Talk:Mercator projection

As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other.

Cylindrical equal-area projection with oblique orientation

The article contains the claim "As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other."

Really? What about "Cylindrical equal-area projection with oblique orientation"?

@Jacobolus and GeogSage: Euro2023 (talk) 03:26, 10 January 2023 (UTC)

Sounds like you have identified an issue with the description. Was this my fault? did you want to fix it? GeogSage ^{(⚔Chat?⚔)} 04:21, 10 January 2023 (UTC)

This description seems entirely fine to me. I believe Euro2023 wants to change this to “As in all cylindrical projections in equatorial aspect, ...” (or perhaps “normal aspect”, “direct aspect”, or another synonym) for precision. I think this is unnecessarily pedantic but don’t really care strongly either way. –jacobolus (t) 04:28, 10 January 2023 (UTC)

Where are the straight lines in the file to the right? Euro2023 (talk) 04:29, 10 January 2023 (UTC)

Wikipedia readers are neither robots nor idiots. They are entirely capable of figuring out for themselves that the term “cylindrical projection” when not otherwise qualified refers to a cylindrical projection in equatorial aspect (otherwise as you point out the claim about a rectangular graticule would be entirely nonsensical). Thus the qualification is not really necessary. Adding extra qualifiers to already functionally unambiguous terms is cumbersome and distracting and can even cause more confusion than it prevents. But in this particular case I wouldn’t care strongly enough to object if someone wanted to add the qualifier to this sentence. –jacobolus (t) 04:35, 10 January 2023 (UTC)

Please refrain from using attack language e.g. "Wikipedia readers are neither robots nor idiots.". It has nothing to do with the observation that I made and the questions I wrote down here. If you cannot find the claimed straight lines in the image and you are correct, i.e. they don't exist, then the statement is simply wrong. Euro2023 (talk) 04:56, 10 January 2023 (UTC)

Setting some baseline for a presumed Wikipedia reader’s basic level of literacy / mental competence is not “attack language”. For an analogous assumption in another field, cf. reasonable person. –jacobolus (t) 05:14, 10 January 2023 (UTC)

The topic of this section aren't Wikipedia readers, nor their "basic level of literacy / mental competence" but the topic is a false claim. Instead of talking about the false claim, you start talking about who is not idiots. What does that help to get rid of the false claim? Did anyone claim that Wikipedia readers are idiots? If not, why did you write it? Did you intend to spread the impression that someone claimed they are idiots. Yes, you did so. You wanted to portray me as a person that did so and needs to be told that "Wikipedia readers are neither robots nor idiots.". Euro2023 (talk) 05:23, 10 January 2023 (UTC)

There is no "false claim" here. The claim is entirely fine. The phrase "all cylindrical projections" implicitly means "all cylindrical projections in equatorial aspect", and this is obvious to any ordinary reader (a presumed character of basic literacy and mental competence). If you strongly care about being pedantically precise in this specific case because you are worried hypothetical robot-minded readers might be confused, you can explicitly add "in equatorial aspect" (or if you prefer, "in normal aspect") to the end of the phrase, and I doubt any other editors will care strongly enough to hassle you about the change, unless you start trying to enforce the same over-qualification all across every Wikipedia article, in which case people will be annoyed, revert your changes, and ask you to stop. –jacobolus (t) 06:07, 10 January 2023 (UTC)

While I provided evidence that the claim is false, you don't provide evidence that it is true nor evidence that a majority of Wikipedia readers want to see claims presented as true that are false.

