Is infinity a misconception?

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #100 on: 03/10/2014 14:10:45 »
Absolutely. If the universe was flat and the cosmological principle (http://en.wikipedia.org/wiki/Cosmological_principle) 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.
I disagree with you. A "principle" is no substitute for scientific evidence. And as for Sean, he thinks there's an evil twin universe where time runs backwards.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #101 on: 04/10/2014 16:01:23 »
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. 

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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

I understand that.  I accept that that is the definition of a mathematical infinity. 

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”.  No problem. 

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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

What is the value of infinity?   Perhaps the second part of the quote addresses that question, but it seems a bit inconclusive.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #102 on: 04/10/2014 16:06:06 »
Quote from: JD
And as for Sean, he thinks there's an evil twin universe where time runs backwards.

Now - there's a cosmological minefield!   [:-X]

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #103 on: 05/10/2014 04:06:29 »
I'm going to do a little more dreaming. Let's consider a cube. We want to extend this cube to infinity so we add 7 more cubes. We still have a bounding surface so we add 19 more cubes. No matter how many extra cubes we add we will never extend this cube to infinity as by definition a cube will always have a boundary. We need a geometry without initial bounds to be able to reach infinity. This then becomes a complex problem. How do we define an object with unbounded geometry? The only 'object' with such a profile is infinity itself which is not a thing made of substance at all. It is a concept of human invention.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #104 on: 05/10/2014 04:08:34 »
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?
« Last Edit: 05/10/2014 04:10:18 by jeffreyH »

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #105 on: 05/10/2014 04:42:06 »
Quote from: Bill S
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.
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.

Quote from: Bill S
You interchange “infinite” and “without bound”.
That's because they're the same thing when used as I posted the definition.

Quote from: Bill S
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.
I'm sorry Bill but you lost me. I have no idea what that means. Please rephrase it so that even I can understand it. :)

Quote from: Bill S
Infinity is not a number; ...
Obviously. :)

Quote from: Bill S
....to treat it as such is simply to use the term as an approximation.
I never said it was a number and if you thought that's what I meant then you misread what I wrote.

Quote from: Bill S
It is in effect saying “this is so large, or small, it is reasonable to regard it as infinite”.
I never said or wrote anything that implied such a thing.

Quote from: Bill S
What is the value of infinity?
Why are you asking me a question for which you know there's no answer to it, i.e. it's meaningless? We both know that infinite is and we both know what the cosmological principle is and that the universe is most likely flat (or we're assuming that for the sake of argument) then the amount of mass/matter in the universe is infinite. That means that there is no number which equals the amount of mass in the universe. You know what infinite mass is since you know what infinite is and how to arrive at the conclusion.

So what's your problem with that, Bill?

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #106 on: 05/10/2014 04:48:23 »
Quote from: JohnDuffield
I disagree with you. A "principle" is no substitute for scientific evidence.
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.

See http://www.gizmag.com/universe-homogeneous-300-million-light-years/24149/
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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.
You should learn about these things before you try to claim that you're right. You do this way too much.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #107 on: 05/10/2014 19:09:56 »
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.

Quote from: PB
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.

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

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #108 on: 05/10/2014 19:26:05 »
Quote from: JH
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?

Only if you accept the myth of the infinite series/sequence.   [:P]

Of course there could always have been an infinite number of quanta, but what am I saying?  Infinity is not a number!
 

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #109 on: 06/10/2014 12:39:26 »
...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...
It isn't based on solid scientific evidence. It's a principle. An axiom. A presumption. For all we know, when some guy 46 billion light years looks up at the night sky, he sees half of it all black and empty. 

Quote from: PmbPhy
That's because you're not a scientist, certainly not a physicist. If you were then you'd understand it.
I am a scientist. I have a Computer Science degree. And whilst I don't have a physics degree, my physics knowledge is very good. Let me demonstrate:

Quote from: PmbPhy
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.
It's a postulate. We have clear evidence that the observable universe is homogeneous and isotropic, but we have no evidence that the entire universe is like this, and nor do we have any evidence that the universe is infinite.

