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Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 23/08/2013 19:18:28

Title: Is infinity an illusion?
Post by: Bill S on 23/08/2013 19:18:28
The Infinity Illusion                 New Scientist 17.08.2013.


Over 40 years ago I had a long discussion with a maths teacher about infinity.  It culminated in his conceding that the series of whole numbers, although apparently unbounded in both directions, was not an example of true infinity.  Now, in 2013, more than 40 years on, could the scientific/mathematical community be moving in that direction?  Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations. 

Max Tegmark, it seems, regards infinity as “…the ultimate untested assumption.”  He says: “All of our problems with inflation and the measure problem come immediately from our assumption of the infinite.”

This must raise the question: How can we test for infinity?  Surely such a test would require an infinite amount of information. 

Later in the article we are told that “The largest number of informational bits a universe of our size can hold is 10^122.”   

Nobel laureate, David Wineland, says: “Certainly we need nothing like that number of bits to record the outcome of experiments.”  Is he saying that experimental science has no need for infinity?  The article points out that “…even the best device will not measure with infinite accuracy….”.

Raphael Bousso says:  “I don’t think anyone likes infinity.  It’s not the outcome of any experiment.”

Mathematician Norman Wildberger says of “potential” infinity:  “This type of infinity allows us to add 1 to any number without fear of hitting the end of the number line, but is never actually reached itself.  That is a long way from accepting “actual” infinity – one that has already been reached and conveniently packaged as a mathematical entity we can manipulate in equations.”

I doubt that Wildberger is, here, criticising Cantor who appears to have achieved precisely that “packaging” in set theory.  However, the fact remains that Cantor’s infinities are “mathematical” infinities, and run into problems with “absolute” infinity”. 

“For the past decade he [Wildberger] has been working on a new, infinity-free of trigonometry and Euclidian geometry.”  He is working to counter the fact that angles are related, via circles, to pi, with its endless digits following the decimal point.  I lack the maths to evaluate Wildberger’s work, but Doron Zeilberger say of it: “Everything is made completely rational.  It’s a beautiful approach.” 

If Wildberger’s approach is revolutionary, surely, Zeilberger’s must be calculated to set the cat among the pigeons. 

Zeilberger, it seems, wants, not only to get rid of infinity; he “wants to dispose of potential infinity as well.” Zeilberger believes there is a largest number.  “Start at 1 and just keep on counting and eventually you will hit a number you cannot exceed – a kind of speed of light for mathematics.”  Zeilberger’s answer to the question as to what happens if you add 1 to this number is that it acts like a computer which has a maximum number it can process.  If you add 1 to it, it either gives you an “error” message, or resets the number to zero.  Apparently, Zeilberger favours the latter option.
 
My own feeling about this is that it draws too heavily on the analogy between a computer and the Universe.  Who, or what, would generate the “error” message, or reset the number?  Zeilberger’s assertion that this largest number is “…so big you could never reach it” seems a bit of a cop out.  Consider what he has actually said: “…eventually you will hit a number you cannot exceed” and “…you could never reach it”.

Tegmark points out that “the calculations and simulations that physicists use to check a theory against the hard facts of the world can all be done on a finite computer. “That” he says “already shows that we don’t need the infinite for anything we’re doing.”  He continues: “There’s absolutely no evidence whatsoever that nature is doing it any differently, that nature needs to process an infinite amount of information.”

Physicist Seth Lloyd points out that “We have no evidence that the universe behaves as though it were a classical computer, and plenty of evidence that it behaves like a quantum computer.”  This reintroduces infinity, because: “If you really wanted to specify the full state of one qubit, it would require an infinite amount of information.” 

Obviously, we do not have an infinite amount of anything at our disposal, so the problem seems academic.

Set theorist, Hugh Woodin suggests separating the two issues of physical and mathematical infinities.  He says: “It may well be that physics is completely finite, but in that case, our conception of set theory represents the discovery of a truth that is somehow far beyond the physical universe.”

Obviously there is more in this article than I have mentioned here, but hopefully others will read it and raise different points.  I have added a few of my own thoughts above, but I would be delighted to have some other people’s input before risking swamping the subject with my own crackpottery.
Title: Re: Is infinity an illusion?
Post by: alancalverd on 24/08/2013 00:00:21
Quote
“For the past decade he [Wildberger] has been working on a new, infinity-free of trigonometry and Euclidian geometry.”  He is working to counter the fact that angles are related, via circles, to pi, with its endless digits following the decimal point.  I lack the maths to evaluate Wildberger’s work, but Doron Zeilberger say of it: “Everything is made completely rational.  It’s a beautiful approach.” 

The "endless digits" business is irrelevant to infinity. Pi is not infinite: it is the quotient of two finite quantities and therefore finite. It just happens that pi is irrational, that is it can't be expressed as the quotient of integers. No big deal: neither can e or log2, both of which are finite, irrational, wholly defined, and extremely useful.

There's no doubt that zero is important and useful. But a lot of useful physics is done in inverse space, so why can't we have a symbol for 1/0? 
Title: Re: Is infinity an illusion?
Post by: Bill S on 24/08/2013 14:31:13
Quote from: alancalverd
The "endless digits" business is irrelevant to infinity.

Would you also apply this to the “endless digits” of number lines?  I look for clarification here because it is so rare to find someone who doesn’t insist that these are examples of infinite series.

Title: Re: Is infinity an illusion?
Post by: alancalverd on 25/08/2013 01:42:06
There's a distinction between the trivial fact that you cannot express pi, e or log2 with a finite number of digits, and the significant fact that all three quantities are finite.

In geometry and electrical engineering we often quantify rotation in multiples or fractions of pi, and e turns up pretty regularly, which helps to make physics rational since exp(ix) = cos x + i sin x , so  e^(pi i) = -1. and. e^(2 pi i) = e^0 = 1 - all very useful identities. But log2 remains stubbornly irrational. 

Not too sure what is meant by number lines. As far as I can gather, these are arbitrary samples of the rational set, used for elementary teaching. The rational set is by definition a countably infinite set of countably infinite sets, which gives it several interesting properties, if you are interested in that sort of thing. In practice it means that (a) the longer you are prepared to wait for a jpeg image to upload and download, the closer it can resemble the object, and (b) you can image as many objects as you like without repeating yourself.
Title: Re: Is infinity an illusion?
Post by: Bill S on 25/08/2013 20:58:23
I'm not sure if my lack of maths is an advantage or a drawback when thinking about infinity.  In most scientific discussion it is a serious disadvantage, but perhaps infinity is sufficiently divorced from science to make a difference. 

For example: Woodin is a mathematician and he obviously sees infinity as part of mathematics, whereas he is quite prepared to remove infinity from physics.  My own feeling is that mathematics in general, and set theory in particular, may cope very well with “infinities”, but they are ultimately finite.  Physical reality, on the other hand, must have its basis in infinity, or there would be no physical reality.

When Woodin says “It may well be that physics is completely finite”.  I would agree, as long as he is talking about our finitely bounded understanding of physics.
Title: Re: Is infinity an illusion?
Post by: alancalverd on 26/08/2013 00:08:14
Consider an everyday concept in classical electrostatics. Potential is the work done to add unit charge: one volt = 1 joule per coulomb.   

The simplest case is to visualise a point charge - say an electron, at a position r = 0. The electric field of an isolated point charge in space extends in all directions with a local strength of 1/r^2 (by Cavendish's experiment). This function is nonzero for any finite r. Now we measure the potential at that point by bringing up another test charge (another electron) and measuring the force required to do so as it approaches the target. The integral of (force x distance) from r to 0 is the work done. Clearly the integral depends on the initial value of r, but there can only be one value for the potential at r = 0, so the definition of potential must be expanded to "work done to bring an additional unit charge from infinity"   

Thus in at least one small area of physics even if the universe is finite, our understanding of it uses the simple infinity defined as the value of r at which 1/r = 0.   
Title: Re: Is infinity an illusion?
Post by: Bill S on 26/08/2013 02:28:49
Quote
the definition of potential must be expanded to "work done to bring an additional unit charge from infinity".

The bit where I am lost is the idea of bringing a unit charge from infinity.  At least I can pretend to understand the rest, but bringing some from infinity.......??   
Title: Re: Is infinity an illusion?
Post by: alancalverd on 26/08/2013 08:03:23
Go back to the preliminary definition: work done to add unit charge. Now clearly I have to do more work to move a charge one meter in a radial field than to move it one centimeter, but due to the 1/r2 relationship the difference gets less as the distances increase. So the reference origin is where 1/r = 0.

This distinguishes between theoretical physics (the definition of potential) and experimental physics (the measurement of potential). Noting that it would take a very long time to move a charge from infinity, we cunning engineering types measure potential difference with reference to something handy like a spike in the surface of the earth or the negative terminal of the battery.   
Title: Re: Is infinity an illusion?
Post by: Bill S on 26/08/2013 15:34:03
Let’s see if I have this right.

1/r is the reciprocal of r.

If 1/r = 0,    r = infinity.

In order to work with this rather inconvenient infinity, those who work with practical reality perform a sort of “renormalisation” and leave infinity to the theorists.

Title: Re: Is infinity an illusion?
Post by: JP on 26/08/2013 17:22:37
I'm not sure if my lack of maths is an advantage or a drawback when thinking about infinity.  In most scientific discussion it is a serious disadvantage, but perhaps infinity is sufficiently divorced from science to make a difference. 

For example: Woodin is a mathematician and he obviously sees infinity as part of mathematics, whereas he is quite prepared to remove infinity from physics.  My own feeling is that mathematics in general, and set theory in particular, may cope very well with “infinities”, but they are ultimately finite.  Physical reality, on the other hand, must have its basis in infinity, or there would be no physical reality.

When Woodin says “It may well be that physics is completely finite”.  I would agree, as long as he is talking about our finitely bounded understanding of physics.


I think its fair to say that in mathematics, infinity is fine and well.  Mathematicians can talk easily about infinite sets because those sets are ideas, not physical objects.  Infinite series consist of infinite numbers of elements but can sum to finite values.


In physics, one has to be a bit more careful.  Infinity most often means "really large."  It's generally easier to do calculus and other calculations with infinity than inserting some arbitray "really large" number and it introduces negligible error.


In some cases such as the size of the universe, some theorists take it literally.  This is where I hedge my bets since you'd have to come up with a testable hypothesis to distinguish between an infinite universe or not.  As far as I know the question isn't settled.  Clearly no experiment has directly measured an infinite number of things.


This is why it's so important to be precise: infinity definitely exists in mathematics, is used but doesn't claim to be a real object in much of classical physics, and may or may not exist in the universe at all in cosmology or quantum mechanics.
Title: Re: Is infinity an illusion?
Post by: alancalverd on 26/08/2013 20:48:51
Let’s see if I have this right.

1/r is the reciprocal of r.

If 1/r = 0,    r = infinity.

In order to work with this rather inconvenient infinity, those who work with practical reality perform a sort of “renormalisation” and leave infinity to the theorists.



Not at all. We make r as large as we need to for the practical purpose. This sort of thing turns up in many aspects of practical science (remember "infiinte dilution" in physical chemistry?) , and our brother engineers are perfectly happy making optical systems focussed at infinity, for instance. 

I have no idea what you mean by "renormalisation" - would appreciate an explanation.
Title: Re: Is infinity an illusion?
Post by: Bill S on 26/08/2013 21:52:26
As I understand it, renormalisation (with a z if you are on the West side of the Atlantic) is a technique for getting rid of unwanted infinities in QM calculations. 

If I remember rightly infinity on a camera’s distance scale originally represented anything greater than one hundred times the focal length of the lens, and may still be used in that sense on occasions.  Obviously this is only loosely connected to anything that might be considered genuinely infinite, and probably is not what the NS article suggests may be an illusion.
Title: Re: Is infinity an illusion?
Post by: Bill S on 26/08/2013 21:57:45
Quote from: JP
Infinite series consist of infinite numbers of elements but can sum to finite values.

So mathematical infinities exist.  I would not question that, but, as Barrow points out, mathematical and physical existence are not necessarily the same thing. 

“Gradually mathematicians lighted upon a new concept of existence.  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

Title: Re: Is infinity an illusion?
Post by: alancalverd on 28/08/2013 09:24:04
If I remember rightly infinity on a camera’s distance scale originally represented anything greater than one hundred times the focal length of the lens, and may still be used in that sense on occasions.  Obviously this is only loosely connected to anything that might be considered genuinely infinite, and probably is not what the NS article suggests may be an illusion.

100f makes sense for a terrestrial camera, where your horizon is a few miles and your resolution is limited by camera shake, but not for an astronomical telescope. Fortunately, classical geometry comes to our aid: "rays from infinity are parallel" so we can build and test a scope on the ground before putting it into orbit. Except of course for Hubble MkI!   
Title: Re: Is infinity an illusion?
Post by: JP on 28/08/2013 13:37:48
If I remember rightly infinity on a camera’s distance scale originally represented anything greater than one hundred times the focal length of the lens, and may still be used in that sense on occasions.  Obviously this is only loosely connected to anything that might be considered genuinely infinite, and probably is not what the NS article suggests may be an illusion.

