Talk:Möbius strip/GA1

GA Review
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Reviewer: Mover of molehills (talk · contribs) 17:10, 28 March 2022 (UTC)

I'll start working on this review soon! It may take me slightly longer than a week, but I'm excited to look at this one.

I'll order the review by the Good Article Criteria:

Well-written
Following is a list of changes I would recommend making for overall clarity. Please feel free to debate with me if you don't think any of these changes would improve the article - I don't have that much expertise with topology, so I might be wrong in some of these places.

Lede

 * Second sentence: for more specifity, could you change "but its appearance in Roman mosaics long predates their work" to "but it has appeared in Roman mosaics as far back as INSERT YEAR"? Mover of molehills (talk) 17:30, 28 March 2022 (UTC)
 * Ok, done. —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * Thank you! Small nitpick for clarity: could you say "it had already appeared... since" instead of "it already appeared... from"? Mover of molehills (talk) 21:15, 28 March 2022 (UTC)
 * Ok. —David Eppstein (talk) 22:41, 28 March 2022 (UTC)
 * Strangely, I still don't see the changes - have you made them yet? Mover of molehills (talk) 22:47, 28 March 2022 (UTC)
 * Special:Diff/1079845424. I changed the tense, but I did not change "from" to "since". The mosaics were from the 3rd century. It would be incorrect grammar to say that the mosaics were since the 3rd century. —David Eppstein (talk) 01:38, 29 March 2022 (UTC)
 * I see, I think I phrased that poorly. The revision I was suggesting was something along the lines of "but it has been featured in Roman mosaics since the third century AD." I understand that this is a very minor change, but I feel like it reads better on my end. Does this work for you? Mover of molehills (talk) 12:40, 29 March 2022 (UTC)
 * But the Roman mosaics that the references discuss were ONLY from the third century. This does not appear to have been a continuing practice from then until now, which your wording would make it seem. —David Eppstein (talk) 16:16, 29 March 2022 (UTC)
 * How is the strip's "embedding in three-dimensional space" any different from the three-dimensional strip itself? Specifically, could you cut this clause to tighten the sentence without sacrificing any meaning?
 * No, it would make it incorrect. It's explained in the "properties" section. The strip itself is a two-dimensional topological surface, with multiple embeddings into three-dimensional spaces (for instance, twisting it three times or knotting it makes it different from one time as an embedding, but the same as a topological surface). In three-dimensional Euclidean space it is always one-sided, no matter how it is embedded, but it has other embeddings in other three-dimensional spaces that are two-sided. This sentence of the lead is intended as a summary of the more detailed explanation later. —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * Got it, thank you for letting me know. Mover of molehills (talk) 21:15, 28 March 2022 (UTC)
 * It would be useful to include a brief one-sentence definition of what "non-orientable" means ("it is the simplest non-orientable surface, meaning that...") Mover of molehills (talk) 17:30, 28 March 2022 (UTC)
 * Ok, I added a little more here. —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * What you have is helpful. However, do you think you could replace/add to this with something a little bit more conceptual (like "meaning that ideas of "clockwise" and "counterclockwise" are not well-defined on it")? What I'm really looking to do is explain what this means to the reader. Mover of molehills (talk) 21:23, 28 March 2022 (UTC)
 * Ok, changed to a lead gloss involving inability to define clockwise, and added more detail in this same interpretation in the later "Properties" section so that the lead would continue to summarize the rest of the article. —David Eppstein (talk) 04:51, 29 March 2022 (UTC)
 * This is exactly what I was talking about, thank you. The lede already looks much better. Mover of molehills (talk) 12:38, 29 March 2022 (UTC)
 * The second paragraph goes into a little bit too much detail into all of the specific ways to create a Möbius strip. I would simplify this part to "There are many geometrical ways to generate a Möbius strip, and a physical model can be created by twisting a strip of paper and gluing together the opposite ends." (This could replace everything up to "an embedded Möbius strip can be stretched"). Mover of molehills (talk) 17:30, 28 March 2022 (UTC)
 * Again, see MOS:LEAD, one of the core requirements of WP:GACR. The lead is supposed to provide a brief summary of the entire rest of the article. The specific ways of constructing the Möbius strip occupy a section of the article with six subsections, averaging roughly three paragraphs and many illustrations each. It is a large fraction of the total article. It seems reasonable to me that summarizing this material properly is worth a whole paragraph, and that each of the subsections deserves at least a sentence (although in fact there are fewer sentences in this summary paragraph than subsections). —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * Okay, I think that we can leave the detail as is for now. Mover of molehills (talk) 21:18, 28 March 2022 (UTC)
 * The section about all the different variations on the Mobius strip could use a sentence of introduction. Specifically, I would preface the sentence "An embedded Möbius strip..." with the sentence "Mathematicians have explored many different variations on the basic Möbius strip, all of which have slightly different properties." Mover of molehills (talk) 18:53, 28 March 2022 (UTC)
 * What, you don't think the sentence "Many different ways of forming geometric structures with the topology of a Möbius strip are known. " already serves this purpose? —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * It does serve the same purpose, I was just trying to reword it so it could be clearer. Do you agree with the rephrasing? Mover of molehills (talk) 21:18, 28 March 2022 (UTC)
 * To me your rewording is vaguer not clearer. It replaces a sentence that contrasts geometry with topology (the point of the section) with inaccurate "variations on the basic": they are not really variations (they are all Möbius strips) and I don't understand which one is called basic and which ones variations. Also "all of which have slightly different properties" doesn't convey any useful information to me: if they are different from each other, of course their properties are different, and "slightly" appears meaningless here. But more to the point, it suggests that the "variations" came first, and then people investigated how they might differ from each other in the properties they had. Really, what came first are the additional properties that mathematicians hoped nice surfaces might have (ruled, polyhedral, developable, curvature-free, etc), and then they found constructions of Möbius strips with those properties. I rewrote the whole paragraph in an attempt to make this point clearer. —David Eppstein (talk) 01:45, 29 March 2022 (UTC)


