Talk:Plimpton 322

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The interpretation of Donald L. Voils (1975 et seq.)[edit]

The interpretation of Donald L. Voils (b. 1934) is worthy of note as being historically intermediate between that of Bruins (1949) and Robson (2001) (at current writing (September, 2010), the main article Plimpton 322 references, but otherwise does not mention, Bruins (1949), notwithstanding that Robson graciously acknowledges it as containing the thesis in Robson (2001) in a different guise). Robson expresses interest in, but ignorance of, Voil's interpretation based on passages in Buck (1980) and indeed one passage in particular resonates with the account of Robson's own thesis as described in the main article Plimpton 322.

Voils, then at the University of Wisconsin at Oshkosh, spoke at the April, 1975 meeting of the Wisconsin Section of the Mathematical Association of America (MAA) on the question Is the Plimpton 322 a Cuneiform tablet dealing with Pythagorean triples?, as reported in the issue of the American Mathematical Monthly for December that year (p. 1043). We may follow Robson (2001) in picking up the story from Buck (1980), p. 344, recalling that Buck was on the faculty at the University of Wisconsin at Madison:

Voils adds to this suggestion of Bruins the observation that the numbers A are exactly the results obtained at the end of the second step in the solution algorithm, (d/2)2, applied to an igi-igibi problem whose solution is x and xR. Furthermore, the numbers B and C can be used to produce other problems of the same type but having the same intermediate results in the solution algorithm. Thus Voils proposes that the Plimpton tablet has nothing to do with Pythagorean triplets or trigonometry but, instead, is a pedagogical tool intended to help a mathematics teacher of the period make up a large number of igi-igibi quadratic equation exercises having known solutions and intermediate solution steps that are easily checked [7].

Unfortunately, Buck's reference [7], apparently an item by Voils slated to appear in Historia Mathematica, was never published. Cooke (2005), pp. 163-164, in an extensive discussion of Plimpton 322, gives a sympathetic account of Voil's interpretation, but again based only on Buck (1980). Voils recalls the submission, written after taking a class in the history of Babylonian mathematics at the University of Wisconsin at Madison, was rejected on some technical ground and is now uncertain whether any copy survives, as he changed interests into computer science at about the same time. The class was taught by William D. Stahlman (1923-1975), who had taken his doctorate at Brown University under Otto Neugebauer.

This quotation from Buck (1980) also serves to remind us that, while this paper does discuss a trigonometic interpretation of Plimpton 322, as noted in the main article Plimpton 322, it was by no means confined to it, nor did it endorse it. Rather, in the light of Robson (2001), Buck's contribution seems to show an uncanny prescience of the limitations of the detective genre (Buck (1980), p. 345):

Unlike Doyle's stories, this has no final resolution. Any of these reconstructions, if correct, throws light upon the degree of sophistication of the Babylonian mathematician and breathes life into what was otherwise dull arithmetic.

Mathematical underpinnings and reconciliation of interpretations[edit]

It is a usual and customary part of the scholarly apparatus in the discussion of multiple interpretations to consider their underpinnings and possible reconciliation qua interpretations. Robson (2001) points the way and sets the standard in volunteering that the thesis being advanced already appeared in Bruins (1949) in a different guise. What is meant here by in a different guise, is that Robson recognises a broad ressemblence between the two interpretations (even if Bruins (1949) might not achieve the same elect state of perfection and grace accorded Robson (2001) in the main article Plimpton 322). But naturally there is no suggestion, nor should readers of Robson (2001) infer, that, say, Bruins thought the same way as Robson or would agree with this assessment. Examination of mathematical underpinnings and possible reconciliation tells us only how interpretations stand one to another, but is neutral on what is being interpreted.

Plimpton 322 has often been taken as the basis of claims that the Babylonians had some early acquaintance with a Pythagorean or diagonal rule, in keeping with the thesis ascribed to Neugebauer in the main article Plimpton 322. On the other hand, the thesis attributed there to Robson, but advanced previously in Bruins (1949) in a different guise, in recontextualizing Plimpton 322 within the corpus of Babylonian mathematics, removes it from this supporting role. It might be helpful to indicate (as the main article Plimpton 322 does not) that the claim to early acquaintance has a firmer, and certainly an independent, foundation in Db2-146 = IM67118, a tablet from Eshnunna from about -1775, as discussed, for example, by Høyrup (2002). The tablet works a computation of the sides of a rectangle given its diagonal and area. The working prefigures a dissection of a square on the diagonal into a ring of four congruent right triangles surrounding a square of side the difference between the sides of the proposed rectangle. The general form of this dissection yields the Pythagorean rule on rearrangement of the pieces, although the working on the tablet skirts this observation (compare also the illustrated discussion in Friberg (2007), pp. 205-207). But, for good measure, the tablet also runs a check on the working by applying the Pythagorean rule to the sides to get back to the prescribed diagonal. (An updated listing of Babylonian appearances of the Pythagorean rule is given in Friberg (2007), pp. 449--451, building on an earlier listing by Peter Damerow as well as Høyrup (2002).)

The theses attributed to Neugebauer and to Robson are linked mathematically by two standard, age old tricks, taking the semi-sum (average) and semi-difference of two quantities coupled with difference of squares (notice that this internal link immediately gives a problem with Wikipedia's policy on references and sources, as this entry is currently flagged as open to challenge and removal). For, suppose that l, s and d stand in the Pythagorean relation l2 + s2 = d2, so that l2 = d2 - s2. Application of difference of squares then yields l2 = (d + s)(d -s). Thus, taking x = (d + s)/l, we also have 1/x = (d - s)/l, and can then recover d and s from x and 1/x by the trick of taking the semi-sum and semi-difference: x + 1/x = 2d/l, x - 1/x = 2s/l. Consequently, we have solved the quadratic equation x - 1/x = c, where c = 2s/l, and for that matter also the quadratic equation x + 1/x = k, where k = 2d/l. The algebra is reversible, so starting from solutions to these quadratics, we can recover three quantities standing in the Pythagorean relation.

This mathematical exercise only tells us how the two theses are related (as the main article Plimpton 322 does not), not what skills the Babylonians possessed, still less what the purpose of the tablet might have been. However, as it happens, it is a commonplace of accounts of Babylonian mathematics that it exhibits a propensity to work with the semi-sum and semi-difference of a pair of quantities, as noted, for example, in Cooke (2005). But the mathematically careful account there misses the trick with the difference of squares, so fails to see that whenever solutions of certain quadratics are present so, too, are Pythagorean triads, and vice versa, although such fraility is itself a corrective in historical analysis. Nevertheless, turing back to Bruins (1958), we find the acknowledged progenitor of the thesis in Robson (2001) in a different guise reprising much of this mathematical exercise, with the claim that the approach was used by the Babylonians (Bruins (1958) is not cited in Robson (2001): it is a minor publication easily overlooked on account of its location; but that it appears in a popular journal makes it more accessible to a general reader in the tradition of Robson (2002)):

We begin by remarking that if we put one of the sides I of a right-angled triangle equal to unity, the Pythagorean relation between the remaining sides d and b is d2 - b2 = (d + b)(d - b) = 1. If therefore we set d + b = λ, then d - b = 1/λ. Now a reciprocal value can be calculated in Babylonian Mathematics only for numbers containing no prime factors other than 2, 3 and 5, i.e. for so-called regular numbers. Extensive tables of such reciprocals were calculated by the Babylonian mathematicians, and therefore by reference to such a table the numbers d = ½(λ+1/λ), b = ½(λ - 1/λ), l = 1, satisfying the Pythagorean relation, could be simply computed. Are there any indications that the Babylonians used this relation? Yes, there are.

Attempt at a scholarly apparatus[edit]

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 (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 (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 (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 (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 (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 (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 (talk · contribs) has added the following to my talk page, coppied here to keep the discussion in one place:

Richard, Thanks very much for entering the discussion and deleting the section on mathematical reconciliation. I was puzzled that a section like that was not there already, and now mystified that anyone should want to excise it altogether. In contrast, the author of one of the leading histories of mathematics in the USA writes privately:
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.
Now, you are an advocate of contacting academics, so just possibly you might want to ask around here among your academic contacts. At the moment, your policy is to guarantee that people go on missing a connection that, once seen, they feel they ought to have noticed. I know that rules are rules, but, with all due respect, might I suggest that you are cutting against the spirit of Wikipedia? —Preceding unsigned comment added by (talk) 23:52, 11 September 2010 (UTC)

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.


  • Bruins, Evert M. (1949), "On Plimpton 322, Pythagorean numbers in Babylonian mathematics", Koninklijke Nederlandse Akademie van Wetenschappen Proceedings 52: 629–632 .
  • Bruins, Evert M. (1951), "Pythagorean triads in Babylonian mathematics: The errors on Plimpton 322", Sumer 11: 117–121 .
  • Bruins, Evert M. (1958), "Pythagoreans triads in Babylonian mathematics", Mathematical Gazette, 41: 25-28,
  • Buck, R. Creighton (1980), "Sherlock Holmes in Babylon", American Mathematical Monthly (Mathematical Association of America) 87 (5): 335–345, doi:10.2307/2321200,
  • Cooke, Roger L. (2005), The History of Mathematics: A Brief Course, 2nd ed., Wiley, pp. 159-164, ISBN 0-471-44459-6.
  • Conway, John H.; Guy, Richard K. (1996), The Book of Numbers, Copernicus, pp. 172–176, ISBN 0-387-97993-X
  • Friberg, Jöran (2007), A Remarkable Collection of Babylonian Mathematical Texts (Sources and studies in the history of mathematics and physical sciences; Volume 1 of Manuscripts in the Schøyen Collection: Cuneiform texts; Volume 1 of Manuscripts in the Schøyen Collection, Springer. ISBN 0-387-34543-4, ISBN 978-0-387-34543-7
  • Høyrup, Jens (2002), Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and its Kin (Sources and studies in the history of mathematics and physical sciences Sources and Studies in the History of Mathematics and The Graduate Texts in Mathematics), Springer, pp. 257-261, ISBN 0-387-95303-5, ISBN 978-0-387-95303-8
  • Knorr, Wilbur R. (1998), ""Rational Diameters" and the discovery of incommensurability", American Mathematical Monthly (Mathematical Association of America) 105 (5): 421-429,
  • Neugebauer, O.; Sachs, A. J. (1945), Mathematical Cuneiform Texts, American Oriental Series, 29, New Haven: American Oriental Society and the American Schools of Oriental Research .
  • Neugebauer, Otto (1969) [1957], The Exact Sciences in Antiquity (2 ed.), Dover Publications, ISBN 978-048622332-2
  • Robson, Eleanor (2001), "Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322", Historia Math. 28 (3): 167–206, doi:10.1006/hmat.2001.2317, MR1849797 .
  • Robson, Eleanor (2002), "Words and pictures: new light on Plimpton 322", American Mathematical Monthly (Mathematical Association of America) 109 (2): 105–120, doi:10.2307/2695324, MR1903149, .
  • Voils, Donald L. (1975), "Is the Plimpton 322 a Cuneiform tablet dealing with Pythagorean triples?". Talk listed by title only in Notice of April Meeting of the Wisconsin Section, American Mathematical Monthly (Mathematical Association of America) 82 (10): 1043,, allusion in Buck (1980).

Exhibit calls for clearer article lead and more focused, balanced sections on varied interpretations of: 1) apparent errors, 2) method of calculation, & 3) function[edit]

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:

  1. Pythagorean triples can be simply defined in context, keeping wikilink for those who want more: two simple examples below.
  2. Otto Neugebauer needs to be given priority in lead and discussion, commensurate with his status as dean of historians of ancient mathematics, his prior status in time re: this artifact, and for NPOV: currently, the vast majority of the cites are to Robson alone. Jury is still out. I've added an External reference to a recent paper that may help restore some sense of balance to these active, competing interpretations and unresolved controversies.
  3. Interpretation falls naturally in two: mechanics of calculations and function of tablet -- these separate questions could be split for clarity. Perhaps even a third category, prior to above, for varying interpretations of apparent errors.

  • NYU exhibit page on Plimpton 322 is esp. clear on two-pronged controversies over method & function:

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.

  • Columbia makes the 2 key interpreters the primary carriers of an interesting storyline in a few sentences:

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.

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)

Real disagreement?[edit]

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)

Something wrong with this maths[edit]

The article says: If p and q are two coprime numbers, then form a Pythagorean triple, and all Pythagorean triples can be formed in this way.

Take the triangle with sides (12, 16, 20), which is both a Pythagorean Triple and is of the form where p = 4 and q = 2 which are not coprime. Therefore, this particular Pythagorean Triple cannot be formed with p, q both coprime and therefore the claim that all Pythagorean triples can be formed in this way is not true. Cottonshirtτ 11:30, 15 September 2012 (UTC)

The formula is valid for all primitive triples, ones that are not integer multiples of some smaller triple. Your example is a multiple of the (3,4,5) triple. I added a clarification.