100f makes sense for a terrestrial camera, where your horizon is a few miles and your resolution is limited by camera shake, but not for an astronomical telescope. Fortunately, classical geometry comes to our aid: "rays from infinity are parallel" so we can build and test a scope on the ground before putting it into orbit. Except of course for Hubble MkI!   

Yep.  And this is the type of infinity that many physicists (and probably all engineers) use.  It's a nice shorthand for "very big."  It would be a waste of time to figure out what "100 f" or another suitably large number was for every case.  So long as the error introduced between using that number and infinity for distance is significantly smaller than the tolerances in the design, it can be done without too much of a problem.
Title: Re: Is infinity an illusion?
Post by: Bill S on 28/08/2013 17:54:18
Max Tegmark says:

"When quantum mechanics was discovered,we realised that classical mechanics was just an approximation. I think another revolution is going to take place, and we'll see that continuous quantum mechanics is itself just an approximation to some deeper theory, which is totally finite."

If a physicist at MIT is seriously making a statement like this, should it not stir some scientific thoughts on a science discussion forum?

Of course, it takes more than one physicist's early suspicions to cause a revolution, but David Hilbert's assertion: "No one shall dispel us from the paradise Cantor has created" could begin to look a little insecure.



Title: Re: Is infinity an illusion?
Post by: JP on 28/08/2013 18:25:46
I agree with most of what you say, Bill, but as a professional physicist I like to be much pickier and more precise about using the term "infinity."    :p  As I pointed out above, infinity certainly exists in the world of thought of mathematical theory.  Infinite sets and infinite series are ideas in mathematics and can be manipulated.  Infinity is used in physics as a stand-in for "very large," and it comes into play with "very small" (infinitesimally small) and we can use the mathematical tools for handling infinity in these cases to produce useful results, often with much less work than would be involved if we tried to plug in large or small numbers.

This discussion seems to be entirely about whether there can physically exist situations consisting of an infinite number of things, an infinitely-sized object (including the entire universe) or an infinitelimally small object.  To me, the most testable one of these ideas is the infinitesimally small--if space is continuous, then no matter what tiny distance you pick, I can divide it in half.  This means there is no smallest size and infinitesimal distances are real things.  If, on the other hand, there is some limit to how far you can divide up a distance before you get into discrete units of space, then infinitesimal distances are just an approximation.  They work well because these distances are so small compared to what we're looking at that we don't notice the error introduced by this approximation.

I think this is what Max Tegmark is getting at.  The problem with an in-depth discussion of this is that there isn't a lot of scientific evidence one way or the other since our measurements aren't precise enough.  If there is discretization, the obvious place to look is near the Planck length, since that's where we expect quantum effects on space-time to become important.  I don't see a reason to discount this idea, and I'm actually fairly partial to it.  At the same time, there's also no reason to jump into the no-infinity boat until there's evidence to refute it.  Right now, infinity serves us well whether or not we think it really describes a physical object.
Title: Re: Is infinity an illusion?
Post by: Bill S on 31/08/2013 17:31:02
I have no quarrel with infinite sets/series as mathematical tools.  As far as the extremely small is concerned, I am fine with “infinitesimally small”.  I wish scientists would use it instead of “infinitely small”, which, in my opinion, is tantamount to saying it cannot be further divided, even in principle.  If space is continuous, this must be the same as saying it is nonexistent.

Unfortunately, there seems to be no term, equivalent to “infinitesimal”, to cover things that are “sort of” infinitely large.     

I would certainly not “jump into the no-infinity boat”.  Without infinity, what would I argue about?  :)

Seriously, though, I see no realistic way round the idea that something must be eternal/infinite, otherwise we would not be here.  This has caused me to do a lot of thinking about infinity, which might well be considered as being philosophy rather than science.  I would not argue with that, except to say that if it is something so fundamental to our existence, then perhaps it has as much right to a place in scientific thought as does the underlying “reality” of QM.

Title: Re: Is infinity an illusion?
Post by: JP on 02/09/2013 16:44:36
I have no quarrel with infinite sets/series as mathematical tools.  As far as the extremely small is concerned, I am fine with “infinitesimally small”.  I wish scientists would use it instead of “infinitely small”, which, in my opinion, is tantamount to saying it cannot be further divided, even in principle.  If space is continuous, this must be the same as saying it is nonexistent.
Most scientists who are being precise would use "infinitesimally small" instead of "infinitely small."  I don't think "infinitely small" means much in a technical sense, while infinitesimal has a precise meaning.  I don't read too many pop-sci books, but I wouldn't be surprised if they abuse terminology by saying "infinitely small." 

Quote
Unfortunately, there seems to be no term, equivalent to “infinitesimal”, to cover things that are “sort of” infinitely large.     
That's because "sort of" infinitely large isn't precise.  Do you mean "big enough that we can treat it as infinity in our equations"?  When we simply call it infinity and acknowledge that we mean "big enough that we can treat it as infinity."  That might not be the best way to express things for a layperson, but its efficient and universally understood by physicists.

In pop-sci books, the standard should probably be to write all this out before introducing the word "infinity" so readers understand how it's being used (an approximation or an absolute?"

Quote
I would certainly not “jump into the no-infinity boat”.  Without infinity, what would I argue about?  :)

Seriously, though, I see no realistic way round the idea that something must be eternal/infinite, otherwise we would not be here.  This has caused me to do a lot of thinking about infinity, which might well be considered as being philosophy rather than science.  I would not argue with that, except to say that if it is something so fundamental to our existence, then perhaps it has as much right to a place in scientific thought as does the underlying “reality” of QM.

Well, the issue is that QM provides testable predictions.  Testing whether "infinity" is real or not is probably not feesable in the near future.  That doesn't make it unscientific to discuss it, but it puts it on less of a hard-science ground than QM and limits what scientific details we can actually add to the discussion. 
Title: Re: Is infinity an illusion?
Post by: yor_on on 02/09/2013 19:11:46
Infinity is not a definition making sense. everything having a stop make sense, even when we don't know where that stop exist. But infinity make sense, considering our universe. It's definitely not defined, neither from relativity, nor from QM.
Title: Re: Is infinity an illusion?
Post by: Bill S on 04/09/2013 21:09:38
Quote from: JP
  I don't read too many pop-sci books, but I wouldn't be surprised if they abuse terminology by saying "infinitely small."

Hunting through pop-sci books for examples would be very time consuming and of little ultimate value, but Paul Davies, John Gribbin , Peter Cattermole and Stuart Clark come readily to mind.

Quote
Do you mean "big enough that we can treat it as infinity in our equations"?  When we simply call it infinity and acknowledge that we mean "big enough that we can treat it as infinity."

That’s fair enough, and I how I now accept it when I read “infinite/infinity” in the context of science or maths.  I wish the authors of pop-sci books would make this clear, as there must be a risk that their readers will conclude that they are talking about some sort of “absolute” infinity, when they are talking about an approximation.  It is easy for “hitch-hikers”, like myself, to believe we have something sussed, just because an expert has said it.  As a child, someone said to me: “Question everything, not just because you think the person saying it is wrong, but because you may have misunderstood it.  Never believe you understand something until you know you understand it”.  I still try to maintain that attitude, but sometimes it annoys the hell out of people!
Title: Re: Is infinity an illusion?
Post by: alancalverd on 04/09/2013 21:27:59
Yep.  And this is the type of infinity that many physicists (and probably all engineers) use.  It's a nice shorthand for "very big." 

No. Infinity isn't shorthand for"very big"  but for "bigger than anything you can define".

Which makes an interesting point. I mentioned parallel rays of light as having their common source at infinity. So where is the common source for converging rays? 
Title: Re: Is infinity an illusion?
Post by: Bill S on 05/09/2013 03:34:14
Quote from: alancalverd
So where is the common source for converging rays? 

Do converging rays have a common source?
Title: Re: Is infinity an illusion?
Post by: JP on 05/09/2013 04:17:26
Yep.  And this is the type of infinity that many physicists (and probably all engineers) use.  It's a nice shorthand for "very big." 

No. Infinity isn't shorthand for"very big"  but for "bigger than anything you can define".

Which makes an interesting point. I mentioned parallel rays of light as having their common source at infinity. So where is the common source for converging rays? 

If you read what I wrote carefully, you'll notice that I said a certain use of infinity is shorthand for very big, and it indeed it.  The parallel ray assumption is used all the time in practice and no one literally assumes that a planet or star is really infinitely far from the telescope.  It's even used commonly in designing consumer cameras for use in photography on earth where distances are in tens or hundreds of meters.  All that matters is that distances are significantly larger than the camera aperture so that the actual angle of rays is negligibly different from parallel--at least compared to other sources of error in the design.  I can guarantee this is true because I am a trained optical physicist who does this type of calculation on a daily basis. 

All applied physics involves approximations, and infinity used as a stand-in for "very big" pops up ubiquitously in most branches of physics (except for the most fundamental questions) and engineering.  It is regularly used anywhere where the error introduced by letting "very large" be infinity is small compared to other sources of error. 

I brought this up to point out to Bill that infinity is a useful concept, even if we don't take it literally.  It comes with a host of mathematical tools that simplify things greatly.  Try computing the electric field emitted by an oscillating dipole on earth by rigorously accounting for all matter on earth, all planets, moons, the sun, all stars in our galaxy, all other galaxies, etc. and compare this to just assuming the source radiates away to infinity to see the use of this.  Unless there are other sources/sinks nearby this dipole, the two calculations will give nearly identical results, and the one using infinities will actually be do-able.  :)

I wholeheartedly agree that the question of whether physical infinities exist is separate and interesting, but infinity is a real concept in mathematics and is extremely useful in practice, regardless of whether it is physically realizable or not.
Title: Re: Is infinity an illusion?
Post by: JP on 05/09/2013 04:22:40
Quote from: JP
  I don't read too many pop-sci books, but I wouldn't be surprised if they abuse terminology by saying "infinitely small."

Hunting through pop-sci books for examples would be very time consuming and of little ultimate value, but Paul Davies, John Gribbin , Peter Cattermole and Stuart Clark come readily to mind.

Quote
Do you mean "big enough that we can treat it as infinity in our equations"?  When we simply call it infinity and acknowledge that we mean "big enough that we can treat it as infinity."

That’s fair enough, and I how I now accept it when I read “infinite/infinity” in the context of science or maths.  I wish the authors of pop-sci books would make this clear, as there must be a risk that their readers will conclude that they are talking about some sort of “absolute” infinity, when they are talking about an approximation.  It is easy for “hitch-hikers”, like myself, to believe we have something sussed, just because an expert has said it.  As a child, someone said to me: “Question everything, not just because you think the person saying it is wrong, but because you may have misunderstood it.  Never believe you understand something until you know you understand it”.  I still try to maintain that attitude, but sometimes it annoys the hell out of people!


I agree with you that pop-sci should be as rigorous as possible to as not to confuse people.  To be honest, I don't read much of it since I'm so busy keeping up on technical literature in my field that my pleasure reading tends to be as non-sciencey as possible (fantasy or history).  I did read a book recently, "The Disappearing Spoon" that was quite good.  But even though I enjoyed it, and most of it involved chemistry that was outside my field, I noticed one rather glaring error in its physics.  It compared the idea of an electron orbiting an atom without spiraling into the nucleus as being as shocking as if a radio worked indefinitely without needing its battery replaced.  To a physicist the former is possible, if implausible, since it conserves energy.  The latter is impossible since sound waves leaving the radio take away energy, so that a radio that works forever without replacing the batteries generates infinite power--it's basically a perpetual motion machine.
Title: Re: Is infinity an illusion?
Post by: Bill S on 05/09/2013 22:13:10
Quote from: JP
....the idea of an electron orbiting an atom without spiraling into the nucleus....

For a long time that gave me problems; then I, sort of, got my head round the idea that it was the quantization of energy that prevented spiraling.  However, there was still the problem that if the electron was orbiting, it must be accelerating, so where was the energy coming from?  I suppose it's blatant thread drift to talk about it here, but am I right in thinking that we should no longer think of the electron as orbiting, but rather as being in any, or all, of an "infinite" (See! I just brought it back on topic) range of positions at the same time?

Title: Re: Is infinity an illusion?
Post by: alancalverd on 05/09/2013 23:02:12
Yes.
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/09/2013 14:08:17
Great, but does that mean that the electron/wave is stationary, or is that too intuitive for thinking about QM?
Title: Re: Is infinity an illusion?
Post by: Bill S on 07/09/2013 21:02:25
Quote from: JP
In some cases such as the size of the universe, some theorists take it literally.  This is where I hedge my bets since you'd have to come up with a testable hypothesis to distinguish between an infinite universe or not.  As far as I know the question isn't settled. 

