicate the essence of what I study to the non-specialists that I interact with, and if they don't exist I am forced to use some far-fetched analogies to make this point. I would be much happier if the statement was that pure mathematicians are not motivated by applications. My second tweak is very technical. In the reference to Einstein's Theory of Relativity a link is made to Non-Euclidean geometry and I think the connection should be made to "a geometry that is not Euclidean" since traditionally the term "non-Eulidean" is restricted to either elliptic or hyperbolic geometry and Minkowski space doesn't appear on that page. --Bill Cherowitzo (talk) 22:06, 25 November 2018 (UTC)

 * The second sentence piles up a lot of negatives. This does not mean that these concepts do not originate in the real world nor that the obtained results cannot be useful for modeling the real world, but rather that the pure mathematicians do not care about applications. Can we make the same point more directly? How about this: These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but the pure mathematicians are not primarily motivated by such applications. XOR'easter (talk) 00:17, 26 November 2018 (UTC)

 * Additionally, mathematics for itself does not sound quite idiomatic. How about mathematics for its own sake? XOR'easter (talk) 22:49, 26 November 2018 (UTC)

 * I like both of these suggestions. Pushing the logic behind the first suggestion, should we perhaps make a statement about what does motivate a pure mathematician? I realize that this may open a can of worms that we do not wish to open.--Bill Cherowitzo (talk) 23:29, 26 November 2018 (UTC)

I would really like to be able to cite some reliable sources, for a definition. Perhaps we can make use of Browder's definition: "that part of mathematical activity that is done without explicit or immediate consideration of direct application"? Also something perhaps from Hibert's (Hardy's of course), A Mathematician's Apology? I think this quote must be from there: "We are often told that pure and applied mathematics are hostile to each other. This is not true. Pure and applied mathematics are not hostile to each other. Pure and applied mathematics have never been hostile to each other. Pure and applied mathematics cannot be hostile to each other because, in fact, there is absolutely nothing in common between them."Paul August ☎ 00:22, 27 November 2018 (UTC)
 * I believe that should be G.H. Hardy rather than Hilbert. The sentiment of the quote is clearly in line with Hardy, but I can not find any mention of hostility in A Mathematician's Apology. On the other hand, section 22 starts with

"It is quite natural to suppose that there is a great difference in utility between 'pure' and 'applied' mathematics. This is a delusion: there is a sharp distinction between the two kinds of mathematics, which I will explain in a moment, but this hardly affects their utility."

 * His explanation of the difference goes on for two sections and would be hard to distill into a pithy quote.--Bill Cherowitzo (talk) 19:09, 27 November 2018 (UTC)
 * Oops, yes of course Hardy;-) Paul August ☎ 19:57, 27 November 2018 (UTC)

I think the level of the proposed lead is too high. We should aim the lead, and a good deal of the start of the article, so it can be understood by people who might want to know about the topic. I would put in there principally high school students who might be thinking of what they want to do. There is no point in aiming it at people who already know about Hilbert's basis theorem. Perhaps the picture of one ball becoming two is okay as an object of wonder in how pure mathematics has no relationship to the real world, but I think perhaps that is just a bit too ivory tower right at the beginning of the article. Dmcq (talk) 13:37, 5 December 2018 (UTC)

Discussion for choosing the version
Incorporating the comments above, I get the following:

How unhappy are we with this? XOR'easter (talk) 18:32, 5 December 2018 (UTC)
 * Fine for me. D.Lazard (talk) 18:52, 5 December 2018 (UTC)

 * Certainly better. The distinction started with the Greeks like the article says and I'd say an earlier applied mathematics use of pure mathematics was when Newton used the theory of conics from Apollonius to show how gravitation produced elliptical orbits. Dmcq (talk) 23:29, 5 December 2018 (UTC)

 * I think it would be desirable to say what does motivate the pure mathematician in addition to saying what doesn't. Perhaps something like: "... but the pure mathematicians are not primarily motivated by such applications, but rather by the intellectual challenge and esthetic beauty of working out the logical consequences of basic principles."--agr (talk) 03:14, 6 December 2018 (UTC)

 * I think that referring to motivation is at best reporting of retold hearsay (relata ... relata refero). There is no chance for evidenced motivation. That pure mathematicians often tell tales about the challenge and beauty of their profession might have a foundation in their abundant social competence. Sometimes even I (no pure mathematician) claim to see beauty in proofs from the book. Purgy (talk) 07:23, 6 December 2018 (UTC)

Revised accordingly:

XOR'easter (talk) 03:48, 6 December 2018 (UTC)

engels quote
just in the off-chance and  engage in a dispute over the quote, i want to say that i like it.

and while applied mathematics isn't explicitly mentioned by engels, he does specifically state 'pure mathematics'. the question i guess would be: was there any distinction at that time?

since engels was born in 1820 it would be fair to say we had a few titans who were active in this time period, Lords rayleigh and kelvin immediately coming to mind.

what do others think? i will admit i'm not a huge hardy fan, but that in no way affects my opinion on the relevance of the engels quote.

what do you think dr ?

maybe some context around the quote would help, but it seems to stand well on its own. 198.53.108.48 (talk) 20:13, 12 June 2021 (UTC)

 * Keep - as i said before: i like it. it sums up my opinion on what pure mathematics is as well. it may be 'theoretical', but the foundations are certainly grounded in reality. 198.53.108.48 (talk) 20:13, 12 June 2021 (UTC)

 * Keep as it provides a good summary of that philosophical position. However, the introduction to the quote needs to be written in proper English. "Friedrich Engels argued in Anti-Dühring that pure mathematics owe to reality for its existence" is very awkward. I suggest something like "Friedrich Engels argued in Anti-Dühring that the concepts of pure mathematics are based on physical reality". Burrobert (talk) 01:30, 13 June 2021 (UTC)
 * Keep—agree with above: the quote is fine, but the English is stilted (presumably in translation). How about: '...that pure mathematics owes its existence to reality, as "it is not true that...'? [NB I think the singular use of 'its' here correctly reflects 'pure mathematics' as being a 'non-count' noun, i.e. a singular concept, and as such takes 'owes' (3rd person singular) rather than 'owe' (3rd person plural!)]Kitb (talk) 10:24, 13 June 2021 (UTC)

 * Keep - Agree with the comments above and also think it would improve the article to paraphrase the quote to something less awkward and more easily understandable. I like what Burrobert suggested: "Friedrich Engels argued in Anti-Dühring that the concepts of pure mathematics are based on physical reality." TrueQuantum (talk) 18:18, 13 June 2021 (UTC)
 * comment I think it's better to stand in the same line of sight as Hardy or ride on Hardy's shoulders. To explain the positional relationship between the two lines, I think it is necessary to look beyond the horizon from a high position. I think the signature and ping are out of sync. So I didn't get any notification either. So --SilverMatsu (talk) 06:00, 14 June 2021 (UTC)
 * As you may already know, I add because I checked the discussion on the talk page and the article newer 50.--SilverMatsu (talk) 08:52, 14 June 2021 (UTC)
 * I don't see why my opinion on this burning issue is so central to have been pinged twice. I'm not familiar with the quote, and don't necessarily agree with it, but that's no matter. I don't see a good reason to exclude it. I am a little concerned, however, with its placement, as if we are saying with Wikipedia's voice that Engels is a complete answer to Hardy and had the final and correct word on this subject. Is there some way to make it more clear that it is merely one more opinion among many? Surely we have a significant body of more recent work in the philosophy of mathematics to draw on. —David Eppstein (talk) 06:12, 14 June 2021 (UTC)
 * Perhaps like a critical reception section of a media article? "Hardy argued X, Engels disagreed, arguing Y." Would just require a change of wording of the quote.Tazerenix (talk) 08:30, 14 June 2021 (UTC)
 * Thank you for your reply. I also think there is more new reference. Maybe move to the 19th century section? And I will act carefully so as not to get burned. I simply pinged everyone who seemed already pinged in this discussion because I didn't get the notification, but I'm sorry if the notification was duplicated.--SilverMatsu (talk) 08:43, 14 June 2021 (UTC)
 * Thank you for your reply. It's to be fair because I think it accurately represents the content added this time. But considering this addition as Hardy's counterargument, the citation is weak. In the current reference, I don't think we can tell that Engels' theory argued against Hardy after looking at modern mathematical theory (In the era when Hardy was alive), just to see that Engels did say so.--SilverMatsu (talk) 14:25, 15 June 2021 (UTC)

 * Keep - However, one should verify that the quote is a correct translation of the German original. Also, if a paraphrasing is added, it must not change Engels' thought: Engels used "reality", and above paraphrase uses "physical reality", which is definitively not the same, and Engels did know well the difference. D.Lazard (talk) 15:14, 15 June 2021 (UTC)
 * Thank you for your reply. Regarding the correctness of the translation, I found the following preprint.--SilverMatsu (talk) 15:47, 15 June 2021 (UTC)
 * Comment I don't see a reason to exclude the Engels quotes, though I can see an argument for paraphrasing them. I trimmed the lead-in to the quoted passages, as that was more awkward English than the translated quotations themselves. Overall, that section looks like a collection of bits and pieces that people happened to like, rather than even an attempt at a systematic overview. In other words, it's Wikipedia prose, hooray. XOR'easter (talk) 17:07, 15 June 2021 (UTC)
 * Thank you for your reply. Apparently, misunderstood the big picture of the section, and from that point of view, it seems to be keep.--SilverMatsu (talk) 02:57, 16 June 2021 (UTC)

Maybe rewrite the article with school(s) of thoughts in mind ??
I know that this is none of my business, cause I do physics, but I noticed the addition of Essay-like tag, it was added and removed multiple times anonymously. I do agree on the tag actually.

