what is infinite?

[bluebanana]

Ok well i was reading a bit about the big bang and stuff but what seems to be said a lot is that the universe is infinite and has always been infintie even at the time of the big bang. So I thought about it a bit and then i kinda decided that this makes sense:
The universe is infinite and has always been that way so the 'end' of infinity must then be the 'end' of the universe.
Thats the best way i can think of explaining it and it makes more sense in my mind. I guess you could also put it like this:
The universe has always been infinite so therefore infinity is as large as the universe and the universe is as large as infinity.
So now what I want to know is, am I right in asuming this or does somebody else see it some way else?

[Twinsun]

well people believe infinite means it has no limits ... I say we can consider something to be infinite even though it has limits, but are unreachable

also, your statement is correct BUT don't fool yourself in thinking that the universe IS the infinite itself ... no, the infinite is just a concept, appliable in many many domains

[astromark]

No.

If some thing had a beginning and is still expanding into the void, can it be said to be infinite? No, I do not think it can. You can say that it is or will expand into infinity and for a infinite time period. But these are things that we do not know. At best the previously stated; Finite but unbounded. Must apply.

This Universe is very very big. It is expanding at a ever increasing rate. We can never know all of these answers. We can make best guess based on what we can and have observed. The laws of physics as we know them seem to apply across this universe but, we do not understand all of what we see.
So to say this universe is infinite would not be right at this point.

[Van Rijn]

Ok well i was reading a bit about the big bang and stuff but what seems to be said a lot is that the universe is infinite and has always been infintie even at the time of the big bang.

Perhaps it was, perhaps not. We don't know yet. Here's a previous thread on the subject:

http://www.bautforum.com/questions-a...-infinite.html

By the way, notice that Astromark is making the same statement here as he did there, despite being corrected.

[bluebanana]

but if the universe is everything (as in all of the matter and everything else that may exist) then why isn't the definition of infinate the size of the universe? Isn't it the biggest posible thing? How can you have something bigger than the universe (infinite)?

[Van Rijn]

but if the universe is everything (as in all of the matter and everything else that may exist) then why isn't the definition of infinate the size of the universe? Isn't it the biggest posible thing? How can you have something bigger than the universe (infinite)?

Do you mean something bigger than the observable or visible universe? The observable universe may not be the full extent of "everything else that may exist." Here are a couple of links that get into this:

http://curious.astro.cornell.edu/que...php?number=275

http://curious.astro.cornell.edu/que...php?number=364

A couple of quotes:

the term "visible universe" refers to the fact that the actual universe might be bigger than the part of it we can see (in fact, it might be infinitely big). The part we can see is determined by the age of the universe. For example, suppose that the universe is 13.7 billion years old, as indicated by recent measurements from the WMAP satellite. That means that the farthest away from the earth that we can see, in any direction, is 13.7 billion light-years - i.e., the distance light can travel in the time since the universe was formed.


We can define the universe as everything there is, so in that case there is nothing outside of it. We also say that space and time both started at the Big Bang and therefore there was nothing before it.

Another definition for the universe is the observable universe - which is the part of it that we can technically see. We cannot know what is outside of that (since we can't observe it), but we think that physics works the same everywhere and so we think that it should be very similar to the observable universe. We actually think that the universe might be infinite in extent, and so goes on forever, even though we can only see a finite part of it.

[bluebanana]

but what I'm asking is:
If what I said about the universe being an example of what infinite is is incorrect then why do we keep saying that the universe is infinite and how can infinite grow? The universe had to strt out small didn't it? If it was infinite before the big bang then infinite was smaller at the the time than it is now. Thats what I want to know, but its much easier to explain to myself because I know what I want to ask and its just really diffeicult to explain. Well I'm off to bed now to contemplate the universe I guess and I shall get back to this tommorow at school, if it isn't blocked there.

[astromark]

By the way, notice that astromark is making the same statement here as he did there, despite being corrected.