 

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #110 on: 07/10/2014 18:11:25 »
Not if you want a finite universe John. Because if you do then you already have the answer, it is whatever we can measure. And as we only can measure approximately 13.7 Billion light years, being the 'earliest' light reaching us, then the universe must be 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. because you have now passed the earliest light existing, as seen from Earth. Or you will have to find a way to proof that what we call the earliest light isn't the 'earliest' at all, but that it continue, becoming  'earlier' and 'earlier', past that 13.7 billion ly limit.
==

http://www.nasa.gov/audience/foreducators/5-8/features/F_How_Big_is_Our_Universe.html

" It is time, not space, which limits our view. Beyond a certain distance, light hasn't had time to reach us yet."

so what we see far away, defining the 'birth' of our universe, if going there 'instantly', would then change to the exact same view we find from here, homogeneous and isotropic all around us,  but now with our earth non existing as it would be 'placed' at lights limit  (birth) from our new position. And with a 'new' 13.7 billion ly visible in the opposite direction, all the way to lights 'birth'.
« Last Edit: 07/10/2014 18:32:19 by yor_on »
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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #111 on: 08/10/2014 12:17:38 »
...If you don't trust this but assume that your 'finite universe' continue past this limit you automatically define it as infinite.
No I don't. I just say the size is unknown. There's just no evidence at all for declaring the universe to be infinite.
 
...Or you will have to find a way to proof that what we call the earliest light isn't the 'earliest' at all...
No I don't. I accept that the earliest light was 13.8 billion years ago. What I don't accept is the non-sequitur that the universe must be infinite. It's based on a presumption, not evidence. It's like you've got some pompous guy up a mountain who thinks he knows it all. It's homogeneously and isotropically flat and misty where he is, and he declares it's the same for everybody else in the world, and that the world is therefore infinite. And woe betide anybody who might challenge his assertions. 
« Last Edit: 08/10/2014 12:21:10 by JohnDuffield »

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #112 on: 08/10/2014 15:00:55 »
I know John, it's somewhat of a logical conundrum. But the point of it is that the earliest light is around 13.7 ly. And the universe is greater than that. If you define a dimension as being 'bent' you can assume, as a guess, a finite universe, although without a bound. Then you might want to assume that 13.7 is all there is. But if you define dimensions as built through 'degrees of freedom', also defining them as only existing from a inside, infinity does not exist. Infinity is just where our calculations lose their 'finite' meaning.
==

Have a look at http://archive.lib.msu.edu/crcmath/math/math/f/f052.htm and note " The value of the Feigenbaum constant can be computed explicitly using functional group renormalization theory"

Renormalization?
« Last Edit: 08/10/2014 15:26:36 by yor_on »
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Offline yor_on

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Re: Is infinity a misconception?
« Reply #113 on: 08/10/2014 15:08:43 »
Eh, that not meaning that I see the universe as 'finite' :)
Just the opposite, without infinity having a real meaning, except to us, we're the ones getting it wrong.
=

We built our knowledge out of presumed linear systems, recently we've found non linearity everywhere. Think of decoherence, and the way 'emergences' come. As if linearity have bounds defining it. Another type of 'dimensionality' to me.
« Last Edit: 08/10/2014 15:14:37 by yor_on »
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Offline Ethos_

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Re: Is infinity a misconception?
« Reply #114 on: 08/10/2014 15:26:38 »
I just say the size is unknown. There's just no evidence at all for declaring the universe to be infinite.
 
This is true, however, declaring it to be finite is also devoid of positive proof. While our local universe is possibly a finite region, it is very likely that this finite region lies within an infinite bulk. Some will refer to our local region as the whole universe discounting the possibility of the bulk and conclude that it is finite. It all depends on what one means when using the term; "Universe".

Webster's defines "Universe" as; "the totality of all things that exist". Taken in this context, if our local space lies within a larger bulk, the term Universe must also include the infinite Bulk. In my opinion, even though our local region is finite, the extent of all there is includes the infinite bulk making the Universe infinite.

