[PmbPhy]

No, *your* interpretation of infinity is wrong. Infinity is not a number. The usual arithmatic with infinity does not follow the same rules one would expect to find with real numbers:

1 + ∞ = ∞
1000000 x ∞ = ∞
∞ x ∞ = ∞

Literally speaking one should not use an equal sign as you did when dealing with infinities since they only appear when in limits. So one has to use the limit notation on the other side of the equal sign the infinity symbol appears.

[alancalverd]

Infinity is not a number..................there are an infinite number of infinities.

Do you not think those two statements are contradictory?

What is an infinite number, if it is not a number?

No contradiction. A pink elephant is an elephant, not a pink.

[Bill S]

A pink elephant is an elephant, not a pink.

Congratulations on finding such an apt metaphor!

"Seeing pink elephants" is a euphemism for drunken hallucination.

[Bill S]

Pete, you seem to have withdrawn from our part of the discussion.  My wife read the last post I addressed to you and said:  "What do you expect, you've offended the man!"  Such was not my intention, and if you took offence, I apologise.

[PmbPhy]

Pete, you seem to have withdrawn from our part of the discussion.  My wife read the last post I addressed to you and said:  "What do you expect, you've offended the man!"  Such was not my intention, and if you took offence, I apologise.

I'm not sure which one you're referring to but if it's literally the last one you posted to me then you said

Pete, are you, or have you ever been a school teacher?  I ask this because your responses so often seem to follow the pattern: “This is the answer to your question; whatever your question was.”

I will do my best to keep to one question at a time, and if you answer just that question, perhaps we can make progress.
....
Does the cosmological principle apply to anything that did not originate in the Big Bang?

I can't see why your wife would think I'd be offended by that comment. I think I know you too well to think that you'd intentionally offend me so no, I'm not upset with you.

Although I'd be happier if you'd hurry up and join the new forum. Didn't I send you out an invitation? Membership is by invitation only. I'll send you the link in PM. First; please read the forum rules very carefully. If you agree to follow the rules then you're welcome to join. The rules are strict. There's a zero tolerance level for rudeness and flames. Although you can swear to your hears content. I never cared about foul language since I talk like a truck driver. Just don't swear at others.

The idea is to think of the forum as a cocktail party with all of your best friends present. You treat all members with the same respect that you give your friends. If you don't treat your friends with respect then think of them as your employer. You'll get the idea when you finish reading the forum rules. Then fill it out the registration form, submit it and I'll approve it.

Best wishes,
Pete

[jeffreyH (OP)]

On the infinite universe. 13.7 billion years ago light headed towards us. Also at that point light headed exactly away from us. Where did it go? That happened in all directions so it has had 13.7 billion intervening years to continue moving away. At some point that light will also cross the Hubble sphere. What speed does that light travel at? The space we say is expanding the mass apart. Light has to cross this space. Light has a set speed as far as we are concerned. Is it heading out to infinity and ultimately reaching an infinite speed? How can it reach an infinite speed? What exactly does an infinite velocity look like in an infinite universe? Why isn't everything already traveling at infinite velocity. If the universe is infinite then this must follow and must be true.

[Bill S]

Pete, I’ve found a question of yours that I have not answered.  It starts with your saying:

“By definition, a quantity is defined as infinite when it increases without bound. It's said not to have a limit. That's what it means to be infinite.”

In reply to which I said:

“I would not argue with this as being acceptable in maths, but I think that if you apply this definition to reality it leads to the sort of blinkered thinking that results in the repetition of mathematical rationale as though it were a definitive answer to something it does not address.”

You said:

“I'm sorry Bill but you lost me. I have no idea what that means.”

Let’s break it down:

“I would not argue with this as being acceptable in maths,”    Hopefully that’s straightforward.

 “but I think that if you apply this definition to reality…”  Infinity is a valuable and versatile concept in maths, but if, outside of maths, you produce answers that include infinity, or if you are talking, as we are, about the concept of a possibly infinite universe, the situation may be different.

“…..it leads to the sort of blinkered thinking that results in the repetition of mathematical rationale as though it were a definitive answer to something it does not address.”  When talking about a physical entity, such as the Universe, one has to think about the physical constraints imposed by finiteness and infinity, not just the mathematical perspectives; thus, simply repeating mathematical definitions does not constitute giving an answer.