V.R. You are more than welcome to say these things. I may not agree with you. Corrected, you say. What and who does not except finite but unbounded.? and on what evidence? I may not use the words that you might. I feel that what I have said has the weight of science to support it. If Newton, Einstein and Hawking are saying the same thing. who am I to argue. What is it you do not agree with?

[Van Rijn]

but what I'm asking is:
If what I said about the universe being an example of what infinite is is incorrect then why do we keep saying that the universe is infinite and how can infinite grow?

Basically, what we can say is that the universe was much denser.

The universe had to strt out small didn't it?

The visible universe, perhaps. Here's a quote from Misconceptions about the Big Bang:

This ubiquity of the big bang holds no matter how big the universe is or even whether it is finite or infinite in size. Cosmologists sometimes state that the universe used to be the size of a grapefruit, but what they mean is that the part of the universe we can now see--our observable universe--used to be the size of a grapefruit.

Observers living in the Andromeda galaxy and beyond have their own observable universes that are different from but overlap with ours. Andromedans can see galaxies we cannot, simply by virtue of being slightly closer to them, and vice versa. Their observable universe also used to be the size of a grapefruit. Thus, we can conceive of the early universe as a pile of overlapping grapefruits that stretches infinitely in all directions. Correspondingly, the idea that the big bang was "small" is misleading. The totality of space could be infinite. Shrink an infinite space by an arbitrary amount, and it is still infinite.

If it was infinite before the big bang then infinite was smaller at the the time than it is now.

We currently can't say anything about "before" the big bang, including whether there was a "before."

[Van Rijn]

V.R. You are more than welcome to say these things. I may not agree with you. Corrected, you say. What and who does not except finite but unbounded.?

Please see the various links and quotations I have provided here and in the prior thread. Again: The universe may be infinite or it may be finite. Cosmologists don't know. To state that it is certain that the universe is finite, as you have, is repeating a misconception at best, or pushing an ATM concept at worst.

[grant hutchison]

but if the universe is everything (as in all of the matter and everything else that may exist) then why isn't the definition of infinate the size of the universe? Isn't it the biggest posible thing? How can you have something bigger than the universe (infinite)?

You don't need to tie "infinity" to some physical object: it's a mathematical concept. So you can say, for instance, that there are an infinite number of natural numbers; and there are infinitely more natural numbers than there are particles in the observable Universe.

It's a property of an infinite number that if you multiply it by two, you've still got an infinite number. So there's no reason an infinite object can't expand: you'd simply see it becoming less dense everywhere throughout its infinite volume.
There's an idea for playing with these notions, called the "Hilbert hotel". You're in charge of a hotel with an infinite number of rooms. An infinite number of guests arrive, so you put them in consecutive rooms, and find you can accommodate them all. But then another guest arrives. No problem: you ask all the current guests to move out of their current room and into the room with the next highest number (so guest 1 moves to room 2, guest 2 to room 3, and so on). That leaves room 1 free, and you can accommodate your new guest.
But then an infinite number of new guests arrive. Still no problem: you ask every guest to double their current room number, and move to that room. This frees up all the odd-numbered rooms (of which there are an infinite number) so you can now accommodate all the new guests.

There's no doubt that the part of the Universe we can see is finite: we can see only as far as light has had time to travel since the Big Bang.
Beyond that, as Van Rijn says, there might be an infinite or a finite unobserved Universe.

Grant Hutchison

[OldGuySythe]

"Infinite Number" is a mutually exclusive term. To be a "number" it has to be countable. To be "infinite" it has to be "not" countable. You cannot perform any mathematic operations with "infinity". It's a valuable concept, but cannot be taken literally. There is no relationship between infinite and countable.

[grant hutchison]

There is no relationship between infinite and countable.