I run into a problem here.  If the Universe started at the BB, how could it be infinite?

I have been assured that it could have been infinite from the start.  However, I have yet to find an explanation as to how something infinitesimally small could be infinite.
Title: Re: Is infinity an illusion?
Post by: Bill S on 07/09/2013 21:23:32
While looking at the question of infinity I came across the Hartle-Hawking State.

http://en.wikipedia.org/wiki/Hartle%E2%80%93Hawking_state 

A few questions spring to mind.

Planck epoch = 0 to 10^-43 s.  This is a period of time; therefore time must have started at t=0.  Therefore time exists during the Planck epoch.  Do I have the right impression?

They suggest that “….if we could travel backward in time toward the beginning g of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time.”

Does this statement imply that we would see that the condition of “space and no time” exists after t=0, or that we would be able to see beyond the BB?

 “….that at first there is only space and no time”.

Is this before or after the BB?

If there was a time when there was space but no time, how could this condition change?  Surely time is needed in order to allow change.  If there were a condition in which there were space and no time, there would be only space now, unless some outside influence “created” time.

They propose that “the universe is infinitely finite”!   I’m told I am the one with odd ideas about infinity. 

Is there a difference between “infinitely finite” and “unbounded”?
Title: Re: Is infinity an illusion?
Post by: Pmb on 08/09/2013 05:37:35
Quote from: Bill S
Over 40 years ago I had a long discussion with a maths teacher about infinity.  It culminated in his conceding that the series of whole numbers, although apparently unbounded in both directions, was not an example of true infinity.
Do you still believe this? If so, why? It certainly isn't true. Infinity quite litteraly means without bound. In this case for the sequence (not series) of whole numbers, by which I assume that you're referring to a sequence of numbers which increases without bound, then it's an infinite sequence. I don't understand how anyone could conclude otherwise. Please explain.

Quote from: Bill S
Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations. 
Please post the reference to this article. I'd like to read it. I assume you've read it. Would that be a correct assumption?

Quote from: Bill S
This must raise the question: How can we test for infinity?  Surely such a test would require an infinite amount of information. 
That depends highly on what it is that we're trying to measure as being infinite. Can you give an illustrative example?
Title: Re: Is infinity an illusion?
Post by: alancalverd on 08/09/2013 10:04:27
Great, but does that mean that the electron/wave is stationary, or is that too intuitive for thinking about QM?

The key phrase in your question was "think of". By no means the same as "is".

The wave function eloquently and adequately describes the behaviour of electrons in and around atoms, but an isolated electron  in a vacuum behaves delightfully like a charged particle. What it is, is an electron. 

As for measuring infinities, by definition, you can't.
Title: Re: Is infinity an illusion?
Post by: Bill S on 08/09/2013 18:09:18
Quote from: Pmb
Do you still believe this? If so, why? It certainly isn't true. Infinity quite litteraly means without bound. In this case for the sequence (not series) of whole numbers, by which I assume that you're referring to a sequence of numbers which increases without bound, then it's an infinite sequence. I don't understand how anyone could conclude otherwise. Please explain.

I feel sure you did not intend starting an etymological diversion, but if you go back to the Latin root, infinite means without end.   A sequence, such as the whole numbers, has no end, so if it is something that is real, in itself, then it is infinite, within the strict literal meaning of the word, but in both archaic and modern usage the word infinite has acquired wider significance. 

However, the sequence of numbers is something which has no existence other than as a tool for counting objects.  3 x nothing and 300 x nothing are the same thing.  3 and 300 have significance only in respect of the things they enumerate.  3 apples exist, 300 apples exist; an infinite number may exist, but has no real meaning; an infinite number of apples cannot exist in any context that we could recognise as real.

An infinite series (sequence) exists only in the (presumably finite) mind of the mathematician as a useful concept.

I am not questioning the use or value of infinities in mathematics, nor the value, in calculations, of treating infinity as though it were a number.  I simply call attention to the fact that infinity is not a number, and that outside mathematical usage, the concept of infinity is of singular importance in thinking about the origin of the Universe.


Title: Re: Is infinity an illusion?
Post by: Bill S on 08/09/2013 18:43:10
Quote
Please post the reference to this article. I'd like to read it. I assume you've read it. Would that be a correct assumption?

 The article appeared in the New Scientist 17.08.2013.  As far as I am aware, the full article is available on line only to subscribers.  As a non-subscriber, I have access only to a hard copy.  I have not offered to scan and post this as I'm sure it would infringe copyright. 

Your assumption is correct, I have read the article; several times.  Your local library might well have back numbers of NS.
Title: Re: Is infinity an illusion?
Post by: Bill S on 08/09/2013 20:40:45
Quote from: Pmb
That depends highly on what it is that we're trying to measure as being infinite. Can you give an illustrative example?

Surely, whatever we are trying to measure will be either finite, in which case we will, in principle, be able to measure it, or it will be infinite, in which case we will be unable to measure it with any finite measuring tool. 

“Illustrative example”?  Suppose my back garden (yard)  is 20x15m and I want to turf it.  I can measure it, and I will know how much turf to order, and how much this will cost.

Now suppose I decide my garden has infinite length and width.  With only finite measuring instruments, how can I measure it?  How can I know how much turf to order?

You might argue that I need an infinite amount of turf.  True as that might be, mathematically; what does it mean in the real world?

If I go to a supplier and ask for an infinite amount of turf, I suspect I would exit his office very quickly.

However, if he is anxious for business and thinks “I might do well out of this nutter”; how does he work out how much to charge me?  £infinite, perhaps?  What chance does he have of getting that?  In fact, all this example illustrates is that discussing the concept of an infinite amount leads to talking rubbish.


I hope this will prompt you to provide an example of how this “depends highly on what it is that we're trying to measure as being infinite”.  I'm doing my best to see the other side of this, but it's hard going.  :)



Title: Re: Is infinity an illusion?
Post by: Bill S on 08/09/2013 20:53:13
Quote from: alancalverd
The key phrase in your question was "think of". By no means the same as "is".

Although I agree with your statement, I have to say you have lost me.  I think I may have expressed my meaning badly.  I’ll try again.

If we regard the electron as being in any, or all, of an "infinite" range of positions at the same time, do we regard the electron as being in motion, or stationary?  I then wondered if that question, in itself, was too intuitive to have a place in our thinking about QM.

Title: Re: Is infinity an illusion?
Post by: alancalverd on 08/09/2013 21:24:13
Disregarding "regard" for the time being, the wave function does not go to zero anywhere, so there is an infinitesimal probability that whatever it describes could turn up anywhere at all. So in principle, however large you make your search radius, it could be outside.

Turfing the lawn is an interesting question. If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area, so a finite amount of water will flood a hyperbolic lawn, but you can never buy enough turf to cover it.   
Title: Re: Is infinity an illusion?
Post by: dlorde on 08/09/2013 23:08:30
Quote from: Bill S
Imagine my elation when I saw, in the New Scientist an article suggesting that some physicists were trying to remove infinity from scientific – and even mathematical – calculations. 
Please post the reference to this article. I'd like to read it...
This is as close as you'll get without a sub.: Infinity's end: Time to ditch the never-ending story? (http://www.newscientist.com/article/mg21929300.700-infinitys-end-time-to-ditch-the-neverending-story.html)
It talks about the Tegmark's dissatisfaction with the 'measure problem' (that an infinite multiverse predicts everything), and confuses the size of the observable universe with the size of the universe, concluding that 'there's no room for infinity'. It mentions the problem of being unable to measure to infinite precision/accuracy, and of Wildberger's "rational geometry" that, replaces angles with a "spread" defined as a rational output extracted from mathematical vectors representing two lines in space. It mentions Zeilberger idea that the number line is a loop (i.e. that there is a biggest number that 'overflows' when you add 1!). All in all, it's a bit of a hashed together article about opinions on the fringes, although, to be fair, it does give some space to those who don't have a problem with infinity, or think the problem lies elsewhere.
Title: Re: Is infinity an illusion?
Post by: dlorde on 08/09/2013 23:21:53
If we regard the electron as being in any, or all, of an "infinite" range of positions at the same time, do we regard the electron as being in motion, or stationary? 
As I understand it, the wave function doesn't tell you that the electron is everywhere at the same time, but just tells you the probability of detecting it at any given point. What the electron is doing in between measurements is anyone's guess. As the wave function evolves, so the probability of detecting the electron at any given point may change. I expect you may infer, from successive measurements, that an electron has moved, although presumably that involves certain assumptions... 
Title: Re: Is infinity an illusion?
Post by: dlorde on 08/09/2013 23:23:05
Turfing the lawn is an interesting question. If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area, so a finite amount of water will flood a hyperbolic lawn, but you can never buy enough turf to cover it.   
You could paint it green instead, by flooding it with green paint!  ;)
Title: Re: Is infinity an illusion?
Post by: JP on 08/09/2013 23:29:34
Disregarding "regard" for the time being, the wave function does not go to zero anywhere, so there is an infinitesimal probability that whatever it describes could turn up anywhere at all. So in principle, however large you make your search radius, it could be outside.

Just to nitpick--there can be zeros in the wave function, but they are essentially nodes of a standing wave (like the points in a standing wave on a string that don't move).  You're absolutely right that in principle, the wave function does extend out to infinity, though after a point there would be such a small chance of finding the electron that you'll never see it there in practice.
Title: Re: Is infinity an illusion?
Post by: Bill S on 09/09/2013 18:16:42
Quote from: alancalverd
If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area

I could do with an explanation, here, please.  ???
Title: Re: Is infinity an illusion?
Post by: dlorde on 09/09/2013 21:27:46
Quote from: alancalverd
If you rotate a hyperbola around the y axis you will generate a solid with a finite volume but infinite area

I could do with an explanation, here, please.  ???
Torricelli's Trumpet (Gabriel's Horn) (http://en.wikipedia.org/wiki/Gabriel's_Horn).
Title: Re: Is infinity an illusion?
Post by: alancalverd on 09/09/2013 23:50:38
Apologies! Of course, you have to rotate it around an asymptote, not the y axis. Pretty neat trick, though, ain't it?
Title: Re: Is infinity an illusion?
Post by: lean bean on 10/09/2013 13:30:56
Quote from: JP
In some cases such as the size of the universe, some theorists take it literally.  This is where I hedge my bets since you'd have to come up with a testable hypothesis to distinguish between an infinite universe or not.  As far as I know the question isn't settled. 

I run into a problem here.  If the Universe started at the BB, how could it be infinite?

I have been assured that it could have been infinite from the start.  However, I have yet to find an explanation as to how something infinitesimally small could be infinite.
Bill, what are you saying was infinitesimally small?  the universe or the observable universe?

Title: Re: Is infinity an illusion?
Post by: Bill S on 10/09/2013 15:28:53
Torricelli’s Trumpet is another example of a mathematical infinity, with which I have no argument.  I have a little trouble understanding how the volume could be finite; unless there is a mathematical “finiteness” similar to a mathematical “infinity”.  I’m very willing to accept that that may just be my lack of understanding, though.
Title: Re: Is infinity an illusion?
Post by: Bill S on 10/09/2013 15:37:53
Quote from: lean bean
Bill, what are you saying was infinitesimally small?  the universe or the observable universe?

We may be slipping into a terminological pitfall, here.  What do cosmologists believe began its existence at the BB; the universe or the observable universe?
Title: Re: Is infinity an illusion?
Post by: lean bean on 10/09/2013 18:42:31

We may be slipping into a terminological pitfall, here.  What do cosmologists believe began its existence at the BB; the universe or the observable universe?

What began its existence at the BB was a determinable space and time universe, before that equations breakdown. I think It's the density of matter/energy that brings about a breakdown of equations (singularity) not whether the universe is finite or infinite in size.
I know you like the following link...  http://www.astro.ucla.edu/~wright/infpoint.html
:)
You may remember my reply to you here..  Reply #24.
http://www.thenakedscientists.com/forum/index.php?topic=48385.0





Title: Re: Is infinity an illusion?
Post by: JP on 10/09/2013 21:13:35
This comes back to the original point of the post.  We got to the idea of "big bang" because we can only measure the universe where we have measuring devices (for cosmology, the relevant devices are mostly particle colliders and telescopes).  This limits the data we can collect.  From this data, we can figure out physical laws governing the universe.  By extrapolating back in time, we can try to figure out what the universe was like in the past.  This assumes, of course, that laws don't change in time and we're also limited to theories that match our current evidence.  For conditions far outside of what we can observe, we can't be sure our models are correct.

What happens when we extrapolate back far enough is that the models start predicting ever increasing density--a density that tends to infinity at some point in the past.  Most scientists take Bill's point of view here and believe that this infinity is an indication of a flaw in the model, not something that physically existed. 


