Talk:Hawaiian earring

Correct?

The article states: "It has been shown that $G$ embeds into the inverse limit of the free groups with $n$ generators, $F_n$, where the map from $F_n$ to $F_{n+1}$ is just the one sending the generators of $F_n$ to the first n generators of $F_{n+1}$."

This cannot be correct, as in the inverse limit, there is not a map from $F_n$ to $F_{n+1}$ but rather from $F_{n+1}$ to $F_n$. Indeed, the direct limit given by the natural maps from $F_n$ to $F_{n+1}$ is merely the free group on countably infinitely many generators. — Preceding unsigned comment added by 128.252.164.170 (talk) 10:20, 21 April 2006

When comparing the Hawaiian earring to the infinite wedge of circles $H'$, the article claims that $H'$ " is the one-point compactification of a countable disjoint union of open intervals." This can't be true, since the infinite wedge of circles is not compact (taking the interior of each 1-cell and a small neighborhood of the point at which they meet gives an infinite open cover with no proper subcover). It seems that this has also caused confusion in the article on Quotient Spaces, which refers to R/Z as the Hawaiian earring. BarrySimington 16:02, 8 March 2007 (UTC)

Abelianization of the fundamental group

The article claims the fundamental group's abelianization "has no known simple description", but Katsuya Eda gives such a description on his home page. I just don't know what "Z-adic completion" means. Ntsimp (talk) 04:08, 8 June 2008 (UTC)

Copy

Does it seem strange that what one editor calls a copy of another editor's comment is not a duplication of what the first editor wrote? Hyacinth (talk) 20:52, 31 December 2017 (UTC)

Inline citations

Where does this article lack inline citations? What claims need citing? What kind of citations does the page need? Hyacinth (talk) 20:59, 31 December 2017 (UTC)

There aren't any inline citations in the article at all, just a list of "References". An inline citation is one where a footnote symbol (typically a number in brackets) is found next to the statement it is used to verify, and refers to a specific source found in the References section. They're standard on Wikipedia, but this article doesn't have any yet. Ntsimp (talk) 22:00, 31 December 2017 (UTC)

It is also standard to give an explanation on a talk page when one adds a tag to an article. Hyacinth (talk) 03:24, 9 September 2018 (UTC)

Last sentence of "Higher dimensions" section is problematic

The last sentence of the section Higher dimensions, is as follows:

"For $q\equiv 1{\bmod {(}}k-1)$ and $q>1,$ Barratt and Milnor have proved that the singular homology groups $H_{q}(\mathbb {H} _{k};\mathbb {Q} )$ are not zero and even uncountable."

It appears that one or more words is missing. I hope someone knowledgeable on this subject can fix it.50.205.142.50 (talk) 14:34, 12 May 2020 (UTC)

Why do you think there's a word missing? It's certainly possible, but there doesn't seem to be anything obviously wrong with it. –Deacon Vorbis (carbon • videos) 14:57, 12 May 2020 (UTC)

I just checked the reference, and this is almost exactly what B&M say: "The rational singular homology groups ... are not zero. In fact these groups are not even countable." Maybe the attempt to reword it has left it a bit awkward, but it's certainly correct. –Deacon Vorbis (carbon • videos) 15:10, 12 May 2020 (UTC)

To clarify, there was a logical issue with the original wording. The phrase "are not zero and even uncountable" can be interpreted as being either "are not zero and are not uncountable" or "are not zero but are countable". Dzackgarza (talk)

Requested move 20 June 2021

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: not moved. This is a highly participated RM with offsite encouragement and the risk of heated feelings between participants. The COMMONNAME argument clearly supports the current title, while the arguments in favour of moving were rarely based in policy and seem to have frequently been made based on offwiki discussion between parties with little policy understanding. Several oppose !votes brought up the possibility of consensus changing in the future, which is an interesting hypothetical outside the scope of present discussion; all I can say is that this close does not prejudice a move if COMMONNAME genuinely changes, but that none of the supports were able to demonstrate such while the opposition demonstrated the opposite. Arguments that could permit a move in the presence of an ambiguous COMMONNAME were not made with any sophistication that could permit their consideration, nor was a convincing case even made that the COMMONNAME was ambiguous in the first place. (closed by non-admin page mover) Vaticidalprophet 02:56, 28 June 2021 (UTC)

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Hawaiian earring → Infinite earring space – The use of "Hawaiian" in Hawaiian earring originated in the 1950's to identify this space as being "exotic." It has no apparent connection to Hawaiian mathematicians. This particular use of "Hawaiian earring" perpetuations the association of Hawaii and Hawaiian native culture with that which is exotic. This kind of association is no longer acceptable. Moreover, this usage is not universally used in mathematics and there is substantial momentum to do away with it. The term "Hawaiian" no longer has a place being the title term for this page. The title of this page should be changed to "Infinite earring" or "Infinite earring space" and all instances of Hawaiian, perhaps with an exception of a remark clarifying the evolution of the name, should be removed.

