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It would be nice to add a picture of the tablet to the article, something like those available at [1] or [2]. The tablet itself is of course in the public domain, but the photographs may not be. We could probably add one under fair use, given the historical importance of the topic, but I was wondering if we could argue that the photograph is in the public domain, according to Bridgeman Art Library v. Corel Corp. ? The tablet is a 3D object, but it is photographed as a flat object, with the goal of reproducing it accurately. Any opinion ? Schutz 11:20, 20 April 2006 (UTC)
I'm bumping the importance in the math rating header to mid. This tablet is the basis of claims that the Babylonians knew the Pythagorean theorem prior to the Pythagoreans themselves and prior to the Sulba Sutras; in terms of the history of mathematics it's quite an important document, although its impact on modern mathematics per se is minimal. — David Eppstein 15:49, 20 May 2007 (UTC)
Neil Parker ( talk) 18:08, 6 August 2009 (UTC)
Clarification: Plimpton 322 has been regarded as a basis of claims that the Babylonians had early familiarity with at least a Pythagorean rule. The thrust of Robson (2001) is to knock Plimpton 322 off this particular pedestal. However, perhaps a firmer, and certainly an independent, basis for the claim is provided by Db2-146 = IM67118, a tablet from Eshnunna from about -1775, as discussed, for example, by Høyrup (2002) (Høyrup is one of the principal authors cited in Robson (2001) for naive geometry, but, of course this book postdates that article).
Col 2 | Col 3 | Calculate | Calculate | Col 1 | 1 + Col 1 | Divide: | Angle x |
---|---|---|---|---|---|---|---|
Opp | Hyp | Adj | Angle x | = tan^2(x) | = sec^2(x) | = sin^2(x) | =60*[sin^2(x)+.25] |
119 | 169 | 120 | 44.76 | 0.9834 | 1.9834 | 0.4958 | 44.75 |
3367 | 4825 | 3456 | 44.25 | 0.9492 | 1.9492 | 0.4870 | 44.22 |
4601 | 6649 | 4800 | 43.79 | 0.9188 | 1.9188 | 0.4788 | 43.73 |
12709 | 18541 | 13500 | 43.27 | 0.8862 | 1.8862 | 0.4698 | 43.19 |
65 | 97 | 72 | 42.08 | 0.8150 | 1.8150 | 0.4490 | 41.94 |
319 | 481 | 360 | 41.54 | 0.7852 | 1.7852 | 0.4398 | 41.39 |
2291 | 3541 | 2700 | 40.32 | 0.7200 | 1.7200 | 0.4186 | 40.12 |
799 | 1249 | 960 | 39.77 | 0.6927 | 1.6927 | 0.4092 | 39.55 |
481 | 769 | 600 | 38.72 | 0.6427 | 1.6427 | 0.3912 | 38.47 |
4961 | 8161 | 6480 | 37.44 | 0.5861 | 1.5861 | 0.3695 | 37.17 |
45 | 75 | 60 | 36.87 | 0.5625 | 1.5625 | 0.3600 | 36.60 |
1679 | 2929 | 2400 | 34.98 | 0.4894 | 1.4894 | 0.3286 | 34.72 |
161 | 289 | 240 | 33.86 | 0.4500 | 1.4500 | 0.3104 | 33.62 |
1771 | 3229 | 2700 | 33.26 | 0.4302 | 1.4302 | 0.3008 | 33.05 |
56 | 106 | 90 | 31.89 | 0.3872 | 1.3872 | 0.2791 | 31.75 |
Compare column 4 and column 8 in the above. "Col 1", "Col 2" etc refer to the column numbers in the Plimpton tablet. Neil Parker ( talk) 18:05, 6 August 2009 (UTC)
Is it beyond the bounds of credibility to imagine that the Babylonians may have in some way noted:
and concluded that if '0:15' is added to the squared sine, it's equal to the angle? And indeed a remarkably linear relationship does exist for angle vs sin^2(angle) in the range 30 to 60 degrees.
It's an accepted part of Maths history that the Babylonians divided the circle into 360 equal parts so we need to ask the question how exactly did they achieve that division and how accurate were they? (presumably they would have had a more sophisticated method than merely marking 360 approximately even divisions around a circle circumference). Neil Parker ( talk) 08:18, 2 September 2009 (UTC)
Exchanges with David Eppstein
Plimpton 322 It is difficult to "source" mathematically elementary observations about right triangles and it would be embarrassing to describe a subject which has been worked over for thousands of years as "original research"; it is just mathematics. In contrast, it is natural and proper to source interpretations, as is done in the article, as they are proposed by individuals. If anything, it is surprising that the mathematical reconciliation, being completely trivial, had not already been included in such a "definitive" article. —Preceding unsigned comment added by 130.194.170.146 (talk) 04:47, 11 September 2010 (UTC)
The calculations themselves may be trivial, but by putting those calculations in that context as if to lead to a conclusion about what Plimpton 322 was used for, you are committing original research by synthesis. —David Eppstein (talk) 04:56, 11 September 2010 (UTC)
However, routine calculations are allowed and what is given is entirely routine. You seem to be misreading the text. No comment is made about what Plimpton 322 was used for, although comment is made about how the Pythagorean rule can and was used (that can be sourced, for example, in the writings of Jens Høyrup. Rather, without giving weight to any interpretation, the remarks show how they are related mathematically. It was puzzling how such an elementary observation had been left out of an otherwise "definitive" article. Let me restore the comments in good faith, since otherwise readers who are not so mathematically deft are deprived of pertinent information. Of course, you are free to edit the section so as to give only mathematical trivialities that say absolutely nothing about the use of Plimpton 322. —Preceding unsigned comment added by 130.194.170.146 (talk) 05:10, 11 September 2010 (UTC) I have now qualified the section heading to emphasise that only the mathematics of two contending interpretations is being reconciled (as you might expect to have been done already in a "definitive" article when mathematically speaking the points are so trivial). You are clearly anxious about the making of inferences about how Plimpton 322 was used. Can you say how clarifying the very simple mathematics in the two interpretations has bearing on that? —Preceding unsigned comment added by 130.194.170.146 (talk) 05:25, 11 September 2010 (UTC)
What is your point in adding that passage to the article? It's not just a calculation — if I wrote 1+1=2 at the end of an article on Fibonacci, it would be a true statement of mathematics, but it would not lead anywhere. I am similarly having a difficult time seeing how what you wrote in Plimpton 322 connects to anything in the article, but if it does connect, it is (I assume) in order to make some particular point about the Babylonians' ability to solve quadratic equations or generate Pythagorean triangles. That point, whatever it is that you are trying to make, needs a source. It is not good enough to say that the mathematics in what you wrote is true, and that any conclusion is in the mind of the reader. Either you are adding pointless irrelevant calculation to the end of the article, or you are committing original research by synthesis. Either way, it doesn't belong. —David Eppstein (talk) 05:40, 11 September 2010 (UTC)
I believe that you are a very distinguished computer scientist, so your comment is bewildering. One interpretation of Plimpton 322 is in terms of Pythagorean triples, another is that it is an exercise set for the solution of a certain quadratic. Non-mathematical readers might not notice that the mathematics of these two interpretations is closely related, indeed that you can use the Pythagorean triples to solve just such quadratics, not just the one mentioned. So, the mathematically trivial computation is closely tied to the existing text and designed to assist those readers. You are reading into this a suggestion of what the Babylonians could do, but it is not there nor does it need to be there, although just such issues have been discussed (as I say, for instance, by Jens Høyrup). Moreover, what you are also throwing out, is the very simple observation that certain right triangles, such as the 3-4-5 triangle, have all their sides determined as segments of grid lines in a square grid. So, in fact, you really do not need to know all that much, other than to count. So, I submit that the section is pertinent to the existing text, helpful to readers, but not original research, whether by synthesis or in some other way. If indeed I am right in thinking you are a computer scientist, I should be surprised if you did not want to help non-mathematical readers see how the mathematics of the two interpretations is related. You do agree that the mathematics is related as stated and also that Pythagorean triples can be generated in the square grid without knowledge of the Pythagorean Theorem or number theory? —Preceding unsigned comment added by 130.194.170.146 (talk) 06:03, 11 September 2010 (UTC)
I think this section needs to be removed. There are several reasons I can see:
It is original research by synthesis given that there are no sources given. The reason given: "Just in case the solution algorithm for the quadratic equation might seem divorced from Pythagorean triples" is not valid. There are already connections to quadratic equations given right above it. Contrary to what is claimed, this will not help any non-mathematical reader in any way shape or form. My experience developing and teaching liberal arts mathematics courses tells me that even the average freshman at a university (so reasonably well-educated) is going to take one glance at the writing and ignore it. The reference to folding squares/triangles is questionable given that they wrote on clay tablets.
I agree with Dave Eppstein, this needs to be removed. --AnnekeBart (talk) 14:11, 11 September 2010 (UTC)
Clearly original research by synthesis resonates in the Wikipedia community. But surely it is to stop synthesis that is tendentious. AnnekeBart helps out by supplying an instance: yes, indeed, quadratic equations are mentioned immediately beforehand, but the elementary calculations connecting them with Pythagorean triples are not. So, that is why the material is inserted, "just in case". As it happens, one of the leading authors in the history of mathematics in the USA has just written in privately to say the reasoning is excellent and he regrets having missed it, simple though it is. Why was it not already in a "definitive" article? The reference to folding right triangles side to side is to help visualise the significance of the half angles. But writing on clay tablets has nothing to do with it - yet another synthesis gone wrong. I agree that, if that is the level of the readership, then very little, not just the inserted section, is going to register - eyes are likely to glaze quickly encountering the elaborate account of the vs in the algorithm for solving the quadratic. Against that, my guess is that college freshmen, like the leading historian, might rather say, "Pyth to solve quadratics. That's cute".
So, let me try to say yet again what this section is intended to do. The Neugebauer thesis draws on Pythagorean triples. The Robson thesis draws on solutions to quadratic equations. Already here then in the article are suggestions of Babylonian skills. But what sort of mathematical threshold do these skills represent? The talk of number theory for the triples might seem to make it less plausible even if the triples themselves are fairly concrete. But, no, this need not be the case, because right triangles with commensurable sides can be identified in playing on the square grid. Again, the talk of solutions of quadratics, with numerous equations for the algorithm, might remind readers of why they were never any good at mathematics and, indeed, where they lost the plot. But, no, this too need not be a challenge, because a computational trick with Pythagorean triples, little more than difference of two squares, brings out the solution. So, the section supports the existing content of the article by indicating the skills threshold that might be required for one or other of these two interpretations. Moreover, it reveals that they are not exactly exclusive. However, it does not come with any tendentious suggestion as to the use of Plimpton 322 or the skills achieved by the Babylonians. Why deprive readers of this support?
Mathematics as elementary as this cannot be said to be original research. Just imagine trying to publish this in order to generate a source. But I suspect that even if there were a published source to quote at this juncture, that does not seem to be really what is troubling David Eppstein or AnnekeBart. I am afraid that they come over as strangely hostile to the idea of noting for readers how the theses of Neugebauer and Robson are linked, so not chalk and cheese, as might appear from the article. To that extent, it is the article that is tendentious. I agree that the section is in the nature of a footnote or an aside. I should hope that Wikipedia was sufficiently versatile to handle this. But Wikipedia does already have options for leaving material in, while cautioning that original research might be present.
On the other hand, there certainly are cognate sources. There is a large body of problems in old Babylonian mathematics. For instance, BM13901 looks at the problem of two squares for which the sum of areas is known along with either the sum or the difference of the sides, giving the same haunting, suggestive mix of the Pythagorean rule and quadratic equations. One researcher who has written extensively about this material and who is widely quoted is Jens Høyrup. I refrained from putting any of this sourced comparative material in because it might upset the focus of the article on Plimpton 322, although it might be helpful to put Plimpton 322 back in a context from which it has become somewhat detached by being such a centre of attention. In that wider context, the comingling of the Pythagorean rule and quadratics is familiar, at least in our latter day understanding of the subject.
As I say, I was startled and amazed not to find the inserted section already present in a "definitive" article, and now I am bewildered that there is this insistence that supportive information of a non-tendentious nature be deleted. —Preceding unsigned comment added by 130.194.170.146 (talk) 21:40, 11 September 2010 (UTC)
If the section is badly written, why not say that at the start? Unhelpful to any reader? You seem to be changing your tune the more your objections are answered.
Here, in contrast, is the message from the author of one of the leading histories of mathematics published in the USA: Your reasoning here is excellent. I feel I ought to have noticed this connection before, but somehow I missed it. Thus, it appears that even if Plimpton 322 is about problems in algebra or Diophantine equations specifically, the connection with Pythagorean triples is quite immediate. And, of course, the argument that shows how to generate all primitive Pythagorean triples in the form (m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2 works off the same idea of factoring the difference of two squares.
