Hacker News Reader

Hacker News

Comment by Bud | Hacker News Reader

Full thread

Bud

"On flat maps, it’s impossible to represent land mass size on a relative scale."

Um, no it's not. TechCrunch needs better editors. You just need to use a non-Mercator projection.

https://en.wikipedia.org/wiki/Gall%E2%80%93Peters_projection

View on HN

You can represent size or shape correctly, not both.

Anyone who uses the Gall-Peters projection is a cop.

Obligatory XKCD

https://www.xkcd.com/977/

Google decided to go with "A Globe".

At low zoom levels.

Given the behavior of the poles (they're not viewable; the south is also a black hole…), I suspect that there's a very smoothly done transition to web mercator for the higher zoom levels.

Correct. At high zooms, the trig required in the spherical math becomes inaccurate, so we fade back to simple web mercator.

Cartography wouldn't be able to use all these cheap tricks if the poles were habitable territory.

Can you imagine the distortion on a map of a small town located at the pole if Mercator was used?

You can get pretty close though. Like a Dymaxion map (shown in sibling's XKCD link) or one of those orange-peel maps if you have enough little slices.

Edit: better Dymaxion link https://en.wikipedia.org/wiki/Dymaxion_map It's made of triangles that you can rearrange, which isn't really shown in the xkcd.

> You can represent size or shape correctly, not both.

You can if you don't mind having a non-rectangular map border.

https://en.wikipedia.org/wiki/Dymaxion_map

Dymaxion maps are still deformed, just not as much as most other projections.

That's still not an accurate map. 3D maps don't have projection issues, they can have near perfect representation of the world.

The eyes see a 2-dimensional picture. Computer displays produce a 2-dimensional picture. There is no such thing as a “3D map” on a standard computer display. Only an orthographic (or maybe perspective) projection which animates in response to user input.

In general an orthographic projection is a poor choice. The thing going for it is that it is easy to understand by analogy to a physical globe, and human spatial understanding can partially compensate for the distortion by imagining a sphere.

But there are also disadvantages, for example on an orthographic projection north is not always vertical, latitude and longitude lines are neither perpendicular nor straight, shapes and areas can be very dramatically distorted near the edge of the map, there are dramatic distance errors between far away points or points not in the center of view, it is impossible to view more than half of the planet’s surface in one view, etc.

There are many other choices of map projections, and for any particular purpose, some other projection is usually better.

Regardless of what the eye sees, the brain perceives three dimensions. This projection happens to be the one that the brain can automatically unpack into an accurate 3D representation. Technically, things near the edges are squished and distorted, but that gets undone in the wetware.

You really can’t get an accurate sense of angles/shapes, areas, distances, or directions with an orthographic projection except by moving the view around. Even when you do, it is very difficult to accurately compare attributes of regions which are far away on the globe, and easy to mislead yourself. (This is a problem with physical globes as well.)

For many types of mapping use cases, orthographic projections are substantially worse than other possible choices.

Sometimes physical spheres (or virtual representations of spheres as dynamic orthographic or perspective projections) are nice. That’s why I spent a whole bunch of time building myself a spherical chalkboard, for example. But they aren’t the best choice for any purpose. Personally I don’t think they make a very good choice for a general-purpose world map. They are better as a supplement to flat maps.

Let me give you a concrete example.

Here is what North America looks like on this new map:

https://i.imgur.com/lCI8DjY.jpg

This is not a good projection to use if you want to see all of North America. There is dramatically more distortion than necessary, and shapes near the edges get very squished (the west coast of the US is okay), but it is not at all obvious to a naïve viewer what kind of distortions are involved, and past experience looking at soccer balls or whatever isn’t going to fix it.

(Note: a Mercator projection is also not a good choice for this. On a Mercator projection sizes are dramatically bloated as you go north.)

I'm not convinced it isn't still the best option. The naive viewer may not properly perceive the distortions, but I bet they'll get closer than with anything else, for general purposes.

What projection would you say would be good for that view?

For North America per se you could e.g. pick the conformal projection with roughly constant scale around the boundary of the continent (one world atlas does this), or you could pick a projection which minimized distance errors (there are several possible ways of quantifying those, which will yield different maps), or you could pick among several equal-area projections (especially useful if you want to make a choropleth map), or for something dynamic you could use an azimuthal equidistant projection or some conic projection (e.g. Lambert conformal conic, Albers equal-area conic), or .... https://pubs.er.usgs.gov/publication/pp1395

There are many choices. An orthographic projection is generally one of the worst except insofar as it gives the impression of a physical sphere when you zoom all the way out.

You can, of course, use VR to get a stereoscopic 3D display as well, like what humans see in the real world. Except for depth of field (which some prototype VR systems can still accomplish), that's as 3D as real life. And Google Maps/Earth VR can indeed do that.

what about focus?

Some VR companies are working on that.

I'm amazed this has been downvoted so much... As the OP stated, "globe" view (a.k.a. orothographic or perspective, depending) is not fundamentally better than other projections. It has tradeoffs. You should always choose the projection that matches your use case.

A map is a visualization tool. The goal is not to reflect reality as accurately as possible. The goal is to communicate data and spatial relationships. Projections are part of that. There is not a "best" projection. Orthographic with some animations is a nice visual tool for some purposes and terrible for others.

How could pointing this out be controversial? A bar graph is not a perfect representation of a group of numbers, but it's a very useful visualization. A map is no different than any other visualization.

it's a theorem of differential geometry that we cannot have a (perfectly) accurate 2d map of the earth.

The author of TFA didn't write "perfectly accurate" but "land mass size on a relative scale". Bud is correct.

the author of TFA probably thought the desire for correct shape in a map is implied and wasn’t trying to defend against map pedantry. of what use is a map if the shapes are wrong?

One of the revolutions in the first Underground/Subway/Metro maps was that by throwing away the actual shapes, it is able to represent the stations and the relationships between them far clearer than otherwise.

a subway map has little to do with a geographic map. only the nodes and time traveled between them matter. the shape of the actual routes is immaterial.

It's much cheaper to make an incorrect statement and let people correct you for free, then edit the article! ;)

Reply on news.ycombinator.com