- #1

- 240

- 1

## 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.

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.