Title: Re: Is infinity an illusion?
Post by: Bill S on 10/09/2013 22:26:41
Quote from: lean bean
You may remember my reply to you here..  Reply #24.

Glad you mentioned that.  I'd lost track of that thread.  Going back over it may save some repetition.  :)
Title: Re: Is infinity an illusion?
Post by: Pmb on 11/09/2013 02:08:58
Quote from: lean bean
You may remember my reply to you here..  Reply #24.

Glad you mentioned that.  I'd lost track of that thread.  Going back over it may save some repetition.  :)
Same here.
Title: Re: Is infinity an illusion?
Post by: Bill S on 11/09/2013 04:54:04
Quote
Same here.

Could it be an age thing, Pete?
Title: Re: Is infinity an illusion?
Post by: lean bean on 11/09/2013 18:46:55
What happens when we extrapolate back far enough is that the models start predicting ever increasing density--a density that tends to infinity at some point in the past.  Most scientists take Bill's point of view here and believe that this infinity is an indication of a flaw in the model, not something that physically existed.
JP
I was answering old Bill's question about what began at the BB in the context  of size of universe being infinite or finite.

I did mention the equations breakdown because of the density of matter/energy.
Even if they didn't breakdown, in what way could they suggest anything about the universe being finite or infinite in size?  that was the context in which I answered old Bill's question on this thread.


I did say something on the other thread here, my reply #29... http://www.thenakedscientists.com/forum/index.php?topic=48385.25

:) :)




Title: Re: Is infinity an illusion?
Post by: JP on 12/09/2013 02:39:04
Lean bean, I wasn't criticizing your points.  I was trying to point out an interesting "infinity" that appears in the equations and how it ties in with Bill's idea that infinities are not generally physical entities.  It's interesting that a few infinities are taken seriously by physicists "infinitesimally small" and "infinitely large universe," while most are not "infinite density" as one example. 

Infinities are funny things.  Even with the equations predicting infinite density, you can still have an infinitely large universe that is ALSO infinitely dense.  It remains infinitely large no matter how dense it is.  That's one of the weird parts of infinity.  If something is infinitely big and you compress it, it's still infinitely big, only denser! 
Title: Re: Is infinity an illusion?
Post by: lean bean on 12/09/2013 17:37:20
Infinities are funny things.  Even with the equations predicting infinite density, you can still have an infinitely large universe that is ALSO infinitely dense.  It remains infinitely large no matter how dense it is.  That's one of the weird parts of infinity.  If something is infinitely big and you compress it, it's still infinitely big, only denser!
Okey-dokey. :)

Title: Re: Is infinity an illusion?
Post by: Bill S on 12/09/2013 22:11:14
Quote from: JP
If something is infinitely big and you compress it, it's still infinitely big, only denser!

  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 

OK, it's only theoretical, but what happens if you try to consider practical applications?
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 13/09/2013 02:18:09
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 13/09/2013 02:20:49
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.
Title: Re: Is infinity an illusion?
Post by: JP on 13/09/2013 03:25:20
Quote from: JP
If something is infinitely big and you compress it, it's still infinitely big, only denser!

  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 

OK, it's only theoretical, but what happens if you try to consider practical applications?

Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe. 
Title: Re: Is infinity an illusion?
Post by: dlorde on 13/09/2013 09:31:03
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Why would that be a problem?

Quote
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.
Again, why would would that be a problem? In an infinite universe, you could have an infinite number of galaxies containing an infinite amount of all the natural elements, and an infinite amount of relatively 'empty' space containing an infinite amount of hydrogen & helium at very low densities.
Title: Re: Is infinity an illusion?
Post by: lean bean on 13/09/2013 17:40:54
  If you start with an infinite amount of low density and compress this to an infinite amount of high density, who/what "creates" the extra density?  Where does it come from? 
OK, it's only theoretical, but what happens if you try to consider practical applications?

who/what? Spacetime. It's a weird one Bill.
If it's spacetime determining the density, then in an infinite universe you have a contracting spacetime increasing density and expanding spacetime lowering density, but no change to size of universe... It's something like I was trying to convey earlier in the other thread #29
http://www.thenakedscientists.com/forum/index.php?topic=48385.25 (http://www.thenakedscientists.com/forum/index.php?topic=48385.25)

My wording there
Quote
‘then what happens in the context of an infinit universe when it is run backwards so that each observable universe ‘closes down’ to its respected point? How many points in an infinite universe? The equations break down ‘everywhere’? singularity everywhere? My sentence ‘an infinite expanse in a state of singularity’ could read as ‘an infinite expanse in an indefinable state.’
This infinity stuff is just so weird. :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/09/2013 17:58:43
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

Do I detect a hint of a "kindred spirit"; someone who has thought beyond mathematical infinities and found something astonishing?

Are you a scientist?
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/09/2013 18:13:45
Quote from: JP
Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe.

By definition, compressing something is making it smaller, but leaving it with the same amount of “stuff”.  If you could compress infinity; which I believe you can’t; you would produce a “smaller infinity”, which, outside mathematics, is nonsense.  If you could do that, your “smaller infinity” would have to be contained in a “larger infinity”; again, nonsense; so more “stuff” would have to come from somewhere to fill the "larger infinity". 

Why can we not unite relativity and QM?  It’s because infinity finds its way into the equations and produces nonsense.
 
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 13/09/2013 18:18:36
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom? That would mix finite and infinite.
Also having infinite helium would preclude having infinite electrons, protons and neutrons. You would have split infinities.

Do I detect a hint of a "kindred spirit"; someone who has thought beyond mathematical infinities and found something astonishing?

Are you a scientist?

I am what you could call a computer scientist if such a thing exists. I have been thinking about infinity since I was 12 and I'm now 53. To me infinity seems to be a singular term and inconsistent with reality. I feel it is more akin to zero than we imagine. Zero could also be considered a singular term although both have a different meaning and application in mathematics. They are abstract and in my opinion break down when applied to perceived reality causing all sorts of paradoxes.
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/09/2013 18:21:35
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/09/2013 18:29:28
Quote
I have been thinking about infinity since I was 12 and I'm now 53.

I started thinking seriously about infinity when I was 19, and I'm now 73.  Between us we chalk up quite a few years of thinking.  :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/09/2013 18:33:25
Quote from: LB
This infinity stuff is just so weird. :)

Agreed, but it is a problem only if you get stuck in "mathematical infinities".
Title: Re: Is infinity an illusion?
Post by: JP on 13/09/2013 18:56:23
Quote from: JP
Why is this a problem?  If the universe is actually infinite, it has an infinite amount of "stuff" so there would be no problem compressing it, having it get denser, and still having an infinite universe.

By definition, compressing something is making it smaller, but leaving it with the same amount of “stuff”.  If you could compress infinity; which I believe you can’t; you would produce a “smaller infinity”, which, outside mathematics, is nonsense.  If you could do that, your “smaller infinity” would have to be contained in a “larger infinity”; again, nonsense; so more “stuff” would have to come from somewhere to fill the "larger infinity". 

Why can we not unite relativity and QM?  It’s because infinity finds its way into the equations and produces nonsense.
 

The problem you've gotten yourself into here is that in the sense used to talk about the universe, compressing does not mean "getting smaller" by definition.  I could take the set of all real numbers and divide each number in it by 2.  I would be "compressing it" in that any two numbers will get closer to 0, but the set is still infinite and contains all real numbers. 

The idea of an infinite universe that could be more or less dense than it is currently while still remaining infinite is very similar.  The distance between any two points would increase or decrease, but if there was an infinite amount of stuff to begin with, you'll still have an infinite amount of stuff after "compressing" it.

You don't get yourself into trouble with conservation of density because there isn't any such law.  You don't violate conservation of energy or mass because in any region of the universe you look at, the conservation laws hold.  It's only when you look at an infinite region where you might have problems, but conservation laws aren't even defined over infinite regions, so that's not a problem either.

It might be the case that infinity is non-physical, but the argument that you couldn't have an expanding (or compressing) infinite universe doesn't forbid an infinite universe.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 13/09/2013 19:03:54
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 

The problem is infinity does occur in equations. In that sense it has to be explained. Zero was first introduced into the numbering system in India. How long ago I do not recall but it revolutionized mathematics and introduced base numbering systems.
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/09/2013 05:30:33
Quote from: JP
The problem you've gotten yourself into here is that in the sense used to talk about the universe, compressing does not mean "getting smaller" by definition.  I could take the set of all real numbers and divide each number in it by 2.  I would be "compressing it" in that any two numbers will get closer to 0, but the set is still infinite and contains all real numbers.

Shades of Hilbert’s Hotel here. The only reason the HH scenario appears to work is that you can never reach infinity.  Once you start moving guests, you never stop, so no one is without a room, but someone is always in transit.  I suspect David Hilbert had a sense of humour.

1> 0.5
2> 1
3> 1.5
Etc.

In what sense are the numbers compressed?

You are still using mathematical approximations to try to explain physical infinity.


Title: Re: Is infinity an illusion?
Post by: Pmb on 14/09/2013 06:23:22
Quote from: JH
If you had an infinite amount of helium in the universe then how could you also have one hydrogen atom?

Please explain this, Jeffrey, I've been trying, on a number of discussion forums, for about three years, to make that point!
Changing just one word in the above quote would take the argument to a whole different level, but let's take one step at a time.
 
Hi Bill,

Don't bother with claims from people who refuse to elaborate or clrarify what they mean. It's a trademark of pseudoscience and should be avoided at all costs.

I don't understand the problem you have with infinity. Could you clarify it for me?

Let me start from the basics:

Definition:

Infinite - )a) having no limit (b) without bound.

Obviously infinite is not a number as one can easily see from the definition. Under nomal situations it cannot take the place of a variable in an algebraic equation. Consider as an exmaple either the mass or charge density of a point particle. Both the mass and the charge are finite but since the mass/charge density = limit as vokume goes to zero of the ratio mass/volume, the mass/charge density is infinite, meaning that as the volume is made smaller and smaller the ratio mass(charge)/volume increases without bound. So in nature there does exist quantities which are infinite. The functions which describe densities of these types are called distributions and are defined using the Dirac delta function.

Typically we define all physical quantities in nature using four basic quantities which themselves cannot be defined in other terms. They are distance, time, mass and charge. These are called "kinematic variables" while things like velocity/speed, acceleration, current, momentum, energy, angular momentum etc. are defined in terms of kinematic variables. These are called dynamnic variables.

There are often disagreement on what are to be though of as representing "real" quantities while all other are derived quantities and as such concepts which exist only in the mind. However that in no way makes them useless.

So to begine with please let me know if you agree with the above and if you don't then please elaborate on it explaining what you agree with and disagree with. Then we can go from there.

Thanks, Bill!
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/09/2013 14:55:10
Quote
I don't understand the problem you have with infinity

 I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.  There is a strong tendency to think that anything outside mathematical infinities smacks of philosophy/theology, but such is not necessarily the case.

I agree with your explanations.  I would take issue with nothing in your last post, but it doesn’t address the major point I am trying to make.

Time is very short at the moment, but I will come back to it later.  Perhaps, if we can take one point at a time, we can achieve some clarity. 
Title: Re: Is infinity an illusion?
Post by: Pmb on 14/09/2013 15:17:27
Quote from: Bill S
I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.
In your mind, what is the difference between a mathematical one and a physical one.

My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.

Quote from: Bill S
There is a strong tendency to think that anything outside mathematical infinities smacks of philosophy/theology, but such is not necessarily the case.
I find that to be confusing. Can you give me a solid example? Thanks.

Quote from: Bill S
I agree with your explanations.  I would take issue with nothing in your last post, but it doesn’t address the major point I am trying to make.
Which is?

Quote from: Bill S
Time is very short at the moment, but I will come back to it later.  Perhaps, if we can take one point at a time, we can achieve some clarity. 
Okay. Let's start with the point that you'd trying to make.
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/09/2013 19:46:51
Quote from: Pete
Okay. Let's start with the point that you'd trying to make.


My starting point was asking the question: “Can there ever have been a time when there was nothing?”

When I first met that question, as a child, the answer, “No”, was cited as a proof of the existence of God.  Later, when I began to think seriously about this, I realised that the question applied to science as much as it did to theology.  One could neither prove, nor disprove the existence of God, but the existence of something eternal/infinite was another matter.

Logically, I could see no way in which, if there had ever been nothing, there could be something now.  There is quite a lot of literature around that suggests that the Universe represents the ultimate “free lunch” – it came from nothing. 

Avidly I sought out anything I could find that might explain this “something from nothing”.  The most recent book being “A Universe from Nothing” (L M Krauss).  I found this the most disappointing, to date.  His most quotable quote has to be: "When I say nothing, I don't mean nothing......"

Unlike Krauss, when I say nothing, I mean nothing: no space, no time, no matter, no energy, no quantum "something" to fluctuate; absolutely nothing.

