I realize this question is so impossibly broad and far out there that it almost seems silly to ask, but I keep finding myself pondering it anyway.
I don’t think the human brain is even truly capable of understanding infinity, much less backwards infinity, but that doesn’t stop me from trying. Let’s say that “existence” (which for this purpose I can only define as the existence of anything) is infinite. We are no closer to the beginning of it than the end because it has always existed and always will. Whether or not this involves anything outside of a universal scale or an infinite loop of big bangs or whatever I really don’t know.
Given this premise, is anything and everything imaginable not only possible but inevitable? If the answer is yes then does that also mean that anything and everything possible has already occurred? The best I can come up with is a very tepid yes.
Has there been discussion of this question in philosophy or am I just crazy for coming up with it?
The answer to your question is no. Even very very likely things are not inevitable - proof as follows:
Consider the mythical ‘fair coin’. This puppy is a coin that has an exactly 50/50 chance of landing on heads or tails no matter how many times you flip it, entirely unaffected by the result of previous flips. (It’s mythical becuase it won’t eventually erode away to nothing from all this flipping.)
Now, consider the question “Is it inevitable that the coin, if flipped long enough, will land on tails eventually?” The answer to this question is no - it could in theory land on heads every time. The likelihood of this happening is infinitessimally small given a large number of flips, but it is still possible, which means that seeing a tail is not inevitable regardless of number of flips, despite being very, very, very likely.
And is something that’s very, very, very likely isn’t inevitable, really unlikely things aren’t either.
That’s actually a very helpful way of looking at it. Of course it seems crazy to say that everything will and has happened, I just couldn’t get around certain snags when trying to contemplate the meaning of infinity. I don’t know why this illustration didn’t occur to me.
ISTR a discussion on this by some physicist once. The gist was that, given an infinite universe, you would have dopplegangers and near-dopplegangers and every possible variation. Don’t ask me for much past that–all this stuff is just wild to me. But fun to think about.
One thing that occurs to me on this point, “very unlikely” is a value judgement that I don’t think applies to a reality where anything is possible. We would use the term to describe things that seem bonkers to us, but from the perspective of that reality our existence seems crazy and “very unlikely”.
I don’t think this ultimately changes your point, but I do think it’s a distinction worth making .
Come to think of it, given the endless possibilities of things that there could be (as opposed to the two possibilities of the coin), ours and any other existence should be categorized as “very unlikely”. Right? Now I’ve gone and seriously confused myself again.
I’ve thought about this question more in the context of infinite parallel universes rather than infinite existence within this universe. It’s been in my mind, on and off, ever since reading this Scientific American article about parallel universes. One thing that amuses me is that if the theory of infinite parallel universes is real–obviously a big ‘if’–then it follows that skeptics have been wrong about almost everything. There’s some planet that’s just like our earth except that the Loch Ness Monster is real. There’s another planet like our earth where Bigfoot exists, and another where extaterrestrials actually landed at Roswell, and so forth.
No. For one thing, some of the things that are imaginable are mutually exclusive, like “the Cubs win a World Series again” and “the Cubs never win another World Series.”
It depends on how you define “infinity”, but there are plenty of ways of having an “infinity” of something that does not imply all possible variations.
If you’re thinking about the universe, do you mean infinite time? Infinite space? Neither one is known, but, let’s assume that the universe is infinitely large and lasts an infinite time. It could still consist of a limited set of events/things occurring over and over.
A simplified version of this claim:
Consider the infinite sequence: 1, 2, 3, 2, 1, 2, 3, 2, 1…
Does it contain all numbers? Clearly no. It contains only a small subset of numbers. But it’s infinite in length. There’s an open question of whether the number pi contains all possible strings of digits. Here there are obviously more levels of what “infinity” means, since the decimal representation of pi is known to be infinite, and pi is known to contain all the digits.
Now, you can certainly say that your concept of “infinity” requires infinite variation, too. But then you’re stating a tautology.
Well, that’s assuming that everything -or anything- actually happens by chance. There’s a possibility that the universe is nearly or purely deterministic, in which case everything that has happened is an inevitability (including those coin flips).
But yes, presuming a certain amount of randomity or possibility of alternate outcomes, the fact that things turned out exactly as they did is astronomically unlikely, and many or most of the other possible existences would be very unlikely as well. But something had to happen, and it turns out that ours is what did.
To use another analogy, consider a large (and fair) 1,000,000-sided dice. When this sphere stops rolling, what is the chance that some specific side will be rolled? One in a million. But what is the chance that some number will be rolled? 100%.
Consider this. You toss a coin over and over, and it always comes up heads, for the rest of eternity. I can imagine that. Now imagine you toss a coin over and over and it always comes up tails, for the rest of eternity. I can imagine that too. However, these two events are mutually exclusive, of one happens then the other cannot happen.
Therefore, I can imagine things, some of which are guaranteed to never happen even in an infinite universe.
Another idea, which another member posted in another thread – and I apologize for not remembering who you were! – was that the universe of events might be “fractal” in some respect. It might be self-resembling.
In the simplest terms, the infinite monkeys on infinite typewriters might spend a disproportionate amount of their time hitting the space bar.
Another point is that if your hypothetical universe follows the second law of thermodynamics, even if time is infinite the amount of “stuff” you can do within that universe is finite, since entropy is always increasing.
One may distinguish between probability one and guaranteed, just as one may distinguish between probability zero and impossible.
begbert2 outlined very clearly the sense in which a coin may come up heads every time: it just comes up heads every time. Why not? Is that sequence of probability zero? Sure, but so is every other coin flip sequence.
I can imagine things that would be outside physical law, and for something to occur, it must be within physical law, so, no, even in an infinite universe, not everything imaginable would occur.
I say no. Infinity doesn’t mean infinite variety. It can just be an infinite combination of a finite set of elements.
Consider pi for example. It’s an infinitely long string of numbers that never repeats. But it still only contains ten digits. No matter how long pi runs, it’ll never produce an A.