Recent scholarship[edit]

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: — Preceding unsigned comment added by 336sunny (talkcontribs) 14:15, 12 December 2016 (UTC)

A very short but very informative article has caught my attention it is 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 (talkcontribs) 03:30, 25 April 2017 (UTC)

Are these articles published somewhere? They need to be published to be usable here. —David Eppstein (talk) 04:29, 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)

Well, there's also not much you or I can do about Wikipedia's standards for reliable sourcing, which require actual publication. —David Eppstein (talk) 23:59, 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 (talk) 11:53, 11 September 2017 (UTC)

Mansfield and Wildberger[edit]

There is an interpretation dated August 24, 2017 here: 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)

As a heads-up for traffic increases, there have also articles been released yesterday/today from The Guardian,[1] The Independent,[2] and The Telegraph[3] relating to Mansfield and Wildberger's publication in Historia Mathematica.[4]Sasuke Sarutobi (talk) 23:03, 24 August 2017 (UTC)
Norman Wilderberg should ring a few alarm bells. He is the guy behind Rational trigonometry a finitist scheme to replace sines and cosines by their squares. One reading of this paper is as an attempt to push Wilderberg's rational trig scheme. --Salix alba (talk): 12:21, 25 August 2017 (UTC)
This is Wildberger's rational-trigonometry hobbyhorse, no? Does he have any recognized expertise in the history of mathematics? —David Eppstein (talk) 12:16, 25 August 2017 (UTC)
Looks like first author is not a history of maths specalist either. One other paper on Ergodic Theory home page.--Salix alba (talk): 16:20, 25 August 2017 (UTC)
There is no reason why Wildberger's interpretation should be smeared across several of our pages as if this was something to be taken seriously. Let's let the academic community have its say on the matter (and we know how reliable these newspaper articles are!) before including this theory here.--Bill Cherowitzo (talk) 15:45, 25 August 2017 (UTC)

The article is available online at There is absolutely no need to mention any newspaper source even if, under wiki guidelines, thet are RS.

this should be included here due to extensive coverage throughout mainstreaam, reliable sources!!! --Sm8900 (talk) 16:11, 25 August 2017 (UTC)
These are the same "reliable sources" that just a few years ago were telling us how Prof. Enoch from Nigeria had solved the Riemann hypothesis (and that included the BBC World Report as well.)--Bill Cherowitzo (talk) 16:30, 25 August 2017 (UTC)
There are already enough sources to support the initial statement. Adding these does not improve the article, and is clearly against a clear consensus in this discussion. ScrpIronIV 16:34, 25 August 2017 (UTC)
For that matter, I don't see why Wildberger should get any credit as the originator of the theory that it's a trig table when the same theory is already credited in our article to Buck (1980). —David Eppstein (talk) 22:55, 25 August 2017 (UTC)
Perhaps because Wildberger's no-angles-approach is sufficiently different to make it not anachronistic, which is the main flaw of Buck's suggestion.
So the part that's original is also the part that's the most fringy? Then per WP:FRINGE we definitely need mainstream mathematical (not newspaper!) sources rather than primary sources if we want to include this material. The inability to add Wildberger's non-angle-things seems like a far more serious flaw to me. —David Eppstein (talk) 16:58, 3 September 2017 (UTC)
I have read the article. I agree that we should wait for consensus to support this as an interesting contribution to the field. But I think this discussion has veered toward being overly criticalBarryriedsmith (talk) 14:41, 26 August 2017 (UTC)
The wiki page does not indicate the Buck is the originator of the trigonometric interpretation of the tablet (since he isn't), and Mansfield and Wildberger do not claim that the trigonometric interpretation is new, even citing Buck (and even earlier, Donald Knuth) as promoters of this idea. The biggest flaw the the Mansfield-Winterberger paper as I see it is a lack of sufficient time addressing potential criticisms of their interpretation. Their only direct address is when they cite Robson's "anachronism criticism", with the Robson quote, "there was no conceptual framework for measured angle or trigonometry [in the OB era]. In short, Plimpton 322 could not have been a trigonometric table." Robson's entire argument in the 2001 paper does indeed rest on the modern definition of trigonometry as being the study of circles/angles. Mansfield and Wildberger argue that the point of the Plimpton was going from one ratio of sides in a right triangle to either of the others, which would not require measured angles or our usual transcendental functions. And they spend two sections coherently arguing that this problem did exist in the framework of OB mathematics. Still, it would seem they have not done due diligence in addressing potential criticisms of their theory.Barryriedsmith (talk) 14:41, 26 August 2017 (UTC)
The article does not read as Wildberger self-promoting his rational trig theory. It is mentioned in two places, and my own feeling is that should be omitted, but they never go nearly so far as to suggest that Babylonian math was somehow related to his rational trig. Rather, it is referenced as a device to attempt to open the minds of the readers to the idea that the ancients had a "different formulation" of trig than we are used to -- and this is useful in supporting their rebuttal to Robson. Regarding the author credentials -- yes, it seems Mansfield is not a preeminent scholar in the field. But while Wildberger is not sitting on a bunch of publications in Inventiones Mathematicae or Annals of Math or the like, he is no research slouch -- he has dozens of peer-reviewed mathematical papers, many of them in at least respectable Tier 2 journals. Also, it should be noted that rational trig should not be lumped in with "crackpot mathematics", i.e., false proofs of FLT and the like. It is a novel and interesting approach to a venerated mathematical subject, and even if it isn't going to replace the standard approach to trig, the mathematics is, at the very least, correct.Barryriedsmith (talk) 14:41, 26 August 2017 (UTC)
"dozens of peer-reviewed mathematical papers, many of them in at least respectable Tier 2 journals" NJW has indeed published good research. Checking MathSciNet however I find that in the last 10 years, his papers, all on his pet theory, are with a few exceptions all in very obscure journals and often not even reviewed (we all know what that means...). The only serious review is in fact a take-down, showing how his work is unoriginal, when not sloppy. — Preceding unsigned comment added by (talk) 08:31, 30 August 2017 (UTC)
Section 6 of the Mansfield-Winterberger paper struck me as quite interesting, at least for the first reading I have given it. They compare the potential use of this table for solving some ancient problems versus a larger table of values of sine to eight decimal places, and the Plimpton 322 table performs better. It is not clear whether this comparison would still hold up against a "random sample" of similar ancient problems, but it seems to me this comparison makes a novel case in support of the trig interpretation. There is, at least the possibility, that this could shift the opinion of modern scholars on the subject.Barryriedsmith (talk) 14:41, 26 August 2017 (UTC)
Little surprised to see controversy with peer reviewers of Historia Mathematica, described as one with 'newspapers'. The controversy is real and ought to be mentioned here not summarily removed from intro. — Preceding unsigned comment added by (talk) 21:34, 26 August 2017 (UTC)
I don't think there is a problem with the Historia Mathematica peer reviewers, as the paper seems to be legit. The problem lies with the newspaper hype over this paper and the attempts by some editors to insert this hype into our article. Let us recall that we base our articles on reliable secondary sources. If this paper is a secondary source, then there is nothing new in it, so nothing to report on beyond what we already have. On the other hand, if it is not a secondary source then it is too soon to bring it up since it has not be dealt with by the academic community.--Bill Cherowitzo (talk) 05:01, 27 August 2017 (UTC)
In the interests of access to information, including a reference to the M&W's Historia Mathematica article would help people to evaluate their theory. — Preceding unsigned comment added by (talk) 22:12, 30 August 2017 (UTC)
Wikipedia is an encyclopedia, it is not a discussion forum (see WP:NOT) or a repository of links for the "interests of access to information". There are lots of papers out there with controversial and non-controversial theories, and we do not link to them so that "people could evaluate" them for themselves. What makes this paper so special in this regard? --Bill Cherowitzo (talk) 22:45, 30 August 2017 (UTC)
Personally, I would say that Mansfield and Wildberger is worth inclusion, even if only to cover the controversy and hype (such as with Lamb's excellent article,[5] courtesy of David Eppstein below). — Sasuke Sarutobi (talk) 23:30, 30 August 2017 (UTC)
If we want to have an article about how Wildberger reinvents known ideas and hypes them up, it should be in a different place than this one, and we'd need much better sourcing than just the Lamb post and the critical MR review mentioned earlier. —David Eppstein (talk) 01:01, 31 August 2017 (UTC)
Ah, I didn't realise that the Lamb post was a blog; I'd assumed it was a column. Does anyone know if there are any replies to Mansfield and Wildberger in the pipelines of appropriate journals? — Sasuke Sarutobi (talk) 08:43, 1 September 2017 (UTC)
Of course not. (1) It's too early for any journal paper in response to have been written, (2) the journal publication pipeline is confidential, so anyone who might know other than possibly the author of a submission would not be allowed to say anything, and (3) academics typically write journal papers to publish novel ideas, not to debunk the non-novel ideas of others. Some journals allow the publication of letters to the editor, where such a response might be more likely to appear, but I think that's rare. —David Eppstein (talk) 08:55, 1 September 2017 (UTC)
Sorry, I wasn't sure; this isn't my field (and I've not been in academia for a while - my field of study was sports sciences, which did tend to feature replies in some journals), so I'm not entirely clear on the processes into mathematical journals. My main concern would simply be a matter of having an agreed mention of the Mansfield and Wildberger paper to address it in an agreed manner to provide context to anyone getting here from newspaper articles. Are there any other sources or ways of providing context to this sort of article that you can recommend? — Sasuke Sarutobi (talk) 13:47, 5 September 2017 (UTC)

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. (talk) 10:35, 8 September 2017 (UTC)


  1. ^ Kennedy, Maev (2017-08-24). "Mathematical secrets of ancient tablet unlocked after nearly a century of study". The Guardian. ISSN 0261-3077. Retrieved 2017-08-24. 
  2. ^ "Ancient Babylonians had trigomometry 3,700 years ago. And it was better than ours, experts say". The Independent. 2017-08-24. Retrieved 2017-08-24. 
  3. ^ "3,700-year-old Babylonian tablet rewrites the history of maths - and shows the Greeks did not develop trigonometry". The Telegraph. Retrieved 2017-08-24. 
  4. ^ Mansfield, Daniel F.; Wildberger, N. J. "Plimpton 322 is Babylonian exact sexagesimal trigonometry". Historia Mathematica. doi:10.1016/ 
  5. ^ Lamb, Evelyn. "Don't Fall for Babylonian Trigonometry Hype". Scientific American Blog Network. Retrieved 2017-08-30. 
words such as 'smeared' and 'hobbyhorse' show are rather hostile attitude of certain editors towards Mansfield and Wildenberger, these are the editors who seem determined to exclude all mention of Mansfield and Wildenberger, but they seem rather biased against them. The words 'our pages' - Cherowitzo and 'our article' Eppstein suggest an attitude of ownership. 9and50swans (talk) 09:45, 9 September 2017 (UTC)
By "our article" I meant "the article here on the English Wikipedia", to distinguish it from other articles (such as the ones in the scientific literature that we are discussing). It was not the imperial or editorial "we" (I don't use that on talk pages), nor intended to differentiate some editors from others. Rather the intent was to include all Wikipedia editors, including the ones I disagree with, as collective owners of the article. If you see evidence of battleground mentality and ownership issues in that phrasing, permit me to suggest that the problem is somewhere else than in what I wrote. —David Eppstein (talk) 00:20, 19 October 2017 (UTC)

Proposal for inclusion[edit]

The consensus is against inclusion.

Cunard (talk) 02:04, 19 November 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.

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 (talkcontribs)


Vote below with agree or disagree and give an explanation.