The question remains, and perhaps we should make it the first point: “Can there ever have been a time when there was nothing?” 

I think not, but I’m open to persuasion.
Title: Re: Is infinity an illusion?
Post by: dlorde on 14/09/2013 21:00:05
The question remains, and perhaps we should make it the first point: “Can there ever have been a time when there was nothing?”
I'm not sure the question makes sense. How can there be time if there is nothing (assuming 'nothing' is the absence of anything, not just 'empty' space)?
Title: Re: Is infinity an illusion?
Post by: niebieskieucho on 14/09/2013 21:40:07
I'm sorry to admit that haven't read all the posts of this thread. I have not enough time to do it. Nevertheless, I feel not contaminated by comments of the participants of this topic.
As regards to infinities, they appear in mathematics playing a useful role, but as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite. You can see mathematician deviding 100 by 13, but you will never see the final result. Infinity is a process of continuation of finite things. In this case 100 is finite number and 13 too and the finite figures can follow one by one without stopping.
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.

--
I had a dream that a UFO landed on my yard, but when I woke up, they had already gone   
Title: Re: Is infinity an illusion?
Post by: JP on 14/09/2013 22:12:04
Quote from: Bill S
I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.
In your mind, what is the difference between a mathematical one and a physical one.

My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.
[/quote]

Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature (examples would be the size of the universe, the infinitesimal sizes of point particles or the infinitesimal division of space if it is continuous).  There's interesting arguments on both sides of the issue, but science is based on evidence, and so far there's nothing convincing either way.  Certainly the lower or upper limit is so small or so large that we can plug infinities into many equations without introducing much error (indeed, the error must be so small that we can't currently measure it or we'd know the answer already!)

What surprises me is seeing so many arguments against infinity based on personal intuition.  Surely, intuition shouldn't guide debates in science.  If we'd relied on intuition, we wouldn't have quantum mechanics or relativity!  Surely it's not intuitive to anyone (at least anyone without serious training in those fields) that particles behave like waves or that time and distance measurements can vary between observers.  Sure, infinity may not be able to exist in nature, but let's admit there's no proof either way, and certainly both equations with and without infinities can match our measurements.  We keep infinities around because it's easier to use calculus than to compute everything in terms of finite differences.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 14/09/2013 22:33:40
Quote from: Bill S
I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.
In your mind, what is the difference between a mathematical one and a physical one.

My own personal feeling is that this is no problem with scientists. In a strong sense of the phrase (and not to come off as too arrogant), we know better. We know that the answer all depends on definition. The author of the book I'm proof reading goes through great lengths to make sure the reader understands this regarding the event horizon of a black hole and the singularity at the center. The former is only a mathematical singularity which can be "transformed" away while the other is "real" and can't be transformed away.

Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature (examples would be the size of the universe, the infinitesimal sizes of point particles or the infinitesimal division of space if it is continuous).  There's interesting arguments on both sides of the issue, but science is based on evidence, and so far there's nothing convincing either way.  Certainly the lower or upper limit is so small or so large that we can plug infinities into many equations without introducing much error (indeed, the error must be so small that we can't currently measure it or we'd know the answer already!)

What surprises me is seeing so many arguments against infinity based on personal intuition.  Surely, intuition shouldn't guide debates in science.  If we'd relied on intuition, we wouldn't have quantum mechanics or relativity!  Surely it's not intuitive to anyone (at least anyone without serious training in those fields) that particles behave like waves or that time and distance measurements can vary between observers.  Sure, infinity may not be able to exist in nature, but let's admit there's no proof either way, and certainly both equations with and without infinities can match our measurements.  We keep infinities around because it's easier to use calculus than to compute everything in terms of finite differences.

I agree with all of the above. The discussion of infinity can become one of philosophy rather than hard science. In science we also have imaginary numbers which perform useful functions and no one would agree that they occur naturally.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 14/09/2013 23:28:18
As my last word on this topic, in relativity we have relativistic beta and gamma which can be used to plot an exponential curve and relates to time dilation, length contraction and energy input. However a lot of physical systems and populations can be described by a logistical s curve which is finite. As most of the physical systems outside of relativity have this behavior then why the exclusivity of relativity? Is there any evidence against the exponential nature? Has anyone even thought about this?
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 18:14:57
Quote from: dlorde
I'm not sure the question makes sense. How can there be time if there is nothing (assuming 'nothing' is the absence of anything, not just 'empty' space)?

You are, of course, absolutely right.  One of the difficulties inherent in talking about infinity is that our terminology is closely tied to the finite reality we perceive.  Some time ago I asked numerous people what they considered to be the difference between infinite and eternal.  The answers varied in form, but all came down to the same thing: eternity is infinite time and infinity is infinite space, or anything else.  Yet infinity is not a number of anything, including cubic metres of space, and eternity is not a vast expanse of time.  The introduction of time and space into the concept of infinity is, at best, a way of trying to imagine infinity.

Your comment is completely justified, but somewhat unhelpful in terms of discussion. 

Let me rephrase the question.  Can there ever have been nothing?  Or, perhaps:

If there had ever been nothing, could there be something now? 


Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 18:23:15
Quote from: Niebieskieucho
as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.


I cannot agree that everything in nature is necessarily finite.  Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t  necessarily so”.

Title: Re: Is infinity an illusion?
Post by: Pmb on 15/09/2013 18:33:21
Quote from: niebieskieucho
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.
That's not necessarily true. At this point in time we don't know either way which is true and which is false.

In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.

In a spatially open system space itself is unbounded, the size has no limit.  That's the very meaning behind the term infinity. Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 19:53:48
 
Quote from: JP
Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature

One of the reasons it has gone on so long is that we tend to talk across one another.  Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?

Does infinity exist in nature?  I neither know, nor pretend to know.

Does nature exist in infinity? The answer to that depends on the answer to  “Can there ever have been nothing”?
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 20:09:54
Quote from: Pmb
In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit.

Agreed.

Quote
That's the very meaning behind the term infinity.

It is, undoubtedly, the “meaning behind the term infinity” used in that sense (in a language such as English in which correct usage is assessed on the basis of "common usage by educated people" it is always possible to argue for or against a particular usage) but, although unbounded, your for ever expanding universe could never become “infinite”, it will always be a finite, expanding universe.

BTW, in the 21st century it is not as easy to distinguish between educated and uneducated people as it probably was when the above criterion was formulated.

Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 20:12:45
Quote from: JeffreyH
The discussion of infinity can become one of philosophy rather than hard science

No comment.   :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 20:20:09
Quote from: Pmb
In a strong sense of the phrase (and not to come off as too arrogant), we know better.

This is one reason why "hitch-hikers" like me come to people like you, looking for answers, and why we are sometimes disappointed when questions seem to be evaded.
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/09/2013 20:26:12
Quote from: Pmb
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.

You might demonstrate that the amount of material in a spatially open system is unbounded; you might theorise that it could be infinite; but could you prove that it was infinite?
Title: Re: Is infinity an illusion?
Post by: dlorde on 15/09/2013 20:33:21
... Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?
That wasn't the question I responded to, and rather than trying to sweep it under the carpet, I was hoping you might be able to explain how it made sense at all. You couldn't, so you changed the question to one that makes no more sense to me than the previous one.

How can nothing 'be'?
Title: Re: Is infinity an illusion?
Post by: niebieskieucho on 15/09/2013 21:09:33
Quote from: Niebieskieucho
as far as reality is concerned, the idea of infinity vanishes, as in nature everything is finite.

Quote
I cannot agree that everything in nature is necessarily finite.  Everything we see, we perceive as finite, but that is only our perception, which, as scientists frequently point out, “ain’t  necessarily so”.
What they consider could be infinite and on what grounds?
Nature (the universe) cannot be infinite, but if scientists claim otherwise, then it would mean that:
Finite matter of the universe is constantly expanding. It’s possible for some time.
Or
The universe is readily infinite. But it’s impossible, as anything real can be closed in a solid. Infinite universe could be compared to a solid without walls. Obviously such solid cannot exist. 
Title: Re: Is infinity an illusion?
Post by: niebieskieucho on 15/09/2013 21:22:17
Quote from: niebieskieucho
In nature everything is finite. We cannot imagine infinite things, thus such in nature do not exist.
Quote
That's not necessarily true. At this point in time we don't know either way which is true and which is false.
There is no problem to make a diagnosis. If one cannot sketch an infinite universe (no matter scale and accuracy) such universe does not exist (as any real things can be sketched).
Quote
In a temporally open system the universe will expand forever, the size of it becoming larger and larger with time, increasing without limit. That's the very meaning behind the term infinity.
I need not to refer to needless, so-called parameter omega. The universe does not expand. It’s a closed system. I realize that it’s hard to imagine “empty” space ending sharp, but there is no other feasibility. It must end sharp. The problem is, that we cannot see spatial structure from the perspective of physical entities of the micro-world hence such limitation gives the impression that the universe is infinite which is impossible. Such is my stance and I am not going to change it. 
Quote
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.
As I said earlier it’s only our human (due to natural limitations) perception. In reality space =/= nothing (lack of space). That implies finiteness of the universe, in other words both the universal space and its content.
Title: Re: Is infinity an illusion?
Post by: Pmb on 15/09/2013 21:37:23
Quote from: Bill S
Quote from: Pmb
In a strong sense of the phrase (and not to come off as too arrogant), we know better.
This is one reason why "hitch-hikers" like me come to people like you, looking for answers, and why we are sometimes disappointed when questions seem to be evaded.
I'm not entirely sure I understand what you mean here. But if I do then I don't think that you're being exactly fair here, Bill. You wrote
Quote from: Bill S
I think my “problem” with infinity is one of persuading people of science that there is a difference between mathematical infinities and physical infinity.
And this is the what I was commenting on. It was a statement which I assumed you meant was true. It wasn't a question. Since I'm a "person of science" I assume that you're referring to people like myself, right? If so then I disagree. I know the difference between a mathematical singularity and a physical one. Other physicists know the difference too. I'll find where in the new version of Black Holes and Time Warps - Second Version by Taylor, Wheeler and Bertschinger talk about the difference. Right now I'lll simply point out where in Gravitation and Spacetime - Third Edition by Ohanian and Ruffini these authors speak of it. Starting on page 325 Chapter 8 is entitled Black holes and gravitational collapse. The title of Section 8.1 is entitled Singularities and pseudosingularities. On page 326 the authors write
Quote
It is important to realize that the Schwarzschild “singularity” at r = rS is not a physical singularity. The “singularity in Eqs. (8.2) and (8.3) is spurious – it is a pseudosingularity or coordinate singularity. It arises from an inappropriate choice of coordinates and can be eliminated by a change of coordinates.
This is a perfect example of a real infinity versus pseudoinfinity. The infinity only arises because of a poor choice of coordinate systems. I don’t know of any relativist who doesn’t know this very elementary fact of differential geometry. So who is it that you’re saying that they don’t know the difference between mathematical infinities and physical infinity? And what is it you yourself mean when you speak of real infinities versus a pseudoinfinity and isn’t it possible that it’s you who don’t know the difference? I’ve asked you to explain them to me above and you went off on something you called a etymological diversion which I had to go look up. I was unable to learn what that phrase meant and forgot to get back to you on that. So what does it mean anyway?

You then later said
Quote from: Bill S
An infinite series (sequence) exists only in the (presumably finite) mind of the mathematician as a useful concept.
Is this what you meant by an infinity that isn’t real? If so then I think that’s misleading. What you really mean is what I’d say a physicist would mean, i.e. non-material infinity. Real to a physicist means something doesn’t exist. Einstein’s field equations only exist in the mind. They can be applied in the material world but that’s different.

Then you write
Quote from: Bill S
I simply call attention to the fact that infinity is not a number,..
I don’t think that any physicist would or has said anything different to you, have they? Nobody could ever claim that I thought infinity was a number since I’ve never thought that. You then write
Quote from: Bill S
…the concept of infinity is of singular importance in thinking about the origin of the Universe.
which I agree with but don’t understand why you posted it.









Title: Re: Is infinity an illusion?
Post by: Pmb on 15/09/2013 21:53:47
Quote from: Bill S
Quote from: Pmb
Also the amount of material in a spatially open system is infinite, the amount of material being unbounded and hence infinite.

You might demonstrate that the amount of material in a spatially open system is unbounded; you might theorise that it could be infinite; but could you prove that it was infinite?
I seem to have neglected from the beginning that physics does not have as its goal to be able to test whether something can be tested and the results prove something to be true. Science has never worked that way. It's not something that can be done in general. While it might be able to be done in certain cases it cannot be done in general.

It's well known that in physics nothing can ever be rigidly proven. Science has never been able to prove anything. That'd be like saying that the speed of light has been proven in all inertial frames. Since there are an infinite number of inertial frames how could that have ever been done in a finite amount of time?

