Page 89 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 11
out, while the other dimensions remain tightly curled up?

One possible answer is the anthropic principle. Two space dimensions do not seem to be enough to allow for
the development 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 digest completely, it would have to bring up the remains the same way it
swallowed them, because if there were a passage right through its body, it would divide the creature into two
separate halves: our two-dimensional being would fall apart Figure 11:8. Similarly, it is difficult to see how there
could be any circulation of the blood in a two-dimensional creature.

Figure 11:8

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 in three dimensions. (In three dimensions, the
gravitational force drops to 1/4 if one doubles the distance. In four dimensions it would drop to 1/5, in five
dimensions to 1/6, 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 from or into the sun. We would either freeze
or be burned up. In fact, the same behavior of gravity with distance in more than three space 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 in an atom would behave in the same way as gravitational forces. Thus the electrons would either
escape from the atom altogether or would spiral into the nucleus. In either case, one could 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
dimension and three space dimensions are not curled up small. This would mean that one could appeal to the
weak anthropic principle, provided one could show that string theory does at least allow there to be such
regions of the universe – and it seems that indeed string theory does. There may well be other regions of the
universe, or other universes (whatever that may mean), in which all the dimensions are curled up small or in
which more than four dimensions are nearly flat, but there would be no intelligent beings in such regions to

file:///C|/WINDOWS/Desktop/blahh/Stephen Hawking - A brief history of time/j.html (8 of 11) [2/20/2001 3:15:56 AM]