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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: jeffreyH on 17/09/2014 22:19:51

Title: Is infinity a misconception?
Post by: jeffreyH on 17/09/2014 22:19:51
If we have a right angled triangle and one side adjacent to the right angle is finite while the other adjacent side is infinite then the hypotenuse must be greater than infinity. What does this say about our view of infinity?
Title: Re: Is infinity a misconception?
Post by: alancalverd on 17/09/2014 22:41:42
It says nothing about "our" view of infininty, but speaks volumes about your understanding of the principal axioms of Euclidean geometry.  The key construction for analysing this triangle is of course to draw a circular square centered on the bisector of the infinite side, using the usual methods.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 17/09/2014 22:59:07
Well then find the radius of the circle whose circumference is infinite.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 17/09/2014 23:04:19
Conversely if the radius is infinite find the circumference.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 17/09/2014 23:34:17
The point here is that any system that can normally be considered as bounded cannot include an infinite component. So if the mathematics of a formerly finite system go infinite somethings is terribly wrong. If we consider the event horizon as our boundary then the black hole can be thought of like a superconductor.

http://arxiv.org/abs/1403.0938
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 18/09/2014 01:54:17
Quote from: jeffreyH
If we have a right angled triangle and one side adjacent to the right angle is finite while the other adjacent side is infinite then the hypotenuse must be greater than infinity. What does this say about our view of infinity?
Nothing. I think that you're confusing infinity with a number. It means increases without bound. Let me make this very clear first; 7ed9abff4dafd78d08e616c899412e92.gif is not a number.

It's defined as follows;
Quote
The notation

c2fc74c007e280c7de4a3682a1d7dafa.gif

means that the values of f(x) can be made arbitrarily large (as large as we please) by taking x sufficiently close to a (on either side) but not equal to a.

Most of the time 7ed9abff4dafd78d08e616c899412e92.gif is used without this detail and in a more at ease manner (i.e. sloppy). When you start studying calculus and you get into limits you'll have to evaluate expressions like f(x)/g(x) where both f(x) and g(x) increase without bound. Sometimes the ratio approaches a limit and sometimes it doesn't. If you choose to study calculus you'll learn L'Hôpital's rule which is used to handle these cases.

http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule
Title: Re: Is infinity a misconception?
Post by: alancalverd on 18/09/2014 06:36:43
The point here is that any system that can normally be considered as bounded cannot include an infinite component.

Precisely. A triangle is by definition bounded by three intersecting sides, so your "triangle with one infinite side" is as meaningless as my "circular square centered on the bisector of the infinte side".

Just because words hold their conventional order in a phrase doesn't imply that the phrase means anything.   

Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 18/09/2014 12:55:40
If we have a right angled triangle and one side adjacent to the right angle is finite while the other adjacent side is infinite then the hypotenuse must be greater than infinity. What does this say about our view of infinity?
I'm not sure that's a great example, but I agree with the thrust of what you're saying. I think infinity is a misconception. IMHO if ever you bump into an infinity in physics, then something is wrong somewhere. As a rule of thumb, there are no infinities in nature. For example, gravitational time dilation is said to be infinite at the black hole event horizon. But did you see the expression pmb referred to?

c2fc74c007e280c7de4a3682a1d7dafa.gif

IMHO it's better to say that the coordinate speed of light is zero at the event horizon.
Title: Re: Is infinity a misconception?
Post by: Bill S on 18/09/2014 17:32:30
Quote from: Pete
I think that you're confusing infinity with a number. It means increases without bound. Let me make this very clear first;  is not a number.

“Infinity is not a number”!  It’s good to hear someone else make that assertion.

“It means increases without bound”.       Would it not be better to use “boundless”?   

Infinite and boundless are not synonymous.
Title: Re: Is infinity a misconception?
Post by: alancalverd on 18/09/2014 18:22:20
Here's an old but very strong example (Cantor?)

There is an infinite number of integers 1,2,3,.... because we can always add one more

There are rational numbers between the integers 1, 3/2, 7/4, 2, 9/4, 19/8, 3....

Indeed there is an infinite number of rational numbers between any two integers

So the number of rational numbers must be greater than the number of integers

So there are at least two classes of denumerable infinity, even in one dimension

And we can fill the spaces between rational numbers with nonrational numbers.....
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 18/09/2014 18:37:54
Quote from: Bill S
“It means increases without bound”.       Would it not be better to use “boundless”?   
Why do you think it'd be better?

Note: The infinity sign is missing when you quoted me. Instead of reading
Quote
Let me make this very clear first;7ed9abff4dafd78d08e616c899412e92.gifis not a number.
Your quote instead reads
Quote
Let me make this very clear first;  is not a number.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 20/09/2014 03:26:58
Quote from: JohnDuffield
IMHO if ever you bump into an infinity in physics, then something is wrong somewhere.
Nonsense. It's beginning to become clear that the universe is flat and boundless and as such goes on forever, never ending. That's what it means to be infinite. It also appears to have approximate uniform mass density which means that there's an infinite amount of hadrons in the universe too.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 20/09/2014 11:34:32
Quote from: JohnDuffield
IMHO if ever you bump into an infinity in physics, then something is wrong somewhere.
Nonsense. It's beginning to become clear that the universe is flat and boundless and as such goes on forever, never ending. That's what it means to be infinite. It also appears to have approximate uniform mass density which means that there's an infinite amount of hadrons in the universe too.

In which case there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity. So to all intents and purposes the contents of the universe is finite even though the universe itself may not be. Given an infinite amount of time there is the possibility of every particle in the universe interacting with every other particle, every field interacting with every other field. The same exact combination of particles also have an infinite time in order to interact in exactly the same way more than once. I am not disagreeing with you here Pete I think this is a fascinating subject.
Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 20/09/2014 15:09:50
Nonsense. It's beginning to become clear that the universe is flat and boundless and as such goes on forever, never ending. That's what it means to be infinite. It also appears to have approximate uniform mass density which means that there's an infinite amount of hadrons in the universe too.
It's beginning to become clear that the universe is flat, but it absolutely isn't clear that it goes on forever. IMHO this is a non-sequitur promoted by cosmologists who have an inadequate understanding of general relativity.
Title: Re: Is infinity a misconception?
Post by: Bill S on 20/09/2014 19:21:10
Pete, sometimes you surprise me.

“Without bound” and “boundless” are synonymous.  I doubt that anyone would argue with that.

“Without bound” and “infinite" may mean the same in certain cases, but there would be at least one person on this forum who would argue with any claim that they are synonymous.

Why introduce doubt unnecessarily?

You are absolutely right about the missing infinity sign, which is odd, as I cut and pasted the quote.  I apologise if this caused you disquiet; but I was agreeing with you. 
Title: Re: Is infinity a misconception?
Post by: Bill S on 20/09/2014 19:37:02
Quote from: alancalvard
Here's an old but very strong example (Cantor?)

There is an infinite number of integers 1,2,3,.... because we can always add one more

The sequence of integers is boundless…. “because we can always add one more”.
It is quite reasonable to refer to this as “infinite”, as long as everyone recognises that this is a mathematical infinity – not some sort of physical infinity.
Title: Re: Is infinity a misconception?
Post by: Bill S on 20/09/2014 19:44:41
Quote from: JD
It's beginning to become clear that the universe is flat, but it absolutely isn't clear that it goes on forever. IMHO this is a non-sequitur promoted by cosmologists who have an inadequate understanding of general relativity.

I believe it also arises from unclear thinking about the way in which a physical infinity (if it exists) would differ from a mathematical infinity; which, as Cantor demonstrates, does “exist”.   
Title: Re: Is infinity a misconception?
Post by: Bill S on 20/09/2014 19:50:35
Quote from: alancalvard
Just because words hold their conventional order in a phrase doesn't imply that the phrase means anything.

That I like!  I hope you will not mind if I borrow it at some time.
Title: Re: Is infinity a misconception?
Post by: alancalverd on 20/09/2014 23:41:02
It is quite reasonable to refer to this as “infinite”, as long as everyone recognises that this is a mathematical infinity – not some sort of physical infinity.


Here's a physical infinity. The gravitational force F exerted by an object of mass m decreases as m/r2, so F→0 as r→∞ . Physical reality? Well we can measure any  F > 0, so it's real 

Now the force exerted by a mass 2m decreases as 2m/r2, so F→0 as r→∞' and clearly ∞' > ∞
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 21/09/2014 01:35:20
Quote from: jeffreyH
In which case there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity. So to all intents and purposes the contents of the universe is finite even though the universe itself may not be.
You're reasoning is wrong. An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Think of the universe like you would a 3D Cartesian coordinate system where a particle is located at the intersection of every grid point where a grid point is the point is of the forum (x, y, z) where x, y, z are all integers. Then the distance between all particles is finite yet the number of particles is infinite.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 21/09/2014 01:36:48
Quote from: Bill
Pete, sometimes you surprise me.
Is that good or bad? In this post is it good or bad?  [:-\]
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 21/09/2014 13:09:10
Quote from: jeffreyH
In which case there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity. So to all intents and purposes the contents of the universe is finite even though the universe itself may not be.
You're reasoning is wrong. An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Think of the universe like you would a 3D Cartesian coordinate system where a particle is located at the intersection of every grid point where a grid point is the point is of the forum (x, y, z) where x, y, z are all integers. Then the distance between all particles is finite yet the number of particles is infinite.

Anything bounded cannot be infinite. The particles are bounded by an infinite extent.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 21/09/2014 16:47:38
Quote from: jeffreyH
In which case there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity. So to all intents and purposes the contents of the universe is finite even though the universe itself may not be.
You're reasoning is wrong. An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Think of the universe like you would a 3D Cartesian coordinate system where a particle is located at the intersection of every grid point where a grid point is the point is of the forum (x, y, z) where x, y, z are all integers. Then the distance between all particles is finite yet the number of particles is infinite.

Anything bounded cannot be infinite. The particles are bounded by an infinite extent.
Who said it was bounded? I don't know where on earth you're getting these ideas from but they sure aren't from me. You should know that I know that already. In fact  I'm the one who made that fact clear in the start of this thread!