  • Agree Directly related, published, peer-reviewed journal, and lots of media attention too. prokaryotes (talk) 19:02, 18 October 2017 (UTC)
  • Oppose. The suggestion that this was an exact trigonometry table is not original to Mansfield and Wildberger (see many many discussions of this on this talk page), should also not be presented as the conclusive interpretation, and the work of Mansfield and Wildberger has no reliable secondary sourcing in the mathematics literature (the mainstream media coverage is secondary but not to my mind reliable) so there are three major problems with this proposal. —David Eppstein (talk) 20:32, 18 October 2017 (UTC)
    If there are other studies which elaborate in the mathematics literature that this was an exact trigonometry table, then this is notable too, and would support their findings. The study is published in what appears to be a major journal Historia Mathematica, and the coverage in secondary sources seem to be at least in part critical. And there is no indication that there will be no mention of this study in the future. And besides mention the study results, selected critical expert opinions could be mentioned too. To not mention the exact trigonometry table at all, and looking at existing studies already part of the article - explicitly hint at trigonometry, appears like there is a void in our advancing understandings and interpretations of Plimpton 322 from the 90s up to now. prokaryotes (talk) 20:54, 18 October 2017 (UTC)
  • Weak support I think it deserves a brief mention. From Mansfield comments here it seems the claimed unique contribution is a process where the Babylonians could have arrived at something like a trig table, so in some case is a response to Robinson's critique. I'm not sure if any of the secondary sources could be used a reference for this subtle point. --Salix alba (talk): 21:00, 18 October 2017 (UTC)
    • 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)
  • Strong oppose. Controversial primary source with insufficient secondary source coverage by peers. Media hype coverage does not count due to dubious expertise of writers.. Staszek Lem (talk) 21:54, 18 October 2017 (UTC)
  • Strong oppose. I don't believe that we are beating this dead horse again! As the rest of this very long talk page attests to, this topic has been examined ad nauseum and I don't see that anything has changed in the brief time since. However, in a nutshell, this paper qualifies as WP:Fringe and that status is not going to change until reliable secondary sources weigh-in on the subject. The current round of newspaper articles are based on the authors's press release and can not be considered reliable (how many serious academic articles come with a press release and a YouTube video to support their findings?). The most favorable comment from any type of expert that I have seen so far has called it "highly speculative". We should not be buying into the hype surrounding this paper and should wait for the academic community to evaluate it.--Bill Cherowitzo (talk) 23:51, 18 October 2017 (UTC)
The article at least contains another study which refers to trigonometry, and editor Eppstein also mentioned other studies on trigonometry table. Doesn't seem like it is that fringe. Even if it were a fringe theory, this is not an exclusion criteria. We mentioned gravitational waves, even when studies on their existence were scarce, and many doubt were raised if they truly could be found. prokaryotes (talk) 11:06, 19 October 2017 (UTC)
While not an exclusion criterion, we are by the same token, not obliged to report on fringe theories. Some editorial judgement is needed in these cases, hopefully based on Wikipedia:Common Sense. The alternative to that is that we (WP) become a repository for everybody's pet theory. The analogy with gravitational wave theory is very superficial. Any new idea will perforce be considered a "fringe theory" under WP's definition, but that is where the similarity stops. Gravitational wave theory was a theory put forth by experts and analyzed by experts while it awaited experimental verification. Our current case is an interpretation put forward by non-specialists obtained through the lens of a well-known fringe theory (that has been around for a while). There will be no experimental verification of this interpretation and its validity will be determined by the experts in the area. We can only wait for their evaluation, otherwise we (WP editors that is) are making determinations about the content, quite contrary to the spirit of WP policies. — Preceding unsigned comment added by Bill Cherowitzo (talkcontribs)
My apologies for not signing the above, I was in a bit of a hurry at the time. --Bill Cherowitzo (talk) 23:54, 19 October 2017 (UTC)
Bill Cherowitzo, what makes you think that the authors are not experts? Wilderberger has been cited over 800 times per Google Scholar, he published several studies on the topic. And by your argument you judge without pointing to any evidence. It is not enough to claim that all the coverage is biased and the study may be not good enough to be mentioned. On top of this my edit was reverted with stating that there is a consensus against it, reading the talk page here shows what appears to be a majority who wants a mention. prokaryotes (talk) 20:02, 19 October 2017 (UTC)
To be an expert in a field requires having appropriate credentials and/or being recognized as such by other known experts in the field. Of the 55 papers of Wildberger that appeared in Math Reviews, not one dealt with the topic of Babylonian mathematics nor even had History of Mathematics as a primary classification. If, as you say, he published several studies on the topic (I could find no evidence of this, but will assume it is true) they were well below the radar in terms of being seen by the experts in the field. --Bill Cherowitzo (talk) 23:54, 19 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. To oppose the mention of this study is de facto censoring of sciences. prokaryotes (talk) 10:04, 20 October 2017 (UTC)
DO you have any possible WP:COI, do you also publish on trigonometry? prokaryotes (talk) 10:14, 20 October 2017 (UTC)
Sorry, but I have no idea of what you meant by "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)
If you are a scholar and publish on trigonometry or related topics, then edit trigonometry related articles in a way to remove certain other authors work you disagree with or on grounds dislike how it is covered in mainstream media, then this presents a conflict of interest. prokaryotes (talk) 18:30, 20 October 2017 (UTC)
If the best argument you can make is that scholars who specialize in the subject should be excluded because of conflicts of interest and scholars who don't specialize in the subject should be excluded because it's different than their expertise, leaving the field open to cranks to add their crankery unhindered, then you are losing the argument. —David Eppstein (talk) 18:48, 20 October 2017 (UTC)
The point is about removing other scholars work. prokaryotes (talk) 19:18, 20 October 2017 (UTC)
  • THIS DUPLICATE SIMULTANEOUS RFC SHOULD BE IMMEDIATELY WITHDRAWN OR CLOSED. On September 9 an RFC on this issue was opened on this page.[1] On October 9 the RFC template expired,[2] and it is awaiting closure. (Which sometimes takes a while.) Nine days later, while that RFC is still officially open, this duplicate RFC was opened. I came close to placing a procedural close on this myself, but I'm involved in the (other) open RFC on this question.
    To more clearly take a position, sources have been cited below (including but not limited to Scientific American) indicating that the "exact trigonometry table" theory does not (yet) appear to have significant acceptance in the field. It appears to fall under our WP:Fringe guideline, as legitimate scientific work which does not (yet) have significant acceptance beyond the original authors. It appears to fail WP:Due weight for inclusion at this time. We can sort out how to cover this in the article if/when others in the field follow up on this idea favorably. So my position is Oppose inclusion at this time. Alsee (talk) 21:57, 19 October 2017 (UTC)
Since we are now here i suggest to close the previously made RFC (wasn't aware). Additional see MOS:ALLCAPS. Surprisingly, all the editors I've identified to oppose inclusion have replied so far, almost in line with the projection. prokaryotes (talk) 22:13, 19 October 2017 (UTC)
(This has also been brought up at AN for those who weren't mass pinged but are following... Keira1996 02:41, 20 October 2017 (UTC)
See also below section Resolving article scope, with a more comprehensive list of comments on WM. prokaryotes (talk) 18:38, 23 October 2017 (UTC)
  • Oppose New here, so not a very strong oppose, because FWIW I frankly cut short my study of the debate after half an hour or so, but until anyone can present a coherent, uncontroversial, substantial, cogent item for inclusion it is better excluded than included. So far I see nothing that I could conscientiously support and have read several criticisms that seem reasonable to me. JonRichfield (talk) 05:31, 25 October 2017 (UTC)
  • Weak Oppose My opposition is only due to the requirement in the proposal that MW be explicitly given as the source. From a tip of David Eppstein, I looked at the Centaurus article by de Solla Price from 1964. The final paragraph regards Plimpton 322 as follows: "In a way, it may be likened (though not precisely) to the tabulation, for those suitable angles, of those special trigonometric functions taking convenient rational values. Thus, on a purely arithmetical basis, there is erected a "trigonometric" corpus that could be used for practical mensuration, or more probably for the setting out of series of practice problems in mensuration, all of which would be capable of exact numerical solution. It is indeed just such extensive series of conveniently constructed numerical examples in mensuration that constitute the greater part of the Babylonian mathematical corpus". As I commented a few weeks ago, MW's contribution seems to be taking this rough speculation and demonstrating its viability by enumerating a few such examples and performing a specific comparison of this use of Plimton 322 against the solutions using an approximate table of values of the sine function produced thousands of years later. While Plimpton 322 performs admirably in these examples, this contribution seems far less important to the "exact trig table" idea than the initial suggestion by de Solla Price. I would, however, support a proposal to include the "exact trig table" idea in the main Plimpton 322 page while including de Solla Price as the originator of this idea. A big argument against even such a mention as this seems to be it's speculative nature -- but other interpretations that are mentioned seem no less speculative to me. MW nudges the idea, ever so slightly, from away from the fringe of speculation. The argument that the idea is too new and not subject to analysis by experts evaporates when de Solla Price is used as the source.Barryriedsmith (talk) 02:53, 26 October 2017 (UTC)

The discussion above 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.

Proposal for alternative inclusion[edit]

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.

Staszek Lem, I would be interested to read who proposed it first, MW stated that their paper presents a merged view. However, since we are not allowed to mention the study in article space we will all remain in ignorance as to who eventually proposed this theory. prokaryotes (talk) 18:59, 25 October 2017 (UTC)
We need independent expert's opinion about what exactly the novelty is. The authors state it is a "merged view". Well, they (and those who regurgitated their press-release) may say whatever they want. Someone independent must evaluate the novelty in the "merged view", whether this is a marketing metaphor or a discovery. Staszek Lem (talk) 19:15, 25 October 2017 (UTC)
Thank you Staszek, that's the first reasoned argument I have read in this RFC. While I would add that there are some signs featured in the Science Magazine article in this regard, it could be argued that this would require a peer-reviewed study, or similar authoritative commentary, ie. in Historica Mathematica. prokaryotes (talk) 19:27, 25 October 2017 (UTC)
  • Comment Cowen's article is ether ignorance or promotional push. The article title "This ancient Babylonian tablet may contain the first evidence of trigonometry" and the whole exposition creates an impression that MW discovered this trig thing. They did not. Further, it says " That means that—as for modern trigonometric tables—someone using the known ratio of two sides can use information in the tablet to find the ratios of the two other sides." -- that's mathematical bullshit. This statement could be valid only for triangles with ratios found in the table. You cannot do it for arbitrary triangles with this table. Not to say that the table lists the ratios of squares of sides. and to find rations of sides you need to do the math involving square roots. Meaning that Cowen's pop-sci article is worthless as a reference. Staszek Lem (talk) 17:48, 25 October 2017 (UTC)
    • Note that the Babylonians did know about the math involving square roots — at least, YBC 7289 has an accurate numerical approximation to the square root of two, as the diagonal length of a unit square. But taking that step throws away all the mystic exactness of MW. —David Eppstein (talk) 17:56, 25 October 2017 (UTC)
  • Oppose. Staszek Lem (talk) 17:49, 25 October 2017 (UTC)
  • Oppose per WP:STICK. We've been through this over and over and over and over. At this point we need to stop thinking this as a content debate, and start thinking of it as tendentious editing. The proper response is not well-thought-out critiques of why it's too soon to include MW; we've done that already, repeatedly. Instead, we should direct a user-conduct warning to Prokaryotes for failing to respect the clear consensus of the closed RFC and past discussions. So, Prokaryotes: please find something else to edit for a while (six months, say). There is no particular urgency in incorporating this material, now that the media flash-in-the-pan has evaporated. Continuing in the same way is likely to lead to escalating warnings or even a topic-ban or block. —David Eppstein (talk) 18:10, 25 October 2017 (UTC)
ANI is just through these gates
Apparently it wasn't a clear consensus, acknowledged by the closer as well, here), and it doesn't factored in my support. If you feel that there needs to be a warning discussion, the right place is at ANI, and then we can talk in detail about your involvement as well. However, I rather follow the RFC here. Please stay calm even if you disagree. The alternative proposal here is a last attempt to find a solution which satisfies all involved opinions. prokaryotes (talk) 18:26, 25 October 2017 (UTC)
So your response to being told that your editing is problematic is WP:IDIDNTHEARTHAT and pointers to more forum-shopping by you, I take it. As for ANI: it's not the place for warning problem editors, but for them to abandon all hope once the big warning on the gates has failed to dissuade them. —David Eppstein (talk) 18:59, 25 October 2017 (UTC)
last attempt – you promise? EEng 00:12, 26 October 2017 (UTC)
  • Oppose and for God's sake this needs to end until there are some real sources on this, per David Eppstein. EEng 18:15, 25 October 2017 (UTC)
  • Oppose. Several comments. First of all, Staszek Lem has it exactly right. There is no reliable secondary source that supports the statement–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)
Either way, don't you think it should be mentioned at least, it is interesting never the less (seriously)? The noted sentiment "In 2017 MW wrote a paper that is criticized for not being based on anything factual." puts the weight on proving that Babylonians actually used the tablet in the proposed way. However, this seems like a tremendous task. At the end of the day, the numbers add up ... Also I have the feeling that the closer judged your participation as opposing inclusion. prokaryotes (talk) 22:57, 25 October 2017 (UTC)
  • support Anything that mentions MW is to be welcomed. But this may need to be qualified. I have been absent from the debate for a while but intend to follow it now there is someone else involved who supports inclusion of MW. I think that one or other RFC should remain open or be reopened, I opened the firtst and have no experience of procedures, Prokatryotes opened the second and has not had much support until now. 9and50swans (talk) 13:19, 26 October 2017 (UTC): apology for inadvertent use of old account.Nine-and-fifty swans (talk) 12:20, 27 October 2017 (UTC)
  • Comment to closer The closer should factor in the votes from the previous RFC, essentially the same matter. That way we would effectively use the sum of opinions, instead of just the opinions from the most active editors. prokaryotes (talk) 07:29, 26 October 2017 (UTC)
  • Oppose, and this is getting disruptive. ~18 sections and subsections on this talk page, with this subsection effectively constituting a third failed RFC attempt, two failed attempts on ANI, and a failed attempt on NPOV/Noticeboard. If this tendentious, forumshopping continues and I have to !vote yet another time on this, my "Oppose inclusion" is going to change to "Support block or topic_ban". Alsee (talk) 00:25, 28 October 2017 (UTC)
Well it's not disruptive editing. Actually I think there was some significant progress in the last of threads, it just needs someone with access to the material to carry out the edit. Nine-and-fifty swans (talk) 21:12, 28 October 2017 (UTC)