Are you not rather undercutting the spirit of Wikipedia here? —Preceding unsigned comment added by 130.194.170.146 (talk) 00:04, 12 September 2010 (UTC)
Reviewing the discussion, and acknowledging the proper place of sources in Wikipedia, it occurs to me that it might be worth reminding ourselves of the abstract for one of the key sources for the Wikipedia article, Robson's contribution to Historia Mathematica in 2001. In view of Robson's final sentence, maybe I was wrong not to have included mention of some of those other texts, such as BM13901: Ancient mathematical texts and artefacts, if we are to understand them fully, must be viewed in the light of their mathematico-historical context, and not treated as artificial, self-contained creations in the style of detective stories. I take as a dramatic case study the famous cuneiform tablet Plimpton 322. I show that the popular view of it as some sort of trigonometric table cannot be correct, given what is now known of the concept of angle in the Old Babylonian period. Neither is the equally widespread theory of generating functions likely to be correct. I provide supporting evidence in a strong theoretical framework for an alternative interpretation, first published half a century ago in a different guise. I recast it using regular reciprocal pairs, Høyrup’s analysis of contemporaneous “na¨ıve geometry,” and a new reading of the table’s headings. In contextualising Plimpton 322 (and perhaps thereby knocking it off its pedestal), I argue that cuneiform culture produced many dozens, if not hundreds, of other mathematical texts which are equally worthy of the modern mathematical community’s attention
130.194.170.146 ( talk · contribs) has added the following to my talk page, coppied here to keep the discussion in one place:
The spirit of wikipedia holds Reliable sources as one of its core principles, this means that every item in wikipedia can be traced back to a verifiable source so people can check the accuracy. Further original research consisting of unsourced results is prohibited. Your addition falls foul of these two principles.-- Salix ( talk): 06:30, 12 September 2010 (UTC) Further, you edits are asserting that the Babylonian knew of this connection between Pythagorean triples and quadratic equations and used a technique based around grids to do this. Yet there is no evidence for such. If we compare your addition to the work of Robinson who has based her theory on extensive research of the other writings of the Babylonian we see two very different level of scholarship. Maintaining high levels of scholarship is the reason behind the policies on original research.
You have also breached WP:3RR which prevents editi waring on pages. Because of that I've protected the main article against edits for three days. -- Salix ( talk): 06:53, 12 September 2010 (UTC)
Richard, Might I just possibly correct you in some places there, apart from the obvious lapses in attention, such as "Robinson" for "Robson". There was no assertion in the excised section that the Babylonians had any particular skills, and indeed when I became aware through exchanges with David Eppstein in which he shifted his ground, I redrafted the text to make that absolutely specific so there could be no doubt. Rather, both the theses of Neugebauer and of Robson presume that the Babylonians had certain skills. All I was doing was pointing to the mathematical level of these skills and a link between them. It just so happens that certain right triangles do have all their sides determined as integral grid-line segments, and they turn out to be the Pythagorean triangles. So, if you were playing on the grid, you might notice that, without having to know the Pythagorean rule or number theory. In a sense, you have them for free. So, the simple point here is that the mathematical level might not be very high, not as high as might be supposed.
Just a comment on mathematical level; nothing about the Babylonians, you understand. It is just a property of right triangles that depends on tangents of half-angles. It is true that Wikipedia does not have that property on in its articles, such as Right_Triangle, so perhaps the way to build the scaffolding of verification and sources is to edit it in.
Again you are completely mistaken about any assertion that the Babylonians knew a link between Pythagorean triples and quadratic equations. I made no such comment. Instead there was a simple mathematical observation that the age-old trick of completing the square does unlock a link of this sort for those who know it. It would seem from the writings of Jens Hoeyrup, which Robson draws on extensively, that this trick, and so this comingling, might not actually have been unknown to some of the Babylonians. But what I wrote was not in any way in competition with Robson's research, so your comparison is otiose as well as gratuitous, I regret to say. Rather the leading historian in the USA has the right reading: completely granting Robson's thesis, nevertheless the connection with Pythagorean triples is immediate. But notice significantly that the leading historian says he had missed this himself, even while feeling he should have spotted it. That is why I did not say, and would never say, the Babylonians or anyone else knew this or that: even the obvious can be hidden in plain sight.
Now, you have exposed yourself brilliantly as having totally misread what was written, even in the face of an explicit disclaimer. But it is some consolation that you are so concerned to maintain high levels of scholarship. Perhaps you might make a start yourself by reading more carefully, instead of jumping to unwarranted conclusions.
You are, in effect making totally false accusations about me in public on this page. I have never written anything of the sort you attribute to me.
I've added references to current exhibit at NYU and NY Times review of same. This article needs work to satisfy the lay public's newly aroused curiosities. This article need not be written in academic style -- this is a subject requiring little more than a few reminders of high school math and elementary number theory and one that if well written could easily engage high school students.
I've also linked to specific pages of Neugebauer & Sachs for those who want to read the original 1945 source. Will do same for his Exact Sciences in Antiquity, also avail. on Google Books, at least in relevant parts of ch. 2. A couple of External links added for inspiration re: clarity is certainly possible.
Lead needs serious work:
The most renowned of all mathematical cuneiform tablets since it was published in 1945, Plimpton 322 reveals that the Babylonians discovered a method of finding Pythagorean triples, that is, sets of three whole numbers such that the square of one of them is the sum of the squares of the other two. By Pythagoras' Theorem, a triangle whose three sides are proportional to a Pythagorean triple is a right-angled triangle. Right-angled triangles with sides proportional to the simplest Pythagorean triples turn up frequently in Babylonian problem texts; but if this tablet had not come to light, we would have had no reason to suspect that a general method capable of generating an unlimited number of distinct Pythagorean triples was known a millennium and a half before Euclid.
Plimpton 322 has excited much debate centering on two questions. First, what was the method by which the numbers in the table were calculated? And secondly, what were the purpose and the intellectual context of the tablet? At present there is no agreement among scholars about whether this was a document connected with scribal education, like the majority of Old Babylonian mathematical tablets, or part of a research project.
http://www.nyu.edu/isaw/exhibitions/before-pythagoras/items/plimpton-322/
Plimpton 322 is known throughout the world to those interested in the history of mathematics as a result of the interest that Otto Neugebauer, chair of Brown University's History of Mathematics Department, took in the tablet. In the early 1940s, he and his assistant Abraham Sachs interpreted it as containing what is known in mathematics as Pythagorean triples, integer solutions of the equation a2 + b2 equals c2, a thousand years before the age of Pythagoras.
Recently, Dr. Eleanor Robson, an authority on Mesopotamian mathematics at the University of Cambridge, has made the case for a more mundane solution, arguing that the tablet was created as a teacher's aid, designed for generating problems involving right triangles and reciprocal pairs. Mr. Plimpton, who collected our tools of learning on a broad scale, would have been delighted with this interpretation, showing the work of an excellent teacher, not a lone genius a thousand years ahead of his time.
http://www.columbia.edu/cu/lweb/eresources/exhibitions/treasures/html/158.html
Given the current interest in this artifact, can't we do better for the lay public? If no objections, I'll revise the lead to more closely match the professionally conceived summaries cited above.
I respectfully challenge the more mathematically qualified to split the interpretation section into two or three manageable pieces and to distribute citations to varied sources more equitably. -- Paulscrawl ( talk) 22:27, 28 November 2010 (UTC)
Robson's main article on the subject is written very polemically, yet buried in it is a conclusion that is much less at odds with the traditional interpretation than one would expect from the way the argument is framed:
[...] the question “how was the tablet calculated?” does not have to have the same answer as the question “what problems does the tablet set?” The first can be answered most satisfactorily by reciprocal pairs, as first suggested half a century ago, and the second by some sort of right-triangle problems.
(Robson, "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322", Historia Math. 28 (3), p. 202).
By the way, Robson takes Voils to task for ignoring the table headings (which make it obvious that the scribe saw the relation to what is now called Pythagoras's theorem, or something very close thereto). Robson's main real contribution seems to have been to make a case for how the table was most likely derived: Babylonian algebra does not equal our high school algebra, even when their methods are mathematically equivalent from our perspective. Van der Waerden also posited what amounts to the derivation Robson believes to have been more likely, but did not emphasise its difference from the form chosen by Neugebauer and others.
I am touching on these issues very briefly at User:Garald/Number_theory, which is intended to become a replacement to the main Number Theory page (once it's finished); we should probably go into greater length about this here. Garald ( talk) 14:13, 8 December 2010 (UTC)
From the article heading:
"Although the table has been interpreted by leading mathematicians as a listing of Pythagorean triples, more recently published theories give it a different function.[2]"
This isn't really an "although". The list is (from our perspective) a listing of Pythagorean triples (that is, integers a, b, c such that ). Moreover, the headings (as Robson herself says) suggests that these were indeed thought of as numbers corresponding to lengths of a right triangle. This says nothing by itself about the *function*. Robson's statements about the function of the table are in logical contraposition, not to the interpretation of the table as a list of Pythagorean triples, but to its interpretation as a trigonometric table. Garald ( talk) 09:10, 6 October 2011 (UTC)
On this note - we should transcribe not just the numbers, but the headings of the columns. They make it clear that these are lengths of sides of triangles; Robson herself makes that they make the extreme position taking by Voils untenable. Garald ( talk) 11:50, 20 October 2011 (UTC)
... and we should point out that the exposition in van der Waerden's Science Awakening is actually very close to what Robson takes to have been the reasoning behind the method used to construct the table. Van der Waerden (a) was fully familiar with Babylonian methods, and thus had a good feel for what would have been natural to a very able scribe; (b) was a mathematician, and thus may not have been inclined to see much of a difference between two interpretations (Neugebauer's and his own) that are after all mathematically equivalent. Garald ( talk) 11:54, 20 October 2011 (UTC)
Robson's work now being over a dozen years old, it would be nice if those who have contributed to this article would consider adding references to more recent scholarship. The only more recent paper I know of is
Britton, John P., Proust, Christine, and Shnider, Steve, Plimpton 322: a review and a different perspective, Arch. Hist. Exact Sci. 65 (2011), no. 5, 519–566.
While it comes down on the "reciprocal pair" side of how the tablet was constructed (with refinements to Robson's argument), it argues against the "school text" interpretation of why it was written. I do not feel sufficiently qualified to be bold, and would thus prefer it if someone else took on the task, however. Michael Kinyon ( talk) 15:12, 26 March 2014 (UTC)
I would strongly support rewriting this page to take this new article into account. At any rate, Robson's article was written so polemically that some of her conclusions got obscured. This is a tablet in which reciprocal pairs are the *method*, and constructing Pythagorean triples is the *problem* (and she herself seems to agree with this, if you read her closely). I tried to go into this in the notes to the Number Theory article. Garald ( talk) 22:29, 27 April 2014 (UTC)
There is a recent article that suggests a different approach to Plimpton 322. It suggests that the Pythagorian triples were selected not constructed. Becuase this requires a higher level of mathematical skill, the originator should be called "Teacher" not "Scribe". The six mistakes in the Student Find-Fix Exercise are noted, explained and corrected. Also the missing left hand edge is reconstructed, giving a new meaning to the tablet. The presentation is DECIMAL but the SEXIGESIMAL is referenced thoughout. The article is at: http://members.localnet.com/~tomo — Preceding unsigned comment added by 336sunny ( talk • contribs) 14:15, 12 December 2016 (UTC)
A very short but very informative article has caught my attention it is http://www.math.sjsu.edu/~alperin/Plimpton322.pdf by ROGER C. ALPERIN. It has led me to write an analysis which I will post on my talk page about how p and q were chosen. — Preceding unsigned comment added by 336sunny ( talk • contribs) 03:30, 25 April 2017 (UTC)
Like Wikipedia itself these are internet publications. I'm sure you realize this by the blue highlighting. But no, they're not chiseled in stone. But web pages are the future, library books are the past. Not much either you or I can do about it.
336sunny ( talk) 22:58, 25 April 2017 (UTC)
The interpretation of Britton et. al. and Friberg's factor reduced core theory (in A Remarkable Collection of Babylonian Mathematical Texts, 2007) should also be mentioned as possible interpretations alongside the Buck/Robson igi-igibi interpretation. — Preceding unsigned comment added by 220.233.5.37 ( talk) 11:53, 11 September 2017 (UTC)
There is an interpretation dated August 24, 2017 here: https://phys.org/news/2017-08-mathematical-mystery-ancient-babylonian-clay.html Perhaps this information can be incorporated? — Preceding unsigned comment added by 2601:500:8500:9221:E9B3:E4D8:940C:6B81 ( talk) 22:37, 24 August 2017 (UTC)
The article is available online at http://www.sciencedirect.com/science/article/pii/S0315086017300691. There is absolutely no need to mention any newspaper source even if, under wiki guidelines, thet are RS.