I said think of the universe as you would a  3D Cartesian coordinate system. A  3D Cartesian coordinate system is unbounded, i.e. it's infinitely large, i.e. unbounded!
Title: Re: Is infinity a misconception?
Post by: Bill S on 21/09/2014 19:54:21
Quote from: Pete
Is that good or bad?

Assigning “good” or “bad” involves the sort of subjective value judgement I prefer to avoid in a science thread. 

Quote
In this post is it good or bad?   

That probably depends on whether you are asking this question to avoid answering the ones I asked.
Title: Re: Is infinity a misconception?
Post by: Bill S on 21/09/2014 20:11:07
Quote from: alancalverd
The gravitational force F exerted by an object of mass m decreases as m/r2, so F→0 as r→∞ . Physical reality? Well we can measure any  F > 0, so it's real 

Now the force exerted by a mass 2m decreases as 2m/r2, so F→0 as r→∞' and clearly ∞' > ∞
You are aware that my maths is shaky, so let’s be sure I understand what you are saying.

“The gravitational force F exerted by an object of mass m decreases as m/r2,”

Gravitational force decreases as a square of the distance over which it is measured.
 
“so F→0 as r→∞.”

Gravitational force would be measured as 0 only at an infinite distance from the source.

“Well we can measure any  F > 0, so it's real”

We can measure any force greater than 0, so the gravitational force is real.

Is my understanding OK so far?

Title: Re: Is infinity a misconception?
Post by: Bill S on 21/09/2014 20:24:34
Quote from: Pete
You're reasoning is wrong. An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Pete, I feel sure Jeffrey will correct me if I’m wrong here, but I don’t think this responds to the point he was making.

“….there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity.”

A particle must be somewhere.  Two particles must occupy two places.  If we say there is an infinite distance between these two places, surely, we are placing clear limits on infinity.  A distance that is limited in this way is clearly not infinite, so claiming that two objects can be at an infinite distance apart is a contradiction in terms. 

How is that reasoning wrong?
Title: Re: Is infinity a misconception?
Post by: Bill S on 21/09/2014 20:33:35
Quote from: Pete
A  3D Cartesian coordinate system is unbounded,

Yes.

Quote
i.e. it's infinitely large,

Only in principle.  We know that the Universe physically exists, within our understanding of physical existence, therefore to apply that assumption to the Universe is a leap too far.  It may be metaphysics, but it is not science.
Title: Re: Is infinity a misconception?
Post by: alancalverd on 21/09/2014 21:08:25
Is my understanding OK so far?

So far, so good. Now double the mass, so to measure any given value of F you have to stand √2 times as far away, so r tends to a different infinity as F tends to zero.   
Title: Re: Is infinity a misconception?
Post by: Bill S on 22/09/2014 15:50:58
Quote from: alancalverd
  Now double the mass, so to measure any given value of F you have to stand √2 times as far away, so r tends to a different infinity as F tends to zero.

This is the sort of thing I’m looking for – a learning opportunity.

I understand how I would have to stand  √2 times as far away in order to measure any given value of F, but I do not see how this makes any difference to the infinity towards which r tends.   
Title: Re: Is infinity a misconception?
Post by: alancalverd on 22/09/2014 16:28:43
To experience the same value of F in both cases, you will have to stand further away in the second case. Consider a minute, teen weeny value of F. You will be 1.4 times further away from the source in the second case. So as F→0, r increases faster than in the first case. Therefore when F = 0, you are further away. But r1 → ∞, so r2 must tend to a greater infinity.

It isn't actually a problem, either in maths or physics. You can in principle have an infinite number of infinities, each depending on its definition, and all of various sizes.

Supose we have ten physical components, call them 0 to 9, which we can arrange in any sequence of any length - for instance integer numbers. There is an infinity of such possible combinations. Now suppose we have 26 components, called A to Z. Same rules - any sequence, of any length, e.g. Welsh compound words (no need for vowels!). Must be a bigger infinity!  So take an indefinitely extensible and branchable chemical chain like an aliphatic hydrocarbon: only two components and some strict rules about sequencing, but three dimensions and no limit on chain length: what size infinity describes the number of possible hydrocarbons?   
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 22/09/2014 17:34:06
Quote from: Pete
You're reasoning is wrong. An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Pete, I feel sure Jeffrey will correct me if I’m wrong here, but I don’t think this responds to the point he was making.

“….there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity.”
Let's take this one step at a time. I said ...that there's an infinite amount of hadrons in the universe ... in response to which Jeff replied In which case there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity. which is true. In fact that follows from uniform mass density. Jeff replied So to all intents and purposes the contents of the universe is finite even though the universe itself may not be. However that doesn't follow from what was said before that. That's why I gave him the example using 3D Cartesian coordinates as an example. There being a uniform mass density and no boundary on the universe, which means an infinite amount of space, means that there's an infinite amount of mass. Nothing personal folks but that's an extremely simple fact from algebra. Let u be the mass density, V the volume of the universe and M the mass of the universe. Then

M = u V

Since V is infinite and u finite it follows that M is also infinite.

Quote from: Bill S
A particle must be somewhere.  Two particles must occupy two places.  If we say there is an infinite distance between these two places,
which we aren't. That'd be impossible in itself.

Quote from: Bill S
How is that reasoning wrong?
See above.
Title: Re: Is infinity a misconception?
Post by: Bill S on 22/09/2014 19:15:34
Quote from: alancalverd
Therefore when F = 0, you are further away. But r1 → ∞, so r2 must tend to a greater infinity.

Consider what you are saying;

r1 → ∞, but it could never reach infinity.  However far it goes it is infinitely far from infinity. 

r2 → ∞, but it could never reach infinity.  However far it goes it is infinitely far from infinity.

In both cases you are infinitely far from infinity before you start, and when you finish.  Other than as a mathematical necessity, how does one infinity differ from the other?

Your reasoning is impeccable, as long as you consider infinity as a finite distance, which, manifestly it is not.

In this, and all of your examples, you are using mathematical infinities; I have no problem with that, and your arguments make perfect sense, as long as one remembers that mathematical infinities are approximations.

Interesting that you should mention Welsh words that have no need for vowels.  Let’s take a simple example, the word “pwll”; a Welshman looks at that and says: “lets call w a vowel”.  Now pwll has a vowel in it. 

Ar hyn sail, tybed os bob siaradwyr Cymraeg yn wyddonwyr.   [;D]
Title: Re: Is infinity a misconception?
Post by: Bill S on 22/09/2014 19:22:35
Thanks for that Pete.  It looks as though we had some crossed wires, but, to a great extent were on the same track.

If, as seems to be the case, you are saying it is impossible for two particles to be an infinite distance apart; I'm very happy with that.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 22/09/2014 19:32:11
Quote from: Bill S
If, as seems to be the case, you are saying it is impossible for two particles to be an infinite distance apart; I'm very happy with that.
Absolutely since if two particles exist then they have a finite distance between then and infinite is not a distance.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 22/09/2014 20:43:53
Yes my flawed logic. Apologies Pete.
Title: Re: Is infinity a misconception?
Post by: Bill S on 22/09/2014 22:29:47
Quote from: JeffreyH
The point here is that any system that can normally be considered as bounded cannot include an infinite component.

Great!

Quote from: alancalverd
Precisely.

Terrific!!

Quote from: Pete
Let me make this very clear first; [infinity] is not a number.

It’s all coming together; but wait!  A little voice in the depths of my mathematical ignorance says:  “What about the interval from 1 to 2?  This is bounded on both sides by an integer, yet - 

Quote from: alancalverd
  Indeed there is an infinite number of rational numbers between any two integers.

Does it all depend on what we decide that “infinite” should mean?"

Take consolation from the fact that AC got the number of his verb to agree with that of the noun with which it is construed.  That’s more than most people seem to be able to manage in that sort of sentence.    [;)]
Title: Re: Is infinity a misconception?
Post by: alancalverd on 22/09/2014 22:54:40


r1 → ∞, but it could never reach infinity.
obviously, by definition. 

Quote
r2 → ∞, but it could never reach infinity.
also true, but as it is increasing more quickly than r1 it must at all times be greater than r1 and increasingly so, which means the inifinity iit is tending to must be larger than that of r1.

Quote
Your reasoning is impeccable, as long as you consider infinity as a finite distance, which, manifestly it is not.
No, it's only impeccable if you understand that there are different infinities.

Quote
In this, and all of your examples, you are using mathematical infinities; I have no problem with that, and your arguments make perfect sense, as long as one remembers that mathematical infinities are approximations.
Not at all. The definition of any infinity is absolutely precise. Take the simplest infinity: 1/x where x→0. x=0 is an absolutely precise statement, not an approximation to anything.

As for Welsh, there must surely be an infinity of words if any letter can be considered a vowel and any consonant can be pronounced in any way as long as it doesn't sound like English.  The clever bit is that they all mean "the beautiful sadness of the oppressed". Or was my Welsh neice lying about the song she sang at the last Eisteddfodd?
Title: Re: Is infinity a misconception?
Post by: alancalverd on 22/09/2014 23:10:43
Quote from: JeffreyH
The point here is that any system that can normally be considered as bounded cannot include an infinite component.

It’s all coming together; but wait!  A little voice in the depths of my mathematical ignorance says:  “What about the interval from 1 to 2?  This is bounded on both sides by an integer, yet - 

Quote from: alancalverd
  Indeed there is an infinite number of rational numbers between any two integers.



Not a problem. A bounded set can contain anything and everything that can fit between the bounds. But the number of objects in the set is not necessarily a member of the set. Consider how many cats can sit on a roof. The number of cats is not a cat, and is not located on the roof.

Now the number of numbers in a set is an integer but not necessarily a member of the set. Consider the number of integers between 11 and 16: it is 6, which is not between 11 and 16. and the number of quarters between those bounds is 64, which is also not a member of the set, so the number of objects in a denumerable set need not be a member of that set. Rational numbers are denumerable (you can write them all down in sequence and count them, and you can write a recursive algorithm for generating them) but there is an infinite number of rational numbers in any interval.       
Title: Re: Is infinity a misconception?
Post by: evan_au on 23/09/2014 12:54:51
A radical idea:
Rather than teaching young kids arithmetic on the numbers 1 to 12, how about starting by teaching them arithmetic on the 3 numbers 0, 1 and ∞?