It really all depends upon whether one views the Hypothetical Bulk as proper scientific logic. In my case, I prefer to as many credible scientists also do.
« Last Edit: 08/10/2014 15:33:07 by Ethos_ »
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Offline yor_on

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Re: Is infinity a misconception?
« Reply #115 on: 08/10/2014 15:36:51 »
Well Ethos, you will need 'bent dimensions' in some way to keep the universe relativity defines, if you want it to be finite, although 'infinite', all as I see it. If you on the other hand define it locally, then there are no points differing inside that universe from any other 'point', that is what repeatable experiments tells us, and constants. So where is the bound? It can't be equivalent, even if impossible to observe astronomically. It's not simple to me. the simplest thing is a infinite universe, homogeneous and isotropic without 'bounds' of any kind, more than what causality demands. It's us demanding 'finity', as in a linear definition of physics.
==

It's also so that from a strict locality you can't use 'gravity' as something defining a 'possible universal' curvature. You can use it from a container concept in where you keep one definition of a gravitational field, being the 'inertial' far observers. But locally, free falling, actually inseparable from any other uniform motion ideally defined, there are no 'gravity' for you, inside that 'black box'.

But WMAP, Maxima etc all agree, the universe, at least the 'visible' (13.7 or 13.8 :) part of it is 'flat' measured at a 'universal scale'. so whatever curvature one need for a 'finite universe' is non existent in the visible part we have. http://curious.astro.cornell.edu/question.php?number=171

(if you read this link you will notice him using an idea of a balloon expanding, as describing inflation. But you can also use a plane, filling in 'new points' everywhere, or some other 'dimensionality'. That we find three room dimensions and one time dimension do not tell us how they come to be for us.)

Thinking of it as a infinite bulk, using my definitions the only bulk existing is what we measure to exist. Without a 'outside' only measurements define what we can observe. So whatever infinity I want to define should already be here, inside our linearity. We so much want a clock work universe, linear. But what I think we will get instead is causality. That's what defines it.
« Last Edit: 08/10/2014 16:51:58 by yor_on »
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Offline Bill S

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Re: Is infinity a misconception?
« Reply #116 on: 09/10/2014 22:38:44 »
Quote from: Ethos
It all depends on what one means when using the term; "Universe".

I think this might be less confusing if John Gribbin’s usage were followed:

Cosmos = everything that exists, or can exist.
Universe = our (in principle) observable portion of spacetime and its contents.
universe = any other universe that may, or may not, exist.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #117 on: 09/10/2014 22:52:59 »
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.
« Last Edit: 09/10/2014 23:21:40 by jeffreyH »

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Offline chiralSPO

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Re: Is infinity a misconception?
« Reply #118 on: 10/10/2014 00:12:29 »
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.

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 ∞ = ∞

That does not mean, however that all infinities are the same, but there are an infinite number of infinities that are equivalent.

I know of ℵ null (countably infinite) and ℵ 1 (uncountably infinite), but I don't know if there are other larger (or subtler) infinities out there.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #119 on: 10/10/2014 02:34:31 »
Quote from: ChiralSPO
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?

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #120 on: 10/10/2014 04:26:44 »
Quote from: chiralSPO
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.

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Offline alancalverd

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Re: Is infinity a misconception?
« Reply #121 on: 10/10/2014 07:13:22 »
Quote from: ChiralSPO
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.
helping to stem the tide of ignorance

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #122 on: 10/10/2014 15:24:23 »
Quote from: AC
A pink elephant is an elephant, not a pink.

Congratulations on finding such an apt metaphor!

Quote from: Wiki.
"Seeing pink elephants" is a euphemism for drunken hallucination.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #123 on: 11/10/2014 21:13:02 »
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.

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #124 on: 12/10/2014 01:36:36 »
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
Quote from: Bill S
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

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #125 on: 12/10/2014 11:05:43 »
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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #126 on: 14/10/2014 15:41:20 »
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. 

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #127 on: 14/10/2014 16:08:00 »
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.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #128 on: 14/10/2014 22:35:59 »
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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #129 on: 16/10/2014 23:27:18 »
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?"

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #130 on: 17/10/2014 06:39:45 »
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."

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #131 on: 17/10/2014 20:14:56 »
 [;D]
Quote from: Pete
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.     [:P]

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #132 on: 18/10/2014 00:51:02 »
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?

