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Absolutely. If the universe was flat and the cosmological principle (...sorry, you cannot view external links. To see them, please REGISTER or LOGIN) is correct (both of which are widely beginning to be accepted as true) then the universe unbounded and not finite, i.e. the space is not bounded and goes on forever which means that the number of hadrons and hence the amount of matter is infinite. I can't imagine Sean disagreeing with me.

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

A limit is the value that a function or sequence "approaches" as the input or index approaches some value. If there is no such number and the sequence increases without bound then

And as for Sean, he thinks there's an evil twin universe where time runs backwards.

Pete, I have never made any secret of the fact that I lack a background in maths; I have always regarded this as a disadvantage, but perhaps it is not as disadvantageous as the apparent disability to see beyond mathematical definitions when that becomes appropriate or necessary.

You interchange “infinite” and “without bound”.

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.

Infinity is not a number; ...

....to treat it as such is simply to use the term as an approximation.

It is in effect saying “this is so large, or small, it is reasonable to regard it as infinite”.

What is the value of infinity?

I disagree with you. A "principle" is no substitute for scientific evidence.

One bit of evidence pointing to a homogeneous Universe is the isotropy of the cosmic microwave background (CMB). The CMB has very nearly the same intensity regardless of which direction you look from Earth - it is isotropic from our vantage point. Moreover, that it still appears isotropic after travelling through the Universe for 13.7 billion years suggests that the early Universe was highly homogeneous, and that it has remained rather homogeneous since then.

We really don't need a solid math background other than simple concepts. We start with the axiom (i.e. law, principle, etc. these terms all mean the exact same thing) cosmological principle. It's a very simply concept and based on solid scientific evidence. The cosmological principle states that the universe is homogeneous and isotropic when viewed on a large enough scale which means that the distribution of matter, and therefore mass, is homogenous and isotropic. Based on the recent Wilkinson Microwave Anisotropy Probe measurements we know that the universe is flat with only a 0.4% margin of error, according to NASA scientists. According to cosmologists the observational data best fits with the conclusion that the shape of the universe is infinite and flat. If the mass density of the universe is uniform and space is infinite then it directly follows that the amount of mass is infinite. It's as simple as that.

Think of this also, as we have quanta built into the theories of quantum mechanics, which by definition have a boundary, can these then be extended to infinity?

...We start with the axiom (i.e. law, principle, etc. these terms all mean the exact same thing) cosmological principle. It's a very simply concept and based on solid scientific evidence. The cosmological principle states that the universe is homogeneous and isotropic when viewed on a large enough scale...

That's because you're not a scientist, certainly not a physicist. If you were then you'd understand it.

Your problem is that you don't know that the cosmological principle was postulated because scientific evidence shows that the matter density in the observable universe, on a large scale, is homogeneous and isotropic.

...If you don't trust this but assume that your 'finite universe' continue past this limit you automatically define it as infinite.

...Or you will have to find a way to proof that what we call the earliest light isn't the 'earliest' at all...

I just say the size is unknown. There's just no evidence at all for declaring the universe to be infinite.

It all depends on what one means when using the term; "Universe".

We determine that the earliest light was 13.7 billion years ago and came from distance X. That distance existed 13.7 billion years ago dx will determine where that position now resides outside our light cone. As the universe has had 13.7 billion years of intervening time to continue expansion we would need to use Hubble data to see what the extent of the universe is now. That portion may already be outside the Hubble sphere and traveling away at superluminal speed exponentially. If the universe is infinite then it is growing to be larger than infinite simply because an expansion takes up more space. Therefore our view of infinity, which is a human invention, is wrong.

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

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 ∞ = ∞

Quote from: ChiralSPOInfinity 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?

A pink elephant is an elephant, not a pink.

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

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.

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?

Jeffrey, have you seen the "calculator" here? ...sorry, you cannot view external links. To see them, please REGISTER or LOGINI've been trying to get my head round it with limited success, but have still found it useful.

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'm not posting anymore in this thread

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.

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”.

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.

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?

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?

Quote from: Ethos_ on 18/10/2014 01:33:31If 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.

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?

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..........

It's no substitute for scientific evidence. And we have scientific evidence that the universe is flat, and is expanding. I think that's also scientific evidence for a finite universe.

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

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

Yes. An infinite extent can have a beginning.

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;

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.

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.

Maybe now's a good time to remind you that the word universe comes from "uni" as in one and "verse" as in vice versa. It means turned into one. It means everything. What you're asking about, is more than one everything. Does the universe, this everything, go on forever? If the answer is no, it doesn't make sense to say there's an infinity of other everythings beyond it.

......better minds than anyone of us conclude that flat space defines an infinite universe.

I think I'll have to agree with Pete about things here. When ever I hear someone use the term: "it seems to me", that usually means they are not bright enough to understand or they simply refuse to consider the facts.

The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation.

Possibly you and Ethos are understanding different things when using the word “universe”.

It is unclear if you are saying that you consider “middle” to be meaningless, or just that the logic I applied would make it meaningless. However, I would contend that middle, beginning or end; or indeed any position, in infinity is meaningless, but that’s probably a step further than we would be ready to go until we can progress beyond constantly returning to mathematical “infinities”.

You have two unbounded roads, but I argue that unbounded and infinite are not necessarily synonymous.

Beginning and end are directional concepts. Turn round and your beginning becomes an end which, by definition, infinity cannot have.

I too believe that points in infinity cannot be related by measurement; but take that logic a step further and it becomes: Two points in infinity cannot be distinguished from each other.

Cantor’s infinities are valuable as mathematical tools, but let’s not forget that even Cantor had problems dealing with “absolute infinity”.

... Cantor’s work on infinities is a masterpiece, but it should not be expected to apply beyond the sphere of maths.

That has to be one of Pete’s more elitist comments.

No..............better minds than anyone of us conclude that flat space defines an infinite universe.

Either way, you seem to have missed my points JD. I think I'll have to agree with Pete about things here. When ever I hear someone use the term: "it seems to me", that usually means they are not bright enough to understand or they simply refuse to consider the facts. Which ever case is true concerning this debate is something we will all have to decide at the personal level.

Whether material space is infinite or whether nothingness is infinite, the fact is, that infinity is inescapable. I suggest that if our material universe is finite, then your supposed nothingness beyond our present bubble is infinite.

If you can't "seem to get this" we have nothing left to discuss.

I think we are running into semantic troubles here. John, correct as your etymology of “universe” is; you have to allow language to evolve.

I hesitate to keep on about John Gribbin’s usage, but it does tend to militate against confusion. Possibly you and Ethos are understanding different things when using the word “universe”.

As far as what “better minds than anyone of us conclude”, let’s not forget that most of the best minds in geology thought that Wegener was wrong.

It seems I may not be “the voice of one crying in the wilderness”. Unbounded does not necessarily equal infinite! Even Stephen Hawking agrees with that....sorry, you cannot view external links. To see them, please REGISTER or LOGIN Quote The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago. The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation.