Talk:Mercator projection

Article needs to explain difference between Mercator and central cylindrical projections

Almost every source I've seen on the internet about map projections confuses the Mercator and central cylindrical projections. We would be doing the world a huge favor by concisely and clearly explaining the differences in this article. Perhaps it could be a paragraph or subsection under the Properties section. Nosferattus (talk) 03:01, 18 August 2022 (UTC)

@Justinkunimune: I think you might be the best candidate for this heroic task! Nosferattus (talk) 03:03, 18 August 2022 (UTC)

Lol sure, I can do that. I added a note to the bottom of Properties as you suggested; what do you think? It could also go in the Mathematics section, but that section is pretty long and structured so I didn't see a good spot for it. Justin Kunimune (talk) 11:34, 18 August 2022 (UTC)

That’s a good observation. Strebe (talk) 05:29, 18 August 2022 (UTC)

y(φ) "must" be antisymmetric

A note at the bottom of the page says, "The function y(φ) is not completely arbitrary: it must be monotonic increasing and antisymmetric (y(−φ) = −y(φ), so that y(0)=0): it is normally continuous with a continuous first derivative."

Why must it be antisymmetric? I see no reason why it must be so. 31.52.108.53 (talk) 20:56, 21 November 2022 (UTC)

That’s just the conventional definition of cylindric projection. Strebe (talk) 04:08, 22 November 2022 (UTC)

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)