Can "Infinity" ever be more than a mathematical abstraction?

[Write4U]

The Observerable Universe is larger by one light year every year.

Are you sure? If it the radiation reaches us from further back in time by one light year every year, the universe should appear to become smaller, no?

Otherwise, how can we claim an expanding universe at all? It has to be biggest in the present and smaller the further back in time we go. Can't have it both ways.

 

[Seattle]

Are you sure? If it the radiation reaches us from further back in time by one light year every year, the universe should become smaller, no?

Otherwise, how can we claim an expanding universe at all? It has to be biggest in the present and smaller the further back in time we go. Can't have it both ways.

The radiation is from the same point in time, another year has passed and so more light reaches us. The Universe was bigger than the Observable Universe from the beginning as well.

 

[Write4U]

The radiation is from the same point in time, another year has passed and so more light reaches us.

Ah ok, maybe I can make sense of that. I'll have to think that through.

The Universe was bigger than the Observable Universe from the beginning as well.

Not according to anything I have read. How big was the universe before the inflationary epoch, at time of the BB?

Is infinitely small the same as infinitely large?

 

[Seattle]

Ah ok, maybe I can make sense of that. I'll have to think that through. Not according to anything I have read. How big was the universe before the inflationary epoch, at time of the BB?

Is infinitely small the same as infinitely large?

We are talking about two different things here. The Observable Universe is a reference from our location (Earth) and from the present (today). So, what we can see is just a function of how far light could have traveled in 13.8 billion years.

The CMB (Cosmic Microwave Background) that we are looking at was roughly 400,000 years after the Big Bang. We don't know how big the Universe was (or is). It could be infinite (or not). It's unlikely that the Universe is exactly the same size as the Observable Universe. That would be odd.

Regarding an infinity with a beginning...I don't think that can happen. Consider an infinite space that is compressed into an infinitely dense point. Now expand it by increasing the space between any two points.

That is how you could have an infinite Universe from the Big Bang on. That's not to say that the Universe is infinite. I don't think there are any infinities but that's just my viewpoint.

 

[arfa brane]

We are talking about two different things here.

Indeed there are two different things. There is an expanding universe which logically must have been smaller in the past, and there is an observable universe.
The latter is true because there are observers, they have figured out that they can see only those objects which aren't so far away they haven't seen any light from them (the too far objects).

Which means they will see more and more of the universe as it expands, because of the speed of light. We will see more stars that formed earlier in the history of the universe.

 

[someguy1]

Whether or not map = territory, how many maps are there? Is the territory a singleton set?

I myself tend to doubt that mathematical set theory applies literally to the real world. There are collections of things as a philosopher would explain them. But sets as mathematicians understand them are very strange. I don't think the empty set has physical existence, let alone all the other wild sets mathematicians use. That's my opinion.

So I don't personally think any physical object is a singleton. I don't believe in singletons either. I see an apple on the teacher's desk. I do not see the set containing the apple.

I enjoy set theory as a mathematical pastime. I just don't happen to think it has anything to do with the real world. As far as I know, not many people have even gotten around to asking the question. And by the way: To the extent that nobody asks the question, to that extent they are not serious about grappling with physical infinity. Because if set theory is about anything, it's about highly weird and counterintuitive infinite sets.

It occurs to me that, for instance, because the earth is rotating about an axis, we can't choose a map that has poles on the equator.

Cartography, and the theory of how to make a flat map of a sphere, are interesting subjects. In this convo I'm using map to mean a theory or a model. The map of the earth is not the earth, and the Hilbert space formulation of QM is not literally how the world "is," it only describes how the world appears to act, to the limit of our experiments. The most accurate prediction ever made by physics is good to 12 decimal places. In the context of the mathematical real numbers, that's barely accurate at all.

That's all I mean by "the map is not the territory." You want to do QM on Hilbert space, fine by me. Just please don't come back and say that because you got a 12 decimal place prediction that you think that proves that the world "IS" a Hilbert space. It is not. The model is not the thing it's modeling. The map is not the territory.

 

[arfa brane]

I do not see the set containing the apple.

Ok. But what if someone throws the apple up in the air? What would you say "the territory" is?

I enjoy set theory as a mathematical pastime. I just don't happen to think it has anything to do with the real world.

Seriously? You don't think sets have anything to do with tallying, something humans do every day? And speaking of tallying, it's also occurred to me that the people who wrote computer programs to determine how many moves you can possibly make with a Rubik's cube (the answer is 20), is the solution to a counting problem.

