Maps in 2D

Main Question or Discussion Point

Suppose we were completely two-dimensional creatures, two dimensions plus time. How would we make maps?

The obvious idea is that we make a 2-D map which is our world on a smaller scale. But there is a problem with that. If the map is 2D paper then we can only sense the edge, so it's useless. Instead it would have to be something like glass. It would be necessary to look through the map and triangulate by moving around. I guess that would work. Would be difficult to make.

A more practical way would be a line with a perspective drawing on it. It would depend on a certain view though. It would be a "this is what you would see if you are standing at this point looking in a certain direction." Taking it a step further, the map could be a circle that one gets inside by opening the circle, entering, and closing the circle again. Then one would see a perspective drawing in every direction. It would be centered at one specific point of the region. One would have to imagine oneself inside the scene to estimate distances between two points not at the map's origin.

What if instead of a circle we made a ring of glass, and moved around inside of that? I think relations would be distorted. It would be of some use but would take practice to make sense of, and if you wanted to be exact you would have to use math.

I think that this is the best you could do. You couldn't make a map that didn't assume a point of view. The only way we get away with making paper maps like that is that our 3rd dimension is insignificant. One does not find one hundred cities stacked on top of one another.

Related Other Physics Topics News on Phys.org
DaveC426913
Gold Member
In our 3D world we make 2D maps of 2D objects, such as the surface of the Earth.

So a map in a 2D world would analogously be a 1D map of a 1D object (line segments).

A 2D denizen attempting to make a 2D map of a 2D object is analogous to us in our 3D world trying to make a 3D map of a 3D object. It would have a be a 3D scale replica of the 3D object. And, unless it were transparent, we would only be able to see its outer surface.

The surface of the earth IS 3d, not 2d(bet this starts a fight), as patrick said, we can simplify it to 2d because the height is insignificant in most cases.

Depending on what we are mapping you could use color to indicate distance, just as we use color to indicate the 3rd dimension of the surface in a topographical map

The 2d surface would only be true of a smooth sphere whose height was a constant distance to the center, otherwise using only longitude and latitude does not tell you the radius from the center.

DaveC426913
Gold Member
The surface of the earth IS 3d, not 2d(bet this starts a fight), as patrick said, we can simplify it to 2d because the height is insignificant in most cases.
Yes.