A dose of anti-hype[edit]

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)

I'd call this "negative hype". This blog post is still hype, just in the negative direction. It quotes a publicity video and not the article.
Yes, it is a blog and we would not use this as a reliable source. But, it is at least written by a mathematician with some familiarity with the history of mathematics (according to her blog); not something that could be said about those newspaper reporters who clearly used that publicity video and/or its accompanying material to write their articles. The likelihood that they read the paper is approximately zero. --Bill Cherowitzo (talk) 04:03, 1 September 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. ----

Newspapers are not more reliable than journals; especially when it comes to technical fields such as mathematics, most newspapers have few technically-qualified writers, so many of these newspaper articles are simply framing press releases that the authors send out (as Bill Cherowitzo pointed out). Historia Mathematica is a reliable source, yes, but it is also important that articles are framed in terms of their relevance. The point of view put forward by the article is not consistent with other scholarship on the tablet, so it is just as important that it is not put forward in a way that gives it undue weight. Reliability of the source is not the only criterion for inclusion of information. — Sasuke Sarutobi (talk) 12:09, 8 September 2017 (UTC)

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 (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 (talk) 14:28, 8 September 2017 (UTC)

Two points. Wikipedia is an encyclopedia, not a debating forum. We don't present all sides of current events and let the public decide what is true! We report on what is in the secondary literature and if there are differences of opinion in that literature we will report on it. There has not been enough time for the secondary literature to catch up to this paper, so Wikipedia should not be reporting on it. As to the Lamb blog, what part of "Weblog material written by well-known professional researchers writing within their field" do you not understand? Lamb is an assistant professor with no background in the history of math (according to her CV). Mind you, I think that she is a good writer with valuable opinions and I wish her all the best in her career, but that does not change the fact that this is still a blog that we would not consider to be a reliable source. --Bill Cherowitzo (talk) 17:47, 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)

Google scholar lists approximately 1000 published journal articles related to Plimpton 322. Obviously we have to pick and choose from them rather than citing them all, based on considerations such as what new information they bring to bear on the subject that is not already covered by other sources. So what new information do you think this paper brings? —David Eppstein (talk) 20:37, 8 September 2017 (UTC)
Well given that this paper achieved such publicity that is reason enough to mention it. Anyway I would have thought that Historia Mathematica carries rather more prestige than most publications in the field. If it doesn't say anything new then there will have been time for responses in the secondary literature, hence you are invalidating Bill Cherowitzo's objection, unsupported by wiki guidelines, above. Sorry I logged out accidentally. — Preceding unsigned comment added by (talk) 21:02, 8 September 2017 (UTC)
So you think that whether we use publications like this one as sources should be based on how much hype they generate rather than on whether they actually source any information in our article? I disagree. And I note that you also avoided answering the question: for what claims, exactly, should we use this publication as a source? —David Eppstein (talk) 21:21, 8 September 2017 (UTC)

If it doesn't say anything new then why did HM carry the article? (talk) 21:29, 8 September 2017 (UTC)

You can find some reliably sourced rejection of Mansfield and Wildenberger from Eleanor Robson here

so there is some negative reaction to mention with the article. 9and50swans (talk) 16:25, 10 September 2017 (UTC)

Request for comment[edit]

Consensus is to exclude reporting of the Historia Mathematica article, and to omit it as a reference unless and until there is relevant content requiring its citation.- MrX 12:09, 23 October 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

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, and should be reported.

9and50swans (talk) 20:57, 8 September 2017 (UTC)

We can't add something as a source without knowing what claims in our article it should be used to source, something you have refused to answer when asked. —David Eppstein (talk) 21:23, 8 September 2017 (UTC)
The claims are in the abstract of the article. They seem pretty radical to me. Either it makes frsh claims or it supports existing claims. In case of thevlatter it should be mentioned. But I think the editors who refuse to mention this should be exposed to some comments from disinterested wikipedia editors.----
The claims in the abstract of the article are obviously non-novel. Why the editors and referees let them stand is a mystery. One needs a more careful reading of the paper (verging on WP:SYN) to find what is actually novel in it. —David Eppstein (talk) 17:10, 9 September 2017 (UTC)
Highlights 2 and 3 at the head of the article aren't mentioned in the wiki article. It's not for us to take issue with the editors and referees of HM, that's original research. We have to report what they say. 9and50swans — Preceding unsigned comment added by (talk) 22:10, 9 September 2017 (UTC)
Highlight 2 is mentioned, it is merely given a more appropriate credit (Buck 1980). Highlight 3 has no substantive support within the actual article, which actually says that the table was likely used as an approximate trig table (not exact!) via linear interpolation, something that can again already be found in Buck's paper. —David Eppstein (talk) 22:45, 9 September 2017 (UTC)
Buck does not actually propose that the tablet is trigonometry. In fact he says "the Plimpton tablet has nothing to do with Pythagorean triples or trigonometry but, instead, is a pedagogical tool" (p 344, see section below for more a detailed quote). Many have mused upon the possibility that the Plimpton tablet could be trig. But to my knowledge, the M&W article is the first peer-reviewed mathematics history article to proposes the Plimpton tablet is trigonometry of some kind.
Personally I think it worth about one sentence. Something like "In a 2017 paper Mansfield and Wildberger return to the idea of a trigonometric table and posit that it is a form of exact trigonometry".--Salix alba (talk): 22:56, 8 September 2017 (UTC)
Agreed, with a link to rhe article, that's all. Reaction, when it appears, can be included. The press coverage has raised the profile of the table, which is in itself significant. — Preceding unsigned comment added by (talk) 05:33, 9 September 2017 (UTC)
While a reasonable suggestion, I would be concerned that once we provide a "foot in the doorway" there will be requests to modify other parts of the page to be in accordance with the content of this paper. --Bill Cherowitzo (talk) 17:17, 9 September 2017 (UTC)
This does not seem like a sound reason for refusing to mention it. Future requests should be dealt with on their merits. 9and50swans (talk) 21:41, 9 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)

This RFC has the purposes of sources backwards. We cite sources to support claims in our articles; we don't cite them because the sources themselves have become famous. It would make sense to have an RFC on whether some specific claim should be added to the article, if there were some contention about such an addition. It makes no sense to have an RFC asking us to add a source, because it's famous (i.e. hyped up) rather than because it makes any particular claim, and only later to try to figure out whether we can twist the article to state a claim that it can support. —David Eppstein (talk) 23:55, 9 September 2017 (UTC)
Please excuse me if I do not participate further in this debate whilst awaiting comments from outside. It seems on the one hand someone is saying that the article in question shouldn't be mentioned because it contributes nothing new and on the other hand you have someone saying that a trigonometrical interpretation has hardly be mentioned before, in which case the article must be saying something new. This is such a flagrant breach of wiki principles that I will be quite happy to push it further if need be. 9and50swans (talk) 15:18, 10 September 2017 (UTC)
  • Do not cite without a claim to back up -- per David Eppstein, there's no point citing the source, really. Including a source purely because it has attracted attention is utterly pointless. Keira1996 07:58, 11 September 2017 (UTC)
The source should be cited for laying out the trigonometric interpretation of Plimpton 322. Several notable people (de Solla Price,Knuth) have suggested this possibility, but it has never been followed up until this article. The talk of hype and media attention is a distraction from the core issues that an encyclopedia should focus on.
There is no denying that with Wilderberg's PR stunt Plimpton322 hit the headlines worldwide. And this has nothing to do with the interpretation. It is a sure bet that P322 will not be again in the headlines any time soon, so this is notable fact about its history. 'Attracting attention' is just an understatement, it was indeed a causeless sensation which we can explain only as lucky PR. A good place to sneak a reference to this Aug.2017 episode is before the end of the lede, imo. (talk) 08:37, 11 September 2017 (UTC)
  • Do not cite without context -- per David Eppstein and Keira1996. As I've said elsewhere, WP:RS is not the sole criterion for inclusion of content into an article; as part of NPOV guidelines, due vs. undue weight should be taken into consideration, and this appears to be the case where this article is concerned. If there is a way of providing context to the Mansfield & Wildberger claims, then by all means include it, but with criticism of the article having come from several authors in the same field, including Eleanor Robson (who is the most-cited author in the present article), then it is difficult to currently contextualise it.[1] As a further note, I don't see anything to construe use of the term "our article" by some editors as any further restrictive than "Wikipedia's article". — Sasuke Sarutobi (talk) 12:45, 11 September 2017 (UTC)
Perhaps the more recent interpretation of Britton, Proust and Snhider should be included, as well as the factor reduced core theory of Friberg. This would put Robson's interpretation into context. — Preceding unsigned comment added by (talk) 21:11, 11 September 2017 (UTC)
In case anyone else cares to look at these, the more complete references are:
  • Britton, John P.; Proust, Christine; Shnider, Steve (2011), "Plimpton 322: a review and a different perspective", Archive for History of Exact Sciences, 65 (5): 519–566, doi:10.1007/s00407-011-0083-4, JSTOR 41287706, MR 2838357 
  • Friberg, Jöran (1981), "Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples and the Babylonian triangle parameter equations", Historia Mathematica, 8 (3): 277–318, doi:10.1016/0315-0860(81)90069-0, MR 0631810 
  • Friberg, Jöran (2007), "Appendix 8: Plimpton 322", A remarkable collection of Babylonian mathematical texts, Sources and Studies in the History of Mathematics and Physical Sciences, Springer, New York, pp. 433–451, doi:10.1007/978-0-387-48977-3, ISBN 978-0-387-34543-7, MR 2333050 
I appear to have online access to the two journal papers, but I haven't had time to look at them yet. I also have online access to the main part of Friberg's book, but not the appendices where this material is to be found. —David Eppstein (talk)

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)

The tweets from Robson which appear in the NYT appear to have been deleted from her Twitter account.9and50swans (talk) 21:25, 11 September 2017 (UTC)
I would not read too much into Robson's tweets or their removal. Given all the hype surrounding this, a noted professional like her would realize that the cursory condemnation she originally gave would be quoted all over the place and withdrawing it so that she could make a more considered response (if she so desired) would make a lot of sense. It would also help to include more of Jones' quote, yes he said it was plausible possible, but he also said that it was not supported by anything and so quite speculative. I would could interpret that as damning by faint praise. --Bill Cherowitzo (talk) 00:05, 12 September 2017 (UTC)
Again, no. There are 1000 or so journal papers that mention Plimpton 322 and we can't cite them all. Also, "appearing in a journal" is a bad criterion for mentioning a reference; references are used here to back up statements in our articles, not as things to mention for their own sake. What I want is a clear and specific description of a new fact or idea that was brought to light by this paper and not already present in the earlier literature. So far nobody can provide one. —David Eppstein (talk) 20:44, 11 September 2017 (UTC)
  • Suggestion. We should mention and cite the M&W paper, and the fact that it was widely reported in the press: this is easily supported by references. We should say what new understanding is given in the M&W paper; except that, as far as I can tell, there is none. So, we should say that the widely-reported M&W paper contributed nothing new: do we have a reference for this? Maproom (talk) 06:57, 14 September 2017 (UTC)
    • The only in-depth published criticism we have is Lamb's piece [3], it doesn't go so far as to say there's "nothing new", and I don't think it's sufficiently reliable to use for such a purpose. I also found a piece by Assyriologist Eduardo Escobar that takes issue with the Wildberger paper over a a different point (whether there is any evidence that the mathematics from the tablet might have been applied to architecture) [4] but it relies on Lamb for discounting the trigonometric hypothesis. I also found a couple of blog posts that do not come with major-magazine bylines, and thus are even less usable as references [5] ("I would stop short of saying that the claims of the authors are fraudulent, but I would go way further than to say they are simply overreaching. Let’s stick with saying that they are vastly overstated purely in order to drum up public interest for their own professional enhancement.") and [6] ("Yes, two guys at the University of New South Wales published a paper on this tablet, but they didn't really make any progress in understanding it. In fact, their press release spreads some bizarre misinformation! For example, they claim this tablet is “superior in some ways to modern trigonometry". It's not.") —David Eppstein (talk) 07:27, 14 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)


  1. ^ Chang, Kenneth (2017-08-29). "Hints of Trigonometry on a 3,700-Year-Old Babylonian Tablet". The New York Times. ISSN 0362-4331. Retrieved 2017-09-11. 

