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Author Topic:   Is Infinity Real?
nwr
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Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 16 of 48 (599145)
01-05-2011 8:32 AM
Reply to: Message 13 by slevesque
01-05-2011 3:53 AM


slevesque writes:
But Zeno's paradox is only called so because it is counter-intuitive (veridical paradox), since it is solved through Calculus in Mathematics.
There are still people who argue that the calculus does not solve the problem.
The real problem is that we construct abstract models of reality, and do our computations in those abstract models. The mistake is to assume that the model is reality. Zeno's paradox was due to a model that didn't fit well enough. It's a good illustration of why we need empirical evidence, and cannot just go by our theoretical deductions.
slevesque writes:
I think the paradox of infinite regression not being possible falls into the category falsidical paradoxes.
But it is still based on an abstract model. And whenever the model talks about the infinite, it has gone beyond what has been tested empirically.
slevesque writes:
But if the premises are true and no fallacy is involved, then there is no place for skepticism, unless you put into question the laws of logic.
The laws of logic don't apply to reality. They apply to the human constructs that we use to model and describe reality. The logic can be done correctly, yet reach wrong conclusions, if it is used with respect to a model that does not fit well enough.

Jesus was a liberal hippie

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Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 17 of 48 (599161)
01-05-2011 9:51 AM
Reply to: Message 16 by nwr
01-05-2011 8:32 AM


The laws of logic don't apply to reality. They apply to the human constructs that we use to model and describe reality. The logic can be done correctly, yet reach wrong conclusions, if it is used with respect to a model that does not fit well enough.
I guess that's why slevesque said "if the premises are true".

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slevesque
Member (Idle past 4641 days)
Posts: 1456
Joined: 05-14-2009


Message 18 of 48 (599204)
01-05-2011 2:49 PM
Reply to: Message 14 by cavediver
01-05-2011 5:26 AM


I have no problem with the mathematics of it. On paper time, past and future, can be infinite and the math will all work out.
However, when we translate this to reality, here is the problem I see. Future time can be theoretically infinite, but in fact it never truly will be. We will advance in time and it will be an ever growing number yet we won't ever reach infinity, ie we will only tend towards it.
Similarily, past time is an ever growing number as time passes by, and in this regards also tends towards infinity. Yet to say that it is infinite means that it no longer tends towards infinity, but in a sense that it has reached it.
It's the difference then from the potential of being able to go on forever, and that we have already been going on forever.
I hope it's clear cause I don't have the feeling it isn't. As I said, I don't have any problem when discussing infinite time mathematically, only when we are supposed to apply it to reality.

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AdminSlev
Member (Idle past 4641 days)
Posts: 113
Joined: 03-28-2010


Message 19 of 48 (599205)
01-05-2011 2:57 PM
Reply to: Message 16 by nwr
01-05-2011 8:32 AM


There are still people who argue that the calculus does not solve the problem.
I would guess that they are wrong.
The real problem is that we construct abstract models of reality, and do our computations in those abstract models. The mistake is to assume that the model is reality. Zeno's paradox was due to a model that didn't fit well enough. It's a good illustration of why we need empirical evidence, and cannot just go by our theoretical deductions.
Zeno's paradox is due to a false premise: An Infinite sum cannot give a finite number. Calculus showed that this premise was false.
The laws of logic don't apply to reality. They apply to the human constructs that we use to model and describe reality. The logic can be done correctly, yet reach wrong conclusions, if it is used with respect to a model that does not fit well enough.
How would you define ''a model that does not fit well enough'' ? Would it not simply be a model that is missing some premises, or that some premises are false ? If this is the case then you are still well within the boundaries of logical thinking.
An argument that uses true premises and involves no fallacy will automatically give you a true conclusion, wether it concerns reality or abstract thought.
AbE I wrote it with the wrong ID and for some unknown reason I cannot edit it back.
AbE2 I don't want to be misunderstood here. I think I can accept that some abstract models do not apply when translated into reality. But this has nothing to do with logic, rather, it would be because of the difference between the nature of abstract thought and the nature of reality. (This is in fact what I am saying in my previous reply to CD)
Edited by AdminSlev, : No reason given.
Edited by AdminSlev, : No reason given.

