explain xkcd - User contributions [en]

Talk:2951: Bad Map Projection: Exterior Kansas

2024-06-29T14:47:53Z

Ivansanchez: oblique stereographic demo

Seems weird that it's just the contiguous US, with "hints" about what lies within. I hope Randall will release another version with the rest of the world included.[[Special:Contributions/162.158.158.61|162.158.158.61]] 03:20, 27 June 2024 (UTC)

Would the center be both poles ''and'' Kansas's antipode? --[[Special:Contributions/172.68.27.150|172.68.27.150]] 03:58, 27 June 2024 (UTC)

Including Hawaii would have been the cherry on the cake. [[Special:Contributions/198.41.242.174|198.41.242.174]] 05:42, 27 June 2024 (UTC)

: As the center of the map corresponds to Kansas' antipode (Kerguelen in the Indian Ocean https://www.geodatos.net/en/antipodes/united-states/kansas-city), Hawaii isn't really "near the center", but rather to the right of the center (in the direction of the "Pacific Ocean" tag). --[[Special:Contributions/162.158.86.100|162.158.86.100]] 05:58, 27 June 2024 (UTC)

:: Admittedly, I guessed where they would be. [[Special:Contributions/172.71.174.139|172.71.174.139]] 06:09, 27 June 2024 (UTC)

I don't think the middle part is meant to be seen as 'water', just 'out of scope'. [[User:Jaap-Jan|Jaap-Jan]] ([[User talk:Jaap-Jan|talk]]) 07:44, 27 June 2024 (UTC)
:Yeah, this is similar to a map like https://suncatcherstudio.com/uploads/patterns/us-maps/pdf-png/usa-map-states-names-color-010101.png In that map, Canada and Mexico aren't "rendered as water", they're not rendered at all, and neither are the oceans. I'm going to edit that. [[Special:Contributions/162.158.78.73|162.158.78.73]] 13:34, 27 June 2024 (UTC)

== How would the rest of the world look? ==

Currently the center is all water. If I understand correctly the rest of the world could be added, but how would it look? For example, would Europe and Asia cover a good part of the water or would they be tiny specs in the middle (almost making this a world map already)
:My impression (without measuring/replicating) is that this is mathematically (or whatever) a gnomonic projection (which can only show half the world, anyway, even on a sheet stretching up to infinity) radially inverted. As such quite a lot of features that aren't shown ('beyond/within' the 'coastline'/borders) couldn't be, anyway, as more than half the world away. Map-centre would be the compressed singularity of the Great Circle exactly 90° off the 'centre of Kansas' that itself now exists at infinite-radius-every-angle far off the page.
:Though it could just be stereographic with any negatively positioned projection origin. Instead of -1, for gnomonic, with a -2 radii origin you would get the whole surface (at infinity!) in ways that whatever you do to radially invert (probably the direct reciprocal) and otherwise scale (clearly choosing the additional 'zoom level' factor that neatly brings the Kansas border more or less into frame) to compress all offshore/over-border territories into the 'oceanic' centre. Or it could just be a useful rescale of a -2r projection ''of'' the Kansas-antipode, such that all borders of Kansas are pulled into frame.
:(Regarding Hawaii, if quick googling is right about Hawaii being 3,600km from Kansas(-centre?), then that puts it at various preskewed factors towards the 'hemispherical horizon' of ~10,000km or the antipodal point at ~20,000km, before then being further squashed by the particular coordinate conversion system in use. If it's a near-side orthographic projection and, say approaching +1 radii up from the surface-tangent, then it could perhaps be 'over the horizon' in the direct projection and thus 'beyond the singularity' of the inverted-radius version.)
:I'd have to mess with some map data, to be sure the existing features fit either idea of projection (or find the actual one (ab)used), but this'd probably be what I'd do, straight off the bat. And then I could apply it to extraterratorial features, also. I've got some of the necessary data and mungable code handily sitting on a machine that I am ''unhandily'' not going to next use until at least the weekend, and reimplimenting it on this tablet would mean starting from first principles again/testing/etc... ;) [[Special:Contributions/172.70.163.120|172.70.163.120]] 09:23, 27 June 2024 (UTC)