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 (talk) 08:29, 14 September 2017 (UTC)

  • (bot-summoned) Procedural oppose, though I do not know what I am opposing exactly, which kind of is the problem. If the paper itself is somewhat worth mentioning even after taking WP:NOTNEWS into account (maybe not notable per se, but more than just a random paper), then sure, mention it, but as a subject of news hype rather than as an outstanding academic source.
I am more dubious about using it as a source for outstanding statements. I am not saying Historia Mathematica is a predatory journal that will let any garbage through peer review, because that is probably not true, but it does not look like a leading journal either (impact factor of 0.4, editors are redlinks on Wikipedia, I cannot find much about it on the internet); so a random paper from it should certainly not be hyped as if it was the be-all and end-all of research on Plimpton 322. TigraanClick here to contact me 15:51, 20 September 2017 (UTC)
  • (bot-summoned) Oppose "Wide media coverage" is a subjective judgement. Quite often media jumps on a bandwagon of hype for things well known for quite some time, simply because in modern popular media sensationalism spreads like prairie fire. Scientific articles are to be judged by scientific merits. Staszek Lem (talk) 18:33, 20 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). TigraanClick here to contact me 09:11, 21 September 2017 (UTC)
Well, first of all it is our job to perform judgement of the relevance of the sources. If we go on summarizing "literature consensus" blindly, what a garbage heap of Wikipedia we will have. "Also", we are talking here precisely about science, not "homeopathy, creationism and the like". 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. Since there are doubts, we have to have secondary scholarly sources, which say "yes, this is a new word". The fact that it was published in a peer-reveiewed sources is irrelevant: there is no obligation for them to publish only novelty. Staszek Lem (talk) 21:25, 21 September 2017 (UTC)
If what they publish isn't in some way new but is presented as new then the journal and authors are surely plagarising. Nine-and-fifty swans (talk) 14:39, 22 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...
While we do have to judge the relevance of the source, this is not done by examining ourselves the accuracy of the article, but by what the rest of the literature has said. Unsurprisingly, a new article has generated little coverage beyond the WP:NOTNEWS noise; but that has little to do with the scientific merits of the article, since it would be the case for pretty much anything that was published in scientific literature ever. Hence why I dispute your assertion that Scientific articles are to be judged by scientific merits. TigraanClick here to contact me 11:21, 22 September 2017 (UTC)
In my understanding, whether an article contributes something new is the litmus test of scientific merit (unless it is a survey article (merits of survey articles also scientific but somewhat different, closer to Wikipedia's :-)). Staszek Lem (talk) 16:29, 22 September 2017 (UTC)
  • Like many responses above, effectively Oppose unless/until there is support for some particular text to improve the article. While the paper has gotten some hype in regular press, the most significant claims do not appear to have much support among other experts. (i.e. WP:Fringe.) If we did include something, it would almost certainly need a counterpoint from Scientific American or somewhere. Inclusion of this source at all seems a bit borderline, however we don't even have a suggestion of what what the source would be used for. The RFC here seems a bit backwards. We normally don't decide to use a source and then pick out what to take from the source. Normally we start with some proposed improvement to the article, then we sort out whether we have good enough sourcing for the new content. If/when there is a supported text to improve to the article, the natural next step is to sort out whether the edit should be cited to this source or cited to some other source. Per policy page WP:PRIMARY citing primary sources is sometimes allowed, however there are several reasons that secondary sources are strongly favored. Alsee (talk) 19:10, 21 September 2017 (UTC)
I am not clear what is primary and secondary here. The counterpoint to M and W is given in advance by Robson. And think of it this way, if someone comes here looking for information on M and W and finds nothing they will think it odd and maybe that the article hasn't been updated. If they find a mention in relation to Robson then they can consider Robson's critique of the trigonometrical approach. I am not sure what we are voting for or against here, if I wasn't clear in my RTC that's because I am not familiar with the procedure. Alsee who is opposing nonetheless changed the lead, I simply changed the body to reflect the lead. Nine-and-fifty swans (talk) 15:38, 22 September 2017 (UTC)
Nine-and-fifty swans, 'primary' sources are things like publishing scientific research, a novel and autobiography a diary or facebook page, a witness to a crime, personal account of a religious experience, advertizing or the website published by a company, entertainment-movies. A secondary source is based on primary sources. 'Secondary' sources are things like newspaper and magazine stories, TV news, most books, scientific-survey papers, movie-reviews, documentary-movies. 'Tertiary' sources are based on secondary sources. An encyclopedia is the archetype of a teriary source. An encyclopedia explicitly aims to summarize the broad body of information in secondary sources.
Shifting topic, I see you changed the body of the article. I see David Eppstein reverted the edit. First, to David: Please use edit summaries on reverts. The WMF has done research showing that unexplained reverts leave newer users particularly confused, upset, and that they are extremely likely to quit editing after an unexplained revert. Unexplained reverts are really really bad. New users are mostly accepting of explained reverts. Back to the point: We are currently in the middle of an RFC discussing whether to add the new paper to the article. The edit to add the paper was clearly controversial, and the RFC discussion is clearly leaning against it. While edits are allowed during an RFC, and sometimes they an be helpful, extra care needs to be used to avoid increasing the tensions. Adding the paper when the RFC discussion is leaning against it can look combative or disrespectful of the consensus process. You should have suggested the edit here on talk.
The positive thing is that we now have a concrete proposed-edit[7] to consider.
Mansfield and Wildberger (2017) have restated this interpretation in relation to rational trigonometry.[1]
On the positive side this is a modest addition, and it is clearly factual. On the negative side, when I clicked the link to rational trigonometry I found that the lead says this To date, rational trigonometry is largely unmentioned in mainstream mathematical literature. It was a plausible edit, but it uncomfortably feels like promoting a concept that has no traction beyond Mansfield and Wildberger. Consider my position at this time to be "hesitantly neutral". Let's see what other people think. Alsee (talk) 21:32, 22 September 2017 (UTC)
On the negative side Swans' new edit under the new user name was clearly disrespectful of the sense of the discussion (and just this side of WP:SCRUTINY, noting for instance that the new account seems to have tricked you into thinking that Swans is a newer user) and I see no point in being deferential in response. Swans already knows why I reverted; why belabor the point. As for the proposed edits, I am tempted to paraphrase de Solla Price (see later in this talk for the actual quote): In a way, Wildberger's work on Plimpton 322 may be likened (though not precisely) to his promotion of rational trigonometry: both take things that were well known (the trigonometric interpretation of the tablet, and the special trigonometric functions taking convenient rational values) and take credit only for repackaging them. —David Eppstein (talk) 21:45, 22 September 2017 (UTC)
David Eppstein, I didn't even notice the change from '9and50swans' to 'Nine-and-fifty swans'. If it were an attempt to evade scrutiny, it failed spectacularly. Chuckle. I referred to them as relatively new because I had previously seen they have less than a hundred edits, and they don't seem very familiar with how we work yet. I try to lean toward generous with new users, but don't worry. That generosity evaporates when it comes to respecting consensus. Alsee (talk) 00:04, 23 September 2017 (UTC)
I was getting ready to revert Swans' latest addition when David beat me to it. My edit summary would have included a reference to WP:PROFRINGE. I can understand being frustrated with this editor given the long string of what I would call combative edits to this page. I have consistently held the position that inclusion of any mention of this paper needs to have the reaction of the scientific community via reliable secondary sources incorporated in it. The more adamant Swans gets about his inclusion, the more convinced I am that this is the correct posture to take.--Bill Cherowitzo (talk) 23:07, 22 September 2017 (UTC)
I greatly appreciate the intervention of Alsee in this debate, they appear not to have an axe to grind. By the definition of primary sources most of the article appears to be based on primary sources, if it were based only on secondary sources then all we could say is that Robson won a medal. However the point of a refereed journal is that the interpretation is at least considered by referees as having merit. Regarding 'rational trigonometry' as fringe, see the section of 'notability and criticism' I am not suggesting that M and W be given more than a passing mention in this article, but I think they should be mentioned to show that the 'trigonometric' interpretation is not completely dead. And I keep coming back to the point, if M and W have been published in the leading journal for the history of maths, the fact that the referees have passed it is surely sufficient grounds for them to get a mention. Bill Cherowitzo wrote 'I have consistently held the position that inclusion of any mention of this paper needs to have the reaction of the scientific community via reliable secondary sources incorporated in it.' we do have quite a bit of this reaction through comments in the press, but if you look at the article in relation to Buck the only reaction mentioned is negative, from Robson. Are we to wait until someone criticises M and W in a journal before we can mention them? I'm not saying we should give M and W lots of space, just a mention.Nine-and-fifty swans (talk) 00:07, 23 September 2017 (UTC)

Primary or Secondary Source[edit]

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)

This is not as clear cut as you are trying to make it seem. A source can be both primary and secondary, depending upon what it is being used for. To claim that all writing about Plimpton 322 is secondary (I suppose because there are no living Babylonians who can give eyewitness accounts) is simplistic. An interpretation of what is on this artifact is an event and a paper that proposes a new interpretation is a primary source for that interpretation. If this same paper also reviewed other interpretations it could also be used as a secondary source for those interpretations. As to the paper being considered, to the extent that it is a secondary source, one would need to know for what statement in the article it is being used as a supporting citation. You have failed to supply this information after being repeatedly asked for it. The paper is a primary source for the interpretation that links to rational trigonometry, but this is WP:FRINGE and we should not consider it by WP:PROFRINGE. Your overly repeated claim that we should mention this paper just because it got published has no basis in Wikipedia policy that I can see and how it should be classified as primary or secondary or both is really a very moot point. --Bill Cherowitzo (talk) 18:38, 23 September 2017 (UTC)
It would support is statement from the lead "There has been significant scholarly debate on the nature and purpose of the table." where 'might' might be replaced by 'is' especially if the Britton et al. article does not fully agree with Robson. Re. policy I cite the lead fromWikipedia:Neutrality of sources "On controversial topics, Wikipedians often need to deal with sources that are reliable but non-neutral. The best solution to this is to acknowledge that a controversy exists and to represent different reliable points of view according to the weight that reliable sources provide. Intelligent readers will weigh the opposing sides and reach their own conclusions." It is not a question that M and W are published in a refereed journal but in the top journal for the History of Maths. All I am suggesting that is that M and W be mentioned, not expounded as with Robson. Nine-and-fifty swans (talk) 10:58, 24 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. TigraanClick 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)

The discussion above 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.

Outdated statement in lead[edit]

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 (talk) 08:04, 9 September 2017 (UTC)

A short fix would be to say that "Although the tablet was interpreted in the past as a list of circular functions comprising a trigonometric table..."
But even saying that the tablet has been interpreted in the past as trigonometry overstates the case. The statement refers to a single paragraph in Buck's article:
"Variants of this explanation have been proposed. If one computes the values of the angle for each line of the tablet, they are seen to decrease steadily from about to about , in steps of about . Is this an accident? Could this tablet be a primitive trigonometric table, intended for engineering or astronomic use?" But again, why is useful?" [1]
Buck does not actually advance a trigonometric argument, and instead proposes that Plimpton 322 was used as a school text
"... the Plimpton tablet has nothing to do with Pythagorean triples or trigonometry but, instead, is a pedagogical tool intended to help a mathematics teacher of the period..."[2]


