# Infinity

• February 10th, 2010, 05:27 PM
Sukidoo
Infinity
I've just watched Horizon. It was an episode about infinity - I have a question!

Apparently our universe is infinitely big and it does not end. Also there are infinite universes. However if our universe is infinitely big then it therefore fills all of the space available forever, so what space are these other universes in? Our universe is obviously not infinte then if it does not include this space that is part of these other universes - and if it did then it would just be one big universe?!?

• February 10th, 2010, 05:36 PM
mathman
Re: Infinity
Quote:

Apparently our universe is infinitely big and it does not end.
This is a guess - nobody knows for sure. Anything beyond 13.7 billion light years is out of reach.

Quote:

Also there are infinite universes.
This is a wild guess. The only thing that is certain is that there is one.
• February 10th, 2010, 05:45 PM
Sukidoo
I thought it was a load of b*llox...just because it's possible it doesn't mean it is. Thanks for replying!
• February 10th, 2010, 05:54 PM
Arcane_Mathematician
It's theoretical. In application, 'infinity' doesn't really exist anywhere. The universe most certainly is finite, not infinite. This conversation would be better carried out in Physics
• February 10th, 2010, 06:05 PM
Sukidoo
Sorry, I thought it was a mathematical concept. No one really knows then. Why on earth do you use it in equations then if you're not even sure if it's real?
• February 10th, 2010, 06:14 PM
MagiMaster
Just because it may or may not physically exist doesn't make it any less useful (if handled correctly).

Also, on a theoretical level, it's still possible that the universe is infinitely big and there are still infinitely many universes in the multiverse. Consider this. Take an infinitely big sheet of paper. It goes on forever in either direction (up/down or left/right). How many of those sheets of paper can you stack up? Just because each is infinitely big doesn't mean it takes up everything available.

Similarly, the universe can be infinitely big in 3 directions while there are other universes in the remaining 8 (if there really are 11 total). Whether or not there is actually anything beyond the visible horizon is currently unknown.
• February 11th, 2010, 06:07 PM
Sukidoo
Thank you for the explanation, you've made it a lot clearer.
• February 11th, 2010, 07:01 PM
DrRocket
Re: Infinity
Quote:

Originally Posted by Sukidoo
I've just watched Horizon. It was an episode about infinity - I have a question!

Apparently our universe is infinitely big and it does not end. Also there are infinite universes. However if our universe is infinitely big then it therefore fills all of the space available forever, so what space are these other universes in? Our universe is obviously not infinte then if it does not include this space that is part of these other universes - and if it did then it would just be one big universe?!?

The use of the terms "infinite" and "finite" to describe possible topologies of the universe are inapproprite. The universe in cosmological models based general reltivity is a 4-dimensinal Lorentzian manifold, space-time, and under some assumptions that simplify the analysis it is possible to decompose it as a 0ne-parametre foliation by space-like 3-dimensional hypersurfaces of constant curvature. It is the topology of these hypersurfaces that is what is meant by an "infinite" or "finite" universe and the correct terminology is "open" or "closed" in the sense of a manifold.

Whether or not the universe is open or closed, it is the universe and there is nothing else, and in particular there is no notion of any available volume into which the universe fits -- the universe is, by definition, the whole enchilada.

It is not known whether the universe is open or closed.
• February 15th, 2010, 01:55 AM
Somanayr
Think of it as a new dimension.
So every universe follows the 4 dimensions or 11 dimensions or whatever. Then add a new spatial dimension or two. That's what the various universes float around in.

Basically, imagine living on a plane. The plane is infinitely large. There are infinite planes. In the same way, each universe is infinitely large and there are infinite universes.
• February 15th, 2010, 02:32 PM
DrRocket
Quote:

Originally Posted by Somanayr
Think of it as a new dimension.
So every universe follows the 4 dimensions or 11 dimensions or whatever. Then add a new spatial dimension or two. That's what the various universes float around in.

Basically, imagine living on a plane. The plane is infinitely large. There are infinite planes. In the same way, each universe is infinitely large and there are infinite universes.

This utter nonsense.

It proves notihng other than that you have a complete misconception of the definition of "dimension".

"That's not right. It's not even wrong." -- Wolfgang Pauli
• February 15th, 2010, 09:17 PM
Somanayr
Quote:

Originally Posted by DrRocket
This utter nonsense.

It proves notihng other than that you have a complete misconception of the definition of "dimension".

