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Talk:History of calculus

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From Infinitesimal Calculus
Content from former Infinitesimal calculus moved into History of Calculus. Peter Grey 21:32, 23 Jun 2005 (UTC)

Newton, Leibniz Controversy
I tried to edit and reorganize this article to be a little cleaner. Also, I deleted some statements about the Newton - Leibniz controversy that I feel were dubious. I am not the foremost expert on this subject, but I do know some about it. Unfortunately, much of what is left is rather vague and uninformative. If someone has some good sources on this subject, please provide them! If people can provide good sources for some of the statements I deleted, by all means, reinsert them! Grokmoo 05:05, 7 February 2006 (UTC)

I wish that you (and everyone) would move deletions of that sort to the discussion page. Some controversies, including this one, are still being argued after the elapse of centuries, but that doesn't inherently mean that old arguments have no merit at all -- they can be good starting material.

I mean, think about it -- I have several books concerning the history of calculus, and if I'm in a wikipedia mood, I might see your deleted material here on TALK, check various things in my books, and attempt to insert material into the article that is backed-up by my references.

But since you simply deleted the controversial phrasings, where does that leave people like me? The wording that bothered you is completely gone; we have no idea what it was about. We can no longer simply react and improve, instead we must spontaneously generate new material, which is much, much harder, in many senses, and tends to be of high quality only when done by a true expert on the topic, whereas simple fact-checking of controversies may eventually be done by the mere enthusiast, if you see what I mean.

In summary, clearly bad or wrong stuff should of course be deleted, but merely questionable but possibly-a-good-springboard material should be moved, at most, until it can be improved.

Think about it -- if you could have improved it, rather than deleting it, you would have, but by deleting it (and calling attention to your deletion), you are asking for volunteers who are more expert than you to exert more effort than you -- not that I'm in that category, but why demand so very much from those whom you are envisioning will correct your deletion???

Don't expect more than incremental improvements. Make edits in a way that inherently supports incremental improvements. Dougmerritt (talk) 04:27, 24 September 2008 (UTC)

I'd say that we should forget the controversy and move on. Here in Finland we always tell that 'Leibniz and Newton were...' and if someone asks, we tell that the order of the names is just alphabetical. So I suggest that in the context of differential calculus the names of Leibniz and Newton are always presented in alphabetical order.

Linkato1 (talk) 14:27, 15 March 2012 (UTC)

Egypt
I have deleted the following... The method of integration can be traced back to the Egyptians, in the Moscow Mathematical Papyrus circa 1800 BC, which gives the formula for finding the volume of a pyramidal frustrum.

This is misleading in many ways... First of all. Well before the Egyptians the people from ancient Mesopotamia had deduced formulas for the volume of the frustum of a pyramid. Secondly. In neither case do we have evidence that the "method of integration" can be traced back to either of these civilizations. It is true that one cannot prove the result using finite geometrical constructions Paul Dehn 1902 however this is not to say that the result was derived by purely speculative means.

Regardless we have no evidence that the Egyptians ever used any methods of calculus.

 * "Paul Dehn" seems to be a mistake for "Max Dehn". — Preceding unsigned comment added by 86.176.100.209 (talk) 12:56, 26 January 2012 (UTC)

In February 1933 while on a visit to the United States, Einstein decided not to return to Germany due to the rise to power of the Nazis under Germany's new chancellor.[55][56] He visited American universities in early 1933 where he undertook his third two-month visiting professorship at the California Institute of Technology in Pasadena. He and his wife Elsa returned by ship to Belgium at the end of March. During the voyage they were informed that their cottage was raided by the Nazis and his personal sailboat had been confiscated. Upon landing in Antwerp on 28 March, he immediately went to the German consulate where he turned in his passport and formally renounced his German citizenship. — Preceding unsigned comment added by 24.187.113.156 (talk) 20:31, 29 October 2012 (UTC)

India
There is a referenced sentence in "Indian mathematicians": "In 499 CE, the mathematician-astronomer Aryabhata used a form of infinitesimals to express an astronomical problem in the form of a differential equation."

with the reference being Aryabhata the Elder But the referenced article says nothing of the sort. selfworm - just downgraded to version 0.4B! 07:50, 6 March 2007 (UTC)

I have removed the ill-referenced sentence after waiting a day. selfworm _ _ ( Give me a piece of your mind ·  Userboxes  ·  Contribs ) _ 23:59, 6 March 2007 (UTC)

This now seems to be a crucial section. See the news here.
 * "The beginnings of modern maths is usually seen as a European achievement but the discoveries in medieval India between the fourteenth and sixteenth centuries have been ignored or forgotten," he said. "The brilliance of Newton's work at the end of the seventeenth century stands undiminished — especially when it came to the algorithms of calculus.
 * "But other names from the Kerala School, notably Madhava and Nilakantha, should stand shoulder to shoulder with him as they discovered the other great component of calculus — infinite series."
 * "There were many reasons why the contribution of the Kerala school has not been acknowledged," he said. "A prime reason is neglect of scientific ideas emanating from the Non-European world, a legacy of European colonialism and beyond."

Since the Western-bias has been decried as a weakness of Wikipedia, I suggest this section be given top priority. -JTBurman 19:01, 14 August 2007 (UTC)

I think it's just a statement told by a person not a historian. Obiwana (talk) 12:42, 23 December 2022 (UTC)

Analytic geometry
The Analytic geometry section does not belongs in the history of calculus article since firstly, Analytic geometry has traditionally not been a part of calculus and secondly, it is woefully underdeveloped in comparison to the main article Analytic geometry. I have removed this section and placed an internal link to Analytic geometry in the see also section. selfworm Talk ) 18:06, 17 July 2007 (UTC)

 * Go ahead and remove, if someone wants to come back and develop it later they can do so.--Cronholm144 18:43, 17 July 2007 (UTC)
 * Very well, I will remove it and if someone disagrees with its remove then they can undo the change and discuss it here. selfworm Talk ) 20:07, 17 July 2007 (UTC)

Symbolic methods
This section makes very little sense to me. Not only does the wikilink point to an article on symbolic methods in invariant theory, almost certainly wrongly, but after reading it, I cannot even deduce what is the subject of the section. The few mathematical statements that are in it are rather confused (e.g. "the analogy between successive differentiation and ordinary exponentials" and Grassman's "theory of complex numbers"). What is the relevance for history of calculus, if any? Arcfrk 20:12, 14 August 2007 (UTC)

China
I've removed this paragraph:
 * The method of exhaustion was rediscovered in China by Liu Hui in the 3rd century AD, who used it to find the area of a circle. It was also used by Zu Chongzhi in the 5th century AD, who used it to find the volume of a sphere. (ref cited: Helmer Aslaksen. Why Calculus? National University of Singapore.)

The claim is not supported by the given reference (which is a course syllabus and does not qualify as a reliable source anyway). Similar claims are also not found in the articles about these gentlemen, which should be the primary locations. --Lambiam 08:58, 28 November 2007 (UTC)

Etymology
A recent addition has greatly expanded the coverage of Newton and Leibniz's contributions. However, its use of the term "Calculus" is ahistorical and the explanation of the etymology in the very paragraph,
 * "the Calculus has become a popular term for a field of mathematics based upon their insights"

is wrong: it was not until the mid-twentieth century that the expressions "Differential calculus" and "Integral calculus", which in their turn are descendants of "Calculus of infinitesimals", "Calculus of fluxions", and so on, lost their adjectives. Let us not project the convention adapted by most authors of recent college textbooks back into the seventeenth century. Arcfrk (talk) 05:13, 31 March 2008 (UTC)

 * I wrote something on this in this thread: Talk:Integralpermalink (skip to the last paragraph). Since this keeps coming back (see Talk:Calculus/Archive 2 and Talk:Calculus), it would be nice if we could write a paragraph or so about this shift in usage either here or in the main Calculus article. It may be hard to find citable sources, though. --Lambiam 19:55, 31 March 2008 (UTC)

Cavalieri?
Where is his treatise?Likebox (talk) 22:56, 12 December 2008 (UTC)