I do not agree on the proposed new lead by the way, few comments on the lead:
 * Every single existing mathematical concept has a nearby or faraway application, or concrete intuition at least, outside mathematics (at least in physics).
 * "but the pure mathematicians are not primarily motivated by such applications. Instead, the appeal lies in is attributed to the intellectual challenge and esthetic beauty of working out the logical consequences of basic principles.": essay style - sales pitch - beauty is not objective - working out logical consequences can be done by a computer. Seems a religion, where the pure mathematicians are the priests. See "Athya is math invented or discovered ?". Much of it is subjective.
 * Greeks had not whatsoever clue of pure math, they mostly do geometry and there is not much distinction between geometry and physics either. I believe this a historical gross invention, you shall prove this based on original greek sources only actually.
 * Non euclidean geometry was deeply rooted in geometry if you look at works of Gauss, Lobachesky and Poincare, and in general if you use embeddings.
 * Cantor was mangling with paradoxes, infinities and fractals in the scope of infinite sets (which are all rooted in geometry).
 * Nowadays Mathematical rigor is questionable outside automatic theorem proving
 * Again on rigor to be relevant nowadays one shall include type theory, higher order categories, isomorphisms between hierarchies of types, hott etc. One may argue that category theory in that sense is trendy but not rigorous.
 * On rigor: maybe is worth mentioning the bankrupcy of the algebraic geometry school of Italy, or author like elie Cartan which often do not separate out or formalize proofs
 * On rigor: two words on education are worth while, rigor is subjective, every time there is novelty one way or another there is less rigor.
 * The lead is too long, it shall be 5 lines max. This proves the kitchen sink approach of the article.
 * Philosophical approach: there is a need of full departments called pure mathematics to be funded. This is a biased opinion.
 * Philosophy of science and mathematics is not objective, it is relative and it changes over time.
 * Last Abel prize: Michel Talagrand was also a physicist, isn't this debate pure vs applied obsolete ?

If you want to leave in the article each of these statements, they deserve one citation for each, and eventually also counter arguments somewhere else in the article. I would argue that the best way is to rewrite the article in terms of school(s) of thought.

In regards to the historical section
 * Most of the examples in the greek section are related to geometry, maybe useless geometry at that time, but pretty far from the definitions of "pure/abstract" of nowadays.
 * The number theory example comes from Plato. Plato was selling his idea of the cave, so is a source with a distinct "pure" and biased opinion. Aristoteles for example would go the opposite way.
 * Number theory can manage to be very ugly if you look at the amount of special cases. Number theory has applications also, there is no boundary between pure and applied again.

In regards to the generalization/abstraction section:

 * Same essay-style/ sales pitch style
 * Most arguments are repetitive
 * Short vs long proof again subjective
 * Each of the 400 proofs of pythagora's theorem may give you a different insight
 * You can argue that all abstractions are just type theory alike constructions, a ring is a type and so forth, they shall belong to math on the same footing of the rest (they are not special).
 * Again following Arnold Abstract algebra does not exist
 * On abstraction: "two words on the constructivist approach and the example as the testimony" are worth it
 * On abstraction: "proof by negation" does it belong to the axioms of mathematics or not ? do we always need a testimony ?
 * "A steep rise in abstraction was seen mid 20th century". This was a French prob to fix the Italian bankrupcy of algebraic geometry. Is this hiding bourbaki under the carpet ? It does not belong to Russian math for quite long time really. Again subjective. If I like graph theory I may not have such a problem.

I see a kinda funny debate here, it remembers these bourbaki style discussions + restart from scratch approach they used to do with books. The debate around the engels quote also shows the same trouble with this essay-style article, again either embrace in full this philosophy of math approach showing pros / cons or don't include it at all. The discussion may become obsolete by the time is complete.

I am actually writing this comment cause this morning I found this wonderful piece from Arnold which states mathematics is part of physics. Arnold also states that limiting mathematics to this definition + axioms + theorem + proof is not enough. You cannot promote axioms and definitions out of the hat. A small variation in the definitions may create a huge discrepancy in the consequences (i.e. this is actual chaotic behaviour - where is the rigor ?). The scope of mathematics is much wider, it includes this finding the best approach to definitions and axioms, it includes creating general tools (e.g. Gelfand), it includes experiments, induction and so forth and in some shape of way mathematics is at least part of natural sciences.

There was another quote from Von Neumann stating that mathematics without physics is at best baroque, plus you can mention also Gelfand, Kolmogorov, Klein, Poincare (who considered set theory a disease) and a few others.

Maybe a "School of thoughts" style approach in both the lead and the article, with a good amount of citations, would help a bit to make the article looking more objective, unbiased and professional. Flyredeagle (talk) — Preceding undated comment added 17:34, 15 April 2024 (UTC)

title: Talk:Pure mathematics


text:
Calcium release activated channel

Calcium release-activated channels (CRAC) are specialized plasma membrane Ca2+ ion channels. When calcium ions (Ca2+) are depleted from the endoplasmic reticulum (a major store of Ca2+) of mammalian cells, the CRAC channel is activated to slowly replenish the level of calcium in the endoplasmic reticulum. The Ca2+ Release-activated Ca2+ (CRAC) Channel (CRAC-C) Family (TC# 1.A.52) is a member of the Cation Diffusion Facilitator (CDF) Superfamily. These proteins typically have between 4 and 6 transmembrane α-helical spanners (TMSs). The 4 TMS CRAC channels arose by loss of 2TMSs from 6TMS CDF carriers, an example of 'reverse' evolution'.

Homology
There are several proteins that belong to the CRAC-C family. A list of the currently classified members of the CRAC-C family can be found in the Transporter Classification Database. This classification is based on sequence similarity which also happens to coincide with functional and structural similarities between homologues.

Structure
Almost all CRAC homologues are about 250 residues long, but some are up to 100 residues longer (e.g., the Drosophila melanogaster Olf186-F, TC# 1.A.52.1.5).

The plasma membrane protein "Orai" (ORAI1 and ORAI2 in humans) forms the pore of the CRAC channel. The protein ORAI1 is a structural component of the CRAC calcium channel. ORAI1 interacts with the STIM1 protein. STIM1 is a transmembrane protein of the endoplasmic reticulum (ER). STIM1 can sense the concentration of Ca2+ inside the ER. When the concentration of Ca2+ inside the ER becomes low, STIM1 proteins aggregate and interact with ORAI1 located in the cell surface membrane. When the concentration of Ca2+ inside the ER approaches an upper set point, another protein, SARAF (TMEM66) associates with STIM1 to inactivate the store-operated calcium channel (SOCE).

The crystal structure of Orai from Drosophila melanogaster has been determined at 3.35 angstrom resolution. The calcium channel is composed of a hexameric assembly of Orai subunits arranged around a central ion pore. The pore traverses the membrane and extends into the cytosol. A ring of glutamate residues on its extracellular side forms the selectivity filter. A basic region near the intracellular side can bind anions that may stabilize the closed state. The architecture of the channel differs markedly from other ion channels and provides insight into the principles of selective calcium permeation and gating.

Function
In electrically non-excitable cells (i.e., blood cells), Ca2+ influx is essential for regulating a host of kinetically distinct processes involving exocytosis, enzyme control, gene regulation, cell growth and proliferation, and apoptosis. Capacitative calcium entry appears to also be a major means of signal transduction. The major Ca2+ entry pathway in these cells is the store-operated one, in which the emptying of intracellular Ca2+ stores activates Ca2+ influx (store-operated Ca2+ entry, or capacitative  Ca2+ entry). This is often referred to as the store-operated current or SOC.

A common mechanism by which such cytoplasmic calcium signals are generated involves receptors that are coupled to the activation of phospholipase C. Phospholipase C generates inositol 1,4,5-trisphosphate (IP3), which in turn mediates the discharge of Ca2+ from intracellular stores (components of the endoplasmic reticulum), allowing calcium to be released into the cytosol. In most of the cell, the fall in Ca2+ concentration within the lumen of the Ca2+-storing organelles subsequently activates plasma membrane Ca2+ channels.

STIM Complex
STIM1 is a Ca2+-sensor protein specialized for electrical signaling in the endoplasmic reticulum (ER). It interacts with and mediates store-dependent regulation of both Orai1 and TRPC1 channels. TRPC1+STIM1-dependent SOC requires functional Orai1. STIM1 is the mechanistic 'missing link' between the ER and the plasma membrane. STIM proteins sense the depletion of luminal Ca2+ from the ER and trigger activation of CRAC channels in the surface membrane after Ca2+ store depletion. The process involves oligomerization, then translocation to junctions adjacent to the plasma membrane, by which the CRAC channels become organized into clusters and then open to bring about SOC entry.