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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 20 of 48 (599211)
01-05-2011 3:59 PM
Reply to: Message 19 by AdminSlev
01-05-2011 2:57 PM


slevesque writes:
Zeno's paradox is due to a false premise: An Infinite sum cannot give a finite number. Calculus showed that this premise was false.
That's one way of looking at it. The other way is to see it as saying that movement requires infinitely many stages, and we can only carry out a finite number of those.
slevesque writes:
How would you define ''a model that does not fit well enough'' ? Would it not simply be a model that is missing some premises, or that some premises are false ? If this is the case then you are still well within the boundaries of logical thinking.
We don't apply logic to reality. We apply it to our sentences that we use to describe reality. Our descriptions are generally imperfect and incomplete.

Jesus was a liberal hippie

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Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 21 of 48 (599240)
01-05-2011 11:56 PM
Reply to: Message 18 by slevesque
01-05-2011 2:49 PM


It's the difference then from the potential of being able to go on forever, and that we have already been going on forever.
Yes, but why not?
If science has taught us anything, it's that we can't rule stuff out a priori just 'cos it makes our little human brains boggle.
Think of time as being like space, and imagine viewing it sub specie aeternitatis --- a God's-eye view if you will. From that point of view, wouldn't it look even odder if it just started at some point?

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slevesque
Member (Idle past 4641 days)
Posts: 1456
Joined: 05-14-2009


Message 22 of 48 (599244)
01-06-2011 12:41 AM
Reply to: Message 21 by Dr Adequate
01-05-2011 11:56 PM


Yeah I juste want to make it clear: This is a tentative position I have right now, I have no strong reason to rule anything out a priori, only my intuition on the subject.
But I would see time as analog not to space, but rather to moving through space. Saying past time is infinite would them be like saying something moving through space has come from an infinitely far distance.

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Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 23 of 48 (599260)
01-06-2011 4:40 AM
Reply to: Message 22 by slevesque
01-06-2011 12:41 AM


But I would see time as analog not to space, but rather to moving through space.
In this analogy, what would space represent?
Surely it is the passage of time which is like moving through space, and time itself is like space.
Saying past time is infinite would them be like saying something moving through space has come from an infinitely far distance.
I think it would be like saying that there was an infinitely long line embedded in the universe.

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slevesque
Member (Idle past 4641 days)
Posts: 1456
Joined: 05-14-2009


Message 24 of 48 (599351)
01-06-2011 4:13 PM
Reply to: Message 23 by Dr Adequate
01-06-2011 4:40 AM


In this analogy, what would space represent?
Surely it is the passage of time which is like moving through space, and time itself is like space.
Yeah this is where it's tricky, can time exist without it 'passing' ? Can we really dissociate 'passage of time' and time like that ? Intuitively no, and this is why I find it better to compare passage of time with moving through space, instead of just space and time.
Because I really see it like this. In the case of space, if it is infinite, it means to me that I could potentially travel for as long as I want, tending towards infinity without ever in reality reaching it.
Same applies to future time. I (meaning the energy composing me) can potentially live forever, but never actually will have lived on forever.
But past time being infinite, means that it is no longer just 'potential' but reality. It means I have actually lived on forever.

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Dr Adequate
Member (Idle past 285 days)
Posts: 16113
Joined: 07-20-2006


Message 25 of 48 (599359)
01-06-2011 5:25 PM
Reply to: Message 24 by slevesque
01-06-2011 4:13 PM


Yeah this is where it's tricky, can time exist without it 'passing' ? Can we really dissociate 'passage of time' and time like that ? Intuitively no, and this is why I find it better to compare passage of time with moving through space ...
In that case we are not in disagreement.
If we say that passage of time is like passage through space, then to the extent that this is true and meaningful (and I have my doubts about that) we have to say that time is the analog of space.
But past time being infinite, means that it is no longer just 'potential' but reality. It means I have actually lived on forever.
No, it doesn't. There is no way in which this relates to you or me personally. The proposition that past time is infinite does not conflict with the statement that I was born in 1974 any more than the proposition that 1973 existed conflicts with that same statement. Why would it?
The proposition that the past is infinite does not contradict the proposition that certain specific things had beginnings.

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Phat
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Posts: 18262
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.1


Message 26 of 48 (599363)
01-06-2011 5:57 PM
Reply to: Message 3 by anselm
01-03-2011 11:03 AM


Why is there something rather than nothing?
Just out of curiosity, Anselm, did you get any of your material for this topic here?