Construction of a misleading narrative
The article overall appears to try to weave a misleading historical narrative out of various threads that used calculus-like ideas throughout the world in ancient and modern times, as if to suggest that they were all somehow a part of the development of what is today known as calculus. Even if this were ultimately true, it is unsupported by sources: the cited Katz source states that it is not known whether and how much the predecessors of Newton and Leibniz were aware of the results of the earlier Indian and Islamic mathematicians. The article goes way too far to avoid a "western" bias that now it contains virtually nothing of what might be called the "mainstream" treatment of the history of calculus. I think the article should be rewritten entirely from a good, standard source, like the definitive (if a bit dated) Boyer source that is currently referenced. The stuff about Indian/Islamic/Chinese mathematics should of course be dealt with, but not presented as part of the same historical narrative unless there are reliable sources to serve as a guide on precisely how to do this. Otherwise, connecting these historical facts into a misleading narrative is WP:OR par excellence. Sławomir Biały (talk) 13:49, 21 July 2010 (UTC)
 * I hope you don't mind me renaming this section. "Article problem" could apply to a lot of discussions so I have come up with something more specific.
 * In terms of your actual complaint, I think you have a very good point, but I think I would split it into two points
 * The validity of statements and implications made in the article.
 * Whether, true or not, such statements should be given so much space near the top of this article. i.e. Are we giving themWP:UNDUE weight?
 * I think the first issue could perhaps be improved by renaming the section currently called "precursors to calculus". I'm not sure what to "Discoveries prior to calculus" maybe.  And then a certain amount of explanation would have to go near the start of that section.  Something like "Some of the concepts of calculus, such as infinitesimals, were explored to a certain extent by earlier mathematicians.  The extent to which any of these developments influenced Newton and Leibniz is disputed but there was certainly no rigorous study of the topic until the 17th century."
 * I think the second issue could perhaps best be solved by moving the section to lower down the article. e.g. immediately above "See also".
 * Another thing, which Sławomir Biały hasn't mentioned is that the lead of the article talks a lot about what calculus is and not much about the history of calculus. e.g. it doesn't mention Newton and Leibniz.  If we gave the article a proper lead then everything else could be seen in the proper context.
 * Yaris678 (talk) 17:36, 21 July 2010 (UTC)

 * Yaris, I don't think that any historian of mathematics ever claimed that Newton and Leibniz were influenced by Chinese or Indian "precursors". The "revisionist" view, which is to some extent supported by the evidence, is that some discoveries that are now seen as part of Calculus had independently been made much earlier. However, they remained so isolated that, for example, the work of Kerala school was largely unknown in India itself. Of course, all sorts of fringe views may show up on Wikipedia, sometimes because of nefarious edits and sometimes because the most accessible sources on the internet are rarely the most scholarly ones. Arcfrk (talk) 05:40, 22 July 2010 (UTC)
 * Sure, my main point was that we could write an introductory paragraph for that section, putting it into context. My example of the sort of text this could contain might not have been the most knowledgeble but then by discussing it like this and referring to sources we can come up with something better.

Responding to Sławomir's very valid argument about misleading historical narrative, I'd like to propose to farm out the section "Precursors to calculus" into a separate article. I see no connections between that part and the rest of the article, and it would be a pity to lose some reasonably researched material simply because it appears under the wrong heading. Arcfrk (talk) 06:07, 22 July 2010 (UTC)
 * I was gonna suggest putting it in a separate article too, but you would still have the issue of what to call it. I think moving it to near the end of the article is better but I'm not too bothered either way.  Yaris678 (talk) 10:44, 22 July 2010 (UTC)
 * Actually, thinking about it, there is the potential for a separate article to become a POV fork. So it's probably best to keep it all in one place if we can.  Yaris678 (talk) 10:48, 22 July 2010 (UTC)
 * I don't know about the rest of the multicultural material, but the calculations in Archimedes come to close to what was done in the 17th century (and later) as to rub one's eyes in disbelief. It would be a mistake to "farm" Archimedes out as suggested above.  On the other hand, it would be good to clarify just what the status of the other pre-Barrow material is.  Tkuvho (talk) 11:17, 22 July 2010 (UTC)
 * I would also be happy to see a one-article solution if possible. I should have added here that with this edit I fixed what I believed to be the worst of the article's excesses: reorganizing the "precursors" geographically rather than chronologically, and eliminating language like "...the next big development in calculus was... discovered by the Kerala school."  However, I do think that further remedy is desirable, and that the main line of the history deserves much more focus than it currently has.  Probably the best way to give the article an appropriate focus is to move the "Precursors" section to the very end.  Sławomir Biały  (talk) 12:09, 22 July 2010 (UTC)
 * Good idea. Some of them are not even precursors of the calculus by any stretch of the imagination.  Calculating the volume of a pyramid?  I would suggest leaving Archimedes as a true precursor, and moving the rest of this material to a comments section at the end. Tkuvho (talk) 12:38, 22 July 2010 (UTC)
 * I reorganized the page in accordance to what I saw as a consensus here. No doubt there will be further reogranisations.  Tkuvho (talk) 11:17, 25 July 2010 (UTC)

Archimedes of Syracuse
I included Archimedes in the title of the subsection on ancient greek mathematicians because Syracuse is not technically speaking in Greece. Tkuvho (talk) 04:29, 26 July 2010 (UTC)

 * Well, the whole issue "who should be considered Greek" is murky: arguments have been made that at least some mathematicians of the Alexandrian school, including Diophantus, weren't ethnically Greek. On the other hand, I agree that section titles should be kept simple. Arcfrk (talk) 05:32, 26 July 2010 (UTC)
 * This issue is expanded upon in the article on Greek mathematics. I think treating Archimedes as Greek is fine for our purposes.  Yaris678 (talk) 11:53, 26 July 2010 (UTC)
 * When titling the section, I was aware of precisely this issue. Alexandrian Greece would have been a better choice in retrospect, I think.   Sławomir Biały  (talk) 19:07, 26 July 2010 (UTC)
 * Alexandrian Greece? Does that mean Greece at the time of Alexander the Great?  I don't think that helps.  Yaris678 (talk) 17:26, 27 July 2010 (UTC)

Barrow
If we are to attribute the fundamental theorem of calculus to Barrow, such an attribution should be sourced. Tkuvho (talk) 13:12, 14 December 2010 (UTC)

 * See the wikipedia page on the fundamental theorem of calculus. 131.111.184.95 (talk) 17:17, 14 December 2010 (UTC)

 * The claim is similarly unsourced there. Do you have a source?  Tkuvho (talk) 17:31, 14 December 2010 (UTC)

 * http://www.lucasianchair.org/17/barrow.html 131.111.184.95 (talk) 17:41, 14 December 2010 (UTC)

 * Not quite. The article says The first full proof of the fundamental theorem of calculus was given by Isaac Barrow.. Your ref says The fundamental theorem of calculus is the recognition that differentiation and integration are the inverse of each other. This is a key realization in mathematics and it was provided by Barrow in his Lectiones.14 It is a critical building block in the development of calculus, which was later formalized by Newton. From that, you can't tell if Barrow just realised it or proved it. Certainly the "later formalized by Newton" suggests Barrow didn't prove it William M. Connolley (talk) 17:57, 14 December 2010 (UTC)

 * The source for this seems to be D. J. Struik, A Source Book in Mathematics, 1200-1800 (Princeton: Princeton University, 1986), page 262. If someone has access to this, could they look it up?  Tkuvho (talk) 18:11, 14 December 2010 (UTC)

 * By the same reasoning, Newton did not prove anything about calculus either, as it is well known that the rigorous foundations only came later. If this is the viewpoint you wish to adopt, then we can change "proved" to "discovered". 131.111.184.95 (talk) 19:55, 14 December 2010 (UTC)

 * The question is not who proved the fundamental theorem of calculus, but rather what the sources out there say about who proved the fundamental theorem of calculus. Unless you have a source saying that Barrow did it, we cannot make such a claim here.  Tkuvho (talk) 07:58, 15 December 2010 (UTC)

 * We have a source which says that Barrow discovered it; we can change the verb to "discovered" if you object to the word "proved". Note that we don't have any sources supporting the assertion that Newton proved it, as was previously claimed. 131.111.184.95 (talk) 08:24, 15 December 2010 (UTC)