A different counting problem is determining the number of permutations of the Rubik's cube which are the same distance (number of moves) from the start position. How many maps are there for either problem, or for their solution?

The territory is obviously physical, an object that looks like a cubic stack of 27 smaller cubes, with the faces identified by different colours. Or can I describe the object differently, so differently the description doesn't look at all like the previous one? (sure I can)

 

[Speakpigeon]

But does the picture not show the entire universe, before it became too large to see all of it? As I understand it the picture is the actual size of the background glow, very shortly after the BB, clearly showing it was finite in size, which in itself would indicate that the universe was even smaller shortly before then.

No, "the picture" can only show what is observable from now. If there was something else that isn't observable now it isn't on "the picture", obviously.
Further, the EM radiation for some time after the Big Bang had all the time necessary to spread around the little space there was available. So, seen from now it's just a smudge spread over the entire night sky, as if the EM radiation came for all directions. It is all around us. So, I don't think we could infer the size of the Big Bang from that.

IMO, our universe is clearly finite.

Absurd.

If it had a beginning then logically it cannot be infinite in size.

Could you explain that?!
Sorry, but me, I can't see that there's any logical problem with the idea of having a universe with a beginning in time that would have been infinite in size right at the beginning.
I may not sound plausible, but plausibility doesn't tell us anything about logicality. You seem to be confused about that.

There may be an infinite void beyond that, but that is the speculative part, not our universe.

Or there may have been a Big Bang infinite in size.
And if a speculation is true, then it's the universe as it is.
And all that we think we know about the universe rest on speculative grounds that may well be wrong.
So, all your opinions here are without foundation.
EB

 

[Speakpigeon]

Which means nothing in terms of ontology. Newtonian gravity has amazing predictive power but it turns out to be incorrect at high velocities and for large masses.
All scientific theories are approximations. If you don't understand that you don't understand the first thing about science.
Are you making the claim that current scientific theories are the absolute and final truth, and will never be refined or extended or modified in any way? I hope you're not saying that but if you are, admit it now.
Newton famously understood that natural science is DESCRIPTIVE and not EXPLANATORY. Do you understand this point? Science builds mathematical models that match known observations to some satisfying number of decimal places. We do not know anything about ultimate causes. Ultimate causes are metaphysics and not physics.
Oh. Ok. You do understand this point. So why are you typing in arguments in support of a thesis you already know is wrong? And aiming them at me?
Oh. So there is no objective reality. It's only about what I believe. I believe in magical fairies and someone else believes in modern physics. What of it? All points of view are equally valid. "It all comes down to what you believe."
Don't you see that you keep contradicting yourself? If it's "all in the mind" and "it all comes down to what you believe" then you aren't in much of a position to be defending the thesis of objective science dispassionately studying an external reality.
Well then what is your point and why are you aiming it at me?
Uh-oh you're about to fall into a trap of your own making.
Really? Multiverse theory is falsifiable? True pointlike particles are falsifiable? Tell me about this. Make sure to supply peer-reviewed references. This is going to be interesting.
You see you just wrecked your own thesis. Much of modern physics is not falsifiable. This is a serious problem that a lot of people are noticing. "Landscape" theories are not falsifiable.
Well, objective evidence to contrary would convince me. But nobody has provided any objective evidence for the multiverse and for actual physical infinities.
Having studied a bit of infinitary set theory, infinities are very much like fairies. They're imaginary things that we make up stories about and then reason logically from the stories.
Please understand once and for all that infinity exists in mathematics by ARBITRARY FIAT.
https://en.wikipedia.org/wiki/Axiom_of_infinity
Turns out you can. The negation of the axiom of infinity is consistent with the other axioms of set theory. When you negate the axiom of infinity you get Peano arithmetic. There's 1, and there's 2, and there's 3, ... but there is not a completed set containing all of them. You can do math in this system just fine, a lot of number theory still works.
Physics, not so much. But this is just the same problem we've already noted. Abstract crazy math is often useful to physicists even though it's not "true" in any meaningful sense. Wigner again.
Nobody has ever provided evidence for the existence of physical infinities. If anyone ever did they'd get the Nobel prize immediately. I really hope you understand this. There is no evidence for physical infinities. All we have is the fact that mathematical infinities, which are highly abstract and which only exist by arbitrary fiat, turn out to be useful. Wigner again.
Isn't the burden of proof on those who claim something exists that there's no evidence for? There's no evidence for physical infinities.
I have to say I have no idea what you're talking about or why you aimed this post at me. You're not arguing with anything I've said or anything I believe.
QuarkHead dropped in to mention that the Hilbert space formulation of QM uses infinities. I pointed out why this is a mathematical idealization and not to be taken as having ontological value. QuarkHead has not seen fit to come back and explain himself or reply to my points. I'm disappointed in that, I wish I knew why he posted as he did and whether I've addressed his point or missed it.