'When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean - neither more nor less.'
Lewis Carroll

* * * * * * * * * *
Half of the harm that is done in this world is due to people who want to feel important.~T.S.Eliot

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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 27 of 48 (599398)
01-07-2011 4:42 AM
Reply to: Message 24 by slevesque
01-06-2011 4:13 PM


Yeah this is where it's tricky, can time exist without it 'passing' ? Can we really dissociate 'passage of time' and time like that ? Intuitively no...
Intuitive or not, we have to. The one theory we have that teaches us the nature of "time" has no concept whatsoever of "passage of time" - we have time as a dimension and proper time as a distance measure. There is no universal clock that ticks away some universal time, by which we all move forward through time, our conciousnesses all sharing the same "now". "Passage of time" is, as far as I can tell, simply conciousness itself - and hence wholely individual and subjective.
And so there is no concept as having to wait an infinite amount of time for "now" to arrive in a Universe with an infinite past. You experience "passage of time" at your place in the Universe, and no where else. This place begins around your birth and ends around your death.

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Straggler
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Posts: 10333
From: London England
Joined: 09-30-2006


Message 28 of 48 (599446)
01-07-2011 1:45 PM
Reply to: Message 27 by cavediver
01-07-2011 4:42 AM


Entropy and the arrow of time?
Cavey writes:
The one theory we have that teaches us the nature of "time" has no concept whatsoever of "passage of time" - we have time as a dimension and proper time as a distance measure.
To throw in a Penrose-ism - What about entropy as pertaining to the arrow of time?
What are current thoughts on that?

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Noetherian Atheist
Junior Member (Idle past 4553 days)
Posts: 7
From: London
Joined: 08-19-2010


Message 29 of 48 (599461)
01-07-2011 3:59 PM
Reply to: Message 1 by anselm
01-02-2011 1:24 PM


Just a couple of points
I think you misunderstand Hilbert's Infinite Hotel Paradox. The point is, in mathematics a "paradox" is just a fancy way of describing a contradiction. When you reach a contradiction, logic demands that you back-track through your reasoning to find an error (incorrect assumption or deduction). In Hilbert's case it was the assumption that you can do normal arithmetic with the mathematical concept of infinity. This led to the development of transfinite numbers where things work rather differently etc. But there is no real problem here, and it certainly does not demostrate that infinity doesn't exist in some sense.
However, to adress you question directly: I'm not sure. (And I'm a mathematician.) I can think of 2 good candidates for examples of an "infinity" in reality: either time might be of infinite "length" (as argued elsewhere); or the infinite divisibility of space there could provide an example of an infinite collection. Not sure if, in reality, space is made up of infinitely many infinitessimal "bits" or if there's a minimal size to things. In maths, a line does have an infinite number of points along it (even in a line of finite length - see Zeno's Paradox). I suspect there is some minimum size to things, but completely without foundation of course.

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Rrhain
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Posts: 6351
From: San Diego, CA, USA
Joined: 05-03-2003


Message 30 of 48 (599498)
01-07-2011 11:35 PM
Reply to: Message 20 by nwr
01-05-2011 3:59 PM


nwr writes:
quote:
The other way is to see it as saying that movement requires infinitely many stages, and we can only carry out a finite number of those.
And that would be a false premise. Each stage takes less and less time such that you can carry out an infinite number of them in a finite time.
The original problem was brought up as a means to point out how the way in which you count something can have an effect on the cardinality of the set which you calculate, but applies here:
For this thought experiment, we must assume a few things:
1) Superman and Captain Marvel both exist and can move any amount of speed in any amount of time.
2) There are an infinite number of coconuts in a pile, all numbered: 1, 2, 3, ...
3) There is a pit that can hold them all.
At noon, they decide to play a game. Captain Marvel throws coconuts numbered 1 and 2 into the pit. Superman flies in, grabs coconut number 1, and tosses it out of the pit.
They then sit around for half an hour, discussing their various exploits, when at 12:30, Captain Marvel throws in coconuts 3 and 4. Superman flies in, grabs coconut number 2, and tosses it out of the pit.
They repeat the process, only waiting 15 minutes this time. In go 5 and 6, out comes 3. This process repeats, each time halving the amount of time they wait between tossing coconuts.
When 1 pm comes around, and 1 pm always comes around, how many coconuts are in the pit?
The answer, of course, is none of them. They have all been tossed out. Why? Because for every coconut you can identify, I can give you a precise time when it was tossed out of the pit. Number 1 came out at noon, number 2 at 12:30, number 3 at 12:45, etc., etc.
And thus, an infinite process can be carried out in a finite amount of time.
What Xeno had wrong is that yes, you have to cover an infinite number of half-distances in order to reach the end, but each of those half-distances takes half as much time to carry out.
If Xeno had had the tools of analysis (not so much calculus, per se), he would have been able to see that his infinite sum converged.

Rrhain

Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.

Minds are like parachutes. Just because you've lost yours doesn't mean you can use mine.

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