Lymphocytes
The primary mechanism of extracellular Ca2+ entry in lymphocytes involves CRAC channels. STIM1 is a crucial component of the CRAC influx mechanism in lymphocytes, acting as a sensor of low Ca2+ concentration in the ER and an activator of the Ca2+ selective channel ORAI1 in the plasma membrane. Yarkoni and Cambier (2011) reported that STIM1 expression differs in murine T and B lymphocytes; mature T cells express about 4 times more STIM1 than mature B cells. Through the physiologic range of expression, STIM1 levels determine the magnitude of Ca2+ influx responses that follow BCR-induced intracellular store depletion.

SCID
Antigen stimulation of immune cells triggers Ca2+ entry through tetrameric Ca2+ release-activated Ca2+ (CRAC) channels, promoting the immune response to pathogens by activating the transcription factor NFAT. Cells from patients with one form of hereditary Severe Combined Immune Deficiency (SCID) syndrome are defective in store-operated Ca2+ entry and CRAC channel function. The genetic defect in these patients appears to be in ORAI1 (TM protein 142A; TMEM142a), which contains four putative transmembrane segments. SCID patients are homozygous for a single missense mutation in ORAI1, and expression of wild-type ORAI1 in SCID T cells restores store-operated Ca2+ influx and the CRAC current (ICRAC).

SOCE
Store operated calcium entry (SOCE) is used to regulate basal calcium, refill intracellular Ca2+ stores, and execute a wide range of specialized activities. STIM and Orai are the essential components enabling the reconstitution of Ca2+ release-activated Ca2+ (CRAC) channels that mediate SOCE. Palty et al. (2012) reported the molecular identification of SARAF as a negative regulator of SOCE. It is an endoplasmic reticulum membrane resident protein that associates with STIM to facilitate slow Ca2+-dependent inactivation of SOCE. SARAF plays a key role in shaping cytosolic Ca2+ signals and determining the content of the major intracellular Ca2+ stores, a role that is likely to be important in protecting cells from Ca2+overfilling.

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

title: Calcium release activated channel


text:
Talk:Education in Finland

Article sorely lacks citations and has had many tags placed long ago that have apparently been ignored
AFAICT, more than HALF of this article lacks any citations whatsoever. The "pillar" of WP:No original research is NOT optional. Moreover, the article has been tagged in places for two years or longer! That is MORE THAN ENOUGH time for any editors wanting to keep unsourced material to cite sources that faithfully depict the content. Readers and editors of this article should without further delay add competent sources or expect large amounts of content to be chopped, starting with long-tagged content AND grandiose generalizations such as "In most countries, the term "comprehensive school" is used to refer to comprehensive schools attended after primary school, and up to 12th and 13th grade in some countries..." — Preceding unsigned comment added by 62.248.208.251 (talk) 13:10, 18 October 2023 (UTC)

title: Talk:Education in Finland


text:
Talk:Saul Steinberg

Untitled
I'm sorry I have to turn this page into utter stubness (in order not to revert it to pure blankness), but it is a verbatim copy of http://www.saulsteinbergfoundation.org/life_work.html, explicitly copyrighted (see "Contact" page on that site): Copyright Notice: All texts and images on this website are copyrighted by The Saul Steinberg Foundation and cannot be used in any way except by express written permission of the Foundation. RodC 00:49, 1 Dec 2004 (UTC)

Wouldn't it be the case of having the Saul Steinberg (business) page created before disambiguating? Saul Steinberg is a fairly common name, but the "artist" is undoubtedly the most famous. BTW, there's a funny story about him: he looked up other Saul Steinbergs in the phone book and called one who lived nearby - "Are you Saul Steinberg?", he asked. "Yes", the guy replied. "But are you the real Saul Steinberg?". And the poor fellow sighed: "No..." ;)   RodC 18:50, 10 Feb 2005 (UTC)

I propose that this article be moved to Saul Steinberg, leaving Saul Steinberg (disambiguation) to take care of other people with the same name. RodC 18:00, 05 Jun 2005 (UTC)

WikiProject class rating
This article was automatically assessed because at least one article was rated and this bot brought all the other ratings up to at least that level. BetacommandBot 04:14, 28 August 2007 (UTC)

Removed broken/wrong cite
I removed a cite that linked to a photo. I believe this is probably the one that was intended. Is there another source from a 3rd party rather than the subject's foundation? TIA, --Tom 17:09, 3 December 2007 (UTC)
 * I'm not certain, but I do not think there is a relibility issue with the foundation as a source, do you? -- Avi 17:37, 3 December 2007 (UTC)
 * Its more a conflict of interest issue. I would rather have a 3rd party reliable source rather than the subjects own foundation tell us about the man, but thats just my 2 cents. --Tom 19:25, 3 December 2007 (UTC)
 * Conflicts of interest are issues when editing, in general, and, contrary to popular belief they do not prohibit editing, but require more care. While it is true that foundations set up to preserve people's memory are usually slanted more to the congratulatory than the denigrating, it does not mean that they are considered unreliable. If anything, they have more research, papers, interviews, and history than most any other site. It is our job to assemble it in a neutral fashion, not to ignore treasure troves of information if they are available. Just my opinion. -- Avi 19:58, 3 December 2007 (UTC)
 * I like the word "slanted" you used. Agreed that they can be be good sources for other 3rd party sources but I would be careful as to their "commentary" and "opinions" as you have pointed out. Anyways, do you have an opinion about the nationality naming convention outlined below? I have been dealing mostly with bios, lead sentences, and MOS issues lately, Cheers, --Tom 20:48, 3 December 2007 (UTC)

Nationality in lead sentence
It seems that he spent most of his life as a US citizen and it is here that he did most of his notable work. Per WP:MOSBIO, Romaian-born American is the best. I am no expert on this gentleman so I will look for other imput. It seem that the project is trying to avoid these duel nationality descriptors in the LEAD sentence. Anyways, --Tom 19:35, 3 December 2007 (UTC)ps, I know I didn't want to use the foundation as a source :), but they describe him as "one of America’s most beloved artists". Anyways --Tom 19:37, 3 December 2007 (UTC)

Improvement suggestions
Try to find an image of Saul Steinberg

Elaborations on Steinberg's specific works

Possibly find images of Steinberg's main works. ZH92 (talk) 02:28, 25 September 2013 (UTC)

title: Talk:Saul Steinberg


text:
Template:Kraków

{{Documentation|content= {{Collapsible option}}

title: Template:Kraków


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Talk:Iram of the Pillars

Omar Khayyam on Iram of the Pillars
Zelda hasn't commented on the reference to Khayyam. I've removed and copy it below:

... and the Rubaiyat of Omar Khayyam:
 * ''Iram indeed is gone with all its Rose,
 * And Jamshyd's Sev'n-ring'd Cup where no one knows; (1859 version)

– Kaveh (talk)  00:49, 1 Dec 2004 (UTC)

Contradiction
At the beginning, the article states that Ubar was founded around 3000 BC, but later on, the date of 900 BC is given.

1984 NASA Challenging imaging was Side Looking Radar. These are not photographs. These images, when combined with image processed LandSat and SPOT data helped substantiate presence of the ancient caravan routes partially buried by sandd dunes and seen by earlier ground forays (1920's not 1953 as reported). These images did not show buried cities!

Nicholas Clapp's book's copywright date is 1998, 1992 as reported.

Four subsequent excavations were conducted by Dr. Juris Zarins, then of SE Missouri State University, that traced the historical presence by the peoople of 'Ad, assumed ancestral builders of Ubar.

Why is this listed among "fictional cities" if it in fact did exist? --217.127.191.232 (talk) 15:19, 28 May 2008 (UTC)
 * It has not yet been found. Past writers might be talking about different cities, and some of them reported it as an already lost city. Phlegm Rooster (talk) 18:36, 28 May 2008 (UTC)

name of the city
the city name is "Aram; آرام" in arabic not Iram or Erum... the semitic group name "Aramaeans" came from this city (Aram: Aram Damascus).. —Preceding unsigned comment added by 217.132.114.154 (talk) 16:37, 19 July 2008 (UTC)

I found this video on a City of 1000 Pillars in Turkey which appears to have been burried suddenly with sand. The descrption matches 'Aaad, but the location is different. See http://www.snotr.com/video/7612/12_000_Year_Old_Unexplained_Structure. — Preceding unsigned comment added by 68.34.78.156 (talk) 14:36, 13 August 2011 (UTC)

Destroyed by fire?
I have read that the Qu'ran says Ubar was destoyed by fire. Is this so? Or are the quotes given in this article the only ones from the Qu'ran that deal with Ubar? 86.150.97.35 (talk) 10:43, 18 November 2009 (UTC)

What a mess
This article is a right old mess. The confusion/conflation of Ubar/Iram is made worse by this article! I've tried to take out some of the non-encyclopedic tone material - a lot of is isn't cited but I haven't removed it as I don't know too much about the subject. 86.138.46.145 (talk) 09:29, 22 December 2009 (UTC)

 * Indeed. It seems we have mentions of a people called the Iobaritae from classical times, of a city of Iram from the Koran, and great expansions on the city of Iram from later legend (eg the Arabian Nights). The article doesn't really explain how the connection was made between the Iobaritae and the city of Iram (or how Iram and 'Ubar' were identified), however, or how the Shisar archaeological site was identified with either (or both) - presumably it is in the region ascribed to the 'Iobaritae', but if so the article doesn't actually say so. Vultur (talk) 19:56, 12 May 2011 (UTC)

