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Author Topic: Is infinity what you get when youu place to plan mirrors parallel to each other?  (Read 9222 times)

Offline Foolosophy

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So the amount of light remaining in the reflecting beam approaches ZERO as the "n" goes off to infinity.

And as we know it will take an infinite anoutn of time to acheive this

So the remaining light will never completely vanish to zero
 

Offline JP

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In theory, yes.  In practice, you'll eventually have so little light that you can't hope to measure it any more.
 

Offline JP

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This also ties in very closely with what Soul Surfer put very well here:

http://www.thenakedscientists.com/forum/index.php?topic=36266.msg336978#msg336978

There's a lot of processes in nature in which things decrease exponentially so that they "never" stop decreasing.  In practice, there's a point at which you can't really see them anymore, since the thing you're trying to measure has become too small for your measuring equipment.
 

Offline Foolosophy

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In theory, yes.  In practice, you'll eventually have so little light that you can't hope to measure it any more.

true - but it can never be equal to ZERO (exactly)
 

Offline yor_on

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ahh yes, forgot about that one. But may I point out that they can't exist either, those perfect mirrors :)

So I would like to point out that the universe in which those mirrors are situated will be a 'perfect' one, me as its master, working through eternity..

Yes, I'm building it as we write..
 

Offline Bill S

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Quote
true - but it can never be equal to ZERO (exactly)

It's Zeno's paradox, again, but when the bouncing light gets down to one photon, any further reduction must result in zero.   
 

Offline Bill S

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Quote from: JP
In practice, all you're really doing here is using the bounces to time the age of the universe, so if the universe's age isn't infinite, this won't form infinite images.

Interesting point,JP.  The corollary of this is that if the Universe's age is not infinite, which seems to be the case, it can never become infinite, even though it may be boundless.
 

Offline yor_on

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:)

A new one to me, not bad either as we talk about 'SpaceTime'.
But it build on the premise that 'times arrow' disappear as entropy takes its toll.
And also on that there is no such concept as a 'time' without an arrow.

As if that was, then it doesn't really matter if we have an arrow or not. It will still be 'there', whatever that may be :)
 

Offline QuantumClue

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Xeno's paradox indeed, Bill.

However the paradox is not a paradox anymore.
 

Offline JP

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Quote from: JP
In practice, all you're really doing here is using the bounces to time the age of the universe, so if the universe's age isn't infinite, this won't form infinite images.

Interesting point,JP.  The corollary of this is that if the Universe's age is not infinite, which seems to be the case, it can never become infinite, even though it may be boundless.

Unless the universe was infinite to begin with, which is apparently consistent with the big bang.  (Don't ask me for proof, since I'm not a cosmologist.)  The general idea I've read is that the universe could be hot and dense, but still infinite in size just after the big bang.

But in general, I think you're right that it isn't possible to build something infinite in size from a bunch of finite steps. 
 

Offline yor_on

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JP, its a paradox in more than one way, what you are doing is to define 'discrete events' namely the 'light clock ticks'. Then you state that as soon there are 'discrete events' there can be no infinity.

That should mean that as soon we allow the concept of a 'discrete event' we disallow the concept of infinity. So either we have 'discrete events' or we have infinities, But we can't have both :)

Like it:)

It seems like a debate sailing up here ::))
 

Offline JP

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You're right, Yor_on.  I think my original post was imprecise.

What I was trying to say is that you can't get an infinite set of things by a process that adds one object to the set at a time, when each step takes finite time and the universe is only 14 billion years old... This is a physical limitation, not a mathematical one.  In this case, each bounce generates one more image, but each bounce takes finite time, so you can't generate infinite images in finite time.
 
You can certainly form an infinite set of things from discrete elements.  For example, there are infinitely many natural numbers (i.e. 1,2,3,4,5,...), but these are clearly discrete elements.  The trick is that I just constructed this set theoretically--in other words, I didn't physically list each number.  If I tried to write out, or have a computer compute, each natural number, it would never finish since that would take infinite time.
 

Offline yor_on

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I know JP :)

It was just such an opportunity for a tease.
Not everyday one get a chance with you :)

Not that you don't have humor, far from it..

Eh..

That sounds?
A double negation?

Let me state this way. I know you have a humor..
Thank God.
 

Offline Foolosophy

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The Phantom Scientist vanishes into the abyss of silence once again
 

Offline Bill S

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Quote from: JP
You can certainly form an infinite set of things from discrete elements.  For example, there are infinitely many natural numbers (i.e. 1,2,3,4,5,...), but these are clearly discrete elements.

Here comes the infinite series, again! ::)  You are right, of course, if you tried to write down, compute or do anything practical with these numbers you would never reach infinity.  We can say that the natural numbers (etc.) are boundless; I just think its unfortunate that we use the word infinite, rather than boundless, in this context. 
 

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