If you didn't understand my last post, there's no point carrying on this conversation.
Have a nice day.
EB

 

[Speakpigeon]

No, we are seeing the light/radiation that has had time to reach us. That's the only reason that it is the shape that it is. You aren't looking at a "picture" of a small Universe that falls off into nothingness.
Our Universe could be infinite if it started out that way. All that has happened is that the space between any two points has expanded.
There is no void beyond the Universe. That would still be the Universe.

Exactly, all of it.
EB

 

[Speakpigeon]

As an aside - any description whatever about the so-called real world is a representation, whether it be a string of words or mathematical symbols

Exactly.

Let me ask you all...... is there ANY description of the the "real world" that does NOT use a representation of this sort?

Well, said like this... Sure, a "description" has to use some form of representation and a description is a representation, and it doesn't matter whether the representation is symbolic or not. I'm not even entirely sure how we could define "symbolic" here.
Still, perhaps I need to say that whatever the representation you use, you have to know something in itself, which is the representation itself. So, you wouldn't know what is represented except perhaps through the representation, but you'd have to know the representation, and this irrespective of whether it's symbolic or something else.
And, I also have to add, our own perception of the world around us is indeed such a representation. We have at least to know the representation.
And I would say that the representation of the world we form through our senses is indeed essentially "symbolic", so you could argue that we're doing something equivalent to maths already when we are little kiddies. Or perhaps I should say that our brain does that at least.
EB

 

[Write4U]

I can't see that there's any logical problem with the idea of having a universe with a beginning in time that would have been infinite in size right at the beginning.

So how would you account for inflation if something begins as an infinity? I understand the Hilbert Hotel, but that assumes the hotel itself is already full and does not inflate any further, it just accomodates more guests ad infinitum.

 

[Write4U]

And I would say that the representation of the world we form through our senses is indeed essentially "symbolic", so you could argue that we're doing something equivalent to maths already when we are little kiddies. Or perhaps I should say that our brain does that at least.
EB

Lemurs already do that. They recognize more from less, clearly without using numbers, but just as well as humans can without counting. And according to the study there seems to be no upper limit.
Actually many animals use rudimentary or even very sophisticated mathematics in their daily lives. They just do not use or need symbolic representation.

 

[TheFrogger]

What if I developed a theory that persisted for eternity, that convinced every man and woman I meet, would that be infinity that was non-mathematical?

 

[Seattle]

What if I developed a theory that persisted for eternity, that convinced every man and woman I meet, would that be infinity that was non-mathematical?

You've answered the question yourself and without the theory part. If there is an eternity, that's an infinity. I don't personally think anything lasts forever, including time.

 

[Write4U]

What if I developed a theory that persisted for eternity, that convinced every man and woman I meet, would that be infinity that was non-mathematical?

Depends on the theory, not the time it persists. Religion is an example of a non-mathematical theory which has persisted for a long time. But it is based on a false premise and therefore can never yield an answer which is testable. The false premise being ID by a sentient Designer.

 

[TheFrogger]

The time a theory persists depends upon the theory. Quality remains, and should it be of the highest quality, it will remain forever. I'm not denying that religion will not persist, or that the writer (s) of the bible also wrote an ending, but any decision made of the strongest will, will bring that decision into being. The future WILL occur...

 

[Write4U]

The time a theory persists depends upon the theory. Quality remains, and should it be of the highest quality, it will remain forever. I'm not denying that religion will not persist, or that the writer (s) of the bible also wrote an ending, but any decision made of the strongest will, will bring that decision into being. The future WILL occur...

Yes, the future will occur, but man will not necessarily be a part of it. IMO, we're not doing a very good job of ADAPTING, unlike the insect.

 

[TheFrogger]

A creature consumes a meal giving the animal enough energy to find another meal. Such a thought could give the creature eternal life. What I find most remarkable about the theory of Evolution is that creatures survive long enough to reproduce. And as Darwin wrote, nothing is more difficult than getting a pair of animals to breed in captivity. Early man could hunt and kill an animal for a meal or two, but capture a breeding pair (perhaps by digging a hole) and you have as many meals as you can kill...

 

[someguy1]

If you didn't understand my last post, there's no point carrying on this conversation.

Another approach would be for you to try to state your ideas in a more clear, concise, and consistent manner. But if that's out of the question, all the best.