True, but using specific examples is folly here. Sure, we can think that Al Gore could have won instead of Bush, but could he really? It certainly seems plausible, but it’s possible that in the grand scheme of things some really, really gnarly math proves that false. Of course, we still talk about it as a possibility because that’s useful to us humans, but we can’t conflate human notions of “possibility” with more abstract, fundamental mathematical ones. It’s kind of like Shroedinger’s Cat – it’s a really cute thought experiment originally meant to point out an absurdity, but fundamentally the nature of observation and waveform collapse and so on as a mathematically grounded physical concept doesn’t really lend itself well to cats in boxes.
I agree. We do tend to think of possibility in terms of configuration of things at a point in time, rather than possibility of those things arising.
As long as we don’t fall into the irreducible complexity trap that bedevils creationism, that is.
This.
If we are considering an infinite universe or indeed infinitely many infinite universes then we have an infinite number of elementary particles. This infinity is the number of natural numbers.
However, arranging those elementary particles in time and space involves a different measure of infinity. I could have two hydrogen atoms that are 0.214 angstroms apart and another two that are 0.215 angstroms apart and an infinite number of possibilities in between. This is the infinity of real numbers. It is larger than the infinity of natural numbers.
It follows that all the hydrogen atoms in an infinite number of infinite universes will not be sufficient to position two of them in all possible configurations. Therefore the notion that there must be an identical earth out there is without foundation.
Some universes have light and mass, numbers do not. If there were infinite universes, a subset of them would have light and mass. In fact, a subset of infinity can still be infinity. If we found any physical evidence of another universe, it would have light or mass. An infinite amount of light and mass would be really bright and heavy.
There is no infinity of anything with light and mass for this reason. Infinity exists only as a concept. If you disagree, demonstrate to me an infinity set of anything with light or mass.
Saying that infinity exists as just a concept sidesteps the issue. There are certainly an infinite number of points between 1 and 2 on a number line but we have no problem holding a ruler. Brain Greene’s book The Hidden Reality discusses nine mathematically distinct types of multiverses. Nobody knows whether these exist, but they cannot be dismissed simply because you don’t like the concept.
Some people have postulated that we in fact live in an infinite universe with an infinite number of observable universes, meaning that each one is too far away from any other for the light and mass to affect each other given the limitation of the speed of light. There’s your infinite light and mass. Coming up with sets of infinite multiverses that don’t put an infinite amount of mass into a finite space is trivial.
The real problem is that the current discussion depends almost as much on logic and philosophy as physics, and calls for a precision of definition that’s mostly being ignored.
Then where is your scientific evidence of these things people have postulated? Light is something you can see. If there is an infinite amount of it, we’d see it, in fact, we would see nothing else. Same with mass. You can have infinite numbers without filling up space of having effects in a world of reality, but you cannot have an infinite number of photons. If you can’t point to evidence of it in science, then it doesn’t exist. If you can point to evidence of it, it does exist. But that existence isn’t infinite unless there is infinite evidence.
Postulate all you like, and that is fine. But it isn’t science until there is verifiable and repeatable evidence. Infinite has a distinct meaning. Infinite universes that can be verified would be infinitely verified merely by the light and mass they would generate, which would overwhelm everything. Since we are not floating in infinite light and mass, it is pretty safe to say that there isn’t such a thing.
There is no evidence that anything in the universe meets the criteria of infinity except concepts.
Unless there had only been a finite time until now.
Only, we know how our universe began and have a good grasp on its evolution. Space may very well be infinite, but we can’t see anything beyond the recombination period (the cosmic microwave background radiation) about 400,000 years after the Big Bang the universe was literally opaque with photons.
Though that’s sort of a different thing than I think you’re getting at. Are you saying in an infinite universe with infinite matter and energy, space would be white with the light of stars since no matter where we looked, our eyeline would fall on a star?
