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Sen Turner
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Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?
Sen Turner said:Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?
As far as we are able to realize for the moment... Who knows...PeroK said:"Growing" or "expanding" can also mean simply that the distances between points is getting larger with time.
If you know a little mathematics, you could imagine an infinite plane (the x-y plane, say) and a mapping that expands the distance between any two points over time. The x-y plane is simply mapped to itself by this process. There is no outside to grow into and no outside is needed.
Ever hear of the balloon analogy?Sen Turner said:Our general understanding of the universe is that it is infinite, so how can it be growing? If the universe is everything then what is it growing into?
acidmatic said:As far as we are able to realize for the moment... Who knows...
Sen is not asking about how it's infinite (or how to comprehend it), but rather how something infinite can expand. This can be explained easily through the balloon analogy, as long as one does not begin to think that the universe is on a curved 2 dimensional plane, such as the balloon.Daisyroots said:I'd suggest, Sen, that the question you put forward here may strictly belong more to philosophy than to physics. It arises because the finite (i.e. 'us'; at least in how we observe and think of ourselves) can have no realistic comprehension of 'infinite'. I.e. we can only possible think in terms of limitation. Thus since we have no prospect of defining (at least) one of the terms of the question, it is rendered meaningless. Sorry, I don't mean to be a killjoy.
Not true at all. His question is very clear and has a definite answer. Google "Hilbert Hotel"Daisyroots said:I'd suggest, Sen, that the question you put forward here may strictly belong more to philosophy than to physics. It arises because the finite (i.e. 'us'; at least in how we observe and think of ourselves) can have no realistic comprehension of 'infinite'. I.e. we can only possible think in terms of limitation. Thus since we have no prospect of defining (at least) one of the terms of the question, it is rendered meaningless. Sorry, I don't mean to be a killjoy.
Hi Phindsphinds said:Not true at all. His question is very clear and has a definite answer. Google "Hilbert Hotel"
But if in the course of inflating my 'balloon' the one-way air valve should fail, where does all the 'universe' end up then? Presumably in the same 'space' it was in the process of 'moving into' anyway(?).Comeback City said:Sen is not asking about how it's infinite (or how to comprehend it), but rather how something infinite can expand. This can be explained easily through the balloon analogy, as long as one does not begin to think that the universe is on a curved 2 dimensional plane, such as the balloon.
What "start point" ? If the universe is infinite it has always been infinite and there is no starting point to the growth other than infinite. If it is not infinite now, then it did not start out infinite.Daisyroots said:Hi Phinds
I looked at 'Hilbert's Hotel' as you suggested and I see that the idea uses as its basis a never ending series of numbers, extending, then, naturally, into infinity. But the question that occurs to me is, is a uni-directional 'infinity' plausible? I.e. can you have a viable idea of infinity that possesses, yet, a start point?
Well, I was just pointing to what looks like a hole in Hilbert's 'hotel' idea. The 'hotel' has rooms of infinite numerical extension, but the numerical series starts at room #1. Therefore the particular variety of 'infinity' indicated is unidirectional. I agree with you that a unidirectional infinity is a nonsense. It's what I meant.phinds said:What "start point" ? If the universe is infinite it has always been infinite and there is no starting point to the growth other than infinite. If it is not infinite now, then it did not start out infinite.
There's no one on the other side actually pumping their carbon dioxide breath into a latex sheet. The balloon analogy is simply an analogy. And just as much as the balloon analogy is an analogy, the universe is still expanding. It isn't "failing".Daisyroots said:But if in the course of inflating my 'balloon' the one-way air valve should fail, where does all the 'universe' end up then? Presumably in the same 'space' it was in the process of 'moving into' anyway(?).
I just don't follow you at all. The choice of which of the existing infinite number of rooms to choose to call "1" can be arbitrary so you are setting up a strawman to knock down. How would YOU label the elements of an infinite set that has the same cardinality (Aleph null) as the integers?Daisyroots said:Well, I was just pointing to what looks like a hole in Hilbert's 'hotel' idea. The 'hotel' has rooms of infinite numerical extension, but the numerical series starts at room #1. Therefore the particular variety of 'infinity' indicated is unidirectional. I agree with you that a unidirectional infinity is a nonsense. It's what I meant.