Atlantis of the Sands
I agree that this article is confused. I think it is shame that this topic has been dealt with under the title "Iram of the Pillars" because the case for Iram being Ubar being Omanus Emporium being the "Atlantis of the Sands" is not compelling. ArabianLeopard (talk) 07:41, 29 June 2011 (UTC)

I would recommend merging this page with Atlantis of the Sands. AusJeb (talk) 20:32, 29 July 2013 (UTC)

 * I would too! It is utter - sorry for my language - idiocy to have these two articles about what is really the same lost place! 146.90.0.47 (talk) 23:19, 18 April 2022 (UTC)

Not a page worthy of Wikipedia
This page is a mess. It mixes archaeology with mythology and makes assertions without any reason or source. It is a mix of myths and legends, using a religious book as base. No pillars and nothing of a city indicating that it is Iram has been found. The entire page is based on a sentence in the Koran and the 1978 article in National Geographic, where it says that a tablet excavated in the city of Ebla contains the name of Iram. No pillars, no details whatsoever, which makes this pure speculation.WilliamBillyB (talk) 23:14, 10 February 2012 (UTC)

TE Lawrence
Besides the fact that Henry Stewart Edgell says it isn't true, I found " T.E. Lawrence (Lawrence of Arabia) called the vanished city “Atlantis of the sands” in his 1926 book Seven Pillars of Wisdom" - well, that book is searchable, and doesn't mention it. So I've removed it for the time being. Once I get Edgell's article I'll probably replace it saying it isn't correct. Dougweller (talk) 12:53, 12 July 2012 (UTC)

Way forward
I think we need one article, not this article and Atlantis of the Sands, as they are all really about a "Lost city of the sands". We certainly don't need this article - as Edgell says, "However, the Qu'ran does not state that Iram was a city, and "lofty pillars" is simply one interpretation among many of the phrase dãti °l-cimãd". I'll try to work on this over the next few days. Dougweller (talk) 17:41, 12 July 2012 (UTC)

Move all Lost City stuff to "Atlantis of the Sands"? Separate Iram, Ubar and Lost City stuff.
I suggest moving the "Identification with Ubar" (including photos), and most or all of "In Fiction" to Atlantis of the Sands, and adding a link from Ubar to Atlantis of the Sands with an explanation why. Then this page would remain for the referance to Iram/Aram in the Koran, with a links to/from Atlantis of the Sands as a possible if unproven link. Currently this page conflates -- a reference to Iram or Aram in the Koran; "Ubar", whatever that might be; and the ida that the site found in Oman in 1991 near Shisr might be the same place as both or one of Iram of the Pillars and/or Ubar. Each of these three things can be addressed in different pages in Wikipedia with appropriate links between them. ReedHedges (talk) 18:32, 22 May 2014 (UTC)

the National Geographic reference
Let's stick to the facts. There is no evidence that Iram is associated with "Atlantis of the Sands" or any other city. In fact, the only appearance of Iram in archeological records that this article has ever presented is mentioned in the December 1978 National Geographic reference that was removed by Dougweller as he stated: "National Geographic not a reliable source, tablet was "Iram dagan" meaning "Dagan (a god) loves"". Thanks to Dougweller for inspecting it.

So the article should only contain the known references to Iram, which are, as WilliamBillyB said, "a sentence in the Koran and the 1978 article in National Geographic". These are the only two elements that this wiki page stands upon. We need a decisive reference (expert opinion I guess) that would decide whether Iram in that tablet has anything to do with the Iram in The Quran. If there is no relation, then the Quranic reference should return to its normal long-held status, i.e., unknown reference. That is until some archeological finding can be linked to it in the future.

Also, Iram should not be confused with the "City of a Thousand Pillars" or "Atlantis of the Sands" or others. At best, they should be put in the 'See Also' section. --3omarz (talk) 05:51, 6 October 2012 (UTC)

 * I more or less agree, except that I think that we'd need a very reliable source associating the tablet with the Quran to include it. And thanks for the compliment. :-) Dougweller (talk) 06:21, 6 October 2012 (UTC)

Is this an Article for deletion?
The talk page of this Article looks like a talk page (as it should). But the Article itself could be mistaken for a talk page (which ought not to be possible).

CBHA (talk) 22:00, 3 July 2014 (UTC)
 * It would easily survive an AfD, but do you have any practical suggestions? Dougweller (talk) 07:26, 4 July 2014 (UTC)
 * Thank you. Sorry no practical suggestions to offer.  CBHA (talk) 16:24, 4 July 2014 (UTC)

 * Hello! I do have several suggestions (after more than a year, but hey, better latter than never). First, I think the lead should be changed to something that reflects what the name Iram means, and the different interpretations it has had. As I understand it, at its most basic it is a Islamic tradition which may be based in the ruins of the several ancient cities that dot the arabian peninsula (I personally always thought that Iram was born when the beduins confronted abandoned cities like Palmyra and tried to give then an explanation, and the pillars make reference to the striking columns that are many times the only vestige of old buildings, but my personal opinion does not have a place here). This tradition was later received in the Western world, in two main contexts: the scholars seek to understand what the name means and if might have been related to some real world location, and the fiction writers have used it as magic place. I have written a proposal below, but as I am not a native english speaker, I will not edit it directly:

"Iram of the pillars is a location mentioned in the Quran (89, 7) as having been destroyed by an act of divine punishment, similar to Sodom and Gomorrah in the judeochristian tradition.

(Here I would put the quote itself)

The obscurity of the quranic quote led to many debates already among medieval Muslim exegetes about the nature of Iram, as it is not immediately clear if the name refers to a city, an area or even a particular tribe.

In islamic folklore, the name became associated to several myths and legends about cities lost in the desert of the arabian peninsula, and appears in One Thousand and One Nights in that sense. Since the nineteen century Iram has gained some popularity also in western culture: In academic circles the original debate about the exact nature of Iram and its possible location is still alive, while the name has become something of a staple in works of fiction, like those of Lovecraft, Clive Owen or Neil Gaiman as an archetypical magic city lost in the sands of Arabia."

With the introduction out of the way, I would add four sections: Iram in the islamic exegesis, Iram in folklore and mythology, Scholarly View/ Interpretation and Reception in popular western culture.

This kind of oversees the attempts of locate Iram, but I think that can be just noted in passing, as the "Atlantis of the Sands" page already covers most of that issue. 195.53.233.213 (talk) 15:12, 11 January 2016 (UTC)

"translated by"...who?
The article uses, but for some reason ends with "translated by" without any name. I don't know if it's a mistake in the use of the template or in the template itself (and I can't find usage documentation for the template). Does anyone know how/where to fix it? Zeniff (talk) 01:07, 30 November 2016 (UTC)

Rewrite with "Iram in the islamic exegesis, Iram in folklore and mythology, Scholarly View/ Interpretation and Reception in popular western culture."
The current article misses out a lot - the identification of Iram with Damascus (probably because of Columns and Hiram), it's identification as the palace of King Shaddad, etc. I actually agree with the suggestion made above that it should be recasted.

I have found for instance this which says, among other things, "Commentators and historians were to argue hotly about whom, or where, Iram might signify and how the disaster came about. Iram occurs as a tribal name of ‘Adites, who were in Northern Arabia as well as the Yemen.5 A sober reappraisal by Ibn Khaldun (d. 808/1406) suggested that a disaster which befell an affluent urban society, or even a nomadic group who lived in tents,6 was the true subject of this lesson of scripture, not a specific folly.But, correct or incorrect, his reinterpretation was already too late. As early as Wahb b. Munabbih al-Yamanl7 (d. 114/732), the verse was seen as an allusion to the exploits of Shaddad b. ‘Ad, a mythical conqueror of lands between Morocco and Tibet. In Marib “he built the noble palace which is named by some storytellers ‘Iram of the columns’”. The fabulous abode was a storehouse of riches. Its floors were of red and white marble.8 “Beneath it he placed cisterns and conduits down which poured the water of the [Marib] dam.”" Or this by Bruce Fudge, an expert on Arab literature now at the University of Geneva. (as it's on JSTOR I can get it). William Jones, Robert Southey and William Coleridge are among Western writers who have mentioned it. Doug Weller  talk 19:34, 5 March 2018 (UTC)

Islamic Hadith section
I just added that section if anyone has any note please reply to me here before you make any change,thank you. SharabSalam (talk) 21:12, 28 July 2018 (UTC)

"Citation needed" on The Seventh Sanctuary
I have removed the above template from the In fiction: Literature sub-section. My understanding is that fiction books serve as their own reference for their plot details, and there can be no doubt that the seach for Iram is a major plot point of Easterman's novel. {The poster formerly known as 87.81.230.195} 90.197.179.175 (talk) 09:31, 21 January 2023 (UTC)

title: Talk:Iram of the Pillars


text:
Ear piercing instrument

An ear-piercing instrument (commonly referred to as a piercing gun or an ear-piercing gun) is a device designed to pierce earlobes by driving a pointed starter stud through the lobe. Piercing guns are typically used for ear piercing in mall jewelry shops, beauty salons, pharmacies, and doctors' offices.

Piercing guns have been widely criticized as dangerous among professional body piercers. The use of older designs of piercing gun can possibly carry an increased risk of disease transmission, as compared to methods used by professional piercers. Piercing guns have been criticised for causing damage (sometimes mischaracterised as blunt-force trauma) to the skin and underlying tissue. Diminished air and blood circulation in tissue compressed by a piercing gun can lead to prolonged healing, minor complications and scarring.