You've got to be a little careful with a declaration like that, since the terms "countable infinity" and "uncountable infinity" are in quite standard use to distinguish different orders of the infinite cardinal numbers.
The problems dealt with in the Hilbert Hotel work out because we're dealing with countable infinities in each case: infinities that can be set in a one-to-one mapping with the natural numbers. (The set of real numbers can't be mapped to the natural numbers, and so is an example of an uncountable infinity.)

Grant Hutchison

[OldGuySythe]

I am aware of what you are saying...I just don't agree with it. An example of my concern is the use of the term "countable infinity". Logically, it is not possible. More to the point, an integer is by it's very definition countable. An even integer is by it's very definition, evenly divisible by 2. Therefore, there can be no such thing as an infinite integer, by the very definitions that these terms are given. You cannot "map 1 to 1" with infinity simply because you cannot count to infinity.

When you mix infinity with mathematics, you leave the realm of science, and enter the realm of philosophy. You are at a point where "you just have to accept that it's true", and I cannot make that "leap of faith".

If this position flies in the face of accepted mathematics, then that makes me an outsider...dunce...but I have yet to hear an acceptable argument that would change my mind.

[grant hutchison]

I am aware of what you are saying...I just don't agree with it.

Your choice, of course.
But it would have been helpful if you'd mentioned up front that you were stating an opinion that diverges from 125 years of standard mathematical usage: bluebanana seems to be confused enough already, and any search on the topic of infinite numbers is going to turn up the work of Cantor and his successors.

Grant Hutchison

[OldGuySythe]

I do agree that it diverges from standard usage, I just don't agree that my position diverges from logic.

By the way...doing something wrong for 125 years doesn't make it right

[grant hutchison]

I do agree that it diverges from standard usage, I just don't agree that my position diverges from logic.

So, in the Q&A section, it would be helpful if you made it clear when you were simply asserting a divergent view you feel strongly about. It reduces confusion.

By the way...doing something wrong for 125 years doesn't make it right

That seems incontrovertible.
Nevertheless, 125 years have allowed mathematicians who followed Cantor's lead to produce a very large quantity of writing on the topic of "countable infinities", some of which will be readily retrievable by bluebanana. That's where the potential for confusion comes in.
But now that we know a bit more about your opinion and its relationship to mainstream usage, the likelihood of confusion diminishes.

Grant Hutchison

[01101001]

So, in the Q&A section, it would be helpful if you made it clear when you were simply asserting a divergent view you feel strongly about. It reduces confusion.

Amen.

Could the management put up a sticky topic here, or maybe amend an existing one, describing their expectations for answers in Q&A? It seems like lately there's been a lot of unlabeled speculation, even plain old made-up stuff, masquerading as mainstream thought.

Meanwhile: Members, if you know your answer is unfounded, say so. If you don't know the material well enough to know whether or not you're providing mainstream answers, assume your answer needs an opinion-disclaimer. People come to this Q&A subforum for answers to their questions. People come here to learn. They are counting on you for answers that make sense and are supportable. Warn them when you are offering up less.

Thanks.

[bluebanana]

Well, I guess seeing other peoples' opinions really helps. I kinda get it now so now I don't have to bug my physics teacher and waste class time. By the way I'm in high school,so some of what is being said is just going straight over my head. But now you've got me curious on Cantor and countable infinities......

[grant hutchison]

By the way I'm in high school,so some of what is being said is just going straight over my head. But now you've got me curious on Cantor and countable infinities......

Well, it doesn't take much high school maths to get your head around the basic ideas of mathematical infinity: knowing about the different kinds of numbers (natural, rational, real), and having an idea about very very basic set theory (like, what a "set" is!) is about all that you need.
If you're really interested, the best popular introduction to the whole thing that I know of is Rudy Rucker's Infinity and the Mind: The Science and Philosophy of the Infinite, which you can pick up cheaply and easily from an internet bookstore.

Grant Hutchison

[OldGuySythe]

I apologize for not making it clear that my post was my opinion, an opinion not shared by the main stream. I will endevor to do better in the future.

