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Old 08-02-2011, 08:50 PM   #91 (permalink)
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Quote:
Originally Posted by tore View Post
I don't necessarily believe that our universe is infinite, but how can you say it isn't?
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Originally Posted by lucifer_sam View Post
As a logical argument, this is perfectly acceptable. Effectively, it is infinite.

There is no possible way for us to measure the known size of the universe, or even the rate of expansion, but assuming the universe is indeed expanding...

...it's mathematically fallible. Consider:

(Infinity) + 1 = (Infinity)
(Infinity) * 2 = (Infinity)
or even
(Infinity) * (Infinity) = (Infinity)

If the universe is indeed expanding, it follows there MUST be some change in its size from state 1 to state 2. However, since

(Infinity) - (Infinity) = 0

it follows that an infinitely large universe would be a static one.
You're confusing a mathematical abstraction with physical reality. Math isn't an observational science. It's a purely artificial invention with arbitrary rules that's used to *model* the real world. The actual world isn't compelled to conform to this model. Moreover, arithmetic operations like addition are only defined for numbers. Since 'infinity' isn't a number, you can't add anything to it. Therefore, your proof fails even as a model. However, I agree with your conclusion that the universe is finite because I don't believe in actual infinities. But it's an arbitrary choice.

Last edited by skaltezon; 08-03-2011 at 12:52 AM.
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Old 08-02-2011, 10:31 PM   #92 (permalink)
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Originally Posted by lucifer_sam View Post
Double posting because something egregious caught me eye...


As a logical argument, this is perfectly acceptable. Effectively, it is infinite. There is no possible way for us to measure the known size of the universe, or even the rate of expansion, but assuming the universe is indeed expanding...

...it's mathematically fallible. Consider:

(Infinity) + 1 = (Infinity)
(Infinity) * 2 = (Infinity)
or even
(Infinity) * (Infinity) = (Infinity)

If the universe is indeed expanding, it follows there MUST be some change in its size from state 1 to state 2. However, since

(Infinity) - (Infinity) = 0

it follows that an infinitely large universe would be a static one.
I think you misunderstood. When I wrote infinite, I didn't mean infinite in size, but that it exists infinitely without an event to start it or end it. You wrote that there has to be a starting point and my reply was basically something like "how do you know that"?
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Old 08-02-2011, 11:11 PM   #93 (permalink)
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Apologies, tore, I misunderstood.

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Originally Posted by skaltezon View Post
You're confusing a mathematical abstraction with physical reality. Math isn't an observational science. It's a purely artificial invention with arbitrary rules that's used to *model* the real world. The actual world isn't compelled to conform to this model. Moreover, arithmetic operations like addition are only defined for numbers. Since 'infinity' isn't a number, you can't add anything to it. Therefore, your proof fails even as a model. However, I agree with your conclusion that the universe is finite because I don't believe in actual infinities.
Sure you can, it functions the same as any other variable in the mathematical world. It just so happens 'infinity' is the upper limit for all numerical calculations. Replace (infinity) with (x) or any other suitable variable and take the limit as x approaches infinity, you arrive at the same answer. I may have made gross simplifications and egregious assumptions on my way there, but all I was trying to illustrate was a very simple premise: an infinite universe cannot expand.

Which you could arrive at using logical arguments too, I suppose.
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Old 08-03-2011, 12:01 AM   #94 (permalink)
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Originally Posted by lucifer_sam View Post
Sure you can, it functions the same as any other variable in the mathematical world. It just so happens 'infinity' is the upper limit for all numerical calculations. Replace (infinity) with (x) or any other suitable variable and take the limit as x approaches infinity, you arrive at the same answer. I may have made gross simplifications and egregious assumptions on my way there, but all I was trying to illustrate was a very simple premise: an infinite universe cannot expand.

Which you could arrive at using logical arguments too, I suppose.
Ah, a math man.

Sorry, but infinity can't be a variable. X can *approach* infinity (which is just another way of saying it can increase without limit) through numbers within its domain, and you can calculate the limit of functions of x as x approaches infinity if the limit exists (if the limit is a number). If the limit itself approaches infinity, then there is no limit. X and functions of x can never equal infinity because infinity isn't a number. Mathematical operations on non-numbers are undefined.

Infinities are interesting because no one has ever seen one. I don't think anyone can describe the consequences of an infinite anything, because we don't know what the rules are. Your intuitive sense that something without limits can't possibly get any larger seems reasonable, though.

Last edited by skaltezon; 08-03-2011 at 05:47 AM.
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Old 08-03-2011, 12:29 AM   #95 (permalink)
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Quote:
Originally Posted by tore View Post
I don't necessarily believe that our universe is infinite, but how can you say it isn't?
Well see, now I believe you're ignoring the second part of my initial post.

