"Two space dimensions do not seem to be enough to allow for the developement of complicated beings like us. For example, two- dimensional animals living on a one-dimensional earth would have to climb over each other in order to get past each other. If a two- dimensional creature ate something it could not ingest completely, it would have to bring up the remains the same way it swallowed them, because if there was a passage right through its body, it would divide the creature into two seperate halves; our two- dimensional being would fall apart. Similarly it is difficult to see how there could be any circulation of the blood in a two- dimensional creature.
"There would also be problems with more than three space dimensions. The gravitational force between two bodies would decrease more rapidly with distance than it does with three dimensions. (In three dimensions. the gravitational force drops to 1/4 if one doubles the distance. In four dimensions it would drop to 1/8, in five dimensions to 1/16, and so on.) The significance of this is that the orbits of planets, like the earth, around the sun would be unstable; the least disturbance from a circular orbit(such as would be caused by the gravitational attraction of other planets) would result in the earth spiraling away into or away from, the sun. We would either freeze or be burned up. In fact, the same behavior of gravity with distance in more than three dimensions means that the sun would not be able to exist in a stable state with pressure balancing gravity. It would either fall apart or it would collapse to form a black hole. In either case, it would not be of much use as a source of heat and light for life on Earth. On a smaller scale, the electrical forces that cause the electrons to orbit round the nucleus of an atom would behave in the same way as gravitational forces. Thus the elecrons would either escape from the atom altogether or would spiral into the nucleus. In either case one coudl not have atoms as we know them.
"It seems clear then that life, at least as we know it, can exist only in regions of space-time in which one time and three space dimensions are not curled up small."
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