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Offline Ethos_

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Re: Is infinity a misconception?
« Reply #133 on: 18/10/2014 01:33:31 »
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!

« Last Edit: 18/10/2014 04:29:32 by Ethos_ »
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Offline dlorde

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Re: Is infinity a misconception?
« Reply #134 on: 18/10/2014 12:27:17 »
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.

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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.

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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.

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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.

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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.

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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.

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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.

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #135 on: 18/10/2014 13:29:29 »
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.

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Offline Ethos_

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Re: Is infinity a misconception?
« Reply #136 on: 18/10/2014 15:15:14 »
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..........
« Last Edit: 18/10/2014 15:53:30 by Ethos_ »
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Offline yor_on

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Re: Is infinity a misconception?
« Reply #137 on: 18/10/2014 16:08:31 »
Good ideas all of you. We're here to use our minds.
"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #138 on: 18/10/2014 16:11:09 »
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?
"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."

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Offline dlorde

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Re: Is infinity a misconception?
« Reply #139 on: 19/10/2014 11:44:50 »
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?

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #140 on: 19/10/2014 13:36:22 »
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.
No it isn't. This nothingness is not space. It isn't some void. There is no place for light to go beyond the edge of space.

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?
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.

As you may have already figured out, I tend to believe in either flat space or the Multiverse concept.
WMAP found that space looks flat, so we have evidence to support the idea that space is flat. But we have no evidence to support the idea of a  multiverse. None whatsoever.

In either case, space would be infinite.
Not so. It's a non-sequitur to say space is flat and therefore infinite. It's like the old flat-Earth belief, only back to front. In ancient times people (allegedly) believed the world was flat, and therefore had an edge. In modern times people believe the universe is flat, but they cannot believe it has an edge.   

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?
If can't see how the universe can be infinite, because an infinite universe can't expand. And I can't see how you can have more than one everything.

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.

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Offline Ethos_

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Re: Is infinity a misconception?
« Reply #141 on: 19/10/2014 17:59:49 »
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.
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.
« Last Edit: 20/10/2014 04:17:30 by Ethos_ »
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Offline Bill S

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Re: Is infinity a misconception?
« Reply #142 on: 19/10/2014 18:09:08 »
Hi Dlorde, you are right, we have been here before.  We have seen these questions, and these answers, before.  The trouble is, as I said to Pete earlier in this thread, answers tend to take the form: “this is the answer, whatever the question was”. 
 
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By that logic, anywhere on the road is the middle, which makes 'middle' meaningless in this context.

Great! 

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”.

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

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

“Unbounded” can be quite different from “infinite”, because, although infinity can rightly be said to be boundless, all that is boundless is not necessarily infinite.  For example, in an infinity of nothingness there could, in theory, exist a universe.  The surrounding nothingness would place no limit on the amount of matter or energy that could be added to that universe, nor would there be any limit to the extent to which the universe could expand.  Nevertheless, however much was added to the universe, or however great was its expansion, it would always be finite. 

Its potential might be said to be infinite, as it has an infinity of nothingness into which it can expand, but even this is not strictly correct.  It can never reach infinity; therefore it does not have the potential to become infinite.  Nothing finite can become infinite.

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Yes. An infinite extent can have a beginning.

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

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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;

Does it seem strange that something that constantly returns to mathematical definitions cannot be related by measurement?  I am not disagreeing with you here; 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.

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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.

This is a recurring problem when trying to discuss infinity.  Cantor’s infinities are valuable as mathematical tools, but let’s not forget that even Cantor had problems dealing with “absolute infinity”. 

Quote
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.

This is another of those things that always comes up, but is never resolved.  This, I think, is a shame, because Cantor’s work on infinities is a masterpiece, but it should not be expected to apply beyond the sphere of maths.   

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #143 on: 19/10/2014 22:29:09 »
Quote from: JD
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.

Quote from:  Ethos
  ......better minds than anyone of us conclude that flat space defines an infinite universe.

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.

Quote from: Ethos
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.

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

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #144 on: 19/10/2014 22:52:20 »
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.

http://www.hawking.org.uk/the-beginning-of-time.html

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.

