Q: In an infinite universe, does everything that’s possible have to happen somewhere?

The original question was: Lets say that we determine that an event is physically possible. So that means the probability of that event is greater than zero. Right? So my question is this. Is there any sense in saying that the event will NEVER happen even if it has a non-zero probability? In other words, if it can happen, will it happen given enough or infinite time? Does it have to happen eventually?


Physicist: There are a lot of subtleties in this question!  The answer is basically yes, but there are some sneaky assumptions worked into that.

Right off the bat, a probability is always based on “priors”.  For example, “the probability that it will rain today” or “the probability that a 4 will be rolled” are not, completely on their own, well-defined probabilities.

The probability of a particular event is dependent on “priors” or “conditions”.  In order to know the probability of getting a particular result, you must have prior knowledge of what die is being rolled.

Before you can find a probability that’s an actual number, you need to know something about the priors.  The probability that it will rain depends on the place, time, season, whether or not it rained yesterday, etc.  The probability that a 4 will be rolled depends on what kind of die is being rolled, if it’s weighted, or even if dice exist.

In this general case, you may have a tiny, non-zero probability, but if it’s based on priors that are themselves impossible, then the event itself may also be impossible.  You can generalize the priors a lot, but you can never quite get rid of all of them.  For example, it may be possible to prove, beyond a shadow of a doubt, that the probability that a unicorn is violent is 5%, given that unicorns exist (when a scientist says “given”, they’re about to spit out some priors).  However that doesn’t guarantee that a violent unicorn must exist, because it requires that unicorns (with their magic, and virgin sensing powers, and whatnot) must already exist in general.

But (and this may be more at the heart of the question), given an infinitely large universe that’s more or less homogeneous (lots of “stuff”, like the part of the universe we can see with telescopes, instead of just being empty forever), then pretty much anything that’s remotely possible, that could conceivably be the result of a string of remotely possible causes (e.g., horse begets unicorn begets violent unicorn), will happen somewhere.

As a slightly less fantastical example, we can imagine creating, say, an array of Tinker Toys™ linked together and spanning light-years of space.  If this could be instantaneously constructed, somehow teleported into existence, then it would continue to exist for a little while (its self-gravity would start to crush it in fairly short order).  It is not, by itself, an impossible configuration of stuff.

Light years of tinker toys. Its existence is possible, but there is no set of circumstances that would lead to it happening.

However, due to laws like the conservation of mass, the light-speed speed limit, and the nature of gravity, there’s no way to put together a structure this big and massive (or for it to form naturally).  Long before you even got to the business of connecting everything together you’d find that there was already far too much mass, far too close together.  No matter how fast you tried to get everything in place you’d find that the arrangement is smaller than its own Schwarzschild radius, which means that a Tinker Toy™ construction of this size and density is already a black hole (“teleporting it together” gives it a little time because no part of it would “know” that it was too big for a while).

So, we can sit back as say things like, “well, there are X many possible arrangements of atoms, or quantum states, or whatever, and this is one of them…” and can then calculate a ball-park estimate of the probability of this massive wooden grid existing (“1/X” maybe?).  Unfortunately, the answer we’d get would be incorrect, because the priors are messed up.  While it could exist, it could not be formed.  So simply knowing that something is “possible” doesn’t mean that the universe can ever be in a state that would eventually lead to that thing happening.

As far as happening eventually: if it’s not happening now (in an infinite universe), it almost certainly never will.

The tinker toy picture is of a “clockwork” tick-tac-toe playing computer.

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64 Responses to Q: In an infinite universe, does everything that’s possible have to happen somewhere?