The arithmetic on these 3 is somewhat simple; a syllabus might look something like:
Addition (can be viewed as repeated counting up)Subtraction (Can be viewed as repeated counting down)Multiplication (can be reviewed as repeated addition)Division (can be viewed as repeated subtraction)For precise answers, use a calculator; humans should use estimation.
Later introduce square roots (via Pythagoras leads to geometry and trigonometry; irrational numbers  & imaginary numbers).
Also introduce exponention (which can be viewed as repeated multiplication; leads to Cantor's hierarchy of infinities in university).
Title: Re: Is infinity a misconception?
Post by: Bill S on 23/09/2014 14:12:02
Quote from: alancalverd
The clever bit is that they all mean "the beautiful sadness of the oppressed". Or was my Welsh neice lying about the song she sang at the last Eisteddfodd?

Your niece was not lying, but there is so much more to Welsh speaking than sadness and oppression.  It embodies the strength and determination of a people moving forward and taking their rich tradition with them.


I have no problem with the number of cats you may have on your roof, nor would I dispute the intricacies of set theory.  What I have to ask is: Are you saying that Jeffrey was wrong when he said that “any system that can normally be considered as bounded cannot include an infinite component.”? 
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 23/09/2014 15:29:06
Quote from: jeffreyH
Yes my flawed logic. Apologies Pete.
No problem my dear Jeff. What I admire about you is your astute ability to both recognize your mistakes and admit them. Something a lot of people don't have the ability to do.
Title: Re: Is infinity a misconception?
Post by: Bill S on 23/09/2014 17:11:45
Quote from: evan
n+∞=∞

That’s OK as long as you are talking about mathematical infinities.  If you are talking about an infinite cosmos, then n+∞=∞ has no real meaning, because the infinite cosmos is all that exists, or can exist; in which case there is no 1 to add to infinity.
Title: Re: Is infinity a misconception?
Post by: Bill S on 23/09/2014 17:18:26
Quote from: alancalverd
Not at all. The definition of any infinity is absolutely precise. Take the simplest infinity: 1/x where x→0. x=0 is an absolutely precise statement, not an approximation to anything.

This is probably a very naïve question, but is x→0 the same as x→ ∞?
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 23/09/2014 18:41:00
Quote from: jeffreyH
Yes my flawed logic. Apologies Pete.
No problem my dear Jeff. What I admire about you is your astute ability to both recognize your mistakes and admit them. Something a lot of people don't have the ability to do.

Reasoned debate is more productive than unreasoned bile. I would rather learn from mistakes than keep repeating them. I often spout nonsense but it takes me a while to realize it.
Title: Re: Is infinity a misconception?
Post by: Bill S on 23/09/2014 21:41:45
Quote from: evan
n-∞=-∞

I've been trying to get my head round that one.  How do you define minus infinity?  It's a fascinating thought, but it beats me.   [???]

Alright, already! I know that's easy when it comes to maths.
Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 23/09/2014 22:16:54
That’s OK as long as you are talking about mathematical infinities.  If you are talking about an infinite cosmos, then n+∞=∞ has no real meaning, because the infinite cosmos is all that exists, or can exist; in which case there is no 1 to add to infinity.
We just don't know that the universe is infinite, Bill. I don't think it can be, because the universe has a finite age, I do not accept that it was already infinite when the big bang occurred, and I don't see how an infinite universe can possibly expand because the "pressure" is counterbalanced at all locations.

Quote from: Bill S
This is probably a very naïve question, but is x→0 the same as x→ ∞?
No. We have plenty of instances where something diminishes to zero, but we have no evidence that there are any infinities in nature. When they crop up, such as with a black-hole point-singularity, they are thought to signify some breakdown in the mathematics and in our understanding.
Title: Re: Is infinity a misconception?
Post by: alancalverd on 23/09/2014 23:06:45
I have no problem with the number of cats you may have on your roof, nor would I dispute the intricacies of set theory.  What I have to ask is: Are you saying that Jeffrey was wrong when he said that “any system that can normally be considered as bounded cannot include an infinite component.”? 


Yes, he was wrong. Hence my example that there is an infinity of rational numbers in any interval. The interval between 0 and 1 contains 1/2, 1/3, 1/4....2/3, 2/4, 2/5,....3/4, 3/5, 3/6....and so on - i.e. an infinite number of rationals exist between the bounds of 0/1 and 1/1. Whilst the number of rationals in an interval is not a component of that interval, there is an infinite number of components, so the set of components is infinite and thus the bounded interval contains an infinite component.
Title: Re: Is infinity a misconception?
Post by: evan_au on 23/09/2014 23:07:39
Quote from: Bill S
is x→(Finite number) the same as x→∞?
It's not the same, but the two are often related.
For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

This relationship has been validated to many decimal places in successively higher energies of particle accelerators.

JohnDuffield points to another example in a black-hole point-singularity, but in that case it is likely that the quantum nature of space and particle tunneling will provide a lower limit on the degree to which the inverse square law applies as distance x→0 (but we currently have no tested theory of quantum gravity).
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 23/09/2014 23:37:50
I have no problem with the number of cats you may have on your roof, nor would I dispute the intricacies of set theory.  What I have to ask is: Are you saying that Jeffrey was wrong when he said that “any system that can normally be considered as bounded cannot include an infinite component.”? 


Yes, he was wrong. Hence my example that there is an infinity of rational numbers in any interval. The interval between 0 and 1 contains 1/2, 1/3, 1/4....2/3, 2/4, 2/5,....3/4, 3/5, 3/6....and so on - i.e. an infinite number of rationals exist between the bounds of 0/1 and 1/1. Whilst the number of rationals in an interval is not a component of that interval, there is an infinite number of components, so the set of components is infinite and thus the bounded interval contains an infinite component.

Physically you cannot go on sub-dividing space. You hit the Planck scale before you know it. As far as maths goes you are right but you soon run into a Zeno's paradox at very small physical scales.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 24/09/2014 14:29:10
JohnDuffield is a major crackpot - Beware!!!!
Title: Re: Is infinity a misconception?
Post by: Bill S on 24/09/2014 20:02:59
Quote from: Pete
JohnDuffield is a major crackpot - Beware!!!!

The geological cognoscenti said that about Alfred Wegener. 

Many still say it about Warren Carey, but he is still a geologist of considerable stature.
Title: Re: Is infinity a misconception?
Post by: Bill S on 25/09/2014 20:01:46
In another thread; in response to my saying that there could never have been nothing, otherwise there would still be nothing now; JP pointed out that we could not make this claim because, outside the Universe conditions could exist in which something could come from nothing. He assured me that to substantiate my claim scientifically I would have to provide proof that such conditions could not exist.

Let’s apply this to the infinity argument.

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc? 

Can anyone identify an “infinite” point?   Of course not; in fact that is a ridiculous question.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.
Title: Re: Is infinity a misconception?
Post by: Bill S on 25/09/2014 20:06:45
Quote from: evan
For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 25/09/2014 20:26:17
Quote from: evan
For example, relativity has many expressions like 1/√(1-v2/c2)

As v→c, 1/√(1-v2/c2) →∞.

Does 1/√(1-v2/c2) go to infinity, or to 0?

When v^2 = c^2 the square root operates on zero. Within the currently known laws of physics V cannot exceed c so zero would be the limit when velocity is increasing. However we then end up with 1/0 which is undefined. I disagree with this equaling infinity. When v tends to zero the square root then is √(1-0/c^2). Then we have 1-0 and with the square root of 1 being 1 the whole expression is 1/1. So in this situation the limit is 1. We can equate this to multiplying by one which gives us 100% of an original value. This means that as the value tends towards undefined we end up with a decreasing amount of the original value until the mathematics eventually breaks down at undefined.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 25/09/2014 20:33:00
Let us take a simple equation A*B = C. It follows that A = C/B. What if we set B to zero. A*B = C then becomes A*0 = 0. Now if A > 0 what is the meaning of A = C/B if C is also > 0? In this case and to make sense C has to tend towards zero and equal B when exactly zero. This is why were are missing a component in the relativistic equations. This does not mean that C and B are always equal but they must be equivalent when they reach zero. They must both cross the origin.
Title: Re: Is infinity a misconception?
Post by: Bill S on 26/09/2014 15:37:38
Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0
Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 26/09/2014 16:05:46
...Let’s apply this to the infinity argument.

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim?
No. Take a look at your ruler. There isn't an infinite number or amount of anything between the 0 and the 1. People who talk about dividing up that distance into some infinite subdivision are getting lost in abstraction. 

How could anyone prove that there was not something that would prevent this from being a physical reality?  Smallest possible divisions, quanta etc?
You can't disprove this sort of thing, just as you can't disprove fairies. 

Can anyone identify an “infinite” point? Of course not; in fact that is a ridiculous question.
It all gets very abstract and very ridiculous very quickly. But when you point this out, some guy who can't point to any supporting scientific evidence starts calling you names.

If a physical infinity exists, it cannot exist within a finite universe – in fact the finite universe would have to exist within the infinite entity.
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.


Quote from: jeffreyH
...However we then end up with 1/0 which is undefined. I disagree with this equalling infinity...
Well said Jeffrey. We talk about infinite time dilation for the hypothetical guy travelling at c, but what it really is, is zero local motion.   
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 26/09/2014 19:05:24
Jeff (is it OK to call you Jeff), I usually have to substitute numbers for letters to make sure I have grasped algebraic equations. 

In this case I get:

A*B=C     A=C/B     If A=2 & B=0

2x0=0        2=0/0 which makes no sense to me.

After that you lose me.  How do you get from C=0 to C tends towards 0

Sorry Bill that was rushed. You are right that when A = 2 then both C and B cannot both be zero. I set A to 2 to show that the only way round the division by zero was for C also to equal zero which then invalidates A. Anyway that was the point I was trying to make. In my view setting a denominator to zero means your value ceases to exist. Whatever the value be it radius, mass or anything else. In calculus this can be used as a limit in determining a derivative but to think of it actually representing a physical value is not at all useful.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 26/09/2014 19:25:47
Quote from: JohnDuffield
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 26/09/2014 19:41:12
Quote from: JohnDuffield
I agree. There ain't no infinities in nature. None that we know about. And I don't see that changing any time soon.
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.

What does the self energy correction say about the state of the field energy in the immediate vicinity of the electron?
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 13:17:32
Quote from: Pete
Even in classical electromagnetism, if one can calculates the energy needed to assemble an electron, the result is infinite, yet electrons exist. The quantum self energy correction is also infinite although it can be rendered finite if we accept the fact that out theories are not valid up to infinite energies.

Is this not tantamount to saying that we cannot work with infinities unless we modify them in some way; in which case they are not infinite?
Title: Re: Is infinity a misconception?
Post by: alancalverd on 27/09/2014 13:43:43

Quote from: alancalverd
……an infinite number of rationals exist between the bounds of 0/1 and 1/1.

Is this a scientifically valid claim? 

Interesting question. A hypothesis is scientifcally valid if it is (a) consistently predictive and (b) not disproved by experiment. It also has to be explanatory and consistent with previous observations. But a mathematical hypothesis is subject to absolute proof or disproof. So let's attempt an absolute proof. For any number a/b there exists a number a/(b+1) which is smaller and a/(b-1) which is larger. If b > a then a/b lies in the interval between 0 and 1. For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b. 
Title: Re: Is infinity a misconception?
Post by: yor_on on 27/09/2014 14:57:28
Assume that for any point in a matrix there can be a defined distance. Then ask yourself how you can define it. By being 'inside' with it, measuring. 'Inside' is equivalent to the universe you're in, measuring on. Inside we need it, it's one of those things making macroscopic values work. It does not state what it should be from any thought up 'outside though. The simple solution to a outside is the idea of a universe as some physical entity, forming for example a sphere, or just a self enclosed barrier. If you instead define a 'outside' as being where distances won't hold anymore, then 'outside' can be thought of as a 'inside' too, but without arrow, and so without form.
=

Using that argument a distance becomes a sub division of another type of 'universe', where infinity loses its meaning, unless you want to define a infinity to anything lacking that arrow (clock). If you do, how will you treat the displacements between two 'ticks' on your clock? Also a question of discreteness.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 16:44:06
Quote from: alancalverd
For any a there exists at least one  number a+1 > a so for any a I can define an appropriate b > a and hence numbers each side of a/b. There being an infinity of a there must thus be an infinity of a/b.

"Mathematical ‘existence’ meant only logical self-consistency and this neither required nor needed physical existence to complete it.  If a mathematician could write down a set of non-contradictory axioms and rules for deducing true statements from them, then those statements would be said to ‘exist’.”  John Barrow.

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 16:49:16
Yor_on.  Your last post seemed to say something interesting; I just wish I knew what it was.   [:(]
Title: Re: Is infinity a misconception?
Post by: alancalverd on 27/09/2014 17:04:49

Your statement is a mathematical “truth” which neither requires nor needs physical truth to complete it.


Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 17:11:27
Quote from: Pete
JohnDuffield is a major crackpot - Beware!!!!

If that's based on his posts in this thread, I guess I'm in danger of acquiring the same label.

Crackpots of the world unite,
Our limit is the skies;
Won’t they be pissed if we are right,
And win a Nobel Prize?



Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 27/09/2014 17:16:43
Yet another ignorant comment again. The self energy of any point charged particle is infinite. See http://quantummechanics.ucsd.edu/ph130a/130_notes/node44.html
Geddoutofit. The electron energy is 511keV. Not infinite. And you can diffract electrons. They aren't point particles. 

The mass/energy density of the universe is uniform so since a certain percentage of that matter consists of hadrons it follows that there are an infinite number of hadrons. All of these are infinite and known to all physicists who know what they're talking about.
What!? It doesn't follow that there's an infinite number of hadrons, they don't have infinite energy. And you don't have a clue what you're talking about.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 17:25:57
Quote
Exactly so. The fact that you would run out of patience long before you ran out of possible subdivisions of the set of rational numbers between 0 and 1 does not however negate the assertion that the set is itself (a) infinite (b) larger than the set of integers and (c) not a continuum.

Absolutely!  These assertions are correct, but can exist only in the, presumably finite, minds of rational beings. 

A circular square centred on the bisector of the infinite side of a physically impossible triangle can exist in your mind, but, as you indicated, that does not make it a physical reality. 
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 27/09/2014 18:24:31
We pass through grass behush the bush to. Whish! A gull. Gulls. Far calls. Coming, far! End here. Us    then. Finn, again! Take. Bussoftlhee, mememormee! Till thous-endsthee. Lps. The keys to. Given! A way a lone a last a loved a long the


riverrun, past Eve and Adam's, from swerve of shore to bend of bay, brings us by a commodius vicus of recirculation back to Howth Castle and Environs.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 20:40:45
“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

Title: Re: Is infinity a misconception?
Post by: chiralSPO on 27/09/2014 21:20:30
Infinities are very useful mathematical concepts. We can never observe an infinity in the real world, but that does not necessarily mean that there isn't any physical infinity, it is just a restriction on our ability to observe and verify.

Infinitesimals are also very useful mathematically. I am not sure if quantization rules out any possibility of a physical infinitesimal, or just out ability to observe one.

A photon with zero energy would have an infinite wavelength. But again, even if it made sense for such a thing to exist, how could it be observed?
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 27/09/2014 22:22:07
“I done me best when I was let. Thinking always if I go all goes. A hundred cares, a tithe of troubles and is there one who understands me?"

Then there's the Three quarks for Muster Mark!

And we're back to physics.

You are a cut above the rest Bill.
Title: Re: Is infinity a misconception?
Post by: Bill S on 27/09/2014 23:11:23
Quote from: Jeff
You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   [;D]
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 28/09/2014 00:45:11
Quote from: Jeff
You are a cut above the rest Bill.

I could be a crackpot, though, couldn't I?   [;D]

I think we all have that potential.  [:P]
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 28/09/2014 06:52:57
Quote from: jeffreyH
I think we all have that potential.  [:P]
No. I don't believe that. It takes a particular personality for that.
Title: Re: Is infinity a misconception?
Post by: Bill S on 28/09/2014 14:26:50
Quote from: Pete
It takes a particular personality for that.

Would that be someone capable of original thought, like Copernicus, Newton or Wegener?

We are drifting away from the OP; does that mean we are running out of relevant things to say?

If that’s the case, perhaps we should ask Jeff if the original question has been answered.  To me, that is much more important than identifying crackpots.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 28/09/2014 14:55:43
Well any jokes about crackpot potential aside I think some very interesting thoughts were expressed. All worth thinking about. It really isn't a question we can easily answer. We need to make sure we are thinking about how infinity relates to some of the functions we depend upon in the equations we use to describe nature. So no it wasn't answered but I didn't expect a concrete answer.
Title: Re: Is infinity a misconception?
Post by: Bill S on 28/09/2014 20:50:28
I have long thought that with a thread like this, which contains a lot of interesting material it seems a shame that it often just fades out without any conclusion or summary.  I wondered about the value of a summary at some point by the OP, and whether this would be a good habit to cultivate. 

Although not the OP of this thread, I thought it might be worth summarising what I had gained from it.  I’m hardly past the first page, and I think I know why people don’t generally attempt this. [:D]
Title: Re: Is infinity a misconception?
Post by: Bill S on 28/09/2014 21:08:26
Quote from: Pete
An boundless universe with uniform mass density has an infinite number of galaxies, particles, stars and planets in it and thus an infinite amount of matter.

Surely a finite universe, which is all that exists, and is therefore expanding into nothing, is boundless, but finite.  This could not contain an infinite amount of matter.
Title: Re: Is infinity a misconception?
Post by: evan_au on 28/09/2014 22:10:12
Quote from: alancalverd
the set of rational numbers between 0 and 1 ...is (a) infinite (b) larger than the set of integers

This didn't quite gel with me - I vaguely recall from university seeing a proof that the number of rational numbers between 0 & 1 was countably infinite. It was a geometric construction on the number plane, effectively making use of the mathematical fact that ∞2=∞.

In doing a quick search, I found a different proof (https://proofwiki.org/wiki/Rational_Numbers_are_Countably_Infinite) that shows that members of the set of all rational numbers (from -∞ to +∞) has the same quantity as the number of positive integers.

Like a lot of things in maths, it comes down to being clever about how you count. In this case, the cleverness comes in being able to count an infinite number of things in a finite time.

But similar kinds of cleverness in counting are implicit in common mathematical operations like integration, differentiation and probability.
Title: Re: Is infinity a misconception?
Post by: Bill S on 29/09/2014 18:41:13
Quote from: evan_au
∞2=∞.

From this it might be argued that we must be dealing with two infinities of different sizes.  However 0^2=0, so are we dealing with different sixes of zero?
Title: Re: Is infinity a misconception?
Post by: yor_on on 29/09/2014 18:53:00
Yor_on.  Your last post seemed to say something interesting; I just wish I knew what it was.   [:(]

Call it meta physics, the question of what exactly we think we're doing :)
As long as you just accept bases you won't move forward in your questioning. define that inside, don't accept a outside. then start to ask yourself how the unknown will fit such a proposal.
=

If you do it as me then the unknown will be what 'is', we being a symmetry break :) Well, possibly? and then dimensions should lose their former 'idea history', as I think then, needing to be reevaluated.
Title: Re: Is infinity a misconception?
Post by: Bill S on 30/09/2014 16:37:47
I have started working through the thread picking out some bits which seem important to me, and adding some comments relevant to my understanding.  Lack of time has prevented me from getting very far, but I would really appreciate some comments.
 
Quote from: JH
Well then find the radius of the circle whose circumference is infinite.

This is a mathematical question, so mathematical infinities would be appropriate.  If the circumference is infinite, then the radius is also infinite, but they must be different sized infinities, and different infinities are acceptable in mathematics.  We cannot assign any finite value to either radius or circumference, effectively, infinite means so large that we might as well consider it infinite. 