And for you bluebannana, if my comments peaked your curiosity, I am happy. It is my opinion, that you should question everything that is taught to you. We will not find the errors of our ways if we just accept what is taught.

have fun and always ask questions.

[Van Rijn]

Well, I guess seeing other peoples' opinions really helps. I kinda get it now so now I don't have to bug my physics teacher and waste class time. By the way I'm in high school,so some of what is being said is just going straight over my head. But now you've got me curious on Cantor and countable infinities......

I'm happy your curiosity was piqued by the thread. Don't worry about things going over your head - you'll pick up more as you go along. Just don't stop asking questions!

[Van Rijn]

And for you bluebannana, if my comments peaked your curiosity, I am happy.
[snip]

have fun and always ask questions.

I did not see this before I wrote my post. Get out of my head!

[01101001]

Quit peeking!

[grant hutchison]

A group of maths students got together and formed a rock group called "Cantor and the Transfinite Cardinals" when I was at university.
In a sort of extended pun, they would come on with the lead singer dressed as a Jewish cantor, and the band dressed as Catholic cardinals.
Curiously, but perhaps fortunately, they never really had much success ...

Grant Hutchison

[bluebanana]

yeah, my teachers sometimes get annoyed when I ask a lot of quetions and my maths teacher has refused to explain imaginary numbers to me. I don't like her. Yeah I don't know what to ask now. My mind hasd gone blank for like the whole afternoon. Its annoying.

[bluebanana]

ok now i remember what else I wanted to know about.
Ok well, I followed one of the links that somebody had posted and then I found something that got me curious:
What is a white hole? So I went to go look at it and I got interested. So would anybody care to explain a bit more about them if you know anything about them?

[GoshawkJV]

From everything I have read and what professors have told me, space unfolded upon itself. Without matter there would be no space. Infinite sort of makes me think of 4 dimensional space, or a space much like a globe. I cant think of how Hawking described this space. If youre standing on earth do you know its round if you didnt know already? But if I put you on a baskeball you would see different. There really is no end to the universe becuase you cant reach the end. I beleive youll think youre reaching it, and suddenly you find yourself at an entirely different area, perhaps one you been before.. much like an ant walking on a basketball. It doesnt see its world as round and swelling, thus it walks around and around but never goes up. I may be getting myself lost here, but I tried.. you cant reach the end basicially becuase you will simply never know it. you will curve around the surface of the universe based on gravity and matter. after all it is matter and gravity that define space!

[grant hutchison]

What is a white hole? So I went to go look at it and I got interested. So would anybody care to explain a bit more about them if you know anything about them?

Hi, bluebanana.
This question, introduced late in a thread on another topic, might well not be noticed by people who are interested in this sort of thing.
So you might consider starting a new thread for your new question, mentioning white holes in the title.

Grant Hutchison

[grant hutchison]

From everything I have read and what professors have told me, space unfolded upon itself. Without matter there would be no space. Infinite sort of makes me think of 4 dimensional space, or a space much like a globe. I cant think of how Hawking described this space. If youre standing on earth do you know its round if you didnt know already? But if I put you on a baskeball you would see different. There really is no end to the universe becuase you cant reach the end. I beleive youll think youre reaching it, and suddenly you find yourself at an entirely different area, perhaps one you been before.. much like an ant walking on a basketball. It doesnt see its world as round and swelling, thus it walks around and around but never goes up. I may be getting myself lost here, but I tried.. you cant reach the end basicially becuase you will simply never know it. you will curve around the surface of the universe based on gravity and matter. after all it is matter and gravity that define space!

This is the "finite but unbounded" idea that astromark was talking about. It's a way for the Universe to be finite in extent but without edges, if it curves around in a higher dimension to form something like the surface of a four-dimensional sphere.
So it's not an example of an infinite Universe.

Grant Hutchison