: Check out the Wikipedia article "Azimuthal equidistant projection" and scroll to "Sample azimuthal equidistant projection maps". There is an inverse example, that puts California at the center of a world map. Now imagine everything else in the "great sea" of Randall's map, using a similar projection. [[Special:Contributions/172.71.99.32|172.71.99.32]] 13:48, 27 June 2024 (UTC)

: Yay! A task for a geography teacher (i.e. me, and I'm a big fan of Randall's work with maps), and I just happen to have the right bookmarks for this kind of thing in my browser. So here's a little toy to play around with: [https://www.worldmapgenerator.com/en/wizard/step/centering/?config=eyJpZCI6IkNVU1RPTV9XSVpBUkQiLCJsYXllcklkcyI6WyJDTElQX1BBVEgiLCJCQUNLR1JPVU5EIiwiU1BIRVJFIiwiR1JBVElDVUxFUyIsIkxBTkQiLCJPQ0VBTiJdLCJwcm9qZWN0aW9uSWQiOiJBWklNVVRIQUxfRVFVSURJU1RBTlQiLCJyZW5kZXJpbmdBZGFwdGVySWQiOiJDQU5WQVMiLCJtYXBUaGVtZUlkIjoiREVGQVVMVCIsImNlbnRlciI6WzAsMF0sInJvdGF0aW9uIjpbLTgxLDQwLDBdLCJ6b29tIjowLjksIndpemFyZFN0ZXBQcm9ncmVzc0lkeCI6MywidmVyc2lvbiI6IjEuMC4wIn0%3D] I hope my settings got preserved in the link as they should, else whoever added all those letters and numbers clearly has something to answer for! If the link works as it should it'll show you what a map of the whole wide world would look like in an Azimuthal Equidistant Projection with Kansas on the exterior. That is, I first used this Antipodes Map [https://www.antipodesmap.com] to locate the point opposite to Lebanon, Kansas at 39°48'35"S, 81°26'39.8"E , which is quite literally in the middle of the Indian Ocean, near the islands of Saint Paul and Nouvelle Amsterdam (which, incidentally, belong to France and are mainly known for being as far away from anything as you can possibly get on this planet*) and then set the centre of the worldmapgenerator.com map approximately there. It's not a very precise tool, but it'll do - it's precise enough for me to use in lessons anyway. Surprisingly, you actually get a more or less usable map for much of the world (if you're not too fussy or trying to navigate with it or anything), ''except only'' for North and Middle America. :D [[User:PaulEberhardt|PaulEberhardt]] ([[User talk:PaulEberhardt|talk]]) 16:04, 27 June 2024 (UTC)
:: * At least, you can say that if you happen to land there, you're really not in Kansas any more. ;) [[User:PaulEberhardt|PaulEberhardt]] ([[User talk:PaulEberhardt|talk]]) 16:30, 27 June 2024 (UTC)
::Oh, I really like map stuff, but: "This site uses cookies to improve the results of our bakery. With your acceptance we can add more honey, sugar and flour to improve the website. [Accept]". Only "[Accept]", no other options (even long-winded 'deselect "things ''we'' suggest are important" options that I might disagree with'). I really don't like that. And then it also offers to install an App, apparently... Oh, website builders, just because I'm currently on a mobile device, it doesn't mean I'm eager to "app everything"; entirely the opposite, perhaps! Yeah, I know script/cookie blockers or specialist browsers exist to avoid these things, but... Anyway, nice to see a geography teacher taking it seriously, even if I've got my own conflicting issues in picking up on what you've found. (Behind/before the popup stuff, it truly looked interesting. Don't know if there's a legit way to get a screenshot of it. Don't break any Ts&Cs in doing so!) [[Special:Contributions/141.101.98.164|141.101.98.164]] 17:03, 27 June 2024 (UTC)
::: The joke is that worldmapgenerator doesn't store ANY cookies. Meanwhile the site you are posting from stores 63 kB of browser data just visiting the homepage. [[User:Quantum7|Quantum7]] ([[User talk:Quantum7|talk]]) 21:08, 27 June 2024 (UTC)
:::: Hmm, I get the "This site uses cookies to improve the results of our bakery." too. If they don't use cookies, then they shouldn't have that.
:::: I am actually on a desktop system, I can probably go in there and remove the "don't do anything until the Accept is clicked" popover ''without clicking on the popover'', and even check out what it tries to store, or doesn't... I'm not even overly paranoid about these things, but I agree with above poster that it's bad form. ''Especially'' if it's a joke (no reason to suppose it is).
:::: Yeah, I'll accept Cookies if essential, but often they aren't, so it's not even a very good joke to make. Maybe they do just do everything in URL-encoded/GET data. It's my own prefered method, to make fully transparent GET data on websites I use (barring anything that needs to be POST-submitted), and if I ever use cookies it's a single own-site-only cookie for session control, not the mass of "Legitimate Use" (as if!) items.
:::: Have you ever gone and looked in the list? (Assuming the "Do you accept cookies" doesn't do a "Yes, accept all"/"No, reject all (inessential)" and gives you the 'option' to painstakingly turn off half a dozen "default cookie sets".) It's frightening how many 'interested parties' are potentially getting info (dozens to hundreds, at a time). And, realistically, I'm not sure I even believe that by selecting 'off' on that kind of dialogue that I'm actually not being Cookified just as much as if I accidentally clicked on the prominent "Accept All".
:::: Sorry, the above comment just resonates with me, too. Decided I had to vent a bit. [[Special:Contributions/172.70.163.121|172.70.163.121]] 23:51, 27 June 2024 (UTC)
:::: I checked the cookies it uses, none of them contain any sort of tracking identifier. It stores the selected language, whether you accepted cookies, and for which screens of the wizard you've seen the tutorial screen. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 03:14, 28 June 2024 (UTC)