More modern designs of reusable ear-piercing instruments, such as Inverness and Studex System 75, use self-contained, single-use, sealed, and sterilised disposable cartridges or cassettes. The studs used with such systems often have thinner posts (normally 20 gauge) with sharper tips, as opposed to the thicker (16 gauge), blunter posts of the "standard" ear-piercing guns. This makes the piercing somewhat less painful, and lessens trauma to the skin and tissue, but may still cause more trauma compared to hollow needles used by professional body piercers. Modern ear-piercing studs are also more likely to be made from materials certified as safe for long-term implant in the human body, such as titanium.

Traditional model
The older designs of ear-piercing gun, which came widely into use in the 1970s but are still in widespread use (e.g., "Studex Universal" ) employ a spring that stores potential energy when the instrument is "cocked" ready for piercing by pulling back a plunger.

The starter studs and friction clasps that are used with these instruments typically come in pairs, in sealed, sterilized packages. The studs have a pointed tip designed to pierce the earlobe rapidly when the trigger mechanism is released, and a "shoulder" to hold the clasp in place, and to maintain appropriate spacing between the clasp and the stud head, such that the earlobe is not squeezed while healing. The studs are slightly thicker, 16-gauge, and are made of surgical steel, 24 karat gold-plated steel, 14-karat gold, or titanium.

To conduct the ear piercing, the instrument is first cocked by drawing the plunger back. The piercer inserts the head of one of the pair of starter studs selected by the client into an adapter in the barrel in the body of the instrument, and the clasp is slid into the clasp retainer at the front of the instrument. The piercer then positions the client's earlobe between the point of the stud and the clasp retainer, and squeezes the instrument closed such that the tip of the stud is aligned with the mark where the piercing is to be placed, and to hold the earlobe in place during the piercing. When the alignment of the stud is correct, the piercer releases the trigger, and the force of the spring causes the instrument to fire with considerable pressure, snapping the plunger forward, pushing the point of the stud rapidly through the earlobe, and engaging it with the clasp behind the earlobe, completing the ear piercing. As necessary, the procedure is repeated to pierce the other ear.

The older designs of ear-piercing gun cannot easily be sterilized, which led to the development of more modern systems that employ single-use, disposable cartridges.

Disposable-cartridge designs
Most newer models of piercing guns use a disposable cartridge, sometimes called a "cassette". With these models, the stud holder and clasp holder are fully disposable. In some parts of the world, this modification is either specifically required (e.g., in Scotland) or implied by Health and Safety legislation.

Hand-pressure designs
In certain more modern designs, such as Inverness 2000 and Studex System 75, the instrument operates via hand pressure, whereby the piercer squeezes the instrument closed to push the stud rapidly through the ear, instead of via the force of a spring when a trigger is released. These models work with piercing studs housed in disposable, single-use cassettes, which are loaded into the instrument without the operator touching either the studs or the clasps; sufficient force to pierce the ear rapidly is attained when the stud breaks apart its plastic mount inside the cassette. The ease of operation, the greater variety of stud designs (different materials, jewels, settings, and shapes), and the relative painlessness of the piercing, and the absence of a sudden "snap" facilitated by such instruments is likely to have contributed to the widespread increase in popularity in ear piercing since the late 20th century, and in trends such as multiple piercing, piercing among both sexes and in younger children, and the abandonment of the perception of ear piercing as an ordeal.

Another design for a hand-pressure ear-piercing instrument is Coren, which comprises a small U-shaped plastic holder pre-loaded with a standard 16-gauge ear-piercing stud in one arm of the device and the clasp in the other. To pierce the ear, the operator closes the instrument around the earlobe, aligning the point of the stud with the mark for the desired placement of the piercing, and squeezes a plastic plunger with sufficient pressure to break two plastic flanges on either side of the plunger, forcing the stud rapidly through the earlobe, and engaging the stud with the clasp behind the earlobe. The used instrument is then discarded.

Criticism
Ear-piercing "guns" have been widely criticized in the body piercing community, which advocates piercing with needles. Shannon Larratt, editor and publisher of BME and a vocal critic of the piercing gun, penned an essay titled Piercing guns are blasphemy!, where he described the piercing gun as an inherently flawed, dangerous instrument that should never be used. Larratt also printed T-shirts which featured an image of a piercing gun with a red circle and line through it, to mean No Piercing Guns. BME also published an article titled Do Piercing Guns Suck?.

Use on areas other than the ear lobe
While they are sometimes used for this purpose, ear-piercing guns were not originally designed to pierce through the cartilage of the upper ear, or to pierce any part of the body other than the earlobe. Some U.S. states and some European countries have banned piercing guns for use on ear cartilage and nostrils. Improper use of ear-piercing instruments on areas of the body not intended for their use can lead to problems with healing and placement. Ear-piercing studs can be too short or wrongly shaped for the tissue, especially for oral piercings, and can lead to problems with "embedding" in which the wound effectively heals over it. In some cases this has necessitated surgical removal of the stud and can lead to abscesses, infection and scarring. For other body piercings, the gauge of the studs used by piercing guns is too narrow and can lead to tearing and other trauma that expose the body to infection and can cause permanent scarring.

title: Ear piercing instrument


text:
Campus of Iowa State University

The Iowa State University campus contains over 160 buildings, several of which are listed on the National Register of Historic Places. Iowa State University's campus, specifically its Central Campus, has been recognized as one of the nation's most beautiful and was listed as a "medallion site" by the American Society of Landscape Architects in 1999.

Campus
Iowa State's main campus features 490 acres of trees, plants and classically designed buildings. The concept of an open central campus encircled by buildings, was the vision of Iowa State's first president, Adonijah Welch. The campus is dominated by a large 20 acre central lawn known as Central Campus. Along with the University of Virginia and Yale University, ISU's central campus was listed as a "medallion site" by the American Society of Landscape Architects in 1999. It was listed as one of 25 most beautiful sites in the United States in the book The Campus as a Work of Art.

Fountain of Four Seasons
The fountain was sculpted by Christian Petersen in 1941 after a request from Iowa State President Charles Friley. The previous fountain was a vertical water tower on which students would place toilet seats. President Friley hoped that with a new, beautiful fountain, students would no longer make jokes of it.

Lake LaVerne
Named for Dr. LaVerne W. Noyes, who also donated the funds to see that Alumni Hall could be completed after sitting unfinished and unused from 1905 to 1907. Dr. Noyes is an 1872 alumnus. Lake LaVerne is located west of the Memorial Union and south of Alumni Hall, Carver Hall, and Music Hall. The lake was a gift from Dr. Noyes in 1916.

Lake LaVerne is the home of two mute swans named Sir Lancelot and Elaine, donated to Iowa State by VEISHEA 1935. In 1944, 1970, and 1971 cygnets (baby swans) made their home on Lake LaVerne. Previously Sir Lancelot and Elaine were trumpeter swans but were too aggressive and in 1999 were replaced with two mute swans. In early 2002 Sir Lancelot suffered a broken foot from chasing a campus lawnmower. Sir Lancelot underwent surgery at Iowa State's College of Veterinary Medicine, but after months of physical therapy efforts in returning him to Lake LaVerne were unsuccessful. Early spring 2003 Lake LaVerne welcomed is new and current mute swan duo. However, in support of DNR efforts to re-establish the trumpeter swans in Iowa, university officials avoided bringing breeding pairs of male and female mute swans to Iowa State which means the current Sir Lancelot and Elaine are both female.

Marston Water Tower
Iowa State is the home of the first elevated steel water tank west of the Mississippi River. Named the Marston Water Tower, it was erected in 1897 under the supervision and design of Anson Marston and his assistant Elmina Wilson. The water tower was constructed due to a severe water shortage in 1895 that forced cancellation of classes. In 1978, the water tower was disconnected when the university switched to municipal water. It was listed in the National Register of Historic Places on May 27, 1982, and restored in 1987.

The water tower stands 168 ft tall on an octagonal base. The tank holds 162,000 US gallons (613 m3) and is 24 ft in diameter and 40 ft tall. When full, the 72,400 ft3 of water would weigh 2,050 t.

Reiman Gardens
Roy Reiman is a 1957 graduate of Iowa State in agriculture journalism and he is the founder of Reiman Publications. The Reiman Gardens are named for Roy and his wife Bobbi who donated $1.3 million to begin their development. Located south of Jack Trice Stadium. Opened in 1995, the gardens have grown to become the largest public garden in the state. The popular Christina Reiman Butterfly Wing was opened in November 2002.

Veenker Memorial Golf Course
Named for George F. Veenker, head football coach at Iowa State from 1931 to 1936. He was also athletic director from 1933 until 1945. The golf course was completed in 1938 and given its current name in 1959.

Research farm
The Western Iowa Experimental Farm is to be found in Castana.

Current buildings
This is an incomplete listing of buildings at Iowa State University. Click on the building title for additional building information.

Facilities
The Iowa State University/Ames YWCA is on the campus grounds, at the Knapp-Storms Commons.