It is clear that the opposition has not attempted to actually parse mathematics references and has only conducted a quick internet search of the term "Hawaiian earring" which will obviously pull up the many references that do use this term. This space is called the "infinite earring" on Section 71 of James Munkres' book "Topology." This is the most commonly used textbook for teaching topology. This space is called the "shrinking wedge of circles" in Alan Hatcher's standard book "Algebraic topology." Some older texts use "clamshell." The term "Hawaiian earring" is indeed popular but is not standard.

Jtbrazas (talk) 18:10, 20 June 2021 (UTC)

— Jtbrazas (talk • contribs) has made few or no other edits outside this topic.

• Oppose: Despite the desire to WP:RIGHTGREATWRONGS here, as expressed in the unsourced commentary above by an WP:SPA with practically no edit history, the WP:COMMONNAME of this topic is very clearly "Hawaiian earring". Nearly all of the cited sources have "Hawaiian earring" in their titles, and a web search shows that "Hawaiian earring" is much more common than "Infinite earring space". There was no evidence given that "Infinite earring space" is used by anyone at all, although by searching I did find one 2015 blog article on the web that uses "Infinite earring" (without appending "space"). Inside that article, it says the subject is also known as "Hawaiian earring". —⁠ ⁠BarrelProof (talk) 19:51, 20 June 2021 (UTC)

Note: The second paragraph of the move proposal statement was added after I made the comment above. Before making that remark, I did web searches for both the current article name and the proposed article name. There were no exact hits for the proposed article name. —⁠ ⁠BarrelProof (talk) 20:22, 21 June 2021 (UTC)

• Strongly Support: In this instance, I don't think individual edit history is a material concern. I can attest that this discussion originated among working mathematicians, not all of whom have necessarily have an account or have edited a page on Wikipedia. I think that appealing to its usage in cited sources perhaps misses the point: its usage there is equally problematic and partially due to historical inertia. It's also extremely likely that its popular usage (as evidenced by web searches) is caused by the name of this page, which puts the page in the position of actively doing harm. Since Munkres and Hatcher are by far the standard modern references for this topic and neither use this term, it seems extremely reasonable to move/rename the page here and provide disambiguation as a first effort to fix/change this usage. – Dzackgarza (talk) 18:40, 21 June 2021 (UTC)

I think that appealing to its usage in cited sources perhaps misses the point: its usage there is equally problematic and partially due to historical inertia. Sorry, but this is totally antithetical to policy. "But the published sources are wrong. Trust me, I know better than them" is not an effective argument here, especially when "wrong" is being used in a deontological rather than factual sense. If you haven't already, I suggest reading the supplement linked above by BarrelProof at WP:RIGHTGREATWRONGS. Your last sentence is getting closer to a policy-based argument, but even if the current name isn't universally used in RS, you haven't made an argument for why the proposed name better satisfies WP:CRITERIA. Colin M (talk) 23:20, 21 June 2021 (UTC)

Worth noting here also that both Hatcher and Munkres use *different* terms for it. If they both used "infinite earing" that argument might have some validity. But they don't, so all they suggest is that there isn't a strong consensus, not that there's a consensus for some other specific term. JoshuaZ (talk) 14:04, 24 June 2021 (UTC)