As a layperson with an interestbin this subject I am veryvsurprised that Mansfield/Wildberger don't get a mention in the article as rhey have been published in a reputable journal. Just because it is the most recent interpretation to be published doesn't mean it supercedes all others and I don't think any intelligent reader would see it as such, if it is presented in appropriate manner. Excluding it smacks of wishing to exclude contrary views. 128.68.56.38 ( talk) 10:35, 8 September 2017 (UTC)
References
This Wikipedia page should mention the Babylonian Exact Sexagesimal Trigonometry table, discovered by Mansfield and Wildberger. See my edits of the main conclusions here. The main differences are the Babylonian exact sexagesimal trigonometry uses exact ratios and square ratios instead of approximation and angles. These are two different approaches for the same problem solving. This research is based on Plimpton 322, not mentioning this peer reviewed research seems odd. The open access study can be read here. This proposal is to add the main finding (Exact Sexagesimal Trigonometry table based on Plimpton 322, and difference of exact ratios and square ratios instead of approximation and angles) into lede space of this article (and mention in article space of related pages), as guide for future inclusion, outlined ( here). prokaryotes ( talk) 19:02, 18 October 2017 (UTC)
— Preceding unsigned comment added by prokaryotes ( talk • contribs)
Vote below with agree or disagree and give an explanation.
From Mansfield comments here it seems the claimed unique contribution is ...- this is precisely what secondary sources are required for in wikipedia. Staszek Lem ( talk) 21:54, 18 October 2017 (UTC)
It is ridiculous to suggest he has to publish more on this topic when there are only so much numbers to calculate." You asked why I thought he was not an expert and I responded with my reasons, but I can not parse your reaction so that it makes any sense to me. Pulling out the "censure card" is a typical gambit when one has run out of rational things to say, as is turning to personal attacks. Just to clear the air, my publications and expertise lie in the areas of geometry and combinatorics although my interests are much wider than that. In particular, I have an interest in the history of mathematics, a course that I have taught many times. None of this, however, has anything to do with the arguments I have been making here, which need to be evaluated on their merits and not my background. -- Bill Cherowitzo ( talk) 17:13, 20 October 2017 (UTC)
Mention of the study and key points (as above), with keeping the main article lede in tact, or alternatively suggest your alternate solution below.
I propose to make it more clear (with sub-section headings) that there are two main interpretations, and that the new study merges both. Hence, the article should read along the lines of, "MW proposed a new theory in 2017, which merges previous interpretations. However, it has been criticized, lacking proof that Babylonians actually used it that way." This is common practise in all Wikipedia entries i came across, unless the source is not reliable sourced. But here we have Science commentary - essentially concluding mathematical robust, but subjective since it lacks proof that Plimpton was used as proposed, this comes from actual experts studying Plimpton 322. The study was published in the authoritative journal Historia Mathematica, otherwise the article is not balanced when it comes to interpreting Plimpton, see WP:NPOV.
new theory in 2017, which merges previous interpretations? It seems many people in this talk page say there is nothing new. Staszek Lem ( talk) 17:48, 25 October 2017 (UTC)
last attempt– you promise? E Eng 00:12, 26 October 2017 (UTC)
MW proposed a new theory in 2017, which merges previous interpretations.–and until there is I will continue to object to its inclusion. The Cowen article is not a particularly high quality source. After stating something about the MW paper that sounds like a press release, he goes on to summarize some statements by three researchers (and does not give credit as to where these statements can be found). Ossendrijver is fairly neutral and states that this is an open issue and lacks any proof that the tables were used in that way. Friberg blasts the idea behind the paper and Proust, putting the paper in its most positive light, says that it is "mathematically robust, but for the time being, highly speculative." This statement that something is "mathematically robust" is very interesting because it has no clear meaning. With tongue-in-cheek I might interpret that as saying that "the mathematics has taken a beating but none-the-less has managed to bounce back." If one were actually praising the paper, that is a funny way to do it. What these three experts do agree on is that there is no actual evidence that supports the MW claim. The only statement that this Cowen article can support is, "In 2017 MW wrote a paper that is criticized for not being based on anything factual." As to the now closed RfC, as anyone will tell you, it is not a matter of votes but rather the strength of the arguments that carries the day. But, if it makes you feel better, note that while I did make some comments, I did not "vote" in the original RfC. I felt that my position was clearly made elsewhere and there was no need to repeat myself. Finally, as to your concern about balance and NPOV, I think that Wikipedia:PROFRINGE is the most relevant aspect of that policy to this discussion. And of course, I agree with the other editors ... enough is enough, it is time to put this aside. -- Bill Cherowitzo ( talk) 21:47, 25 October 2017 (UTC)
See Evelyn Lamb's Scientific American column for some counters to all the hype surrounding the recent paper on Plimpton 322. — David Eppstein ( talk) 23:43, 29 August 2017 (UTC)
But newspapers and Historia Mathematica are most definitely reliable sources and you are refusing to use them! Mansfield and Wildberger may be writing nonsense but under all wikipedia guidelines they have to be mentioned. This page isn't here to report only views which a small number of editors find acceptable. ----
The very fact that it has appeared in Historia Mathematica is criterion for mentioning it. Are you going to wait for someone to criticise it in an RS before mentioning it? find the blog that someone referred to here very useful, thank you. I think if you are going to exclude a newspaper as unreliable you can under circumstances use a blog as reliable. I'm a lay person and this comes across to me as a conspiracy by a group of scholars to exclude a view with which they disagree. That can be done behind closed doors in deciding who gets to speak at a conference or publish in a journal, the beauty of wikipedia is that it has to be done openly on talk pages for all to see. Thank you for the enlightenment. I've seen this elsewhere on wikipedia in other fields and it's probably helpful to know that it exists in the History of Science too. — Preceding unsigned comment added by 128.68.56.38 ( talk) 12:43, 8 September 2017 (UTC)
Life is too short to get into discussion about wiki guidelines with editors with an agenda but I thought I'd look up the guidelines on blogs. Common sense tells me that Lamb's blog would be acceptable and so do wiki guidelines: it is Bill Cherowitzo who doesn't seem to have read them in full. The is written by a professional researcher and hosted by a newspaper.
> Are weblogs reliable sources? In many cases, no. Most private weblogs ("blogs"), especially those hosted by blog-hosting services such as Blogger, are self-published sources; many of them published pseudonymously. There is no fact-checking process and no guarantee of quality of reliability. Information from a privately-owned blog may be usable in an article about that blog or blogger under the self-publication provision of the verifiability policy. Weblog material written by well-known professional researchers writing within their field, or well-known professional journalists, may be acceptable, especially if hosted by a university, newspaper or employer (a typical example is Language Log, which is already cited in several articles, e.g. Snowclone, Drudge Report). Usually, subject experts will publish in sources with greater levels of editorial control such as research journals, which should be preferred over blog entries if such sources are available.<
Mention the article and mention the blog. I imagine that I'll end up inclining towards Lamb position but I think everyone should have the chance to make up their mind. In suppressing this you are suppressing free discussion. — Preceding unsigned comment added by 128.68.56.38 ( talk) 14:28, 8 September 2017 (UTC)
Are you happy to request a third opinion on this, or to seek dispute resolution. I note you are not quoting any guidelines in your latest reasons for not mentioning this here. Maybe there are not going to be any differences in the secondary literature. I can't believe that any editor or administrator who doesn't have a particular interest in the history maths would agree with your attempt to block mention of an article which has been published in a prestigiuous RS journal. 9and50swans ( talk) 20:14, 8 September 2017 (UTC)
If it doesn't say anything new then why did HM carry the article? 128.68.56.38 ( talk) 21:29, 8 September 2017 (UTC)
https://www.nytimes.com/2017/08/29/science/trigonometry-babylonian-tablet.html?mcubz=0
so there is some negative reaction to mention with the article. 9and50swans ( talk) 16:25, 10 September 2017 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
I propose posting this on the relevant notice board for requests for comments. Anyone editor wish to comment on this.
Plimpton 322 Request for Comment
The Babylonionan Tablet known as Plimptom 322 was recently the subject of an article in Historia Mathematica
http://www.sciencedirect.com/science/article/pii/S0315086017300691
which is “A publication of the International Commission on the History of Mathematics of the Division of the History of Science of the International Union of the History and Philosophy of Science.” gaining wide media coverage – try googling Plimpton 322 News. Since them traffic to the wikiedpia article “Plimpton 322’ has soared and remains five times that since before the article was published two weeks ago, as of yesterday 351 hits. However there is not a mention of the article on the site. I think many readers coming to the site will find that strange.
A group of editors are blocking mention of the article. I don’t think that given the appearance of the article in an extremely prestigious journal and the wider media coverage in ‘highbrow’ newspapers, there can be the slightest justification for it. The only reason I can see for this is that the group of editors don’t agree with the conclusions of the article and do not wish Wikipedia readers to know about it. I can hardly imagine a clearer breach of the spirit and letter of what Wikipedia stands for. Whether I or they like the article is neither here nor there, it is out there in the public domain having passed the referees of Historia Mathematica – you can read the names of the editorial board here, https://www.journals.elsevier.com/historia-mathematica/editorial-board and should be reported.
9and50swans ( talk) 20:57, 8 September 2017 (UTC)
A recent article in a prestigious academic journal Historia Mathematica which received wide media coverage has led to a great increase in hits on this site and yet a group of editors, who are clearly hostile towards the article and two of whom refer to the wikipedia article as 'our' article, refuse to allow any mention of this article. This is quite clearly against the aims of wikipedia, to report all mainstream points of view. 9and50swans ( talk) 10:27, 9 September 2017 (UTC)
The fact that it appears in a journal such as Historia Mathematica is sufficient to mention it. It passed their referees. It's been described as plausible by Alexander Jones. What more do you want? If Eleanor Robson has made any comment on it other than a couple of tweets, which appear to me to pretty much ad hominem attacks on Mansfield and Wildberger, I'd love to hear of it. 9and50swans ( talk) 20:30, 11 September 2017 (UTC)
and the fact that it was widely reported in the press: this is easily supported by references-- which references have the statement " it <i.e., this paper> was widely reported in the press" or something similar? Staszek Lem ( talk) 18:41, 20 September 2017 (UTC)
References
Robson endorsed Lamb's article in a tweet. >Aug 30 Hurrah! Very well done @evelynlamb (& h/t @schrisomalis) for writing sense about this subject that I don't have to. #endofsillyseason Evelyn Lamb @evelynjlamb Don't fall for Babylonian trigonometry hype< which may give added justification for using Lamb. Personally I saw little of substance in Lamb, just picking up a couple of insubstantial errors and suggesting M and W had an agenda. There must be many readers who have read about the tablet in the press who come to the page and find nothing about it and are puzzled. Surely if you want them to know it has been criticised it's better to mention it and the negative reactions, then they can go to the sources and try and make up their own minds. 9and50swans — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:29, 14 September 2017 (UTC)
Scientific articles are to be judged by scientific merits- well, first of all that is not our job to perform a second peer-review, we should just summarize the literature consensus (which is pretty much never based on a single article, no matter how outstanding). Also, that only applies if we want to present the article as a source of science, but that is not the only way to get notable enough to mention (we have articles on homeopathy, creationism and the like). Tigraan Click here to contact me 09:11, 21 September 2017 (UTC)
Your argument could have made sense if we were discussing an article about this paper. Here we are discussing whether it contributes something new to the subject.It may be that the paper is not notable enough for a standalone article, yet notable enough to have a due weight mention in that article (or another parent article, but there really is no other candidate). It is in that context that I mentioned pseudoscience, as a poor testimony to the fact that something that is not a solid source scientifically could still be worthy of mention. Had the RfC asked a clear question, the confusion between the two would have been avoided...
Scientific articles are to be judged by scientific merits. Tigraan Click here to contact me 11:21, 22 September 2017 (UTC)
Mansfield and Wildberger (2017) have restated this interpretation in relation to rational trigonometry. [1]
Having studied the material on primary and secondary sources I am not quite sure where the various journal article stands. For example this definition is referenced.
> University of California, Berkeley library defines "secondary source" as "a work that interprets or analyzes an historical event or phenomenon. It is generally at least one step removed from the event". <
By the first sentence all writing about Plimpton 322 is secondary. But in any case we are allowed to use primary sources with care. Even if articles are considered primary sources there is surely a distinction between a self-published article and one which has been refereed, the latter is closer to being a secondary source even if the referees comments are not available for inspection. I am not proposing any analysis of M and W's claims, just to mention them because they have been judged suitable for publication by the referees of Historia Mathematica. The arguments mentioned here may be perfectly suitable for not discussing the claims at any length, but the discussion is whether they should be mentioned at all. Nine-and-fifty swans ( talk) 11:07, 23 September 2017 (UTC)
significant scholarly debate≠ one article contradicting the rest of the literature. Of course there can be no scholarly debate just after the first paper of one side of the debate has been published, even if that is at the front page of Nature. See the related WP:TOOSOON. Tigraan Click here to contact me 09:41, 25 September 2017 (UTC.)
M and W represent the latest contribution to a debate which, by their account, has been going on since 1949, or by the wiki article since at least 2001.
