I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...
I've thought about trying to build an app that does what that animation on the Wikipedia page does [0], but I'm not sure where I'd find spherical (or near enough) textures of the world map to experiment with.
To make it less distorted, you will have to make more cuts, seriously increasing the risk that the map does not accurately show the distance between points P and Q because the shortest path between them on the globe goes through a cut on your map.
But the Peters projection is a lot easier to read with the expectations most people have for the word "map." The Dymaxion map illustrates to me why it's not always best to solve for a single variable without making any concessions elsewhere. You have something that works really well for that one problem, but it potentially becomes unusable in real life.
What "size problems" are you referring to? The Peters projection really is equal-area. When you say "size" are you referring to something else, like shape?
Dymaxion map is beautiful. But I consider it critically flawed for "general use". Understanding the distances between points on Dymaxion map is nigh impossible (at least for me).
I think Bucky's point was to show the world as a single continent. Kind of subverting the cold war a bit by showing our continents in closer proximity, and emphasizing our common interests. He also envisioned a worldwide electrical grid that would span the North pole.
This projection looks fantastic. It would b great if people actually started using this in schools and what not. With the advent of tablets and the general digitsation that's been going around, you can have "rotable" Dymaxion maps -- maps that could be rotated and oriented in such a manner as to look like what we're used to -- but when zooomed out, the Dymaxion/Fuller projection gives students/people an accurate picture of what the earth truly looks like.
If only they made real life rotating, oriented maps. They'd need a new name, perhaps something emphasizing their roundness...balls? No, the kids would make fun of that. Spheres? Too generic.
Good point. I think real life globes would take up too much space though. On the other hand, Google Earth looks like it does a good job depicting everything in proportion.
I wonder if there is some sort of theorem that describes which fidelities you can get out of a flat projection of the surface of a sphere. For example, a projection could have accurate area ratios or accurately reflect point to point distances but not both.
Essentially: conformal (angles are equal in different areas of the map -- this is the purpose of Mercator, for sailing), equal-area (regions of the same area are represented equally), contiguous (paths between regions do not leave the map, e.g. not a Goode homolosine, Dymaxion, etc). Pick two.
There is a lot of theory surrounding map projections. I only took an introductory GIS course in college, but it was clear that there is an incredible amount of work behind the scenes there.
I have a globe, which should be the best way to represent the earth's surface. However even that is biased -- I'm fairly sure the UK is bigger than it should be.
Rather than misleading maps, I'd say misleading title: The article asks if we've been using misleading maps for over 500 years and then presents an alternative which is just as misleading (another rectangular projection, just as Mercator).
>have our world maps been wrong or misleading for 500 years?
No, they were just used mainly for navigation. The reason why the Mercator projection was popular for so long is that its angles correspond to compass points and you navigate by a trivial algorithm:
1. Draw a line to your destination on the map and determine its angle with the north, say 25 degrees north-east.
2. Set your course at 25 degrees north-east and keep it constant. Your will arrive to your destination by a rhumb line [1], which is only slightly less efficient than a great circle.
That is also the explanation they gave in the video. When they say "wrong or misleading", are referring to the fact that this is not always obvious when this projection is used, so it can make people think they can actually compare areas with it.
Oh, so what you are saying is that they have been wrong and misleading for the past 500 years?
Yeah, projections are always wrong and misleading in some ways and it’s certainly important to point that out – but the Mercator projection has certain properties that are desirable for navigation but also properties that are completely undesirable for how many maps are typically used today. All that navigational stuff? Completely irrelevant for all typical use cases nowadays. Distortions of sizes? Quite relevant for typical use cases.
a) zeteo doesn't seem to be saying it is "good". b) The statement that something is "misleading" is a tense that indicates some kind of objective truth, potentially even an intention; this objectivity is certainly the case once the word "wrong" is used: "wrong" implies a rather strong statement about the map. zateo is thereby providing the context to understand that the map has a purpose, and what that purpose is; I am not certain why your response seems to take offense at that. If you are willing to state something is "wrong" if you are using it incorrectly, then all attempts to demonstrate any form of information ever are "wrong".
That's an argument for ship captains and airplane pilots to have Mercator projection maps.
It is not an argument for Mercator projection maps to appear as the canonical Earth map in textbooks, on classroom walls, or anywhere else where education is concerned.
Also when zoomed in. For computer maps it certainly has nice properties when your map is rectangular. Not that Mercator is the only one that is, but it's probably the most-widely known.
Having lived in equatorial Africa for a decade, and having spent weeks driving to cross a single given country, I always get a kick of out conversations where someone asks, "Oh, you lived in Africa--did you know So-and-so?"