1. Is it true that the claim is "As in all cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other." - YES Y
2. Is it true, that that the claim can be either false or true but not true and false - YES Y
3. Is it true, that that if the claim is not true, it is false - YES Y
4. Are there "cylindrical projections" for which "parallels and meridians" are not "straight and perpendicular to each other" - YES Y
5. Does "all cylindrical projections" include "all" (cf. wikt:all#Determiner) projections that are "cylindrical projections" - YES Y
6. Does "all cylindrical projections" include those for which "parallels and meridians" are not "straight and perpendicular to each other" - YES Y
7. Are there "cylindrical projections" for which "parallels and meridians" are "straight and perpendicular to each other" and at the same time NOT "straight and perpendicular to each other" - NO N
8. Is it true for "all cylindrical projections" that "parallels and meridians" are "straight and perpendicular to each other" - NO N
9. Is the claim true? - NO N
10. Is there evidence that a majority of readers of Wikipedia want to see claims presented as true that are false - NO N

Euro2023 (talk) 14:32, 10 January 2023 (UTC)

Again, if you want to change the phrase "as in all cylindrical projections" to instead say "as in all cylindrical projections in equatorial aspect" or "as in all cylindrical projections in normal aspect" in this specific example, you can go ahead and make that edit. I doubt anyone is going to mind enough to fight about it unless you start trying to enforce the same terminology broadly. Please do not try to change this to the phrase "as in all normal cylindrical projections", because this is non-standard terminology not supported by reliable sources and likely to confuse readers.

But as for your checkmarks, your summary is just not how human language/communication works. Ordinary written/spoken language does not consist of formally defined mathematical statements expressed with complete precision, but instead saves effort by relying on conventions and writers'/readers' common sense to interpret statements and fill in implicit context. Statements that would be too underspecified or ambiguous for a computer software proof assistant to interpret can nonetheless be entirely unambiguous to ordinary human readers, because human readers are not idiots or robots. –jacobolus (t) 22:41, 10 January 2023 (UTC)

Stop your adhominem attacks. Euro2023 (talk) 22:53, 10 January 2023 (UTC)

You seem to misunderstand what ad hominem means. This is a discussion about terminology conventions, writing style for Wikipedia, and what can be expected from Wikipedia readers, not about you personally.

Nobody has insulted you or attacked your character, much less fallaciously used such attacks to dismiss/discredit unrelated arguments.

Please assume good faith and stop making yourself out to be a victim, and instead focus on the topic(s) under consideration. –jacobolus (t) 23:11, 10 January 2023 (UTC)

Stop your attacks and ad hominem statements. Euro2023 (talk) 23:15, 10 January 2023 (UTC)

You were helpful at removing "gigantic" from the article map projection, that's why I pinged you. If the image presented here shows a "Cylindrical equal-area projection" and if such a projection is a "cylindrical projection", and the blue lines in the image are not straight, then I think the statement given in the headline of this talk, is wrong. Maybe the following statement would be correct: As in all normal cylindrical projections, parallels and meridians on the Mercator are straight and perpendicular to each other. Euro2023 (talk) 04:28, 10 January 2023 (UTC)

For context we've been having a dustup over at Talk:Cylindrical equal-area projection. –jacobolus (t) 04:29, 10 January 2023 (UTC)

Again an attack? Can't you stop that? Why would that what you call a "dustup" be a context for the question here? Euro2023 (talk) 04:31, 10 January 2023 (UTC)

I can only assume you pinged me here based on our discussion over there. Other editors coming to our in-progress conversation without context are going to be confused, so sending them to see the context is a service. Characterizing our conversation as a dustup is not an “attack”; dustup is a light-hearted synonym for “argument”. –jacobolus (t) 04:33, 10 January 2023 (UTC)

"I can only assume you pinged me here based on our discussion over there." - And if so? "Other editors coming to our in-progress conversation without context are going to be confused" - which "in-progress conversation"? Here the topic is clearly defined. I just spotted yet another bug. The attack lies in the fact that you point to the other place where you attacked me over and over again. Euro2023 (talk) 05:00, 10 January 2023 (UTC)

I appreciated the context. Since these discussions are closely related, many points made there apply here. Justin Kunimune (talk) 14:41, 10 January 2023 (UTC)

"Since these discussions are closely related, many points made there apply here." - Which made there applies to the statement from 03:26, 10 January 2023 (UTC)? Euro2023 (talk) 22:52, 10 January 2023 (UTC)

I suppose mostly the point that "equatorial aspect" is usually implied when one mentions a cylindrical projection, and the counterpoint that WP should precisely state when nonequatorial aspects are included and when they aren’t. Those were my two main takeaways from that discussion. Justin Kunimune (talk) 23:46, 10 January 2023 (UTC)

