skaltezon

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.

Guybrush

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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lucifer_sam

Apologies, tore, I misunderstood.

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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skaltezon

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.

RVCA

Well see, now I believe you're ignoring the second part of my initial post.

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

skaltezon

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?

VEGANGELICA

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.

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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Guybrush

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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SIRIUSB

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.

lucifer_sam

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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