"That's not right. It's not even wrong." -- Wolfgang Pauli

I guess you may be right to an extent. But my analogy applies. I'm not very good at explaining myself.

One way of thinking about how the various universes interact and coexist, in my understanding, is in a different spatial dimension.

So just like planes that shift around in space would coexist, and can interact, similarly universes can coexist and interact.

If you feel like opposing me, go ahead. But please explain yourself. Otherwise it's just flaming.

Oh, and not all theories support four dimensions. Take a look at M-theory. It suggests 11 dimensions.
• February 16th, 2010, 01:26 AM
DrRocket
Quote:

Originally Posted by Somanayr
Quote:

Originally Posted by DrRocket
This utter nonsense.

It proves notihng other than that you have a complete misconception of the definition of "dimension".

"That's not right. It's not even wrong." -- Wolfgang Pauli

I guess you may be right to an extent. But my analogy applies. I'm not very good at explaining myself.

One way of thinking about how the various universes interact and coexist, in my understanding, is in a different spatial dimension.

So just like planes that shift around in space would coexist, and can interact, similarly universes can coexist and interact.

If you feel like opposing me, go ahead. But please explain yourself. Otherwise it's just flaming.

Oh, and not all theories support four dimensions. Take a look at M-theory. It suggests 11 dimensions.

Nope. Not flaming. Not even worth the effor to light a match.

You are simply talking gibberish and don't have any idea what your are talking about

Your post is complete nonsense and there is no point in trying to correct it. It is simply beyond redemption.
• February 16th, 2010, 12:23 PM
Somanayr
Quote:

Originally Posted by DrRocket

Nope. Not flaming. Not even worth the effor to light a match.

You are simply talking gibberish and don't have any idea what your are talking about

Your post is complete nonsense and there is no point in trying to correct it. It is simply beyond redemption.

Elaborate
• February 16th, 2010, 02:09 PM
DrRocket
Quote:

Originally Posted by Somanayr
Quote:

Originally Posted by DrRocket

Nope. Not flaming. Not even worth the effor to light a match.

You are simply talking gibberish and don't have any idea what your are talking about

Your post is complete nonsense and there is no point in trying to correct it. It is simply beyond redemption.

Elaborate

Not worth the trouble.
• February 18th, 2010, 08:47 AM
mpaulj781
Horizon programme on Infinity
As a newcomer to these forums, I think it worth mentioning that in my view mathematics is not reality any more than the map is the territory.
To avoid philosophical argument, I will define reality as that which can or will be deduced from our senses, experimentation and instrumentation. Of course this means "our" reality is different from all past realities (and all future realities) and is just as likely to be considered wrong by our descendants as we consider the reality of the Earth being the centre of the Universe to be wrong, although it was once believed implicitly by our ancestors. All other "realities" are in my opinion mere philosophy and not worthy of discussion by science.
As for mathematics not being reality, take the simple statement that 1=1. This is fine in mathematics but has no correlation in reality, for if we say one entity is the same as another, we are denying the two entities have a separate existence in space/time, as equality of one entity with another demands each entity shares the same attributes, one of which is its space/time position.
Similarly it appears to me that although infinity certainly exists in various forms in mathematics, there is no evidence to show it has any correlation with reality. That being said, I maintain that the Universe is in fact finite and talk of an infinite Universe or Universes is mere philosophy, although I accept that I may be wrong and positive evidence to the contrary may yet be discovered. However Ockhams Razor says "thou shalt not multiply entities unnecessarily" so I will not believe in such entities as infinite Universes without proof.
The Phlogiston theory to explain combustion, the Ether theory to explain the propogation of light in space, Einstein`s constant are all examples of unnecessary entities, and I strongly suspect that "Dark matter" and "Dark energy" are in the same category.

As for a monkey typing the works of Shakespeare ( or a random computer program for that matter) given infinite time (and resources) I maintain it is impossible. You will then turn round and say my belief shows a lack of understanding of the meaning of infinity, so I will further maintain that any sufficiently complex product of an intelligent mind is impossible to replicate by blind chance, and make the following argument:-
If it is possible for blind chance to replicate these works of Shakespeare in infinite time and with infinite resources, then the possibility of blind chance replicating the typewriter used by the monkey and the computer used by the program is equally likely, indeed must be equally likely. The production of fully functioning railway networks, the bycycle, the wristwatch, the space shuttle and any other complex product of intelligent thought by blind chance is also equally likely, and in an infinite Universe where all things are possible, such productions of blind chance must be occuring even as I type these words and even as you read them.
To me this is obvious nonsense, from which I conclude that some things will always be impossible, as stated above, and even in infinity all that will ever be produced by blind chance is an infinity of errors.