Lack of Sources

I'm reading through the "History" section of this article and there's a whole string of paragraphs with a lot of different information and assessments and not one citation in sight. Can someone address this? 104.181.215.171 (talk) 18:21, 15 April 2023 (UTC)

I didn’t write any of this, but I notice Monmonier is cited in there. Pretty well everything in that section is covered in his book. Feel free to go track down more sources though, or skim through that book looking for specific pages covering particular sentences. –jacobolus (t) 18:45, 15 April 2023 (UTC)

In the main article, the claim "As a result of these criticisms, modern atlases no longer use the Mercator projection for world maps or for areas distant from the equator, preferring other cylindrical projections, or forms of equal-area projection." has zero sources. Without evidence I think it reasonable to delete such a definitive claim about the entire world's atlas makers. — Preceding unsigned comment added by VilaRest (talk • contribs) 14:49, 11 May 2023 (UTC)

Chapter 9 of Monmonier, "Wall Maps and Worldviews", attests to the latter part of the claim, though Monmonier argues that the cause was anti-isolationist sentiments in the US and the availability of better equal-area and compromise projections, not criticisms from academic circles. Justin Kunimune (talk) 17:54, 11 May 2023 (UTC)

Size distortion image

@Erickespinal26 can you explain the reasoning for including this Reddit image? It seems to accomplish the same thing as the animated image already shown, but is much worse because it's hosted externally. I can see that it might make sense to replace the animated image if the Reddit one were uploaded to the Commons, but we hardly need both, do we? Justin Kunimune (talk) 11:54, 20 September 2023 (UTC)

Mercator projection in Song China?

According to this article (I haven't looked it up) Needham's Science and Civilization in China claimed that certain maps (and maybe star charts?) from the Song Dynasty were based on the same principle as the Mercator projection, because they were based on a rectangular grid. An IP editor recently removed (special:diff/1183748240; the sarcastic edit summary "... illustrating 'so-called' discoveries made by the west through mathematical rigors were already well-known in China for centuries" leads me to believe this edit has some ideological motives) an unsourced claim that Needham was incorrect about this. From a cursory skim of the academic literature it seems like the previous claim in the article was right, i.e. Needham was incorrect and these maps don't have anything to do with the Mercator projection, despite using rectangular grids.

Does anyone know more about the research literature on this topic? It would be helpful to write a properly sourced summary of the current scholarly consensus (or lack thereof). The IP editor's version gives in my opinion a misleading impression. –jacobolus (t) 07:28, 6 November 2023 (UTC)

The only source I found was this rice.edu page, which seems to be a preprint of a chapter from this book by Richard Smith, which says "Overall, Chinese cartographers treated large-scale space, including the world itself, as essentially flat." and "Each side of each square represents 100 li (c. 33 miles).", which suggests that there isn't really a projection here. I don't have access to Smith's actual book to confirm, but based on this I suspect you're right. I do have access to Needham's book, so I can look more specifically at his claims later this week. Justin Kunimune (talk) 13:10, 6 November 2023 (UTC)

Here are a couple other sources: 1, 2. –jacobolus (t) 15:23, 6 November 2023 (UTC)

I reverted that edit before I realized this was under discussion. I believe I recall Snyder addressing this, but I don’t have access to my library at present. Sorry for the hasty edit. Strebe (talk) 16:32, 6 November 2023 (UTC)

The reason I didn't revert the change outright is that I'm not sure the previous claim (that these maps were based on an equirectangular projection) is correct either. It would be better I think to be very precise in describing Needham's claim(s) (which we should probably describe as "speculation" or similar, since they don't seem to be based on much evidence), and cite some sources about any dispute of that. –jacobolus (t) 18:09, 6 November 2023 (UTC)