  1. Bill S says:

    Don’t know what happened there. I’m still Bill S. 🙂

  2. Anonymous says:

    As we are human we have our own thoughts and feelings about this. Regardless of our expertise or knowledge we are still just humans. We have small minds. When you think about all the other civilizations another beings out there that have contemplated this and known the exact truth and knowledge of this over maybe billions and billions of years we are absolutely nothing when it comes to this question it’s an absolute fact it right now somewhere else out there there’s a person that looks like me sitting with a cell phone in his hand making stupid remarks about infinity everything is possible what you see on TV all the scenarios they’re happening it may sound silly as hell but that’s a fact I’m not adding any numbers to it I’m not making up things it’s just that’s the way it is where small very small

  3. Bill S says:

    Anonymous says:

    “We have small minds”

    Come back Uriah Heep, all is forgiven!

    “When you think about all the other civilizations another beings out there that have contemplated this and known the exact truth and knowledge of this…”

    “…it’s an absolute fact it right now somewhere else out there there’s a person that looks like me sitting with a cell phone in his hand making stupid remarks about infinity everything is possible…”

    You know about these people, how?

  4. Bill S says:

    BTW: Absolute facts tend to have more to do with dogma than science.

  5. Anonymous says:

    True absolute facts as far as the knowledge that we have here on this planet as humans. When I say we’re thinking too small I mean we’re thinking as humans as humans we have a beginning and an end that’s all we’re taught our whole lives is beginning and end from the time that you can understand human language you know that eventually one day that your life will end a tree will die eventually this planet will end eventually. But there are civilizations out there that have been around for hundreds of thousands of years maybe billions well actually billions of years. I mean we’re just a little drop in the bucket what we know is nothing that’s why I believe in in infinity everything’s possible scientist approving today things that weren’t possible. But you know you’re going to go by what you learned out of a book or what somebody taught you and you’re going to give your conception your thoughts and your feelings. But they are your thoughts and your feelings not mine. We all have different minds we all think differently no one’s going to change my mind about how I feel about something and neither am I going to do that for you but what I believe I pretty much said what you believe I’m happy for you you go there you stay there you enjoy that moment. But unless you’re reincarnated in an entity that’s may be roughly three or four hundred thousand light-years from this specific vicinity that we’re in now you can’t tell me any different than any other human if you don’t understand what I’m getting at well we’re insignificant what we think doesn’t matter anyway you can attach numbers to infinity it doesn’t mean anything I have been closer to Infiniti than a lot of people and I think there’s people out there that know what I’m talking about when I say that think about it all day long and try to understand infinity the closer you get to it I guess the crazy are you get but in there I believe that once you understand it you become a part of it I believe there’s power in that just haven’t gone that far

  6. Anonymous says:

    When we say absolute facts do we mean absolute facts out of a book out of a scientific study done by humans? Or is it a absolute fact as you see them or has as a group of people see them? are are they absolute facts throughout the universe and all the other universes? See our FAQ stop here at Earth I mean you don’t get off the planet give it for you can’t hear human voices anymore we are insignificant what we think really doesn’t matter what I say is just my opinion I mean I could learn all kinds of things I can sit here and quote things out of a book but that doesn’t make me that much more intelligent I can go on Google any day and Google something it doesn’t make me more intelligent just buy me me speaking it or writing it down or texting it or commenting this doesn’t mean anything and as far as asking a mathematician I have to say I don’t look at numbers when I’m thinking about infinity I just don’t see it but I mean if they try to intertwine the two

  7. Bill S says:

    “True absolute facts as far as the knowledge that we have here on this planet as humans”.

    Science does not provide us with absolute facts. Religions may try to, but that just comes down to personal belief.

    “When I say we’re thinking too small I mean we’re thinking as humans”

    Of course, and our thoughts have as much validity as the thoughts of any other creature, real or imagined. Just because we have a beginning and an end does not devalue us, or our thoughts.

    “But there are civilizations out there that have been around for hundreds of thousands of years maybe billions well actually billions of years”.

    You state this as though you think it is an “absolute fact”. Do you have any scientific basis for this?

    “But they are your thoughts and your feelings not mine”.

    That’s part of what makes us individuals. Perhaps, try to value that.