The Ames-ISU Student YMCA used to be in the Lab of Mechanics, Room 109. The chapter was established in 1887. It became affiliated with the national YMCA in 1900. Originally in Alumni Hall, it moved to Room 109 in 1993.

title: Campus of Iowa State University


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Monks Orchard

Monks Orchard is a suburb on the edge of the London Borough of Croydon, in the ceremonial county of Greater London, England, prior to 1965 it was located in the historical county of Surrey. It is situated about 10 miles (16.1 km) south south-east of Charing Cross, south of Elmers End and Eden Park, west of West Wickham, and north and east of Shirley and Shirley Oaks.

History
Monks Orchard is not named after a monastery in the area, but in fact commemorates a family named Monk, from Addington, who owned a farm (Monksmead) and a wood (Monks Orchard) here in the 17th century. The land was acquired by Lewis Lloyd in 1854, who built a mansion here and adopted the name of the Monks Orchard wood for the whole estate. Lloyd's Monks Orchard House was one of the most substantial mansions in the Croydon area. It had 19 bedrooms, a billiard room, library, and numerous other rooms; the Dining Hall alone was over 36 ft x 21 ft. The estate covered a huge area, 1540 acre, stretching northwards from the Wickham Road almost to Elmers End, southwards nearly as far as Addington, and eastwards across the County boundary into West Wickham. It also included several other major residences, such as Spring Park, farms, including Eden Park, Ham Farm, Shirley Farm, Spring Park Farm and Oak Lodge Farm, two dozen or so cottages, The Rising Sun, The Cricketers and the White Hart, and Beckenham Golf Course.

As late as 1923, the area was described in the following way: "The Estate, which has an extensive frontage to the road between the villages of Shirley and West Wickham, is delightfully rural in character, typifying that which is best in the unspoiled English countryside. The land seems adapted by nature for those who are seeking country houses not too far from London, being already park-like meadow land, well timbered, and dotted with coppices; thus affording almost unlimited scope for imagination, and taste, in laying out grounds, by utilising the natural advantages already there."

When the estate came up for sale in 1920, only parts of it found buyers, and the rest, including the part now known as Monks Orchard, was offered again in 1924, and this was finally purchased by the Corporation of London for the relocation of the Bethlem Hospital, which had long outgrown its Lambeth home. Building of the new hospital started in 1928, which involved pulling down Lloyd's old mansion. The hospital development did not require all of the land and the remainders of it were sold off for housing development.

By 1937-1939, most of the current streets had been developed - Orchard Grove, Elstan Way, Greenview Avenue, and so on. A 1937 prospectus for the Tudor-style "Homes of Distinction" in Greenview Avenue extols the virtues of local building ("There are no mass production houses and no mass production methods") and after describing the houses in great detail, claim that the fitted kitchenettes are "the Housewife's Dream virtually come true".

The Lawdon Estate was developed in the late 1960s and includes Regency Walk, Sloane Walk and Kempton Walk.

In 2015 the Bethlem Museum of the Mind opened in Bethlem Royal Hospital, which covers the history of the institution and changing attitudes to mental health over the decades.

Amenities
The area contains a small row of shops on Bywood Avenue, with a smaller parade on Orchard Way now reduced to just a Co-op supermarket following the closure of The Orchard pub in 2019. There is also an Anglican church, St George the Martyr, located on Elstan Way; the original church (now the church hall) was built in August 1937, with the current edifice being constructed in August 1952.

Nearest stations

 * Eden Park railway station
 * Elmers End railway station
 * Norwood Junction railway station
 * West Wickham railway station
 * Woodside tram stop

title: Monks Orchard


text:
Maximilian III, Archduke of Austria

Maximilian III of Austria (12 October 1558 – 2 November 1618), was a member of the House of Habsburg and the Archduke of Further Austria from 1612 until his death. He was also briefly known as Maximilian of Poland during his claim for the Polish throne. He would try to be elected as King of Poland he was defeated. He was also Grand Master of the Teutonic Order

Biography
Born in Wiener Neustadt, Maximilian was the fourth son of the Emperor Maximilian II and Maria of Spain. He was a grandson of Anna of Bohemia and Hungary, daughter and heiress of Vladislaus II of Bohemia and Hungary, who himself was the eldest son of Casimir IV of Poland from the Jagiellonian dynasty.

In 1585, Maximilian became the Grand Master of the Teutonic Order; thanks to this he was known by the epithet der Deutschmeister ("the German Master") for much of his later life.

In the 1587 Polish–Lithuanian royal election Maximilian stood as a candidate for the throne of the Polish–Lithuanian Commonwealth, following the death of the previous king, Stephen Báthory. Nonetheless, a portion of the Polish nobility elected Maximilian king, but another faction elected Prince Sigismund of Sweden, grandson of Sigismund I the Old, as Sigismund III Vasa. However, he faced considerable opposition as well due to same reasons as before. Maximilian then invaded Poland, starting the War of the Polish Succession (1587–1588). He had considerable support in Poland, but fewer Poles flocked to his army than to that of his rival. In late 1587, he tried and failed to storm Kraków. At Pitschen in Silesia, he met Sigismund's army, commanded by Polish hetman Jan Zamojski. In the Battle of Byczyna (24 January 1588), Maximilian was defeated and captured. He was released a year and half later after the intervention of Pope Sixtus V in the aftermath of the Treaty of Bytom and Będzin. In 1598, he formally renounced his claim to the Polish crown. The inactivity of his brother, Emperor Rudolf II, in this matter contributed to Rudolf's poor reputation.

From 1593 to 1595, Maximilian served as regent for his young cousin, the future Emperor Ferdinand II as Archduke of Inner Austria. In 1595, Maximilian succeeded to the territories of their uncle Ferdinand II, Archduke of Further Austria, including Tyrol, where he proved to be a solid proponent of the Counter-Reformation. He also worked to depose Melchior Khlesl, and to ensure that Ferdinand succeeded as Holy Roman Emperor.

Today, Maximilian is perhaps best remembered for his baroque archducal hat, exhibited in the treasury of the monastery of Klosterneuburg and was used for ceremonial purposes as late as 1835.

He died at Vienna in 1618, and is buried in the canopied tomb in Innsbruck Cathedral.

title: Maximilian III, Archduke of Austria


text:
Battle of Gaza (312 BC)

The Battle of Gaza of 312 BC, was fought between the invading army of Ptolemy I Soter and his ally Seleucus I Nicator and the defending army of Demetrius I of Macedon, son of Antigonus I Monophthalmus. The battle was part of the Third War of the Diadochi and was fought near the city of Gaza.

In late 312 BC, Ptolemy launched an invasion into the Levant from Egypt, he marched with 18,000 infantry and 4,000 cavalry along the northern edge of the Sinai Peninsula. Receiving timely intelligence, Demetrius recalled his troops from their winter quarters and concentrated them at Gaza. Demetrius' advisors had apparently told him to avoid a military confrontation with Ptolemy and Seleucus, who had more military experience, but he ignored their advice; the conflict ended in a decisive defeat for Demetrius, subsequently enabling the absorption of his controlled territory by Ptolemy and Seleucus.

Troop strength
Demetrius deployed 2,900 elite cavalry, 1,500 light infantry, and 30 Indian war elephants under his command on the left. The Antigonid phalanx of some 11,000 was deployed in the center, with 13 war elephants in front and light infantry protecting the main line. On the Antigonid right, there were 1,500 cavalry.

Ptolemy and Seleucus originally put most of their cavalry on the left, but when they learned of Demetrius' disposition, they massed their 3,000 heavy cavalry to the right, under their personal command. An anti-elephant corps of 3,000 light infantry (peltast, archers and slingers) equipped with anti-elephant devices (spikes connected by chains) were positioned in front of the cavalry,– with orders to throw the devices in the path of the elephants and then target the mahouts. Their phalanx was stationed in the center, with the remaining 1,000 cavalry deployed on the right.

Order of battle
Antigonid:
 * left wing: 2,900 cavalry, 1,500 light infantry and 30 war elephants under Demetrius command
 * center: 11,000 infantry phalanx and 13 elephants
 * right wing: 1,500 cavalry

Ptolemaic:
 * left wing: 3,000 cavalry, under Ptolemy and Seleucus
 * center: 18,000 phalanx
 * right wing: 1,000 cavalry

Engagement
The battle opened with the advance guards of the stronger cavalry wings engaging each other. Demetrius drove off the enemy. Ptolemy and Seleucus responded by riding around Demetrius's left flank to attack. A fierce melee ensued, with the cavalry of both sides fighting with their swords after their lances had been shattered. While the cavalry battle on the flank was taking place, Demetrius brought forward his elephants apparently hoping to demoralize the Ptolemaic phalanx. As the elephants approached, the Ptolemaic archers and javelinmen began showering the elephants and their crews. This, along with some elephants stepping on the spiked chains, led to them becoming panicked. After shooting down nearly all the crews, the Ptolemaic light infantry were able to capture and kill most of the elephants. The loss of the elephants panicked Demetrius' cavalry and many of his men retreated. The infantry then engaged, and the fight was stiff. However, neither phalanx could gain the upper hand. After trying to keep more cavalry from retreating, Demetrius and the remaining cavalry fell back but still managed to stay in formation while retiring over the open plain. This discouraged Ptolemy and Seleucus from pursuing the enemy. The Ptolemaic phalanx began to push back the Antigonid phalanx, and the Antigonid Phalangites threw down their arms and retreated in chaos. Ptolemy and Seleucus had won a hard-fought victory.

