Talk:Ostomachion

Am I missing something?

In trying to see how many ways the 14 irregular pieces could be put together to make a square, it now appears that Archimedes anticipated aspects of combinatorics.

I am sorry, but I fail to see how this follows from the translated text provided in the article. Where does it say Archimedes was specifically trying to see how many ways the square can be constructed? And did he get a result, or even a constraint on the result? -- Cimon Avaro; on a pogostick. (talk) 11:39, 13 December 2007 (UTC)

I seem to recall seeing something in print saying he actually got a particular very large number. Maybe you're missing something simply because no one's inserted what you're missing into the article, and should have. I'll see if I can find anything. Michael Hardy (talk) 20:18, 13 December 2007 (UTC)

One of the links provided at the bottom of the article makes oblique reference to some palimpsest or another having words that are suggestive of the combinatorics angle to the original text, but the whole thing seems very conjectural indeed. Very little actual text from archimedes himself is spelled out in that. Mostly it appears that the guy "recreated" archimedes thought processes based on vague clues in the palimpsest, without providing clear connection to the text. It may be that that abstract merely fails to mention the specific textual bits, or that there are none. I don't know. But the linked to abstract is far from conclusive in my view. -- Cimon Avaro; on a pogostick. (talk) 07:19, 14 December 2007 (UTC)

---

Some info currently at Archimedes#Surviving works... AnonMoos (talk) 11:08, 30 July 2009 (UTC)

Original research tag

Several unstated presumptions to obtain the number 17,152, the most troubling being that we reach for a Stomachion board proposed in a questionable translation of another text which does not match the Archimedes Codex. It is unclear where Dr. Netz ever comes to grips with this problem.

Unfortunately the source you are using is not reliable in this case precisely because of tacit assumptions. To be reliable in combinatorial mathematics you have to state the assumptions. The point about turning over pieces simply was not mentioned. The numbers 64 and 4 which you have now edited out were obtained by Bill Cutler who did the original research back in 2003. Somehow, they have just never been mentioned. But why not check with Bill Cutler at <billcutler@comcast.com>. If you really want to stick with Dr. Netz, you need to edit out the phrase about turning over pieces, because he never mentioned it explicitly. That is why the source is tendentious and so less than reliable.

I have taken the liberty of undoing your edit in good faith while accepting your edit itself was in good faith. The problem for you is that what got formally published in 2003 was selective: it left out qualifying phrases that make the published counts precise; and it left out the alternative counts, when the qualifying phrases do not apply. You will notice that later on it is mentioned that there are three other boxes for the Codex board, so there are at least six other counts. Bill Cutler has those worked out, too, but they are not yet in general circulation. Naturally, I am encouraging him to publish his entire suite of results. Then they can be inserted, too. But the 64 and 4 have been known for six or seven years.

As the saying goes, I don't make the rules around here. Wikipedia articles have to stick to what has been published and peer reviewed. The material added to Ostomachion is unsourced commentary, which is against guidelines. Other editors are justified in removing material of this kind. See also Wikipedia's guidelines on original research.--♦IanMacM♦ ^{(talk to me)} 20:15, 17 June 2010 (UTC)

That is your problem or rather the problem for Wikipedia, which is why I flagged the matter for you in the first place. I am grateful to you for your speedy response, as that will surely encourage others to pay closer, more critical attention. As you will see, attribition of combinatorial counts to Bill Cutler has now been included in the body of the text, while external links that allow readers to inspect the works of Suter, Gow and Ball have been added. Notice that the published materials are largely silent on these sources, while mention of Oldham has only recently been included in the website of Chung (and Graham); Gina Kolata's article in The New York Times in December, 2003 did not pick up on the backstory of Oldham's article there in August, 1926. But what is commentary? Is it commentary to observe that Sutter has a problem with his fn6: presumably he is thinking to tell us that the sides of the board are equal; instead he equates side and diagonal? Is it commentary to observe that Suter is making the false presumption that, if the pieces form a square, the board has to be a square, when perhaps the most celebrated and memorable scene from Greek mathematics is Socrates instruction of the slave boy in Plato's Meno? The entire published and peer-reviewed literature can fall into a trap like that. Fortunately in this case, Oldham rescued us from that trap in 1926. But you would hardly know that from published and peer-reviewed material this last decade or so, just as you would not know about Gow or Ball.

