3 ms·
Look at a game of Asteroids: https://www.youtube.com/watch?v=_TKiRvGfw3Q https://www.youtube.com/watch?v=_TKiRvGfw3Q It takes place on what is topologically a
by jerf 6y ago
Look at a game of Asteroids: https://www.youtube.com/watch?v=_TKiRvGfw3Q https://www.youtube.com/watch?v=_TKiRvGfw3Q
It takes place on what is topologically a torus, because the top of the screen and the bottom are the same, and the left and right are the same. From the point of view of the player, the space never ends; if there were no asteroids and you simply went left forever, you'd never find the end. Nevertheless, the X and Y dimensions are finite, because that is the shape of space in that game. But note you could grow or shrink those all you like, and all you'd change is the size of the playspace; nothing else about such shrinking or growing would be impossible or fundamentally change anything.
There is more than one way to hook such structures together: https://www.youtube.com/watch?v=jj5lDmaQTuo&t=0s https://www.youtube.com/watch?v=jj5lDmaQTuo&t=0s In that video the author plays with discrete cases of topologies like the asteroids case where otherwise flat space is just glued together in various configurations but there are continuous analogues to at least most, if not all of them, along with options on how to handle the curvature.
The video also deal with macroscopically-sized things, using a model of Earth as its example, but if you can imagine it being shrunk down arbitrarily small in one dimension you can get an idea. Obviously, if you shrink one of them down arbitrarily small you would get a "3D space" that is effectively only 2D, because one of the numbers would seem to be irrelevant since it is always very small. In the real universe this would be some set of dimensions beyond the usual 3 spatial dimensions.