Posts Tagged ‘Finite’
Finite worlds I have loved
We are utilized to a finite globe getting a sphere, but we also have encounter of a finite world getting other shapes, even if most of us don’t think about it that way.
For example, the classic video game Asteroids was on a torus. That’s the same topology as a donut, which may possibly appear odd, considering that the screen is flat. But in Asteroids, if you fly off the screen to the correct, you display up once again on the left side of the screen. Similarly, if you fly up, you seem once more at the bottom of the screen. If you think about it, this is exactly what happens if you stroll around a donut.
You can see that it’s far more like a donut than like a sphere if you believe about two characters standing side-by-side going close to the globe and coming back to in which they every started out. On a sphere, their paths will cross along the way. On a torus (this kind of as the world of Asteroids) their paths will never ever cross.
In the early Charlie Kaufman film Human Nature, there is a scene with Tim Robbins in the afterlife where his character tries to leave by a door to the left, only to discover himself walking back into the same room via an identical door on the proper. At that point the character realizes he is trapped in a tiny self-contained universe.
This notion was blatantly ripped off two years later in Matrix: Revolutions, when Neo runs along a set of train tracks only to find himself arriving back at the same station from the other direction. The sad sad factor is that this was the only actual clever second in the complete film.
Finite worlds
Our Earth is, topologically, a finite planet. If you go far enough in any one direction, in a “straight” line, you are in fact traveling in a fantastic circle close to the globe, so you will sooner or later end up back exactly where you started.
For most folks this is a theoretical concept. It is rare that everyone has occasion to go totally around the globe, so the finiteness of the Earth is in a lot of ways disconnected from our everyday knowledge of life.
But suppose we lived in a universe that was actually finite, at a scale tiny adequate for it to matter on a human level. Suppose that any time you walked, say, a mile in any path, you discovered yourself back in which you started. What would that be like?
Points grow to be even a lot more radically different as the scale gets smaller. Visualize a globe that repeated on such a tiny scale that if you looked out into the distance, you could see the back of your own head. In which if you shone a laser beam, it would come back from the other direction. In such a world, guns would be worse than useless — if you shot off a firearm, the most probably outcome would be suicide. Now we are obtaining to the kinds of queries that M.C. Escher was obviously considering about.
How would living in such a planet transform the way we consider about issues? It would surely adjust the way we think about city planning and architecture, but would it also transform our aesthetics, our mathematics, our music and art?