We don’t. It doesn’t matter. There are multiple ways of getting to infinite universes. If any of them are true, then the logic of infinity holds.
As Jragon rightly points out, this states that an infinite number of logically possible entities exist. Physically impossible entities are not logically possible. What logically possible means for other universes, though, is beyond my SHIELD clearance.
I’m more worried about the worlds where all the men look like Marilyn Monroe and all the women look like Hitler.
Why couldn’t there exist an infinity of worlds where none harbor life (except ours)?
I really don’t see why so many people fail to understand why Cantor’s powerset argument rules this out.
The set of all possible “chunks” of space is so numerous that the Universe can’t possibly hold them all (including an infinitely long lived Universe).
The chances of there being another identical Earth is so close to zero we can safely ignore the possibility.
Even leaving the notion that it’d be impossible to search an infinitude aside, is there some universal “law of infinity” which states any possible, arbitrary configuration of atoms and events must eventually form and also infinitely recreate itself across the universe(s)?
This seems to be what some are arguing here.
The argument, as I understand it, amount to this.
Any object can be reduced to a coded string of numbers representing every atoms’ position and movement (within the bounds of uncertainty). This is a finite string of numbers. Any finite string of numbers must show up in a random infinite string of numbers. In fact, it must show up an infinite number of times.
A simpler equivalent is noting that the works of Shakespeare can be expressed as a coded string of numbers that can be found in the infinite expansion of pi. Not only that, any variation, from a single typo, to the words of Hamlet being replaced with lines from an Adam Sandler movie, must also be found. Again, all must be found an infinite number of times each.
Whether encoding the universe as a string of numbers is physically possible is beyond me. If it is, though, the argument logically follows. Even if not, there may be other more sophisticated ways of representing reality.
And of course, there’s room for an infinite number of universes in an infinite time span.
I’m familiar with that logic, though that sounds to me as if it makes the notion possible, not necessarily inevitable.
Multiple universes are possible.
Infinite universes are not possible. If there were infinite universes, at least one of them would learn to project light into or travel into another universe. However, since there are postulated to be infinite universes, this would happen infinitely and we would be swamped with photons and travelers from other universes, and in fact overwhelmed with them. Since that isn’t a really annoying phenomena like Jehovah’s Witnesses or Mormons coming to your door (multiplied by 1000 – nay infinity) it is safe to conclude that for the purposes of our universe, there are not infinite universes.
However, one infinite universe is theoretically possible.
Infinitely multiple infinite universes might be possible if they exist on separate “branes”, assuming those are real too.
I don’t think that’s a given.
Just because there are infinite universes, that doesn’t mean that the nature of those universes is infinitely varied. They might all have the same natural laws, which might preclude them from communicating with other universes.
Out of curiosity, do you recall what the argument was, and who made it?
That’s entirely possible, but has probability 0. To see this, consider a ‘universe’ in which three possible things, A, B and C, may happen. The entire history of such a universe can be described by an infinite string of the letters A, B, and C—ABAACCAAA… and so on. Thus, all possible such universes correspond to such a string.
Imagine all these strings in a hat, from which you randomly draw them. Among those strings, there will be some of the form ABABA… or AAAAA… where one event never occurs—these correspond to universes like the one you describe, where life only occurs once, say. But drawing from the hat, you will never produce one: they are massively outcrowded by those strings which do contain all events—consider that for every ‘deficient’ universe, interspersing a C at any of the infinitely many places creates a valid history where all three events take place, so there are ‘infinitely many’ more histories containing all events than there are histories in which some possible event never occurs.
The same holds for infinite universes where something despite being possible never occurs (like the Hitler/Monroe-world).
Of course, the whole thing depends on what’s possible—and on that, we don’t have a nearly good enough handle to decide whether the actual universe, should it be infinite, contains some such ‘freak’ world.
Fair enough, but does it make sense to weight “C” equally with “B” or “A”?
In other words, let’s say the abiogenesis of life is “A”, while formation of a solar system identical to our own down to the atomic level for all of its history through to the death of its sun is “B” and humankind emerging as perfect clones of Marilyn Monroe and Adolf Hitler is “C”, it becomes obvious that each constant has a consequently much lower probability of ever occurring ‘just so’ than the one proceeding it. How this affects the logic you outlined above, I’ll have to give more thought…
Does something exist if the probability of being able to locate it is zero?
Yes. Consider; it’s quite likely that aliens exist somewhere well outside of the range that they will ever be able to see us. They will never be able to locate us; yet, we do exist.
This is a pretty standard thing you learn in calculus. The standard example is the “lightbulb problem”. Given that I have some light switch that I flip on now, knowing that it’s certain that the lightbulb will come on within one second, what’s the probability it turns on exactly .0143 seconds from now?
By the fundamental theorem of calculus:
∫ (from .0143 to .0143) p(t) dt = P(.0143) - P(.0143) = 0.0
(p is the probability density function, the exact form of which is irrelevant to us)
There’s a probability of zero of that lightbulb turning on at any given point in time between 0.0 seconds and 1.0 seconds, but (given the problem constraints) it HAS to turn on at SOME specific time. Yet any time you pick you’ll come up with the answer “there is absolutely no chance the lights will turn on at exactly this time”. This is pretty much what’s going on with the chances of picking an arbitrary element out of an infinite set.
So, parlaying this into the OP, what would it say about some extremely complicated, arbitrary and non-trivial set of circumstances only occurring once (or perhaps never) in an infinite amount of time and matter?
Just because an infinite number of different things exist doesn’t mean that everything must exist. Look at Pi as an example of how that can be: it’s an infinitely long sequence - but you’ll never see an “A” in that sequence.
This not valid. While Little Nemo tries to make the point, it is cheating a little.
There are an infinite number of rational numbers. But the list doesn’t include the square root of 2, Pi, etc. Rational numbers are comparatively uninteresting compared to irrational numbers. There exists irrational numbers that contain an infinite amount of information. No rational number does.
Just because there exists an infinite number of something doesn’t mean there has to one that has a specified property simply by being an infinite set.
Way too many people equate infinite with everything. They are not the same property.
I think this is confusing conceivably with possibility. Take the lightbulb problem again, I can conceive of the light bulb turning on after 1 second, or already being on before 0 seconds (even by some bizarre reverse causality). However, given the problem statement this cannot happen. They have probability zero, and while this is a bit more philosophy than math, IMO it’s a “characteristically different” probability zero than the chance of it turning on at .0143 seconds.
The same with the universe, just because we can conceive of a scenario with incredibly strange parameters, doesn’t mean it can actually happen. Even if it does’t obviously violate any physical laws, it’s simply intractable (and possibly outright fundamentally uncomputable) to make that determination for any scenario.
It may well turn out that there’s due to whatever delicate balance of nature, the only two options are “the universe is exactly as it is now” or “the universe is a bunch of random quantum noise (but in a new and exciting way each time!)”
We simply can’t know whether a universe where Socrates was a great general rather than a philosopher is possible. Maybe any man born at the exact place and time Socrates was HAS to be a philosopher, maybe the only options are being a philosopher or dying as a baby.
It is entirely plausible that any number of things are simply impossible, but it’s so complicated to model we’ll never know the exact, subtle, myriad ways they’re physically impossible. Some state here has a true probability zero chance of having this successor state which means this can never happen. If this happens it causes some other state which means Napolean used a dinosaur army to conquer the world, but it’s impossible for him to use gorillas because for some reason that relies on too much uranium being on the Earth for human life to be feasible. So on and so forth.
Most people in this thread are only arguing that, in an infinite universe, everything that is possible should occur (not everything, including a whole bunch of impossible stuff).