The cylindrical star chart from the Hsin I Hsiang Fa Yao

Needham does claim that several star charts from the Song dynasty used the Mercator projection. Specifically, he says that star charts in the Hsin I Hsiang Fa Yao (1094, see right) used "'Mercator's' projection" (page 277), and he says that the Tunhuang manuscript star chart (10th century) used "a projection analogous to that of Mercator" (page 545). He doesn't provide much supporting evidence for this. My gut reaction is that it doesn't look precise enough to identify a projection; there doesn't seem to be any distortion of constellation size or shape near the poles. Needham also talks about the Yu Ji Tu map, but only remarks on its square grid and its impressive precision compared to contemporary Western T-O maps; he doesn't connect it to the Mercator projection. Justin Kunimune (talk) 20:56, 9 November 2023 (UTC)

Thanks a lot for tracking that down. As an aside: you're quoting pages from Needham Vol. 3. Our current article cites Vol 4, p. 359. (I only have copies of vols. 1–3, but not vol. 4+). Do you have access to vol. 4? –jacobolus (t) 21:13, 9 November 2023 (UTC)

Ah, you are correct. I do have vol. 4. The page numbers seem to be different in my edition, but there are a few mentions of the Mercator projection in the section on nautical technology. In part 3 on page 559–560 he divides navigational technology into three phases and says that China reached phase two – quantitative navigation – before Europe but Europe reached phase three – mathematical navigation, including the invention of the Mercator projection – before China. On page 568 he raises the possibility that Chinese influence contributed to the invention of the Mercator projection. Then on page 569 he repeats the claim that the Mercator projection was used for tenth-century star charts, adding the detail that "the hour-circles between the hsiu formed the meridians, with the stars marked in quasi-orthomorphic cylindrical projection on each side of the equator according to their north pole distances". Justin Kunimune (talk) 22:32, 13 November 2023 (UTC)

Maybe I should write a scholarly article, with cartometric analysis, on this topic, given what a thorn in the side it is. It’s maddening that speculations by an expert in one field about a matter in a different field automatically gets legitimacy. There is every reason to suppose the projection is not Mercator:

• The domain in question isn’t a sphere; it’s a hemisphere, for which Mercator — if they knew about it — would have been a poor choice;
• If they knew about it, then they knew that other projections would be much better choices and would have used them;
• The domain in question isn’t terrestrial or aquatic, and so the redeeming quality of Mercator — straight rhumbs — would be irrelevant;
• The Chinese cosmology of that period was flat-earth, and so we are to imagine that the cosmographers developed map projections solely for celestial charts, including inventing the principle of straight rhumbs, despite having no use for them in that domain;
• The source for the claim provides no evidence beyond the implicit “it’s rectangular”, which, of course, is utterly insufficient.
• I’m probably violating WP:FORUM here, but the only thing keeping the idea from being fringe is the “scholarly reference”. Strebe (talk) 23:52, 9 November 2023 (UTC)

I think Needham had this problem somewhat in general. There's been a discussion on the pages about Hindu–Arabic numbers about whether they may have actually originated in China, based on some speculation in Needham's book which was then followed up by further speculation by a couple of other scholars of Chinese descent. But the provided evidence/analysis doesn't go beyond (paraphrased) "both rod numerals and Hindu–Arabic numerals are positional decimal systems, and there was cultural contact between India and China, therefore one probably influenced the other", and none of the obvious historical/mathematical/philological criticisms of this claim were ever really addressed at all. I appreciate that Needham collected a huge amount of valuable material, but I wish he were a bit more careful to qualify pure speculation in the examples I've seen. –jacobolus (t) 00:14, 10 November 2023 (UTC)

I think if Needham is indeed the only source to make this claim, then it's something of a fringe theory, and it's fair for us to inject some skepticism into the text. Something like "Joseph Needham, a historian of China, claims that the Chinese developed the Mercator projection in the tenth century, during the Song dynasty, and used it in star charts." Justin Kunimune (talk) 22:56, 13 November 2023 (UTC)

I would explicitly use the word "speculate". Along the lines of: "Joseph Needham, a historian of China, speculated that some cylindrical star charts dating from the 10th century, during the Song dynasty, might have been based on the same concept as the Mercator projection. Other scholars remain skeptical of this claim, which was not accompanied by any detailed technical analysis." –jacobolus (t) 23:09, 13 November 2023 (UTC)

As far as I know, we don’t have anything to cite to support “Other scholars remain skeptical of this claim”, but I can agree with the rest, including pointing out that no analysis accompanied the speculation. Strebe (talk) 19:27, 15 November 2023 (UTC)

Miyajima (1998) is more explicit: "Needham's interpretation of the projection method of the Xin yixiang fayao as Mercator's projection is wrong."