• Strongly Support: Munkres is the standard reference, and Evelyn Lamb (whose blog post is mentioned by BarrelProof) is among the best-known current popularizers of research mathematics. Moreover, "infinite earring" is a clearer and more evocative description. – UrsulaGeorges (talk) 23:14, 21 June 2021 (UTC)
• Oppose With all due respect, this nomination evinces a fundamental misunderstanding of article title policy. That some editors find the name morally unacceptable is not a reason to move. By design, Wikipedia follows usage in reliable sources; it does not lead. That the standard text in Topology uses "Infinite earring" rather than "Hawaiian earring" is a useful input to this problem, but even if we assign some extra weight to Mukres as an apparently especially high-quality source, I'm still not seeing how the proposed title can be argued to be the WP:COMMONNAME. "Infinite earring" gets only 6 results on Google Scholar (they range from 2004 to 2017). "Hawaiian earring" gets 59 results since 2020 alone (482 results since 2004, the year of the earliest "Infinite earring" hit, and 614 results over all time). Colin M (talk) 23:35, 21 June 2021 (UTC)
• Support: As stated by others, Munkres is a standard, if not primary, Topology reference. The new suggested title fits several of the considerations for Title Critera While I am not an expert in Topology, if I were to investigate it, I would most likely run across Munkres's usage of "infinite earring space" and would be more familiar with that term. This satisfies both the Recognizability and Naturalness considerations of the Title Criteria. Per the Precision aspect, I would argue that "Infinite Earring Space" is far less ambiguous than "Hawaiian Earring," which users might rightfully search Wikipedia for, expecting jewelry. Amccarter (talk) 23:37, 21 June 2021 (UTC)
• Comment It looks like there is some canvassing happening on Twitter. If you've arrived here by following an off-wiki call to action, welcome, but please make sure you're acquainted with Wikipedia's policy on article titles, and keep in mind that Wikipedia operates on rough consensus, not democracy - the closer of this discussion will weigh the strength of policy-based arguments rather than counting heads. Colin M (talk) 00:30, 22 June 2021 (UTC)
• Oppose. "Hawaiian earring", not "infinite earring space" or any other alternative, is by far the most prevalent in the literature, e.g. as evidenced by Zentralblatt ([1], [2]) and Google Scholar searches, both at present and over a period of several decades. Munkres and Hatcher, while well-known, do not outweigh this significant majority of sources. In determining whether there is a common name, our inquiry is not limited to "the most commonly used" textbooks or even reputable textbooks in general (and for that, consider Lee or Brown), but rather the body of all reliable English-language sources on the topic. The current title is the common name. Adumbrativus (talk) 03:23, 22 June 2021 (UTC)
• Support Although I think it's clear that the term 'Hawaiian earring' has often been used in the past, I see no clear consensus in the mathematical community about the name of this object. As other supporters have mentioned, two of the most popular and most often used topology texts written for both undergraduate and graduate students ('Topology' by Munkres and 'Algebraic Topology' by Hatcher) do not use the term Hawaiian earring. I personally used both of these texts during my education, and struggled with finding this particular space online as a direct result.

  Additionally, some experts in the field — including supporter Dr. Jeremy Brazas who has already made his comment here — use the term 'infinite earring.' At the time of writing, the popular math Q&A site Math StackExchange has roughly 80 posts that use the term 'infinite earring' and roughly 130 posts using the term 'Hawaiian earring.' I don't see an overwhelming majority preference for one term over the other at this time. Wikipedia's policies are clear that common names should be "evidenced through usage in a significant majority of English-language sources," and I simply don't find this to be the case.

  Moreover, the term 'Hawaiian earring' was historically used as a colloquial phrase meant to refer to how 'exotic' this space is. Wikipedia's policies tend to err away from colloquialisms used as titles, and given the support of experts in the field and the differing terms in commonly used textbooks, I think that 'infinite earring' is a more apt and encyclopedic title for this page. I would be remiss not to include in my argument the following quote from Wikipedia's naming policies:"When there are multiple names for a subject, all of which are fairly common, and the most common has problems, it is perfectly reasonable to choose one of the others."

  Lastly, I should mention that the unfortunate popularity of the term 'Hawaiian earring' cannot be ignored. Despite my support for the title change, I do believe that — for now — including a redirect from 'Hawaiian earring' to either 'Infinite earring space' or 'Infinite earring' would be more than appropriate. As outlined in Wikipedia's policies, titles are meant to be searchable and descriptive. Although I find that 'infinite earring' is a common term, the commonality of 'Hawaiian earring' requires some form of redirect here. Santana Afton (talk) 03:34, 22 June 2021 (UTC)

On Math Stack Exchange I get 130 results for "Hawaiian earring" and 23 for "infinite earring". I think you might have forgotten to enclose the latter term in quotes when you got the 80 figure? (Though I don't think it's particularly consequential either way, since user-generated content doesn't really help us determine the commonly used name in reliable sources.) Colin M (talk) 05:11, 22 June 2021 (UTC)

Interesting! Reading that particular policy feels a bit incongruous to this discussion, only because a large amount of mathematics produced (in English) is user-generated. Various professional mathematicians have their own blogs and websites where they share mathematics outside the scope of textbooks or published articles. Many such blogs are considered credible and are often invaluable resources within the community — some have even significantly changed research directions for a whole (sub)field. Sites like MSE and MathOverflow are particular touchstones for many in the mathematical community. I would encourage whoever makes this decision to consider this particular kind of user-generated content. Your point still stands, though; I checked and it does seem as though I forgot to use quotations when finding those numbers. Santana Afton (talk) 06:04, 22 June 2021 (UTC)