 * The problem is that your source goes on to imply that what Barrow fell short of what Newton did in the context of the fundamental theorem of calculus, and to conclude that in fact we cannot attribute the discovery of the calculus to Barrow, if I understood it correctly. This is not necessarily the final word, as it could be that Struik and company are insufficiently appreciative of Barrow's geometrical methods.  Be that as it may, the source you provided tends to undermine your case.  Tkuvho (talk) 08:36, 15 December 2010 (UTC)

 * You may find a more careful discussion of Barrow's work in the translation Geometrical Lectures of Isaac Barrow By Isaac Barrow, J. M. Child. Page 31 reviews the results. The proof is in chapters X and XI. See here: http://www.archive.org/details/geometricallectu00barruoft —Preceding unsigned comment added by 131.111.184.95 (talk) 17:23, 15 December 2010 (UTC)

 * You should indicate the page number in the footnote. Tkuvho (talk) 18:14, 15 December 2010 (UTC)

(Outdent) Is this a translation of his work itself? It seems that wouldn't work as a supporting reference. I think we should use this one: The History of Calculus Arthur Rosenthal, The American Mathematical Monthly, Vol. 58, No. 2 (Feb., 1951), page 83, who clearly gives credit to Barrow. Thenub314 (talk) 21:42, 4 May 2011 (UTC)

 * Excellent, please add it in. Tkuvho (talk) 04:40, 5 May 2011 (UTC)

Dates
I find the dates in the opening to be rather inappropriate. I know of no other history article that inserts dates needlessly in such a way, and I can think of no motivation other than the bias the article towards Newton. The article already has a bit of bias towards Newton, in that it arranges the names "Newton and Leibniz" out of alphabetical order. As it is generally agreed both of them developed calculus independently, I think issues of priority should be relegated to the calculus dispute page. It is worth pointing out that someone could have just as easily inserted dates in favor of Leibniz, by saying "Leibniz (published in ...)". 131.111.184.95 (talk) 17:37, 14 December 2010 (UTC)

non-European antecedents of the calculus
There appears to be a disagreement regarding Indian contributions to the calculus. Edits in this direction should be placed in the section http://en.wikipedia.org/wiki/History_of_calculus#Non-European_antecedents_of_the_calculus. Please avoid further edit-warring. Tkuvho (talk) 04:32, 24 April 2011 (UTC)

POV-pushing
This is nationalistic POV-pushing. The addition is unsourced, untrue, and its placement in the lede totally against WP:UNDUE. I have consequently removed it. Athenean (talk) 04:58, 24 April 2011 (UTC)

 * Well we do acknowledge Indian contributions in the section http://en.wikipedia.org/wiki/History_of_calculus#Non-European_antecedents_of_the_calculus, so the additions are not completely unsourced. As I recall, there were some impressive power series developments that anticipated modern European ones by quite a number of years.  Tkuvho (talk) 05:03, 24 April 2011 (UTC)

 * That may well be, however, the tenor of the additions is highly tendentious, and the way they were added in the lede is a case of WP:UNDUE. As for the non-European section, I don't see such a section in any other history of mathematics articles. Significant advances by non-European cultures should simply be worked into the rest of the article rather than being in a separate section by themselves. It's as if there is "western calculus" and "non-western calculus", almost apartheid-like. I also note that much of the section is unsourced or extremely poorly sourced, which is not surprising since the main contributor to the article is none other than Jagged 85. Instead of tendentious edits to the lede, what needs to be done is to go over the non-European section carefully, throw out what is unsourced or poorly sourced, and what has nothing to with calculus (e.g. the frustum stuff), and merge what is significant (e.g. the Madhava series) into the rest of the article. Athenean (talk) 06:06, 24 April 2011 (UTC)

 * One rationale for keeping them separate is that, according to a majority of scholars, they have had little influence on the development of analysis as it actually happened. I agree that irrelevant material should be deleted, of course.  Tkuvho (talk) 06:22, 24 April 2011 (UTC)

14th century Indian differentiation
A recent edit attributes the concept of differentiation to a 14th century Indian astronomer. Whoever is knowledgeable on this subject please comment on this attribution. Tkuvho (talk) 08:04, 1 May 2011 (UTC)

 * The cited source doesn't mention differentiation. It also doesn't mention iterative solutions to nonlinear equations (although there is an iterative solution for some special equations, and this is how he arrived at a series expansion of π).  I've edited the text accordingly.   Sławomir Biały  (talk) 14:43, 1 May 2011 (UTC)

 * This is dodgy. Someone has added the text, but the reference remains the same. Furthermore the ref (which is only a web page) says Historians have claimed that the method used by Madhava amounts to term by term integration. which seems very weak (if you want someone to judge the claim, you want a mathematician, not a historian); and it itself contains no refs. I've removed it as essentially unverified William M. Connolley (talk) 15:54, 1 May 2011 (UTC)
 * I have no objection to the removal of the statement. However, I'd like to emphasize that MacTutor is generally regarded as quite a reliable source on the history of mathematics, so please let's not paint this with the "only a web page" brush.  Also, it does have references of its own; see .   Sławomir Biały  (talk) 16:23, 1 May 2011 (UTC)
 * Agreed. But whilst it has refs of its own, it has no refs for that statement William M. Connolley (talk) 16:35, 1 May 2011 (UTC)
 * I'll grant that. I wasn't sure how to handle the unattributed statement either.  I just wanted to make sure we're on the same page.   Sławomir Biały  (talk) 18:47, 1 May 2011 (UTC)
 * Also is broken so I've removed it. Re [[Yuktibhāṣā]], I didn't find that text on the mactutor page, so I'm not sure why the ref is there William M. Connolley (talk) 15:54, 1 May 2011 (UTC)

Japan
I removed

 * In 17th century Japan, Japanese mathematician Kowa Sekihttp://www2.gol.com/users/coynerhm/0598rothman.html made a number of contributions, namely in methods of determining areas of figures using integrals, extending the method of exhaustion. While these methods of finding areas were made largely obsolete by the development of the fundamental theorems by Newton and Leibniz, they still show that a sophisticated knowledge of mathematics existed in 17th century Japan.

as sourceless William M. Connolley (talk) 15:56, 1 May 2011 (UTC)

Cleanup
Per the ongoing Jagged 85 cleanup, I checked the sources in the articles, and found a lot that was questionable. Specifically:

 * Regarding ancient Egypt, calculating the area of a pyramidal frustum is not calculus, or anywhere close to calculus. It is geometry.

 * In the section on China, the Pythagorean theorem likewise has nothing to do with calculus. The section was entirely unsourced, even though bold claims about calculus were made.

 * In the India section, Joseph's book was completely misused. First, the claim that Aryabhatta used a differential equation is complete bunk. The search term "Aryabhatta" and "differential equation" do not even appear in the book !

 * The sources on Manjula and Bhaskara II were similarly misused. I rephrased the article per the sources. Athenean (talk) 18:10, 3 May 2011 (UTC)

 * Thanks. Re Indian, The mathematician Manjula, in the 10th century, was aware of differentiation doesn't sound plausible. One of the refs appears to be, but a similar one doesn't mention this claim at all. Is  really reliable, or is it just some blokes web page? Also, the details there are less than sketchy: Evidence suggests Bhaskara was fully acquainted with the principle of differential calculus, and that his researches were in no way inferior to Newton's,, with no refs provided William M. Connolley (talk) 21:11, 3 May 2011 (UTC)

As far as MacTutor is concerned, this is not their regular history page, but rather a "project" by a bloke named Ian Pearce. This link is definitely unreliable. Tkuvho (talk) 14:07, 4 May 2011 (UTC)

 * Yes, see http://turnbull.mcs.st-and.ac.uk/~history/Projects/index.html. It's a student writing. That page isn't a "reliable source" in the meaning of the act. Charles Matthews (talk) 14:26, 4 May 2011 (UTC)

 * The Indian section turns out to have originated in Jaggedese so I removed it because it means none of the refs can be trusted (unless someone has fixed it later; sorry I may have missed that) William M. Connolley (talk) 14:46, 4 May 2011 (UTC)