Quote from: JH
The point here is that any system that can normally be considered as bounded cannot include an infinite component. So if the mathematics of a formerly finite system go infinite something is terribly wrong.

The first sentence is true if it refers to what we might need to call “absolute” infinity.   If we are using mathematical infinities, then it can be argued that, for example, there is an infinite number of rational numbers between any two integers.  However, Zeno’s paradox leads us to suspect that that this is a “fact” only in principle.

The second sentence must be true, as any finite thing would approach infinity infinitely, thus it would never “arrive”.     

Quote from: Pete
Let me make this very clear first; {infinity} is not a number.

As far as I can tell, everyone in this thread agrees with this statement.

Quote from: AC
There is an infinite number of integers 1,2,3,.... because we can always add one more

There are rational numbers between the integers 1, 3/2, 7/4, 2, 9/4, 19/8, 3....

Indeed there is an infinite number of rational numbers between any two integers

So the number of rational numbers must be greater than the number of integers

As so often happens when talking to scientists about infinity, we return here to mathematical infinities.  Although these are boundless, their “infinite” nature can never be physically demonstrated, because it is not possible to count to infinity, nor to enumerate all the rational numbers between two integers.

Quote from: JD
IMHO if ever you bump into an infinity in physics, then something is wrong somewhere.

Quote from: PB
Nonsense. It's beginning to become clear that the universe is flat and boundless and as such goes on forever, never ending. That's what it means to be infinite.

Quote from: Sean Carroll. “The particle at the end of the universe”
Infinite answers are certainly not right, so they are a sign that your theory is not very good.  A theory needs to fit the data, but it also needs to make mathematical sense.

Do we lack reasonable consensus between scientists as to exactly what is meant by “infinity” in individual cases?  It seems so, but that presents a problem for non-experts.  How does one choose whom to believe? 

Quote from: JH
…… there can never be an infinite amount of distance between any two particles as that would place a boundary on infinity.

That makes perfect sense to me, as long as we accept that mathematicians will always be able to fit mathematical infinities into finite spaces.
Title: Re: Is infinity a misconception?
Post by: Bill S on 30/09/2014 21:24:53
I posted the last bit in a hurry without checking for typos, crackpottery etc, nor did I ask if anyone objected to my using initials with the quotes.   
Title: Re: Is infinity a misconception?
Post by: chiralSPO on 01/10/2014 00:23:41
The only way would be able to prove something is infinite would be by abstraction. I don't think we could ever claim to have measured or experimentally determined an infinite value, countable or uncountable.

In the same way, zero is also kind of an infinity. Reciprocal and logarithmic relationships abound in physice. For instance, one cannot actually actually achieve absolute zero on the Kelvin scale (for many reasons!), only arbitrarily close to it; the distance between two particles cannot really be zero or infinite, only arbitrarily far or close. Yet there are also laws of conservation--meaning a derivative implied to be precisely zero, but verified to be zero within some small, but obviously nonzero confidence interval.


Does the fact that we cannot experimentally verify something make it untrue through?

The math predicts infinities or zeros, but we must be careful here, also to remember that our beloved equations are ALL MODELS. And all models have implicit assumptions and limitations. So an equation having a nonsensical infinite or zero value could  just as much signify a problem with the model as reflect reality. Often these ridiculous failures of our equations happens at boundaries or limits (absolute zero, speed of light, discontinuity in another parameter [phase change], etc.) But overall, we can do amazing things with infinities in models, giving real predictive power for experimental physics, chemistry and cosmology.

Most people have misconceptions about infinities, myself included--little is intuitive, only protracted analysis and mathematical rigor works here. One can do some really crazy things with them mathematically, or by logical induction (Cantor actually went crazy, but that's another story).
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 01/10/2014 00:49:58
If the universe was flat then Sean Carroll would not disagree with me.
Title: Re: Is infinity a misconception?
Post by: yor_on on 01/10/2014 17:53:13
It's actually conceptually simple to think of any thought up outside as an inside too. If you do infinities becomes what we can't measure on, getting a linear answer. Doesn't matter if it is a actual experiment or a mathematical hypothesis. then what we are, to me looks more as a break than as 'what is'. We're an exception in my mind, and our ideas of what infinities should be defined as should then become a answer from what cultural and physical reality, we define as our seamlessly existing 'common' universe. Infinity loses its meaning.
Title: Re: Is infinity a misconception?
Post by: yor_on on 01/10/2014 18:00:50
Eh, doesn't state that a Victorian description would be fitting. Just that if you define a inside and let the rest be a part, although not linearly measurable as we would prefer/expect a inside to be. Then our 'infinities' just may be what is, us being a slightly different version, from our linear definitions. It turns it upside down :) and force you to define what, and why, we are from a different base.
=
are, not 'exist'
Title: Re: Is infinity a misconception?
Post by: Bill S on 01/10/2014 20:18:35
Quote from: Pete
If the universe was flat then Sean Carroll would not disagree with me.

OK; but could you explain why, please.
Title: Re: Is infinity a misconception?
Post by: Bill S on 01/10/2014 20:29:06
Quote from: ChiralSPO
Does the fact that we cannot experimentally verify something make it untrue through?

I feel sure it doesn't.  However, such possible things can always be relegated to metaphysics or philosophy if they become irritating.  Otherwise, they can just be part of some theory. 
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 01/10/2014 20:51:44
Quote from: Bill S
Quote from: Pete
If the universe was flat then Sean Carroll would not disagree with me.

OK; but could you explain why, please.
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.
Title: Re: Is infinity a misconception?
Post by: jeffreyH on 02/10/2014 01:44:18
Quote from: Bill S
Quote from: Pete
If the universe was flat then Sean Carroll would not disagree with me.

OK; but could you explain why, please.
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.

Surely infinity is an unbounded continuity whereas hadrons are discontinuous having gaps of varying magnitude between them. For hadrons to be infinite it would require there being only 1 hadron of infinite size. For multiple hadrons there would also have to be an infinity of empty space. If infinity is all inclusive how can you divide it in 2 or more portions? Mathematically this would not work.
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 02/10/2014 06:18:53
Quote from: jeffreyH
Surely infinity is an unbounded continuity whereas hadrons are discontinuous having gaps of varying magnitude between them. For hadrons to be infinite ...
No. It's the mass density that is uniform and as such when you multiply a constant mass density by the infinite volume of the universe you get an infinite mass. It's as simple as that. I used hadrons as an example so people can visualize it.

Quote from: jeffreyH
it would require there being only 1 hadron of infinite size.
Come on Jeff. Let's be real here. Hadrons are point particles having zero radius. A hadron can't be infinite in size. Let's try to understand the difference between the exact calculation and the example given to illustrate it.

Quote from: jeffreyH
For multiple hadrons there would also have to be an infinity of empty space.
That's what a flat universe implies Jeff. IK thought I explained that above. You didn't realize that?

Quote from: jeffreyH
If infinity is all inclusive ..
What in the world does that mean???

This is very simple, Jeff. Mass density = constant. Volume of universe = infinite.

If you need to see this from a university professors notes like a lot of people do to make them feel confident about the answer then see http://www.astronomy.ohio-state.edu/~ryden/ast162_9/notes40.html 
Quote
Precise measurements lead cosmologists to conclude that the universe is flat, and thus has infinite volume.
Do you understand now? Please stop confusing yourself with these bizarre and unphysical dreams of yours and stick with the physical universe. Okay? :)
Title: Re: Is infinity a misconception?
Post by: Bill S on 02/10/2014 16:19:34
Quote from: Pete
This is very simple, Jeff. Mass density = constant. Volume of universe = infinite

Pete, what you say is undoubtedly right, but, as has already been mentioned, mathematical reality and physical reality are not necessarily the same thing.  E.g. with the “book stacking problem” it is possible, in theory, to reach an infinite overhang with an infinite number of books, but would you claim that is physically possible?


Title: Re: Is infinity a misconception?
Post by: PmbPhy on 02/10/2014 17:08:31
Quote from: Bill S
Pete, what you say is undoubtedly right, but, as has already been mentioned, mathematical reality and physical reality are not necessarily the same thing.
You're wrong, Bill. What math does is to allow us to describe physical reality. Start with a universe having a uniform uniform mass density which as the value at time t of rho. Let the volume of the universe be V. Then the total mass in a universe at time t is M = rho*V. For larger and larger universes we have more and more mass given the same mass density. If that volume increases without limit it means that the mass increases without limit. That's what it means to be infinite.

Quote from: Bill S
E.g. with the “book stacking problem” it is possible, in theory, to reach an infinite overhang ..
What do you mean by an infinite over hang? Do you mean that the center of mass of the next book to be put on the stack is not right above the previous one and thus there is an increasing over hang? If so then that's not possible because it'd collapse before that.

Quote from: Bill S
with an infinite number of books, but would you claim that is physically possible?
Of course not but those two problems are like comparing apples and oranges and as such it's not the same thing as in this or with all other physics problems. Try using your argument on every single exercise problem in any physics textbook and you'll see that it's the wrong answer.

This is a very simple idea. If people are having a difficult time with it then you're missing something, i.e. there is a hole in your education somewhere. Let's find out where that hole is.
Title: Re: Is infinity a misconception?
Post by: Bill S on 02/10/2014 23:40:55
Quote from: Pete
What do you mean by an infinite over hang? Do you mean that the center of mass of the next book to be put on the stack is not right above the previous one and thus there is an increasing over hang? If so then that's not possible because it'd collapse before that.

You must be familiar with the book-stacking problem.  The books have to be stacked so that the centre of gravity of the stack never lies beyond the edge of the table.  Once it does they will start to topple.  If each book has size 1 then the maximum possible overhang of N books is just one half of the sum of the harmonic series up to N terms:

    Maximum Overhang Distance = 1/2X {1+1/2+1/3+1/4+1/5…+1/N}

John Barrow points out that the overhang distance can be made as large as you like by making N big enough. 

"To make the overhang 10 times the size of a single book would need a stack of 272,400,600 books.  In an ideal world without friction and imperfect surfaces and smallest particles of matter, the overhang could be infinite.” 

Barrow concedes that: “This is possible in principle, not in practice.”