  1. ^ Buck, Creighton (1980). "Sherlock Holmes in Babylon". American Mathematical Monthly. 41: 344. 
  2. ^ Buck, Creighton (1980). "Sherlock Holmes in Babylon". American Mathematical Monthly. 41: 344. 
A longer, but more contentious, fix would be to state that the trigonometric interpretation has never been given serious consideration.
Is that actually true? Buck cites several others for this interpretation. And more recently there have been others, e.g. Kazuo Muroi, "Babylonian Number Theory and Trigonometric Functions: Trigonometric Table and Pythagorean Triples in the Mathematical Tablet Plimpton 322", in Seki, Founder of Modern Mathematics in Japan, Springer, 2013, doi:10.1007/978-4-431-54273-5_3 (which by the way includes linear interpolation explicitly in the abstract, so we can strike off that part of the interpretation as another thing Wildberger did not invent). For that matter the idea that it differs from a modern trig table in the fact that it is exact rather than numerical is also not novel: see de Solla Price (1964, doi:10.1111/j.1600-0498.1964.tb00385.x), "In a way, it may be likened (though not precisely) to the tabulation, for those suitable angles, of those special trigonometric functions taking convenient rational values. Thus, on a purely arithmetical basis there is erected a 'trigonometric' corpus that could be used for practical mensuration, or more probably for the setting out of series of practice problems in mensuration, all of which would be capable of exact numerical solution." —David Eppstein (talk) 23:38, 9 September 2017 (UTC)
M&W cite Knuth for the idea of linear interpolation. They expand upon this suggestion, but do not claim to have invented it.
More importantly the quote from de Solla Price does not mention how the Plimpton tablet might be trigonometry, just that it might be trigonometry. I'm sure that de Solla Price gave this paragraph, and the end of his very influential article, serious consideration. Perhaps it is worth expanding upon? It seems that this is what M&W have done. And unlike Muroi, they approach the idea without anachronistic trigonometric functions. — Preceding unsigned comment added by (talk) 01:08, 10 September 2017 (UTC)
The point is that neither linear interpolation, nor exactness, are original to Wildberger. So what is? Only his specific variant of what order the entries in the table were calculated? —David Eppstein (talk) 01:26, 10 September 2017 (UTC)
The contribution of M&W is to build upon the suggestion of de Solla Price. While Buck, Knuth and de Solla Price have all suggested the tablet might be trigonometry it has never progressed further than a suggestion, and after Robson's article this line of thought had been mostly abandoned. So while it has been suggested many times, it has never been properly followed up. — Preceding unsigned comment added by (talk) 02:19, 10 September 2017 (UTC)
How is Wildberger's more of a proper follow-up than Muroi? What novel idea, if any, does it actually contribute to the trigonometric hypothesis? If I seem to be asking this same question over and over and over, it's because I have yet to get an informed answer. —David Eppstein (talk) 03:51, 10 September 2017 (UTC)
Muroi is concerned with the generation of the Plimpton tablet, which he supposes was "constructed by making use of a trigonometric table, , ()" (p 46). I hope we can at least agree that Muroi's approach is clearly anachronistic, as the concept of angle and circular functions had not developed at this time. Wildberger's approach is more of a proper follow-up because it is not anachronistic. — Preceding unsigned comment added by (talk) 11:36, 10 September 2017 (UTC)
"Avoiding anachronism" is not a specific novel contribution. So yet again you have avoided answering my question. —David Eppstein (talk) 17:48, 11 September 2017 (UTC)
Building a non-anachronistic trigonometric interpretation is the novel contribution. — Preceding unsigned comment added by (talk) 21:08, 11 September 2017 (UTC)
Perhaps you could explain how Muroi is more of a proper follow-up than M&W? — Preceding unsigned comment added by (talk) 23:53, 11 September 2017 (UTC)
Why? I'm not pushing to cite Muroi in our article, only using that pub as evidence that some other claims used to push Wildberger (that he's the first to seriously consider the trigonometric hypothesis) are clearly false. So there's no point in defending Muroi against a charge that is both original research and irrelevant to the inclusion of Wildberger. —David Eppstein (talk) 01:28, 12 September 2017 (UTC)
I think we agree that Muroi should not be cited, as this is clearly anachronistic and so can not be a serious consideration of trigonometry. To your knowledge, are there any non-anachronistic explanations of how Plimpton 322 might be interpreted as a trigonometric table? — Preceding unsigned comment added by (talk) 02:47, 12 September 2017 (UTC)
I don't think it's for us to judge who is being anachronistic and who not. That way lies WP:OR. —David Eppstein (talk) 05:10, 12 September 2017 (UTC)
In that case, which peer-reviewed articles show that Plimpton 322 is a trigonometric table as de Solla Price suggested? Muroi, regardless of anachronism or peer-review status, does not suggest this since his article is about angles and trigonometric functions, not exact ratios. — Preceding unsigned comment added by (talk) 11:51, 12 September 2017 (UTC)
Nobody shows this; they all suggest it but without any convincing evidence. Wildberger doesn't even try to guess how such a table might have been used. So anyway, authors mentioning the trigonometric hypothesis include de Solla Price, Knuth (apparently, I haven't checked this one), Buck, Muroi, and now Wildberger. And your explanation for discounting Muroi comes out as word salad; what does the mention of exact ratios (an idea present in plenty of earlier works) have to do with the use of this as a trig table? Especially when the supposed use of trig tables involves approximation via linear interpolation? —David Eppstein (talk) 16:19, 12 September 2017 (UTC)
So nobody has previously developed de Solla Price's suggestion that it might be a trig table of exact ratios. A proper follow-up of this suggestion would necessarily involve exact ratios. Muroi does not, hence Muroi does not constitute a proper follow up of de Solla Price as you suggested earlier. As for the supposed use of the trig table, that is a separate question from the original discussion, and one that I would be happy to debate in a separate section should you wish to create one. Returning to the original question: the trigonometric interpretation had not been developed before, which I believe is justified because neither of us can find a peer-reviewed article which lays out a trigonometric interpretation of Plimpton 322, either in the modern anglular sense or as per de Solla Price's suggestion. Furthermore, I do not believe it is WP:OR to say there can be no reputable source for the modern angular trigonometric interpretation. This point has been made quite clear by Robson, if it was not clear before. — Preceding unsigned comment added by (talk) 22:13, 12 September 2017 (UTC)

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)

That's not actually true. This source, for instance, cites Buck, Robson, and Friberg as the go-to sources for this material. (The Friberg publication that they cite is more recent than Robson, and we don't currently cite Friberg here; we probably should, if only to make clear that Robson is not the last word on the subject. I haven't done anything about that omission yet myself because, as explained elsewhere on this talk, I don't seem to have easy EEng 02:32, 23 September 2017 (UTC)accessb to the part of Friberg's book that discusses Plimpton 322.) —David Eppstein (talk) 01:18, 23 September 2017 (UTC)
David Eppstein: I'll email it to you tomorrow. EEng 02:32, 23 September 2017 (UTC)
Oops, I see the problem. Well, I can scan the hardcopy if you want, but not for a few weeks likely. Let me know if you want that. EEng 16:06, 23 September 2017 (UTC)

Request for more balanced discussion of Mansfield and Wildberger[edit]

The current discussion of the recent article lacks balance.

  1. The claim by individual editors that this is a fringe theory must stop. According to WP:FRIND this determination should be made by independent reliable sources. Comments such as "Norman Wilderberg should ring a few alarm bells" and "So the part that's original is also the part that's the most fringy?" are predetermined personal opinions, or at best WP:OR. In either case they do not belong here.
  2. Independent reliable sources have described the Mansfield and Wildberger article as "possible but speculative", see the academic quotations in [1] and [2]. This is a significant change in academic opinion regarding the trigonometric interpretation, which as has shifted from "completely anachronistic" to "possible but speculative". This change in thinking has been disregarded as criticism by faint praise, and that comment is a personal opinion which dismisses the words of the independent reliable sources.
  3. The article [3] is published in a peer-reviewed academic journal specialized in this history of mathematics, and so is a WP:RS according to the guidelines. Robson's article, published in the same journal, is another WP:RS, and so is the article by Britton, Proust and Shnider. [4]. Yet only Robson's interpretation is presented. There are at competing interpretations here, and presenting only one conflicts with WP:BALANCE.

Daniel.mansfield (talk) 03:21, 13 September 2017 (UTC) Daniel Mansfield Daniel.mansfield (talkcontribs) has made few or no other edits outside this topic.


  1. ^ Chang, Kenneth (August 29, 2017). "Hints of Trigonometry on a 3,700-Year-Old Babylonian Tablet". New York Times. 
  2. ^ Cowen, Ron (August 24, 2017). "This ancient Babylonian tablet may contain the first evidence of trigonometry". Science News. 
  3. ^ Mansfield, Daniel; Wildberger, Norman. "Plimpton 322 is Babylonian exact sexagesimal trigonometry". Historia Mathematica. doi:10.1016/ 
  4. ^ Britton, John; Proust, Christine; Shnider, Steve. "Plimpton 322: a review and a different perspective". Archive for History of Exact Sciences. 65 (5): 519–566. doi:10.1007/s00407-011-0083-4. 
I note that you are new here so you may not be familiar with our policies on WP:RS. It is important that reliability of a source is not a binary thing: a source may be reliable for one type of claim but unreliable for another. So in evaluating reliability, you need to ask "reliable for what claim"? The NY Times, and other mainstream journalists, are very reliable for basic factual claims like "Mansfield and Wildberger published a paper". They are not reliable for evaluation of academic research. Basically, journalists have no expertise in this area and are too easily taken in by hype; all they can do is repeat what the subjects of their stories claim. We need other academics with expertise in this specific subject area to weigh in. The best we have so far (and that not so reliable either) is the Lamb Scientific American blog. Lamb has apparently taught this material before, but hasn't published in this area, and it's a blog, so it's also not likely usable as a reliable source. I also note that you have a username that matches one of the authors of this study. If you are the same Daniel Mansfield, you should not be promoting your own theories here; see WP:COI. If you are a different person who is merely using that name as a fan of Mansfield, you need to change your user name before you are blocked for impersonation; see WP:UPOL. —David Eppstein (talk) 04:03, 13 September 2017 (UTC)
I was talking about academic quotations referenced in the newspaper articles: Alexander Jones, Christine Proust and Mathieu Ossendrijver. Not the journalists. I am one of the authors, but I have no intention of editing the article to push my theory. I recognize that it is a very new and different theory that, in the best case scenario will take a years to develop (I will nonetheless declare my connection in the comments as per WP:COI). I decided to write something on the talk page because the talk appears to have gone in a direction which is inconsistent the wiki guidelines. Also the page does not cite Britton et. al., which I feel it should. Daniel.mansfield (talk) 04:41, 13 September 2017 (UTC) Daniel Mansfield
Ok, maybe you can answer the question that the IPs keep failing to answer. You say it is "very new and different". What, specifically, is new? —David Eppstein (talk) 05:04, 13 September 2017 (UTC)
What I think is new is irrelevant. It's really up to the academic community to decide what aspects are new and worthwhile. So far, the only aspect that I think meets the WP:INDEPENDENT criteria for inclusion in Wikipedia is that the article makes a trigonometric interpretation possible. This is new and different because prior to this article the idea of Plmipton 322 being trigonometry of any kind was dismissed entirely by the academic community.[1]. If the academic community decides there are other worthwhile aspects of the article, then they can be included. If the academic community decides that the article is complete rubbish, then that can be included too. I expect it will take years before there is enough research to form a consensus that the trigonometric interpretation is any more or less than a possibility. But right now the important contribution of the article is to bring the trigonometric interpretation out of extinction and into the realm of what is considered possible by independent WP:RS. Daniel.mansfield (talk) 06:18, 13 September 2017 (UTC) Daniel Mansfield


  1. ^ Robson, Eleanor (2001). "Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322". Historia Mathematica. 28: 182. 
I actually agree with most of the above comment. We (by which I mean WP editors) should not be determining what is new and important in a recently published paper, this is a job for the academic community and we only report on what they say on the matter. By the same token, we are not obligated to report on every theory that makes it onto the pages of a respected academic journal (we should not second guess the editorial decisions to publish or not, the process that leads to that is not perfect). When the academic community has passed judgement then that can be reported on. As this takes time to develop, I am of the opinion that we should not even mention new publications for a while (not all editors will agree with me on that point, but I believe that my position is in the correct spirit of Wikipedia policies).--Bill Cherowitzo (talk) 17:06, 13 September 2017 (UTC)
That seems like a reasonable standard, and would also give a better reason than the ones advanced so far for omitting Muroi. We probably should say something about Britton et al and Friburg, though — Friburg has been out for a while and is reasonably well cited, while Britton et al are more of a review (secondary source) than a new synthesis (primary source). —David Eppstein (talk) 18:04, 13 September 2017 (UTC)
Presumably the editor/s and perhaps also the referees of Historia Mathematica determined there was something sufficiently new and important in this paper to merit publication, therefore it should be mentioned. I'd suggest some sort of tag on neutrality or balance at the top of the article to alert readers. 9and50swans — Preceding unsigned comment added by (talk) 05:48, 14 September 2017 (UTC)
Many readers are coming to this page looking for information relating to M and W's article and finding none. They may be puzzled but I imagine most will go away thinking that M and W have been accepted and that the page has not been updated. It would be much more informative if M and W are mentioned along with some initial scholarly reactions from RS, including Robson's tweets from NYT, then readers would be aware that M and W have not met with immediate universal acceptance. If you don't want the public at large to make wrong assumptions then not mentioning them may NOT be the best way to acheive this. 9and50swans — Preceding unsigned comment added by (talk) 13:39, 14 September 2017 (UTC)
It's become a scandal that this article doesn't include mention of Mansfield and Wildberger's work, when it's appeared in the leading journal in the field and has been a huge international story in the New York Times and many other organs. It's not for followers of an alternative interpretation of the tablet to censor information so that Wikipedia readers can't read about something significant. Jimmaths (talk) 08:02, 15 September 2017 (UTC)
What strikes me as new is the statement at the top of p.5 of the Mansfield and Wildberger article: "Each of the 15 values of l_n have the form 2^a x 3^b x 5^c ... this guarantees that the quantities delta_n and their squares ... can be written as finite sequences of sexagesimal digits without approximation." When working with the primitive form of trigonometry that employs ratios of side lengths of right triangles, providing exact values for the ratios is possible only when writing them as fractions or as terminating "decimals" in some place numeration system. MW note that the first entry in each row of the table provides the square of a ratio, and the entry minus 1 provides the square of another such ratio, as the first column heading essentially points out. The new idea is that the denominators of these ratios seem chosen so that these ratios are "terminating sexagesimals", hence can be provided exactly (as opposed to, say, sine of 1 degree in a modern table, which does not have a terminating decimal and must be truncated, making the value only an approximation). MW then give some examples demonstrating how much more accurate results can be obtained for certain ancient computational problems using Plimpton 322 as a table in place of a much more modern table that rounds its entries to eight decimal digits. Regardless of whether triginometry was its original use, the examples demonstrate that it would be, for its time, a very powerful tool if it had been employed for this purpose.Barryriedsmith (talk) 21:19, 11 October 2017 (UTC)
You appear to have been taken in by the hype. The idea that restricting attention regular numbers allows fractional values to be represented exactly, without non-terminating fractional parts (decimal is the wrong word, as this is all in sexagesimal) is extremely standard in the study of Babylonian mathematics; see e.g. Aasboe 1965, JSTOR 1359089. And the idea that this table provides the values of certain special trigonometric functions that can be represented exactly was stated explicitly by de Solla Price 1964. —David Eppstein (talk) 21:38, 11 October 2017 (UTC)
"You appear to be taken in by the hype." Watch your tone. I was taken in by the article, which I read in full in August and found to be, for the most part, quite a charming read. See my commentary above from August. If you actually read my comment, you would see that I used the word "sexagesimal", rendering your condescending remark impotent. *Of course* it is ancient knowledge that regular denominators provide "terminating sexagesimals", just as reduced rationals with denominators that have the form 2^a x 5^b are those with terminating decimals -- I never suggested that in itself is new. Unfortunately, I don't have access to the de Solla Price article, but I'll request it now through my ILL. Did de Solla Price, like MW, give examples that demonstrate the power of the table when used as a tool when calculating with similar triangles, i.e., a convincing argument that it could serve as such a tool? I find this situation analagous to when someone idly speculates about a specific method ancient peoples could have used to sharpen tools. Above, we find references to a bunch of "trig table speculators", and the MW contribution is then analogous to when someone goes and actually tries the method "in the world" and demonstrates its viability.Barryriedsmith (talk) 22:49, 11 October 2017 (UTC)