M and W part 5 opening paras >There are two main theories as to how an OB scribe might have generated P322. The original proposal of Neugebauer and Sachs (1945, 40), modified by de Solla Price (1964), and more recently by Proust (2011, 663), emphasizes the role of two generators r and s used to create the Pythagorean triple (2¯(rs¯−sr¯),1,2¯(rs¯+sr¯)), while Bruins' theory (1949, 1957), supported by Robson (2001, 194), claims that a reciprocal pair (x,x¯) was used to create normalized Pythagorean triples as (2‾(x−x¯),sq.rt.(xx¯),2‾(x+x¯)). The relative merits of both points of view, particularly with respect to the errors on the tablet, are well presented by Britton et al. (2011). We propose a modification of these already established theories which blends their respective advantages. Expanding upon the work of Proust (2011, 664), we give an explicit procedure by which the scribe first iterates through the standard table of reciprocals for the values of s, and then finds all possible corresponding values of r. Furthermore, we have a different suggestion for why the procedure terminated. <
Are you suggesting that the latest contribution to any scholarly debate is always off-limits on wikipedia? I see no evidence that this contradicts 'the rest of the literature', in fact it has been criticised elsewhere on this page for adding nothing new. Nine-and-fifty swans ( talk) 10:35, 25 September 2017 (UTC)
Given the article in HM this statement is clearly incorrect. How should it be amended?
Although the tablet was interpreted in the past as a trigonometric table, more recently published work sees this as anachronistic, and gives it a different function.[2] — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:04, 9 September 2017 (UTC)
References
The following Wikipedia contributor has declared a personal or professional connection to the subject of this article. Relevant policies and guidelines may include
conflict of interest and
neutral point of view.
|
The only sources for the view that Robson's interpretation has become normative in the history of maths community, so that alternative views are held only by an insignificant minority appears to be the fact that she won a prize in 2003. That doesn't seem to me to be sufficient reason to imply that trigonometrical interpretations are a thing of the past. 9and50swans ( talk) 05:10, 16 September 2017 (UTC)
The current discussion of the recent article lacks balance.
Daniel.mansfield ( talk) 03:21, 13 September 2017 (UTC) Daniel Mansfield — Daniel.mansfield ( talk • contribs) has made few or no other edits outside this topic.
References
References
We could always take a vote, there may be a few new editors here. Alternatively someone could edit the article and mention M and W and see what happens. Alternatively we could seek dispute resolution but that may take forever. 9and50swans. — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:09, 15 September 2017 (UTC)
It is clear from the preceding discussion that a number of editors regard the article as unbalanced because it does not mention trigonometrical interpretations, such as Britton et al. and Mansfield and Wildberger, so I have added the template. I am not sure how we can resolve this without outside intervention. 9and50swans ( talk) 20:56, 15 September 2017 (UTC)
To put the dispute succinctly, a recent paper on this artefact in a prestigious journal attracted wide publicity. Some editors wish to mention the paper, others do not. At present it is not mentioned. 9and50swans ( talk) 21:04, 15 September 2017 (UTC)
/info/en/?search=Template:Unbalanced
>You may remove this template whenever any one of the following is true:
1 There is consensus on the talkpage or the NPOV Noticeboard that the issue has been resolved. 2 It is not clear what the neutrality issue is, and no satisfactory explanation has been given. 3 In the absence of any discussion, or if the discussion has become dormant.<
9and50swans ( talk) 21:43, 15 September 2017 (UTC)
On further thought I restored the template. If anyone wished to remove it please could they state which of the three enumerated conditions has been met. I can't see how either 1 or 3 is applicable and with regard to 2 the issue is clearly that some editors wish to exclude mention of two articles expressing a particular point of view which have appeared in high-quality academic journals. 9and50swans ( talk) 22:28, 15 September 2017 (UTC)
Why are trigonometric interpretations a thing of the past when we have Britton et al and Mansfield and W since the publication of Robson? 9and50swans ( talk) 05:58, 16 September 2017 (UTC)
'in the past' implies they are not doing it in the present.
This page in a nutshell: Articles must not take sides, but should explain the sides, fairly and without editorial bias. This applies to both what you say and how you say it. All encyclopedic content on Wikipedia must be written from a neutral point of view (NPOV), which means representing fairly, proportionately, and, as far as possible, without editorial bias, all of the significant views that have been published by reliable sourceson a topic. NPOV is a fundamental principle of Wikipedia and of other Wikimedia projects. It is also one of Wikipedia's three core content policies; the other two are "Verifiability" and "No original research". These policies jointly determine the type and quality of material that is acceptable in Wikipedia articles, and, because they work in harmony, they should not be interpreted in isolation from one another. Editors are strongly encouraged to familiarize themselves with all three. This policy is non-negotiable, and the principles upon which it is based cannot be superseded by other policies or guidelines, nor by editor consensus.
This article violates one of the three fundamental pillars of wikipedia by failing to mention Mansfield and Wildberger's recent article in Historia Mathematica. Please not the wording "it...cannot be superseded by other policies or guidelines, nor by editor consensus."
At least two other editors have agreed with me on this.
I may be unable to edit for most or all of the next three days. 9and50swans ( talk) 19:55, 18 September 2017 (UTC)
I am not arguing that M and W should have equal space with Robson but it deserves a mention. 9and50swans ( talk) 22:16, 18 September 2017 (UTC)
I think that the behaviour of certain editors and adminsitrators on this page is a very serious abuse of wikpedia's practices Eeng's remarks are quite inappropriate and he makes no answer on the talk page. I am am pushed further I will seek advice on how I pursue a complaint on this against these individuals. 9and50swans ( talk) 20:13, 18 September 2017 (UTC)
I have placed a notice about this on the Neutral Point of View noticeboard. 9and50swans ( talk) 21:28, 18 September 2017 (UTC)
The fact that I got nowhere in my view reflects badly on wikipedia's administrationis a very common but mislead accusation and belief. Without those policies Wikipedia would become an indiscriminate directory, including original research on every topic and every fringe belief represented as fact. These policies are necessary for Wikipedia to be a respectable encyclopedia. — Paleo Neonate – 21:49, 18 September 2017 (UTC)
No administrator to my knowledge has looked at this, apart from David Eppstein who clearly has an interest. The shortage of adminstrators has been mentioned ion the NYT as a danger to wikipedia. This is not a question of representing a fringe belief as fact simply of mentioning something which has been published in a highly respected academic journal. 9and50swans ( talk) 22:07, 18 September 2017 (UTC)
I note that nobody who has accused me of being tiresome has supported my call for independent people to look at this either for balance or neutrality. If this continues this would be a very good reason for me to call for outside neutral intervention, and I will continue to do this. 9and50swans ( talk) 22:16, 18 September 2017 (UTC)
If there's only one source saying something, it's an overreach to say NPOV mandates that it MUST be included, but that's not the same as
Any "significant view" must be present in multiple Reliable Sources, which is what you said before. A view in only a single source can still be a significant one e.g. if the source was written by an established expert on the topic. E Eng 05:05, 22 September 2017 (UTC)
Who was first to suggest trigonometrical interpretation? If it was Buck (1980), as wikipedia claims, then then phrase "more recently published work sees this as anachronistic, and gives it a different function" is false. Because the described "different function" is an exercise book. However Buck (1980) himself attributes this interpretation to Voils, i.e., this "different function" predates Buck (1980).
Please clarify. Staszek Lem ( talk) 19:10, 20 September 2017 (UTC)
Offtopic wisecrack. Uncollapse to enjoy (or not)
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I came across this. The 'teacher's aid' concept sounds to me a bit like Robson's interpretation. This also appeared in an article Historia Mathematica. Is it worth a mention?
Thus it appears that the reason for the construction of the tables on the Plimpton tablet was not an interest in numbertheoretical questions, but rather the need to find data for a "solvable" mathematical problem. More precisely, it is my belief that the purpose of the author of Plimpton 322 was to write a "teacher's aid" for setting up and solving problems involving right triangles. In fact, a typical Babylonian problem text contains not only the formulation of the problem but also the details of its numerical solution for the given data. Hence the contents of the table on the (intact) Plimpton tablet would have given a teacher the opportunity to set up a large number of solved problems involving right triangles, with full numerical details, as well as to formulate a series of exercises for his students where only the necessary data were given, although the teacher knew that the problem was solvable, and where he could check the numerical details of the students' solutions by using the numbers in the table. For example, if the given problem was to find the diagonal c Nine-and-fifty swans ( talk) 09:25, 5 October 2017 (UTC)
I found 31 refs to Friberg in Robson's 2001 article including
EARLIER PROPONENTS OF THE RECIPROCAL THEORY The theory set out here is not new and I certainly would not want to claim it for myself. It was first proposed by Bruins [1949; 1955] soon after the tablet was published, then reappeared in various guises some 25 years later in three apparently independent studies by Schmidt [1980]; Voils apud Buck [1980]; and Friberg [1981], although none had the supporting linguistic and conceptual evidence cited here but presented it in modernising algebraic form like Neugebauer’s p, q theory. So why has it been largely ignored by the authors of generalist histories of mathematics, and why should it no longer be? Nine-and-fifty swans ( talk) 09:31, 5 October 2017 (UTC)
I don't have time, energy or even understanding to make it fully comprehensive, but it might be expanded to point to a wider range of interpretations. These could be indicated in a list of references at the end. For the reader it may be better to have an article which looks unfinished and has a wider range of references than one which looks finished and has a much narrower range of references. There is clearly a lot more to this than just Robson. Nine-and-fifty swans ( talk) 17:45, 5 October 2017 (UTC)
Everybody who edits the page, or who votes in RFCs should read WP:COI. State here if you have a COI, that is for instance if you publish on trigonometry, or Plimpton, or sexagesimal, etc. Therefore it is also recommended that you strike your votes above, and remove yourself from those discussions. It is perfectly fine to suggest edits here on that page, and I think for general uncontroversial article space edits, including vandalism, or gross errors. However, it is not okay to involve yourself when you try to prevent addition of a colleagues work, you disagree with. Notice that you can get banned or blocked if you do not disclose your COI. prokaryotes ( talk) 13:46, 23 October 2017 (UTC)
As the person who made the RFC I do not remember it being formally closed with any consensus, it fizzled out without anyone much commenting. I have up and have since cited this page elsewhere as an example of how wikipedia is defective. There are probably thousands of other wiki pages equally defective. It's not worth wasting energy on, just educate people about the 'fake' element in wikipedia. forgot password, am in transit, nine-and-fifty Swans — Preceding unsigned comment added by 81.198.102.150 ( talk) 23:00, 23 October 2017 (UTC)
Frivolous COI claims, censorship claims, conspiracy claims, and similar, only help bury your position. The author of the paper, or anyone connected the author or connected to the paper, have a conflict of interest. It is absurd to try to argue the unconnected people have a conflict of interest. Alsee ( talk) 21:14, 24 October 2017 (UTC)
The recent study by Mansfield and Wildberger 2017, with what appears supported by earlier studies by Buck 1980, Joyce 1995, Maor 2002, Chang 2017, Cowen 2017, highlights a robust interpretation of Plimpton 322. Britton 2011 seems to have outlined two groups of interpretations in their study Plimpton 322: a review and a different perspective. MW notes in their study:
"There are two main theories as to how an OB scribe might have generated P322. The original proposal of Neugebauer and Sachs (1945, 40), modified by de Solla Price (1964), and more recently by Proust (2011, 663), emphasizes the role of two generators r and s used to create the Pythagorean triple (2¯(rs¯−sr¯),1,2¯(rs¯+sr¯)), while Bruins' theory (1949, 1957), supported by Robson (2001, 194), claims that a reciprocal pair (x,x¯) was used to create normalized Pythagorean triples as (2‾(x−x¯),sq.rt.(xx¯),2‾(x+x¯)). The relative merits of both points of view, particularly with respect to the errors on the tablet, are well presented by Britton et al. (2011). We propose a modification of these already established theories which blends their respective advantages. Expanding upon the work of Proust (2011, 664), we give an explicit procedure by which the scribe first iterates through the standard table of reciprocals for the values of s, and then finds all possible corresponding values of r."
Thus, to resolve the issues discussed above, the interpretation section should mention the more recent sciences too. Already there is mention in article space of Buck, Joyce, and Neugebauer. It then could also be made more clear that the more established view is per Robson etc. Omitting MW entirely is against Wikipedia's aim to present a balanced view of the subject, and is counterproductive to understand the mathematics of ancient Babylonians, and hampers our efforts to learn and understand the past. prokaryotes ( talk) 16:58, 23 October 2017 (UTC)
I took some reading of the "news" about WM and made two conclusions for myself:
Conclusions:
SUGGESTION:
Stop wasting Wikipedians' time and put a moratorium on beating dead horse for 6 months
.