:: Thanks for the wonderful link. I suggest we include an image from this in the article. Your settings were preserved nicely. Given how little of north America is visible, I suspect that Randal must have used an even more extreme azimuthal protection than the equidistant one to shrink the center. [[User:Quantum7|Quantum7]] ([[User talk:Quantum7|talk]]) 21:18, 27 June 2024 (UTC)
::: Added [[:File:Exterior_Kansas_Azimuthal_Projection.png]][[User:Quantum7|Quantum7]] ([[User talk:Quantum7|talk]]) 07:53, 28 June 2024 (UTC)

I have made an image adapting the comic to add the rest of the world if anyone was curious about it. I tried adding to the explanation but I don't have the permissions for such. If anyone wants it, feel free to grab it and put it here, since it's a derivative of Randalls work it is licensed as Creative Commons too. -- avsa

https://x.com/avsa/status/1806312234894659589

==Adding an image?==
Is it possible to add an image to the description? I'm looking at the Wikipedia article "Azimuthal equidistant projection" and the "external Antarctica" map is relevant. https://en.wikipedia.org/wiki/File:Azimuthal_equidistant_projection_SW.jpg Thanks! [[Special:Contributions/172.71.99.32|172.71.99.32]] 13:43, 27 June 2024 (UTC)
:You could use a variation on <code><nowiki>[[File:Azimuthal_equidistant_projection_SW.jpg|300px]]</nowiki></code> maybe. Add align/wrap options, as necessary, and use a size that seems to work. Remember to try it with Preview, before you're submitting it for real, lets you fine-tune to your liking without spamming the edit-history. Doesn't need (explicit) uploading to the wiki, this way. [[Special:Contributions/172.69.194.97|172.69.194.97]] 17:11, 27 June 2024 (UTC)
:I added [[:File:Exterior_Kansas_Azimuthal_Projection.png]]. Is that what you had in mind? It's an equidistant projection; I haven't found a tool that lets you change the projection radius to better match Randal's projection.[[User:Quantum7|Quantum7]] ([[User talk:Quantum7|talk]]) 07:51, 28 June 2024 (UTC)

Should Now [https://xkcd.com/1335/] be mentioned? Same type of projection. [[Special:Contributions/162.158.159.90|162.158.159.90]] 20:51, 27 June 2024 (UTC)