Might it not be useful to flag specific passages that are felt to need improvement or verfication, for example, by showing them in italics or red, so as to pinpoint more exactly where further work might usefully be done? What more do you want to see done on this entry?

The article needs more sourcing, as the "Mathematical problem" section still reads as a commentary. Any criticism of the work on the problem by Reviel Netz would need reliable sourcing. Could you look out some more sourcing in this area?--♦IanMacM♦ ^{(talk to me)} 08:10, 20 June 2010 (UTC)

From User talk:164.111.195.140: Archimedes Codex: Suter board vs. Codex board for Stomachion

The Archimedes Palimpsest is known to scholars as the Archimedes Codex. If you read the entry Stomachion, you will see that comparison is already made between the Arabic and the Greek texts. It is the Arabic text that is the more complete, so complete that Suter produced a board for the Stomachion, which, in turn, was taken over by Netz, seemingly without comment or critical reflection on Suter's translation, even although Netz was handling the Greek text, not the Arabic text. However, the Greek text, as established before Netz, and seemingly agreed by him, suggests that Archimedes was studying a double square, not a single square. That is why the Suter board has to be stretched by a factor of two to bring it into line with the figures implicit in the Codex; the unpointed Arabic text supports this reading, in that, as Suter allows elsewhere in his translation, equals and twice are easily confused. It should be understood that Suter gives no reason for making his board a square. Equally, Netz gives no reason for seemingly ignoring the diagrams implicit in the Greek text for Stomachion, although elsewhere in his study of the Codex he places great enphasis on the diagrams as especially faithful to Archimedes. To sum up, while the Arabic text is the more complete, the Greek text provides a check - and, indeed, a corrective. But Netz goes the other way.

From Usertalk: IanMacM: Stomachion: Netz-Acerbi-Wilson article in SCIAMVS 5

In this scholarly article Netz and his co-authors repeat what are essentially the figures for Stomachion that have been agreed since Heiberg first published on the Archimedes Codex. It is clear that they set up a double square, not a single square. Netz, in his popular account of the Codex with Noel, berates Heiberg for his neglect of figures. Netz also argues that we come as close as is likely to Archimedes' original figures in the Codex. It is therefore a complete mystery why Netz opts in that book for the Suter Board, rather than the Codex Board. The Suter Board is associated with an unpointed Arabic text and is most obviously inconsistent with the Greek text because the diagonals of a square cross at right angles, rendering the surviving propositions in the Greek text trivial if they referred to the Arabic text. Suter conceded elsewhere that twice and equals are easily confused and that seems to be the explanation of why the Suter Board is mistaken. Netz does not argue for the Suter Board, he just adopts it; this is also what he did in working with Diaconis, Graham and others. It was Oldham, in a letter to Nature in March, 1926, who pointed out the reconciliation of the two texts. But he did not go into the geometrical or linguistic objections to the Suter Board.

I do not know whether you have a serious interest in the matter. I also do not know what you can do about the Wikipedia articles touching on Archimedes and Stomachion under Wikipedia policies, since it is certainly true that Netz has published his ideas in a popular book. It is just that his own scholarly article undermines the book, which, being a popular work, was probably not, strictly speaking, peer reviewed.

However, if you are interested, and would like to be sent the relevant material for your own inspection, do please indicate how that might be arranged.