 * For brevity, I would replace "the same circular boundary shape" with "this same shape." Mover of molehills (talk) 18:53, 28 March 2022 (UTC)
 * In your proposed replacement, does "this same shape" refer to the circular boundary or to the shape of the entire Sudanese Möbius strip? It is unclear, in a way that we should try to avoid. —David Eppstein (talk) 20:52, 28 March 2022 (UTC)
 * That's fair. Maybe you could just say "circular boundary" instead of "circular boundary shape"? Mover of molehills (talk) 21:12, 28 March 2022 (UTC)
 * Ok. I took the opportunity to rearrange the prose to be a little tighter here. —David Eppstein (talk) 22:43, 28 March 2022 (UTC)
 * That's great, thank you. My last comment would be that it's confusing to mention a cross-cap without defining what it is, so I would say "another version, the self-intersecting cross-cap..." Mover of molehills (talk) 22:46, 28 March 2022 (UTC)
 * I almost think that it would be worth cutting out the whole chunk of words "has realizations... and its points" (second-to-last sentence of second paragraph). The sentence seems to flow better without it, and I feel once again like this is a level of detail not appropriate for the lede (it would make a lot of sense to move the info into a "variations" section or subsection later if you want to). Mover of molehills (talk) 18:53, 28 March 2022 (UTC)
 * So you want to completely omit the subsection "Surfaces of constant curvature" from being summarized in any way in the lead? —David Eppstein (talk) 20:52, 28 March 2022 (UTC)

Thank you for moving through this first round of edits. I apologize if my cuts sometimes feel too draconian, and I agree with a lot of the counterarguments you have made. My main goal here is to get a lede that can be understood fairly well by the average person, because I think that Möbius strips are a topic which is potentially of interest to people with non-mathematical backgrounds. This doesn't mean that you shouldn't go into the more technical details later, I'm just trying to make the opening of the article easier to read while still summarizing the article's contents. Mover of molehills (talk) 21:25, 28 March 2022 (UTC)


 * I definitely agree that this part of the article should, as much as possible, be readable by non-mathematicians. There is some unavoidable technicality later, but this is a widely-known enough topic that we cannot reasonably expect all readers to be mathematicians. —David Eppstein (talk) 22:44, 28 March 2022 (UTC)

