Size of universe - rewinding big bang versus "flat" universe

[HomesliceMMA]

I don't know anything about cosmology, but this notion that infinite universe means "this conversation is going on an infinite number of times" just doesn't make sense to me. The set of real numbers is infinite, and yet there is only one "2" and only one $\sqrt 3$. The numbers do not repeat, why should the conversations?

See my post above. What you are claiming to be "infinite" matters - sometimes it can make sense, other times it doesn't. For example, if you say there can be an infinite number of numbers, starting with 1 and counting forward by 1 at a time, forever and ever, there CAN be an infinite number of numbers, in theory. But if you did that you would NEVER hit an infinite number of numbers. You would get to 1 million. Or 1 billion. Or 1 trillion, and so on and so on, but you would never get to infinity. So there is nothing weird about that statement or formulation.

But if you say "the size of the universe is infinite", then, assuming the physical properties in each is the same at least, this conversation is going on not just once, but an infinite number of times. So in this context in my mind at least that is just silly. You guys are rejecting it like I am, but I'm telling you that is what infinity literally means in this context.

There is only one number 2 in your example because it involves starting with a 1 or 0 and counting forward, but never going back or repeating. If you change it to say there is an infinite amount of random numbers, then there will not just be two 2s, there will be an INFINITE number of 2s.

 

[phinds]

then, assuming the physical properties in each is the same at least

But that's my POINT. The universe is indeterminate and statistical, so "same physical properties" is very misleading. The HUP is the Heisenberg Uncertainty Principle and if you don't understand it, you should stop this conversation until you do. The "same physical properties" WOULD lead to the same outcomes in a deterministic universe but we don't live in one of those.

 

[HomesliceMMA]

Imagine two parallel perfect laser beams. If they stay parallel forever we say the Universe is flat. Calling it "straight" might have been better, but that's what we've got. If the beams converge then the Universe is spherical. If they diverge then U is hyperbolic.

As to that stuff about the conversation going on an infinite number of times I don't take that seriously. I'd say this comes up from people who don't know measure theory. To make a long story short, probability zero is not the same as impossible. I expect that in an infinite Universe your conversation has probability zero.

Basic measure theory is quite simple, it's just abstract and not widely taught. Suffice to say that all finite subsets of an infinite set have measure zero. Even an infinite subset may or may not have measure zero.

Well, can you explain that in plain English? If the universe is infinite in size (and like I said the physical properties are the same in all parts, that sort of thing), this conversation WOULD be happening an infinite number of times. That is what infinite necessarily means in that context. That is why I submit that an infinite universe is BS.

 

[HomesliceMMA]

But that's my POINT. The universe is indeterminate and statistical, so "same physical properties" is very misleading. The HUP is the Heisenberg Uncertainty Principle and if you don't understand it, you should stop this conversation until you do. The "same physical properties" WOULD lead to the same outcomes in a deterministic universe but we don't live in one of those.

Yes, absolutely indeterminate, but you'd still get there eventually. Yes, all the probabilities would have to have come out exactly the same, one photon or electron that goes a different way because its "roll of the dice" differed would obviously mean the conversation was not happening twice. But, if one says the universe is infinite, you'd just keep going farther along, until you find one that matches. If our physics only applies to our patch of the universe, or there is only matter in our universe, then that would not likely hold true. But if the same physical properties exist, etc., there would have to be infinite conversations like this one.

 

[phinds]

... there would have to be infinite conversations like this one.

see post #19

 

[HomesliceMMA]

Imagine two parallel perfect laser beams. If they stay parallel forever we say the Universe is flat. Calling it "straight" might have been better, but that's what we've got. If the beams converge then the Universe is spherical. If they diverge then U is hyperbolic.

As to that stuff about the conversation going on an infinite number of times I don't take that seriously. I'd say this comes up from people who don't know measure theory. To make a long story short, probability zero is not the same as impossible. I expect that in an infinite Universe your conversation has probability zero.

Basic measure theory is quite simple, it's just abstract and not widely taught. Suffice to say that all finite subsets of an infinite set have measure zero. Even an infinite subset may or may not have measure zero.