Staszek Lem (
talk) 22:26, 23 October 2017 (UTC)
This is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Archive 1 | Archive 2 |
It would be nice to add a picture of the tablet to the article, something like those available at [1] or [2]. The tablet itself is of course in the public domain, but the photographs may not be. We could probably add one under fair use, given the historical importance of the topic, but I was wondering if we could argue that the photograph is in the public domain, according to Bridgeman Art Library v. Corel Corp. ? The tablet is a 3D object, but it is photographed as a flat object, with the goal of reproducing it accurately. Any opinion ? Schutz 11:20, 20 April 2006 (UTC)
I'm bumping the importance in the math rating header to mid. This tablet is the basis of claims that the Babylonians knew the Pythagorean theorem prior to the Pythagoreans themselves and prior to the Sulba Sutras; in terms of the history of mathematics it's quite an important document, although its impact on modern mathematics per se is minimal. — David Eppstein 15:49, 20 May 2007 (UTC)
Neil Parker ( talk) 18:08, 6 August 2009 (UTC)
Clarification: Plimpton 322 has been regarded as a basis of claims that the Babylonians had early familiarity with at least a Pythagorean rule. The thrust of Robson (2001) is to knock Plimpton 322 off this particular pedestal. However, perhaps a firmer, and certainly an independent, basis for the claim is provided by Db2-146 = IM67118, a tablet from Eshnunna from about -1775, as discussed, for example, by Høyrup (2002) (Høyrup is one of the principal authors cited in Robson (2001) for naive geometry, but, of course this book postdates that article).
Col 2 | Col 3 | Calculate | Calculate | Col 1 | 1 + Col 1 | Divide: | Angle x |
---|---|---|---|---|---|---|---|
Opp | Hyp | Adj | Angle x | = tan^2(x) | = sec^2(x) | = sin^2(x) | =60*[sin^2(x)+.25] |
119 | 169 | 120 | 44.76 | 0.9834 | 1.9834 | 0.4958 | 44.75 |
3367 | 4825 | 3456 | 44.25 | 0.9492 | 1.9492 | 0.4870 | 44.22 |
4601 | 6649 | 4800 | 43.79 | 0.9188 | 1.9188 | 0.4788 | 43.73 |
12709 | 18541 | 13500 | 43.27 | 0.8862 | 1.8862 | 0.4698 | 43.19 |
65 | 97 | 72 | 42.08 | 0.8150 | 1.8150 | 0.4490 | 41.94 |
319 | 481 | 360 | 41.54 | 0.7852 | 1.7852 | 0.4398 | 41.39 |
2291 | 3541 | 2700 | 40.32 | 0.7200 | 1.7200 | 0.4186 | 40.12 |
799 | 1249 | 960 | 39.77 | 0.6927 | 1.6927 | 0.4092 | 39.55 |
481 | 769 | 600 | 38.72 | 0.6427 | 1.6427 | 0.3912 | 38.47 |
4961 | 8161 | 6480 | 37.44 | 0.5861 | 1.5861 | 0.3695 | 37.17 |
45 | 75 | 60 | 36.87 | 0.5625 | 1.5625 | 0.3600 | 36.60 |
1679 | 2929 | 2400 | 34.98 | 0.4894 | 1.4894 | 0.3286 | 34.72 |
161 | 289 | 240 | 33.86 | 0.4500 | 1.4500 | 0.3104 | 33.62 |
1771 | 3229 | 2700 | 33.26 | 0.4302 | 1.4302 | 0.3008 | 33.05 |
56 | 106 | 90 | 31.89 | 0.3872 | 1.3872 | 0.2791 | 31.75 |
Compare column 4 and column 8 in the above. "Col 1", "Col 2" etc refer to the column numbers in the Plimpton tablet. Neil Parker ( talk) 18:05, 6 August 2009 (UTC)
Is it beyond the bounds of credibility to imagine that the Babylonians may have in some way noted:
and concluded that if '0:15' is added to the squared sine, it's equal to the angle? And indeed a remarkably linear relationship does exist for angle vs sin^2(angle) in the range 30 to 60 degrees.
It's an accepted part of Maths history that the Babylonians divided the circle into 360 equal parts so we need to ask the question how exactly did they achieve that division and how accurate were they? (presumably they would have had a more sophisticated method than merely marking 360 approximately even divisions around a circle circumference). Neil Parker ( talk) 08:18, 2 September 2009 (UTC)
Exchanges with David Eppstein
Plimpton 322 It is difficult to "source" mathematically elementary observations about right triangles and it would be embarrassing to describe a subject which has been worked over for thousands of years as "original research"; it is just mathematics. In contrast, it is natural and proper to source interpretations, as is done in the article, as they are proposed by individuals. If anything, it is surprising that the mathematical reconciliation, being completely trivial, had not already been included in such a "definitive" article. —Preceding unsigned comment added by 130.194.170.146 (talk) 04:47, 11 September 2010 (UTC)
The calculations themselves may be trivial, but by putting those calculations in that context as if to lead to a conclusion about what Plimpton 322 was used for, you are committing original research by synthesis. —David Eppstein (talk) 04:56, 11 September 2010 (UTC)
However, routine calculations are allowed and what is given is entirely routine. You seem to be misreading the text. No comment is made about what Plimpton 322 was used for, although comment is made about how the Pythagorean rule can and was used (that can be sourced, for example, in the writings of Jens Høyrup. Rather, without giving weight to any interpretation, the remarks show how they are related mathematically. It was puzzling how such an elementary observation had been left out of an otherwise "definitive" article. Let me restore the comments in good faith, since otherwise readers who are not so mathematically deft are deprived of pertinent information. Of course, you are free to edit the section so as to give only mathematical trivialities that say absolutely nothing about the use of Plimpton 322. —Preceding unsigned comment added by 130.194.170.146 (talk) 05:10, 11 September 2010 (UTC) I have now qualified the section heading to emphasise that only the mathematics of two contending interpretations is being reconciled (as you might expect to have been done already in a "definitive" article when mathematically speaking the points are so trivial). You are clearly anxious about the making of inferences about how Plimpton 322 was used. Can you say how clarifying the very simple mathematics in the two interpretations has bearing on that? —Preceding unsigned comment added by 130.194.170.146 (talk) 05:25, 11 September 2010 (UTC)
What is your point in adding that passage to the article? It's not just a calculation — if I wrote 1+1=2 at the end of an article on Fibonacci, it would be a true statement of mathematics, but it would not lead anywhere. I am similarly having a difficult time seeing how what you wrote in Plimpton 322 connects to anything in the article, but if it does connect, it is (I assume) in order to make some particular point about the Babylonians' ability to solve quadratic equations or generate Pythagorean triangles. That point, whatever it is that you are trying to make, needs a source. It is not good enough to say that the mathematics in what you wrote is true, and that any conclusion is in the mind of the reader. Either you are adding pointless irrelevant calculation to the end of the article, or you are committing original research by synthesis. Either way, it doesn't belong. —David Eppstein (talk) 05:40, 11 September 2010 (UTC)
I believe that you are a very distinguished computer scientist, so your comment is bewildering. One interpretation of Plimpton 322 is in terms of Pythagorean triples, another is that it is an exercise set for the solution of a certain quadratic. Non-mathematical readers might not notice that the mathematics of these two interpretations is closely related, indeed that you can use the Pythagorean triples to solve just such quadratics, not just the one mentioned. So, the mathematically trivial computation is closely tied to the existing text and designed to assist those readers. You are reading into this a suggestion of what the Babylonians could do, but it is not there nor does it need to be there, although just such issues have been discussed (as I say, for instance, by Jens Høyrup). Moreover, what you are also throwing out, is the very simple observation that certain right triangles, such as the 3-4-5 triangle, have all their sides determined as segments of grid lines in a square grid. So, in fact, you really do not need to know all that much, other than to count. So, I submit that the section is pertinent to the existing text, helpful to readers, but not original research, whether by synthesis or in some other way. If indeed I am right in thinking you are a computer scientist, I should be surprised if you did not want to help non-mathematical readers see how the mathematics of the two interpretations is related. You do agree that the mathematics is related as stated and also that Pythagorean triples can be generated in the square grid without knowledge of the Pythagorean Theorem or number theory? —Preceding unsigned comment added by 130.194.170.146 (talk) 06:03, 11 September 2010 (UTC)
I think this section needs to be removed. There are several reasons I can see:
It is original research by synthesis given that there are no sources given. The reason given: "Just in case the solution algorithm for the quadratic equation might seem divorced from Pythagorean triples" is not valid. There are already connections to quadratic equations given right above it. Contrary to what is claimed, this will not help any non-mathematical reader in any way shape or form. My experience developing and teaching liberal arts mathematics courses tells me that even the average freshman at a university (so reasonably well-educated) is going to take one glance at the writing and ignore it. The reference to folding squares/triangles is questionable given that they wrote on clay tablets.
I agree with Dave Eppstein, this needs to be removed. --AnnekeBart (talk) 14:11, 11 September 2010 (UTC)
Clearly original research by synthesis resonates in the Wikipedia community. But surely it is to stop synthesis that is tendentious. AnnekeBart helps out by supplying an instance: yes, indeed, quadratic equations are mentioned immediately beforehand, but the elementary calculations connecting them with Pythagorean triples are not. So, that is why the material is inserted, "just in case". As it happens, one of the leading authors in the history of mathematics in the USA has just written in privately to say the reasoning is excellent and he regrets having missed it, simple though it is. Why was it not already in a "definitive" article? The reference to folding right triangles side to side is to help visualise the significance of the half angles. But writing on clay tablets has nothing to do with it - yet another synthesis gone wrong. I agree that, if that is the level of the readership, then very little, not just the inserted section, is going to register - eyes are likely to glaze quickly encountering the elaborate account of the vs in the algorithm for solving the quadratic. Against that, my guess is that college freshmen, like the leading historian, might rather say, "Pyth to solve quadratics. That's cute".
So, let me try to say yet again what this section is intended to do. The Neugebauer thesis draws on Pythagorean triples. The Robson thesis draws on solutions to quadratic equations. Already here then in the article are suggestions of Babylonian skills. But what sort of mathematical threshold do these skills represent? The talk of number theory for the triples might seem to make it less plausible even if the triples themselves are fairly concrete. But, no, this need not be the case, because right triangles with commensurable sides can be identified in playing on the square grid. Again, the talk of solutions of quadratics, with numerous equations for the algorithm, might remind readers of why they were never any good at mathematics and, indeed, where they lost the plot. But, no, this too need not be a challenge, because a computational trick with Pythagorean triples, little more than difference of two squares, brings out the solution. So, the section supports the existing content of the article by indicating the skills threshold that might be required for one or other of these two interpretations. Moreover, it reveals that they are not exactly exclusive. However, it does not come with any tendentious suggestion as to the use of Plimpton 322 or the skills achieved by the Babylonians. Why deprive readers of this support?
Mathematics as elementary as this cannot be said to be original research. Just imagine trying to publish this in order to generate a source. But I suspect that even if there were a published source to quote at this juncture, that does not seem to be really what is troubling David Eppstein or AnnekeBart. I am afraid that they come over as strangely hostile to the idea of noting for readers how the theses of Neugebauer and Robson are linked, so not chalk and cheese, as might appear from the article. To that extent, it is the article that is tendentious. I agree that the section is in the nature of a footnote or an aside. I should hope that Wikipedia was sufficiently versatile to handle this. But Wikipedia does already have options for leaving material in, while cautioning that original research might be present.
On the other hand, there certainly are cognate sources. There is a large body of problems in old Babylonian mathematics. For instance, BM13901 looks at the problem of two squares for which the sum of areas is known along with either the sum or the difference of the sides, giving the same haunting, suggestive mix of the Pythagorean rule and quadratic equations. One researcher who has written extensively about this material and who is widely quoted is Jens Høyrup. I refrained from putting any of this sourced comparative material in because it might upset the focus of the article on Plimpton 322, although it might be helpful to put Plimpton 322 back in a context from which it has become somewhat detached by being such a centre of attention. In that wider context, the comingling of the Pythagorean rule and quadratics is familiar, at least in our latter day understanding of the subject.
As I say, I was startled and amazed not to find the inserted section already present in a "definitive" article, and now I am bewildered that there is this insistence that supportive information of a non-tendentious nature be deleted. —Preceding unsigned comment added by 130.194.170.146 (talk) 21:40, 11 September 2010 (UTC)
If the section is badly written, why not say that at the start? Unhelpful to any reader? You seem to be changing your tune the more your objections are answered.
Here, in contrast, is the message from the author of one of the leading histories of mathematics published in the USA: Your reasoning here is excellent. I feel I ought to have noticed this connection before, but somehow I missed it. Thus, it appears that even if Plimpton 322 is about problems in algebra or Diophantine equations specifically, the connection with Pythagorean triples is quite immediate. And, of course, the argument that shows how to generate all primitive Pythagorean triples in the form (m^2 - n^2)^2 + (2mn)^2 = (m^2 + n^2)^2 works off the same idea of factoring the difference of two squares.