Ignorance of the Indian contributions to calculus
This article by all mean is WESTERN BIASED. There is now well documented evidence that many important results in calculus like power series expansion of pi and so on were given by Kerala School of Mathematics 300 years before Newton or Leibniz. What is wrong in acknowledging that. It is definitely not acknowledged and everything is written from Western perspective emphasizing NEWTON-LEIBNIZ war. Does this mean other parts of the world need to write their own evidence-based history of calculus?.Chenna001 (talk) 10:27, 6 May 2011 (UTC)

 * Chenna, please sign your comments. The consensus among editors seems to be that the addition you proposed should be in the non-european section of the article.  Tkuvho (talk) 08:24, 6 May 2011 (UTC)

 * Incidentally, I was not the one who removed the Indian subsection. I just restored it a few minutes ago.  The great Indian mathematical tradition should be represented here, while avoiding excesses of ethnomathematics.  I look forward to a productive collaboration. Tkuvho (talk) 08:34, 6 May 2011 (UTC)

 * OK. I restored Indian section. For whoever removed the entire section, I would like to mention that such intolerance will make things only worse. For those who are complaining about sources, you cannot expect that things in AMerican or European journals can only be credible. There are sources which are original about which we do not need any recommendations. For example, the book YukthiBhasha discusses a lot of mathematical material and it is preserved in a fine condition from ancient times. Now when the original source exists, if you(those who are deleting stuff citing no credible source or something like that) again persist for some document written by westerner talking about YukthiBhsha to take YukthiBhasha seriously, then you can judge yourself about your own "western bias". Chenna001 (talk) 09:27, 6 May 2011 (UTC)

 * It may also be more appropriate to rename this whole topic as Western History of Calculus and start another topic with Eastern History of Calculus.Chenna001 (talk) 09:32, 6 May 2011 (UTC)

For whoever removed the entire section: this page isn't write-only you know; please bother to actually *read* it too. As I said above, The Indian section turns out to have originated in Jaggedese [7] so I removed it because it means none of the refs can be trusted. I've removed it again. If you wish to restore it, please state clearly that you have personally verified all the references that you restore. And please drop the nonsense about "war" (note: C later silently removed this ) William M. Connolley (talk) 10:28, 6 May 2011 (UTC)

 * The point is that not all the sources cited there are from Ian Pierce. You also need to read what I have written there. I do not need some westerner telling me that Yukthibhasha is a book in this world. I am restoring it on these grounds. If you want to say something is unreliable then prove it to be unreliable. You cannot state something is unreliable as if you have complete knowledge about everything. Also, you cannot say somebody is bloke if you don't like what he/she writes. It would be best if you maintain some respect for others. This is not a place for your personal opinion.Chenna001 (talk) 10:41, 6 May 2011 (UTC)
 * Thank you for removing your talk of "war". But can you not see that I do not need some westerner... is equally unacceptable? The point is that not all the sources cited there are from Ian Pierce. No, that isn't the point. Please cast your eyes up above to the section about the Jagged cleanup. The *point* is that most of that text comes from Jagged, who is known to abuse his sources. Unless you have personally verified that the sources you've re-inserted actually say what it claims, please don't re-insert them again William M. Connolley (talk) 11:05, 6 May 2011 (UTC)

 * Chenna, please keep in mind that most editors here are interested in the important Indian contribution to mathematics, and agree with you that certain original contributions preceded European discoveries. Avoiding blanket anti-western rhetoric will help your cause. Tkuvho (talk) 11:09, 6 May 2011 (UTC)

I think it's better to rewrite the Indian section from reliable sources. I'm a bit of a novice when it comes to the History of Mathematics, but even Morris Kline's "Mathematical thought from ancient to modern times" acknowledges some of the discoveries of Indian mathematicians. That might be a place to start. There shouldn't be a need to rely on questionable sources like the Pearce paper. Sławomir Biały (talk) 11:33, 6 May 2011 (UTC)

 * Thanks everybody. I will check relevant sources myself and re-write stuff later. I am having my exams now...Chenna001 (talk) 19:29, 6 May 2011 (UTC)

(outdent) Here is a reference which I haven't read, but I will if someone doesn't beat me to it "Was Calculus Invented in India?" by David Bressoud, College Mathematics Journal, Vol. 33, No. 1, Jan., 2002. He seems to cite a few other papers about it which might give some more details. If it helps with the current dispute the opening sentences are: "No. Calculus was not invented in India. But two hundred years before Newton or Leibniz, Indiana astronomers came very close to creating what we would call calculus." Thenub314 (talk) 19:37, 6 May 2011 (UTC)
 * PS The author then give a description of the power series expansions that Chenna001 mentions, so I am not trying to be dismissive to Indian contributions to calculus. Just want to give some reliable sources to base them on so we don't need to argue about it. Thenub314 (talk) 19:53, 6 May 2011 (UTC)
 * PPS Here is the JSTOR link for anyone interested who has access to JSTOR:

Jaggedalia, part 2
At ghosts of departed quantities, a few editors are attempting a whiggish rewriting of the history of the calculus. George Berkeley criticized both the infinitesimal and fluxional procedures of the calculus, which he claimed amounted to the same thing. Weierstrass and his followers in the 1870s did 3 things: (1) they largely accepted Berkeley's critique of infinitesimal procedures; (2) they sought to eliminate infinitesimals; and (3) they developed infinitesimal-free foundations for analysis, namely foundations based on the real numbers and epsilontics. Then in the 1960s, Robinson came along and restored infinitesimals to respectability, in particular removing whatever logical inconsistencies were present in dy/dx style definition of derivative. He was thus the first one to resolve the paradox of the infinitesimal procedures criticized by Berkeley.

The paragraph above is agreed to by all the historians I have read. Now a few editors have come along and rewritten history. The page ghosts of departed quantities no longer mentions Robinson. Instead, it claims that Weierstrass resolved Berkeley's paradoxes. This does not compare favorably with Jagged's efforts, to the extent that Jagged at least left the old material in while adding his new material. Some input would be appreciated. Tkuvho (talk) 13:36, 25 May 2011 (UTC)

Fermat
The following comment was recently deleted: "Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which influenced further work in quadrature". What the comment did not mention is that these results, like those on maxima and minima as well as tangents, of Fermat were applications of his method of adequality. Fermat's role as a pioneer of calculus is indisputable. I don't think we can err by overemphasizing Fermat in this section. The comment should be restored and expanded upon (incidentally, it was originally added by another editor). Tkuvho (talk) 08:49, 16 December 2011 (UTC)
 * I also support the reinsertion of the removed text, as well as further expansion of the section "Pioneers of modern calculus". More detail rather than less is called for here.  Other topics this article could touch upon include the development of the integral (e.g., Riemann and Lebesgue) and some more information on the contributions of Cauchy and Weierstrass to its foundations.  — Myasuda (talk) 14:25, 16 December 2011 (UTC)
 * Currently the material is poorly organized. Thus, Bolzano is mentioned before Newton and Leibniz.  Some restructuring may be in order.  Tkuvho (talk) 13:10, 29 December 2011 (UTC)
 * Agreed. Much of the article should be restructured and expanded.  In addition to chronological issues, the hatnote for the Leibniz–Newton calculus controversy would be better placed in the "Legacy" subsection (which should probably be renamed).  And the post Leibniz and Newton material needs to be significantly elaborated upon.  — Myasuda (talk) 21:40, 29 December 2011 (UTC)
 * Great, give it a try. Note also the section which is two sections below.Tkuvho (talk) 09:23, 30 December 2011 (UTC)

Two different methods
The method of exhaustion and the method of indivisibles are two genuinely different methods, contrary to what the page currently states. Tkuvho (talk) 12:58, 29 December 2011 (UTC)

World as infinite aggregate
The page currently claims that Leibniz viewed the world as an infinite aggregate (of monads), as well as "aggregate of infinitesimal points". Is there a source for this claim? Tkuvho (talk) 10:44, 28 February 2012 (UTC)

Kepler
I am surprised there is mention of Johannes Kepler's work on Wine Barrels. This work was fairly important in the evolution of calculus, see Roberto Cardil (MatematicasVisuales), "Kepler: The Volume of a Wine Barrel - Kepler's Era," Convergence (January 2012), DOI:10.4169/loci003499 Rhodydog (talk) 21:25, 9 August 2022 (UTC)
 * The work mention in the first bit about Kepler "Stereometrica Doliorum" is about that problem. NadVolum (talk) 20:47, 14 December 2022 (UTC)

Orphaned references in History of calculus
I check pages listed in Category:Pages with incorrect ref formatting to try to fix reference errors. One of the things I do is look for content for orphaned references in wikilinked articles. I have found content for some of History of calculus's orphans, the problem is that I found more than one version. I can't determine which (if any) is correct for this article, so I am asking for a sentient editor to look it over and copy the correct ref content into this article.

