Is infinity a misconception?

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #50 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #51 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #52 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?

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #53 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.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #54 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #55 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

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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #56 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.   

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #57 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.

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #58 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.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #59 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?

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #60 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?

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Offline alancalverd

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Re: Is infinity a misconception?
« Reply #61 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. 
helping to stem the tide of ignorance

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #62 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.
« Last Edit: 27/09/2014 15:10:03 by yor_on »
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Offline Bill S

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Re: Is infinity a misconception?
« Reply #63 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #64 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.   [:(]
« Last Edit: 27/09/2014 16:52:25 by Bill S »

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Offline alancalverd

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Re: Is infinity a misconception?
« Reply #65 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.
helping to stem the tide of ignorance

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #66 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?




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Offline JohnDuffield

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Re: Is infinity a misconception?
« Reply #67 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #68 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. 

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #69 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #70 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.


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Offline chiralSPO

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Re: Is infinity a misconception?
« Reply #71 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?

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #72 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #73 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]
« Last Edit: 27/09/2014 23:15:48 by Bill S »

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #74 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]

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #75 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #76 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.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #77 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #78 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]

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #79 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.

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Offline evan_au

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Re: Is infinity a misconception?
« Reply #80 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 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #81 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?

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #82 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.
« Last Edit: 29/09/2014 18:59:00 by yor_on »
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Offline Bill S

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Re: Is infinity a misconception?
« Reply #83 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #84 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.   

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Offline chiralSPO

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Re: Is infinity a misconception?
« Reply #85 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).

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #86 on: 01/10/2014 00:49:58 »
If the universe was flat then Sean Carroll would not disagree with me.

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Offline yor_on

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Re: Is infinity a misconception?
« Reply #87 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.
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Offline yor_on

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Re: Is infinity a misconception?
« Reply #88 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'
« Last Edit: 01/10/2014 18:11:33 by yor_on »
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Offline Bill S

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Re: Is infinity a misconception?
« Reply #89 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #90 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. 

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #91 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.

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Offline jeffreyH

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Re: Is infinity a misconception?
« Reply #92 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.

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #93 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? :)

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #94 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?



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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #95 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.

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #96 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. 

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Offline Bill S

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Re: Is infinity a misconception?
« Reply #97 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.   

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #98 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

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Offline PmbPhy

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Re: Is infinity a misconception?
« Reply #99 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?