== Actual azimuthal projection centered at Kansas' antipode ==

It turns out that, this being the internet, there's an actual tool for generating azimuthal projections ([https://ns6t.net/azimuth/]). For the curious minds out there, here's what the exterior Kansas would look like as an actual azimuthal projection: [https://www.dropbox.com/scl/fi/i87r5524u952cam4dbtdx/Kansas-Azimuthal.pdf?rlkey=h5f3qp8esotyk50uaurht8gj4&st=drjzszjk&dl=0]. [[Special:Contributions/172.69.90.178|172.69.90.178]] 21:05, 27 June 2024 (UTC)

:[https://i.ibb.co/W33xmKC/Screenshot-2024-06-27-3-17-30-PM.png Here's one where the conformal lines are still latitude and longitude], from https://maps.ontarget.cc/azmap/en.html which releases it as CC-BY-SA if someone wants to upload it. [[Special:Contributions/172.68.23.73|172.68.23.73]] 01:24, 28 June 2024 (UTC)

Someone please call out the homage to Frank L. Baum. Dorothy started her trip from Kansas, house and all. She landed in the fabulous Land of Oz, a rectangle surrounded by the deadly desert. This map shows Kansas surrounding the rest of the USA. (My screen name's Trelligan, don't blame anyone else for this.) [[Special:Contributions/172.70.214.254|172.70.214.254]] 12:18, 28 June 2024 (UTC)

New Flerf lore just dropped. [[User:RegularSizedGuy|RegularSizedGuy]] ([[User talk:RegularSizedGuy|talk]]) 15:54, 28 June 2024 (UTC)

Me being a geomatician and having a couple of friends who are map projection nerds, we had a short discussion (https://mastodon.social/@EvenRouault/112688667438256248) and I ended up implementing a web map version of a Oblique Stereographic map in the style of this: https://ivan.sanchezortega.es/2024-06-exterior-kansas/ . You'll notice that a Oblique Stereographic projection does create a coastline that matches the one in the comic much closer to the Azimuthal Equidistant projection (and therefore, I'll hypothesize that Randall used a compromise projection). I'd like to add an image of my map to this explanation, but I seem to lack permissions. [[User:Ivansanchez|Ivansanchez]] ([[User talk:Ivansanchez|talk]]) 14:47, 29 June 2024 (UTC)

2613: Bad Map Projection: Madagascator

2022-04-29T22:07:12Z

Ivansanchez: /* Explanation */ italics

{{comic
| number = 2613
| date = April 29, 2022
| title = Bad Map Projection: Madagascator
| image = bad_map_projection_madagascator.png
| titletext = The projection's north pole is in a small lake on the island of Mahé in the Seychelles, which is off the top of the map and larger than the rest of the Earth's land area combined.
}}

{{Talk:2613: Bad Map Projection: Madagascator}}

==Explanation==
{{incomplete|Created by MADAGASCAR (2005) - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This is another comic in the [[:Category:Bad Map Projections|Bad Map Projections]] series. This time, Randall used the classic {{w|Mercator projection}} but instead of placing the North Pole on top and the South Pole on the bottom it is oriented so that the top is the island of {{w|Mahé, Seychelles|Mahé}}. The map projection is technically a {{w|Oblique Mercator projection}}, with an unusual choice of the cylinder's axis. Since the Mercator projection tends to visually distort areas near the top and bottom of the resulting map, this gives some areas, notably Madagascar, very unusual shapes.

The Mercator projection became the standard projection for world maps during the 1800s because it is ''conformal of normal aspect'': a {{w|rhumb line}} is displayed as a straight line in a Mercator map. During the age of sail, when navigation was performed by compass - this was a very valuable feature, since one could plot a course between two locations by measuring the direction from one to another on the map and then accounting for the difference between the magnetic and actual north poles to determine which rhumb should be taken. In the mid-20th century this trend was {{w|Mercator_projection#Criticism|criticized}} because the distortion towards the north and south poles gave an inaccurate impression of relative sizes. The most common example given of this distortion is that on a Mercator map of the world Greenland looks to have more area than Africa, when in real life Africa covers 14 times that of Greenland. Thus the reference to making Madagascar larger in this projection. Madagascar is a large island off the south east coast of the main African continent, but has only a quarter the coverage of Greenland. Greenland is often listed as the largest island in the world (which excludes continents in their own right, e.g. Australia) followed by New Guinea, Borneo and then Madagascar in fourth place.