You can weight C any way you want, and the conclusion doesn’t change. The probability of C is just its relative frequency across the ensemble, but even if you don’t intersperse C at every other place in the infinite string, but at any thousandth, millionth, billionth…, making its likelihood arbitrarily small, you will be able to construct from every infinite string of As and Bs infinitely many different strings with some occurrences of C; thus, drawing a string with no occurrence of C (or any finite number of occurrences of C, in fact) will still have probability 0.
Anyone for an Axiom of Choice?
Whether we can prove an infinite number of pocket universes or not, your statement is factually wrong given current scientific understanding of physics. If the light can never reach us then we can never be overwhelmed by it. The philosophy of infinite universes may not have scientific confirmation and there may not in fact be infinite pocket universes within an infinite extent of our universe, but your statement about that universe is demonstrably wrong and so irrelevant.
Well, again, you are postulating. You have no evidence to back it up. If there are an infinite number of pocket universes and the light of only one of them reaches us then you haven’t proven an infinite number of pocket universes, you’ve proven one of them only. If there were an infinite number of them, we wouldn’t be seeing the light of only one of them, we would see the light of very many, a subset of an infinite number to be sure, but still, an infinity. I can postulate an infinite number of narwahls populating your planets in your infinite number of universes, but I can only prove the ones I see in this world. Once I postulate infinite points of light, however, I expect to see them, or I am just postulating.
You are the one making a claim. Where is your proof that this claim is true?
I can refute it by noting that within our own pocket universe we know there are stars we can never see because they are beyond the observation horizon. As long as our system of stars is expanding, these will never be seen and can never affect us.
This is the answer for Olbers’ paradox, which asks why the night isn’t blazing white if there are an infinity of stars. Two things - the speed of light and an expanding universe - ensure that the night will be black. These are known scientific facts.
You’re making a claim that stars beyond our observable universe can be seen. I can’t seem to make you understand how oxymoronic that claim is. By everything we know about the universe, stars beyond the observable universe cannot be seen, cannot affect us, cannot be interacted with. That isn’t a concept; it’s as solid a fact as anything we have in science. Why do you keep claiming otherwise? You certainly offer no scientific argument for doing so.
I have to disagree. You’ve said that there are/can be an infinite number of universes. Show me the evidence. The evidence indicates that there are a finite number of universes. There is very solid evidence for the universe that we live in. There is an inference for one other universe that some scientists postulate explains a slight gravitational flow of every galaxy we can see traveling in one direction toward a presumably non-parallel universe. That is evidence for two. Two is finite.
When you insist that there are (or it is possible there are) infinite numbers of universes, that isn’t science, it is science fiction. When you can prove it, then that is science.
I say that there cannot be an infinite number of parallel universes because that would require infinite evidence in the form of some sort of radiation (light etc) leaking through. Even if light could only leak through at one point in our universe from one point in a subset of parallel infinite universes, the nature of infinity is that an infinite number of universes would be doing so. That is the nature of infinity, as compared to “a whole lot”.
Think of it as the concept of an infinite number of monkeys typing away at an infinite number of typewriters eventually coming up with the complete works of Shakespeare. The answer is no, they would come up with the complete works of Shakespeare in as much time as it takes to type out the complete works of Shakespeare without any typos, and not just one complete work of Shakespeare, but an infinite number of copies of the complete works so Shakespeare, not to mention the entire run of the scripts from Sanford and Son too.
It is easy enough to wrap our heads around the concept of an infinite series of real numbers 1, 2, 3, 4 … but there is no evidence that there are an infinite number of electrons or even neutrinos or even close to an infinite number of them. There are a lot of grains of sand on the beach and a lot of sub-atomic particles in our universe, but nowhere near an infinite number, probably far less than a google. Well, you are postulating a number of universes that makes a google-plex approach zero by comparison.
There are an infinite number of real numbers between 0 and 1. If I were to randomly pick one of them, the probability of it being 2 is 0.*
All I am saying is that an infinite number of possibilities does not always mean that anything is possible.
I’m not sure how relevant this is to the OP scenario though.