Sorry to go further into the weeds, but just FYI, the blog case is covered by WP:SELFPUB, which does allow blogs and other self-published sources to be admitted as reliable if authored by established subject-matter experts. This could be applied to content on a site like StackExchange as well, but it would require scrutinising individual contributions on a case-by-case basis. Colin M (talk) 14:34, 23 June 2021 (UTC)

The reference to Math StackExchange posts is pure astroturfing. One day ago, there were a mere 2 posts on MSE that contained "infinite earring". All of the other results were edits that you (Santana Afton) personally made a few hours ago. You can see the most recent editors of the search results at https://math.stackexchange.com/search?tab=active&q=%22infinite%20earring%22. 69.203.83.19 (talk) 06:41, 22 June 2021 (UTC)

Wow, good catch. That's... not a good look. Colin M (talk) 14:36, 23 June 2021 (UTC)

That wasn't my intention, and as already discussed above, that point I made is moot. I had simply forgotten to add quotations when finding those numbers, and 130 vs 23 is not a good argument. I certainly didn't edit 80 posts by hand in the span of a half hour. Santana Afton (talk) 09:09, 22 June 2021 (UTC)

• Oppose per BarrelProof and Colin M. Google Scholar shows no results for "infinite earring space", versus 374 for "Hawaiian earring" since 2010 alone. While the balance may shift in favor of the proposed title in the future, it is clearly not the WP:COMMONNAME at present. Rublov (talk) 17:12, 22 June 2021 (UTC)
• Oppose. The well-known and widely used terminology for these spaces is indeed "Hawaiian earrings". For instance, among the references and "further reading" for this article, Cannon, Conner, Spencer, Eda, and Fabel refer to "Hawaiian earring[s]" in the titles of their respective articles; Morgan and Morrison prove a more general theorem (on weak joins), but start their article with the words, "The infinite Hawaiian earring"; finally, Barratt and Milnor discuss a much more general theory, and do not specifically mention these specific examples by name. Turgidson (talk) 18:55, 23 June 2021 (UTC)
• Weak Oppose This is the standard term. It isn't Wikipedia's job to make judgements about what terms are good or bad. If the standard mathematical term changes then it can change. I also haven't seen any evidence that the name arose from any idea about Hawaiian culture being exotic anyhow (Repeating this claim doesn't make it so, and incorrect etymological claims involving oppressed groups are common; see for example "rule of thumb" and recent claims that the word picnic relates to lynching). The argument about recognizability is interesting but not persuasive given that based on usage, more people will recognize the common name. (I for example know what a Hawaiian earring is but would not have immediately realized what an "infinite earing space" was without more prompting). And despite the original proposer's statement here that the term isn't standard, the OP in their own Twitter comments where they've apparently been trying to rally people here stated that they used the term all through grad school and it was the common one they used then. While Munkres is a common enough topology textbook, and probably the most common, it is just one of many, and others don't use that term. Furthermore, Munkres only has 1.5 pages on the topic, while others which discuss the space and its properties in more detail use Hawaiian earring. Edit: Thinking about this more, opposition is only weak, because Hatcher uses the phrase "Shrinking wedge of circles." In that context I'm not convinced that Hawaiian earring is a majority usage, but it is clearly the most common usage. JoshuaZ (talk) 13:43, 24 June 2021 (UTC)
• Strongly oppose as per BarrelProof, JoshuaZ, Rublov, and Turgidson. In the absence of reliable sources, it is not Wikipedia's job to determine the "correct" name of a space. (Not to mention that the original proposal for why the name should be changed is poor philosophy at best. If identifying an ethnicity with the material culture of that ethnicity is exoticization, then exoticization is not something to avoid.) Many folks mention that Munkres doesn't use the term, but Munkers isn't the standard resource — that's Hatcher, which uses yet a third term. I'm not sure these works are actively trying to avoid the name; if they are, then their disparate usage suggests academics trying to avoid the name have not yet coalesced on a single alternative. Unless/until they do so, we should stick with the name that is clearest, most evocative, and most commonly used in the existing literature. Bernanke's Crossbow (talk) 02:14, 27 June 2021 (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.

• Tragic. Of course, oppose, after the fact. This type of social warfare is truly and wholly detrimental to Western Civ and the mental health of society as a whole. This is poisonous. I'm not entirely sure why we are even keeping a record of this discussion. It's shameful, its toxic. Bury this thing where it can no longer do harm. 67.198.37.16 (talk) 06:02, 4 March 2024 (UTC)