Re: Are we eternal? (Eternal Recurrence)
Posted: Thu Jan 29, 2015 3:47 pm
Nietzsche's idea is based on a very basic error in logic that will be apparent if we think carefully at all.
An "Eternal Return" can only happen if two conditions apply:
1. An infinite span of time in which for events to recur, and
2. A finite number of variables capable of recurring.
If either of these two conditions is not applicable, his supposition becomes at least unnecessary, but more accurately, it becomes so mathematically improbable as to be (rationally) impossible.
Now #1 is possible, though we have no confirmation of it. It's perhaps even probable. So let's grant it. But #2 is certainly not applicable.
For supposing #1 to be true, there are an infinite number of universes or possible combinations of events -- in the dimension of time, certainly, as is obvious from the word "infinite," but then very likely in the dimension of space as well. So time and space are probably both of infinite largeness, if #1 is true. So far so good?
But if there is infinite time, infinite space, or both, then by definition there are also infinite variables within those dimensions. There are, in short, an infinite number of ways the universe could be.
Infinity is an odd thing. As the "Hilbert's Hotel" thought experiment shows, the rules of logic and mathematics simply dissolve when we try to use it to describe physical reality. And one of the odd effects that follows for the "Eternal Return," is that there is no longer any reason to suppose the universe must "return" to any state in which it has been already, no matter how long time persists.
And why is that? It's because no matter how much time there is, there are always an infinite number of other ways for things to be or become. So the way we are is one state out of an infinite number of possibilities, and the chances against any such state occurring are quite simply -- infinite!
In short, there is no "Eternal Return" if the universe is actually infinite. And postulating additional "bigness" does not make it any more likely, but rather infinitely less likely.
An "Eternal Return" can only happen if two conditions apply:
1. An infinite span of time in which for events to recur, and
2. A finite number of variables capable of recurring.
If either of these two conditions is not applicable, his supposition becomes at least unnecessary, but more accurately, it becomes so mathematically improbable as to be (rationally) impossible.
Now #1 is possible, though we have no confirmation of it. It's perhaps even probable. So let's grant it. But #2 is certainly not applicable.
For supposing #1 to be true, there are an infinite number of universes or possible combinations of events -- in the dimension of time, certainly, as is obvious from the word "infinite," but then very likely in the dimension of space as well. So time and space are probably both of infinite largeness, if #1 is true. So far so good?
But if there is infinite time, infinite space, or both, then by definition there are also infinite variables within those dimensions. There are, in short, an infinite number of ways the universe could be.
Infinity is an odd thing. As the "Hilbert's Hotel" thought experiment shows, the rules of logic and mathematics simply dissolve when we try to use it to describe physical reality. And one of the odd effects that follows for the "Eternal Return," is that there is no longer any reason to suppose the universe must "return" to any state in which it has been already, no matter how long time persists.
And why is that? It's because no matter how much time there is, there are always an infinite number of other ways for things to be or become. So the way we are is one state out of an infinite number of possibilities, and the chances against any such state occurring are quite simply -- infinite!
In short, there is no "Eternal Return" if the universe is actually infinite. And postulating additional "bigness" does not make it any more likely, but rather infinitely less likely.