- you might counter that the probability of my choice being any specific number is 0 to which I would say: fine, I will pick infinite number of numbers between 1 and 0. The probability that I will eventually get the number 2 is 0.
That seems to accurately describe the concept of infinity as I understand it.
Excellent point, well put. Thanks.
Right, but keep in mind that there are different infinities. Some are infinitely bigger than others (as I know you know, but more on this later.)
Can you please clarify this? First, time isn’t an issue. We can have infinite space with an infinite number of galaxies, or an infinite number of such universes, all at the same time. Let’s assume the cardinality of galaxies is aleph-null. Can you state Cantor’s powerset argument and explain how it rules out the OP’s premise? (Thanks big time, in advance.)
I believe it’s “the strong law of large numbers” that leads to “any finite digit sequence will appear in an infinite stream of random digits, with probability 1.” It’s a probability argument that only takes high-school math to show, and it’s pretty astounding at first, isn’t it?
But is it really true that everything that’s important must be reducible to a string of digits? I’m not sure I agree with this possibility. I confess I don’t have a good argument against it, and a lot of what I do believe about consciousness implies that at least those are reducible to strings of digits. But can the physics of a real setup truly be reduced to the digital domain without significant loss of precision? Even given the limit of the planck length … I’m not sure.
You are assuming they share the same space-time continuum, which isn’t necessarily so.k
Thanks, you put that in far fewer words than I was planning. 
Right: this is called speculation.
According to those who understand cosmology, you’re mistaken. So far, you haven’t presented a good argument.
Of course, there’s the not just possibility, but requirement, that no light or evidence of mass “leaks through”. It’s a requirement, because otherwise, it’s not another universe, it’s part of ours.
Back to the OP.
The problem I have is that if there are “multiple universes” (rather than "a continuum of universes) then the cardinality of universes (and thus, the cardinality of galaxies, stars, planets, etc.) is aleph-null – the smallest infinity, the number of integers.
I’m not convinced that this infiniteness is big enough to encompass all possible worlds. It seems to me that it pretty much boils down to my question about Exapno’s claim that an object (including a world) can be effectively reduced to a sequence of digits. Of course, that’s limited by jtgain’s point of “reachability” – it has to be a possible world to have a nonzero probability. And it all might be moot, if ftg’s point about Cantor’s work is valid.
When it comes to infinities, I’m familiar with only two: the number of integers and the number of points on a line. Cantor goes into quite a bit more detail than that, and I haven’t ever quite followed it.
Actually, the problem is a bit more complex than that, because we don’t just come up with such a world by fiat. It has to be arrived at. So, we’d have to describe not the world, but the entire process of the development of such a world. It would be sufficient to posit the initial conditions that would create it, but as we know reality is chaotic so we wouldn’t be able to reduce it this way – and I wonder if we can even make the mathematical argument that it’s even theoretically possible to reduce it that way.
Cantor’s diagonalization argument isn’t relevant here. We’re not positing an entire universe identical to ours aside from the Monroes and Hitlers. We’re positing a finite-sized chunk of universe meeting that description. You can say that that chunk just needs to be planet-sized, or maybe it needs to be the size of the entire observable Universe if “just like ours” includes the results of astronomical observations, but either way, it’s finite.
I’m not an “expert” in this area, the only poster in this thread that I know to be a physicist is Chronos. I notice that he hasn’t said my argument is not good.
The evidence for other “space-time” continuums, much less infinite ones, is slim to none, with the emphasis on “none”.
If I have can posit a super-advanced civilization on another planet or space station somewhere in our universe, with a scientist alien peering into a extra-dimensional telescope of some sort and seeing a couple of pieces on information on his screen back home, I can buy another universe, parallel or not. But if such universes are infinite, it is infinitely occurring in an infinite subset of those universes, which requires infinite energy and matter, which would fill they skies with the energy from those displays, no matter how faint they were, because there were an infinite number of them, they would light up everything.