Aftermath
Demetrius lost 8,500 men (500 were killed in battle, a further 8,000 taken prisoner), including generals such as Andronicus of Olynthus, and all his elephants. He retreated to Tripolis in Phoenicia, and started to rebuild his army. He also sent a report to his father, who had just finished his campaign in Caria, urging him to send help.

Meanwhile, Seleucus had convinced Ptolemy to release him from service and give him an army to try and take back his old province of Babylonia which was now without a governor (Peithon had died in the battle). Ptolemy agreed, and sent off Seleucus with a small force of around 1,000 troops.

In popular culture
Alfred Duggan's novel on the life of Demetrius, Elephants and Castles, covers the battle.

The third novel in Christian Cameron's Tyrant series, Funeral Games features the Battle of Gaza.

title: Battle of Gaza (312 BC)


text:
Francisco Garcés

Francisco Hermenegildo Tomás Garcés O.F.M. (April 12, 1738 – July 18, 1781) was a Spanish Franciscan friar who served as a missionary and explorer in the colonial Viceroyalty of New Spain. He explored much of the southwestern region of North America, including present day Sonora and Baja California in Mexico, and the U.S. states of Arizona and California. He was killed along with his companion friars during an uprising by the Native American population, and they have been declared martyrs for the faith by the Catholic Church. The cause for his canonization was opened by the Church.

History
Garcés was born April 12, 1738, in Morata de Jalón, Aragon, north-central Spain. He entered the Franciscan Order about 1758 and was ordained a priest in 1763 in Spain.

New Spain
Garcés travelled to New Spain (Mexico) and served at the Franciscan college of Santa Cruz in Querétaro. In 1768, when the King of Spain expelled the Jesuits from their extensive mission system in northwestern New Spain (within present-day Baja California, northwestern Mexico, and the southwestern United States), Garcés was among the Franciscan replacements. He was assigned to Mission San Xavier del Bac in the Sonoran Desert, near present-day Tucson, Arizona.

Missionary
The expulsion of the Jesuits by the Spanish King set in motion a sequence of dramatic events in the missions. The Franciscans from the college of Santa Cruz in Querétaro took over responsibility in the Sonoran Desert missions region in the present-day Mexican state of Sonora and the U.S. state of Arizona. Meanwhile, other Franciscans from the college of San Fernando in Mexico City under the leadership of Junípero Serra, were assigned to replace the Jesuits in the Baja California missions of the lower Las Californias Province.

Explorer
Garcés became a key player in this effort, conducting extensive explorations in the Sonoran, Colorado, and Mojave Deserts, the Gila River, and the Colorado River from the Gulf of California and Lower Colorado River Valley to the Grand Canyon. He encountered and recorded accounts of the Native American tribes in their desert and riparian valley homelands, and established peaceable relations for the Crown, including with the Quechan, Mojave, Hopi, and Havasupai. Many journeys were explorations on his own in the deserts. He accompanied soldier-explorer Juan Bautista de Anza part way in both his large overland expeditions: the 1774 De Anza Expedition - first to reach Alta California's Pacific coast from the east; and the 1775-76 Anza Colonizing Expedition, which traveled as far north as San Francisco Bay. Garcés also crossed the Mojave Desert on the Mohave Trail and then the Old Tejon Pass and explored the southern San Joaquin Valley in 1776. The eastern part of the route Garcés took from the Colorado River across the Mojave Desert is known to four-wheel-drive adventurers today as the Mojave Road.

Death
In 1779–81 Garcés and Juan Díaz established two mission churches (Mission Puerto de Purísima Concepción and Mission San Pedro y San Pablo de Bicuñer) on the lower Colorado River at Yuma Crossing, as part of a new pueblo (secular settlement), in the homeland of the Quechan peoples (Yuma or Kwítsaín). Garcés tried to keep peace between all parties. The formerly peaceful rapport with the Quechan was lost due to Spanish settlers allegedly violating the treaty with the native peoples, resulting in the losses of crops and farmlands. In July 1781, Garcés, Díaz and their fellow friars were among those killed in a violent uprising at the Mission San Pedro y San Pablo de Bicuñer, known as the Yuma Uprising and Yuma Revolt.

Garcés' body was later reinterred at Mission San Pedro y San Pablo del Tubutama. He and the other friars killed at those missions are considered martyrs by the Catholic Church.

Legacy
The El Garces Hotel, named in Francisco Garcés' honor, is the historic 1908 Santa Fe Railroad station and Harvey House hotel 'oasis' located in the City of Needles. It is located in eastern California above the Colorado River, a site Garcés passed through during the 1776 Anza expedition. The El Garces Hotel was built by the Santa Fe Railroad under contract with the Fred Harvey Company. It is designed in an elegant Neoclassical and Beaux-Arts style, and the El Garces was considered the "Crown Jewel" of the entire Fred Harvey chain.
 * El Garces Hotel

Garces National Forest was established by the U.S. Forest Service in southern Arizona on July 1, 1908, with 78480 acres from portions of Baboquivari, Tumacacori and Huachuca National Forests. The name was discontinued in 1911 when it was combined with Coronado National Forest.
 * National Forest

The first Tejon Pass (original) between the Mojave Desert (and New Spain) over the Tehachapi Mountains to the southern San Joaquin Valley floor (future site of Bakersfield), California, had been discovered by Garcés in 1776, eastward from the Anza Colonizing Expedition route. Therefore, there are several landmarks for Francisco Garcés in Bakersfield, California: Garces Memorial High School, the city's Catholic high school; and on Chester Avenue Garces Memorial Circle, with a memorial statue of Garcés.
 * Bakersfield

The original platted east–west streets of the 1905 Las Vegas Township are all named for significant North American explorers, beginning with Stewart on the north, then Ogden, Fremont, Carson, Bridger, Lewis, Clark, Bonneville, Gass, and finally Garces on the south.
 * Las Vegas, Nevada

St. Thomas Aquinas Cathedral has a stained glass window dedicated to Fray Garces.
 * Reno, Nevada

title: Francisco Garcés


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Gyromagnetic ratio

In physics, the gyromagnetic ratio (also sometimes known as the magnetogyric ratio in other disciplines) of a particle or system is the ratio of its magnetic moment to its angular momentum, and it is often denoted by the symbol $γ$, gamma. Its SI unit is the radian per second per tesla (rad⋅s−1⋅T−1) or, equivalently, the coulomb per kilogram (C⋅kg−1).

The term "gyromagnetic ratio" is often used as a synonym for a different but closely related quantity, the $g$-factor. The $g$-factor only differs from the gyromagnetic ratio in being dimensionless.

For a classical rotating body
Consider a nonconductive charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment due to the movement of charge and an angular momentum due to the movement of mass arising from its rotation. It can be shown that as long as its charge and mass density and flow are distributed identically and rotationally symmetric, its gyromagnetic ratio is
 * $$ \gamma = \frac{q}{2m} $$

where $${q}$$ is its charge and $${m}$$ is its mass.

The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an integration. Suppose the ring has radius $r$, area $A = πr^{2}$, mass $m$, charge $q$, and angular momentum $L = mvr$. Then the magnitude of the magnetic dipole moment is
 * $$ \mu = I A = \frac{q v}{2 \pi r} \, \pi r^2 = \frac{q}{2m} \, m v r = \frac{q}{2m} L ~.$$

For an isolated electron
An isolated electron has an angular momentum and a magnetic moment resulting from its spin. While an electron's spin is sometimes visualized as a literal rotation about an axis, it cannot be attributed to mass distributed identically to the charge. The above classical relation does not hold, giving the wrong result by the absolute value of the electron's $g$-factor, which is denoted $g_{e}$: $$ \gamma_\mathrm{e} = \frac{-e}{ 2 m_\mathrm{e}} \, |g_\mathrm{e}| = \frac{ g_\mathrm{e} \mu_\mathrm{B} }{ \hbar } \, ,$$ where $μ_{B}$ is the Bohr magneton.

The gyromagnetic ratio due to electron spin is twice that due to the orbiting of an electron.

In the framework of relativistic quantum mechanics, $$ g_\mathrm{e} = -2 \left(1 + \frac{\alpha}{\,2\pi\,} + \cdots\right)~,$$ where $$\alpha$$ is the fine-structure constant. Here the small corrections to the relativistic result $g = 2$ come from the quantum field theory calculations of the anomalous magnetic dipole moment. The electron $g$-factor is known to twelve decimal places by measuring the electron magnetic moment in a one-electron cyclotron: $$g_\mathrm{e} = -2.002\,319\,304\,361\,18(27).$$

The electron gyromagnetic ratio is  $$ \gamma_\mathrm{e} = \mathrm{-1.760\,859\,630\,23(53) \times 10^{11} \,rad{\cdot}s^{-1}{\cdot}T^{-1}}$$ $$ \frac{\gamma_\mathrm{e}}{2\pi} = \mathrm{-28\,024.951\,4242(85) \,MHz{\cdot}T^{-1}} .$$

The electron $γ$-factor and $γ$ are in excellent agreement with theory; see Precision tests of QED for details.

