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Author Topic: Is infinity an illusion?  (Read 68651 times)

Offline Bill S

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Re: Is infinity an illusion?
« Reply #125 on: 18/09/2013 20:08:45 »
I’ve just found a few minutes to read the past dozen or so posts properly.  There are several points to which I must respond, but first, Dlorde’s last post raises a point which, in different guises, keeps appearing, but remains unresolved. May I suggest that, for the moment, we draw a line under all that has gone before and see what we can do with this.

 
Quote from: dlorde
  If time begins with the universe, there is no prior temporal extent because there is no prior time, so in what sense can it be temporally infinite?

For convenience, let’s use the term “eternity/eternal” here.

Is eternity a very long time?

My answer would be “no”, it is not.  In fact it is not time at all.  We are creatures of time so it is practically impossible for us to imagine timelessness.  As JP points out, our intuition is often wrong.  IMO it is intuition that makes us attach any temporal significance to eternity.  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.

This brings us back to Dlorde’s question: “there is no prior temporal extent because there is no prior time, so in what sense can it be temporally infinite?”

I would argue that if there is a prior temporal extent, then we are not talking about eternity.  There is no such thing as “temporally infinite”.  Outside of mathematics, time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.

I know this seems to contradict my assertion that there would need to be time before the Universe to permit the change, but let's deal with one thing at a time.


 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #126 on: 18/09/2013 21:49:11 »
Pete, if the Universe had no beginning, is it not unbounded in that direction, and therefore infinite?
It is not temporally bounded, yes.

Let me expound on this a bit more since I just realized something. Something can have no lower limit and still be bounded. The value x in the relationship 0 < x < 1. This is bounded since we cannot decrease the value of x as much as we want to. The same thing holds for the upper limit.

But what if we have ? <= x <= infinity? What is denoted by the question mark? Also can we insert equality for infinity?
 

Offline Pmb

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Re: Is infinity an illusion?
« Reply #127 on: 18/09/2013 23:10:29 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.
 

Offline AndroidNeox

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Re: Is infinity an illusion?
« Reply #128 on: 18/09/2013 23:41:31 »
While we cannot necessarily know whether any infinities 'exist', it's simple enough to show that they cannot be observed, and so have no directly detectable existence for us. Bell's Inequality, though, shows that the multiplicity of states for unobserved systems are real and measurable, but only while they are unobserved. Whether the totality of all possibilities is finite... I dunno.

Personally, I think that spigot algorithms (like the Bailey-Borwein-Plouffe, BBP, algorithm) could not work if we didn't exist within a background of infinite information. Just because pi can be described in terms of a few algebraic symbols doesn't mean that it possesses finite information. I find it telling that all such concise descriptions include terms, like e, which likewise cannot be fully described in finite information.

There are two ways to identify a specific piece of information: calculate it or look it up. Calculation would correspond to the pre-BBP method of starting at 3 and working along the string (3.14...) to the desired digit. Spigot algorithms don't behave that way. A spigot algorithm finds any desired digit of the irrational number in a fixed number of steps, just as a look-up algorithm does (it takes essentially the same computational effort to identify the 100th word on the 10th page of a book as it does to identify the 10th word on the 100th page).

When the BBP algorithm was first proposed, theoretical physicists argued that it could not work because a finite (and small) amount of computation could access an unlimited quantity of information. Then, when BBP was proven to be correct, they all shut up. I don't think they should have. I think they were right and the fact that spigot algorithms work actually reveals something fundamental about reality.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #129 on: 19/09/2013 09:26:19 »
For convenience, let’s use the term “eternity/eternal” here.

Is eternity a very long time?

My answer would be “no”, it is not.  In fact it is not time at all.  We are creatures of time so it is practically impossible for us to imagine timelessness.  As JP points out, our intuition is often wrong.  IMO it is intuition that makes us attach any temporal significance to eternity.  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.
...
I would argue that if there is a prior temporal extent, then we are not talking about eternity.  There is no such thing as “temporally infinite”.  Outside of mathematics, time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition, the latter used more in a theological context (the 'afterlife', etc).

If we take eternity to mean timelessness, rather than infinite time, then I would broadly agree with what you say - except that I don't see why you assert 'There is no such thing as “temporally infinite”'. The extent of time into the future may be infinite - we can't know, but it does seem there will be no big crunch, just continuing expansion (although there is talk of a 'big rip' if the acceleration of expansion continues).
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #130 on: 19/09/2013 15:14:34 »
Quote from: Dlorde
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition

Reality (whatever that might be) is surely not a matter of democratic “vote”.  As a "general definition" it is a handy approximation, but that may be all it is. 

Quote
the latter used more in a theological context (the 'afterlife', etc).

This is unfortunate, because it is off-putting to most scientists, but Julian Barbour (for example) would certainly disagree that timelessness is not a scientific concept.

Quote
I don't see why you assert 'There is no such thing as “temporally infinite”'.

I refer you to extracts from my previous post. 

“Is eternity a very long time?     My answer would be “no”, it is not.  In fact it is not time at all……..  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.”

“I would argue that if there is a prior temporal extent, then we are not talking about eternity. ……… time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.”

Quote
The extent of time into the future may be infinite - we can't know

Unbounded, perhaps, but it can never become infinite.

 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #131 on: 19/09/2013 16:33:30 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.

That is the problem. Only infinity can equal itself. It can be considered as 1 where this represents "the whole thing" rather than a numerical value.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #132 on: 19/09/2013 18:49:05 »
Quote from: jeffreyH
But what if we have ? <= x <= infinity? What is denoted by the question mark?
Also can we insert equality for infinity?
Equal signs in relationships involving infinity have no meaning.

That is the problem. Only infinity can equal itself. It can be considered as 1 where this represents "the whole thing" rather than a numerical value.

That isn't true.  If I take the whole set of real numbers, it has infinite elements.  If I remove from it all the natural numbers, what remains is clearly not all the real numbers, yet it still has infinite elements.  Hence, infinity = infinity makes no sense and as Pmb said, it has no meaning.

This is why in calculus, when you see infinity appear, it appears at limits in integrals or in taking a limit.  It does not appear in algebraic statements where numbers would appear.  This is because it is not a number and does not have the properties of a number.
 

Offline JP

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Re: Is infinity an illusion?
« Reply #133 on: 19/09/2013 18:58:08 »
Quote from: Dlorde
There seem to be two subtly different relevant definitions of eternity; one being an infinite or unbounded extent of time, the other being timelessness. The former is the more general definition

Reality (whatever that might be) is surely not a matter of democratic “vote”.  As a "general definition" it is a handy approximation, but that may be all it is. 

Quote
the latter used more in a theological context (the 'afterlife', etc).

This is unfortunate, because it is off-putting to most scientists, but Julian Barbour (for example) would certainly disagree that timelessness is not a scientific concept.

Quote
I don't see why you assert 'There is no such thing as “temporally infinite”'.

I refer you to extracts from my previous post. 

“Is eternity a very long time?     My answer would be “no”, it is not.  In fact it is not time at all……..  Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.”

“I would argue that if there is a prior temporal extent, then we are not talking about eternity. ……… time and eternity are completely incompatible.  If you argue for no time before the Universe, then surely you are arguing for unmeasurable, indivisible eternity.”

Quote
The extent of time into the future may be infinite - we can't know

Unbounded, perhaps, but it can never become infinite.



Bill, what scientific reasons do you have for claiming that time can be unbounded but not infinite?  In fact, given that time can be measured by numbers "1 second, 2 seconds, 3 seconds..." wouldn't unbounded time necessarily mean infinite time?  You'd at least have all the natural numbers of seconds, and that's an infinite set.

I don't know if anyone has scientifically defined "eternity," but if I were to do so, I'd define it akin to "infinity."  It describes a concept of something increasing without bound, just as taking a limit as some variable goes to infinity does.  In this sense, eternity and infinity are very closely linked.  Whether one can exist or not is another question and one that we can't answer scientifically (yet).
 

Offline JP

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Re: Is infinity an illusion?
« Reply #134 on: 19/09/2013 21:33:35 »
One other interesting thought (as long as I'm spamming the thread and it's well into the speculative rather than concrete science): in statistical mechanics, we talk of microstates of a system, each of which corresponds to a single possible arrangement of the particles that make up a system.  From that point, you can derive entropy and enforce an arrow of time by looking at the probabilities involved in going from one microstate to the next.

One could imagine that the universe is represented by something akin to a single microstate, and that space and time might be emergent properties due to considerations of how these universe-states are linked together.  I think this is similar to what Julian Barbour argues (though I haven't read any of his works).  If this were the case, then time wouldn't really have a meaning when we look deeper than our universe, and it's an emergent property based upon how our minds work and the ordering of states through which our minds pass.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #135 on: 19/09/2013 22:42:09 »
Quote from: JP
In fact, given that time can be measured by numbers "1 second, 2 seconds, 3 seconds..." wouldn't unbounded time necessarily mean infinite time?  You'd at least have all the natural numbers of seconds, and that's an infinite set.