Reference named "ReferenceB": From History of logarithms:  From Science and technology in Iran:  From Law: Robertson, Crimes against humanity, 90.

I apologize if any of the above are effectively identical; I am just a simple computer program, so I can't determine whether minor differences are significant or not. AnomieBOT ⚡ 13:02, 5 February 2023 (UTC)

title: Talk:History of calculus


text:
Talk:Andrew Weiss (musician)

Untitled
why redirect to the Rollins Band page? Weiss isn't even in that band anymore. He's more associated with Ween than other bands. Changing back to original stub.

This article is bit droll 74.77.110.124 (talk) 01:12, 25 April 2008 (UTC)

Is he the related to Jon Weiss from Jello Biafra's band? --88.72.34.35 (talk) 12:47, 1 July 2011 (UTC)

Biography needs rewrite
Weiss contributed his own bio (as noted in this previous version). I added a COI tag. Might return.Tactical Fiend (talk) 22:07, 26 September 2018 (UTC)

Move to Andrew Weiss (producer)
He's not really known as a guitarist, more of a producer and or bassist, I propose the page is moved to Andrew Weiss (record producer) or Andrew Weiss (bassist) etc. 80s Sam (talk) 20:57, 27 October 2022 (UTC)

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

title: Talk:Andrew Weiss (musician)


text:
User talk:SimonW

Since you are the only editor to have touched the redirect Center for computer research in music and accoustics, you can simply request speedy deletion rather than asking for a vote. To do so, just put on the page. Wolfman 07:57, 18 Dec 2004 (UTC)
 * thanks! That was my first ever deletion request. SimonW 12:24, 18 Dec 2004 (UTC)

title: User talk:SimonW


text:
Classicomm

Classicomm was a small cable provider in Canada serving communities in southern York Region from its offices in Richmond Hill, Ontario.

Classicomm, or Classic Communications Ltd, was founded in the late 1960s by John O. Graham and Stewart H. Coxford, who were granted a cable television (CATV) licence by the CRTC for Richmond Hill and several other small communities north of Toronto.

By the 1980s the cable system had acquired additional licences, and soon covered a geographic area taking in most of southern York Region. With Steeles Avenue as its southerly service boundary, the cable system spanned the width of York Region from Markham in the east to Woodbridge in the west. Its coverage area stretched north to include communities such as Stouffville, King City, Kleinburg and Gormley.

Southern York Region experienced tremendous growth beginning around 1982. During the period of 1986–90 Classicomm was connecting up to 10,000 new subscribers each year, making it the fastest growing cable system of its day.

In 1984, the company applied to the Canadian Radio-television and Telecommunications Commission for permission to launch a classified advertising channel on the service, but the application was denied on the basis that cable companies were not permitted to compete with radio or television broadcasters for advertising revenue. The regulation was changed in 1986 to permit advertising channels. It was also one of the first cable companies in Canada to offer X*Press X*Change, an early foray into electronic news delivery.

The company was sold in 1995 to Shaw Communications of Calgary, for a purchase price of $240 million. When the transaction was first announced in 1994, Classicomm had 102,000 subscribers; when it was finalized the following year, the company had 105,000 subscribers. Along with Shaw's simultaneous acquisition of Trillium Cable, the deal helped to make Shaw the second-largest cable company in Canada.

A few years later, Rogers Cable of Toronto and Shaw Cable rationalized their cable holdings in Canada, with Shaw consolidating in western Canada and Rogers in central and eastern Canada. The Classicomm service area is now entirely part of Rogers Cable.

title: Classicomm


text:
Potassium ferrate

Potassium ferrate is the chemical compound with the formula K2FeO4. This purple salt is paramagnetic, and is a rare example of an iron(VI) compound. In most of its compounds, iron has the oxidation state +2 or +3 (Fe(2+) or Fe(3+)). Reflecting its high oxidation state, FeO4(2−) is a powerful oxidizing agent.

Synthesis and structure
Georg Ernst Stahl (1660 – 1734) first discovered that the residue formed by igniting a mixture of potassium nitrate (saltpetre) and iron powder dissolved in water to give a purple solution. Edmond Frémy (1814 – 1894) later discovered that fusion of potassium hydroxide and iron(III) oxide in air produced a compound that was soluble in water:
 * 8 KOH + 2 Fe2O3 + 3 O2 → 4 K2FeO4 + 4 H2O

The composition corresponded to that of potassium manganate. In the laboratory, K2FeO4 is prepared by oxidizing an alkaline solution of an iron(III) salt with concentrated chlorine bleach.:
 * 3 ClO− + 3 Fe(OH)3(H2O)3 + 4 K+ + 4 OH− → 3 Cl− + 2 K2FeO4 + 11 H2O

The salt is isostructural with K2MnO4, K2SO4, and K2CrO4. The solid consists of K+ and the tetrahedral FeO4(2−) anion, with Fe-O distances of 1.66 Å. The poorly soluble barium salt, BaFeO4, is also known.

Properties and applications
The main difficulty with the use of K2FeO4 is that it is often too reactive, as indicated by the fact that it decomposes in contact with water, especially in acidic water:
 * 4 K2FeO4 + 4 H2O → 3 O2 + 2 Fe2O3 + 8 KOH

At high pH, aqueous solutions are stable. The deep purple solutions are similar in appearance to potassium permanganate (KMnO4). It is stronger oxidizing agent than the latter. As a dry solid, K2FeO4 is stable.

Because the side products of its redox reactions are rust-like iron oxides, K2FeO4 has been described as a "green oxidant". It has been employed in waste-water treatment as an oxidant for organic contaminants and as a biocide. Conveniently, the resulting reaction product is iron(III) oxyhydroxide, an excellent flocculant. In organic synthesis, K2FeO4 oxidizes primary alcohols. In contrast, related oxidants such as chromates are considered environmentally hazardous.

K2FeO4 has also attracted attention as a potential cathode material in a "super iron battery."

Stabilised forms of potassium ferrate have been proposed for the removal of transuranic species, both dissolved and suspended, from aqueous solutions. Tonnage quantities were proposed to help remediate the effects of the Chernobyl disaster in Belarus. This new technique was successfully applied for the removal of a broad range of heavy metals.

Work on the use of potassium ferrate precipitation of transuranics and heavy metals was carried out in the Laboratories of IC Technologies Inc. in partnership with ADC Laboratories, in 1987 though 1992. The removal of the transuranic species were done on samples from various Dept. of Energy nuclear sites in the USA.

It has been proposed as a bleeding stopper for fresh wounds.

title: Potassium ferrate


text:
Wikipedia:Articles for deletion/Ebrief

Ebrief
Dictdef. Has not been edited since it was created nearly three weeks ago. →Iñgólemo←  (talk)  08:05, 2004 Dec 18 (UTC)

 * neologism, and yet another e-thingy with numerous non-meanings. Delete in the cruelest possible manner. iMeowbot~Mw 10:08, 18 Dec 2004 (UTC)
 * Delete. Selfconfessed neologism. This IP has had three distinct editing sessions each some weeks from the others; On this date three edits were made and the other two have both already been reverted as vandalism. Andrewa 13:53, 18 Dec 2004 (UTC)
 * Speedy delete as stealth spam. Wyss 15:07, 18 Dec 2004 (UTC)
 * Delete spam page - kaal 05:41, 23 Dec 2004 (UTC)

title: Wikipedia:Articles for deletion/Ebrief


text:
Peter Davis (sociologist)

Peter Byard Davis (born 25 April 1947) is a New Zealand sociologist, professor, and the husband of Helen Clark, who was the Prime Minister of New Zealand from 1999 to 2008.