I mentioned this only as an example of something that might work in principle but would not work in practice.

To suggest that this particular example could be applied to every problem in physics would be absurd, and is certainly not something I said. 
Title: Re: Is infinity a misconception?
Post by: Bill S on 02/10/2014 23:55:59
Quote from: Pete
If that volume increases without limit it means that the mass increases without limit. That's what it means to be infinite.

I am neither qualified, nor would I wish, to suggest that this is not a mathematical reality.  However, if you are talking of something "increasing", that something is not infinite.  If it is not infinite it is finite and therefore it can never become infinite.   
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 03/10/2014 06:49:39
Quote from: Bill S
I am neither qualified, nor would I wish, to suggest that this is not a mathematical reality.  However, if you are talking of something "increasing", that something is not infinite.  If it is not infinite it is finite and therefore it can never become infinite.
Hi Bill,

May I ask you a personal question? Have you ever studied calculus or real analysis? If so then surely you learned about what infinity is. If not then I see where the problem lies. If that is indeed the case then let me explain it to you if you, if you don't mind that is? 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. For example; what is the value of the function f(x) = 1/x as x approaches 0? This is called a limit. In this case f(x) increases without bound and we say that f(x) becomes infinite as x approaches 0.

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
Title: Re: Is infinity a misconception?
Post by: PmbPhy on 03/10/2014 07:00:18
Quote from: Bill S
To suggest that this particular example could be applied to every problem in physics would be absurd, and is certainly not something I said.
I wasn't referring to the example. I was referring to your comment "mathematical reality and physical reality are not necessarily the same thing". In what I've been talking about I've only been using math to describe why there's an infinite amount of matter in the inverse. I don't see how your example applies to this problem. In fact it doesn't.

However, suppose I was asked to prove that E = mc2 and I posted the math to prove it's true. Could someone logically respond to my derivation by saying "mathematical reality and physical reality are not necessarily the same thing" and have a valid point? If not, why?
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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. 

Quote
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. 

Quote
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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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]
Title: Re: Is infinity a misconception?
Post by: jeffreyH 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.
Title: Re: Is infinity a misconception?
Post by: jeffreyH 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?
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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?
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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/
Quote
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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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?
Title: Re: Is infinity a misconception?
Post by: Bill S 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!
 
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.

 
Title: Re: Is infinity a misconception?
Post by: yor_on 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'.
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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. 
Title: Re: Is infinity a misconception?
Post by: yor_on 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?
Title: Re: Is infinity a misconception?
Post by: yor_on 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.
Title: Re: Is infinity a misconception?
Post by: Ethos_ 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.
Title: Re: Is infinity a misconception?
Post by: yor_on 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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.
Title: Re: Is infinity a misconception?
Post by: jeffreyH 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.
Title: Re: Is infinity a misconception?
Post by: chiralSPO 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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?
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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.
Title: Re: Is infinity a misconception?
Post by: alancalverd 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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.
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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
Title: Re: Is infinity a misconception?
Post by: jeffreyH 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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. 
Title: Re: Is infinity a misconception?
Post by: Bill S 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.
Title: Re: Is infinity a misconception?
Post by: jeffreyH 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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?"
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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."
Title: Re: Is infinity a misconception?
Post by: Bill S 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]
Title: Re: Is infinity a misconception?
Post by: Bill S 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?
Title: Re: Is infinity a misconception?
Post by: Ethos_ 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!

Title: Re: Is infinity a misconception?
Post by: dlorde 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 (http://en.wikipedia.org/wiki/Georg_Cantor).

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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.
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.
Title: Re: Is infinity a misconception?
Post by: Ethos_ 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..........
Title: Re: Is infinity a misconception?
Post by: yor_on on 18/10/2014 16:08:31
Good ideas all of you. We're here to use our minds.
Title: Re: Is infinity a misconception?
Post by: yor_on 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?
Title: Re: Is infinity a misconception?
Post by: dlorde 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?
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.
Title: Re: Is infinity a misconception?
Post by: Ethos_ 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.
Title: Re: Is infinity a misconception?
Post by: Bill S 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”. 
 
Quote
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.   
Title: Re: Is infinity a misconception?
Post by: Bill S 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.   
Title: Re: Is infinity a misconception?
Post by: Bill S 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.
Title: Re: Is infinity a misconception?
Post by: Ethos_ 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.
Title: Re: Is infinity a misconception?
Post by: dlorde 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. 

Quote
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.

Quote
... 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?
Title: Re: Is infinity a misconception?
Post by: PmbPhy 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".
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.
Title: Re: Is infinity a misconception?
Post by: JohnDuffield 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.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 20/10/2014 21:42:13
While we are trying to get our minds wrapped around the meaning of infinity, something occurred to me that might be of interest for some of our members.

Let's ask ourselves; "What existed before the big bang?"

While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.

We've reasoned in prior posts that maybe it would be time to define what we mean when we say "Universe". But it would also be a step forward to define what we mean when we say "Nothingness"

My point with these thoughts are this:

Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.

So to clarify my position on what I mean when I say: "Universe"

"All that is." This would include our present material existence and all that nothingness which our present material universe sprang up within during the big bang.

Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 20/10/2014 22:19:40
Let's ask ourselves; "What existed before the big bang?" While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing.
Not me. I just don't believe in creation ex nihilo.   

But it would also be a step forward to define what we mean when we say "Nothingness". My point with these thoughts are this:

Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.

So to clarify my position on what I mean when I say: "Universe"

"All that is." This would include our present material existence and all that nothingness which our present material universe sprang up within during the big bang.
I think the pre-big-bang universe was something like a "frozen star" black hole myself. Interestingly, when you look at the gravastar (http://en.wikipedia.org/wiki/Gravastar), which is somewhat similar to the frozen star black hole, you can read this: "This region is called a 'gravitational vacuum', because it is a void in the fabric of space and time." It's like a black hole really is a hole in space. Sounds unfamiliar I know, but note the shear stress in the stress-energy-momentum tensor (http://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor), and think of space as something like gin-clear ghostly elastic. Then think of a party balloon, then look at this picture:

(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F5%2F5e%2FBH_LMC.png%2F236px-BH_LMC.png&hash=381d20950705e45d56b33a6f86d489c5)
CCASA image by Alain r, see http://en.wikipedia.org/wiki/Black_hole

See it? The depiction looks like a balloon with a hole in it. Like a black hole really is a hole. A hole in space. I have a hunch the early universe was something similar. Only there wasn't any space around it. Maybe this deserves a thread all of its own.   
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 20/10/2014 22:34:26
Let's ask ourselves; "What existed before the big bang?" While proving any particular theory about this question is impossible, most of us will reason that what existed before the big bang was simply nothing.
Not me. I just don't believe in creation ex nihilo.   


I was under the impression that you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?
Title: Re: Is infinity a misconception?
Post by: dlorde on 20/10/2014 22:37:34
Let's ask ourselves; "What existed before the big bang?"

... most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.
I'd like to see your data supporting 'most of us'; I, for one, don't reason that. 

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... it would also be a step forward to define what we mean when we say "Nothingness"
Please do, your usage makes no sense at all to me.

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Before the big bang, nothingness was truly infinite. If nothing else existed in this historical epic, then nothing anywhere but nothing is logically an infinity of nothingness.
Nothing has no properties - it is a negation, the absence of anything, even empty space. It doesn't exist - it has no extent of any kind, so it can't be infinite. What 'nothingness' means, apart from a poetic appeal to a sense of nothing, I'm curious to know; please enlighten me.
Title: Re: Is infinity a misconception?
Post by: dlorde on 20/10/2014 22:40:51
... you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?
A finite region of nothingness? how does that work? You seem to be using 'nothingness' in the sense of being something that can exist and can occupy a region... I don't understand.

Are you sure you don't mean some kind of empty space?
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 20/10/2014 22:43:39


See it? The depiction looks like a balloon with a hole in it. Like a black hole really is a hole. A hole in space. I have a hunch the early universe was something similar. Only there wasn't any space around it. Maybe this deserves a thread all of its own.
"A hole in space." "Only there wasn't any space around it."

Now you've really sent my train off the tracks.......................
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 20/10/2014 22:49:28
... you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?
A finite region of nothingness? how does that work?
I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 20/10/2014 22:54:36
Let's ask ourselves; "What existed before the big bang?"

... most of us will reason that what existed before the big bang was simply nothing. And even now, as we exist in a universe which many assume is finite, this present universe sprang up within this nothingness.
I'd like to see your data supporting 'most of us'; I, for one, don't reason that. 



I stand corrected dlorde.................That was very presumptuous of me.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 21/10/2014 02:57:44
This discussion would benefit from:

The Man Who Knew Infinity, a book about the life of Srinivasa Ramanujan

While I agree that infinity is not a number, it is worthy of being called; A mathematical abstraction. And Ramanujan was, by all accounts, one of the greatest mathematical genius's, if not the greatest, to ever live.

 
Title: Re: Is infinity a misconception?
Post by: dlorde on 21/10/2014 09:29:04
I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.
Sorry, my mistake. So you reject the idea of a 'region of nothingness'?

I'm still curious to hear your definition of nothingness and how it could be infinite (e.g. infinite in what respect?).
Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 21/10/2014 09:56:49
I was under the impression that you believe our universe is a finite region of material existence lying within a region of absolute nothingness. If that is so, why didn't that nothingness also exist before the big bang?
There is no region of absolute nothingness. It's like what dlorde said. Nothing is the absence of anything, even empty space. It doesn't exist, it has no extent of any kind, and it isn't infinite. And I just can't see how you can get something from nothing. 

Quote from: Ethos
"A hole in space." "Only there wasn't any space around it." Now you've really sent my train off the tracks...
Take it one step at a time. Read up about the gravastar and the frozen-star black hole, and have a dig around about the way the early universe is likened to a black hole.
Title: Re: Is infinity a misconception?
Post by: Bill S on 21/10/2014 22:59:05
Quote from: dlorde
The 'middle' means equidistant from specified extremes. Infinite extremes are not measurable so equal distance can't be known.