As an example I would argue that if the Universe was ever finite, it could continue to expand without limit, it would be boundless, but it could never become infinite.  If the Universe, or anything, is finite at t=1, it must still be finite at t=10, or any other time.  Mathematically, it might be argued  that at t=∞ it would be infinite, but obviously that is meaningless. 

[Bill S]

Jeffrey, have you seen the "calculator" here? 

http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html

I've been trying to get my head round it with limited success, but have still found it useful.

[jeffreyH (OP)]

Jeffrey, have you seen the "calculator" here? 

http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html

I've been trying to get my head round it with limited success, but have still found it useful.

Thanks Bill I will look at it properly when I get some free time. Ha Ha! I am in the middle of a project with a strict deadline so it may be a while.

[Bill S]

Pete, I've also found a question of mine that you have not answered.  May I prompt you?

"Does the cosmological principle apply to anything that did not originate in the Big Bang?"

[PmbPhy]

Pete, I've also found a question of mine that you have not answered.  May I prompt you?

"Does the cosmological principle apply to anything that did not originate in the Big Bang?"

I don't understand the question. What do you mean by "anything that did not originate in the Big Bang". The cosmological principle applies to the uniform distribution of matter in this universe and nothing else.

By the way. I've stopped posting in this forum because I've said all there is to say about the subject and my replies stand as they are. I find all counter arguments to be flawed but have already stated why. I don't wish to argue forever so I'm not posting anymore in this thread. At least I won't try to make an argument again. I still hold that given the cosmological principle and a flat universe the amount of mass in the universe is not finite, i.e. it can not be assigned a fixed number. It can be shown, as I already have, that the amount of mass in the universe is in fact infinite under those circumstances according to the definition of "infinite."

[Bill S]

 []

I'm not posting anymore in this thread

I respect that, Pete.

I think that what I have to do now is go back over the thread and see what makes sense to me, perhaps post some sort of summary and assess where that leaves me with regard to the original question.

On second thoughts, I may post a "thought scenario" first.     []

[Bill S]

There is a road of infinite length, in the middle of which there is a bridge.

How do I know the bridge is in the middle? I know that because the road must extend to infinity on either side.

Of course, we all know that, physically, there cannot be a road of infinite length because, as far as we know, the only places where a road could be placed are finite, but this is a "thought scenario".

One night the Finite Defence League blow up the bridge, so no one can cross from one side to the other. We know that the road extends to infinity in both directions, but can each section really be considered infinite?

What do we have? Is it two halves of infinity, two infinite roads or two finite roads?

Intuitively, one might say that, as each half goes to infinity, we must have two infinite roads. That seems more reasonable than "two halves of infinity".

However, consider that if you are at a point (eg 1km from the bridge site) along the road, and you travel towards the break; in 1km you come to the end of "infinity". Does this make sense?

Because we reach an end, whichever side we approach from, it is tempting to argue that the road segments are finite. However, if members of the People’s Infinite Front decide to repair the bridge, but they are infinitely far away along the road; can they ever reach the bridge? The answer must surely be “no”.

We were able to reach the end, so in our frame of reference, the road is finite; but the PIF, who were infinitely far away could never reach the bridge, so in their frame of reference it must be infinitely far away. For them, the road segments go on infinitely in both directions. 

Wait!  This can’t be right.  If they were infinitely far away, they were at the end of the road, which is not possible if the road has no end.  Enter the mathematician who points out that there are different sizes of infinity.  Could it be that the PIF are infinitely far from the bridge, but their infinity is smaller than that of the road, or of this segment of the road?  Am I alone in thinking that this is rubbish? 

Does this mean that infinity is relative? It would seem to suggest that, but what does that mean?

[Ethos_]

Speculating about infinities; if we had an infinite amount of time, we could rationalize an infinite amount of scenarios theoretically disproving infinity. Seriously though, thinking about infinity. It occurs to me that for anything to exist, it must lie within a space. And if space is flat, we're talking about infinity.

If on the other hand, our space is finite it is also possible that M-theory might be correct and our universe lies within an infinite Bulk filled with an infinite number of other universes. In either case, we're still talking about infinity.

If one declares that our universe is closed, one must ask: What is outside? If we say; "nothing", one must ask: What is nothing if not more space?

I believe in infinity!

[dlorde]

I think we already covered all this is another thread, but...

There is a road of infinite length, in the middle of which there is a bridge.

How do I know the bridge is in the middle? I know that because the road must extend to infinity on either side.

