[JohnDuffield]

I was under the impression that you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?

There is no region of absolute nothingness. It's like what dlorde said. Nothing is the absence of anything, even empty space. It doesn't exist, it has no extent of any kind, and it isn't infinite. And I just can't see how you can get something from nothing. 

"A hole in space." "Only there wasn't any space around it." Now you've really sent my train off the tracks...

Take it one step at a time. Read up about the gravastar and the frozen-star black hole, and have a dig around about the way the early universe is likened to a black hole.

[Bill S]

The 'middle' means equidistant from specified extremes. Infinite extremes are not measurable so equal distance can't be known.

Granted, equal distance can't be known, but by the same token, nor can unequal distances.  Since distances must be either equal or unequal, does this imply that no distance in infinity is measurable?

On the other hand, if you decide the infinities either side are effectively equal in size, then any point qualifies, which means all points are the middle; which, I submit, makes it meaningless.

If they are not measurable, how can you decide that your “infinities” are equal, or unequal?  That is as meaningless as the concept of “middle”, or indeed of any distinguishable point in infinity.

As far as I know, the only framework for dealing with the concept of infinity is mathematical. It's a mathematical abstraction. What else can we use when considering thought experiments about physical infinities?

We seem unable to escape the mathematical infinities, even when talking about physical entities.  If we use infinite as though it were synonymous with boundless we will always run into problems.  The universe may be boundless. If it is, we can still apply mathematics to it – measure it.  If we claim it is infinite, we are saying more about it.  Infinity “is a mathematical abstraction”.  What is an abstraction if it is not the quality of dealing with mental concepts, rather than with concrete objects?  The Universe is a concrete object, we need more than a mathematical abstraction in order to understand it.

That's just semantics. I can equally say that depending which way you turn, you either have an infinite extent ahead of you or behind you.

You can say you have an unbounded extent “ahead of you or behind you”, but you cannot establish that it is infinite.

can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?

Consider two points in infinity – A and B.  If you are at A you assess that you are centrally placed, according to your assessment B is therefore not central.  Now move from A to B.  Once there you assess that you are central, so A is not. If you measure the distance between A and B as 100 km, then the distance between the centre of infinity and the centre of infinity is 100km, which is nonsense.  A and B are distinguishable only if there are objects there.  The points themselves are indistinguishable.  If you remove the ability to relate A and B by measurement, you remove the ability to distinguish between them. Each is the centre of infinity, whatever that might be.

I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.

Apart from some vague hand waving in the direction of God, what is absolute infinity?

[dlorde]

Granted, equal distance can't be known, but by the same token, nor can unequal distances.  Since distances must be either equal or unequal, does this imply that no distance in infinity is measurable?

Only where they involve infinities. You could have measurable distances on a hypothetical infinitely long road - e.g. two points a mile apart.

On the other hand, if you decide the infinities either side are effectively equal in size, then any point qualifies, which means all points are the middle; which, I submit, makes it meaningless.

If they are not measurable, how can you decide that your “infinities” are equal, or unequal?

I was covering the possible argument that infinities of the same order could be claimed to be the same size (because they are not different sizes of infinity). Even if it was valid, I don't think it's a useful argument, but someone might be tempted by it.

We seem unable to escape the mathematical infinities, even when talking about physical entities.

Infinity is a mathematical concept, so - yes, if you want to talk about physical infinities, the model is mathematical. Likewise, if you want to talk about the physical effects of gravity, the model is also mathematical. What's the problem?

Infinity “is a mathematical abstraction”.  What is an abstraction if it is not the quality of dealing with mental concepts, rather than with concrete objects?  The Universe is a concrete object, we need more than a mathematical abstraction in order to understand it.

The universe seems surprisingly amenable to modelling through mathematical abstractions - that's how we understand its physical behaviour; we don't yet know whether it makes sense to apply the mathematical concept of infinity to our models of it, but that doesn't prevent us hypothesising the cases. But I agree in that I don't see how we can ever know if the model matches the reality in that respect.

You can say you have an unbounded extent “ahead of you or behind you”, but you cannot establish that it is infinite.

That it was an infinite road was the premise of your thought experiment. In the real world I don't see how you could never know or establish it was infinite - that's why it must be a thought experiment. If you were on a finite circular road, you would indeed have an unbounded but finite extent ahead or behind.

can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?

Consider two points in infinity – A and B.  If you are at A you assess that you are centrally placed, according to your assessment B is therefore not central.

That doesn't get off the ground - above, you agreed that the idea of equidistance or a middle to infinity was a meaningless idea. 

I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.

Apart from some vague hand waving in the direction of God, what is absolute infinity?

I suspect only Cantor knows. I don't know why you brought it up in the first place.

[Ethos_]

I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.

Sorry, my mistake. So you reject the idea of a 'region of nothingness'?