I get asked that all the time. But I'm from Iceland. With only a population of 300.000 it's to be expected. Funny thing is I've actually known the person twice when asked (but it's out of hundreds of queries).
But sometimes, you do know them, and it's like HOLY SHIT SMALL WORLD. I was on a subway in Paris one night with two friends. A group of (American) girls heard us speaking english, we got to talking, they found out where I went to school (Penn State, huge effin uni), and were like "do you know so and so". Turns out so and so was my roommates ex-girlfriend. Small world, eh?
As a Brit holidaying in the States, I have been asked many many times in the most serious of tones if I know Prince Charles/the spice girls/David Beckham. Quite bizarre.
When you project a map, there are three properties you would like to maintain: shape (aka conformality), size (aka equal-area), and direction. But you can have at most two of these properties.
Mercator preserves shape and direction at the expense of size. Peters preserves size and direction at the expense of shape. Peirce Quincuncial preserves shape and size at the expense of direction. Here's a transverse Peirce Quincuncial map I generated: http://frammish.org/tpq.jpg
Many other projections try to combine these, like the Miller projection maintains direction but strikes a balance between shape and size, getting neither one right, but neither is horribly wrong either. The Winkel Tripel projection tries to balance all three attributes.
Something else I'm interested in is if somebody has ever tried using Pierce's projection for texturing spheres or doing environment mapping. It seems like it would be perfect for the job - it's square so it would fit perfectly in a texture, it can be tiled and the formula for mapping a point on the sphere from spherical coordinates to uv coordinates on the texture seems simple enough.
The main problem I see is that it's a nonlinear projection and thus generating one procedurally on the GPU (render to texture) is rather challenging. Hardware support for cube maps places them in a sweet spot between efficiency, accuracy, practicality for generating and practicality for applying.
That example isn't an equal-area projection, it's just better on average at preserving size than Mercator. It does still have significant size distortions, such as making Sri Lanka look massive, when it's really slightly smaller in total area than Ireland.
Your example does not preserve size, because it makes Arabian peninsula (area ~2.3 million km2) look almost as big as Europe (area ~10 million km2). Also compare India with Australia. I think this map preserves shape and direction, but not size.
I've been saying this for years. The Earth is egg-shaped and fatter in the southern hemisphere, not a perfect sphere. Logic would dictate that any surface with steep mountains, continental tectonic shifts, and deep trenches is not perfectly spherical. Coincidentally, I have an uncle who was a geodecist and one of the world's GPS experts.
I knew college professors who believed that most map projections have a eurocentric bias, but it makes almost as much sense that creating maps and globes is easier to do if you assume the Earth is a perfect sphere.
Those things, while important to consider if you are trying to do something like hit hit a target within a few kilometers with an ICBM (http://en.wikipedia.org/wiki/International_Geophysical_Year), are not significant when dealing with general purpose mapping.
>The Peters Projection World Map is one of the most stimulating, and controversial, images of the world. When this map was first introduced by historian and cartographer Dr. Arno Peters at a Press Conference in Germany in 1974 it generated a firestorm of debate.
I get the impression that calling it Peters instead of Gall-Peters is a good sign that the speaker is a Peters-evangelist, rather than someone who actually cares about cartography.
A word of warning to visitors: the site is broken. It pops up an ad after about a minute of letting you read the content.
I've seen this behavior previously (it's becoming more common) and I reward it the same way each time: closing the site and putting it on my proxy's blocklist.
Quite sure. It popped up something about "liking" them on this thing called "Facebook", which I've gathered is some form of virus that has infected the minds of most individuals on the net.
I'm a little disappointed in HN for the fact that this is on the front page. The wikipedia article on Gall-Peters is much more accurate and informative, and even the whole (misleading) "oh look what I just found out but barely anyone else knew" thing with projections has been done before, and better (e.g., by Arno Peters himself).
I might take up the project of posting the relevant wikipedia links as stories, and in turn linking those in the comments of all shoddily written blog posts, in the hope of righting these wrongs.
Not that it is terribly relevant, but I question the authors aptitude in science journalism. I encourage anyone curious to see his articles on the vaccine/autism controversy. Oh, and he's a 9/11 truther, illuminati conspiracist, etc., etc.
Gall-Peters clearly has the best PR, since it always gets mentioned as the primary candidate for a replacement map. And while it's definitely more suitable for getting a good "feel" for the world than Mercator, the enormous shape distortions still don't make it a very good map. There are better ones out there.
Personally I'd prefer a map that emphasizes that the world is actually a sphere, rather than a rectangle. I also have a soft spot for Dymaxion, although I don't use Dvorak.