More feedback:
 * I like the sentence about applications of the Möbius strip, but the part about the world map is a little bit confusing. Could you phrase that as "so that points on opposite sides of the earth appear on opposite sides of the strip"? Mover of molehills (talk) 22:50, 28 March 2022 (UTC)
 * But the strip only has one side. What are its opposite sides? Instead I tried rewriting it as "opposite each other", without talking about sides. —David Eppstein (talk) 05:37, 29 March 2022 (UTC)
 * "Möbius strips appear in molecules..." What does this mean? Are there actually molecules with a Möbius-strip geometry? Mover of molehills (talk) 22:50, 28 March 2022 (UTC)
 * Yes. Most obviously in graphene, which naturally has a two-dimensional structure that can be formed into twisted ribbons. I tried looking on commons for molecular diagrams that we could use to illustrate this point but didn't find any. —David Eppstein (talk) 05:42, 29 March 2022 (UTC)
 * I'm kind of confused by the final sentence of the lede, where it describes stories with "events that repeat with a twist." This feels like conflating a topological twist with the word "twist" as a plot device. Do you have a reference for this idea, or could you rephrase it? Mover of molehills (talk) 22:53, 28 March 2022 (UTC)
 * This is supposed to summarize the paragraph about fictional Möbius strips, which cites a reference for exactly this conflation of ideas. It appears to be a fairly common metaphor in literary analysis. Our article for of the pieces of fiction linked in that paragraph, Lost in the Funhouse, suggests that at least in that case it was deliberately written with the Möbius strip metaphor in mind, and that this idea was incorporated into its typography. —David Eppstein (talk) 02:03, 29 March 2022 (UTC)

History

 * For simplicity, would it be possible to replace "lemniscate-shaped" with "figure eight"? Mover of molehills (talk) 14:48, 29 March 2022 (UTC)
 * Ok. —David Eppstein (talk) 18:42, 29 March 2022 (UTC)
 * Similar edit: could you change "annuli" to "simple rings"? I know that "annuli" carries a slightly more precise meaning, but I think that the History section is one that should be accessible to the general reader, and the repeated use of longer words like this makes it a much denser read. Mover of molehills (talk) 14:48, 29 March 2022 (UTC)
 * "Simple ring" may be less confusing for non-mathematicians, but it is much much more confusing for mathematicians. The reason is that "simple ring" is the kind of phrasing used for technical jargon in mathematics, compound terms with a specific meaning that you have to know if you want to understand sentences that use them. So a mathematician is either going to want to know "what exactly is a ring? what property of a ring makes it simple? where is this defined?" or is going to already know a meaning of "simple ring" and plug that meaning in. But the only standard meaning of the term "simple ring" is something totally unrelated from algebra. Instead, I used "untwisted ring". —David Eppstein (talk) 18:42, 29 March 2022 (UTC)
 * I think "untwisted ring" is a good compromise, thanks. Mover of molehills (talk) 19:21, 29 March 2022 (UTC)
 * There are a few parts throughout this section where it feels like a lot of the sentences are run-ons. I would recommend breaking them up differently, while preserving the same content and wording, so that they read better:
 * Suggested rephrasing: "In particular, Roman mosaics have contained images of coiled ribbons since the third century AD. These ribbons can be either Möbius strips or simple rings, depending on whether the number of coils is odd or even, and the existence of odd ones may be purely coincidental."
 * Suggested rephrasing: "Independently of the mathematical tradition, machinists have long known that mechanical belts wear half as quickly when they form Möbius strips. By using both sides (or rather the single continuous side) of the strip at once, the Möbius shape also evens out any curvature that may develop in the belt."
 * I copyedited the paragraph with some attention to avoiding overlong sentences. I didn't use your specific wording, though. —David Eppstein (talk) 18:42, 29 March 2022 (UTC)


 * Grammar nitpick: Change "Much older, an image of a chain pump... depicts" to "Much earlier, an image of a chain pump... depicted." Mover of molehills (talk) 14:48, 29 March 2022 (UTC)
 * Ok. —David Eppstein (talk) 18:42, 29 March 2022 (UTC)
 * Change "without clear dates for the origin of this task" to "it is unknown when this practice began." Mover of molehills (talk) 14:48, 29 March 2022 (UTC)
 * That's a stronger assertion and would need a better source. The source for this part of the article does not identify a date. It does not, however, state that the date was unknown. The date is unknown to me, because it is not stated in the source. But I am unsure whether the date is unknown to historians of this practice, or merely unstated in the source I used. —David Eppstein (talk) 18:42, 29 March 2022 (UTC)
 * Other than that, this section is overall very clear! Mover of molehills (talk) 14:48, 29 March 2022 (UTC)