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On the other hand, it's entirely possible that there were events that occurred before that-thing-fourteen-billion-years-ago. It's just that we have no evidence of them. We have no reason to believe that they exist. Everything we've ever seen adds up to the conclusion that the thing that happened fourteen billion years ago was event one. Is it necessarily true that that's the case? No. But it's not reasonable to believe otherwise unless and until some kind of evidence to that effect makes itself known.
In that vein, sure, we could assume that the universe is infinite. But that necessarily defeats what got this discussion started in the first place: something infinite cannot have a period of nothingness like Stu was pondering aloud about

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Old 08-03-2011, 02:47 AM   #96 (permalink)
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Originally Posted by tore View Post
I think you misunderstood. When I wrote infinite, I didn't mean infinite in size, but that it exists infinitely without an event to start it or end it. You wrote that there has to be a starting point and my reply was basically something like "how do you know that"?
A bottomless past careening into an end of all things would make a good science fiction story. No beginning but a certain end. That would be infinite time too, wouldn't it?

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Old 08-03-2011, 10:13 AM   #97 (permalink)
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Originally Posted by skaltezon View Post
I agree with your conclusion that the universe is finite because I don't believe in actual infinities. But it's an arbitrary choice.
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Originally Posted by skaltezon View Post
Infinities are interesting because no one has ever seen one. I don't think anyone can describe the consequences of an infinite anything, because we don't know what the rules are. Your intuitive sense that something without limits can't possibly get any larger seems reasonable, though.
I imagine that the universe always existed as an infinite space that nevertheless can expand.

When the Big Bang is described as the event during which the cosmos went through a superfast "inflation," expanding from the size of an atom to the size of a grapefruit in a tiny fraction of a second (as shown in Jackhammer's original post: http://ssscott.tripod.com/bang.jpg), I imagine the universe as having consisted of an infinite space full of those tiny atom-sized areas expanding.

The universe would then be an infinite space where expansion occurs at every point within that space.

If the universe at the time of the Big Bang was an infinite space of dense matter and expanded at every point within that space, then we would have something without limits that expands yet isn't actually getting "larger" because the space was infinite to begin with. When I write that, it sounds contradictory, but for some reason it doesn't bother my intuitive sense!

Since the expansion of the observable universe occurs faster than the speed of light, and thus prevents us from seeing beyond the cosmological horizon (beyond which light heading in our direction will never get to us, since space is expanding faster than light travels), we are doomed to never know what is beyond the observable universe (Observable universe - Wikipedia, the free encyclopedia).

Nevertheless, I imagine the unobservable areas of our universe as being fundamentally the same as what we can see because I have no reason to think they would be different. If the current universe is infinite, then it makes sense to me that the universe at the time of the Big Bang was infinite, as well, and able to expand.

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According to the The Big Bang theory, our universe started with a "big bang" (or rapid expansion rather), but predicting what happened before that when you have all the matter of the universe in one place is not really simple.
Did our universe really *start* with a Big Bang? I didn't think there was any evidence for a lack of matter and energy before the Big Bang.
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Old 08-03-2011, 11:59 AM   #98 (permalink)
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Did our universe really *start* with a Big Bang? I didn't think there was any evidence for a lack of matter and energy before the Big Bang.
No, it's true .. Careless writing on my part I know (even without looking it up) that big bang theory concerns itself with the big bang and it's consequences, not whatever may have preceded it!
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Old 08-03-2011, 12:26 PM   #99 (permalink)
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Has anyone brought up the theory that a Subjective Universe always existed?

That a consciousness is not aware of Itself until it reflects upon itself, then starts the process of creating a perception format (Objective Universe) in order for a consciousness to become material/physical.
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Old 08-03-2011, 12:45 PM   #100 (permalink)
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Originally Posted by VEGANGELICA View Post
I imagine that the universe always existed as an infinite space that nevertheless can expand.

When the Big Bang is described as the event during which the cosmos went through a superfast "inflation," expanding from the size of an atom to the size of a grapefruit in a tiny fraction of a second (as shown in Jackhammer's original post: http://ssscott.tripod.com/bang.jpg), I imagine the universe as having consisted of an infinite space full of those tiny atom-sized areas expanding.

The universe would then be an infinite space where expansion occurs at every point within that space.

If the universe at the time of the Big Bang was an infinite space of dense matter and expanded at every point within that space, then we would have something without limits that expands yet isn't actually getting "larger" because the space was infinite to begin with. When I write that, it sounds contradictory, but for some reason it doesn't bother my intuitive sense!

Since the expansion of the observable universe occurs faster than the speed of light, and thus prevents us from seeing beyond the cosmological horizon (beyond which light heading in our direction will never get to us, since space is expanding faster than light travels), we are doomed to never know what is beyond the observable universe (Observable universe - Wikipedia, the free encyclopedia).

Nevertheless, I imagine the unobservable areas of our universe as being fundamentally the same as what we can see because I have no reason to think they would be different. If the current universe is infinite, then it makes sense to me that the universe at the time of the Big Bang was infinite, as well, and able to expand.
I think I understand what you're trying to say here, but the issue is that space itself (i.e. the cosmological bounds of non-matter) is expanding, for which we have irrefutable evidence (you mentioned it yourself in the next paragraph). It's a bit of a logical non-sequitur to suggest that space was infinite to begin with, because it contradicts the significance of the singularity event and the colossus of the oblivion that precluded it.

Which is one of the pitfalls of human cognition: we cannot truly grasp the idea of oblivion, nonbeing, nothingness.
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