However I do not believe in infinities existing in our reality and would further argue as follows:-
1) All our observations of the Universe show constant change with increasing entropy indicating all that we observe has a finite existence. It seems only logical to therefore conclude the Universe itself is finite.
2) For an infinite Universe to exist surely implies it is infinite in extent both forwards and backwards in time, yet this would contradict the Big Bang Theory and fly in the face of the evidence.
3) If the Universe is infinite, then the Big Bang must have produced an infinity of matter and energy (and space/time?). I find it (slightly) easier to believe the Big Bang produced finite quantities, leading to a finite Universe.
None of these are conclusive arguments, but I find them easier to believe than the alternatives and therefore reject the idea of infinity having any real existence in the Universe.

Finally, which would you rather live in, the real Universe or a mathematical construct?

Regards,
Mike, Wilmslow, UK.
• February 18th, 2010, 01:13 PM
agingjb
The Horizon program, supposedly on infinity, seemed to me to be a little incoherent. Very large numbers, Cantor's cardinals (but not ordinals), cosmology, and so on; it was a mixture, some of which was interesting, some of which was portentous.

One point: it was argued that, in an infinite universe (whatever that may be), every possible eventuality must occur infinitely many times. I can't see this. An analogy (that may be imperfect): the integers are infinite - there is only one even prime. Objects with unique properties exist in infinite sets; why not unique events within an infinite physical domain?
• February 18th, 2010, 04:14 PM
DrRocket
Re: Horizon programme on Infinity
Quote:

Originally Posted by mpaulj781
As for a monkey typing the works of Shakespeare ( or a random computer program for that matter) given infinite time (and resources) I maintain it is impossible. You will then turn round and say my belief shows a lack of understanding of the meaning of infinity, so I will further maintain that any sufficiently complex product of an intelligent mind is impossible to replicate by blind chance, and make the following argument:-
Mike, Wilmslow, UK.

Long post. Little point. This excerpt selected to demonstrate problems with your perception. Yes, indeed, you completely fail to understand the concept of probability or of infinity.

It is only possible, but with probably 1 a random printine of letters, i.e. a monkey at a typewriter, will produce the complete works of Shakespeare given sufficient time. That is a FACT. It is provable and not open to debate. See the Law of Large Numbes in any good text on probability, Loeve's Probability Theory will do nicely. Your counter-argument is simply wrong.

What is also true is that at any reasonable rate of typing a monkey would not have had adequate time to have with a significant positive probability produced the complete works of Shakespeare in the time span that is estimated to be the age of the universe.
• February 18th, 2010, 04:22 PM
DrRocket
Quote:

Originally Posted by agingjb
One point: it was argued that, in an infinite universe (whatever that may be), every possible eventuality must occur infinitely many times. I can't see this. An analogy (that may be imperfect): the integers are infinite - there is only one even prime. Objects with unique properties exist in infinite sets; why not unique events within an infinite physical domain?

That argument is based on the theory of probability and the law of large numbers.
What that inplies is that in infinitely many independent trials, any event of positive probability will occur infinitely many times. That is a valid theorm of mathematics.

However, the cosmological argument to which you refer, while commonly made is not correct. There are a couple of problems. First, as you note the term "infinite universe" is meaningless in this context. Second, the mathematical argument is based on the properties of a probability space, and in the ocntext of an "inifinte universe" there is no probability space in evidence.

If one becomes a bit more precise, there is the notion of a "multiverse" which consists of a number, possibly infinite, of pocket universes, of which our own universe is one. There is zero scientific evidence for this. Even, if you accept the hypothesis of a multiverse. the problem of assigning probabilities is not solved, and in fact is recognized among cosmologists who think about such things as the "probability problem?.

On the other hand your argument regarding unique events in an infinite set, both correct and irrelevant. It has nothing to do with probability theory.

Probability theory is one of the most misunderstood and inappropriately applied branches of mathematics. One should be very skeptical on being approached with an argument based on probability and check to see if the subject is being applied rigorously and correctly. Sadly, in many cases it is not, even by people that you might think would know better.