The other day I had an idea. What if you took a map of some country, and from each coordinate computed the time it took to any other coordinate. The basic assumptions are that you can drive on road by car from parking lot to parking lot, and from parking lot to another point you can get only by foot. You can also add trains, and airplanes, each having less routes, but are actually faster. So for example, traveling from city A’s center to city B’s center is quite fast, but traveling from city A’s center to some point near the road from A to B will take some time.
This is a bit similar to computations done by game AI’s to determine how to get from point A to point B on a game board.
Now let us assume assume we want to draw the resulting graph on some kind of a 3D map, where the distance of each point from other points is determined by the time it takes to reach from that point to the others. Actually, it might not always be possible to plot this graph on a 3D map as a friend pointed to me, as 3 neighboring points already lock our point in space. But let us say that you can plot this 3D map. A’s center and B’s center will be near each other, a bit like a paper folding – which is incidentally the most common depiction of ‘science fiction wormholes’ explanations to laymen. It was pretty nice to try and visualize this kind of map. It is also interesting to think what is the least number of dimensions required to plot a given map.
Although I couldn’t come up with ideas about how this kind of visualization might be useful, it was still fun to to think of.