To put this in perspective, the area of Alaska, the largest US state, is twice that of Texas - many Americans have at least a basic idea of how large Texas is, if not Alaska. The area of Africa is 18 times that of Alaska.
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[ 0.13 ms ] story [ 293 ms ] threadhttp://calabarboy.com/2010/10/11/the-true-size-of-africa-kai...
they list 9.629M for USA, Google says 9.827M. Alaska, according to Google = 1.718M.
WAT?
Sahara desert: 3.629 million sq miles (9.4 million km²) Canada: 3.855 million sq miles (9.985 million km²)
At the time, the Economist also redid the exercise starting with an equal-area projection: http://www.economist.com/blogs/dailychart/2010/11/cartograph...
http://en.wikipedia.org/wiki/Dymaxion_map
If you are interested in a size-accurate map, you can't get much better than that.
I've always wondered, however; why not increase the density of faces (or vertices?) from an icosahedron, and have an even less distorted map? What would the monstrosity look like?...
[0] http://en.wikipedia.org/wiki/File:Dymaxion_2003_animation_sm...
Also, maybe you can find a database of the countries border as lat/lng polygons and just draw the countries.
In the limit, you could get something like http://en.wikipedia.org/wiki/Goode_homolosine_projection, but with infinitely many lobes. And that is a _could_: you can add branches like in Dymaxion wherever you feel like it.
Wait, I got it.
Let's call them globes.
I wonder if there is some sort of theorem that describes which fidelities you can get out of a flat projection of the surface of a sphere. For example, a projection could have accurate area ratios or accurately reflect point to point distances but not both.
http://en.wikipedia.org/wiki/Geographic_information_system
No, they were just used mainly for navigation. The reason why the Mercator projection was popular for so long is that its angles correspond to compass points and you navigate by a trivial algorithm:
1. Draw a line to your destination on the map and determine its angle with the north, say 25 degrees north-east.
2. Set your course at 25 degrees north-east and keep it constant. Your will arrive to your destination by a rhumb line [1], which is only slightly less efficient than a great circle.
[1] http://en.wikipedia.org/wiki/Rhumb_line
Yeah, projections are always wrong and misleading in some ways and it’s certainly important to point that out – but the Mercator projection has certain properties that are desirable for navigation but also properties that are completely undesirable for how many maps are typically used today. All that navigational stuff? Completely irrelevant for all typical use cases nowadays. Distortions of sizes? Quite relevant for typical use cases.
Just because it’s old doesn’t mean it’s good.
Umm no. You can also mislead yourself by using a slide rule to measure lengths, but that doesn't make the slide rule wrong.
It is not an argument for Mercator projection maps to appear as the canonical Earth map in textbooks, on classroom walls, or anywhere else where education is concerned.
Obviously not the best for navigation, but considered the best compromise for viewing the entire Earth in two dimensions.
[1] http://en.wikipedia.org/wiki/Robinson_projection
If only. Mercator projection is still quite widespread. Try google image search of world map.
Wow. That question is annoying enough when the subject is a large university. I can't believe you were asked that.
Mercator preserves shape and direction at the expense of size. Peters preserves size and direction at the expense of shape. Peirce Quincuncial preserves shape and size at the expense of direction. Here's a transverse Peirce Quincuncial map I generated: http://frammish.org/tpq.jpg
Many other projections try to combine these, like the Miller projection maintains direction but strikes a balance between shape and size, getting neither one right, but neither is horribly wrong either. The Winkel Tripel projection tries to balance all three attributes.
I knew college professors who believed that most map projections have a eurocentric bias, but it makes almost as much sense that creating maps and globes is easier to do if you assume the Earth is a perfect sphere.
I'm not sure any of this is really accurate. Go read the wikipedia page: http://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection#...
tl;dr:
-Peters wasn't novel. An identical projection was created a century earlier (that's why it's called Gall-Peters).
-Peters made completely BS claims about his projection.
-Cartographers had already been using plenty of projections beyond Mercator for a long time and they knew very well that it had problems.
By the way, I'm pretty sure the xkcd about projections has a punchline and hover text that is directly related to the information above.
Don't the mean "in some spheres"? ;)
I've seen this behavior previously (it's becoming more common) and I reward it the same way each time: closing the site and putting it on my proxy's blocklist.
I might take up the project of posting the relevant wikipedia links as stories, and in turn linking those in the comments of all shoddily written blog posts, in the hope of righting these wrongs.
CE sucks.
Personally I really like this one: https://en.wikipedia.org/wiki/Dymaxion_map It's basically a net that you can print of and fold together.
Personally I'd prefer a map that emphasizes that the world is actually a sphere, rather than a rectangle. I also have a soft spot for Dymaxion, although I don't use Dvorak.