<http://en.wikipedia.org/w/index.php?title=User_talk:Ianmacm&oldid=463126884>

Exchange with Slashme and David Eppstein

Slashme, in August, 2012, deleted a passage from Ostomachion on the grounds that it missed the point, but did not indicate what the point missed might be. It is not clear, from his qualifications and expertise, whether Slashme has any special expertise in enumerative combinatorics. On the other hand, David Eppsten, who has also engaged recently in editing this entry, certainly does. So, I should like to remind both Users of the passage in question in seeking their consent to restoring the passage, perhaps with some further comment:

So, there are at least four different answers that we might give just considering Suter's proposal. Clearly, to count, you have to know what counts. When, as here, the number of outcomes is so sensitive to the assumptions made, it helps to state them explicitly. Put another way, combinatorics can help sharpen our awareness of tacit assumptions. If, say, answers like 4 or 64 are unacceptable for some reason, we have to re-examine our presumptions, possibly questioning whether Suter's pieces can be turned over in reforming their square. As emerges below, there is also some objection to Suter's proposal which would render this combinatorial discussion of the Suter board academic.

As it seems to me, the point the writer intends is that a problem in enumerative combinatorics has to be well-posed in order for it to be possible to answer it and that wide variation in potential answers is an indication that the problem has not been well posed. What is missing here is the further observation that Netz, in the referenced book with Noel, just jumps into his conjecture that Archimedes was doing high-level enumerative combinatorics leading to a large number, which is then confirmed by producing a suitable large number, but without any discussion of the underlying assumptions need to produce that large number. Two possible reasons for this reticence occur to me: (i) the writer wished to avoid being unduly adversarial; and (ii) the writer considered Netz' adoption of the (flawed) Suter Board, again without discussion why this Board is privileged over that emerging from the Archimedes Codex, a more serious obstacle.

So, I propose for your consideration and, as I hope, approval restoration of the deleted passage, with the further observation of how it relates to Ntezt' presentation in his book with Noel.

Now, also missing in the entry is discussion of Netz more scholarly discussion, jointly with Fabio Acerbi and N. G. Wilson, that came out in SCIAMVS in 2004:

• Towards a reconstruction of Archimedes' Stomachion, SCIAMVS, 5 (2004), 67-97.

The account here is decidely lower key than the earlier book and, if anything, supports the thrust of the Wiki entry in faulting the account in the book. In the first place, we see, not the Suter Board, but the outlines of a board that is two squares side by side, just as Hedberg had suggested (although in the book, Netz takes Hedberg to task for neglecting figures). Secondly, following the discussion in footnotes referring to Suter, the article recognises Suter's own admission of the provisional nature of his reconstruction (but not the typo in fn 6, where Suter has AD = DB, where presumably AD = AB is intended, not Suter's later conncession that, in the unpointed Arabic of his text, twice and equals are easily confused, not that Suter recognizes that this opens the possibility that the sides might be related as AD = 2AB, as seen in the Archimedes Codex). Thirdly, the authors have studied Hedberg and Suter sufficiently thoroughly to be able to say where Hedberg diverges from Suter. Fourthly, the authors even have reference to the note on Lucretius in 1956 by H. J. Rose from which they could have been led, by equally close reading, to Oldham's letter to Nature in 1926, although, particularly for a senior classicist, such as N. G. Wilson, Rose's standard Handbook of 1934, would be the more obvious source of acquaintance with Oldham's letter. For further reference here, we can consult Suter's article of 1899:

• Der Lochulus Archimedius ....

Comparison of book and paper does invite question about Netz' approach to scholarship? As it happens, an extended answer has been given by Netz' co-author, Fabio Acerbi, whose own work delving into Ancient Greek enumerative combinatorics seems, by Netz' own account, to have been an inspiration for Netz to emulate and equal.

• Archimedes and the Angel: Phantom Paths from Problems to Equations, Aestimatio, 2 (2005), 169--226; see esp. 178--179.

The pointis not even whether Netz' approach should be labeled as history of mathematics, or whether, more likely, he is inventing a new genre ... Netz' book simply raises problems of methods: ...

Netz' earlier showmanship in publicizing his conjecture on Archimedes' Stomachion, namely that it was an exercise in high-level enumerative combinatorics, was sprung on a less suspecting audience.

So, with all due respect to your expertise and judgement, I should also like to add these references.