Talk:Mathematics and art/GA3

GA Review
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Reviewer: David Eppstein (talk · contribs) 05:02, 27 October 2015 (UTC)

First review of new nomination
I reviewed an earlier version of this article (Talk:Mathematics and art/GA2) and found significant issues with GA criterion 3 (broadness of coverage), but the new article has been so heavily revised that there is nothing worth repeating from the previous review. So better to treat this as an entirely new nomination.


 * Many thanks for taking this on. I'll get to it as soon as I can. Chiswick Chap (talk) 08:43, 27 October 2015 (UTC)

General assessment of GA criteria

 * 1a, prose quality
 * On the whole the prose is good but I found some points where the writing could be improved, detailed below.


 * 1b, MOS compliance
 * Lead section: unsourced and with four paragraphs as is normal for a lead. The grouping into paragraphs makes sense and all material here is treated in more detail later on.
 * Layout, words to watch, fiction, and list incorporation: no issues found.


 * 2a, references are presented and styled appropriately
 * Yes. The article uses the common footnote style and separates out notes (additional text giving a tangential remark from the main text) from references to source works; I think this is appropriate and well formatted. References appear to generally be consistently formatted in Citation Style 1 (the one produced by the cite templates). I do have detailed remarks on two of the notes below.


 * 2b, references are reliable
 * Mostly, but with some apparent exceptions detailed below.


 * 2c, no original research
 * None that I noticed.


 * 3a, addresses the main aspects of the topic
 * Yes; this is a big improvement from my previous review.


 * 3b, stays focused without going into unnecessary detail
 * Mostly, but some parts of the article look like a catalog of detail rather than a focus on the big picture. Maybe that is inevitable for this subject.


 * 4, neutral
 * Yes, as far as I can see.


 * 5, stable
 * There have been a lot of edits even since the nomination but I think they've slowed down and are fixing more minor issues now. None of the suggestions below require major change to the article.


 * 6a, images are tagged with copyright status and have valid fair use rationales
 * Most images are on commons, most are out of copyright, and the remainder appear to have valid free-use copyrights. A few of the images are on Wikipedia rather than commons but most are public domain or freely licensed and are candidates to move to commons.
 * An exception is File:Objet mathematique by Man Ray.jpg, listed with a fair use rationale. This image is discussed in detail in the article, and its rationale appears valid. Similarly, File:René Magritte The Human Condition.jpg, File:Print Gallery by M. C. Escher.jpg, and File:Max Ernst making Lissajous Figures 1942.jpg also have detailed descriptions in the text and valid-looking fair use rationales
 * However, File:Escher Circle Limit III.jpg requires a fair use rationale, doesn't have an adequate one, and would seem to be difficult to justify, because it is used only to illustrate the concepts of tessellation and hyperbolic geometry in art and other freely licensed illustrations of the same combination of concepts would seem possible.
 * Image Circle Limit III removed. Chiswick Chap (talk) 08:46, 27 October 2015 (UTC)
 * For File:Dali Crucifixion hypercube.jpg the description in-text and the rationale are both weak, however I think both can be strengthened (as discussed below).


 * 6b, relevance and captioning of images
 * For the most part this is good; I'm not a big fan of articles filled with many big image galleries but for this article in particular I think the relevance of each of the images can be justified, and the gallery formatting is necessary to fit them all in.
 * I have a couple minor issues with captions detailed below.

Lead

 * "The construction of models of mathematical objects for research or teaching has led repeatedly to artwork, sometimes by mathematicians such as Magnus Wenninger who creates colourful stellated polyhedra.": I found this segue from general to specific to be unnecessarily awkward. It doesn't help introduce the additional specific examples in the following sentences.
 * Reworded. Chiswick Chap (talk) 14:36, 27 October 2015 (UTC)


 * "algorithimic": sp.
 * Done. Chiswick Chap (talk) 14:36, 27 October 2015 (UTC)


 * "use of the golden ratio in ancient times": maybe more specifically "use of the golden ratio in ancient art and architecture"?
 * Good idea, one. Chiswick Chap (talk) 14:36, 27 October 2015 (UTC)


 * Since the previous sentence is specifically about the golden ratio, maybe the sentence about Pacioli should be more specific: "on the use of the golden ratio in art" rather than "on the use of proportion in art"?
 * Done. Chiswick Chap (talk) 14:36, 27 October 2015 (UTC)


 * Is there a source for the catalog of mathematical references in the image caption?
 * Added. Chiswick Chap (talk) 17:02, 27 October 2015 (UTC)


 * In what way are cellular automata examples of recursion or logical paradox? And why is the Mandelbrot set listed as a separate thing from fractals?
 * Split sentences and reworded. Chiswick Chap (talk) 14:36, 27 October 2015 (UTC)