Gyromagnetic factor not as a consequence of relativity
Since a gyromagnetic factor equal to 2 follows from Dirac's equation, it is a frequent misconception to think that a $g$-factor 2 is a consequence of relativity; it is not. The factor 2 can be obtained from the linearization of both the Schrödinger equation and the relativistic Klein–Gordon equation (which leads to Dirac's). In both cases a 4-spinor is obtained and for both linearizations the $γ$-factor is found to be equal to 2; Therefore, the factor 2 is a consequence of the minimal coupling and of the fact of having the same order of derivatives for space and time.

Physical spin $g$ particles which cannot be described by the linear gauged Dirac equation satisfy the gauged Klein–Gordon equation extended by the $g$ $e⁄4 σ^{μν }F_{μν}$ term according to,

\left[\, \left( \partial^\mu \, u + i\, e\, A^\mu \right)\, \left( \partial_\mu + i\, e\, A_\mu \right) + g \, \frac{e}{\, 4\,} \, \sigma^{\mu\nu} \, F_{\mu\nu} + m^2 \,\right] \; \psi \; = \; 0 ~, \quad g \ne 2 ~. $$

Here, $1⁄2σ^{μν}$ and $F^{μν}$ stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while $A^{μ}$ is the electromagnetic four-potential. An example for such a particle, is the spin $1⁄2$ companion to spin $g$ in the $D^{(½,1)} ⊕ D^{(1,½)}$ representation space of the Lorentz group. This particle has been shown to be characterized by $g$ = $s$ and consequently to behave as a truly quadratic fermion.

For a nucleus
Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally written in terms of the proton mass and charge, even for neutrons and for other nuclei, for the sake of simplicity and consistency. The formula is:
 * $$ \gamma_\text{n} = \frac{e}{\, 2m_\text{p}\,} \, g_{\rm n} = g_{\rm n}\, \frac{\,\mu_\mathrm{N} \,}{\hbar}~,$$

where $$\mu_\mathrm{N}$$ is the nuclear magneton, and $$ g_{\rm n} $$ is the $+$-factor of the nucleon or nucleus in question. The ratio $$\,\frac{\gamma_n}{\, 2 \pi \, g_{\rm n}\,}\, ,$$ equal to $$\mu_\mathrm{N}/h$$, is 7.622593285(47) MHz/T.

The gyromagnetic ratio of a nucleus plays a role in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). These procedures rely on the fact that bulk magnetization due to nuclear spins precess in a magnetic field at a rate called the Larmor frequency, which is simply the product of the gyromagnetic ratio with the magnetic field strength. With this phenomenon, the sign of $−$ determines the sense (clockwise vs counterclockwise) of precession.

Most common nuclei such as 1H and 13C have positive gyromagnetic ratios. Approximate values for some common nuclei are given in the table below.

Larmor precession
Any free system with a constant gyromagnetic ratio, such as a rigid system of charges, a nucleus, or an electron, when placed in an external magnetic field $B$ (measured in teslas) that is not aligned with its magnetic moment, will precess at a frequency $−$ (measured in hertz), that is proportional to the external field:
 * $$f=\frac{\gamma}{2\pi}B.$$

For this reason, values of $ψμ$, in units of hertz per tesla (Hz/T), are often quoted instead of $1⁄2$.

Heuristic derivation
The derivation of this relation is as follows: First we must prove that the torque resulting from subjecting a magnetic moment $$\mathbf{m}$$ to a magnetic field $$\mathbf{B}$$ is $$\, \boldsymbol{\Tau}=\mathbf{m}\times\mathbf{B}\, .$$ The identity of the functional form of the stationary electric and magnetic fields has led to defining the magnitude of the magnetic dipole moment equally well as $$m=I\pi r^2$$, or in the following way, imitating the moment $p$ of an electric dipole: The magnetic dipole can be represented by a needle of a compass with fictitious magnetic charges $$\pm q_{\rm m}$$ on the two poles and vector distance between the poles $$\mathbf{d}$$ under the influence of the magnetic field of earth $$\, \mathbf{B} \, .$$ By classical mechanics the torque on this needle is $$\, \boldsymbol{\Tau} = q_{\rm m} (\mathbf{d}\times\mathbf{B}) \, .$$ But as previously stated $$\, q_{\rm m}\mathbf{d}=I\pi r^2\hat{\mathbf{d}} = \mathbf{m} \, ,$$ so the desired formula comes up. $$\hat{\mathbf{d}}$$ is the unit distance vector.

The model of the spinning electron we use in the derivation has an evident analogy with a gyroscope. For any rotating body the rate of change of the angular momentum $$\, \mathbf{J} \,$$ equals the applied torque $$\mathbf{T}$$:
 * $$\frac{d\mathbf{J}}{dt}=\mathbf{T}~.$$

Note as an example the precession of a gyroscope. The earth's gravitational attraction applies a force or torque to the gyroscope in the vertical direction, and the angular momentum vector along the axis of the gyroscope rotates slowly about a vertical line through the pivot. In the place of the gyroscope imagine a sphere spinning around the axis and with its center on the pivot of the gyroscope, and along the axis of the gyroscope two oppositely directed vectors both originated in the center of the sphere, upwards $$\mathbf{J}$$ and downwards $$\mathbf{m}.$$ Replace the gravity with a magnetic flux density $$\, \mathbf{B} ~.$$

$$\frac{\,\operatorname{d} \mathbf{J}\,}{\,\operatorname{d} t \,}$$ represents the linear velocity of the pike of the arrow $$\,\mathbf{J}\,$$ along a circle whose radius is $$\, J\sin{\phi}\, ,$$ where $$\,\phi\,$$ is the angle between $$\,\mathbf{J}\,$$ and the vertical. Hence the angular velocity of the rotation of the spin is
 * $$\omega = 2\pi \,f = \frac{1}{ \, J \, \sin{\phi}\,}\,\left|\frac{\,\rm{d}\,\mathbf{J}\,}{\,\rm{d}\,t\,}\right| = \frac{\,\left| \mathbf{T} \right| \,}{\, J \, \sin{\phi}\,} = \frac{\,\left| \mathbf{m} \times \mathbf{B} \right| \,}{\, J \,\sin{\phi} \,} = \frac{\,m\,B\sin{\phi}\,}{\, J \,\sin{\phi}\,} = \frac{\, m\, B\,}{J} = \gamma\, B ~.$$

Consequently, $$f=\frac{\gamma}{\,2\pi\,}\,B~.\quad \text{q.e.d.}$$ This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from γύρος, "turn") property (i.e. angular momentum), it is also, at the same time, a ratio between the angular precession frequency (another gyric property) $ω = 2πf$ and the magnetic field.

The angular precession frequency has an important physical meaning: It is the angular cyclotron frequency, the resonance frequency of an ionized plasma being under the influence of a static finite magnetic field, when we superimpose a high frequency electromagnetic field.

title: Gyromagnetic ratio


text:
Dean Chamberlain

Dean Chamberlain is a photographer who specializes in unique lighting effects and extended exposure times. Famous models for his pictures sit for up to five hours as he leaves the camera shutter open and "paints" the space around them with carried and projected lights of various colors and shapes, creating luminous and colorful images. His technique was described by one of his exhibitions as "Painting With Light Through Time and Space."

Chamberlain served as Artist in Residence at Dartmouth College in 1989. In 1994 his work appeared in Nervous Landscapes, a book which accompanied an exhibition at the Southeast Museum of Photography. He co-founded the Light Space Gallery in Venice, California in 2001, and serves as its co-director. Since 2003 Chamberlain has been a contributor to Mao Mag, an insiders' art and fashion magazine. A documentary of his work is planned for release on Ovation TV in 2010.

He has taken art photographs of people from many walks of life. A "Psychedelic Pioneers" series of limited edition prints included portraits of Timothy Leary, Ram Dass, Albert Hofmann, Laura Huxley, Alexander Shulgin, Rick Doblin, Oscar Janiger, Stan Grof, Terence McKenna, and John C. Lilly.; another series documented artists like Keith Haring and Jeff Koons. He has also created portraits for musicians such as David Bowie, Duran Duran, Debbie Harry, Paul McCartney, Madonna, Arcadia, Roy Orbison, and directed music videos using the same long exposure techniques:  "This One" for Paul and Linda McCartney, "Missing" for Arcadia and "All She Wants Is" for Duran Duran. "All She Wants Is" won an MTV Video Music Award for innovation.

Chamberlain was born in Boston, Massachusetts. He first became interested in photography when he was thirteen using a Polaroid camera, and by fifteen had acquired his first Konica. He had always wanted to be an artist and was inspired by his grandmother who encouraged him to paint on canvas. He attended Sheridan College and Rochester Institute of Technology and by his early twenties he knew he was a light painter, and has focused on this technique ever since. He was very interested in the psychedelic movement, and became a friend to Timothy Leary late in his life. In 2003 his gallery put on a showing of art and memorabilia that Chamberlain selected from Leary's archives after his death.

title: Dean Chamberlain


text:
User:Rpugatch

nothing here.

title: User:Rpugatch


text:
Wikipedia:Articles for deletion/Making Basic Armor

Making Basic Armor
Making Basic Armor was proposed for deletion. This page is an archive of the discussion about the proposed deletion. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was transwiki to wikibooks and delete.

A howto. Trankswiki to wikibooks, maybe. --DMG413 01:02, 1 Dec 2004 (UTC)
 * The author has been notified on his Talk page. I think it's safe to speedie delete as having been transwikied.  (But check before you do) JesseW 03:30, 5 Dec 2004 (UTC)

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