You will always be able to counter any argument about infinity by quoting mathematical infinities and regarding them as being the same as the one non-mathematical infinity, if such a thing exists.  In mathematics I am happy to believe that finite things like individual numbers can become infinite, but apart, perhaps, from the example Pete gave, on which I am not qualified to comment, I know of no physical thing that, being finite, can become infinite.

Consider, for example, speed.   John Gribbin says: :  “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.  At what point could you say: the speed is now infinite?  What is infinite speed?

Quote
  It describes a concept of something increasing without bound

Precisely – increasing without limit, but never becoming infinite.  At any stage in its increase it is a number, and infinity is not a number.  I thought we had agreed on that.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #136 on: 19/09/2013 23:13:57 »
... I know of no physical thing that, being finite, can become infinite.

Consider, for example, speed.   John Gribbin says: :  “So if a tachyon were created in some violent event in space, it would radiate energy away furiously…..and go faster and faster, until it had zero energy ……and was travelling at infinite speed”.  At what point could you say: the speed is now infinite?  What is infinite speed?

Quote
  It describes a concept of something increasing without bound

Precisely – increasing without limit, but never becoming infinite.  At any stage in its increase it is a number, and infinity is not a number.  I thought we had agreed on that.

These ideas go way back to ancient times - Aristotle & co. said that infinities are potential rather than actual.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #137 on: 20/09/2013 04:02:24 »
Quote from: dlorde
These ideas go way back to ancient times

So do I, doesn't mean I'm wrong.  :D

Potential infinity?  Now there's an interesting concept.  If it is a potential infinity, it isn't infinite.  If it isn't infinite, it's finite.  If it's finite it can't become infinite.  How can it be potentially infinite? 
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #138 on: 20/09/2013 10:18:34 »
Quote from: dlorde
These ideas go way back to ancient times
So do I, doesn't mean I'm wrong.  :D
Of course not ;)

Quote
Potential infinity?  Now there's an interesting concept.  If it is a potential infinity, it isn't infinite.  If it isn't infinite, it's finite.  If it's finite it can't become infinite.  How can it be potentially infinite? 
Quoting from the article I linked:
Quote
An actual infinity is something which is completed and definite and consists of infinitely many elements, and according to Aristotle, a paradoxical idea, both in theory and in nature. In respect to addition, a potentially infinite sequence or a series is potentially endless; being a potentially endless series means that one element can always be added to the series after another, and this process of adding elements is never exhausted.
The way I see it, he calls it potential because it can't be directly demonstrated or enumerated, it can only be inferred from its definition or properties. This doesn't mean it's finite, just that, by definition, it's not physically completed or actualised. So while the digital representation of pi is an infinite series of digits, you'll only ever see a finite decimal approximation.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #139 on: 20/09/2013 18:42:28 »
It’s many decades since I studied Latin, but I’m fairly sure that:-

Potentiale = potential; from potens = able or able to….

So to be potentially infinite something must be able to become infinite.

I think that "quasi infinite" might be a less confusing term, but I’m not going to argue with the use of “potentially infinite” for things like numbers; I just think it is important that we all know what we mean. 
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #140 on: 20/09/2013 18:50:51 »
Quote from: dlorde
So while the digital representation of pi is an infinite series of digits, you'll only ever see a finite decimal approximation.

I have seen it argued that pi cannot be infinite as it is the ratio of two finite numbers.  I'm not sure that I agree with the logic, but in any case it is a mathematical infinity, so it is not just the digital representation that is an approximation, it is the "infinity" itself.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #141 on: 20/09/2013 19:12:53 »
I have seen it argued that pi cannot be infinite as it is the ratio of two finite numbers.  I'm not sure that I agree with the logic, but in any case it is a mathematical infinity, so it is not just the digital representation that is an approximation, it is the "infinity" itself.
I don't quite follow; pi itself is exactly the ratio of circle circumference to diameter - a value which is a little over 3; there's nothing infinite about that - except that being an irrational number, the value can't be expressed as a simple fraction, so its decimal representation is infinite.