Are you not rather undercutting the spirit of Wikipedia here? —Preceding unsigned comment added by 130.194.170.146 (talk) 00:04, 12 September 2010 (UTC)
Reviewing the discussion, and acknowledging the proper place of sources in Wikipedia, it occurs to me that it might be worth reminding ourselves of the abstract for one of the key sources for the Wikipedia article, Robson's contribution to Historia Mathematica in 2001. In view of Robson's final sentence, maybe I was wrong not to have included mention of some of those other texts, such as BM13901: Ancient mathematical texts and artefacts, if we are to understand them fully, must be viewed in the light of their mathematico-historical context, and not treated as artificial, self-contained creations in the style of detective stories. I take as a dramatic case study the famous cuneiform tablet Plimpton 322. I show that the popular view of it as some sort of trigonometric table cannot be correct, given what is now known of the concept of angle in the Old Babylonian period. Neither is the equally widespread theory of generating functions likely to be correct. I provide supporting evidence in a strong theoretical framework for an alternative interpretation, first published half a century ago in a different guise. I recast it using regular reciprocal pairs, Høyrup’s analysis of contemporaneous “na¨ıve geometry,” and a new reading of the table’s headings. In contextualising Plimpton 322 (and perhaps thereby knocking it off its pedestal), I argue that cuneiform culture produced many dozens, if not hundreds, of other mathematical texts which are equally worthy of the modern mathematical community’s attention
130.194.170.146 ( talk · contribs) has added the following to my talk page, coppied here to keep the discussion in one place:
The spirit of wikipedia holds Reliable sources as one of its core principles, this means that every item in wikipedia can be traced back to a verifiable source so people can check the accuracy. Further original research consisting of unsourced results is prohibited. Your addition falls foul of these two principles.-- Salix ( talk): 06:30, 12 September 2010 (UTC) Further, you edits are asserting that the Babylonian knew of this connection between Pythagorean triples and quadratic equations and used a technique based around grids to do this. Yet there is no evidence for such. If we compare your addition to the work of Robinson who has based her theory on extensive research of the other writings of the Babylonian we see two very different level of scholarship. Maintaining high levels of scholarship is the reason behind the policies on original research.
You have also breached WP:3RR which prevents editi waring on pages. Because of that I've protected the main article against edits for three days. -- Salix ( talk): 06:53, 12 September 2010 (UTC)
Richard, Might I just possibly correct you in some places there, apart from the obvious lapses in attention, such as "Robinson" for "Robson". There was no assertion in the excised section that the Babylonians had any particular skills, and indeed when I became aware through exchanges with David Eppstein in which he shifted his ground, I redrafted the text to make that absolutely specific so there could be no doubt. Rather, both the theses of Neugebauer and of Robson presume that the Babylonians had certain skills. All I was doing was pointing to the mathematical level of these skills and a link between them. It just so happens that certain right triangles do have all their sides determined as integral grid-line segments, and they turn out to be the Pythagorean triangles. So, if you were playing on the grid, you might notice that, without having to know the Pythagorean rule or number theory. In a sense, you have them for free. So, the simple point here is that the mathematical level might not be very high, not as high as might be supposed.
Just a comment on mathematical level; nothing about the Babylonians, you understand. It is just a property of right triangles that depends on tangents of half-angles. It is true that Wikipedia does not have that property on in its articles, such as Right_Triangle, so perhaps the way to build the scaffolding of verification and sources is to edit it in.
Again you are completely mistaken about any assertion that the Babylonians knew a link between Pythagorean triples and quadratic equations. I made no such comment. Instead there was a simple mathematical observation that the age-old trick of completing the square does unlock a link of this sort for those who know it. It would seem from the writings of Jens Hoeyrup, which Robson draws on extensively, that this trick, and so this comingling, might not actually have been unknown to some of the Babylonians. But what I wrote was not in any way in competition with Robson's research, so your comparison is otiose as well as gratuitous, I regret to say. Rather the leading historian in the USA has the right reading: completely granting Robson's thesis, nevertheless the connection with Pythagorean triples is immediate. But notice significantly that the leading historian says he had missed this himself, even while feeling he should have spotted it. That is why I did not say, and would never say, the Babylonians or anyone else knew this or that: even the obvious can be hidden in plain sight.
Now, you have exposed yourself brilliantly as having totally misread what was written, even in the face of an explicit disclaimer. But it is some consolation that you are so concerned to maintain high levels of scholarship. Perhaps you might make a start yourself by reading more carefully, instead of jumping to unwarranted conclusions.
You are, in effect making totally false accusations about me in public on this page. I have never written anything of the sort you attribute to me.
I've added references to current exhibit at NYU and NY Times review of same. This article needs work to satisfy the lay public's newly aroused curiosities. This article need not be written in academic style -- this is a subject requiring little more than a few reminders of high school math and elementary number theory and one that if well written could easily engage high school students.
I've also linked to specific pages of Neugebauer & Sachs for those who want to read the original 1945 source. Will do same for his Exact Sciences in Antiquity, also avail. on Google Books, at least in relevant parts of ch. 2. A couple of External links added for inspiration re: clarity is certainly possible.
Lead needs serious work:
The most renowned of all mathematical cuneiform tablets since it was published in 1945, Plimpton 322 reveals that the Babylonians discovered a method of finding Pythagorean triples, that is, sets of three whole numbers such that the square of one of them is the sum of the squares of the other two. By Pythagoras' Theorem, a triangle whose three sides are proportional to a Pythagorean triple is a right-angled triangle. Right-angled triangles with sides proportional to the simplest Pythagorean triples turn up frequently in Babylonian problem texts; but if this tablet had not come to light, we would have had no reason to suspect that a general method capable of generating an unlimited number of distinct Pythagorean triples was known a millennium and a half before Euclid.
Plimpton 322 has excited much debate centering on two questions. First, what was the method by which the numbers in the table were calculated? And secondly, what were the purpose and the intellectual context of the tablet? At present there is no agreement among scholars about whether this was a document connected with scribal education, like the majority of Old Babylonian mathematical tablets, or part of a research project.
http://www.nyu.edu/isaw/exhibitions/before-pythagoras/items/plimpton-322/
Plimpton 322 is known throughout the world to those interested in the history of mathematics as a result of the interest that Otto Neugebauer, chair of Brown University's History of Mathematics Department, took in the tablet. In the early 1940s, he and his assistant Abraham Sachs interpreted it as containing what is known in mathematics as Pythagorean triples, integer solutions of the equation a2 + b2 equals c2, a thousand years before the age of Pythagoras.
Recently, Dr. Eleanor Robson, an authority on Mesopotamian mathematics at the University of Cambridge, has made the case for a more mundane solution, arguing that the tablet was created as a teacher's aid, designed for generating problems involving right triangles and reciprocal pairs. Mr. Plimpton, who collected our tools of learning on a broad scale, would have been delighted with this interpretation, showing the work of an excellent teacher, not a lone genius a thousand years ahead of his time.
http://www.columbia.edu/cu/lweb/eresources/exhibitions/treasures/html/158.html
Given the current interest in this artifact, can't we do better for the lay public? If no objections, I'll revise the lead to more closely match the professionally conceived summaries cited above.
I respectfully challenge the more mathematically qualified to split the interpretation section into two or three manageable pieces and to distribute citations to varied sources more equitably. -- Paulscrawl ( talk) 22:27, 28 November 2010 (UTC)
Robson's main article on the subject is written very polemically, yet buried in it is a conclusion that is much less at odds with the traditional interpretation than one would expect from the way the argument is framed:
[...] the question “how was the tablet calculated?” does not have to have the same answer as the question “what problems does the tablet set?” The first can be answered most satisfactorily by reciprocal pairs, as first suggested half a century ago, and the second by some sort of right-triangle problems.
(Robson, "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322", Historia Math. 28 (3), p. 202).
By the way, Robson takes Voils to task for ignoring the table headings (which make it obvious that the scribe saw the relation to what is now called Pythagoras's theorem, or something very close thereto). Robson's main real contribution seems to have been to make a case for how the table was most likely derived: Babylonian algebra does not equal our high school algebra, even when their methods are mathematically equivalent from our perspective. Van der Waerden also posited what amounts to the derivation Robson believes to have been more likely, but did not emphasise its difference from the form chosen by Neugebauer and others.
I am touching on these issues very briefly at User:Garald/Number_theory, which is intended to become a replacement to the main Number Theory page (once it's finished); we should probably go into greater length about this here. Garald ( talk) 14:13, 8 December 2010 (UTC)
From the article heading:
"Although the table has been interpreted by leading mathematicians as a listing of Pythagorean triples, more recently published theories give it a different function.[2]"
This isn't really an "although". The list is (from our perspective) a listing of Pythagorean triples (that is, integers a, b, c such that ). Moreover, the headings (as Robson herself says) suggests that these were indeed thought of as numbers corresponding to lengths of a right triangle. This says nothing by itself about the *function*. Robson's statements about the function of the table are in logical contraposition, not to the interpretation of the table as a list of Pythagorean triples, but to its interpretation as a trigonometric table. Garald ( talk) 09:10, 6 October 2011 (UTC)
On this note - we should transcribe not just the numbers, but the headings of the columns. They make it clear that these are lengths of sides of triangles; Robson herself makes that they make the extreme position taking by Voils untenable. Garald ( talk) 11:50, 20 October 2011 (UTC)
... and we should point out that the exposition in van der Waerden's Science Awakening is actually very close to what Robson takes to have been the reasoning behind the method used to construct the table. Van der Waerden (a) was fully familiar with Babylonian methods, and thus had a good feel for what would have been natural to a very able scribe; (b) was a mathematician, and thus may not have been inclined to see much of a difference between two interpretations (Neugebauer's and his own) that are after all mathematically equivalent. Garald ( talk) 11:54, 20 October 2011 (UTC)
Robson's work now being over a dozen years old, it would be nice if those who have contributed to this article would consider adding references to more recent scholarship. The only more recent paper I know of is
Britton, John P., Proust, Christine, and Shnider, Steve, Plimpton 322: a review and a different perspective, Arch. Hist. Exact Sci. 65 (2011), no. 5, 519–566.
While it comes down on the "reciprocal pair" side of how the tablet was constructed (with refinements to Robson's argument), it argues against the "school text" interpretation of why it was written. I do not feel sufficiently qualified to be bold, and would thus prefer it if someone else took on the task, however. Michael Kinyon ( talk) 15:12, 26 March 2014 (UTC)
I would strongly support rewriting this page to take this new article into account. At any rate, Robson's article was written so polemically that some of her conclusions got obscured. This is a tablet in which reciprocal pairs are the *method*, and constructing Pythagorean triples is the *problem* (and she herself seems to agree with this, if you read her closely). I tried to go into this in the notes to the Number Theory article. Garald ( talk) 22:29, 27 April 2014 (UTC)
There is a recent article that suggests a different approach to Plimpton 322. It suggests that the Pythagorian triples were selected not constructed. Becuase this requires a higher level of mathematical skill, the originator should be called "Teacher" not "Scribe". The six mistakes in the Student Find-Fix Exercise are noted, explained and corrected. Also the missing left hand edge is reconstructed, giving a new meaning to the tablet. The presentation is DECIMAL but the SEXIGESIMAL is referenced thoughout. The article is at: http://members.localnet.com/~tomo — Preceding unsigned comment added by 336sunny ( talk • contribs) 14:15, 12 December 2016 (UTC)
A very short but very informative article has caught my attention it is http://www.math.sjsu.edu/~alperin/Plimpton322.pdf by ROGER C. ALPERIN. It has led me to write an analysis which I will post on my talk page about how p and q were chosen. — Preceding unsigned comment added by 336sunny ( talk • contribs) 03:30, 25 April 2017 (UTC)
Like Wikipedia itself these are internet publications. I'm sure you realize this by the blue highlighting. But no, they're not chiseled in stone. But web pages are the future, library books are the past. Not much either you or I can do about it.
336sunny ( talk) 22:58, 25 April 2017 (UTC)
The interpretation of Britton et. al. and Friberg's factor reduced core theory (in A Remarkable Collection of Babylonian Mathematical Texts, 2007) should also be mentioned as possible interpretations alongside the Buck/Robson igi-igibi interpretation. — Preceding unsigned comment added by 220.233.5.37 ( talk) 11:53, 11 September 2017 (UTC)
There is an interpretation dated August 24, 2017 here: https://phys.org/news/2017-08-mathematical-mystery-ancient-babylonian-clay.html Perhaps this information can be incorporated? — Preceding unsigned comment added by 2601:500:8500:9221:E9B3:E4D8:940C:6B81 ( talk) 22:37, 24 August 2017 (UTC)
The article is available online at http://www.sciencedirect.com/science/article/pii/S0315086017300691. There is absolutely no need to mention any newspaper source even if, under wiki guidelines, thet are RS.