Miyajima, K. (1998), "Projection Methods in Chinese, Korean and Japanese Star Maps", Highlights of Astronomy, 11 (2): 712–715, doi:10.1017/s1539299600018554.

–jacobolus (t) 20:10, 15 November 2023 (UTC)

Wonderful! Strebe (talk) 08:01, 16 November 2023 (UTC)

Maybe, “Joseph Needham, a historian of China, speculated that some star charts dating from the 10th century Song Dynasty and presented on an apparent cylindrical projection were based on the Mercator projection. However, using cartometric analysis, Miyajima finds Needham's interpretation to be wrong. Instead, the charts are on the equirectangular projection.” Strebe (talk) 16:47, 17 November 2023 (UTC)

Okay, I put a similar version into the article (and also changed a few other examples of this claim around Wikipedia, though I didn't exhaustively search for it). Feel free to tweak further if you want. –jacobolus (t) 17:35, 19 November 2023 (UTC)

Shouldn't the history section start with the context of Portolan charts?

My impression (not knowing much about this) is that the Mercator projection emerged as part of a historical process of developing maps for sailing based on following "rhumbs" (i.e. bearings, found by astronomical observation or a magnetic compass). It seems like it would be worth discussing this at least a little bit for context, and linking to Portolan chart and rhumbline network, etc. One of the reasons that the speculation about Song Dynasty star charts using the Mercator projection are so implausible is that from what I can tell Chinese navigation did not have the same historical or technological context/process [the compass as a needle in a bowl of water was known in Song China, but I'm not sure if it was being widely used by sailors, and I'm not sure if there were any maps with windrose lines all over them] and star charts per se have no particular reason to make rhumb lines straight. Does anyone have any favorite sources about this topic, or enough knowledge to summarize off the top of their head? –jacobolus (t) 17:39, 19 November 2023 (UTC)

@Alvesgaspar: I imagine you could answer this easily? Strebe (talk) 21:49, 23 May 2024 (UTC)

Irrelevance of Non-Coaxial Mercator

User:Kencf0618 is insisting on including an image from a website that generates non-coaxial Mercator projections. These are not relevant to understanding the standard Mercator projection and confuse the issues with Mercator by appearing completely different. The author’s argument is that it demonstrates the distortions in Mercator, but there are already several pictures that serve that purpose. If there were actually any applications of such variants of Mercator, they would warrant inclusion in a separate section, right after Web Mercator. But so far as I know they’re just a toy and the author has not presented such uses. Since these variants are confusing, uneducational, non-standard, and not useful, they are irrelevant and I do not think they belong in this article. Andy Anderson 17:37, 23 May 2024 (UTC)

I disagree that the topic is irrelevant. In concept, it is a good idea and illustrates the inflation problem evocatively. Unfortunately, (1) this is WP:OR and therefore not allowed, including the external link at the bottom; (2) the wording is invented: there is no such thing as “coaxial”, let alone “non-coaxial” in this context; and (3) the implementation is faulty and confusing: the lobes at the extreme level of distortion are not a feature of the Mercator projection. Strebe (talk) 18:34, 23 May 2024 (UTC)

I applied the term “co-axial” to indicate that the axis of the cylinder of projection is different than the Earth’s axis. Seemed more descriptive than “Mercator Extreme” :-). Andy Anderson 19:12, 23 May 2024 (UTC)

I see now that the “lobes” are intersecting streets stretched nearly infinitely. That leaves only the WP:OR problem. Also, however, the image as given is unacceptably large for an article. Strebe (talk) 21:54, 23 May 2024 (UTC)