Also, while one of the meanings of infinite is "without end" that is not the only one. It also means - http://www.merriam-webster.com/dictionary/infinite

Quote
Infinite - (1) having no limits (2) extremely large or great (3) extending indefinitely (4) endless <infinite space> (5)  immeasurably
To me immeasurably[/n] means <infinite amount of matter etc>

Quote from: Bill S
I have not offered to scan and post this as I'm sure it would infringe copyright. 
Oh well. However it'd probably be legal for a one time scan and e-mail. Some people do it all the time when they go to the library and want to share what they read in a magazine article. But no biggy. That probably mostly applies to research articles.

This thread is too long to cover all of these comments so I'll stop now.

Title: Re: Is infinity an illusion?
Post by: JP on 16/09/2013 01:39:33
Quote from: JP
Yes!  That's the issue at the heart of this thread (and it surprises me it's gone on so long).  I'd hope any physicist would admit that we don't know the answer to the question of whether infinities can exist in nature

One of the reasons it has gone on so long is that we tend to talk across one another.  Apart from dlorde’s attempt to brush it under the carpet, who has actually responded to the question: “Can there ever have been nothing”?

Does infinity exist in nature?  I neither know, nor pretend to know.

Does nature exist in infinity? The answer to that depends on the answer to  “Can there ever have been nothing”?

What scientific reason do you have for saying this?  My point is that much of what's being presented in this thread as obvious fact has no scientific merit.  If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?" I can see how the two are related.  (I can see how they're related intuitively, but intuition is a poor guide when dealing with the creation of the universe and possible infinities, and certainly intuition isn't scientific.)

Now, as for the question of whether there could have been nothing, most physicists would say no.  It's hard to really consider the question in terms of current science, though, and may never be possible.  To develop a theory that uses nothing would be so difficult/impossible because it could have no properties, so what would our theory and equations tell us?  The moment we wrote an equation about now "nothing" behaves, it has properties and is no longer nothing.  To write an equation that tells us how the universe comes from "nothing" would also endow "nothing" with properties, hence it isn't nothing.  As far as I can tell, it's a scientific catch-22.  That doesn't mean that "nothing" can't exist, but we're probably not equipped to handle it scientifically yet (and maybe never will be). 
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 04:26:18
Quote from: dlorde
That wasn't the question I responded to, and rather than trying to sweep it under the carpet, I was hoping you might be able to explain how it made sense at all. You couldn't, so you changed the question to one that makes no more sense to me than the previous one.

How can nothing 'be'?

Dlorde, I appreciate your input, not just in this thread, but also elsewhere.  I have no intention of insulting your obvious intelligence by accepting your invitation to assume that you failed to understand what I meant by either of those questions.  I am not looking for a battle of words, but a discussion of something I believe is relevant to scientific thought. 

I will infer that you are not really trying to sink the discussion in a see of semantics.

Picking up on your last question, may I ask what "is" when no thing exists?
Title: Re: Is infinity an illusion?
Post by: Pmb on 16/09/2013 04:35:16
I'd like to give an example from general relativity: Let us consider a spacetime devoid of all matter. Consider two systems S and S' where S is an inertial system and S' a non-iniertial system which is rotating uniformly relative to the first system. Both systems are devoid of all matter and of infinite extent. There is a time depenance relavant here in the absense of matter since the inertio-gravitational field is time depenant. This qualifies as a system devoid of all matter and has a time dependance on it. Is this what one of you were looking for?
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 04:41:36
Quote from: Pmb
I'm not entirely sure I understand what you mean here. But if I do then I don't think that you're being exactly fair here, Bill.

Pete, I apologise if my answer offended you, I certainly intended nothing personal.  However, if you were to look back through this and other threads in which infinity has been discussed, I think you will find that almost every point I have tried to make about physical infinity has been countered by arguments involving mathematical infinities.

Quote
I know the difference between a mathematical singularity and a physical one.

Never in question, as far as I am concerned.  I understand that infinity is involved in the concept of singularities, but I am not aware that that is what we were talking about.
Title: Re: Is infinity an illusion?
Post by: Pmb on 16/09/2013 04:54:09
Quote from: Bill S
Pete, I apologise if my answer offended you, I certainly intended nothing personal. 
No worries my friend. I know that. :)

Quote from: Bill S
However, if you were to look back through this and other threads in which infinity has been discussed, I think you will find that almost every point I have tried to make about physical infinity has been countered by arguments involving mathematical infinities.
I disagree. To me a mathematical infinity is something like f(x) = limit(x->0) 1/x. A physical infinity is limit (r->0) kQq/r  where Q is charge on particle #1, q = charge on particle #2 and k = Coulomb's constant (not exactly sure of name). I think that a lot of people, including yourself, perhaps see both as being only mathematical where I see the former as mathematical since it pertains only to quantities which have a mathematical meaning whereas the second pertains to physical quantities and results in a physical force and the meaning of infinity has its usual meaning.

I'll speak only for myself now: When I say that I know this kind of thing what I'm saying is that I have a different opinion on the definition.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 04:55:16
Quote from: Pmb
isn’t it possible that it’s you who don’t know the difference?

Yes, it is quite possible.

Quote
I’ve asked you to explain them to me above and you went off on something you called a etymological diversion

Pete, if you would remind me of the context (and post) in which I used the term etymological diversion in response to a question from you I will gladly try to clarify it.

Quote
Real to a physicist means something doesn’t exist.

You have lost me there, Pete.
Title: Re: Is infinity an illusion?
Post by: Pmb on 16/09/2013 05:06:23
Quote from: Bill S
Quote from: Pmb
isn't it possible that it's you who don't know the difference?
Yes, it is quite possible.
It's funny. I don't like talking to my friends with that tone. Sorry about that, Bill. :(
Quote from: Pmb
I've asked you to explain them to me above and you went off on something you called a etymological diversion.

Quote from: Bill S
Pete, if you would remind me of the context (and post) in which I used the term etymological diversion in response to a question from you I will gladly try to clarify it.
See post #32 on page 2.
Quote from: Bill S
Quote from: Pmb
Real to a physicist means something doesn't exist.
You have lost me there, Pete.
Yeah. Me too! LOL!! I think I meant to say that Real to a physicist means that something exists. I.e. in a sense they're synonyms.
Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 12:40:31
I will infer that you are not really trying to sink the discussion in a see of semantics.
I'm trying to clarify and make sense what is being talked about, if only for my own understanding, and I think the semantics are central to that understanding.

Quote
Picking up on your last question, may I ask what "is" when no thing exists?
No thing 'is'. The problem for me here is that you're trying to treat an absence, a negation, as if it was something (some thing). But although it's used colloquially as if it were a thing, it's generally used relatively or comparatively regarding the absence of certain groups of things, e.g. "What's in the box? - nothing" means no objects, 'just air', or even 'just vacuum (empty space)'.  If there really was nothing at all in the box, its sides would have to be collapsed together, it would be flat; ironically, in this situation you wouldn't colloquially say "there's nothing in the box", because it isn't really a box when flat - a box always contains something.

So 'nothing' isn't a physical thing, it doesn't exist except as a concept. Physical existence is a property of things. If we're being strict about its meaning, i.e., beyond the colloquial, it seems to me that it doesn't make sense to treat it as something physical.

So a question like "what is there in the complete absence of anything?" can be answered with "nothing" only in a tautological sense, because an absence isn't something that physically exists. I suspect this is partly why physicists like Lawrence Krauss (A Universe From Nothing (http://www.amazon.co.uk/s/?ie=UTF8&keywords=krauss+universe+from+nothing&tag=googhydr-21&index=aps&hvadid=23547114632&hvpos=1t1&hvexid=&hvnetw=g&hvrand=830531812103162363&hvpone=&hvptwo=&hvqmt=e&hvdev=c&ref=pd_sl_96ju5faapo_e)) don't literally mean 'nothing', but some kind of 'empty' spacetime that makes sense physically.

As I said, it seems to me that the semantics of 'nothing' are crucial to understanding what we're talking about. However, I'm open to be persuaded that my interpretation of the semantics is faulty.



Title: Re: Is infinity an illusion?
Post by: JP on 16/09/2013 16:13:04
Well put, dlorde.

I suspect a problem with 'absolute nothingness' is that it's scientifically useless. 

It's like thinking of the process of building models of the universe (or parts of it) as starting with a blank sheet of paper and writing down all the properties of the model on it.  Eventually, you'd hope to have a model that made predictions about measurable quantities in order to be scientifically useful.  If you want to ask 'what initial states of the universe are possible?' you'd be asking for what initial states you could write on the paper that, coupled with a set of laws you also write down, would match what can be observed/measured. 

The problem with 'absolute nothingness' is that it would be a completely blank piece of paper, which clearly in no way relates to measurements/observations we can make today.  Even if you could somehow have the 'initial state' of the universe be a blank part of the paper, you'd still have to have another part dealing with measurable quantities: position, time, energy, momentum.  Since the paper has something written on it, it's necessarily not dealing with 'absolute nothing.'

The 'nothing' that Lawrence Krauss and other scientists are talking about is similar to having the universe part of the paper blank, but the physical laws part of the paper covered with equations: quantum mechanics, general relativity, space, time, etc. We can start from a universe in a 'blank state,' but because physical laws describe the behavior of measurable properties of that blank state (energy, distance, etc.) we aren't describing 'absolute nothing.'
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 18:31:55
Quote from: JP
If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?"

That’s not quite what I said, JP.  As you accurately quoted, what I said was: “Does nature exist in infinity? The answer to that depends on the answer to “Can there ever have been nothing”?”

In other words: if something has always existed, then the Universe must be intimately linked to that something.  In fact, if causality is relevant to the situation, that something must be causally related to the Universe.

Quote
Now, as for the question of whether there could have been nothing, most physicists would say no

That’s encouraging.  Would I be right in thinking that those who would say yes would claim that the Universe came from nothing? 

Would it also be the case that they would redefine nothing so as to make it something?

If nothing has a different meaning in science than it does in general parlance, I am neither qualified – nor anxious – to argue with that.  I think it would good if scientists who write Pop Sci books made that distinction clear to their readers, who, in general, will be non-scientists, but that’s another matter.

Quote
The problem with 'absolute nothingness' is that it would be a completely blank piece of paper

Have we reached the stage where, if we mean nothing we have to say absolutely nothing, otherwise we are talking about something?

I like your analogy using the sheet of paper to represent nothing, but we might change the perspective slightly and consider that “absolutely nothing” is represented by no paper.  In that case there will be nothing to write on so we will never have our model universe, however we redefine nothing.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 19:03:50
Quote from: Pmb
See post #32 on page 2.

Thanks Pete, I had lost sight of that. 

What I said was “I feel sure you did not intend starting an etymological diversion”.  Obviously that was not as reassuring as it was intended to be.  :(

I always try to answer questions, but of late my visits to the computer have been brief and hurried, so I may have fallen short on occasions.  I think we are very close to the point where I shall have to look at how my thoughts on infinity have been influenced by this discussion.  Hopefully comparing older with newer thoughts will provide some answers. 

Title: Re: Is infinity an illusion?
Post by: JP on 16/09/2013 19:29:51
Quote from: JP
If you can tell me why, scientifically, "can there be infinity in nature" depends on "can there ever have been nothing?"

That’s not quite what I said, JP.  As you accurately quoted, what I said was: “Does nature exist in infinity? The answer to that depends on the answer to “Can there ever have been nothing”?”

In other words: if something has always existed, then the Universe must be intimately linked to that something.  In fact, if causality is relevant to the situation, that something must be causally related to the Universe.
That argument works if you expect any two events in the universe to be causally connected, but clearly this isn't the case!  A star in our galaxy and a star outside the visible universe can both go supernova and these events have no causal connection to each other.  Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it. 

This is tough to get one's head around, but when dealing with ideas like the creation of the universe, our poor brains aren't very well equipped to deal with it.  We have a hard enough time thinking beyond our low velocities/accelerations and large size to accept relativity and quantum mechanics, let alone thinking about the creation of space and time themselves!

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Now, as for the question of whether there could have been nothing, most physicists would say no

That’s encouraging.  Would I be right in thinking that those who would say yes would claim that the Universe came from nothing? 

Would it also be the case that they would redefine nothing so as to make it something?

If nothing has a different meaning in science than it does in general parlance, I am neither qualified – nor anxious – to argue with that.  I think it would good if scientists who write Pop Sci books made that distinction clear to their readers, who, in general, will be non-scientists, but that’s another matter.

Yes.  As much as I respect Lawrence Krauss, I strongly dislike the title "A Universe from Nothing."  I haven't read it, but from hearing him speak about his ideas, I believe he's arguing that the universe came from quantum fluctuations.  But for quantum fluctuations to exist, quantum mechanics must exist and therefore there are properties to the pre-universe: at least the properties necessary to support some flavor of quantum mechanics.At any rate, there must be some physical laws existing that describe how to go from pre-universe to having the universe.