As a layperson with an interestbin this subject I am veryvsurprised that Mansfield/Wildberger don't get a mention in the article as rhey have been published in a reputable journal. Just because it is the most recent interpretation to be published doesn't mean it supercedes all others and I don't think any intelligent reader would see it as such, if it is presented in appropriate manner. Excluding it smacks of wishing to exclude contrary views. 128.68.56.38 ( talk) 10:35, 8 September 2017 (UTC)
References
This Wikipedia page should mention the Babylonian Exact Sexagesimal Trigonometry table, discovered by Mansfield and Wildberger. See my edits of the main conclusions here. The main differences are the Babylonian exact sexagesimal trigonometry uses exact ratios and square ratios instead of approximation and angles. These are two different approaches for the same problem solving. This research is based on Plimpton 322, not mentioning this peer reviewed research seems odd. The open access study can be read here. This proposal is to add the main finding (Exact Sexagesimal Trigonometry table based on Plimpton 322, and difference of exact ratios and square ratios instead of approximation and angles) into lede space of this article (and mention in article space of related pages), as guide for future inclusion, outlined ( here). prokaryotes ( talk) 19:02, 18 October 2017 (UTC)
— Preceding unsigned comment added by prokaryotes ( talk • contribs)
Vote below with agree or disagree and give an explanation.
From Mansfield comments here it seems the claimed unique contribution is ...- this is precisely what secondary sources are required for in wikipedia. Staszek Lem ( talk) 21:54, 18 October 2017 (UTC)
It is ridiculous to suggest he has to publish more on this topic when there are only so much numbers to calculate." You asked why I thought he was not an expert and I responded with my reasons, but I can not parse your reaction so that it makes any sense to me. Pulling out the "censure card" is a typical gambit when one has run out of rational things to say, as is turning to personal attacks. Just to clear the air, my publications and expertise lie in the areas of geometry and combinatorics although my interests are much wider than that. In particular, I have an interest in the history of mathematics, a course that I have taught many times. None of this, however, has anything to do with the arguments I have been making here, which need to be evaluated on their merits and not my background. -- Bill Cherowitzo ( talk) 17:13, 20 October 2017 (UTC)
Mention of the study and key points (as above), with keeping the main article lede in tact, or alternatively suggest your alternate solution below.
I propose to make it more clear (with sub-section headings) that there are two main interpretations, and that the new study merges both. Hence, the article should read along the lines of, "MW proposed a new theory in 2017, which merges previous interpretations. However, it has been criticized, lacking proof that Babylonians actually used it that way." This is common practise in all Wikipedia entries i came across, unless the source is not reliable sourced. But here we have Science commentary - essentially concluding mathematical robust, but subjective since it lacks proof that Plimpton was used as proposed, this comes from actual experts studying Plimpton 322. The study was published in the authoritative journal Historia Mathematica, otherwise the article is not balanced when it comes to interpreting Plimpton, see WP:NPOV.
new theory in 2017, which merges previous interpretations? It seems many people in this talk page say there is nothing new. Staszek Lem ( talk) 17:48, 25 October 2017 (UTC)
last attempt– you promise? E Eng 00:12, 26 October 2017 (UTC)
MW proposed a new theory in 2017, which merges previous interpretations.–and until there is I will continue to object to its inclusion. The Cowen article is not a particularly high quality source. After stating something about the MW paper that sounds like a press release, he goes on to summarize some statements by three researchers (and does not give credit as to where these statements can be found). Ossendrijver is fairly neutral and states that this is an open issue and lacks any proof that the tables were used in that way. Friberg blasts the idea behind the paper and Proust, putting the paper in its most positive light, says that it is "mathematically robust, but for the time being, highly speculative." This statement that something is "mathematically robust" is very interesting because it has no clear meaning. With tongue-in-cheek I might interpret that as saying that "the mathematics has taken a beating but none-the-less has managed to bounce back." If one were actually praising the paper, that is a funny way to do it. What these three experts do agree on is that there is no actual evidence that supports the MW claim. The only statement that this Cowen article can support is, "In 2017 MW wrote a paper that is criticized for not being based on anything factual." As to the now closed RfC, as anyone will tell you, it is not a matter of votes but rather the strength of the arguments that carries the day. But, if it makes you feel better, note that while I did make some comments, I did not "vote" in the original RfC. I felt that my position was clearly made elsewhere and there was no need to repeat myself. Finally, as to your concern about balance and NPOV, I think that Wikipedia:PROFRINGE is the most relevant aspect of that policy to this discussion. And of course, I agree with the other editors ... enough is enough, it is time to put this aside. -- Bill Cherowitzo ( talk) 21:47, 25 October 2017 (UTC)
See Evelyn Lamb's Scientific American column for some counters to all the hype surrounding the recent paper on Plimpton 322. — David Eppstein ( talk) 23:43, 29 August 2017 (UTC)
But newspapers and Historia Mathematica are most definitely reliable sources and you are refusing to use them! Mansfield and Wildberger may be writing nonsense but under all wikipedia guidelines they have to be mentioned. This page isn't here to report only views which a small number of editors find acceptable. ----
The very fact that it has appeared in Historia Mathematica is criterion for mentioning it. Are you going to wait for someone to criticise it in an RS before mentioning it? find the blog that someone referred to here very useful, thank you. I think if you are going to exclude a newspaper as unreliable you can under circumstances use a blog as reliable. I'm a lay person and this comes across to me as a conspiracy by a group of scholars to exclude a view with which they disagree. That can be done behind closed doors in deciding who gets to speak at a conference or publish in a journal, the beauty of wikipedia is that it has to be done openly on talk pages for all to see. Thank you for the enlightenment. I've seen this elsewhere on wikipedia in other fields and it's probably helpful to know that it exists in the History of Science too. — Preceding unsigned comment added by 128.68.56.38 ( talk) 12:43, 8 September 2017 (UTC)
Life is too short to get into discussion about wiki guidelines with editors with an agenda but I thought I'd look up the guidelines on blogs. Common sense tells me that Lamb's blog would be acceptable and so do wiki guidelines: it is Bill Cherowitzo who doesn't seem to have read them in full. The is written by a professional researcher and hosted by a newspaper.
> Are weblogs reliable sources? In many cases, no. Most private weblogs ("blogs"), especially those hosted by blog-hosting services such as Blogger, are self-published sources; many of them published pseudonymously. There is no fact-checking process and no guarantee of quality of reliability. Information from a privately-owned blog may be usable in an article about that blog or blogger under the self-publication provision of the verifiability policy. Weblog material written by well-known professional researchers writing within their field, or well-known professional journalists, may be acceptable, especially if hosted by a university, newspaper or employer (a typical example is Language Log, which is already cited in several articles, e.g. Snowclone, Drudge Report). Usually, subject experts will publish in sources with greater levels of editorial control such as research journals, which should be preferred over blog entries if such sources are available.<
Mention the article and mention the blog. I imagine that I'll end up inclining towards Lamb position but I think everyone should have the chance to make up their mind. In suppressing this you are suppressing free discussion. — Preceding unsigned comment added by 128.68.56.38 ( talk) 14:28, 8 September 2017 (UTC)
Are you happy to request a third opinion on this, or to seek dispute resolution. I note you are not quoting any guidelines in your latest reasons for not mentioning this here. Maybe there are not going to be any differences in the secondary literature. I can't believe that any editor or administrator who doesn't have a particular interest in the history maths would agree with your attempt to block mention of an article which has been published in a prestigiuous RS journal. 9and50swans ( talk) 20:14, 8 September 2017 (UTC)
If it doesn't say anything new then why did HM carry the article? 128.68.56.38 ( talk) 21:29, 8 September 2017 (UTC)
https://www.nytimes.com/2017/08/29/science/trigonometry-babylonian-tablet.html?mcubz=0
so there is some negative reaction to mention with the article. 9and50swans ( talk) 16:25, 10 September 2017 (UTC)
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
I propose posting this on the relevant notice board for requests for comments. Anyone editor wish to comment on this.
Plimpton 322 Request for Comment
The Babylonionan Tablet known as Plimptom 322 was recently the subject of an article in Historia Mathematica
http://www.sciencedirect.com/science/article/pii/S0315086017300691
which is “A publication of the International Commission on the History of Mathematics of the Division of the History of Science of the International Union of the History and Philosophy of Science.” gaining wide media coverage – try googling Plimpton 322 News. Since them traffic to the wikiedpia article “Plimpton 322’ has soared and remains five times that since before the article was published two weeks ago, as of yesterday 351 hits. However there is not a mention of the article on the site. I think many readers coming to the site will find that strange.
A group of editors are blocking mention of the article. I don’t think that given the appearance of the article in an extremely prestigious journal and the wider media coverage in ‘highbrow’ newspapers, there can be the slightest justification for it. The only reason I can see for this is that the group of editors don’t agree with the conclusions of the article and do not wish Wikipedia readers to know about it. I can hardly imagine a clearer breach of the spirit and letter of what Wikipedia stands for. Whether I or they like the article is neither here nor there, it is out there in the public domain having passed the referees of Historia Mathematica – you can read the names of the editorial board here, https://www.journals.elsevier.com/historia-mathematica/editorial-board and should be reported.
9and50swans ( talk) 20:57, 8 September 2017 (UTC)
A recent article in a prestigious academic journal Historia Mathematica which received wide media coverage has led to a great increase in hits on this site and yet a group of editors, who are clearly hostile towards the article and two of whom refer to the wikipedia article as 'our' article, refuse to allow any mention of this article. This is quite clearly against the aims of wikipedia, to report all mainstream points of view. 9and50swans ( talk) 10:27, 9 September 2017 (UTC)
The fact that it appears in a journal such as Historia Mathematica is sufficient to mention it. It passed their referees. It's been described as plausible by Alexander Jones. What more do you want? If Eleanor Robson has made any comment on it other than a couple of tweets, which appear to me to pretty much ad hominem attacks on Mansfield and Wildberger, I'd love to hear of it. 9and50swans ( talk) 20:30, 11 September 2017 (UTC)
and the fact that it was widely reported in the press: this is easily supported by references-- which references have the statement " it <i.e., this paper> was widely reported in the press" or something similar? Staszek Lem ( talk) 18:41, 20 September 2017 (UTC)
References
Robson endorsed Lamb's article in a tweet. >Aug 30 Hurrah! Very well done @evelynlamb (& h/t @schrisomalis) for writing sense about this subject that I don't have to. #endofsillyseason Evelyn Lamb @evelynjlamb Don't fall for Babylonian trigonometry hype< which may give added justification for using Lamb. Personally I saw little of substance in Lamb, just picking up a couple of insubstantial errors and suggesting M and W had an agenda. There must be many readers who have read about the tablet in the press who come to the page and find nothing about it and are puzzled. Surely if you want them to know it has been criticised it's better to mention it and the negative reactions, then they can go to the sources and try and make up their own minds. 9and50swans — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:29, 14 September 2017 (UTC)
Scientific articles are to be judged by scientific merits- well, first of all that is not our job to perform a second peer-review, we should just summarize the literature consensus (which is pretty much never based on a single article, no matter how outstanding). Also, that only applies if we want to present the article as a source of science, but that is not the only way to get notable enough to mention (we have articles on homeopathy, creationism and the like). Tigraan Click here to contact me 09:11, 21 September 2017 (UTC)
Your argument could have made sense if we were discussing an article about this paper. Here we are discussing whether it contributes something new to the subject.It may be that the paper is not notable enough for a standalone article, yet notable enough to have a due weight mention in that article (or another parent article, but there really is no other candidate). It is in that context that I mentioned pseudoscience, as a poor testimony to the fact that something that is not a solid source scientifically could still be worthy of mention. Had the RfC asked a clear question, the confusion between the two would have been avoided...
Scientific articles are to be judged by scientific merits. Tigraan Click here to contact me 11:21, 22 September 2017 (UTC)
Mansfield and Wildberger (2017) have restated this interpretation in relation to rational trigonometry. [1]
Having studied the material on primary and secondary sources I am not quite sure where the various journal article stands. For example this definition is referenced.
> University of California, Berkeley library defines "secondary source" as "a work that interprets or analyzes an historical event or phenomenon. It is generally at least one step removed from the event". <
By the first sentence all writing about Plimpton 322 is secondary. But in any case we are allowed to use primary sources with care. Even if articles are considered primary sources there is surely a distinction between a self-published article and one which has been refereed, the latter is closer to being a secondary source even if the referees comments are not available for inspection. I am not proposing any analysis of M and W's claims, just to mention them because they have been judged suitable for publication by the referees of Historia Mathematica. The arguments mentioned here may be perfectly suitable for not discussing the claims at any length, but the discussion is whether they should be mentioned at all. Nine-and-fifty swans ( talk) 11:07, 23 September 2017 (UTC)
significant scholarly debate≠ one article contradicting the rest of the literature. Of course there can be no scholarly debate just after the first paper of one side of the debate has been published, even if that is at the front page of Nature. See the related WP:TOOSOON. Tigraan Click here to contact me 09:41, 25 September 2017 (UTC.)
M and W represent the latest contribution to a debate which, by their account, has been going on since 1949, or by the wiki article since at least 2001.