Mahé, mentioned in the title text as the north pole's new location, is the largest island in Seychelles, with an area of 60.7 square miles. The claim in the title text, however, that it is "larger than the rest of the Earth's land area combined", is hard to verify when it is not actually displayed in the projection. That is, if you limit yourself to the comic. Clicking on the actual comic will open a website that displays Mercator projections with the North Pole transplanted to various locations, with the location of the one opened set to Mahé. With this, it is possible to see that the island is indeed larger than the rest of the map's land area combined, with a single national park within the island rivalling Africa in size, and eventually reaching a scale of distortion where a road is thicker than Panama. This also reveals that the location of the North Pole, the lake mentioned by Randall, is the Rochon Dam.

===Comparison of actual/proportional areas===
{| class="wikitable" style="margin:auto"
! Landmass !! Status !! Official Area (in Millions of Km²) !! Proportion in image (as % of listed areas)
|-
| Africa || Continent 2nd largest || 30.3 || 35%
|-
| Eurasia || Continent Largest || 55.0 || 30%
|-
| North America || Continent 3rd largest || 24.709 || 15%
|-
| South America || Continent 4th largest || 17.840 || 7.8%
|-
| Antarctica || Continent 5th largest || 14.2 || 5.3%
|-
| Madagascar || Island 4th largest || 0.587 || 2.9%
|-
| Australia || Continent smallest || 7.6 || 2.5%
|-
| Greenland || Island Largest || 2.13 || 0.87%
|-
| Borneo || Island 3rd largest || 0.748 || 0.37%
|-
| New Guinea || Island 2nd largest || 0.786 || 0.32%
|-
| Japan || Island 7th largest || 0.377 || 0.10%
|-
| Mainland Britain || Island 9th largest || 0.208 || 0.10%
|-
| Island of Ireland || Island 20th largest || 0.084 || 0.03%
|}

* Comic measurements are strictly only of contiguous 'mainland' or main-island areas (outlined area plus outline itself)
** Excludes various off-shore islands (often significant, e.g. Baffin Island)
** Also excludes any drawn internal lakes/seas (except their drawn lines) where large enough to show such a gap
* Real-world areas are compiled from Wikipedia
** Land areas only, where established (accuracy is dubious in the case of those with significant ice-sheets)
** These figures usually including all islands, and no attempt has been made to subtract any other listed area
* For the purposes of this table, "Eurasia" continent is the whole of Europe, Asia, India, etc and was clipped from Africa in the area of Suez (and Straits Of Gibraltar, where the drawn lines touch!)
* Similarly, North/South Americas are clipped from each other in the vicinity of Panama 

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Bad map projection #248: Madagascar

Mercator projection but with the North Pole in the Indian Ocean so it exaggerates the size of Madagascar instead of Greenland

{{comic discussion}}
[[Category:Bad Map Projections]]

2613: Bad Map Projection: Madagascator

2022-04-29T22:04:46Z

Ivansanchez: /* Explanation */ oblique mercator, rhumb lines

{{comic
| number = 2613
| date = April 29, 2022
| title = Bad Map Projection: Madagascator
| image = bad_map_projection_madagascator.png
| titletext = The projection's north pole is in a small lake on the island of Mahé in the Seychelles, which is off the top of the map and larger than the rest of the Earth's land area combined.
}}

{{Talk:2613: Bad Map Projection: Madagascator}}

==Explanation==
{{incomplete|Created by MADAGASCAR (2005) - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
This is another comic in the [[:Category:Bad Map Projections|Bad Map Projections]] series. This time, Randall used the classic {{w|Mercator projection}} but instead of placing the North Pole on top and the South Pole on the bottom it is oriented so that the top is the island of {{w|Mahé, Seychelles|Mahé}}. The map projection is technically a {{w|Oblique Mercator projection}}, with an unusual choice of the cylinder's axis. Since the Mercator projection tends to visually distort areas near the top and bottom of the resulting map, this gives some areas, notably Madagascar, very unusual shapes.