So his "nothing" is indeed "something" that has very precise properties!  Of course, the title "a universe from something" doesn't have the same ring to it.

(As an aside, even talking about pre-universe is problematic, since the universe defines all time that we know of, so it's questionable if time exists if the universe doesn't... Talk about mind-benders!)

Physicists don't ever really talk about "absolute nothing" (my definition, hence the quotes) which would be the absence of all properties of the model as well as the model itself--the "blank sheet of paper."  Since there would be no rules to cover quantum fluctuations or any other means of generating the universe, it wouldn't allow us to describe the creation of the universe.  Moreover, there would be no definitions of energy, time, distance or any other measurable quantity, which is why it's not useful to physicists!  We may be able to talk about it in metaphysics, but if it in no way relates to anything we can observer or measure, it's not useful to scientists.

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The problem with 'absolute nothingness' is that it would be a completely blank piece of paper

Have we reached the stage where, if we mean nothing we have to say absolutely nothing, otherwise we are talking about something?

I like your analogy using the sheet of paper to represent nothing, but we might change the perspective slightly and consider that “absolutely nothing” is represented by no paper.  In that case there will be nothing to write on so we will never have our model universe, however we redefine nothing.

[/quote]

:)

This is the problem with dealing with metaphysical concepts.  I like the blank paper, and I think it works so long as we say "whatever I write on this paper represents nature."  Then the only way we could describe a nature that is "absolute nothing" is to remove all properties from it, hence a blank sheet of paper.

We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk, you'd now have an empty desk.  And you'd have to remove that desk.  Then you'd have an empty room, but you'd have to remove the room.  Then you'd have empty space, but you'd have to remove space.  Then you'd have an empty [whatever contains space], and you'd have to remove that, etc. etc. etc. 

It's an interesting metaphysical exercise, but I'm not sure it's of use to scientists.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 19:34:42
Quote from: dlorde
I'm open to be persuaded that my interpretation of the semantics is faulty

I think your interpretation of the semantics is spot on. 

Perhaps I should continue working on the wording of “the question”.  As I am confident you know what I am really asking, and as you obviously have a facility with words, and an enviable feeling for semantic rectitude, your help would be appreciated. 
Title: Re: Is infinity an illusion?
Post by: yor_on on 16/09/2013 19:58:34
How about the Copenhagen model? In where consciousness is a non ignorable part of any 'system'. To make a measurement, as we think of it normally, consciousness must be involved, and so 'histories' as our definitions of a past, a 'now', and a future. What would a quantum computer have to say about those ideas?
Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 20:09:51
... As much as I respect Lawrence Krauss, I strongly dislike the title "A Universe from Nothing."  I haven't read it, but from hearing him speak about his ideas, I believe he's arguing that the universe came from quantum fluctuations.  But for quantum fluctuations to exist, quantum mechanics must exist and therefore there are properties to the pre-universe: at least the properties necessary to support some flavor of quantum mechanics.At any rate, there must be some physical laws existing that describe how to go from pre-universe to having the universe.

So his "nothing" is indeed "something" that has very precise properties!  Of course, the title "a universe from something" doesn't have the same ring to it.
Yes, pretty much; Krauss explains his views on the different 'levels' or semantics of nothing in this interview (http://www.abc.net.au/radionational/programs/scienceshow/lawrence-krauss-discusses-nothing/3992246) (click on 'Show' to the right of 'Transcript').
Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 20:33:09
How about the Copenhagen model? In where consciousness is a non ignorable part of any 'system'. To make a measurement, as we think of it normally, consciousness must be involved, and so 'histories' as our definitions of a past, a 'now', and a future. What would a quantum computer have to say about those ideas?
Strictly speaking, it's the Copenhagen Interpretation, and its principles don't invoke consciousness. But wave function collapse is fundamental, and is said to occur when an observer (a classical device) registers an outcome.

As Heisenberg said, "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; but the registration, i.e., the transition from the "possible" to the "actual," is absolutely necessary..." (my bolding).

Eugene Wigner and a few others proposed that minds were external observers, not amenable to QM, and minds perform the measurements that collapse the wave function. It is not a popular idea among physicists, but very popular in pseudoscience.
Title: Re: Is infinity an illusion?
Post by: yor_on on 16/09/2013 20:59:01
A pleasure to see you here Dlorde :) As for any interpretation I, as always, get stuck on the question of 'observing'. I have an idea in where you can't separate a system of non conscious able 'observers' from one in where consciousness must be involved. Can a universe 'exist' without consciousness being involved?
=

Heh, as seems Heisenberg. It's the simplest explanation to me, assuming that logic is what defines a universe. Although :) I do like fantasy, and sometimes your fantasies might define physics, presuming you have a way to translate it into a logic.
Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 21:23:58
I think your interpretation of the semantics is spot on.
OK, good... 

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Perhaps I should continue working on the wording of “the question”.  As I am confident you know what I am really asking, and as you obviously have a facility with words, and an enviable feeling for semantic rectitude, your help would be appreciated.
This discussion has got me thinking again about infinity and nothing, and it now seems to me that absolute nothing (Krauss's 3rd 'nothing', which he kind of skirts around in the interview) is not a coherent physical concept, so there can't 'have been' absolute nothing, any more than 'not stamp collecting' is a hobby, or 'an absence of cotton' is a saleable commodity.

Krauss's 2nd nothing is no particles, or radiation, or even space itself, but the laws of quantum mechanics only - which allow space to appear as a quantum fluctuation:
Quote from: L.Krauss
... space itself is subject to quantum mechanical properties, including the fact that it can fluctuate in an out of existence, just like the particles within space can fluctuate in an out of existence. But if that's possible, you could start with no space itself and create the nucleus, the basis of the universe. You can literally have no space and no time and, poof, suddenly a space can appear and a time within that space.
I'm not qualified to speculate on how, or what it means, that the laws of QM can exist in the absence of spacetime.

Krauss's 1st nothing is the popular concept of 'empty space', the quantum vacuum, which, I think we agreed, doesn't really count as nothing in this context.

The idea of an infinite past doesn't really apply if, as in the 2nd nothing, time itself has a 'start' point. Hawking's (now obsolete) big bang to big crunch sphere model, with time running north to south, provides a visualization of this; where time starts at the north pole of the sphere, the universe expands, reaches a maximum size at the equator, and shrinks back to a big crunch at the south pole, where time ends. In this model, there is no 'before the big bang', in the same way there is no 'north of the north pole'.

Admittedly, it's difficult to conceive of time beginning without intuitively trying to imagine what was before that, but OTOH, is it really any easier to conceive of an infinite past?  I'm currently thinking of a self-contained, finite spacetime 'blob' that has no boundaries - i.e. no edge or 'outside' in either space or time; but I'm open to an infinite past given a plausible argument (and given that I can somehow distinguish it as a better model than a finite past!).
Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 21:47:08
A pleasure to see you here Dlorde :)
Thank you, and likewise, I'm sure ;)

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... Can a universe 'exist' without consciousness being involved?
All the indications are that consciousness (whether ours or alien) must have arrived somewhat after the big bang because, as far as we know, it takes a while to evolve (unless you want to speculate that a rapidly expanding ball of plasma and/or hydrogen can be conscious). Even the idea that consciousness is required to collapse a wave function doesn't preclude it. Also, what level of consciousness would it take to maintain the existence of the universe - would a rat do? a frog? And consider - is it reasonable to suggest the universe will cease to exist when the last consciousness dies?

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Heh, as seems Heisenberg. It's the simplest explanation to me, assuming that logic is what defines a universe.
Sorry, I can't parse that...
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/09/2013 21:58:31
Quote from: JP
"A Universe from Nothing."  I haven't read it

Don’t bother, unless you are keen to know why Krauss thinks God is an outdated concept!

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even talking about pre-universe is problematic, since the universe defines all time that we know of, so it's questionable if time exists if the universe doesn't...

Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?

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Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it.

“…then those points must be causally connected to this event and thus to each other somehow.”  I would accept that if something caused the Universe to come into being it would be causally connected to the Universe, which would include every point.  To argue that this implied that there was any causal link between individual points, apart from their having a common origin, would be very difficult to justify.  My sister and I have a common origin, but neither of us is causally responsible for the other. :)

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We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk......

Not necessarily, because you are constructing the model, you do not have to include the desk in your model.  If you call the paper “nothing”, then you are in the same position as Krauss, you have to accept that your “nothing” is “something”.  Without the paper you really have nothing (unless you choose to add another “something”, like a desk), and with “nothing” you have nowhere to construct your universe.

Title: Re: Is infinity an illusion?
Post by: dlorde on 16/09/2013 22:24:59
Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?

I'd agree that time is required for change, but if time itself begins with the universe, then (as I mentioned previously) there is no 'before', so there can have been no change. IOW it's only a problem if we assume a default timeline within which the universe begins (the intuitive view). Without that timeline, the universe just is, i.e. there's no process by which it 'comes into existence'; it is only from the point of view of its inhabitants that it 'begins' at time=0.
Title: Re: Is infinity an illusion?
Post by: JP on 17/09/2013 00:15:13
Is it not necessary for time to exist in order that change may happen?  The change from “no Universe” to “Universe” would require time to exist in order to let the change happen; wouldn’t it?
Maybe.  At the risk of sounding like a crackpot, a lot of advances in science require throwing out common sense ideas that we trust based on our place in the universe.  For example, particles were particles until we realized that on small scales they might not be.  Time and length measurements should agree between observers according to our intuitive view of the world--only they don't if we imagine traveling fast enough.

Similarly, the idea that time is fundamental might not be true--we're used to it because our brains work by turning energy into order, a process which necessarily follows an arrow of time.  If time is a quanta, which can pop out of some more fundamental "stuff," then our universe and our view that things evolve in time might just be due to the fact that our brains exist in a universe with time and require time in order to function.

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Now, you might say, if some event created all points in the universe, then those points must be causally connected to this event and thus to each other somehow.  But causality applies to events within our universe, and if some external event created the universe, it would not exist within the universe (since this event created the universe).  Therefore, there's no reason to impose causality on it.

“…then those points must be causally connected to this event and thus to each other somehow.”  I would accept that if something caused the Universe to come into being it would be causally connected to the Universe, which would include every point.  To argue that this implied that there was any causal link between individual points, apart from their having a common origin, would be very difficult to justify.  My sister and I have a common origin, but neither of us is causally responsible for the other. :)
I'd argue against the idea that something that "caused" the universe had to be causally connected to it.  Causally connected means something very specific about connections within space-time.  A cause of the universe would exist outside of, or at a more fundamental level than space-time, so there's no reason why causality need to apply to it.  In fact this cause would create space and time somehow, so I suspect it's impossible to apply an idea like causality to it.

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We could say "we'd have to remove the paper," but then things get circular, because if the paper was on a desk......

Not necessarily, because you are constructing the model, you do not have to include the desk in your model.  If you call the paper “nothing”, then you are in the same position as Krauss, you have to accept that your “nothing” is “something”.  Without the paper you really have nothing (unless you choose to add another “something”, like a desk), and with “nothing” you have nowhere to construct your universe.


But "not including the desk" is a property of the model.  ;)  I suspect there's little to be gained by trying to define metaphysical nothingness in terms of precisely what it doesn't contain.  Certainly I don't see how it's got any use in physics.

I don't literally mean we have paper, but if the paper defines the set of properties, then a blank paper would denote nothingness (a set devoid of all properties).  This is problematic, though, since "a set devoid of properties" has the property of being devoid of properties!
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 17/09/2013 02:16:57
I wasn't going to reply to this again but if we consider Newton's third law.

Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.

If we consider the universe to be a body in the sense that it has mass then what opposite effect did the creation of the universe have? The collapse of another universe of the same mass? That seems to be equal and opposite.
Title: Re: Is infinity an illusion?
Post by: dlorde on 17/09/2013 11:23:12
I don't literally mean we have paper, but if the paper defines the set of properties, then a blank paper would denote nothingness (a set devoid of all properties).  This is problematic, though, since "a set devoid of properties" has the property of being devoid of properties!
Again, if you treat the absence of something as a thing in its own right, particularly as the same type of thing that is absent (in this case a property) when dealing with sets, you can get into all kinds of awkward and contradictory logical knots; for example, you can say that not only does the paper have the new property of being devoid of all properties, but it also has the property of being devoid of property A, the property of being devoid of property B, ...etc. This list can include all conceivable properties, not just the properties it would normally have (and, of course, the property of being devoid of all inconceivable properties too). It really doesn't work.

This kind of reminds me of Russell's Paradox (http://en.wikipedia.org/wiki/Russell's_paradox) (i.e. does the set of 'all sets that don't contain themselves' contain itself or not?), where Russell developed a type theory to separate types of sets and where they could be applied, that removed such self-referential loops.

Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.
Title: Re: Is infinity an illusion?
Post by: alancalverd on 17/09/2013 19:18:49
Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.