Polykleitos

 * "he is better known for his approach towards sculpture": this reads ambiguously. Does it mean that Polykleitos is more famous than Phidias (contradicting the earlier part of the sentence) or that Polykleitos' theoretical work is more famous than Phidias's. Did Phidias even have any surviving theoretical work?
 * Reworded. Chiswick Chap (talk) 16:54, 27 October 2015 (UTC)


 * I think the paragraphs could be better reordered context-mathematics-influence rather than the current context-influence-mathematics ordering. It is difficult to make sense of what it means for others to follow his prescriptions when we don't yet know what the prescriptions are.
 * Done. Chiswick Chap (talk) 16:54, 27 October 2015 (UTC)


 * Since Polykleitos's mathematics is heavily based on the square root of 2, a link to our article on the square root of 2 might make sense somewhere in here.
 * Done. Chiswick Chap (talk) 10:44, 27 October 2015 (UTC)

Perspective

 * I think the very beginning of this section is a little abrupt. It may not be obvious to the reader what sizing by importance implies about the appearance of an image. Can you somewhere in that sentence contrast this approach with the later perspective approach, with a bit of an explanation of how they differ? Also somewhere in here (while we're mentioning non-perspective approaches to object sizing) it might be worth mentioning reverse perspective.
 * Done. Chiswick Chap (talk) 10:42, 27 October 2015 (UTC)


 * Is there a contradiction between the first paragraph's claim that these ideas were reborn in the Renaissance and the second paragraph's claim that they began with Giotto in the late middle ages?
 * Fixed. Chiswick Chap (talk) 10:42, 27 October 2015 (UTC)


 * The material about Piero della Francesca seems unbalanced for the paragraph it is in, and maybe worth splitting off into a separate paragraph entirely about della Francesca.
 * Done. Chiswick Chap (talk) 10:42, 27 October 2015 (UTC)

Golden ratio

 * "doubtful mathematical grounds": is doubtful really the right word here? It means either filled with doubt or not known with certainty. I think the grounds on which the arguments were made are known, they are just not very solid. Would "dubious" be better?
 * Done. Chiswick Chap (talk) 10:37, 27 October 2015 (UTC)


 * Could note [c] be moved into the main text? Otherwise it leaves the claim of the golden ratio in Laon to be stated as valid, without any visible refutation.
 * Done. Chiswick Chap (talk) 10:37, 27 October 2015 (UTC)


 * This is more an aside than part of the review, but it's unfortunate for the proponents of the golden ratio in ancient architecture that star forts came into vogue so late. Because when the floor plan is based on a regular pentagon, there are undeniably instances of the golden ratio in it...
 * Indeed. Though not perhaps intentionally golden. Chiswick Chap (talk) 10:37, 27 October 2015 (UTC)

Planar symmetries

 * This section reads a bit too much like a litany of examples without any theme. The connection to mathematics is at times tenuous.
 * Added a lead to summarize theme in the 4 artforms; 1 para per artform; refs. Chiswick Chap (talk) 17:06, 27 October 2015 (UTC)

Polyhedra

 * I wonder whether the material about Dali's Corpus Hypercubus might fit better here than in the sacred geometry section? Or both? The point is both that the hypercube is a four-dimensional regular polyhedron and that what Dali actually depicts is an unfolded three-dimensional net for it, the higher-dimensional version of the unfoldings that this section describes for three-dimensional polyhedra in connection with Dürer. On the other hand Dali's idea that four dimensions represents the divine perspective might better fit in the other section. And of course Dali is well post-Renaissance.
 * Yes. I think it may be best where it is, and I've also mentioned it here as you suggest. Chiswick Chap (talk) 17:12, 27 October 2015 (UTC)


 * Maybe it would be worth mentioning that there are two mathematical subjects in Melancolia that have been the subject of detailed later analysis: the shape of the polyhedron and the properties and construction of the magic square. I think all the references you have are about the polyhedron, though.
 * Done, and used the Ziegler Guardian ref. Chiswick Chap (talk) 17:10, 27 October 2015 (UTC)


 * For sourcing about the Dürer solid, I think Ziegler's Guardian article might be worth using as a source, since it sums up a lot of the earlier academic debate on the subject.
 * Added. Chiswick Chap (talk) 17:00, 27 October 2015 (UTC)


 * The Leonardo image caption seems to cut off the name of the shape: I see it as "rhombicuboctahed". Probably this is because the image is too small so the caption is restricted to a region too narrow to show the whole word.
 * Guess so, the full name is there. Image enlarged. Chiswick Chap (talk) 08:48, 27 October 2015 (UTC)


 * The icosahedron is only a part of the monument, there is also a statue of Spinoza next to it.DFK2021 (talk) 12:09, 1 November 2021 (UTC)

Mathematical tools for art

 * "artists who choose a strict representation": unclear what this means.
 * Removed. Chiswick Chap (talk) 17:22, 27 October 2015 (UTC)