In response to what I THINK you said, I would say this: The probability of this conversation repeating itself, in any large number of universes, any number at all, anything short of infinity, is probability zero. But in an infinite number of universe, it is probably certain.

 

[HomesliceMMA]

It's based on the claim that the number of possible conversations is smaller (in more technical language, has lesser cardinality) than the number of places in an infinite universe that a conversation could take place. If that is true, then the fact that any given conversation must happen an infinite number of times follows from the pigeonhole principle.

AFAIK claims like that are never actually proven in the literature, they are simply assumed (and in fact they are implicitly assumed, at least in the literature that I've read). I personally don't find such claims very credible.

Right, it wreaks of "you want me to believe WHAT"? But that is what an infinite number of universes would clearly require. Thus I submit that the number of universes cannot be infinite. It could also be an indication of something else...

 

[PeterDonis]

a different consideration is whether the number of possible conversations less than some maximum length (e.g. 120 years at the ludicrous extreme) is finite. I presume it is. Then the argument of repeated conversations still applies.

But conversations don't happen in isolation. They happen as part of a larger history, for example, the history of Earth since its formation. And the repetition argument would ultimately have to apply to histories to have any force. But if histories are open-ended to the future, then you can't impose a finite time limit on them, and you can't say that any history must be repeated elsewhere in an infinite universe.

 

[HomesliceMMA]

see post #19

Replied post 19, twice I think.

 

[PeterDonis]

if there IS an infinite number of universe

How did we get to an infinite number of universes? We were talking about just one universe, ours, which, according to our best current model, is spatially infinite.

 

[HomesliceMMA]

But conversations don't happen in isolation. They happen as part of a larger history, for example, the history of Earth since its formation. And the repetition argument would ultimately have to apply to histories to have any force. But if histories are open-ended to the future, then you can't impose a finite time limit on them, and you can't say that any history must be repeated elsewhere in an infinite universe.

If what we are saying is the universe started all at once, but is infinite, then there would be an infinite number of places in this universe that, at this very point in time, are having this exact same conversation, and are otherwise exactly the same. The next micro-second that would no longer be true in an infinite number of locations in this universe, but, given the infinite size of the universe, there would still be an infinite number of locations where it was still true at that later time (and an infinite number of locations where it wasn't true). That is complete silliness, but what comes from using the concept infinite in that context. This is a pill too big for me to swallow and thus I submit that the universe is simply not infinite.

 

[HomesliceMMA]

How did we get to an infinite number of universes? We were talking about just one universe, ours, which, according to our best current model, is spatially infinite.

Sorry, the universe is infinite. So locations in this (supposedly infinite) universe where this conversation is happening. Same silly result really, just semantics at some point.

 

[PeterDonis]

If what we are saying is the universe started all at once, but is infinite

That is what our best current model says, yes.

then there would be an infinite number of places in this universe that, at this very point in time, are having this exact same conversation, and are otherwise exactly the same.

Not necessarily; arguments have been made in this thread for why this would not be the case.

 

[PeterDonis]

This is a pill too big for me to swallow and thus I submit that the universe is simply not infinite.

This is not a proof of anything. The universe doesn't care what kind of pill you are able to swallow.

 

[HomesliceMMA]

This is not a proof of anything. The universe doesn't care what kind of pill you are able to swallow.

That is what our best current model says, yes.Not necessarily; arguments have been made in this thread for why this would not be the case.

But I've debunked them all as far as I can tell LOL.

 

[PeterDonis]

I've debunked them all as far as I can tell

Where? I haven't seen any debunkings by you at all. You have made repeated assertions but I haven't seen any arguments from you.

 

[HomesliceMMA]

This is not a proof of anything. The universe doesn't care what kind of pill you are able to swallow.

And the universe doesn't care how big a pill you are able to swallow. You can believe that the universe is infinite, and thus this conversation is happening right now, not in one other location but an infinite number of locations, if you want, I'll choose not to.