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 (talk) 08:09, 15 September 2017 (UTC)

This discussion is not about censorship, it is about standards. I don't see why we should be lowering ours to include this article because it has engendered media hype. If the media hype is making this paper notable then it deserves its own page. I could support that, after all, how many academic articles come with publicity releases? What I can not support is its inclusion on this page about Plimpton 322 without having the academic community addressing its relevance to the topic. This is an encyclopedia and we must maintain the standards of reliability that that entails. --Bill Cherowitzo (talk) 17:53, 15 September 2017 (UTC)
One possibility of a page on Norman Wildberger. Currently, this is a redirect to the rational trigonometry page. I suspect there is enough material there to make a notable page. On that page his work and his work with collaborators could be discussed in more depth. In such a page the paper would not suffer from problems of undue weight as it does here.--Salix alba (talk): 20:11, 15 September 2017 (UTC)
Maybe, but see Wikipedia:Articles for deletion/Norman J. Wildberger. —David Eppstein (talk) 20:18, 15 September 2017 (UTC)
It only engendered 'media hype' because it was published in prestigiuous journal. The referees of that journal are part of the academic community and it is clearly relevant to the topic. 9and50swans (talk) 21:01, 15 September 2017 (UTC)
The claim that the hype follows from the journal is far-fetched, when one considers the lack of hype for the many other papers published by the same journal. As Lamb describes, hype was generated by the authors sending out press releases and videos making claims far beyond what the actual article can support including what she calls "outright falsehoods". Unfortunately, as we have seen in other past cases, our news media have lost all ability to discern the accuracy of the material they present, and instead present this sort of thing based on whether they think it makes a compelling story rather than based on whether there is any actual scientific contribution. We don't have to sink to that level here. —David Eppstein (talk) 21:45, 15 September 2017 (UTC)
Daniel.mansfield, I'd like to help clarify something. Among editors "fringe" is a very broad term. "Fringe" just means there are currently very few Reliable Sources that currently publish a particular view. It covers everything from ghost-hunters to a real cure for cancer which has not yet been confirmed by anyone else. If someone discovers a cure for cancer, Wikipedia isn't the place to publish it. We cover it after it has been confirmed by other experts. We can't (and don't) cover every new idea published in a journal by every scientist or researcher. Right now it appears that the best that can be said of the ideas in this paper is that some have called it "possible but speculative", while others have rejected it. As you note, it will take time to sort this out. Wikipedia doesn't lead on new ideas, we follow after the ideas have gained acceptance by others. If there is followup work by others in the field developing or echoing the ideas, that establishes weight for inclusion. Hopefully the explanations were helpful. Alsee (talk) 20:30, 21 September 2017 (UTC)
Alsee, thanks, your explanation is helpful. Can I ask that the statement "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" be modified? New readers will see this as referring to my article when it actually refers to Buck. Daniel.mansfield (talk) 03:51, 22 September 2017 (UTC)
Daniel.mansfield, I changed the sentence.[8] Assuming no one else reverts my edit, I think it solves your concerns. Does that look good? Alsee (talk) 04:42, 22 September 2017 (UTC)
Alsee, looks great. Better than I could have done. Daniel.mansfield (talk) 11:49, 25 September 2017 (UTC)
It certainly removes an inaccuracy from the lead. I think that recent trigonometrical interpretations should also get a mention, even if brief, in the body of the text. Nine-and-fifty swans (talk) 10:01, 22 September 2017 (UTC)
I added a small sentence with link to M and W in the body of the article. Readers can place this in the context of rational trig. Robson still gets an overwhelming amount of space. I hope this can satisfy everyone Nine-and-fifty swans (talk) 10:37, 22 September 2017 (UTC)

'unbalanced' template[edit]

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)

To put the dispute succinctly, some editors are focused on the wrong end of the Wikipedia article, and want to choose references based on publicity rather than on article content. —David Eppstein (talk) 21:38, 15 September 2017 (UTC)
I have restored the template. The conditions for its removal have not been met.

>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)

You may restore your template when you can plausibly dispute the consensus that sources can only be added to source content. So far, your approach has been a content-free one of "we must add this source because it got publicity". The RFC you started has so far roundly rejected that point of view, so there remains no current dispute to support that tag. —David Eppstein (talk) 21:48, 15 September 2017 (UTC)
By what authority do you tell me that I may restore the template? Are you the owner of this page? I don't understand the last part of your first sentence. My approach is that we should add M and W, and Britton et al. because they were published in prestigious academic journals. If the claims were published only in popular media I would't press to include them. The RFC has not attracted any outside comments, to my knowledge, but there quite clearly other editors who agree with me. I'll not risk getting into edit-warring by restoring the template, but I think this is now getting to the point when an administrator should take note. Perhaps you could tell me, and any administrator, which of the above three points for you to remove the template? — Preceding unsigned comment added by 9and50swans (talkcontribs) 22:00, 15 September 2017 (UTC)
"because they were published in prestigious academic journals" is a stupid reason for adding a source. We should only add sources when there is something in the article for them to source. —David Eppstein (talk) 01:28, 16 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)

There is a fourth, unstated reason to remove this template and that is that it should never have been put up in the first place. The guidelines for removal assume good faith on the part of the editor placing the template on the page. However, when placing the template is a tactic being used in a content dispute with an ongoing talk page discussion, this assumption of good faith is a bit shaky. WP:UNDUE does not require that all points of view be represented, and in fact says that when a POV is held by a very small population, it should not appear. I am not claiming that this last is true here, but I would need some convincing that it is not true.--Bill Cherowitzo (talk) 22:58, 15 September 2017 (UTC)
Would David Eppstein and Bill Cherowitzo support a request for outside intervention on this matter?9and50swans (talk) 05:01, 16 September 2017 (UTC)

'citation needed' tag in lead[edit]

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)

(1) The lead of an article is supposed to be a summary of the rest of the article. It should not need citations unless claims are made there which are not expanded on in the rest of the article (which should not happen). See MOS:LEAD.
well there are citations there
(2) Are you disputing that past researchers considered the trigonometric interpretation, and trying to claim instead that it is brand new? Because that's what it looks like you're trying to claim, and it is not justified by any plausible reading of the literature.

'in the past' implies they are not doing it in the present.

(3) You have been WP:BLUDGEONing this article and its talk page with your repeated demands to add a new source, and your increasingly-contorted justifications for it. How about you take a break from it and find something more constructive to apply your editing energy to? —David Eppstein (talk) 06:11, 16 September 2017 (UTC)
I have already asked for comment and would be delighted to get an uninvolved adminstrator to comment on this as per the advice on the page of bludgeoning and will attempt to do so. I placed the citation needed tag, Another editor removed it referring me to talk but there was nothing there so I restored it until the comment comes. I think I'm up to my 3 reverts, I hope I haven't unwittingly exceeded them, if so I must accept the consequences. 9and50swans (talk) 06:24, 16 September 2017 (UTC)
Further to the above I have placed a notice regarding this on the Administrators' Notice Board, 'Plimpton 322 - accusation of bludgeoning'. I don't feel I have been bludgeoning and will continue to engage in polite and reasoned discussion here if I feel it is being constructive. 9and50swans (talk) 06:36, 16 September 2017 (UTC)
I agree. 70K of going around in circles is not bludgeoning. It's only bludgeoning when it gets to 100K. EEng 17:47, 16 September 2017 (UTC)

Neutral Point of view dispute[edit]

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)

As long as you are quoting WP:NPOV you might as well have a look at these aspects of that policy: WP:UNDUE, WP:BALASP and WP:VALID. You have a minority viewpoint that is gaining no traction here and this is getting to be quite tiresome. You have done everything except throw the kitchensink at this and I am just waiting for that to appear! --Bill Cherowitzo (talk) 20:45, 18 September 2017 (UTC) This pillar of wikipedia cannot be superseded by editor consensus. It cannot be superseded by other policies or guidelines. You do not respond to the pillar I quote but just tell me to look at other policies. 9and50swans (talk) 21:14, 18 September 2017 (UTC)
Those are not separate policies, they are part of NPOV. Had you bothered to try to read and understand that policy you should have noticed that. --Bill Cherowitzo (talk) 22:02, 18 September 2017 (UTC)
Neutrality requires that each article or other page in the mainspace fairly represent all significant viewpoints that have been published by reliable sources, in proportion to the prominence of each viewpoint in the published, reliable sources.[3] Giving due weight and avoiding giving undue weight means that articles should not give minority views or aspects as much of or as detailed a description as more widely held views or widely supported aspects.

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)

You already tried this at ANI and got nowhere. You need to drop this. EEng 20:31, 18 September 2017 (UTC)
The fact that I got nowhere in my view reflects badly on wikipedia's administration. You are breaching the instructions on the template in removing it. 9and50swans (talk) 21:09, 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 administration" is 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. —PaleoNeonate – 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)

Incidentally, where is this idea that Historia Mathematica is extraordinarily prestigious coming from? Its Scimago Journal Ranking report [9] ranks it currently as second-quartile among history journals and fourth-quartile among miscellaneous mathematical topics journals. It may well be the top journal devoted purely to the history of mathematics, but with so few to choose from [10] that's not a high bar to clear, and if one widens the scope only a little it looks like it's very similar in impact to Centaurus and a little worse than Archive for History of Exact Sciences. —David Eppstein (talk) 22:10, 18 September 2017 (UTC)
I would think that being the top journal devoted purely to the history of mathematics is an excellent reason for mentioning M and W here. 9and50swans (talk) 22:34, 18 September 2017 (UTC)
See Overwhelming exception. —David Eppstein (talk) 23:26, 18 September 2017 (UTC)
Mercifully Overwhelming exception is not a wikipedia policy, as yet. 9and50swans (talk) 04:01, 19 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)