 * Re the camera obscura: is this really a mathematical tool? Is a modern camera a mathematical tool? Does this belong here or in the perspective section, as one of the possible forces driving Renaissance artists to mathematical perspective?
 * Moved. Chiswick Chap (talk) 17:22, 27 October 2015 (UTC)

From mathematics to art

 * Was Sugimoto really a follower of Ernst? I thought he was more directly inspired by Man Ray. The link given as source only mentions Man Ray but doesn't state it clearly. I happen to have a copy of the Sigimoto exhibit catalog which on page 5 includes a quote from Sugimoto: "In the spring of 2002, I paid a call to Professor Toshitake Kohno at the University of Tokyo's Graduate School of Mathematical Sciences to see the university's collection of plaster mathematical models, all made in Germany at the end of the nineteenth century and imported to Japan as teaching aids. The beauty of these pure mathematical forms was a wonder to behold, far outshining abstract sculpture. I experrienced a déjà vu. Where had I seen them before? Then I remembered: Man Ray's nineteen-thirties series of photographs of mathematical models cast in plaster from similar molds, which I had come across in a vintage photo gallery in Paris. Whereupon I realized the mathematical forms as I perceived them differed from how Man Ray had pictured them. It was a dare – and I accepted the challenge."
 * Said Man Ray. Chiswick Chap (talk) 17:33, 27 October 2015 (UTC)


 * "He used his photograph of the artwork as one of the figures in his 1934 painting Antony and Cleopatra, one of a series he did on Shakespeare's plays.": In fact all of this series of paintings are based on these earlier photographs of mathematical models.
 * Thanks, reworded. Chiswick Chap (talk) 17:33, 27 October 2015 (UTC)


 * What is a "geometrical objects that cannot exist"? What Escher's impossible objects actually depict is not "an object that cannot exist", whatever that might be, but a contradiction between perspective projection and three dimensions: they show things that look like they should be projective drawings, but for which there is no three-dimensional geometry that produces that perspective. As an aside, it is actually computationally infeasible (NP-hard) to tell whether a line drawing is possible or impossible in this sense; if you're interested I can dig up references.
 * Reworded; and yes please on the ref(s). Chiswick Chap (talk) 08:51, 27 October 2015 (UTC)


 * In what sense is Stewart Coffin a mathematician? And I think (but am not sure) that George Hart was an artist before he became an academic. I'd also mention Carlo H. Séquin but he's more a computer scientist than a mathematician...
 * Said "inspired a variety of mathematical artworks", rather than insisting they were all by mathematicians. Chiswick Chap (talk) 17:33, 27 October 2015 (UTC)


 * There's a lot more to the mathematics of paper folding than modular origami. See for instance Maekawa's theorem, Kawasaki's theorem, and Huzita–Hatori axioms.
 * Thanks, wikilinked and reffed. Chiswick Chap (talk) 17:43, 27 October 2015 (UTC)


 * Much of the last paragraph of this section seems borrowed from or duplicative of Mathematics and fiber arts. Shouldn't there at least be a link to that article in the paragraph?
 * Done. Chiswick Chap (talk) 08:53, 27 October 2015 (UTC)


 * The reference at the start of note [e] (in the caption of the Jouffret image) is a little awkward. Why not put the reference before the note, in the caption?
 * Done. Chiswick Chap (talk) 17:43, 27 October 2015 (UTC)

Stimuli to mathematical research

 * Do you have more than one example to include here? Otherwise it hardly seems worth a whole section.
 * I hear this, but the theory of perspective was such a massive contribution, and so interesting an exception to the general flow of ideas from math to art, that a section seems well-deserved. But there is another example: origami. I've moved it into this section. Chiswick Chap (talk) 09:15, 28 October 2015 (UTC)

Summary
I think this is close to ready but with some issues that could use cleanup before passing. —David Eppstein (talk) 07:39, 27 October 2015 (UTC)
 * Thanks. I've responded to all of the comments. Chiswick Chap (talk) 20:41, 27 October 2015 (UTC)

Second pass
Almost everything seems to have been done now. I found only one more very minor issue:
 * "The influence of the Canon of Polykleitos is immense both in [three things]": both is the wrong word.
 * Removed. Chiswick Chap (talk) 08:00, 30 October 2015 (UTC)

Most changes were relatively minor. One that was less minor, the Symmetry section reorganization, has made that section much better.
 * Thank you. Chiswick Chap (talk) 08:00, 30 October 2015 (UTC)

Re the references on difficulty of distinguishing valid line drawings from impossible figures: the original source is

There's also a more recent survey of the same topic in

—David Eppstein (talk) 06:07, 30 October 2015 (UTC)
 * Added. Many thanks for the review. Chiswick Chap (talk) 08:00, 30 October 2015 (UTC)

Third pass (pass)
Ok, I think this can be passed now without any more revisions. —David Eppstein (talk) 22:50, 30 October 2015 (UTC)