The True Size of Africa - Misleading Maps | Hacker News Reader

The True Size of Africa - Misleading Maps

collective-evolution.com

165 pointsgurvinder101 comments

>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.

[1] http://en.wikipedia.org/wiki/Rhumb_line

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.

Just because it’s old doesn’t mean it’s good.

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".

>Oh, so what you are saying is that they have been wrong and misleading for the past 500 years?

Umm no. You can also mislead yourself by using a slide rule to measure lengths, but that doesn't make the slide rule 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.

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.

This is a consequence of theorem discovered by Gauss: Theorema Egregium http://en.wikipedia.org/wiki/Theorema_Egregium

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.

I like your Peirce Quincuncial projection. It makes Florida look much more excited.

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.

I like how there no real sense of up or down in the Peirce Quincuncial map.

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.

Obligatory XKCD: http://xkcd.com/977/

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/Map_projection

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.

http://en.wikipedia.org/wiki/Geographic_information_system

A spherical globe still counts as a projection of our non-spherical planet!

I've always preferred using a globe to get a perspective on the Earth and the various positions of continents and nations.

>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'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.

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.

The wikipedia page says: "Maps based on the projection continue to see use in some circles."

Don't the mean "in some spheres"? ;)

The peters projection doesn't solve the size problems, it just moves them around.

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 was hoping to see someone post 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?...

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.

[0] http://en.wikipedia.org/wiki/File:Dymaxion_2003_animation_sm...

You could "unproject" another projection for which you have texture back to your sphere and then do the isocahedron projection.

Also, maybe you can find a database of the countries border as lat/lng polygons and just draw the countries.

Natural Earth has lots of that kind of databases: http://www.naturalearthdata.com/downloads/

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.

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.

Thank you! :-)

So how is that Dvorak keyboard working out for you?

The toe-shoes are great, at least.

Yes, yes they are.

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?

Distance isn't preserved except along the 45th parallels.

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).

Maybe so, but every straight line is nearly on a geodesic (great circle) until it goes off an edge. Show me another flat map that does that.

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.

Wait, I got it.

Let's call them globes.

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.

Isn't this a regression from Google Earth, a globe zoomed out, zoomed in a flat map?

Yes, the new Google Maps in Earth mode is perfect. But in the normal Maps mode, it's just the old Mercator projection.

Land masses represented in a continuous fashion. Makes us all feel "connected".

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?"

>"Oh, you lived in Africa--did you know So-and-so?"

Wow. That question is annoying enough when the subject is a large university. I can't believe you were asked that.

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).

What I hate even more is when the answer is "Yes".

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.

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.

CE sucks.

This article has been reworded by blogs since 2010 some time:

http://calabarboy.com/2010/10/11/the-true-size-of-africa-kai...

pardon me, but where's Alaska?

they list 9.629M for USA, Google says 9.827M. Alaska, according to Google = 1.718M.

WAT?

Where is Canada? If we are to count huge landmasses hostile to human habitation, here we are:

Sahara desert: 3.629 million sq miles (9.4 million km²) Canada: 3.855 million sq miles (9.985 million km²)

Yes, and the idea of comparing Africa to other countries is certainly not new. Here's an example from 2006: http://bigthink.com/strange-maps/35-the-size-of-africa

At the time, the Economist also redid the exercise starting with an equal-area projection: http://www.economist.com/blogs/dailychart/2010/11/cartograph...

https://www.facebook.com/photo.php?fbid=10201142599660581&se...

This is regrettably hilarious. I'm laughing in shear disappointing hilarity.

I'm almost disappointed that he didn't stick North America in there with the rest of them.

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.

But you do use XML?

I do, though not as much as I used to.

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).

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.

Africa is big. The Sahara desert is also big.

But this whole "true size" is true in measure, but I'm not really comfortable with people using it to push their agenda

Yes, Africa is big, and?

Big countries (yes, Africa is not a country) are usually on the wrong side of the stick. Maybe the USA has the most usable land, but it's still costly for them

Asia is gigantic, where's its population? Concentrated into tiny spaces! Japan, Indonesia, a narrow stretch of India.

And um China.

Yes, in China it's concentrated on coastal areas mostly

http://humangeography.wikispaces.com/file/view/ChinaIndiaPop...

It's concentrated in coastal areas pretty much everywhere.

I'm confused...I thought the Robinson Projection [1] has been the standard for quite some time.

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

> I'm confused...I thought the Robinson Projection [1] has been the standard for quite some time.

If only. Mercator projection is still quite widespread. Try google image search of world map.

Google Maps itself is mercator when fully zoomed out.

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.

See http://xkcd.com/977/ for a summary of even more types.

http://en.wikipedia.org/wiki/List_of_map_projections has many more.

Why does no one seem to care that the bottom 15 degrees is missing from virtually every projection? If it's just because it's un-inhabited why not cut off the top 15 degrees as well?

Among other reasons, because the top 15 degrees aren't uninhabited.

Well, technically the bottom 15 degrees aren't either. What are the other reasons? Because you don't need to navigate around it to get somewhere else? If you're just going to omit parts of the globe because they're empty, why bother mapping seas or the Sahara Desert?

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.

What the fuck? There is an "Eastern Europe" country now? Ukraine alone is larger than Spain.

Maybe some kind of globe like this: https://www.youtube.com/watch?v=ah_gXnjjdk4 or http://workshop.chromeexperiments.com/globe-search/ is best? Otherwise just buying a standard globe will do just fine. Peter's is hardly better. It still destroys the appearance of the earth quite badly.

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.

Antarctica is also the size of Europe. So what? What does geographical size have to do with anything? Kazakhstan is the 9th largest country in the world. What does it mean?

It means that geographically, Kazakhstan is the 9th largest country in the world. And not much else.

Reminds me of this mercator projection puzzle: https://gmaps-samples.googlecode.com/svn/trunk/poly/puzzledr...

I knew Africa was large. I did not know that Antarctica is larger than Europe at 5.5 million square miles (Europe is 4.0 million square miles).

I did not like the picture showing various countries contained within Africa. Why is Alaska not considered part of the "US"?

Several times while driving North through mid-western States I've been startled to realize how much land is north of the US border in Canada. I knew Canada was larger than the US, but I didn't comprehend the scale of that country.

I looked at his packing... he is comparing countries to a continent. In physics, that is called mixing units and your professor marks the answer wrong, regardless of whether the number is "correct."

He is comparing land masses. If he wanted he could stick a city in there for good measure, it's all about comparing things people can images with other things... No mixing of units here.

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.

btw, the surface area of the moon is about the same as Africa's.

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.

I think at this point, those with means should switch to holograms. After all, it's often those with means who can influence those without.

Why does he describe the map as including "[...] Argentina and three Scandinavian countries"? Neither of those is on the map.

For the purposes of most policy making, it would be better to scale maps by population. This would make Africa much smaller.

OT: I love this article just for including the "west wing" video.

Next up: north is not really up, and south is not really down.

Brazil is pretty huge in Gall-Peters too.

Hooray for globes

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.

Sure you don't have some sort of virus or Malware? Didn't do that for me on a couple of browsers.

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.

West Wing - Why we are changing maps? http://www.youtube.com/watch?v=n8zBC2dvERM

You know this video is linked like 4 sentences into the article, right?

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