Verdict

 * Symbol_oppose_vote.svg Not promoted. I'm sorry to jump to this section so early in the review, but it seems so far that improvements on this article have been pretty difficult. I still think that it has the potential to become a GA in the future, but it will need some work, and your comments make it seem like it will take a good deal of time to make the wording of this article more clear without sacrificing mathematical precision. In the meantime, I encourage you to focus on making the wording simpler in sections that are of interest to a general reader, and also to add a bit more information (and maybe a new section) on the properties of geometry on the surface of the strip (as opposed to hyperbolic and Euclidean geometry). Thank you for submitting to GAN! Mover of molehills (talk) 15:31, 30 March 2022 (UTC)
 * WTF WTF was that? It was progressing through minor copyedits and then suddenly complete shutdown for no reason? Can you please point to ANYTHING in the article, anything at all, that is actually far from any of the GACR criteria, before I escalate this serious miscarriage of a review to higher levels? If it's merely that you feel incapable of actually completing the review, because it's going to be too much work (it can be a lot of work), then failing the article is the wrong way to back out. It is punishing me and my efforts for a choice to review that was entirely your responsibility. —David Eppstein (talk) 16:05, 30 March 2022 (UTC)
 * I'm sorry if this feels abrupt to you, but I didn't feel like you were cooperating with some very reasonable edits to improve the wording of the piece and make it more accessible to the average reader. Right now, this piece does not meet the GA criteria because many parts of it are not very well-written, too dense for an average reader to understand, and because the article's scope is missing a good deal of information and additional sections about the properties of geometry on a Mobius strip's surface. After progressing through a few rounds of edits, I just decided that I think there is too much work left to go on the article for it to become a GA right now.
 * I certainly can't stop you from reporting me to "higher levels," but I think that this is a grossly unfair response to the situation. Given the kind of language that you have used in response to my constructive criticism of the article, I suspect that you may not like the outcome of an admin decision. Mover of molehills (talk) 16:09, 30 March 2022 (UTC)
 * Ok, ecalating. This failure is an atrocity and I cannot accept your behavior in it. You cannot fail an article on a technical topic merely because it has technical parts. —David Eppstein (talk) 16:11, 30 March 2022 (UTC)

I hope this GA review will go ahead, and succeed. I have a couple of suggestions:
 * 1) From the first paragraph of the lead: "Its embedding in three-dimensional Euclidean space has only one side". Seems to me, it intrinsically has only one side, regardless of embedding. And this correction would avoid the term "embedding" with its implications not known by many readers.
 * 2) *As I already stated somewhere above, this intuition is incorrect. This is a very common misconception, so it is important to counter it. This sentence of the lead is intended as a summary of the first paragraph of the "properties" section, which goes into some detail about how embeddings of the Möbius strip in other 3d spaces than the familiar Euclidean space may actually be two-sided, in exactly the same way that a sheet of paper in Euclidean space is two-sided. (According to one of the sources for this material,, it's also possible to find spaces in which a torus can be one-sided, something I find even more counterintuitive, but that's one reason we prove things in mathematics: to distinguish correct implications from intuitions that seem natural but turn out to be false.) —David Eppstein (talk) 21:30, 30 March 2022 (UTC)
 * Thank you for convincing me that my intuition is was broken. Yes, I can embed a closed curve in real 2-space so as to be two-sided, and in projective 2-space so as to be one-sided. Maproom (talk) 07:20, 31 March 2022 (UTC)


 * 1) Same paragraph: "one on which it is impossible to consistently distinguish clockwise from counterclockwise". I prefer "one in which", though it'll sound odd to many readers (we've disagreed on this before). You can draw little ↻ symbols consistently all over its surface, if you use a pencil. If you use a pen whose ink soaks into the fabric, of course you can't. Maproom (talk) 21:06, 30 March 2022 (UTC)
 * Ok, that reasoning makes sense to me. Done. I hadn't realized there was a unicode for ↻! Maybe it would be helpful to use that symbol in the text. —David Eppstein (talk) 21:30, 30 March 2022 (UTC)