By that logic, anywhere on the road is the middle, which makes 'middle' meaningless in this context.

One night the Finite Defence League blow up the bridge, so no one can cross from one side to the other. We know that the road extends to infinity in both directions, but can each section really be considered infinite?

What do we have? Is it two halves of infinity, two infinite roads or two finite roads?

Intuitively, one might say that, as each half goes to infinity, we must have two infinite roads. That seems more reasonable than "two halves of infinity".

Half of infinity is still infinity. You have two infinite roads.

However, consider that if you are at a point (eg 1km from the bridge site) along the road, and you travel towards the break; in 1km you come to the end of "infinity". Does this make sense?

Yes. An infinite extent can have a beginning.

Because we reach an end, whichever side we approach from, it is tempting to argue that the road segments are finite. However, if members of the People’s Infinite Front decide to repair the bridge, but they are infinitely far away along the road; can they ever reach the bridge? The answer must surely be “no”.

Clearly, if the road was finite in extent, the PIF couldn't be infinitely far along it.

Wait!  This can’t be right.  If they were infinitely far away, they were at the end of the road, which is not possible if the road has no end.

Infinity is not a number. Infinitely far away is not a particular place. Any specific point you place your PIF along the road is not infinitely far away from the start (or any other specific point on the roadway). You might choose to simply specify that they are infinitely far away on the road, so they would now be infinitely far from the start, and still have an infinite extent of road in the other direction. That's how infinity works, and why your road must remain a thought experiment. You may say that the start is a specific point on the road, and the PIF, infinitely far away, are also at a specific point on the road, but these two points cannot be related by measurement; they are infinitely far apart.

Could it be that the PIF are infinitely far from the bridge, but their infinity is smaller than that of the road, or of this segment of the road?  Am I alone in thinking that this is rubbish?

No, both infinities in this thought experiment are the same size. If you want to know about different 'sizes' or orders of infinity, check out Georg Cantor's Transfinite Numbers.

Does this mean that infinity is relative? It would seem to suggest that, but what does that mean?

I don't know what you mean by it, but there are different orders of infinity. For example, there are an infinite number of natural numbers, but a larger infinity of real numbers.

[JohnDuffield]

If one declares that our universe is closed, one must ask: What is outside? If we say; "nothing", one must ask: What is nothing if not more space?

Nothing. Space isn't nothing. It sustains waves and fields. I can conceive of space having an edge, rather like a water droplet has an edge. A ripple in the droplet would reach the edge and then undergo total internal reflection. I can imagine light waves doing the same when they reach the edge of space. Beyond which there is no more space.

[Ethos_]

If one declares that our universe is closed, one must ask: What is outside? If we say; "nothing", one must ask: What is nothing if not more space?

Nothing. Space isn't nothing. It sustains waves and fields. I can conceive of space having an edge, rather like a water droplet has an edge. A ripple in the droplet would reach the edge and then undergo total internal reflection. I can imagine light waves doing the same when they reach the edge of space. Beyond which there is no more space.

I understand this argument John, but to that argument I will ask you this question:

If our universe occurred within this nothingness, producing waves and fields restrained within our present physical "water droplet", it's logical to assume that this same process can repeat itself again somewhere else in your defined nothingness. Or is our present location the only place where a universe can form? And why would we assume to limit this event to a single location?

As you may have already figured out, I tend to believe in either flat space or the Multiverse concept. In either case, space would be infinite. Given that this may be an accurate view of physical reality, can you see where this view of things would involve an infinite arena or place where present reality exists? If not, why only one finite universe?

Murphy's Law; If it can happen it will.

And if it happened once, it will happen again, and again, and again..........

[yor_on]

Good ideas all of you. We're here to use our minds.

[yor_on]

Then again. A vacuum reduced is nothing, and if you like 'infinite', as it has no bounds intrinsically. Assuming one want to bound it, one need to introduce some property more that the idea of a 'nothing'. Do you see?

[dlorde]

Then again. A vacuum reduced is nothing, and if you like 'infinite', as it has no bounds intrinsically. Assuming one want to bound it, one need to introduce some property more that the idea of a 'nothing'. Do you see?

A vacuum is space with no matter, not nothing. You'll have to explain what you mean by a 'vacuum reduced'. Nothing doesn't exist by definition, so neither infinity nor bounds are applicable. If by 'reduced' you mean everything removed, i.e. the absence of anything & everything, then it's trivially true, but so what?