Originally posted by ChaoticOrder
This really got me thinking about just how far the limits of probability stretch. For instance... if our Universe is Infinite, which it seems to be, then it's a mathematical certainty that somewhere out there is a planet exactly like Earth. And a person exactly like you. In fact there would be an infinite number of copies of you out there. There would even be copies of our Universe out there.
While there is no difference between almost surely and surely (that is, entirely certain to happen) in many basic probability experiments, the distinction is important in more complex cases relating to some sort of infinity. For instance, the term is often encountered in questions that involve infinite time, regularity properties or infinite-dimensional spaces such as function spaces.
The difference between an event being almost sure and sure is the same as the subtle difference between something happening with probability 1 and happening always.
If an event is sure, then it will always happen, and no outcome not in this event can possibly occur. If an event is almost sure, then outcomes not in this event are theoretically possible; however, the probability of such an outcome occurring is smaller than any fixed positive probability, and therefore must be 0. Thus, one cannot definitively say that these outcomes will never occur, but can for most purposes assume this to be true.
Originally posted by john_bmth
reply to post by ChaoticOrder
Yeah, that's why it's a pickle for the mind My brain hurtsedit on 2-10-2012 by john_bmth because: (no reason given)
Originally posted by ChaoticOrder
reply to post by TeslaandLyne
I'm not sure I understood a single thing you said but it sounds interesting.
Originally posted by ChaoticOrder
reply to post by john_bmth
Ok... interesting point. So even though it's almost certain a copy of me exists out there some where, it's not absolutely certain? But it doesn't seem that simple to me... in an infinite Universe there should be an infinite number of copies of me out there. With infinite time there should be an infinite number of copies of me occurring over and over again. I don't see how the mathematics could possibly say it isn't certain when given an infinite amount of time or space, common sense would tell me it is inevitable. But then again common sense doesn't always work in these abstract situations. And that's exactly why I'm asking just how for the limits of probability can go.
Originally posted by ChaoticOrder
reply to post by ImaFungi
Obviously you are correct. There would be no magical connection between me and any of my "copies". But I don't see how that's even relevant really... the point it's weird to think a being "almost surely" exists out there exactly like me. But beyond that it's the math and probabilities which are of real interest here, not the philosophical or metaphysical implications.
So my question to you ... which one of you (you and the mutitude "other" you's) can claim to be the original one?
Originally posted by ChaoticOrder
reply to post by ImaFungi
Obviously you are correct. There would be no magical connection between me and any of my "copies". But I don't see how that's even relevant really... the point it's weird to think a being "almost surely" exists out there exactly like me. But beyond that it's the math and probabilities which are of real interest here, not the philosophical or metaphysical implications.
what if the universe was more like physical pi....... with no repeats...