Granted, equal distance can't be known, but by the same token, nor can unequal distances.  Since distances must be either equal or unequal, does this imply that no distance in infinity is measurable?


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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.

If they are not measurable, how can you decide that your “infinities” are equal, or unequal?  That is as meaningless as the concept of “middle”, or indeed of any distinguishable point in infinity.

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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?


We seem unable to escape the mathematical infinities, even when talking about physical entities.  If we use infinite as though it were synonymous with boundless we will always run into problems.  The universe may be boundless. If it is, we can still apply mathematics to it – measure it.  If we claim it is infinite, we are saying more about it.  Infinity “is a mathematical abstraction”.  What is an abstraction if it is not the quality of dealing with mental concepts, rather than with concrete objects?  The Universe is a concrete object, we need more than a mathematical abstraction in order to understand it.

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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.

You can say you have an unbounded extent “ahead of you or behind you”, but you cannot establish that it is infinite.

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can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?

Consider two points in infinity – A and B.  If you are at A you assess that you are centrally placed, according to your assessment B is therefore not central.  Now move from A to B.  Once there you assess that you are central, so A is not. If you measure the distance between A and B as 100 km, then the distance between the centre of infinity and the centre of infinity is 100km, which is nonsense.  A and B are distinguishable only if there are objects there.  The points themselves are indistinguishable.  If you remove the ability to relate A and B by measurement, you remove the ability to distinguish between them. Each is the centre of infinity, whatever that might be.

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I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.

Apart from some vague hand waving in the direction of God, what is absolute infinity?
Title: Re: Is infinity a misconception?
Post by: dlorde on 22/10/2014 00:42:23
Granted, equal distance can't be known, but by the same token, nor can unequal distances.  Since distances must be either equal or unequal, does this imply that no distance in infinity is measurable?
Only where they involve infinities. You could have measurable distances on a hypothetical infinitely long road - e.g. two points a mile apart.

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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.
If they are not measurable, how can you decide that your “infinities” are equal, or unequal?
I was covering the possible argument that infinities of the same order could be claimed to be the same size (because they are not different sizes of infinity). Even if it was valid, I don't think it's a useful argument, but someone might be tempted by it.

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We seem unable to escape the mathematical infinities, even when talking about physical entities.
Infinity is a mathematical concept, so - yes, if you want to talk about physical infinities, the model is mathematical. Likewise, if you want to talk about the physical effects of gravity, the model is also mathematical. What's the problem?

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Infinity “is a mathematical abstraction”.  What is an abstraction if it is not the quality of dealing with mental concepts, rather than with concrete objects?  The Universe is a concrete object, we need more than a mathematical abstraction in order to understand it.
The universe seems surprisingly amenable to modelling through mathematical abstractions - that's how we understand its physical behaviour; we don't yet know whether it makes sense to apply the mathematical concept of infinity to our models of it, but that doesn't prevent us hypothesising the cases. But I agree in that I don't see how we can ever know if the model matches the reality in that respect.

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You can say you have an unbounded extent “ahead of you or behind you”, but you cannot establish that it is infinite.
That it was an infinite road was the premise of your thought experiment. In the real world I don't see how you could never know or establish it was infinite - that's why it must be a thought experiment. If you were on a finite circular road, you would indeed have an unbounded but finite extent ahead or behind.

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can you detail the logical step that takes them from not being related by measurement to them being indistinguishable?
Consider two points in infinity – A and B.  If you are at A you assess that you are centrally placed, according to your assessment B is therefore not central.
That doesn't get off the ground - above, you agreed that the idea of equidistance or a middle to infinity was a meaningless idea. 

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I don't see how Cantor's ideas of 'absolute infinity' (God) are relevant.
Apart from some vague hand waving in the direction of God, what is absolute infinity?
I suspect only Cantor knows (http://en.wikipedia.org/wiki/Absolute_Infinite). I don't know why you brought it up in the first place.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 22/10/2014 03:45:36
I didn't say "a finite region of nothingness." I was referring to what I understood JD's vision of reality was. A finite region of material existence lying within a region of nothingness.
Sorry, my mistake. So you reject the idea of a 'region of nothingness'?

I'm still curious to hear your definition of nothingness and how it could be infinite (e.g. infinite in what respect?).
I truly think this discussion has become too contentious. Everyone has a right to speculate on issues which are, as yet, unproven. We should all agree to disagree.

As to your question dlorde: If the universe is finite, and nothingness lies beyond, this nothingness is infinite because it would be boundless.

This is just my view and as others also have the right to their personal views, I'll claim the right to mine as well.

Now, for all those who choose to point their finger and accuse me of being wrong, I may well be wrong but I'll take the liberty and suggest that no one here has sufficient evidence to claim infallibility concerning the true nature of the Cosmos, whether finite or infinite, we just don't have convincing evidence either way at the moment. So, everyone just knock yourselves out trying to prove your particular theme. Until better evidence is found, believe what you choose.
Title: Re: Is infinity a misconception?
Post by: dlorde on 22/10/2014 09:05:42
If the universe is finite, and nothingness lies beyond, this nothingness is infinite because it would be boundless.
We've already established that boundless doesn't imply infinite, although the reverse is true. For example, the surface of a sphere is boundless but finite, and the circumference of a circle is boundless but finite.

But how do you define this 'nothingness' you're invoking? The phrase 'lies beyond' the universe suggests something that can lie and some region it lies in. Is this just a question of phrasing? does it actually mean that there is not anything beyond the universe, i.e. there is no 'beyond'? or does it mean something different - some sort of infinite void, perhaps?

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Now, for all those who choose to point their finger and accuse me of being wrong, I may well be wrong but I'll take the liberty and suggest that no one here has sufficient evidence to claim infallibility concerning the true nature of the Cosmos, whether finite or infinite, we just don't have convincing evidence either way at the moment.
Until you explain what you mean we can't even discuss your ideas properly.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 22/10/2014 14:18:23

Until you explain what you mean we can't even discuss your ideas properly.
In simple terms; My thoughts are this:

Either the universe, "Cosmos" or what ever one chooses to define all that is and is not, is infinite. Either flat space is infinite or M-theory is our reality. In either case, the "Cosmos" is infinite.

We have already had sufficient testimony exclaiming distaste for the infinite flat space model so you are now left with M-theory to assassinate. These two models are my personal favorites, but you are free to choose your own. I refuse to argue about this any more. Enjoy.....................................
Title: Re: Is infinity a misconception?
Post by: dlorde on 22/10/2014 17:11:53
We have already had sufficient testimony exclaiming distaste for the infinite flat space model so you are now left with M-theory to assassinate.
I don't know of a reason in physics that proscribes a universe of infinite spatial extent - it would mean it was infinite at the big bang, but that's not a problem. I don't see how it could be tested though.

M-theory looks more interesting, with suggestions for testing (http://phys.org/news/2014-01-scientists-theory.html) some aspects of it, having mathematical correspondence with some interesting areas of current physics, and a wealth of options to select from - perhaps too many for comfort. The anti-de Sitter space formulation of M-theory seems topical - in that it's curved so that all points inside the spacetime are infinitely far from its boundary... unfortunately the details are beyond me.

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I refuse to argue about this any more.
OK.
Title: Re: Is infinity a misconception?
Post by: Bill S on 25/10/2014 16:35:42
I have just looked over the last page of this discussion, and there are several points to which I thought I would respond; then I thought of how much of the discussion goes round in circles.  Dlorde pointed out about the “infinite road” that we had visited it before; that’s true, but the same applies to most of the discussion. 

Most of the sticking points seem to involve the definitions of Universe, infinity and nothingness.

In another thread and a few PMs, JP and I discussed my claim that there could never have been nothing, otherwise there would still be nothing now.   He was adamant that we could not make this claim because, outside the Universe conditions could exist in which something could come from nothing.  I pointed out that “conditions” must surely be something; and although the discussion continued for some time, we never really moved beyond his saying:
“The problem with the idea that "nothing can come from nothing" is that to scientifically discuss this, we need to come up with a model, and we can't even describe "absolute nothing" scientifically (or at least I haven't seen a scientifically workable definition)”.

I think I have correctly quoted JP, but I’m sure he will say if I have not.

There is evidence in this thread that I am not the only person in the world who thinks there can never have been nothing.  If there was never nothing, then there has always been something, and that something must be eternal. 

Can we go as far as to say “I f it is eternal it is infinite”?

Nothingness should be simple to define! It should be the absence of absolutely everything/anything.  As JP pointed out, we can’t even describe nothing scientifically.  Is “the absence of everything” not a reasonable definition?

There has been much discussion about whether the Universe is finite, or infinite.  Much of this hinges on the distinction between infinite and boundless.  It would be a major achievement if we could come to an agreement on that, but let’s not ask too much. 
Title: Re: Is infinity a misconception?
Post by: dlorde on 25/10/2014 21:55:16
I too can't see how something can come from 'true' nothing (i.e. absence of anything, including spacetime). On the other hand, if the universe is closed in time (time has a beginning), what does it mean to say there's always been something...
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 25/10/2014 22:57:24
It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. The following link explains:

http://www.esa.int/Our_Activities/Space_Science/Is_the_Universe_finite_or_infinite_An_interview_with_Joseph_Silk

And for those that would argue that infinite space is an impossibility, this reputable scientist confirms that at least, it is a possibility. If it were not, the question wouldn't even have been asked; "Is the cosmos finite or infinite?"
Title: Re: Is infinity a misconception?
Post by: Bill S on 26/10/2014 00:48:33
Good article, Ethos.  I shall need to read it more than once to get my finite brain around its infinite implications.

One thing that does leap out, even on the first reading is this:

“…you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus”.

So, how do you role up an infinite sheet of anything?  Surely, to do that you would have to bring two edges together, and past, each other.  How do you find the edges of an infinite sheet?  If you could do this, would it still be infinite when you had rolled it up?

This may seem like nit-picking, but is it?  If we accept this thinking are we not subscribing to using something physically impossible as the basis for a physical theory?
Title: Re: Is infinity a misconception?
Post by: Bill S on 26/10/2014 00:55:27
Quote from: Ethos
It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. …………………….. "Is the cosmos finite or infinite?"