    “We all have different minds we all think differently no one’s going to change my mind about how I feel about something…”

    Of course; only you can change your mind, but being open to listening to the views of others can be a learning experience.

    “..we’re insignificant what we think doesn’t matter..”

    To whom should it matter?

    “..anyway you can attach numbers to infinity it doesn’t mean anything”

    Mathematically, it is significant, but beyond that, infinity is not a number, so treating it as though it were, by attaching numbers to it, is meaningless.

    “..is it a absolute fact as you see them…”

    The nearest I come to acknowledging anything like an “absolute fact” is the idea that if there had ever been “nothing”, there would still be nothing, now, and we would not be having this exchange. 🙂

    “…as far as asking a mathematician I have to say I don’t look at numbers when I’m thinking about infinity…”

    Sounds like a good starting point.

  8. Anonymous says:

    I don’t know about you guys but my little tiny insignificant brain can comprehend infinity. It tells me that anything and everything that we can imagine is possible. And weather it happens or not it has already happened. If we imagine something does, does it bring it into existence? I don’t know but it came into existence in my mind, so I think it exists in what form I don’t know. We’ve already proven that history repeats in this little time we’ve been here. Now if I could figure out how I can read what I’m writing that would really help! I want to know if you two that made comments believe in God, the paranormal, UFOs, Aliens, life after death, a spirit, Hell, the devil, out of body’s, etc. Do you think we already have interstellar travel, time machines, telepathic power, physic abilities etc. I believe in all of it and experienced over 50% of this list. Does any of it matter? Who knows but it could give someone hope and a purpose in life because you have something to look forward to. Something I’m still looking for. You both sound very interesting and intelligent, I’m just an average guy with too much on my mind all the time. I turned on the notifications and want to hear more…

  9. Anonymous says:

    I think you have the gist of it. So I agree with what you’re saying. We are so small in this universe and other universes. I mean we only know what humans know what we’ve been taught. And one of the main things that were talk is there’s a beginning and an end. Yes there is a beginning and an end for these human bodies but whilst we are still part of the universe we’re still part of everything in the whole. People think very small

  10. Bill S says:

    Do we have more than one Anonymous, here? Could get confusing for us old gimmers.

    “It tells me that anything and everything that we can imagine is possible. And weather it happens or not it has already happened.”

    A serious block to meaningful discussion of infinity is the fact that, commonly, experts will agree that infinity is not a number, and will then, happily, talk about an infinite sequence; thus treating infinity as though it were a number. Simply using a word like “happens” treats infinity as though it were divisible. If it is divisible, it can be treated mathematically, so it must be a number; but, of course, it is not!

    As I see it; the only way to make the problem go away is to acknowledge that we use “infinity” in two distinctly different ways, and that, simply, adding a lemniscate to a finite calculation does not bring about a transfer from one usage to the other.

  11. Ratna Sanyal says:

    Can there be a universe where the show supernatural with dean and Sam and angels and demons…..etc is happening in real life? Can we physically reincarnate in that reality? Is that a possibility?

  12. Dloyd says:

    It will happen. And it won’t happen. That’s the great thing about infinity. Humans only know beginning and end. There is no end thus we will not understand it.

  13. Infinite Non-Existance? says:

    I had a thought today whilst mowing the lawn (I later googled it and found this thread).

    Assuming there is no afterlife and that when we leave this earth we simply go into an “eternal state of non-existence”. Is this state of non-existence infinite?

    If it is, are we therefore assimilating into infinity?

    My next thought was if we are in a state of nothing, we know from experience that the material plane does not cease to exist when someone passes. Therefore, whilst we are non existent, the material plane continues to exist?

    So, an infinite amount of time will pass on the material plane (as a reference point), whilst we are non existent. In an infinite amount of time, could a new universe be created where we re-exist?

  14. So, If probability is built on priors, then the theory of something arising from nothing, where nothing or void is defined as pre-prior then according to the definition there there could be zero probabilities as there is nothing prior.

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