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Author Topic: Is infinity an illusion?  (Read 68363 times)

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #175 on: 30/09/2013 00:56:32 »
There has to be a limit just because of the size of a finite universe, if that is what we are in.
If...

Even in the infinite situation you would need a proportionally larger data store than available to represent the information. This would mean that the representational system would have to contain the universe and not the other way round. I know this sound very absurd but if you think about it long enough you will see why.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #176 on: 01/10/2013 19:45:56 »
Quote from: jeffreyH
There has to be a limit just because of the size of a finite universe, if that is what we are in. There will be a physical limit past which a numeric cannot be represented as it would require more information than the physical universe can contain.

We may be able to make good arguments for a finite Universe, but it seems quite reasonable to suggest that it could be “embedded” in an infinite cosmos.
 

Offline scienceguy123

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Re: Is infinity an illusion?
« Reply #177 on: 01/10/2013 20:57:07 »
Infinity, I believe is an illusion because it really is everything and anything. For example 1 can be infinity and so can 50. I believe infinity is just the name for all the nameless numbers out there. So any number can be infinity
 

Offline syhprum

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Re: Is infinity an illusion?
« Reply #178 on: 01/10/2013 21:25:59 »
During the war the propaganda ministry operated a ex USA 600Kw radio station about 30 miles from me with a Crystal receiver, a large antenna and a sensitive speaker one could hear this OK with no batteries
 

Offline scienceguy123

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Re: Is infinity an illusion?
« Reply #179 on: 02/10/2013 00:12:49 »
The universe cant be infinity. It either repeats over and over which means that there is infinite copies of the universe or that is is expanding so fast that we will never know if it is in fact infinity. If you tried to see the end of the universe you wouldn't be able to because your eyes perceive things a little slower than the speed of light and the universe would be moving faster than light.
 

Offline scienceguy123

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Re: Is infinity an illusion?
« Reply #180 on: 02/10/2013 00:19:31 »
Nothing tangible is truly infinite, numbers for example are and aren't tangible. They are tangible in the essence that they are the amount of something and like i said, nothing is infinite, but as a written or verbal number, it is in fact infinite. This is of course what i believe in. Nothing tangible is infinite it only has high numbers that dont have names yet, and since we don't know the words, but we know that they are there we call it infinite because we don't know when and if it ends. Am i confusing you?  ???
 

Offline JP

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Re: Is infinity an illusion?
« Reply #181 on: 02/10/2013 14:10:15 »
Infinity, I believe is an illusion because it really is everything and anything. For example 1 can be infinity and so can 50. I believe infinity is just the name for all the nameless numbers out there. So any number can be infinity

With respect, Scienceguy, this isn't true.  Infinity can be used in different contexts (as has been discussed a few times over the course of this very long thread), but it does have definitions.  A very important part of all those definitions is that it is not simply a number.  It is more like a concept of something so big that you can't pick any number that is bigger than it.  Unnamed numbers are simply unnamed, but since they're numbers, they have a numerical value (even if you don't know it).  You can always add one to anything with a numerical value, making a bigger number, so therefore it can't be infinity.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #182 on: 02/10/2013 15:32:47 »
Quote from: JP
You can always add one to anything with a numerical value, making a bigger number, so therefore it can't be infinity.


For some time I have felt that I was alone in saying you can’t add anything to infinity.  Could it be that I am, in fact, in quite illustrious company? :)

Could we have reached a degree of consensus on three points?

1.  Infinity is not a number.

2.  Infinity cannot be measured.

3.  You cannot add anything to infinity.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #183 on: 02/10/2013 16:35:44 »
I agree with points 1 and 3, but...

Point 3 is redundant with point 1 and the definition of addition.  I agree with it, but you don't need to list it separately.  Addition is defined to take two numbers as input and produce a single number as output.  Since infinity is not a number, you can't use it as input into the "addition" operation.  (You can imagine that addition is a compute program that takes numbers--if you input "infinity" it would tell you "Error: Please input only numbers").  Similarly, you can't subtract, multiply or divide with infinity, but these don't have to be listed separately from #1.  In fact, any operation that requires numbers as inputs can't be performed if you try to input infinity.