The Mercator projection became the standard projection for world maps during the 1800s because it is _conformal of normal aspect_: a {{w|rhumb line}} is displayed as a straight line in a Mercator map. During the age of sail, when navigation was performed by compass - this was a very valuable feature, since one could plot a course between two locations by measuring the direction from one to another on the map and then accounting for the difference between the magnetic and actual north poles to determine which rhumb should be taken. In the mid-20th century this trend was {{w|Mercator_projection#Criticism|criticized}} because the distortion towards the north and south poles gave an inaccurate impression of relative sizes. The most common example given of this distortion is that on a Mercator map of the world Greenland looks to have more area than Africa, when in real life Africa covers 14 times that of Greenland. Thus the reference to making Madagascar larger in this projection. Madagascar is a large island off the south east coast of the main African continent, but has only a quarter the coverage of Greenland. Greenland is often listed as the largest island in the world (which excludes continents in their own right, e.g. Australia) followed by New Guinea, Borneo and then Madagascar in fourth place.

Mahé, mentioned in the title text as the north pole's new location, is the largest island in Seychelles, with an area of 60.7 square miles. The claim in the title text, however, that it is "larger than the rest of the Earth's land area combined", is hard to verify when it is not actually displayed in the projection. That is, if you limit yourself to the comic. Clicking on the actual comic will open a website that displays Mercator projections with the North Pole transplanted to various locations, with the location of the one opened set to Mahé. With this, it is possible to see that the island is indeed larger than the rest of the map's land area combined, with a single national park within the island rivalling Africa in size, and eventually reaching a scale of distortion where a road is thicker than Panama. This also reveals that the location of the North Pole, the lake mentioned by Randall, is the Rochon Dam.

===Comparison of actual/proportional areas===
{| class="wikitable" style="margin:auto"
! Landmass !! Status !! Official Area (in Millions of Km²) !! Proportion in image (as % of listed areas)
|-
| Africa || Continent 2nd largest || 30.3 || 35%
|-
| Eurasia || Continent Largest || 55.0 || 30%
|-
| North America || Continent 3rd largest || 24.709 || 15%
|-
| South America || Continent 4th largest || 17.840 || 7.8%
|-
| Antarctica || Continent 5th largest || 14.2 || 5.3%
|-
| Madagascar || Island 4th largest || 0.587 || 2.9%
|-
| Australia || Continent smallest || 7.6 || 2.5%
|-
| Greenland || Island Largest || 2.13 || 0.87%
|-
| Borneo || Island 3rd largest || 0.748 || 0.37%
|-
| New Guinea || Island 2nd largest || 0.786 || 0.32%
|-
| Japan || Island 7th largest || 0.377 || 0.10%
|-
| Mainland Britain || Island 9th largest || 0.208 || 0.10%
|-
| Island of Ireland || Island 20th largest || 0.084 || 0.03%
|}

* Comic measurements are strictly only of contiguous 'mainland' or main-island areas (outlined area plus outline itself)
** Excludes various off-shore islands (often significant, e.g. Baffin Island)
** Also excludes any drawn internal lakes/seas (except their drawn lines) where large enough to show such a gap
* Real-world areas are compiled from Wikipedia
** Land areas only, where established (accuracy is dubious in the case of those with significant ice-sheets)
** These figures usually including all islands, and no attempt has been made to subtract any other listed area
* For the purposes of this table, "Eurasia" continent is the whole of Europe, Asia, India, etc and was clipped from Africa in the area of Suez (and Straits Of Gibraltar, where the drawn lines touch!)
* Similarly, North/South Americas are clipped from each other in the vicinity of Panama 

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
Bad map projection #248: Madagascar

Mercator projection but with the North Pole in the Indian Ocean so it exaggerates the size of Madagascar instead of Greenland

{{comic discussion}}
[[Category:Bad Map Projections]]