| To Infinity and
Beyond! Paradoxes in Finite and Infinite Universes Is an infinite Universe any less counter-intuitive? The following is usually called the infinite replication paradox: Suppose the Universe is infinite and it does look the same everywhere we go (lots of galaxies, stars, etc). Then, any event that has a positive probability (positive chance of happening, even it it is 1 in a billion trillion trillions) happens infinitely often. The consequences of this fact are quite surprising. 1) The existence of planets like earth seems to be of positive probability, since earth exists and astrophysicists are finding many other planets around. Therefore, if the universe is infinite, there are infinitely many planets like earth in the universe. 2) There might be a positive probability for the existence of life. This is not clear, but we know that life exists, and it seems life should appear in any planet like Earth. Thus, if the universe is infinite, there are infinitely many planets which are earth-like and with life. 3) The fact that life might evolve into a being like YOU, exactly like you, is of positive probability (if we assume that life has a positive probability) because there are only so many molecules that can be formed which may be stable in an earth-like planet. Actually, it is of positive probability that a being exactly like you exists at *exactly this time*. So, if the universe is infinite, there are infinitely many copies of you populating the universe at this very moment! 4) Even more... Some theories say that time is infinite, that the universe has been contracting and expanding for ever. If this is true, then there have been infinitely many copies of you before you, in the past which have taken *all possible choices* that you have made in your life, those choices that you have taken and those which you have not!!! |
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