I'm still curious to hear your definition of nothingness and how it could be infinite (e.g. infinite in what respect?).

I truly think this discussion has become too contentious. Everyone has a right to speculate on issues which are, as yet, unproven. We should all agree to disagree.

As to your question dlorde: If the universe is finite, and nothingness lies beyond, this nothingness is infinite because it would be boundless.

This is just my view and as others also have the right to their personal views, I'll claim the right to mine as well.

Now, for all those who choose to point their finger and accuse me of being wrong, I may well be wrong but I'll take the liberty and suggest that no one here has sufficient evidence to claim infallibility concerning the true nature of the Cosmos, whether finite or infinite, we just don't have convincing evidence either way at the moment. So, everyone just knock yourselves out trying to prove your particular theme. Until better evidence is found, believe what you choose.

[dlorde]

If the universe is finite, and nothingness lies beyond, this nothingness is infinite because it would be boundless.

We've already established that boundless doesn't imply infinite, although the reverse is true. For example, the surface of a sphere is boundless but finite, and the circumference of a circle is boundless but finite.

But how do you define this 'nothingness' you're invoking? The phrase 'lies beyond' the universe suggests something that can lie and some region it lies in. Is this just a question of phrasing? does it actually mean that there is not anything beyond the universe, i.e. there is no 'beyond'? or does it mean something different - some sort of infinite void, perhaps?

Now, for all those who choose to point their finger and accuse me of being wrong, I may well be wrong but I'll take the liberty and suggest that no one here has sufficient evidence to claim infallibility concerning the true nature of the Cosmos, whether finite or infinite, we just don't have convincing evidence either way at the moment.

Until you explain what you mean we can't even discuss your ideas properly.

[Ethos_]

Until you explain what you mean we can't even discuss your ideas properly.

In simple terms; My thoughts are this:

Either the universe, "Cosmos" or what ever one chooses to define all that is and is not, is infinite. Either flat space is infinite or M-theory is our reality. In either case, the "Cosmos" is infinite.

We have already had sufficient testimony exclaiming distaste for the infinite flat space model so you are now left with M-theory to assassinate. These two models are my personal favorites, but you are free to choose your own. I refuse to argue about this any more. Enjoy.....................................

[dlorde]

We have already had sufficient testimony exclaiming distaste for the infinite flat space model so you are now left with M-theory to assassinate.

I don't know of a reason in physics that proscribes a universe of infinite spatial extent - it would mean it was infinite at the big bang, but that's not a problem. I don't see how it could be tested though.

M-theory looks more interesting, with suggestions for testing some aspects of it, having mathematical correspondence with some interesting areas of current physics, and a wealth of options to select from - perhaps too many for comfort. The anti-de Sitter space formulation of M-theory seems topical - in that it's curved so that all points inside the spacetime are infinitely far from its boundary... unfortunately the details are beyond me.

I refuse to argue about this any more.

OK.

[Bill S]

I have just looked over the last page of this discussion, and there are several points to which I thought I would respond; then I thought of how much of the discussion goes round in circles.  Dlorde pointed out about the “infinite road” that we had visited it before; that’s true, but the same applies to most of the discussion. 

Most of the sticking points seem to involve the definitions of Universe, infinity and nothingness.

In another thread and a few PMs, JP and I discussed my claim that there could never have been nothing, otherwise there would still be nothing now.   He was adamant that we could not make this claim because, outside the Universe conditions could exist in which something could come from nothing.  I pointed out that “conditions” must surely be something; and although the discussion continued for some time, we never really moved beyond his saying:
“The problem with the idea that "nothing can come from nothing" is that to scientifically discuss this, we need to come up with a model, and we can't even describe "absolute nothing" scientifically (or at least I haven't seen a scientifically workable definition)”.

I think I have correctly quoted JP, but I’m sure he will say if I have not.

There is evidence in this thread that I am not the only person in the world who thinks there can never have been nothing.  If there was never nothing, then there has always been something, and that something must be eternal. 

Can we go as far as to say “I f it is eternal it is infinite”?

Nothingness should be simple to define! It should be the absence of absolutely everything/anything.  As JP pointed out, we can’t even describe nothing scientifically.  Is “the absence of everything” not a reasonable definition?

There has been much discussion about whether the Universe is finite, or infinite.  Much of this hinges on the distinction between infinite and boundless.  It would be a major achievement if we could come to an agreement on that, but let’s not ask too much. 

[dlorde]

I too can't see how something can come from 'true' nothing (i.e. absence of anything, including spacetime). On the other hand, if the universe is closed in time (time has a beginning), what does it mean to say there's always been something...

[Ethos_]

It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. The following link explains:

http://www.esa.int/Our_Activities/Space_Science/Is_the_Universe_finite_or_infinite_An_interview_with_Joseph_Silk

And for those that would argue that infinite space is an impossibility, this reputable scientist confirms that at least, it is a possibility. If it were not, the question wouldn't even have been asked; "Is the cosmos finite or infinite?"

