So I've been thinking about the infinite universes model, where each possible action or event creates a new universe for each outcome. For example, if you flip a coin there will be one universe in which the coin came up heads, and another in which it came up tails. Each new universe then has an entirely new set of possibilities which all spawn yet more universes.
So I was thinking about a machine in which you could simulate the entire universe from beginning to end, and seeing the consequences of each result. Of course there are infinitely many, but if you had perfect information you could pick out your universe by looking at the past. Basically if you looked at it as a tree, where each branch was a new possibility, you could find your branch by following from where it grew.
My question comes when you start trying to look at the future. There are an infinity of possible futures, and this machine could certainly predict one of them, or many of them, but it's very unlikely you'd ever predict the one you are on.
So this has been more philosophical than mathematical, but now I come to my question:
Is it mathematically possible to guess the correct branch in an infinity of choices? Or put another way, if I had an apple, and I threw it into a barrel filled with an infinite number of apples, could I ever correctly guess which one was mine? Is it possible to point to one and correctly say, "I think that one is mine"?