I would also argue that #2 is meaningless unless you precisely define measure.  In the sense of mathematics, you can calculate the measure an infinite set, for example:  http://en.wikipedia.org/wiki/Measure_(mathematics
« Last Edit: 02/10/2013 16:49:29 by JP »
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #184 on: 02/10/2013 17:55:12 »
I suggest that Hilbert's Hotel means point 3 is open to interpretation. Hilbert's Hotel is an infinite hotel with a guest in every room, i.e. fully occupied. But when a new guest arrives, she can be accommodated by moving each guest to the next highest room. This can be repeated for any finite number of new arrivals. An infinite number of arrivals can be accommodated by moving every guest, from room n to room 2n, freeing up an infinite number of odd numbered rooms...

Is adding guests to a fully occupied infinite hotel 'adding' to infinity?
 

Offline JP

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Re: Is infinity an illusion?
« Reply #185 on: 02/10/2013 18:16:29 »
Is adding guests to a fully occupied infinite hotel 'adding' to infinity?

Good point and it comes back to the precision of definitions.  Addition of real (or complex numbers) cannot be performed on infinity for the reasons I stated.  The idea of adding elements to a set CAN be performed on infinite sets without a problem, which is (part of) what's going on in Hilbert's hotel. 
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #186 on: 02/10/2013 20:59:48 »
... The idea of adding elements to a set CAN be performed on infinite sets without a problem, which is (part of) what's going on in Hilbert's hotel. 
You don't want to know the rest of what goes on in Hilbert's hotel - I think there's going to be a TV series, which is likely to drag on ad infinitum, like Lost...
 

Offline JP

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Re: Is infinity an illusion?
« Reply #187 on: 02/10/2013 21:50:35 »
You can check out any time you like, but you can never leave?
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #188 on: 02/10/2013 22:44:18 »
If Hilbert's hotel is infinite then it must contain everything within itself. Therefore all the new guests must already be in the lobby. If the number of new guests is infinite and the number of residents is infinite, then, both of these quantities being infinite and outside any numerical system they CAN be added together.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #189 on: 02/10/2013 23:21:57 »
If Hilbert's hotel is infinite then it must contain everything within itself. Therefore all the new guests must already be in the lobby. If the number of new guests is infinite and the number of residents is infinite, then, both of these quantities being infinite and outside any numerical system they CAN be added together.

That's also not quite right.  If the hotel is the set of natural numbers, it's infinite and all slots are filled.  Any real, non-natural number can come along and be added to the set.  3.1, 3.2, 3.3 can all jump into the hotel.  There would likely be a problem if the (uncountably infinite) set of real numbers wanted to enter the (countably infinite) hotel--a mathematician could probably clarify that one in detail.  But suffice it to say that adding sets with infinite elements doesn't follow intuitive rules.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #190 on: 02/10/2013 23:46:28 »
If Hilbert's hotel is infinite then it must contain everything within itself. Therefore all the new guests must already be in the lobby.
No, that doesn't follow at all. Only the number of rooms is infinite (and consequently the number of occupants). New arrivals come from outside the hotel, where there is an infinite supply of the homeless (that remains infinite, even when an infinite number of them have been housed in Hilbert's hotel).
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #191 on: 03/10/2013 03:19:46 »
I suspect that David Hilbert had a sense of humour, and that he proposed the hotel idea just to see how many highly intelligent people would take it seriously and use it to support arguments about the physical world, in which it makes no sense at all.  The only reason it appears to work is that you could never stop moving guests to higher number rooms; so you cannot actually accommodate more than the infinite number of guests you had to start with. 

You might argue that you would have eternity in which to perform the manoeuver, but in eternity you would already have done this an infinite number of times, and since there seems to be a distinct possibility that you cannot add to infinity, how can you perform the manoeuver again?
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #192 on: 03/10/2013 03:24:09 »
I suspect that David Hilbert had a sense of humour, and that he proposed the hotel idea just to see how many highly intelligent people would take it seriously and use it to support arguments about the physical world, in which it makes no sense at all.  The only reason it appears to work is that you could never stop moving guests to higher number rooms; so you cannot actually accommodate more than the infinite number of guests you had to start with. 