Early life
Davis was born in Milford on Sea, Hampshire, England, on 25 April 1947, and spent his childhood in Tanzania, where his father worked for a mining company. His father was born in China and his mother in India, but a great-great-grandfather had grown up in New Zealand. Davis gained a master's degree in sociology and statistics at the London School of Economics. He moved to New Zealand in 1970 to work at the University of Canterbury and completed a PhD at the University of Auckland. He became a naturalised New Zealander in 1972. He was part of a team investigating oral health in New Zealand and was joint editor of the Australian and New Zealand Journal of Sociology. In 1976 he was appointed a lecturer at the University of Auckland school of medicine.

In 1980 he stood unsuccessfully for the Auckland City Council on a Labour Party ticket. In 1988 he was elected to the Auckland Regional Authority for the Mount Albert ward.

Personal life
Davis met Clark, then a political-science lecturer at Auckland, in 1977 and they married in 1981.

Career
Davis specialises in medical sociology, and from 2004 to 2017 worked as the Director of the COMPASS (Centre of Methods and Policy Application in the Social Sciences) Research Centre at the University of Auckland. In 2014 he was awarded a James Cook Research Fellowship for a research project titled "New Zealand as a 'social laboratory'". He is now Professor Emeritus in the School of Population Health and Honorary Professor in the Department of Statistics at the University of Auckland. Previously he served as Professor of Public Health at the University of Otago's Christchurch School of Medicine.

He has previously served on the Auckland Area Health Board, and was a representative in 1989 when his wife (Health Minister at the time) suspended that body. Davis has achieved international recognition in his field, having worked as a consultant for the World Health Organization.

In 2019 Davis became a City Vision candidate for the Auckland District Health Board and was subsequently elected.

He is Chair of The Helen Clark Foundation board.

title: Peter Davis (sociologist)


text:
Seongjong

Seongjong (성종; from Chinese: ) is the temple name of two Korean monarchs:

 * King Seongjong of Goryeo (r. 981–997)
 * King Seongjong of Joseon (r. 1469–1494)

title: Seongjong


text:
Northeim

Northeim (Nuurten) is a town in Lower Saxony, Germany, seat of the district of Northeim, with a population of 30,118 as of 31 December 2023. It lies on the German Half-Timbered House Road.

History
Northeim is first mentioned in 800 in a document recording a property transfer by a Frankish nobleman to the Abbey of Fulda. In the 10th century the surrounding region became a county, administered by the Counts of Northeim. The first of them, Siegfried is mentioned in 982. From 1061 to 1070 Count Otto II held the stem duchy of Bavaria as an Imperial fief, but lost it again because of his involvement in the Saxon plot against King Henry IV.

The monastery of St. Blasius was founded around 1100. In 1252 Northeim obtained town rights, and from 1384 to 1554 it was a member of the Hanseatic League. When protestantism was introduced in 1532 all the churches were allocated to the protestants. The town became part of the Kingdom of Hanover.

A part of Northeim was devastated by a fire in 1832 when the representative town hall dating from the Middle Ages and more than 40 houses burnt down. Further damage was caused by a fire in 1892 which destroyed several historic buildings in the Market Place.

After the railway from Hanover to Göttingen had been inaugurated in 1854 Northeim gained in importance and became a railway junction. The South Harz Railway was opened in 1868 and the Solling Railway in 1878. During the Second World War Northeim was hit by bombs in September 1944, February 1945 and in March 1945. The railway station, five factories and 18 houses were completely destroyed and 80 houses were damaged. The historic centre did not suffer severe bomb damage.

Northeim, under the pseudonym of Thalburg, is the subject of William Sheridan Allen's book The Nazi Seizure of Power (ISBN 0-531-05633-3), a comprehensive study of the success of Nazism at town level. The book describes how the Nazis took over all social groups in the town and Nazified them, but failed to instill positive enthusiasm for the Nazi state. Instead, the population was "atomized" and deprived of the means to express group grievances. The book has been criticized for neglecting the role of the churches, which remained largely autonomous. However, even its critics say that the book is crucial to our understanding of Nazi Germany and has played a key role in shaping scholarship. Imbshausen, the site of a post-World War II British sector Displaced Persons camp, was incorporated into the town in 1974.

On 15 November 1992 an express train crashed into the wreckage of a derailed freight train near Northeim. Eleven people died and 52 were injured.

Culture
The town has a town museum and archive. There is an outdoor stage outside the town. The town is also home to a puppet theatre, Theater der Nacht, which since 2001 has been housed in a redesigned fire station.

Some of the old town wall still stands, including a watchtower.

Transport
Hanoverian Southern Railway connects Northeim with cities like Göttingen and Hanover. Solling Railway connects Northeim with cities at the southern part of Solling-Vogler Nature Park.

Northeim also provides a small grass airfield (ICAO locator code: EDVN) due east of the town.

Twin towns – sister cities
Northeim is twinned with:
 * 🇫🇷 Cherbourg-en-Cotentin, France
 * 🇦🇹 Gallneukirchen, Austria
 * 🇵🇱 Prudnik, Poland

Inhabitants
(at 31 December each year)

Sights
There are many well-preserved half-timbered houses in the old centre of Northeim, e.g. in Wassergasse, one of the most picturesque lanes, and in Kuhgasse, the narrowest lane of Northeim. The oldest half-timbered houses were built of oak wood in the 15th century. In many façades wood carvings are worth a look.

A part of the historic centre is still surrounded by the medieval wall which was built in 1252–1305.

The oldest church of Northeim is Saint Fabian's and Sebastian's Chapel which was built in a typical gothic style in the middle of the 14th century and renovated in 1985/86. Saint Sixti's Church was built from 1464 to 1517. It houses a gothic altar dating from 1420 and another altar created in the 16th century. After the church had been allocated to the Protestants in 1539 there were no Catholics living in Northeim for several decades. The first catholic church to be built after the reformation was Saint Mary's Church outside the historic town centre which was founded at the end of the 19th century.

Saint Spiritus Hospital is a large half-timbered house with wood carvings built around 1500.

Saint Blasii is a former monastery which was founded in the 11th century and dissolved in 1592 after the reformation.

In the village of Imbshausen which was incorporated into the city in 1974 a castle built 1862–64 in a large park is worth a visit.

Theater der Nacht is located in an old firestation, rebuilt and designed by the artists Ruth und Heiko Brochhausen. It opened in May 1999. The theatre's speciality is Puppetry.

Churches

 * St. Sixti Church
 * Apostel Church
 * Corvinus Church

Notable people

 * Otto of Nordheim (ca 1020–1083), Duke of Bavaria from 1061 until 1070.
 * Heinrich Kreipe (1895–1976), general, died there
 * Georg Diederichs (1900–1983), local politician (SPD)
 * Loriot (1923-2011), humorist, went to school there
 * Hartmut Heinrich (born 1952), marine geologist and climatologist
 * Christian Jung (born 1956), geneticist and plant breeder
 * Edgar Lissel (born 1965), visual artist
 * Anna Naklab (born 1993), singer-songwriter, grew up there
 * Eros Dacaj (born 1996), German footballer, played over 200 games

title: Northeim


text:
Sing Tao Daily (Canada)

The Sing Tao Daily, or Sing Tao for short, is a Chinese language newspaper based in Toronto, Ontario. It is jointly owned by the Hong Kong-based Sing Tao News Corporation.

Sing Tao's was connected to the Toronto Star was through Andrew V. Go, former Star vice president for business ventures. Go's father, Go Puan Seng, was the publisher of The Fookien Times, then the Philippines' largest Chinese-language newspaper which also published the Philippine edition of the Sing Tao, and was a family friend of then Sing Tao Group's Sally Aw.

The Toronto edition is formally called the Canada Eastern Edition (加東版 Pinyin: Jiā Dōng Bǎn). A Canada Western Edition (加西版 Pinyin: Jiā Xī Bǎn) in Vancouver, British Columbia and an Alberta Edition in Calgary, Alberta have also been published since 1988.

