(This is an exercise, be careful not to spoil the answer to yourself)
All world maps are wrong due to the fact that it’s impossible to flatten a sphere without distortions.
there is a simple idea anyone can think of that greatly improves the accuracy of flat maps and that no has tried in the last 2000 years—Until last week, when three Princeton researchers thought about it.
Take a moment to try to think what you might do to improve the accuracy of flat maps.
I’m making this an exercise since this seems like incredibly low hanging fruit that hasn’t been picked up, and the idea will seem obvious in retrospect.
Ok, stop here and think, spoilers ahead:
* * * *
Make a double sided map, of course!
Instead of projecting a sphere to a flat surface, they just projected two hemispheres to two surfaces and glued them together.
“Goldberg and Gott invented a system to score existing maps, quantifying the six types of distortions that flat maps can introduce: local shapes, areas, distances, flexion (bending), skewness (lopsidedness) and boundary cuts (continuity gaps). The lower the score, the better: a globe would have a score of 0.0.”
The previous best on this metric was the Winkel Tripel projection, with a Goldberg-Gott score of 4.563
Their new design is better than the Winkel Tripel on every one of the 6 matrices, with a slightly lower Goldberg-Gott score of 4.497.
The other huge advantage of their design is that it’s the only flat design that has the topology of a sphere. if you go over the edge it’s exactly like going over the equator.
The other advantage is a bit less concrete—Their design just looks fun. it makes me want to hold it in my hands. other designs don’t do that for me.
They also made maps of other solar system bodies, available in their paper (Starting at page 24). Here’s mars:
This is a breathless article about something that’s obvious to people who know the state of the art. (I’ve worked in geoinformational systems.) If you want a map that shows the shapes and sizes of continents without too much distortion, and don’t mind having two circles, the Nicolosi globular projection is a thousand years old.
Huh. Well, thanks for pointing that out. I see that it is part of the collection they mentioned, but they didn’t count it as a two-sided map. Is it suitable for two-sided map? Was it used that way?
I don’t know, something about this smacks of “prestigious people reinvent obvious thing that was previously dismissed out of hand because it didn’t meet the criteria but if you’re prestigious enough people might bend the criteria for you”.
In particular I think the point was largely around having two dimensional projections. Using both sides is, in some sense, not really a 2D projection anymore since you have to interact with it by rotating it. And if you have to do that you’re most of the way to just using a globe instead.
The idea is that it lets you compact a globe from 3D space to 2D space with minimal distortions. You can carry a 100 such maps in less space than one globe would take. (Of course, if your requirements are to be able to see everything at once, then this doesn’t fit)
So what you said in the first paragraph doesn’t seem true to me, but if someone did invent that already and was dismissed i would be interested to hear.
My guess was: you could have a different map, for different parts of the globe, ie a part that focus on Africa (and therefore has minimal distortions of Africa), and a separate part for America, and a separate part for Asia, and so on.
Well, in a way that’s what they did. They have two maps for each hemisphere which connect perfectly when glued together. But the idea of having different maps for different places on it’s own has been done countless times.
The biggest disadvantage of this that I could see is that it prevents you from seeing the entirety of the map at once. This is reflected in the article linked, “”Our map is actually more like the globe than other flat maps,” Gott said. “To see all of the globe, you have to rotate it; to see all of our new map, you simply have to flip it over.”″.
(This is an exercise, be careful not to spoil the answer to yourself)
All world maps are wrong due to the fact that it’s impossible to flatten a sphere without distortions.
there is a simple idea anyone can think of that greatly improves the accuracy of flat maps and that no has tried in the last 2000 years—Until last week, when three Princeton researchers thought about it.
Take a moment to try to think what you might do to improve the accuracy of flat maps.
I’m making this an exercise since this seems like incredibly low hanging fruit that hasn’t been picked up, and the idea will seem obvious in retrospect.
Ok, stop here and think, spoilers ahead:
*
*
*
*
Make a double sided map, of course!
Instead of projecting a sphere to a flat surface, they just projected two hemispheres to two surfaces and glued them together.
“Goldberg and Gott invented a system to score existing maps, quantifying the six types of distortions that flat maps can introduce: local shapes, areas, distances, flexion (bending), skewness (lopsidedness) and boundary cuts (continuity gaps). The lower the score, the better: a globe would have a score of 0.0.”
The previous best on this metric was the Winkel Tripel projection, with a Goldberg-Gott score of 4.563
Their new design is better than the Winkel Tripel on every one of the 6 matrices, with a slightly lower Goldberg-Gott score of 4.497.
The other huge advantage of their design is that it’s the only flat design that has the topology of a sphere. if you go over the edge it’s exactly like going over the equator.
The other advantage is a bit less concrete—Their design just looks fun. it makes me want to hold it in my hands. other designs don’t do that for me.
They also made maps of other solar system bodies, available in their paper (Starting at page 24). Here’s mars:
Now I’m just left with two questions:
How did no one think about this before
Why aren’t they selling maps
See the full article about this here
This is a breathless article about something that’s obvious to people who know the state of the art. (I’ve worked in geoinformational systems.) If you want a map that shows the shapes and sizes of continents without too much distortion, and don’t mind having two circles, the Nicolosi globular projection is a thousand years old.
Huh. Well, thanks for pointing that out. I see that it is part of the collection they mentioned, but they didn’t count it as a two-sided map. Is it suitable for two-sided map? Was it used that way?
In any case, oops.
I don’t know, something about this smacks of “prestigious people reinvent obvious thing that was previously dismissed out of hand because it didn’t meet the criteria but if you’re prestigious enough people might bend the criteria for you”.
In particular I think the point was largely around having two dimensional projections. Using both sides is, in some sense, not really a 2D projection anymore since you have to interact with it by rotating it. And if you have to do that you’re most of the way to just using a globe instead.
The idea is that it lets you compact a globe from 3D space to 2D space with minimal distortions. You can carry a 100 such maps in less space than one globe would take. (Of course, if your requirements are to be able to see everything at once, then this doesn’t fit)
So what you said in the first paragraph doesn’t seem true to me, but if someone did invent that already and was dismissed i would be interested to hear.
My guess was: you could have a different map, for different parts of the globe, ie a part that focus on Africa (and therefore has minimal distortions of Africa), and a separate part for America, and a separate part for Asia, and so on.
Well, in a way that’s what they did. They have two maps for each hemisphere which connect perfectly when glued together. But the idea of having different maps for different places on it’s own has been done countless times.
The biggest disadvantage of this that I could see is that it prevents you from seeing the entirety of the map at once. This is reflected in the article linked, “”Our map is actually more like the globe than other flat maps,” Gott said. “To see all of the globe, you have to rotate it; to see all of our new map, you simply have to flip it over.”″.
Right, it’s not the sort of map you’d want to put on a wall, it’s intended to be interactive and give the benefits of a globe in flat space.