 

[PeterDonis]

You can believe that the universe is infinite

I do.

and thus this conversation is happening right now, not in one other location but an infinite number of location

I don't. This does not follow. See, for example, @martinbn's argument in post #26, and my response in post #38 to a counter-argument from @PAllen. You have not addressed those points at all.

I'll choose not to.

This isn't a matter of anyone "choosing". You can't just wave your hands and make claims. You have to support them with arguments. So far you have not given any arguments, just repeated assertions. If that's the best you can do, we'll just close this thread.

 

[Drakkith]

This is a pill too big for me to swallow and thus I submit that the universe is simply not infinite.

Are you going to debunk quantum physics next?
Because there are plenty of things just as strange and unintuitive there.

 

[Vanadium 50]

Are you going to debunk quantum physics next?

Don't give him ideas.

 

[Hornbein]

Well, can you explain that in plain English?

No. Indeed that is why this question is so widely misanswered.

Basic measure theory is simple, it just requires knowing some subtle definitions. More than I care to try to explain in an Internet post.

If the universe is infinite in size (and like I said the physical properties are the same in all parts, that sort of thing), this conversation WOULD be happening an infinite number of times. That is what infinite necessarily means in that context. That is why I submit that an infinite universe is BS.

Wrong. If the probability of an event is greater than zero, then it happens an infinite number of times in an infinite universe. However just because an event is observed to occur does not mean that its probability is greater than zero. So, how do you tell whether the probability of a singular event is greater than zero? I believe that there is no mechanical/mathematical way to do this. We just don't know.

So what if there are an infinity of Universes like ours? Same thing. The event repeats as many times as it repeats. Whatever that may be. One, 42, six billion, infinity of measure zero, whatever. The way I like to put it is, the infinite pound gorilla does as it pleases.

 

[HomesliceMMA]

I do.I don't. This does not follow. See, for example, @martinbn's argument in post #26, and my response in post #38 to a counter-argument from @PAllen. You have not addressed those points at all.This isn't a matter of anyone "choosing". You can't just wave your hands and make claims. You have to support them with arguments. So far you have not given any arguments, just repeated assertions. If that's the best you can do, we'll just close this thread.

Post 26:

"Say the space is R3, the each such conversation happens in a small part of space and we can assume that all these parts are disjoint. The in each of them pick a point with rational coordinates. This way you get a bijection of all conversation places and some points with rational coordinates. These points are countable."I do not follow this. I have no idea what the R3 is. I don't know what "disjoint" is. Is that supposed to be "disjoined" I have no idea if the poster just speaks (or types LOL) bad English or that is supposed to be some technical term. The second sentence is obviously missing at least a word or two. Have no clue what "bijection" is.

Maybe translate that into plain English so I can understand it? More than happy to shoot it down!Post 38:

"But conversations don't happen in isolation. They happen as part of a larger history, for example, the history of Earth since its formation. And the repetition argument would ultimately have to apply to histories to have any force. But if histories are open-ended to the future, then you can't impose a finite time limit on them, and you can't say that any history must be repeated elsewhere in an infinite universe."

I could have SWORN I already answered this. Yes, the repetition argument would have to apply to history. Yes, histories are open ended. A universe that started all at the same time but was infinite in expanse would have infinite number of histories. And right this second, an infinite number of them would be having this precise conversation (and an infinite number would not be). A slip second later, an *infinite* number of those infinite number that were a split second earlier having this precise conversion would diverge from our own, but an *infinite* number would still be having this very conversation! That is the nature if INFINITE. It is not a large number, that is what follows from the word and meaning of infinite.

Nobody is limiting any time on any thing, you just made that up.

"This isn't a matter of anyone "choosing". You can't just wave your hands and make claims. You have to support them with arguments. So far you have not given any arguments, just repeated assertions. If that's the best you can do, we'll just close this thread."

I'm telling you what infinite means. You (or maybe not you, others here, I lose track), don't seem to grasp it. I'm telling you what the logical conclusion of saying "the universe is infinite in expanse" has to be (unless, like I said, you were to say something like "the universe only has the properties we see in our visible universe, in our visible universe". Infinite is not, like so many here are thinking, some really really REALLY big number. It means keep going, over and over again, FOREVER. So of course in an infinite universe we would be having this exact conversation elsewhere. It naturally and logically follows.