M and W part 5 opening paras >There are two main theories as to how an OB scribe might have generated P322. The original proposal of Neugebauer and Sachs (1945, 40), modified by de Solla Price (1964), and more recently by Proust (2011, 663), emphasizes the role of two generators r and s used to create the Pythagorean triple (2¯(rs¯−sr¯),1,2¯(rs¯+sr¯)), while Bruins' theory (1949, 1957), supported by Robson (2001, 194), claims that a reciprocal pair (x,x¯) was used to create normalized Pythagorean triples as (2‾(x−x¯),sq.rt.(xx¯),2‾(x+x¯)). The relative merits of both points of view, particularly with respect to the errors on the tablet, are well presented by Britton et al. (2011). We propose a modification of these already established theories which blends their respective advantages. Expanding upon the work of Proust (2011, 664), we give an explicit procedure by which the scribe first iterates through the standard table of reciprocals for the values of s, and then finds all possible corresponding values of r. Furthermore, we have a different suggestion for why the procedure terminated. <
Are you suggesting that the latest contribution to any scholarly debate is always off-limits on wikipedia? I see no evidence that this contradicts 'the rest of the literature', in fact it has been criticised elsewhere on this page for adding nothing new. Nine-and-fifty swans ( talk) 10:35, 25 September 2017 (UTC)
Given the article in HM this statement is clearly incorrect. How should it be amended?
Although the tablet was interpreted in the past as a trigonometric table, more recently published work sees this as anachronistic, and gives it a different function.[2] — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:04, 9 September 2017 (UTC)
References
The following Wikipedia contributor has declared a personal or professional connection to the subject of this article. Relevant policies and guidelines may include
conflict of interest and
neutral point of view.
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The only sources for the view that Robson's interpretation has become normative in the history of maths community, so that alternative views are held only by an insignificant minority appears to be the fact that she won a prize in 2003. That doesn't seem to me to be sufficient reason to imply that trigonometrical interpretations are a thing of the past. 9and50swans ( talk) 05:10, 16 September 2017 (UTC)
The current discussion of the recent article lacks balance.
Daniel.mansfield ( talk) 03:21, 13 September 2017 (UTC) Daniel Mansfield — Daniel.mansfield ( talk • contribs) has made few or no other edits outside this topic.
References
References
We could always take a vote, there may be a few new editors here. Alternatively someone could edit the article and mention M and W and see what happens. Alternatively we could seek dispute resolution but that may take forever. 9and50swans. — Preceding unsigned comment added by 128.68.56.38 ( talk) 08:09, 15 September 2017 (UTC)
It is clear from the preceding discussion that a number of editors regard the article as unbalanced because it does not mention trigonometrical interpretations, such as Britton et al. and Mansfield and Wildberger, so I have added the template. I am not sure how we can resolve this without outside intervention. 9and50swans ( talk) 20:56, 15 September 2017 (UTC)
To put the dispute succinctly, a recent paper on this artefact in a prestigious journal attracted wide publicity. Some editors wish to mention the paper, others do not. At present it is not mentioned. 9and50swans ( talk) 21:04, 15 September 2017 (UTC)
/info/en/?search=Template:Unbalanced
>You may remove this template whenever any one of the following is true:
1 There is consensus on the talkpage or the NPOV Noticeboard that the issue has been resolved. 2 It is not clear what the neutrality issue is, and no satisfactory explanation has been given. 3 In the absence of any discussion, or if the discussion has become dormant.<
9and50swans ( talk) 21:43, 15 September 2017 (UTC)
On further thought I restored the template. If anyone wished to remove it please could they state which of the three enumerated conditions has been met. I can't see how either 1 or 3 is applicable and with regard to 2 the issue is clearly that some editors wish to exclude mention of two articles expressing a particular point of view which have appeared in high-quality academic journals. 9and50swans ( talk) 22:28, 15 September 2017 (UTC)
Why are trigonometric interpretations a thing of the past when we have Britton et al and Mansfield and W since the publication of Robson? 9and50swans ( talk) 05:58, 16 September 2017 (UTC)
'in the past' implies they are not doing it in the present.
This page in a nutshell: Articles must not take sides, but should explain the sides, fairly and without editorial bias. This applies to both what you say and how you say it. All encyclopedic content on Wikipedia must be written from a neutral point of view (NPOV), which means representing fairly, proportionately, and, as far as possible, without editorial bias, all of the significant views that have been published by reliable sourceson a topic. NPOV is a fundamental principle of Wikipedia and of other Wikimedia projects. It is also one of Wikipedia's three core content policies; the other two are "Verifiability" and "No original research". These policies jointly determine the type and quality of material that is acceptable in Wikipedia articles, and, because they work in harmony, they should not be interpreted in isolation from one another. Editors are strongly encouraged to familiarize themselves with all three. This policy is non-negotiable, and the principles upon which it is based cannot be superseded by other policies or guidelines, nor by editor consensus.
This article violates one of the three fundamental pillars of wikipedia by failing to mention Mansfield and Wildberger's recent article in Historia Mathematica. Please not the wording "it...cannot be superseded by other policies or guidelines, nor by editor consensus."
At least two other editors have agreed with me on this.
I may be unable to edit for most or all of the next three days. 9and50swans ( talk) 19:55, 18 September 2017 (UTC)
I am not arguing that M and W should have equal space with Robson but it deserves a mention. 9and50swans ( talk) 22:16, 18 September 2017 (UTC)
I think that the behaviour of certain editors and adminsitrators on this page is a very serious abuse of wikpedia's practices Eeng's remarks are quite inappropriate and he makes no answer on the talk page. I am am pushed further I will seek advice on how I pursue a complaint on this against these individuals. 9and50swans ( talk) 20:13, 18 September 2017 (UTC)
I have placed a notice about this on the Neutral Point of View noticeboard. 9and50swans ( talk) 21:28, 18 September 2017 (UTC)
The fact that I got nowhere in my view reflects badly on wikipedia's administrationis a very common but mislead accusation and belief. Without those policies Wikipedia would become an indiscriminate directory, including original research on every topic and every fringe belief represented as fact. These policies are necessary for Wikipedia to be a respectable encyclopedia. — Paleo Neonate – 21:49, 18 September 2017 (UTC)
No administrator to my knowledge has looked at this, apart from David Eppstein who clearly has an interest. The shortage of adminstrators has been mentioned ion the NYT as a danger to wikipedia. This is not a question of representing a fringe belief as fact simply of mentioning something which has been published in a highly respected academic journal. 9and50swans ( talk) 22:07, 18 September 2017 (UTC)
I note that nobody who has accused me of being tiresome has supported my call for independent people to look at this either for balance or neutrality. If this continues this would be a very good reason for me to call for outside neutral intervention, and I will continue to do this. 9and50swans ( talk) 22:16, 18 September 2017 (UTC)
If there's only one source saying something, it's an overreach to say NPOV mandates that it MUST be included, but that's not the same as
Any "significant view" must be present in multiple Reliable Sources, which is what you said before. A view in only a single source can still be a significant one e.g. if the source was written by an established expert on the topic. E Eng 05:05, 22 September 2017 (UTC)
Who was first to suggest trigonometrical interpretation? If it was Buck (1980), as wikipedia claims, then then phrase "more recently published work sees this as anachronistic, and gives it a different function" is false. Because the described "different function" is an exercise book. However Buck (1980) himself attributes this interpretation to Voils, i.e., this "different function" predates Buck (1980).
Please clarify. Staszek Lem ( talk) 19:10, 20 September 2017 (UTC)
Offtopic wisecrack. Uncollapse to enjoy (or not)
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I came across this. The 'teacher's aid' concept sounds to me a bit like Robson's interpretation. This also appeared in an article Historia Mathematica. Is it worth a mention?
Thus it appears that the reason for the construction of the tables on the Plimpton tablet was not an interest in numbertheoretical questions, but rather the need to find data for a "solvable" mathematical problem. More precisely, it is my belief that the purpose of the author of Plimpton 322 was to write a "teacher's aid" for setting up and solving problems involving right triangles. In fact, a typical Babylonian problem text contains not only the formulation of the problem but also the details of its numerical solution for the given data. Hence the contents of the table on the (intact) Plimpton tablet would have given a teacher the opportunity to set up a large number of solved problems involving right triangles, with full numerical details, as well as to formulate a series of exercises for his students where only the necessary data were given, although the teacher knew that the problem was solvable, and where he could check the numerical details of the students' solutions by using the numbers in the table. For example, if the given problem was to find the diagonal c Nine-and-fifty swans ( talk) 09:25, 5 October 2017 (UTC)
I found 31 refs to Friberg in Robson's 2001 article including
EARLIER PROPONENTS OF THE RECIPROCAL THEORY The theory set out here is not new and I certainly would not want to claim it for myself. It was first proposed by Bruins [1949; 1955] soon after the tablet was published, then reappeared in various guises some 25 years later in three apparently independent studies by Schmidt [1980]; Voils apud Buck [1980]; and Friberg [1981], although none had the supporting linguistic and conceptual evidence cited here but presented it in modernising algebraic form like Neugebauer’s p, q theory. So why has it been largely ignored by the authors of generalist histories of mathematics, and why should it no longer be? Nine-and-fifty swans ( talk) 09:31, 5 October 2017 (UTC)
I don't have time, energy or even understanding to make it fully comprehensive, but it might be expanded to point to a wider range of interpretations. These could be indicated in a list of references at the end. For the reader it may be better to have an article which looks unfinished and has a wider range of references than one which looks finished and has a much narrower range of references. There is clearly a lot more to this than just Robson. Nine-and-fifty swans ( talk) 17:45, 5 October 2017 (UTC)
Everybody who edits the page, or who votes in RFCs should read WP:COI. State here if you have a COI, that is for instance if you publish on trigonometry, or Plimpton, or sexagesimal, etc. Therefore it is also recommended that you strike your votes above, and remove yourself from those discussions. It is perfectly fine to suggest edits here on that page, and I think for general uncontroversial article space edits, including vandalism, or gross errors. However, it is not okay to involve yourself when you try to prevent addition of a colleagues work, you disagree with. Notice that you can get banned or blocked if you do not disclose your COI. prokaryotes ( talk) 13:46, 23 October 2017 (UTC)
As the person who made the RFC I do not remember it being formally closed with any consensus, it fizzled out without anyone much commenting. I have up and have since cited this page elsewhere as an example of how wikipedia is defective. There are probably thousands of other wiki pages equally defective. It's not worth wasting energy on, just educate people about the 'fake' element in wikipedia. forgot password, am in transit, nine-and-fifty Swans — Preceding unsigned comment added by 81.198.102.150 ( talk) 23:00, 23 October 2017 (UTC)
Frivolous COI claims, censorship claims, conspiracy claims, and similar, only help bury your position. The author of the paper, or anyone connected the author or connected to the paper, have a conflict of interest. It is absurd to try to argue the unconnected people have a conflict of interest. Alsee ( talk) 21:14, 24 October 2017 (UTC)
The recent study by Mansfield and Wildberger 2017, with what appears supported by earlier studies by Buck 1980, Joyce 1995, Maor 2002, Chang 2017, Cowen 2017, highlights a robust interpretation of Plimpton 322. Britton 2011 seems to have outlined two groups of interpretations in their study Plimpton 322: a review and a different perspective. MW notes in their study:
"There are two main theories as to how an OB scribe might have generated P322. The original proposal of Neugebauer and Sachs (1945, 40), modified by de Solla Price (1964), and more recently by Proust (2011, 663), emphasizes the role of two generators r and s used to create the Pythagorean triple (2¯(rs¯−sr¯),1,2¯(rs¯+sr¯)), while Bruins' theory (1949, 1957), supported by Robson (2001, 194), claims that a reciprocal pair (x,x¯) was used to create normalized Pythagorean triples as (2‾(x−x¯),sq.rt.(xx¯),2‾(x+x¯)). The relative merits of both points of view, particularly with respect to the errors on the tablet, are well presented by Britton et al. (2011). We propose a modification of these already established theories which blends their respective advantages. Expanding upon the work of Proust (2011, 664), we give an explicit procedure by which the scribe first iterates through the standard table of reciprocals for the values of s, and then finds all possible corresponding values of r."
Thus, to resolve the issues discussed above, the interpretation section should mention the more recent sciences too. Already there is mention in article space of Buck, Joyce, and Neugebauer. It then could also be made more clear that the more established view is per Robson etc. Omitting MW entirely is against Wikipedia's aim to present a balanced view of the subject, and is counterproductive to understand the mathematics of ancient Babylonians, and hampers our efforts to learn and understand the past. prokaryotes ( talk) 16:58, 23 October 2017 (UTC)
I took some reading of the "news" about WM and made two conclusions for myself:
Conclusions:
SUGGESTION:
Stop wasting Wikipedians' time and put a moratorium on beating dead horse for 6 months
.
Staszek Lem (
talk) 22:26, 23 October 2017 (UTC)