GGLucas wrote:On the infinite thing, I think you'll need to distinguish between an infinite string of things that are following a pattern, and an infinite amount of things following a chance.
The positive integers follow a pattern, so that might explain why the square root of 2 isn't in there, but look at is in this way:
If the chance of something happening is 1/2, then in 3 scenarios, the chance of it not happening will be (1/2)*(1/2)*(1/2) = 1/8, in an infinite amount of scenarios, the chance would be (1/2)^infinite, which we can accept as being 0 (just like (1/2)+(1/4)+(1/8 )+(1/16)...ad infinitum...is accepted as 1)
Of course, if the chance is 0 in the first place, then it won't be possible in any of the situations, but we can only say something is impossible by looking at the set assumptions that we have, and those can change too.
Hence, if something is a chance (and, mostly, everything is), we can say that in an infinite amount of scenarios, every possible situation will happen.
I have a feeling that ultimately this is going to come down to your gut reaction. Mine is that in an inifinite number of universes, it is NOT the case that everything imaginable happens. Perhaps I'll have difficulty proving it, but I nevertheless think it's true.
To give a possible example that might help explain what I mean: If evolution were to continue ad infinitum on this planet (assume for a moment that the Earth and Sun last for ever and don't change significantly). Would any animals evolve wheels? How about the ability to zap each other with bio lasers? I can dream up quite a few of these - attributes that sound whacky, but are just about believable: and yet, it's quite possible that the way evolution works means that some of them will simply never happen, no matter how long it takes.
Isn't it possible that the laws of physics are like that, too? That there are certain things that we might feel are feasible, but, due to some impenetrably complex phenomenon in physics, of which we are unaware, simply cannot happen, even in an infinite number of universes?
And the same thing applies to hypotheticals...
Or, here's another example. How many times does the letter "G" appear in the decimal expansion of pi? None at all, of course. But if you didn't know what you were looking at, and thought that both letters and numbers could appear, you might say "as this is an infinite, non-repeating sequence, there must be a G sooner or later". Wrong! You missed the fact that G simply cannot be expressed on that substrate...
I'd better stop now. It's late, and I've just played a gig with my band so I'm a bit manic. Can you tell?
I think those are crocodile tears: you must be in de Nile.