fsgregs wrote:Some of the discussion here points out how unlikely it would be to find an exact duplicate of us somewhere else in an infinite universe. Selden put it in molecular/atomic terms. What are the odds that there exists another body in the universe that has the same number, and same arrangement of atoms as us?
Every basis that You have for this is pure speculation. In reality, there are no odds for something to exist. It either exists, or it does not exist. And this is where You misinterpret statistics.
What are the odds for anything
to exist? Is the chance for the existence of the keyboard I am typing on right now greater or lower than the chance for the existence of the bottle of Fanta out of which I am drinking? Which of both is more probable to exist?
Do You notice that these questions are basically senseless?
If everything in the universe would be truly random, then computing such chances would really make sense. But even in an infinite universe, You can never-ever know if something exists infinitely often, only twice or even only once. You can only evaluate a probability when You know in which way the configuration of matter in the universe is structured. But You don't know it, therefore You assume it is random. At least You do so for the rest of these thoughts:
There are approximately 7 x 10^27 atoms in the human body. That is a big number but obviously quite finite.
There are close to 90 natural elements in our body, arranged in particular patterns. I am not a mathematician and would shutter to calculate the # of ways that 90 atoms could be arranged to form a whole that contained 10^27 such atoms.
Did You think of the following: How do You know that every of these possibilities even can
exist in our universe? Maybe the configuration of matter in our universe follows such rules that a large deal of those "thinkable" configurations would not have been possible at all!
Your basic assumption is that every configuration has roughly the same chance of existence. And I don't see at all why this should be so.
The arrangement of these atoms is a finite possibility but the probability that another "object" in the universe has the identical arrangement of atoms is ... well ... very SMALL! Yet, it is not infinitely small. It may be 10^50000 or more, but it is finite. In my understanding of infinity, that means that somewhere in the universe, there MAY BE another human identical to you and me.
There may be, or there may not be. Quite right: No matter how the theoretical chance is - it may even be that the object in question is unique whithin an infinite universe! That's why the next sentence is wrong:
IF you so chose to find two of you, you could theoretically do so ... and three ... and 30 ... and ....
No, you would not find two, or 30, if there is only ONE of You in the universe.
Obviously, this does not mean there are an infinite number of humans exactly like us ... just that there could be ... IF the universe were truly infinite in size and IF the # of atoms in the universe was infinitely large. Since the universe does not appear to be infinite, the point may be moot, but for those who choose to believe the universe is infinite ... this still seems to be one consequence of that belief!
Still, I don't see why it counts as proven that the universe is finite in size. Of course, we would get into problems with gravity if we think of an infinite amount of matter in the universe. But still, we only observed a very small and limited part of the universe, for only a few thousand years. Who could really expect that we had found all the laws dealing with it? - It's obvious that there are still more discoveries ahead than lie behind us. At the current point of knowledge, it can neither be taken for granted that the universe is finite nor that it is infinite.