IOW, the value is finite, but its expression isn't.
« Last Edit: 20/09/2013 19:14:25 by dlorde »
 

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Re: Is infinity an illusion?
« Reply #142 on: 20/09/2013 19:23:36 »
.
For convenience, let’s use the term “eternity/eternal” here.

Eternity cannot be measured in seconds, millennia or any other temporal units. It is not time.

Bill, sorry to butt in, but can you describe what you mean here by eternity without using the concept of duration?  Or, do you mean time is not eternity because it had a beginning, so to speak?
« Last Edit: 20/09/2013 19:25:23 by lean bean »
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #143 on: 21/09/2013 00:38:34 »
Nothing to apologise about, LB, it’s an open thread, not a clique.  The more contributors the better. 

Can I define eternity without using the concept of duration?  Probably not, but I’ll have a go.

We have evolved in 3D of space and 1D of time, so it is extremely difficult for us even to think about timelessness or changelessness. Fred Alan Wolfe might be able to find a yogi who can do it; he might even be able to do it himself, but most of us can’t.

For thousands of years people have been thinking about infinity/eternity, but no one has developed a terminology that is not linked to finite dimensions.  Infinity and eternity became differentiated because philosophers needed to think about spatial and temporal extent. 

My contention is that infinity cannot be measured in units of anything, and eternity cannot be measured in units of time. 

At risk of being accused of repetition, I would say: infinity is not a very big number, in fact it is not a number at all, and eternity is not a very long time, it is not time at all.   That’s probably as close as I can get to answering your question.
 
Quote
do you mean time is not eternity because it had a beginning, so to speak

I assume time, as we perceive it, had a beginning.  Any time now, I imagine there will be some searching questions on that subject, so I would rather wait a while before getting into that.   

 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #144 on: 21/09/2013 00:53:20 »
Quote
so its decimal representation is infinite

So, in common with mathematical infinities in general, it is unbounded, but can never become infinite.

Numbers need to be attached to things as adjectives need to be attached to nouns.  On their own, numbers are just concepts in the mind, so even if you could imagine an infinite number, which you probably can't, it would have no physical significance, unless you could produce an infinite number of objects.
 

Offline dlorde

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Re: Is infinity an illusion?
« Reply #145 on: 21/09/2013 01:12:28 »
Quote
so its decimal representation is infinite

So, in common with mathematical infinities in general, it is unbounded, but can never become infinite.
It's value is bounded - e.g., it's between 3.1 and 3.2, but perhaps one could say it is indefinite (I don't know how mathematicians describe such things). It's decimal representation is infinitely long, so unbounded, so it can't be fully expressed that way.
 

Offline jeffreyH

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Re: Is infinity an illusion?
« Reply #146 on: 21/09/2013 01:33:06 »
How about an infinite time and dimension that is on the equivalent of a mobius strip. Continuous, joined up and unbounded. You would never get back to the same point even though it is connected.
 

Offline yor_on

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Re: Is infinity an illusion?
« Reply #147 on: 21/09/2013 18:40:23 »
This one Dlorde.

""The observer has, ... only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being;"

Observers, do they need a consciousness, and what defines a consciousness?
A arrow?

If I assumed the universe to be a representation of a quantum computer :) Which isn't that far from the idea of multiple universes created as a wave function breaks down, also assuming that this 'universe' contains it all.

Would a observer need to be 'locked' (to be conscious) under a arrow?
How do we define consciousness?
« Last Edit: 21/09/2013 22:09:32 by yor_on »
 

Offline yor_on

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Re: Is infinity an illusion?
« Reply #148 on: 21/09/2013 18:55:22 »
Jeffery, as long as we define a arrow, every point of my journey, from birth to death, must be unique. You don't need a Möbius strip for that one. In a four dimensional universe, allowing time to define a position with the other three, everything must be unique. That 'now' experienced something never coming back, unless I assume that the arrow can be played backwards. From that assumption I also must make one more to make it work. The one in where the other three room dimensions has no 'individuality', unless a arrow becomes involved.
 

Offline Bill S

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Re: Is infinity an illusion?
« Reply #149 on: 21/09/2013 19:24:48 »
Quote from: dlorde
It's decimal representation is infinitely long, so unbounded, so it can't be fully expressed that way

Quote from: Bill S
On their own, numbers are just concepts in the mind
 

Please don’t think I’m objecting to the use of “infinity” in maths, as long as one realises that they are mathematical "infinities". 
 

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Re: Is infinity an illusion?
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