In response to EEng on NPOV noticeboard. M and W should be mentioned in the lead to show that the Trigonometrical interpretations of the tablet are not simply in the past, but current. They should be mentioned in the body of the article and their interpretation should be related to Norman Wildberger's Rational Trigonometry (considered notable enough to have a wikipedia article) with links. This would assist any reader coming to the article from media mention of M and W having some context. Mentioning it need not imply either approval or disapproval of M and W's views but would certainly give the reader some context. 9and50swans (talk) 03:57, 19 September 2017 (UTC)
Specify the actual text you would propose adding (to the article proper, not the lead -- the question of whether any mention belongs in the lead we can deal with later). EEng 04:07, 19 September 2017 (UTC)
You have only recently joined this discussion, I think the type of changes would be apparent to those following for longer. I intend to do so at the weekend. Now I have a plane to catch. 9and50swans (talk) 04:21, 19 September 2017 (UTC)
Yes, but I didn't only recently learn to read. You've been going on and on about this without ever proposing actual text. After your plane lands you'll need a new excuse. EEng 04:35, 19 September 2017 (UTC)
The focus on a specific source itself, rather than article content, is a problem here. Any "significant view" must be present in multiple Reliable Sources, therefore NPOV can't be used to push any particular source. Alsee (talk) 19:57, 21 September 2017 (UTC)
Actually, that's not true. You're confusing notability (essentially, whether a subject should have its own article) with article content -- see WP:NCC. EEng 03:56, 22 September 2017 (UTC)
I intended "significant view" in terms of due weight and fringe. If there's only one source saying something, it's an overreach to say NPOV mandates that it MUST be included. Alsee (talk) 04:15, 22 September 2017 (UTC)
Oh, I agree with 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. EEng 05:05, 22 September 2017 (UTC)
Precisely. This is why I have been asking for context of the proposed theory or suggested wording for any inclusion; that it has been published in Historia Mathematica does not tell us how we write it into an article about the tablet and its interpretations. We are not simply listing all of the interpretations in a bullet-point list, but writing an integrated article in prose. This therefore requires any content to be fluent by providing context, and in cases like this where content's inclusion is disputed, it is generally recommended that proposed wording is discussed on the talk page to assist with building consensus. This is our next step. — Sasuke Sarutobi (talk) 09:55, 22 September 2017 (UTC)

Chronological attribution mess[edit]

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)

Buck also cites de Solla Price (Centaurus 1964), while only listing Voils as to appear (as of Buck's 1980 publication date). Neither Google scholar nor MathSciNet finds anything relevant by anyone named D. Voils. De Solla Price writes:
In a way, [Plimpton 322] may be likened (though not precisely) to the tabulation, for those suitable angles, of those special trigonometric functions taking convenient rational values. Thus, on a purely arithmetical basis there is erected a “trigonometric” corpus that could be used for practical mensuration, or more probably for the setting out of series of practice problems in mensuration, all of which would be capable of exact numerical solution.
In a way it's just a difference of nomenclature — the idea that these entries described Pythagorean triangles goes back to Bruins (1949), and the trigonometric functions are defined as ratios of sides and hypotenuse lengths of right triangles, so whether you call them "side lengths and hypotenuse lengths of Pythagorean triangles" or "numerators and denominators of rational trigonometric functions" is a matter of interpretation and conjectured usage, not of the actual mathematical content of the tables. —David Eppstein (talk) 20:20, 20 September 2017 (UTC)
Offtopic wisecrack. Uncollapse to enjoy (or not)
practical mensuration – Do we have to drag bodily functions into everything? EEng 21:55, 20 September 2017 (UTC)
I'm at least glad you didn't choose to illustrate that one. —David Eppstein (talk) 22:36, 20 September 2017 (UTC)
Practical mensuration
What a crackerjack idea! Honestly, I don't know why I didn't think of it before. See right. EEng 00:00, 21 September 2017 (UTC)
Consider the first comment on this talk page. It seems plausible to me and sounds like it was written by someone who actually knew D. Voils. Robson (ha, I finally spelled it right) gives a nod to Neugebauer & Sachs (1945), in a throw away line of their paper, as the probable source of the trigonometric interpretation (1981, p. 179).--Bill Cherowitzo (talk) 22:43, 20 September 2017 (UTC)
Since "Babilonogists" are a small circle, I have little doubt that the opinion of Voils was known by word of mouth. Whether Voils himself published anything or not, this opinion *was* published in a reliable source, hence must be credited in wikipedia, for priority. (This does not diminish the work of Robson, of course.) Staszek Lem (talk) 23:02, 20 September 2017 (UTC)

Joran Friberg's 1981 article[edit]

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)

This article is very incomplete[edit]

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)

Conflict of interest[edit]

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)

Publishing in a similar area is not a COI. Being the author of a paper that we are debating the inclusion of (as appears to be true for at least one participant above) is, however, a COI. —David Eppstein (talk) 14:23, 23 October 2017 (UTC)
Any external relationship can trigger a conflict of interest, and the author was very open about it, only requested comments (see his username). As mentioned above there is a COI when removing reliable sourced studies as someone who is also publishing in a similar area. It might even conflict or contradict with other authors conclusions. Thus, if these authors remove conflicting studies, there is apparent a COI. prokaryotes (talk) 15:36, 23 October 2017 (UTC)
As your ranting about COI seems to have started after a comment of mine, it appears that you are directing this at me. Let me repeat, perhaps in clearer terms ... I have absolutely no conflict of interest here. My papers in geometry concern structures in finite projective geometries and this has no relationship with Euclidean geometry or trigonometry whatsoever. I do not personally know the authors of this paper or any of their critics. Your charges of COI, if directed against me, are totally baseless and are figments of your imagination. I should remind you that making false accusations against someone in print is called libel and is frowned upon both here in Wikipedia and in the world at large. --Bill Cherowitzo (talk) 17:52, 23 October 2017 (UTC)
I ask you to stop misrepresenting what I actually wrote. prokaryotes (talk) 18:14, 23 October 2017 (UTC)
Since you brought up your comments, there are many comments above critical of your participation in the discussion, including concerning WP:OWN. Or your statement from August 25, "There is no reason why Wildberger's interpretation should be smeared across several of our pages as if this was something to be taken seriously - Bill Cherowitzo" prokaryotes (talk) 18:21, 23 October 2017 (UTC)
Since I did not claim that you said anything, it is hard to see how I could have misrepresented you. Your bringing up my use of "our" and interpreting it to mean that I was claiming ownership is just as silly now as it was when it was originally mentioned; any native English speaker can tell that that doesn't make any sense in this context. It would also seem that if I express an opinion, different from yours, as I have above, then I have a conflict of interest. Hmmm! Very interesting definition of COI. --Bill Cherowitzo (talk) 19:47, 23 October 2017 (UTC)
Why don't you comment below in regards to the commentary published by Science. Those seem to be a reliable secondary source, even you and Eppstein have to acknowledge. Is there any formula under which you would agree to mention MW in article space? This discussion will resurface again and again and again, because other authors will respond to it at one point. prokaryotes (talk) 19:53, 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 (talk) 23:00, 23 October 2017 (UTC)

Please comment here prokaryotes (talk) 23:04, 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)

Resolving article scope[edit]

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)

We have recently had a closed RFC whose consensus was not to include MW. What has changed since then that leads you to try to revive the issue? —David Eppstein (talk) 17:07, 23 October 2017 (UTC)
I think the interpretation is possible - Alexander R. Jones, director of the Institute for the Study of the Ancient World at New York University
I don’t see anything blatantly wrong with the theory - Evelyn Lamb is a freelance math and science writer based in Salt Lake City, Utah
Eleanor Robson, a Mesopotamia expert now at University College London who proposed the idea of the tablet as a teacher’s guide, is not convinced.
What’s still lacking is proof that the Babylonians did in fact use this table, or others like it, for solving problems in the manner suggested in the new paper, Ossendrijver says
The Babylonians “knew NOTHING about ratios of sides!” he wrote in an email to Science. He maintains that P322 is “a table of parameters needed for the composition of school texts and, (only) incidentally, a table of right triangles with whole numbers as sides.”
If the new interpretation is right, P322 would not only contain the earliest evidence of trigonometry, but it would also represent an exact form of the mathematical discipline, rather than the approximations that estimated numerical values for sines and cosines provide, notes Mathieu Ossendrijver, a historian of ancient science at Humboldt University in Berlin
Mathematical historian Christine Proust of the French National Center for Scientific Research in Paris, an expert on the tablet, calls the team’s hypothesis “a very seductive idea.” But she points out that no known Babylonian texts suggest that the tablet was used to solve or understand right triangles. The hypothesis is “mathematically robust, but for the time being, it is highly speculative,”
  • There is enough discussion to make it notable.prokaryotes (talk) 17:35, 23 October 2017 (UTC)
    • What part of since then did you not read? Which of these links occurred subsequently to the RFC? They all appear to be dated back in August. —David Eppstein (talk) 19:00, 23 October 2017 (UTC)
Comments present expert opinions not recently discussed, particular the commentary in Science. prokaryotes (talk) 19:09, 23 October 2017 (UTC)
I didn't think it was possible to lower my opinion of the mathematics coverage in Science but this link has done it. Indistinguishable from the most credulous of the mainstream news candidates. But why did you feel the need to puff it up so that it looked like four different sources in your listing above? —David Eppstein (talk) 20:09, 23 October 2017 (UTC)
And the amount of cherry-picking in the first three entries is almost amusing. How did you manage to find the nine nice words that Lamb has to say in her blog that lambastes this paper? --Bill Cherowitzo (talk) 20:18, 23 October 2017 (UTC)
I understand that you both prefer to only propose the established view. And this could be made more clear (sub-section headings) However, Science is an authority as is Historia Mathematica, if you do not recognize this you apparently create a violation in WP:NPOV. Hence, the article should read along the lines of, "MW proposed a merged theory ... However, it has been criticized, lacking proof that Babylonians actually used it that way." prokaryotes (talk) 20:50, 23 October 2017 (UTC)
Eppstein, Lambs commentary while interesting has less weight than from experts actually studying Plimpton. prokaryotes (talk) 20:58, 23 October 2017 (UTC)
That doesn't explain your quadrupling of a source that is not Lamb. And for that matter, we have already discussed Lamb; why are you even bringing her up again at all? —David Eppstein (talk) 22:03, 23 October 2017 (UTC)

Let the dead horse rest in peace.. at least for a while[edit]

I took some reading of the "news" about WM and made two conclusions for myself:

  • One: Vast majority of "science editors" and "science writers" are quite illiterate in maths: Just read this
    • " Because 60 is far easier to divide by three, experts studying the tablet, found that the calculations are far more accurate." mathematical gobbledygook ,
    • " the world’s oldest and most accurate trigonometric table", -- factual bullshit - the table has errors. Even wikipedia article says so.
    • "The new research shows the Babylonians, not the Greeks, were the first to study trigonometry" - attribution bullshit or "fake news": "Babilonians not Greeks" news is not "new research" at all
  • Two: Nearly all of them seem to be based in the press release circulated by WM.


  • Vast majority of sources are far from what we in wikipedia call "independent reliable sources"
  • Vast majority of sources are orchestrated promotional hype.

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)

To any new editors interested in resurrecting the horse (Mansfield and Wildberger)[edit]

The editors who have taken the lead in blocking any mention of Mansfield and Wildberger's rational trig paper in a leading journal were editing this page before that article is published and I think it is reasonable to conclude that they don't agree with its findings. Some new editors have come along and expressed surprise that M and W don't get a mention but haven't got involved. I did get involved and opened a Request for Comment which was subsequently closed - I was one against several - and when another more experienced editor Prokaryotes tried to open another RFC this was denied. It's quite possible that other potential editors who have heard of M and W's thesis will come to the wiki article and be surprised they are not mentioned and turn to the talk page. If any should read this and think M and W should be mentioned please state so here and add this page to your watchlist, in future there may be a majority for mentioning them.Nine-and-fifty swans (talk) 16:34, 27 October 2017 (UTC)

I commented yesterday, but it's way up the page, so I'm restating it here. I would support adding the "exact trig table" interpretation to the page, since it is no less speculative than some other theories and has been around since at least the 1960's -- see the quote from de Solla Price included in my comment above. I do not see that it is necessary to use MW as the source here -- de Solla Price may be the first and has also been around long enough for sufficient vetting.Barryriedsmith (talk) 17:41, 27 October 2017 (UTC)
I have no particular objection to adding something about this sourced to de Solla Price. It's crediting old ideas to the new paper that I object to. —David Eppstein (talk) 18:06, 27 October 2017 (UTC)
[COI warning] I'm also happy with crediting de Solla Price. But I expect there will be disagreement on the phrasing. Friberg (1981) calls this statement on the intention of the tablet a conjecture, twice (p 287 and 288). Friberg goes on to interpret this conjecture without any reference to trigonometry. So while I'm happy that de Solla Price should be credited with the conjecture, historically the conjecture has not been interpreted in this way. Daniel.mansfield (talk) 23:29, 29 October 2017 (UTC)
Exactly. There are now twenty threads on this page, starting a mere six weeks ago, beating this dead horse. EEng 18:15, 27 October 2017 (UTC)
I'd agree to Barryriedsmith's suggestion. If we can agree on an exact trig reference that is great progress, every type of approach should be traced back to its source, ie the person who originated it. Nine-and-fifty swans (talk) 19:33, 27 October 2017 (UTC) de Solla Price is mentioned several times in MW. If MW are to be mentioned they should be mentioned in context of the history of trignometrical interpretations. The article as it stands at present gives the impression that Robson's interpretation has displaced all others, which is not the case. Leaving aside the question of whether MW contribute anything new their paper is significant for showing the persistence of the trignometrical interpretation. BTW I haven't seen their press release, only the article, which as far as I read it didn't strike me as 'hype' apart perhaps from the very direct titleNine-and-fifty swans (talk) 20:49, 27 October 2017 (UTC)