Not all scientists agree that “universe” and “cosmos” are synonymous. 
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 26/10/2014 02:33:29
Quote from: Ethos
It appears science has no conclusive evidence yet as to whether the universe is finite or infinite. …………………….. "Is the cosmos finite or infinite?"

Not all scientists agree that “universe” and “cosmos” are synonymous.
Point well taken Bill S, I should have said cosmos instead of universe in that sentence.
Title: Re: Is infinity a misconception?
Post by: phyti39 on 27/10/2014 17:47:52
Consulting our primary textbook the dictionary, we conclude something like this.
Infinity is not a number since it has no value. It is a relation/condition about numbers stating there is no limit to a magnitude, there is no final value. It is something NOT measurable.
The common example of the set of integers has a beginning but is 'open ended/without limit/unbounded'.
Another instance of the meaningless term is found in the definition of a limit (by mathematicians no less!).
The limit of (some sequence for x), as x approaches infinity = u.
The question is, how do you approach 'infinity'?  At night, on your tip toes, or while it's sleeping...?
It's a contradiction in terms. You can't approach 'infinity' anymore than you can approach the horizon, or the carrot on the stick, i.e. it's always 'just ahead'.
I prefer "as x increases without limit".

Interesting, all the areas influenced by this word "infinity".

"Nothing" and "existing" are mutually exclusive terms.
Dictionary [nothing]: a state of nonexistence, or the absence of any perceptible qualities
That would exclude the quality of extent.

The universe can be defined as "everything known to exist, visible and invisible", which would include the laws that regulate it.

The idea that earth gravity tends to zero as distance increases (without limit) is true only if earth is the universe (the ideal isolated experiment). In the real world the significant gravitational effects are local. and decrease  rapidly with distance. As probes leave the solar system, the dominate mass is the sun, and the earth can be ignored. In any remote location, far from any significant masses, the total gravitational effect from all mass in the universe is zero.

The expression u=1/x is a precise statement, but when x=0, it does not result in a precise answer. In fact it's defined as indeterminate, i.e. there is no answer. It should be declared illegal as it is in computer programming. Division by zero is another of those nonsensical terms that should be eliminated. You can put an unlimited (not infinite) number of zeroes into a container, but nothing will ever materialize within it. You can't make something from nothing! In the case of the gamma term from Relativity, v will never equal c for a mass, thus that condition will not occur.

The universe can consist of a finite mass, but be closed, in the manner of the spherical earth surface. You can travel indefinitely in it, but eventually will revisit some areas.

Universe (Latin) and cosmos (Greek) are interchangeable, both meaning an integrated entity consisting of everything known.

Cantor was a great illusionist.
 
The silent disclaimer: All things mathematical do not correspond to physical reality.
 
Title: Re: Is infinity a misconception?
Post by: dlorde on 27/10/2014 22:43:31
Welcome phyti39, and congratulations on the clarity and succinctness of your first post. I think I agree with pretty much all of it...  [:D]
Title: Re: Is infinity a misconception?
Post by: Bill S on 28/10/2014 03:49:09
hi phyti39, I'm with dlorde here.  Hope to see more of you in TNS.
Title: Re: Is infinity a misconception?
Post by: phyti39 on 28/10/2014 16:49:25
Thank you for the type of welcome I wasn't expecting, considering my past forum experiences.
I'm just a seeker of truth.
Title: Re: Is infinity a misconception?
Post by: Bill S on 28/10/2014 21:42:46
Quote from: Phyti39
You can't approach 'infinity' anymore than you can approach the horizon, or the carrot on the stick, i.e. it's always 'just ahead'.

In fact, it’s always infinitely far ahead.

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[nothing]: a state of nonexistence, or the absence of any perceptible qualities

Personally, I would exclude “perceptible”.  I would say it’s the absence of anything, perceptible or otherwise.

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The universe can be defined as "everything known to exist, visible and invisible", which would include the laws that regulate it.
 

I would go with that, but would say that this might not include the “cosmos”, but that’s another issue.

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Universe (Latin) and cosmos (Greek) are interchangeable

Originally, I would agree, but I think the meanings have to some extent evolved.  See #116 in this thread.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 28/10/2014 22:15:43
Here is another article which deserves consideration regarding the size and scope of our universe. If you'll notice, the author speculates that while the universe is expanding, this observed expansion is logically moving into new territory of infinite dimension. It is like so many other ideas, not yet proved, but is worthy of reading nevertheless.


http://phys.org/news/2014-10-universe-older.html
Title: Re: Is infinity a misconception?
Post by: JohnDuffield on 29/10/2014 14:06:59
Interesting. But I didn't understand why space had to be expanding into another medium. Space is the medium. How can there be some other medium? Does not parse. 
Title: Re: Is infinity a misconception?
Post by: dlorde on 29/10/2014 14:48:00
Interesting. But I didn't understand why space had to be expanding into another medium. Space is the medium. How can there be some other medium? Does not parse. 
Yes, that puzzled me too.
Title: Re: Is infinity a misconception?
Post by: yor_on on 31/10/2014 19:48:38
Nah, or just maybe?
If you look at the universe as a equilibrium you can pick two choices, a dynamically changing equilibrium, or a static. If we now give a constant to a dynamically changing universe, will it not still be a constant? Assuming the universe have a constant balance.

the third assumption is one in where you have dynamically changing universe in where there can't be constants. But that is not what we see. So I think that link is wrong, if it assume "that Planck's constant is not a pure constant at all but a cosmological variable, a point for which some supported was reported in 2013 by Seshavatharam and Lakshminarayana."

My own outlook is that constants are here to stay, they are what define this universe.
Title: Re: Is infinity a misconception?
Post by: phyti39 on 31/10/2014 20:00:00

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Universe (Latin) and cosmos (Greek) are interchangeable

Originally, I would agree, but I think the meanings have to some extent evolved.  See #116 in this thread.
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#116
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.
This looks more like semantics than science.
We can’t have complete knowledge of definition 1.
The observable universe and the perceptual universe (spacetime) are contained in def.1.
Definition 3 is redundant and meaningless.
The intended purpose of noting one Latin and the other Greek is to show they are different cultural variations for the same entity, all that is known to exist.

Title: Re: Is infinity a misconception?
Post by: chiralSPO on 06/11/2014 22:33:50
I had originally posted this as a reply on another thread, but it probably belongs in this one:

"If the universe is actually globally homogeneous and isotropic, that means that each point is equivalent to every other point within the universe. This type of symmetry can easily be attained by a sphere, in which any point can be transformed into any other point by a simple rotation of the sphere. If we accept that the universe is flat, it cannot be spherical. A flat plane can also satisfy these conditions (homogeneous and isotropic), but only if it is infinite--in this case any point can be transformed into any other point by translation.

As a chemist, though, I have to point out that this is analogous to our theoretical models of crystals. There are 219 (or 230) space groups--the types of symmetry a crystal structure can have. In each there is an assumption that the entire crystal can be translated in one direction or another to line up with itself again. These models are extremely accurate in their predictions of the properties of all types of crystals. However, the models assume an infinite crystal lattice, which we know is not an accurate depiction of any crystal ever observed/characterized (most of those studied are less than 1mm on a side, >1000000 atoms across, though there are single crystals as large as a meter on a side, and possible even larger). It also turns out that while the models work very well at predicting what goes on inside a crystal, they are very poor models of the boundaries of crystals, which we invoke other models for.

My point is, from the viewpoint of an atom near the center of a crystal, the whole universe is an infinite perfect crystal--the model works perfectly as far as the atom can "see" and beyond. But eventually there is a boundary that is completely inexplicable given a perfect crystal model.

The observable universe appears to be flat, homogeneous and isotropic. But in my opinion, there could very well be inhomogeneity, anisotropy or curvature beyond our observable bubble."
Title: Re: Is infinity a misconception?
Post by: Bill S on 06/11/2014 22:52:12
Quote from: ChiralSPO
My point is, from the viewpoint of an atom near the center of a crystal, the whole universe is an infinite perfect crystal--the model works perfectly as far as the atom can "see" and beyond. But eventually there is a boundary that is completely inexplicable given a perfect crystal model.

The observable universe appears to be flat, homogeneous and isotropic. But in my opinion, there could very well be inhomogeneity, anisotropy or curvature beyond our observable bubble."

Interesting point.  We are assured that cosmology would be unworkable without these assumptions, so I suppose it is reasonable to make them, and work with them.  Perhaps trouble comes only when peoples forget that they are assumptions and start treating them as if they were established facts.   
Title: Re: Is infinity a misconception?
Post by: alancalverd on 07/11/2014 07:32:11

Quote

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.
Definition 3 is redundant and meaningless.

Not at all. 1 is the set of all sets, 2 is the finite set bounded by  the Schwarzchild limit, 3 is (1 - 2).
Title: Re: Is infinity a misconception?
Post by: allan marsh on 07/11/2014 22:10:05
If there is zero then there must inevitably be infinity
It took the Romans and those with runic tools to produce zero
Now it is 2014 and infinity is real
Title: Re: Is infinity a misconception?
Post by: Bill S on 07/11/2014 23:18:03
Quote from: Allan
If there is zero then there must inevitably be infinity

I'm not sure that I follow the logic of that.
Title: Re: Is infinity a misconception?
Post by: chiralSPO on 07/11/2014 23:42:59
I agree. Zero (absolute zeros) and infinity go hand in hand.
Title: Re: Is infinity a misconception?
Post by: Ethos_ on 08/11/2014 00:46:14
I agree. Zero (absolute zeros) and infinity go hand in hand.
I agree as well.........................And backtracking to earlier posts about nothingness, what else is nothingness but Zero? When one visualizes the "Universe" as finite, then that "nothingness" which lies beyond being nothingness is also part of the "Cosmos". Where the "Universe" is finite, the "Cosmos" is infinite.
Title: Re: Is infinity a misconception?
Post by: alancalverd on 08/11/2014 12:05:19
It's true that zero and infinity are associated, since 1/x→∞ as x→0.

But I don't think the Romans had a useful concept of zero. This seems to have arrived from India via Arabic mathematicians, who had a symbol for zero, that is lacking in Roman numerals.