According to former editor-in-chief of the newspaper, Victor Ho, and Jonathan Manthorpe, author of Claws of the Panda, the newspaper's editorial stance is pro-Beijing.

Reception
In 2009, the top editor of Toronto's Sing Tao Daily, Wilson Chan, was fired shortly after it was revealed that he drastically modified an original Toronto Star article on Tibet to remove criticisms of the Chinese government, before publishing the story in Sing Tao. The decision to remove Chan is said to have come from Torstar Corp, who owns a majority share in Sing Tao's Canadian edition.

The original story, "Chinese Canadians Conflicted on Tibet", which ran on April 13, 2008, was written by a reporter for the Toronto Star, an English-language newspaper also owned by Torstar Corporation. The relationship gives Sing Tao rights to translate and publish stories from the Star. Chan's edits to the Chinese language story, which were revealed by media outlets in 2009, included changing the headline to, "The West Attacks China With Tibet Issue, Inciting Chinese Patriotism Overseas". The edited version omitted all quotes critical of the Chinese regime's human rights abuses and added comments blaming the West for "suppressing China" with media reports of the crackdown in Tibet.

title: Sing Tao Daily (Canada)


text:
Feast of the Sacred Heart

The Feast of the Sacred Heart is a solemnity in the liturgical calendar of the Roman Rite of the Catholic Church. According to the General Roman Calendar since 1969, it is formally known as the Solemnity of the Most Sacred Heart of Jesus (Sollemnitas Sacratissimi Cordis Iesu) and celebrated on the second Friday after Trinity Sunday Some Anglican Franciscans keep the feast under the name of the Divine Compassion of Christ.

History
The first liturgical feast of the Sacred Heart was celebrated, with episcopal approval, on 31 August 1670, in the major seminary of Rennes, France, through the efforts of John Eudes. The Mass and Office composed by Eudes were adopted elsewhere also, especially in connection with the spread of devotion to the Sacred Heart following on the reported revelations to Margaret Mary Alacoque and Mary of the Divine Heart. In June 1675, according to Margaret Mary Alacoque of the Order of the Visitation of Holy Mary at Paray-le-Monial, France, she had a vision of Jesus Christ in which he asked her "that the first Friday after the octave of the Blessed Sacrament be dedicated to a particular feast to honor my heart, by receiving communion on that day and making reparation to it by honorable amends, to repair the indignities it received during the time it was exposed on the altars".

In 1726 Rome was again asked for a feast with a Mass and Office of its own; this was refused in 1729, but granted in 1765. In that year, at the request of the queen, the feast was received quasi-officially by the episcopate of France. A Mass of the Sacred Heart won papal approval for use in Poland and Portugal in 1765, and another was approved for Venice, Austria and Spain in 1788.

In 1856, at the entreaties of the French bishops, Pope Pius IX extended the Feast of the Sacred Heart to the Latin Church under the rite of double major. It was to be celebrated on the Friday after the Octave of Corpus Christi. In June 1889, Leo XIII raised the feast to the dignity of the first class. In 1928, Pope Pius XI raised the feast to the highest rank, double of the first class, and added an octave; the 1955 reforms of the General Roman calendar suppressed, among others, the octave of the Sacred Heart of Jesus. With the liturgical changes in 1969, the feast was assigned the highest rank of solemnity.

The Mass prayers and readings approved on that occasion were replaced with new texts in 1929, and the lectionary published to accompany the 1970 Roman Missal provides three sets of readings, one for each year of the festive three-year liturgical cycle.

Priests may use this Mass, celebrated with white vestments, as a Votive Mass on other days also, especially on the first Friday of each month (unless falling on a day of higher rank). On this first Fridays it is also common to hold an Eucharistic adoration for a few hours (see First Friday devotion).

In Austria and South Tyrol, the so-called Sacred Heart Sunday, that is the Sunday after the Feast of the Sacred Heart, is also celebrated. Numerous processions take place on this day. Sacred Heart Fires are lit in the Bozen (Bolzano) area of Italy, among others.

Since 2002, the Solemnity of the Sacred Heart of Jesus is also a special day of prayer for the sanctification of priests. In 2009, the feast marked the beginning of a "Year for Priests".

The Feast of the Immaculate Heart of Mary immediately follows on Saturday.

On June 12, 2023, the United States Conference of Catholic Bishops issued the following statement: "This year, on June 16 — the day of the Solemnity of the Sacred Heart of Jesus — a professional baseball team has shockingly chosen to honor a group whose lewdness and vulgarity in mocking our Lord, His Mother, and consecrated women cannot be overstated. This is not just offensive and painful to Christians everywhere; it is blasphemy." The bishops called on Catholics to pray the Litany of the Sacred Heart on June 16, offering this prayer "... as an act of reparation for the blasphemies against our Lord we see in our culture today."

Date
The solemnity is celebrated on the second Friday following Trinity Sunday. The earliest possible date is May 29, as in 1818 and 2285. The latest possible date is July 2, as in 1943 and 2038. Therefore, it is the last feast date of the year dependent on the date of Easter.

In places where the Solemnity of the Most Holy Body and Blood of Christ is perpetually transferred from Thursday to Sunday (such as the United States and United Kingdom), it will appear on the local calendar as the Friday after the Solemnity of Corpus Christi.

title: Feast of the Sacred Heart


text:
Ming Pao Daily News (Canada)

Ming Pao Daily News, or Ming Pao for short, is a Chinese language newspaper in Canada owned by the Ming Pao Group of Hong Kong.

Ming Pao in Canada has two editions. The Eastern edition published in Toronto, Ontario was launched in May 1993 by then Chairman P.H. Yu, and competed in the local Chinese community with Sing Tao Daily and World Journal. The Toronto editorial offices are located in Agincourt. Shortly after in October 1993, the Western edition was launched in Vancouver, British Columbia.

The paper is published 7 days a week in broadsheet format. News coverage include Canadian news (including national, provincial, city and community pages), international news, Hong Kong news, Mainland China and Taiwan news, plus lifestyle, entertainment, and sports sections.

Supplements (magazines)
The Canada Eastern edition of Ming Pao publishes several weekly supplements (magazines). Unlike the situation in Hong Kong where the magazines are sold as separate publications, these are more properly called supplements that come free with the paper. The pages inside the magazines are also printed on newsprint instead of glossy paper.

The free magazines that come with the Canada Eastern edition are:
 * Wednesday —Ming Pao Gourmet Supplement (樂在明廚), a tabloid-sized food magazine for everyone who loves cooking and eating.
 * Thursday — Property Golden Pages (地產金頁), a tabloid-format publication resembling a small newspaper, containing mostly property listings and other data, with some editorial content
 * Friday — Zhōnghuá Tànsuǒ (中華探索, "Exploring China"), a magazine containing political criticism from Hong Kong's Ming Pao Magazine and Yazhou Zhoukan
 * Saturday — Saturday Magazine (星期六周刊), a lifestyle-and-news magazine with substantial original local content
 * Sunday — Ming Pao Sunday Supplement (明報加東周刊), a tabloid-sized entertainment magazine with content mostly written by its reporters in Hong Kong

From time to time, special supplements are also published.