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Offline Ethos_

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Re: Is infinity a misconception?
« Reply #145 on: 19/10/2014 23:26:33 »
Possibly you and Ethos are understanding different things when using the word “universe”.
I agree Bill,......That's the reason I said; "you seem to have missed my points JD". In any event, discussing a concept like infinity is a big challenge. I think it all boils down to whether the individual has the intuition to wrap their minds around this mental abstraction. Those that do will side with infinity and those that don't will contend against it.

So, who's right? It could be that neither one of us is depending on how we define the word. Until we get on the same page with our definitions, this discussion will fail to render any positive results.
"The more things change, the more they remain the same."

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Offline dlorde

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Re: Is infinity a misconception?
« Reply #146 on: 20/10/2014 00:05:11 »
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”.
The 'middle' means equidistant from specified extremes. Infinite extremes are not measurable so equal distance can't be known. On the other hand, if you decide the infinities either side are effectively equal in size, then any point qualifies, which means all points are the middle; which, I submit, makes it meaningless.

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You have two unbounded roads, but I argue that unbounded and infinite are not necessarily synonymous.
I agree - where 'unbounded' means 'having no boundaries' -  a sphere is finite but unbounded. 

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Beginning and end are directional concepts.  Turn round and your beginning becomes an end which, by definition, infinity cannot have.
That's just semantics. I can equally say that depending which way you turn, you either have an infinite extent ahead of you or behind you.

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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.
Only two points infinitely distant from each other will be problematic. It's an interesting point (they're interesting points![;)] ) - can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?

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Cantor’s infinities are valuable as mathematical tools, but let’s not forget that even Cantor had problems dealing with “absolute infinity”.
I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.

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... Cantor’s work on infinities is a masterpiece, but it should not be expected to apply beyond the sphere of maths.
As far as I know, the only framework for dealing with the concept of infinity is mathematical. It's a mathematical abstraction. What else can we use when considering thought experiments about physical infinities?

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #147 on: 20/10/2014 01:57:34 »
Quote from: Bill S
That has to be one of Pete’s more elitist comments.   

You're wrongly accusing me of having made elitist comments. Please show me these elitist comments that I've made to people they didn't actually and accurately apply to.

I may have said that someone wasn't that bright but only in extreme cases and even then only with nutcases like JD but never simply because someone used the phrase "it seems to me".
« Last Edit: 20/10/2014 02:01:47 by PmbPhy »

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #148 on: 20/10/2014 12:41:01 »
No..............better minds than anyone of us conclude that flat space defines an infinite universe.
I reject that. Who concludes that flat space means the universe is infinite? And do they also conclude that the universe was always infinite. 

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.
Ask around about how the universe got to be infinite in a finite time, or was always infinite. You won't get a satisfactory answer.   

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.
You're still not getting the "no space" concept. Space isn't nothing, it's something. See the shear stress in the stress-energy tensor? Note the energy-pressure diagonal? Space is kind of like some ghostly gin-clear elastic that can be deformed or pressurized or curved. If you reached the edge of space, there is no beyond it. Nothing isn't space.   

If you can't "seem to get this" we have nothing left to discuss.
Noted.
« Last Edit: 20/10/2014 12:51:25 by JohnDuffield »

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #149 on: 20/10/2014 12:47:16 »
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 don't there's much of an issue with the word universe. If we do find there's some confusion, we could soon clear it up.

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”.
I don't think so. We seem to have an irreconcileable difference regarding a universe that's infinite. 

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.
Well said. I refuse to be told to just accept something because "better minds than us" say it's right. 

That has to be one of Pete’s more elitist comments.
He thinks of himself as the expert, and reacts badly to any challenge or correction.

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.

http://www.hawking.org.uk/the-beginning-of-time.html

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.
There's no actual evidence to support Hawking's no-boundary hypotheses. Or his imaginary time. Or an infinite universe. But there is evidence to support the idea that space is flat, that it doesn't curve back round on itself, and that it's expanding. IMHO people say the universe is infinite because they just can't conceive of some kind of boundary to it. And then they forget that it can't be infinite unless it was always infinite, which I think is most unsatisfactory.
« Last Edit: 20/10/2014 13:03:42 by JohnDuffield »