You might argue that you would have eternity in which to perform the manoeuver, but in eternity you would already have done this an infinite number of times, and since there seems to be a distinct possibility that you cannot add to infinity, how can you perform the manoeuver again?

I better stop playing now.
 

Offline yor_on

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Re: Is infinity an illusion?
« Reply #193 on: 03/10/2013 10:52:01 »
K. Assume that there is a way to be conscious without a arrow Dlorde, and there I used a 'quantum computer' as a analogue. What defines consciousness? linear time? If you now had a way, as those mysterious men and women meditating sometimes are depicted as, to experience the universe and all in a 'instant', as a gestalt?

Or must a arrow be there, for consciousness to exist?

that's a pretty nice question i think :)
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #194 on: 03/10/2013 11:31:01 »
Or must a arrow be there, for consciousness to exist?
If consciousness is a process, and all the indications are that it is, then, like all other physiological processes, it is driven by the arrow of time, entropy gradients. In a philosophical sense, consciousness is the realisation of awareness and the progression of events, which are temporal phenomena.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #195 on: 03/10/2013 14:39:21 »
I suspect that David Hilbert had a sense of humour, and that he proposed the hotel idea just to see how many highly intelligent people would take it seriously and use it to support arguments about the physical world, in which it makes no sense at all.  The only reason it appears to work is that you could never stop moving guests to higher number rooms; so you cannot actually accommodate more than the infinite number of guests you had to start with. 

You might argue that you would have eternity in which to perform the manoeuver, but in eternity you would already have done this an infinite number of times, and since there seems to be a distinct possibility that you cannot add to infinity, how can you perform the manoeuver again?


I suspect his point was to show that intuitive thinking doesn't apply to the mathematics of infinite sets.  I doubt he meant anyone to take it seriously as something that physically exists.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #196 on: 03/10/2013 15:31:27 »
Quote from: JP
I doubt he meant anyone to take it seriously as something that physically exists.

Precisely. Sadly, it seems to have suffered from the same sort of torsion as Schrödinger’s “cat in a box” example. 

By now, I should know better than to include more than one point in a single post.  Some people never learn. :) So I’m going to have another go with:
 
“You might argue that you would have eternity in which to perform the manoeuvre, but in eternity you would already have done this an infinite number of times, and since there seems to be a distinct possibility that you cannot add to infinity, how can you perform the manoeuvre again?”
 

Offline JP

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Re: Is infinity an illusion?
« Reply #197 on: 03/10/2013 17:16:07 »
I think this thread would really benefit from being split into two: one to address the mathematical aspects of infinity and one to deal with the use of infinity in physics (including whether the universe can be infinite, space can be infinitely subdivided, etc.)

I'm going to stick to mathematics in this thread, since it's too confusing to mix the two.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #198 on: 03/10/2013 21:38:07 »
Quote from: JP
I think this thread would really benefit from being split into two:

I agree, but experience says that “infinity in physics” tends to drift quickly into the mathematical type.  Perhaps I have a reputation (probably justified) as an infinity crackpot.  I am reluctant to start another thread in the wake of this protracted effort.

As an experiment, I posted the same OP, at the same time,  in three forums, by far the most encouraging response has been in TNS.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #199 on: 04/10/2013 16:25:47 »
It has to--mathematics it he language of physics, so we need to fully understand what mathematics says about infinity before we can start thinking about what nature might say about infinity. 

Of course, we might need new math, but existing math is always the best place to start.  If we work out the predictions of an infinite universe based on mathematics, we can then scientifically evaluate those predictions and see if they make sense.  Unfortunately, much of this thread is putting the cart ahead of the mathematical horse and using intuition to argue about infinities, without a firm grounding in how the mathematics of infinities work and what this means for predictions.
 

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Re: Is infinity an illusion?
« Reply #199 on: 04/10/2013 16:25:47 »

 

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