[Bill S]

Good article, Ethos.  I shall need to read it more than once to get my finite brain around its infinite implications.

One thing that does leap out, even on the first reading is this:

“…you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus”.

So, how do you role up an infinite sheet of anything?  Surely, to do that you would have to bring two edges together, and past, each other.  How do you find the edges of an infinite sheet?  If you could do this, would it still be infinite when you had rolled it up?

This may seem like nit-picking, but is it?  If we accept this thinking are we not subscribing to using something physically impossible as the basis for a physical theory?

[Bill S]

It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. …………………….. "Is the cosmos finite or infinite?"

Not all scientists agree that “universe” and “cosmos” are synonymous. 

[Ethos_]

It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. …………………….. "Is the cosmos finite or infinite?"

Not all scientists agree that “universe” and “cosmos” are synonymous.

Point well taken Bill S, I should have said cosmos instead of universe in that sentence.

[phyti39]

Consulting our primary textbook the dictionary, we conclude something like this.
Infinity is not a number since it has no value. It is a relation/condition about numbers stating there is no limit to a magnitude, there is no final value. It is something NOT measurable.
The common example of the set of integers has a beginning but is 'open ended/without limit/unbounded'.
Another instance of the meaningless term is found in the definition of a limit (by mathematicians no less!).
The limit of (some sequence for x), as x approaches infinity = u.
The question is, how do you approach 'infinity'?  At night, on your tip toes, or while it's sleeping...?
It's a contradiction in terms. You can't approach 'infinity' anymore than you can approach the horizon, or the carrot on the stick, i.e. it's always 'just ahead'.
I prefer "as x increases without limit".

Interesting, all the areas influenced by this word "infinity".

"Nothing" and "existing" are mutually exclusive terms.
Dictionary [nothing]: a state of nonexistence, or the absence of any perceptible qualities
That would exclude the quality of extent.

The universe can be defined as "everything known to exist, visible and invisible", which would include the laws that regulate it.

The idea that earth gravity tends to zero as distance increases (without limit) is true only if earth is the universe (the ideal isolated experiment). In the real world the significant gravitational effects are local. and decrease  rapidly with distance. As probes leave the solar system, the dominate mass is the sun, and the earth can be ignored. In any remote location, far from any significant masses, the total gravitational effect from all mass in the universe is zero.

The expression u=1/x is a precise statement, but when x=0, it does not result in a precise answer. In fact it's defined as indeterminate, i.e. there is no answer. It should be declared illegal as it is in computer programming. Division by zero is another of those nonsensical terms that should be eliminated. You can put an unlimited (not infinite) number of zeroes into a container, but nothing will ever materialize within it. You can't make something from nothing! In the case of the gamma term from Relativity, v will never equal c for a mass, thus that condition will not occur.

The universe can consist of a finite mass, but be closed, in the manner of the spherical earth surface. You can travel indefinitely in it, but eventually will revisit some areas.

Universe (Latin) and cosmos (Greek) are interchangeable, both meaning an integrated entity consisting of everything known.

Cantor was a great illusionist.
 
The silent disclaimer: All things mathematical do not correspond to physical reality.
 

[dlorde]

Welcome phyti39, and congratulations on the clarity and succinctness of your first post. I think I agree with pretty much all of it...  []

[Bill S]

hi phyti39, I'm with dlorde here.  Hope to see more of you in TNS.

[phyti39]

Thank you for the type of welcome I wasn't expecting, considering my past forum experiences.
I'm just a seeker of truth.

[Bill S]

You can't approach 'infinity' anymore than you can approach the horizon, or the carrot on the stick, i.e. it's always 'just ahead'.

In fact, it’s always infinitely far ahead.

[nothing]: a state of nonexistence, or the absence of any perceptible qualities

Personally, I would exclude “perceptible”.  I would say it’s the absence of anything, perceptible or otherwise.

The universe can be defined as "everything known to exist, visible and invisible", which would include the laws that regulate it.

 

I would go with that, but would say that this might not include the “cosmos”, but that’s another issue.

Universe (Latin) and cosmos (Greek) are interchangeable

Originally, I would agree, but I think the meanings have to some extent evolved.  See #116 in this thread.

[Ethos_]

Here is another article which deserves consideration regarding the size and scope of our universe. If you'll notice, the author speculates that while the universe is expanding, this observed expansion is logically moving into new territory of infinite dimension. It is like so many other ideas, not yet proved, but is worthy of reading nevertheless.


http://phys.org/news/2014-10-universe-older.html

[JohnDuffield]

Interesting. But I didn't understand why space had to be expanding into another medium. Space is the medium. How can there be some other medium? Does not parse.