Rivals
Besides the traditional rivals Sing Tao Daily and World Journal, Today Daily News, launched November 1, 2005, was also considered a major competitor.

title: Ming Pao Daily News (Canada)


text:
OUA

OUA or Oua may refer to:

Organisations

 * Open Universities Australia, an online higher education organization based in Australia
 * Organisation of African Unity, now replaced by the African Union
 * Ontario University Athletics, a regional membership association for Canadian universities

Places

 * Oua, an island in Tuvalu
 * Oua River, a river in Gabon
 * ʻOʻua, an island in Tonga
 * Ouagadougou Airport (IATA code)

title: OUA


text:
Thermal de Broglie wavelength

In physics, the thermal de Broglie wavelength ($$\lambda_{\mathrm{th}}$$, sometimes also denoted by $$\Lambda$$) is roughly the average de Broglie wavelength of particles in an ideal gas at the specified temperature. We can take the average interparticle spacing in the gas to be approximately $(V/N)^{1/3}$ where $V$ is the volume and $N$ is the number of particles. When the thermal de Broglie wavelength is much smaller than the interparticle distance, the gas can be considered to be a classical or Maxwell–Boltzmann gas. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the interparticle distance, quantum effects will dominate and the gas must be treated as a Fermi gas or a Bose gas, depending on the nature of the gas particles. The critical temperature is the transition point between these two regimes, and at this critical temperature, the thermal wavelength will be approximately equal to the interparticle distance. That is, the quantum nature of the gas will be evident for

$$  \displaystyle \frac{V}{N\lambda_{\mathrm{th}}^3} \le 1 \, {\rm or} \ \left( \frac{V}{N} \right)^{1/3} \le \lambda_{\mathrm{th}} $$

i.e., when the interparticle distance is less than the thermal de Broglie wavelength; in this case the gas will obey Bose–Einstein statistics or Fermi–Dirac statistics, whichever is appropriate. This is for example the case for electrons in a typical metal at T = 300 K, where the electron gas obeys Fermi–Dirac statistics, or in a Bose–Einstein condensate. On the other hand, for

$$  \displaystyle \frac{V}{N\lambda_{\mathrm{th}}^3} \gg 1 \, {\rm or} \ \left( \frac{V}{N} \right)^{1/3} \gg \lambda_{\mathrm{th}} $$

i.e., when the interparticle distance is much larger than the thermal de Broglie wavelength, the gas will obey Maxwell–Boltzmann statistics. Such is the case for molecular or atomic gases at room temperature, and for thermal neutrons produced by a neutron source.

Massive particles
For massive, non-interacting particles, the thermal de Broglie wavelength can be derived from the calculation of the partition function. Assuming a 1-dimensional box of length $L$, the partition function (using the energy states of the 1D particle in a box) is $$ Z = \sum_{n} e^{-E_n/k_{\mathrm B}T} = \sum_{n} e^{-h^2 n^2 / 8mL^2k_{\mathrm B} T} .$$

Since the energy levels are extremely close together, we can approximate this sum as an integral: $$ Z = \int_0^\infty e^{-h^2 n^2 / 8mL^2k_{\mathrm B}T} dn = \sqrt{\frac{2\pi m k_{\mathrm B} T}{h^2}} L \equiv \frac{L}{\lambda_{\rm th}} .$$

Hence, $$ \lambda_{\rm th} = \frac{h}{\sqrt{2\pi m k_{\mathrm B} T}} ,$$ where $$ h $$ is the Planck constant, $m$ is the mass of a gas particle, $$k_{\mathrm B}$$ is the Boltzmann constant, and $T$ is the temperature of the gas. This can also be expressed using the reduced Planck constant $$\hbar= \frac{h}{2\pi} $$ as $$\lambda_{\mathrm{th}} = {\sqrt{\frac{2\pi\hbar^2}{ mk_{\mathrm B}T}}} .$$

Massless particles
For massless (or highly relativistic) particles, the thermal wavelength is defined as $$\lambda_{\mathrm{th}}= \frac{hc}{2 \pi^{1/3} k_{\mathrm B} T} = \frac{\pi^{2/3}\hbar c}{ k_{\mathrm B} T} ,$$

where c is the speed of light. As with the thermal wavelength for massive particles, this is of the order of the average wavelength of the particles in the gas and defines a critical point at which quantum effects begin to dominate. For example, when observing the long-wavelength spectrum of black body radiation, the classical Rayleigh–Jeans law can be applied, but when the observed wavelengths approach the thermal wavelength of the photons in the black body radiator, the quantum Planck's law must be used.

General definition
A general definition of the thermal wavelength for an ideal gas of particles having an arbitrary power-law relationship between energy and momentum (dispersion relationship), in any number of dimensions, can be introduced. If $n$ is the number of dimensions, and the relationship between energy ($E$) and momentum ($p$) is given by $$E=ap^s$$ (with $a$ and $s$ being constants), then the thermal wavelength is defined as $$ \lambda_{\mathrm{th}}=\frac{h}{\sqrt{\pi}}\left(\frac{a}{k_{\mathrm B}T}\right)^{1/s} \left[\frac{\Gamma(n/2+1)}{\Gamma(n/s+1)}\right]^{1/n} , $$ where $Γ$ is the Gamma function. In particular, for a 3-D ($n = 3$) gas of massive or massless particles we have $E = p^{2}/2m (a = 1/2m, s = 2)$ and $E = pc (a = c, s = 1)$, respectively, yielding the expressions listed in the previous sections. Note that for massive non-relativistic particles (s = 2), the expression does not depend on n. This explains why the 1-D derivation above agrees with the 3-D case.

Examples
Some examples of the thermal de Broglie wavelength at 298 K are given below.

title: Thermal de Broglie wavelength


text:
William H. Whyte

William Hollingsworth "Holly" Whyte Jr. (July 11, 1917 – July 11, 1999) was an American urbanist, sociologist, organizational analyst, journalist and people-watcher. He identified the elements that create vibrant public spaces within the city and filmed a variety of urban plazas in New York City in the 1970s. After his book about corporate culture The Organization Man (1956) sold over two million copies, Whyte turned his attention to the study of human behavior in urban settings. He published several books and a film on the topic, including The Social Life of Small Urban Spaces (1980).

Biography
Whyte was born in West Chester, Pennsylvania in 1917. An early graduate of St. Andrew's School in Middletown, Delaware, he graduated from Princeton University in 1939 and then served in Marine Corps between 1941 and 1944. He was commissioned and served as battalion intelligence officer with the 3rd Battalion, 1st Marines in the Guadalcanal Campaign. He left Guadalcanal at the end of the campaign with a serious case of malaria that lingered for years. He spent the rest of the war lecturing and writing at the Marine Corps Staff and Command School at Quantico, Virginia, on the fighting qualities of the Japanese soldier.

In 1946 he joined Fortune Magazine where he remained until 1958.

In 1952, Whyte coined the term "Groupthink":

"Groupthink being a coinage – and, admittedly, a loaded one – a working definition is in order. We are not talking about mere instinctive conformity – it is, after all, a perennial failing of mankind. What we are talking about is a rationalized conformity – an open, articulate philosophy which holds that group values are not only expedient but right and good as well."

Whyte wrote a 1956 bestseller titled The Organization Man after Fortune Magazine sponsored him to do extensive interviews on the CEOs of corporations such as General Electric and Ford.

While working with the New York City Planning Commission in 1969, Whyte began to use direct observation to describe behavior in urban settings. With research assistants wielding still cameras, movie cameras, and notebooks, Whyte described the substance of urban public life in an objective and measurable way. These observations developed into the "Street Life Project", an ongoing study of pedestrian behavior and city dynamics, and eventually to Whyte's books such as The Social Life of Small Urban Spaces (1980) and City: Rediscovering the Center (1988). "City" presents Whyte's conclusions about jaywalking, 'schmoozing patterns,' the actual use of urban plazas, appropriate sidewalk width, and other issues. This work remains valuable because it is based on careful observation, and because it contradicts other conventional wisdom, for instance, the idea that pedestrian traffic and auto traffic should be separated.

Whyte along with Project for Public Spaces worked closely on the renovation of Bryant Park in New York City.

Whyte served as mentor to many, including the urban-planning writer Jane Jacobs, Paco Underhill, who has applied the same technique to measuring and improving retail environments, Dan Biederman of Bryant Park Corporation, who led the renovation of Bryant Park and the Business Improvement District movement in New York City, Fred Kent, who worked with Whyte for a number of years before starting Project for Public Spaces, and future New York City Planning Commissioner, heiress and socialite Amanda Burden.

Whyte married fashion designer Jenny Bell Bechtel in 1964. They had one daughter, Alexandra Whyte.

He is interred at the Oaklands Cemetery in West Chester, Pennsylvania.

Books

 * Is Anybody Listening? (1952)
 * The Organization Man (1956)
 * The Exploding Metropolis (1958)
 * Securing Open Spaces for Urban America (1959)
 * Cluster Development (1964)
 * The Last Landscape (1968)
 * The Social Life of Small Urban Spaces (1980)
 * City: Rediscovering the Center (1988)

title: William H. Whyte