It takes a while for the lobes to sink in. The Mercator projection is asymptotic such that the closer you get to infinity, the bigger things get. States become as large as continents, then blocks, then individual buildings. This exponential distortion of familiar terrain hits like the blank, white bar of Antarctica does not. And it's all geometry, straightforward. kencf0618 (talk) 22:29, 23 May 2024 (UTC)

Coaxial is in the Oxford English Dictionary: "Mathematics. Sharing a common axis". The image can readily be expandable with a click, and the external link should certainly remain. That said, and continents notwithstanding, all geography is local... Perhaps we should make it interactive? That would neatly get around the WP:OR issue... And Mercator: Extreme at least as instructive as Nukemap! kencf0618 (talk) 22:20, 23 May 2024 (UTC)

The term for “non-coaxial” in this context is “oblique”. As for the link at the bottom of the page, it falls squarely in the WP:NOBLOGS prohibition. The WP:OR assessment is more complicated. I don’t know how making it interactive helps. Strebe (talk) 01:33, 24 May 2024 (UTC)

One source for this type of projection is:

Pérez-Duarte, Sébastien; Swart, David (2013). "The Mercator Redemption" (PDF). Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture. pp. 217–224.

–jacobolus (t) 06:09, 24 May 2024 (UTC)

Nukemap is CC-BY-4.0; Mercator: Extreme CC-BY-3.0. Furthermore it's open source on Github. Secondarily, the exemplary example of exponential distortion is linked on the site itself: the Arc de Triumphe. Finally, why don't the salient objections to Mercator: Extreme apply in full measure to Nukemap? kencf0618 (talk) 12:08, 24 May 2024 (UTC)

I don't understand what point you are trying to make. –jacobolus (t) 13:57, 24 May 2024 (UTC)

Nukemap is not relevant to justifying the inclusion of “Mercator: Extreme”: Nukemap has an article because it is based on WP:RELIABLE sources and found to be WP:NOTABLE, not because of subjective statements about how useful it is. If you find other content or articles that do not meet minimal standards, those do not amount to an argument to permit even more. kencf0618, you have ignored the WP:NOBLOGS argument, which the link to your site seems to me to be in clear violation of. Unless other editors contradict that, I will delete it. With respect to the illustration, don’t get me wrong: I like it for the reasons I gave. However, its qualifications are in a gray zone, having no formal validation for correctness. It does help that the code is available for inspection, which is what puts it into the “maybe” category for me. My opinion, as just an editor, is that the image, if it to be included, needs to be of similar size to any other on the page, needs to crop out the application UI elements, and needs to move the informative text into a much more compressed space. Andy Anderson, would those improvements, along with this discussion, allay your concerns? Strebe (talk) 17:33, 24 May 2024 (UTC)

Agreed that the image needs to be smaller, if that were the only issue I would have fixed it myself. As I said previously, because it is not standard Mercator and is not even recognizable as Mercator without some thought, it needs to be in its own section, "Oblique Mercator” as you suggest, with its own informative description, and really should include some justification of “why bother”. I know there are a lot of map projections out there that are not commonly used, but they were typically developed for particular purposes, e.g. transverse Mercator which is useful in the region of particular meridians. Andy Anderson 17:55, 24 May 2024 (UTC)

Oblique Mercator with the code it is. Arc de Triomphe, anyone? kencf0618 (talk) 20:33, 24 May 2024 (UTC)

Terminology in section Properties

The section Properties begins with a very nice diagram illustrating the different possible orientations of the cylinder axis. It uses the term "standard" to refer to the commonly understood representation of the Mercator projection with the Earth and cylinder axes coincident. Jacobolus wants to use instead the synonym "normal" that he asserts is the proper technical term for this orientation. I can find both terms in use, e.g. [1]. However, the paramount consideration here is user understanding, and using a different term from the one in the diagram will certainly be confusing. I have no other objection to the use of "normal", but if it is to be used then the diagram must be changed at the same time. That is Jacobolus' responsibility. -- Andy Anderson 16:42, 26 May 2024 (UTC)