Let me say it another way:

In an infinite universe, whatever is possible, will happen not once, not twice, but an infinite number of times.

Do you actually disagree with that statement? If so, please explain in simple terms how it is wrong!

 

[HomesliceMMA]

No. Indeed that is why this question is so widely misanswered.

Basic measure theory is simple, it just requires knowing some subtle definitions. More than I care to try to explain in an Internet post.Wrong. If the probability of an event is greater than zero, then it happens an infinite number of times in an infinite universe. However just because an event is observed to occur does not mean that its probability is greater than zero. So, how do you tell whether the probability of a singular event is greater than zero? I believe that there is no mechanical/mathematical way to do this. We just don't know.

So what if there are an infinity of Universes like ours? Same thing. The event repeats as many times as it repeats. Whatever that may be. One, 42, six billion, infinity of measure zero, whatever. The way I like to put it is, the infinite pound gorilla does as it pleases.

"
No. Indeed that is why this question is so widely misanswered.

Basic measure theory is simple, it just requires knowing some subtle definitions. More than I care to try to explain in an Internet post.
"

Oh wooooow, "I know you are wrong but I'm not going to tell you why!" OK dude, ssssuuurrreee.....

Wrong. If the probability of an event is greater than zero, then it happens an infinite number of times in an infinite universe. However just because an event is observed to occur does not mean that its probability is greater than zero. So, how do you tell whether the probability of a singular event is greater than zero? I believe that there is no mechanical/mathematical way to do this. We just don't know."Wait, WAT? If the probability of an event is greater than zero, then it happens an infinite number of times in an infinite universe - that is EXACTLY what I am saying. But they you way, "However just because an event is observed to occur does not mean that its probability is greater than zero." WTF? Of course it does! It happened so the probability is greater than zero! You can tell because we are here and we are in the universe we are talking about LOL!

Come on man, at this point you are just pulling my leg, right?

 

[PeterDonis]

I do not follow this. I have no idea what the R3 is.

I don't know what "disjoint" is.

These are fairly basic terms in mathematics. If you're not familiar with them, you would do well to take some time learning the relevant mathematics. In the meantime, $\mathbb{R}^3$ is Euclidean 3-space, and two regions of space are disjoint if they have no points in common (i.e., they do not overlap).

I'm telling you what infinite means.

No, you're not. You clearly are unfamiliar with the mathematics of infinite sets. You need to spend some time remedying that before you presume to tell anyone "what infinite means".

I'm telling you what the logical conclusion of saying "the universe is infinite in expanse" has to be

No, you're not. Your claimed logic is faulty because you don't understand the mathematics of infinite sets.

In an infinite universe, whatever is possible, will happen not once, not twice, but an infinite number of times.

Do you actually disagree with that statement?

Yes.

If so, please explain in simple terms how it is wrong!

That was already explained in earlier posts. A quick summary: if the cardinality of the infinite set of "places where things can happen" is at least as large as the cardinality of the infinite set of "happenings", then each happening can occur only once even in a spatially infinite universe.

Oh wooooow, "I know you are wrong but I'm not going to tell you why!"

The term "measure theory" refers to a well-developed branch of mathematics. If you are not familiar with it, you should become so.

However just because an event is observed to occur does not mean that its probability is greater than zero." WTF? Of course it does!

Not when you are dealing with infinite sets of possibly different cardinalities. Again, you clearly don't understand the mathematics of infinite sets. That is not the sort of thing that can be remedied by a few posts in a discussion thread. You need to spend some time learning the relevant mathematics.

Come on man, at this point you are just pulling my leg, right?

No. The statements you find so unbelievable are true, although they are of course highly counterintuitive to people who are not familiar with the subject.

 

[PeterDonis]

@HomesliceMMA the topics in this thread have been addressed as much as they can be within the scope of a "B" level thread and given your very limited familiarity with the mathematics involved. Therefore, this thread is closed.