Thanks, Comeback city, I appreciate that it's an analogy. It's just that it's an analogy that doesn't (for me anyway) explain the 'pressure' that must surely be requisite for expansion whether or not there's a 'balloon'.Comeback City said:There's no one on the other side actually pumping their carbon dioxide breath into a latex sheet. The balloon analogy is simply an analogy. And just as much as the balloon analogy is an analogy, the universe is still expanding. It isn't "failing".
It's not supposed to. It describes the expansion rather than explains it. No on knows what dark energy is, so you're hardly alone in that.Daisyroots said:Thanks, Comeback city, I appreciate that it's an analogy. It's just that it's an analogy that doesn't (for me anyway) explain the 'pressure' that must surely be requisite for expansion whether or not there's a 'balloon'.
Hmmm... I see we are running into difficulty. The way I'm viewing it is from the perspective of an ongoing numerical count. I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific. So, as you rightly point out, the name of any of them is of course an irrelevance, but Hilbert is effectively forever adding 1 to infinity. The fact is, I think, 'infinity' is an un-graspable concept. Thanks for your effort with me. :)phinds said:I just don't follow you at all. The choice of which of the existing infinite number of rooms to choose to call "1" can be arbitrary so you are setting up a strawman to knock down. How would YOU label the elements of an infinite set that has the same cardinality (Aleph null) as the integers?
But does it 'describe the expansion'? The thread question was 'How can the universe grow if it's infinite?' In your view (I ask genuinely) has our little conversation around the question moved us on at all, as yet?phinds said:It's not supposed to. It describes the expansion rather than explains it. No on knows what dark energy is, so you're hardly alone in that.
What do you mean by it has to be specific? As in it has to be a defined number?Daisyroots said:I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific.
If my understanding is correct, then the whole point of Hilbert's hotel is to show that adding one to infinity still gives you infinity.Daisyroots said:but Hilbert is effectively forever adding 1 to infinity.
Daisyroots said:Hmmm... I see we are running into difficulty. The way I'm viewing it is from the perspective of an ongoing numerical count. I can see that the 'count' has the potential to go on forever, but at any point in time it is necessarily (as I see it) specific. So, as you rightly point out, the name of any of them is of course an irrelevance, but Hilbert is effectively forever adding 1 to infinity. The fact is, I think, 'infinity' is an un-graspable concept. Thanks for your effort with me. :)
Comeback City said:What do you mean by it has to be specific? As in it has to be a defined number?
If my understanding is correct, then the whole point of Hilbert's hotel is to show that adding one to infinity still gives you infinity.
Comeback City said:What do you mean by it has to be specific? As in it has to be a defined number?
Good question. And very interesting: because I do indeed mean that it must consist in a particular quantity; but at the same time, as I think you point out, any specified number is an irrelevance.
If my understanding is correct, then the whole point of Hilbert's hotel is to show that adding one to infinity still gives you infinity.
That makes a lot of sense actually.PeroK said:Not at all. The point of Hilbert's hotel is to show that an infinite set can be mapped to a proper subset of itself. This can't be done for a finite set.
That is basically what I said (even though as you pointed out, is not the main idea of Hilbert's hotel). 1 + infinity = infinityPeroK said:Infinity is not a number and hence cannot be subjected to a numerical operation such as addition.
PeroK said:Infinity is not a number and hence cannot be subjected to a numerical operation such as addition.
Comeback City said:That makes a lot of sense actually.
That is basically what I said (even though as you pointed out, is not the main idea of Hilbert's hotel). 1 + infinity = infinity
There are a few of us about!Daisyroots said:Hi PeroK. It's nice to know somebody knows what infinity represents.
Why are you misquoting me now? Not sure where that middle part even came fromDaisyroots said:Lol... I can't argue with that, Comeback city.
Yes, I know.PeroK said:Infinity is not a number.
Sorry, I'm not aware of having added or removed anything. I was just saying that I couldn't argue with your observation. Ignore me. :)Comeback City said:Why are you misquoting me now? Not sure where that middle part even came from
Comeback City said: ↑Daisyroots said:Sorry, I'm not aware of having added or removed anything. I was just saying that I couldn't argue with your observation. Ignore me. :)