Although somewhat off-topic, I must defend the existence of holes a a thing rather than a non-thing. If you observe the Hall effect in a p-type semiconductor it is obvious that the moving charge really is positive. In a biased p-n junction photodiode, it is clear that the drift velocity of the holes is lower than that of the electrons.
Title: Re: Is infinity an illusion?
Post by: dlorde on 17/09/2013 22:14:20
Although, having said all that, there are physical instances where it is legitimate to treat the absence of something as a thing in its own right, such as the movement of 'holes' in semiconductors, but these are restricted contexts.

... I must defend the existence of holes a a thing rather than a non-thing. If you observe the Hall effect in a p-type semiconductor it is obvious that the moving charge really is positive. In a biased p-n junction photodiode, it is clear that the drift velocity of the holes is lower than that of the electrons.
As I said, it is legitimate in some contexts to treat them as things. In case of confusion, I was thinking of electron holes (http://en.wikipedia.org/wiki/Electron_hole).
Title: Re: Is infinity an illusion?
Post by: Pmb on 17/09/2013 23:07:01
I'd like to point out that there is a difference between things that exist that have no material existance such as credit.

Would you rather have nothing or have nothing as well as owe nobody anything?
Title: Re: Is infinity an illusion?
Post by: dlorde on 17/09/2013 23:24:18
I'd like to point out that there is a difference between things that exist that have no material existance such as credit.
Credit is an interesting one, because it is a provisional or stand-in thing; which makes me wonder about virtual particles and other quantum fluctuations that have a notional quality, only occasionally resulting in 'real' things...
Title: Re: Is infinity an illusion?
Post by: Bill S on 18/09/2013 01:26:10
Quote from: dlorde
Without that timeline, the universe just is, i.e. there's no process by which it 'comes into existence'; it is only from the point of view of its inhabitants that it 'begins' at time=0.


If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?
Title: Re: Is infinity an illusion?
Post by: Pmb on 18/09/2013 01:56:11
Quote from: Bill S
If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?
No neccesarily. If you're educated in calculus then you're familiar with the concept of being bounded below but unbound above or bounded above but unbound below. Both of which are infinite. See http://mathworld.wolfram.com/Infinite.html
Title: Re: Is infinity an illusion?
Post by: Bill S on 18/09/2013 03:46:06
Pete, if the Universe had no beginning, is it not unbounded in that direction, and therefore infinite?
Title: Re: Is infinity an illusion?
Post by: Pmb on 18/09/2013 03:54:03
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.
Title: Re: Is infinity an illusion?
Post by: dlorde on 18/09/2013 09:02:30
If it does not come into existence, then it has no beginning, so is it not, by what seems to be popular definition, infinite?
Depends what you mean by 'infinite' here. 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? and I don't see that infinite spatial extent is a requirement.
Title: Re: Is infinity an illusion?
Post by: Bill S 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.


Title: Re: Is infinity an illusion?
Post by: jeffreyH 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?
Title: Re: Is infinity an illusion?
Post by: Pmb 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.
Title: Re: Is infinity an illusion?
Post by: AndroidNeox 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.
Title: Re: Is infinity an illusion?
Post by: dlorde 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).
Title: Re: Is infinity an illusion?
Post by: Bill S 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. 

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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.

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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.”

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

Unbounded, perhaps, but it can never become infinite.

Title: Re: Is infinity an illusion?
Post by: jeffreyH 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.
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: JP 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.

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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.”

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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).
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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?

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  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.
Title: Re: Is infinity an illusion?
Post by: dlorde 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 (http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Potential_infinity.html).
Title: Re: Is infinity an illusion?
Post by: Bill S 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? 
Title: Re: Is infinity an illusion?
Post by: dlorde 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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. 
Title: Re: Is infinity an illusion?
Post by: Bill S 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.
Title: Re: Is infinity an illusion?
Post by: dlorde 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.
Title: Re: Is infinity an illusion?
Post by: lean bean 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?
Title: Re: Is infinity an illusion?
Post by: Bill S 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.   

Title: Re: Is infinity an illusion?
Post by: Bill S 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.
Title: Re: Is infinity an illusion?
Post by: dlorde 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.
Title: Re: Is infinity an illusion?
Post by: jeffreyH 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.
Title: Re: Is infinity an illusion?
Post by: yor_on 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?
Title: Re: Is infinity an illusion?
Post by: yor_on 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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". 
Title: Re: Is infinity an illusion?
Post by: lean bean on 22/09/2013 10:29:26
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.
I must be missing some deeper  point here...
You seem to be just saying... you can't measure the extent of infinity and you can't measure a total duration period for eternity, is that a surprise?
 
Quote
I assume time, as we perceive it, had a beginning.

Going along with the standard BB model that's right, but as you know ,there are other theories, the eternal inflationary universe idea and others.

Those yoga chappies always seem to END their timeless period! That’s if they say they can go into a ‘timeless’  whatnot.
Title: Re: Is infinity an illusion?
Post by: Bill S on 22/09/2013 13:03:23
Quote from: JeffreyH
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.

With a mobius strip, as with a circle, you do come back to the same place.  The time, of course, is different so you could argue that you were looking at different spacetime events each time round, but I'm a bit doubtful about the value of that.  You could claim that your garden was infinite because you could keep walking round it without returning to the same spacetime event.
Title: Re: Is infinity an illusion?
Post by: Bill S on 22/09/2013 13:07:39
Quote from: lean bean
I must be missing some deeper  point here...
You seem to be just saying... you can't measure the extent of infinity and you can't measure a total duration period for eternity

That's exactly what I'm saying.  Tell me what you feel you have missed and let's see if we can sort it out.
Title: Re: Is infinity an illusion?
Post by: dlorde on 22/09/2013 15:06:06
Observers, do they need a consciousness, and what defines a consciousness?
As I understand it, an observer is potentially anything involved in a measurement, and, in QM terms, a measurement is an interaction. So a particle can be an 'observer'. In macro-scale physics, the observer just provides a disinterested viewpoint; at micro-scales, the 'observer effect' becomes significant, and in some interpretations of QM, the relation between observer and observed is complicated, even incestuous.

As for what defines a consciousness, I'm not sure what you're really after; a dictionary? those behaviours we identify as conscious? claims of qualia?

Quote
A arrow?
?? what about an arrow?

Quote
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?
I have no idea what you're talking about.

Quote
How do we define consciousness?
You go first...
Title: Re: Is infinity an illusion?
Post by: lean bean on 22/09/2013 18:49:27
Quote from: lean bean
I must be missing some deeper  point here...
You seem to be just saying... you can't measure the extent of infinity and you can't measure a total duration period for eternity 

That's exactly what I'm saying.  Tell me what you feel you have missed and let's see if we can sort it out.
Well, I don't think I have missed anything if that's all your saying, I have always thought of infinity and eternity as unmeasurable, that's why I asked '' is that a surprise?'' Here...

You seem to be just saying... you can't measure the extent of infinity and you can't measure a total duration period for eternity, is that a surprise?
My bold.  :)
 
Title: Re: Is infinity an illusion?
Post by: Bill S on 22/09/2013 22:43:17
Quote
is that a surprise?

Not to me; and apparently not to you.  I'm inclined to think that no one will admit to being surprised.  :)
Title: Re: Is infinity an illusion?
Post by: dlorde on 22/09/2013 23:42:22
I'm inclined to think that no one will admit to being surprised.  :)
I'm only surprised (as I think lean bean was) that you said it at all...
Title: Re: Is infinity an illusion?
Post by: Bill S on 23/09/2013 15:21:15
Quote from: dlorde
I'm only surprised (as I think lean bean was) that you said it at all...

Perhaps the surprising thing is that I didn't say it sooner!  One thing I have certainly learned from discussing infinity is that however obvious something may seem to me, it is best to make sure others agree before trying to progress. 

This could be the only point on which we have complete agreement.

After all this time, is it safe to say we agree that infinity/eternity is not measurable?

Is someone going to say: there are countable infinities; if you can count them, you can measure them?  :)
Title: Re: Is infinity an illusion?
Post by: dlorde on 23/09/2013 16:50:47
Is someone going to say: there are countable infinities; if you can count them, you can measure them?  :)
Not exactly; there are countable infinities (http://plus.maths.org/content/maths-minute-countable-infinities); it means you can count them just as you can count the integers (you can only count them all if you've got infinite time off work).
Title: Re: Is infinity an illusion?
Post by: Bill S on 23/09/2013 18:53:10
Quote from: dlorde
Not exactly

Hence the smiley.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 23/09/2013 19:12:00
Quote from: JeffreyH
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.

With a mobius strip, as with a circle, you do come back to the same place.  The time, of course, is different so you could argue that you were looking at different spacetime events each time round, but I'm a bit doubtful about the value of that.  You could claim that your garden was infinite because you could keep walking round it without returning to the same spacetime event.

The point being with an infinite mobius strip you would need an infinite amount of time to get back to where you started. Whilst it would be theoretically possible in reality it would never be achieved.
Title: Re: Is infinity an illusion?
Post by: dlorde on 23/09/2013 20:08:46
The point being with an infinite mobius strip you would need an infinite amount of time to get back to where you started. Whilst it would be theoretically possible in reality it would never be achieved.
Isn't the same true of an infinite simple loop? with the mobius strip you have to go round twice to get back to the same point on the same side, but infinite is infinite...
Title: Re: Is infinity an illusion?
Post by: Pmb on 24/09/2013 03:24:04
At this point I'm curious about something. Has any part of this topic not yet been explored? The reason I'm asking is because I'm interested in how these things progress and am wondering if there is a natural end to them. Sometimes it seems as if the same old things are being discussed but the discussion remains only in the area of semantics.

What new stuff has been covered here since last week before I got sick and had to stay off the interent for a while. Thanks!
Title: Re: Is infinity an illusion?
Post by: dlorde on 24/09/2013 09:56:10
... I'm interested in how these things progress and am wondering if there is a natural end to them.
I suspect they go on for ever :)

Quote
Sometimes it seems as if the same old things are being discussed but the discussion remains only in the area of semantics.
Agreeing the semantics is important to understanding what we're talking about.

Quote
What new stuff has been covered here since last week before I got sick and had to stay off the interent for a while. Thanks!
Not a lot. There was some talk about 'nothing' (can it physically exist if it is literally not something?), and time (what does it mean if time starts when the universe begins?) and eternity as timelessness.
Title: Re: Is infinity an illusion?
Post by: Pmb on 24/09/2013 15:40:38
... I'm interested in how these things progress and am wondering if there is a natural end to them.
I suspect they go on for ever :)

Quote
Sometimes it seems as if the same old things are being discussed but the discussion remains only in the area of semantics.
Agreeing the semantics is important to understanding what we're talking about.

Quote
What new stuff has been covered here since last week before I got sick and had to stay off the interent for a while. Thanks!
Not a lot. There was some talk about 'nothing' (can it physically exist if it is literally not something?), and time (what does it mean if time starts when the universe begins?) and eternity as timelessness.

Then aren't you just repeating yourself at this point? Don't you get frustrated when it gets to where it is now?
Title: Re: Is infinity an illusion?
Post by: dlorde on 24/09/2013 15:54:48
Then aren't you just repeating yourself at this point?
In different ways, yes.

Quote
Don't you get frustrated when it gets to where it is now?
Yes, a little. On the other hand, with semantically messy subjects like this, I'm never sure I fully understand the other person's view, and they mine, so tackling it in different ways helps. It's also good thinking practice; and if it gets boring, one moves on  :)
Title: Re: Is infinity an illusion?
Post by: Pmb on 24/09/2013 15:59:02
Then aren't you just repeating yourself at this point?
In different ways, yes.

Quote
Don't you get frustrated when it gets to where it is now?
Yes, a little. On the other hand, with semantically messy subjects like this, I'm never sure I fully understand the other person's view, and they mine, so tackling it in different ways helps. It's also good thinking practice; and if it gets boring, one moves on  :)
Okay. I guess this is a learning point for me. Other people have much more patients than I do on things like this.

Then again when I was researching the concept of mass in relativity the other people lost their patients and I never did.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 24/09/2013 17:40:54
Quote from: JeffreyH
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.

With a mobius strip, as with a circle, you do come back to the same place.  The time, of course, is different so you could argue that you were looking at different spacetime events each time round, but I'm a bit doubtful about the value of that.  You could claim that your garden was infinite because you could keep walking round it without returning to the same spacetime event.

The point being with an infinite mobius strip you would need an infinite amount of time to get back to where you started. Whilst it would be theoretically possible in reality it would never be achieved.

The difference and the interesting thing is that with the infinite mobius strip you have points that are opposite each other on different planes. In this scenario the two points have an interesting property. Gravitational effects experienced on one plane will have an equal and opposite effect on the other. While these can be considered to be an infinite distance apart and to all intents and purposes in a different universe. This results in a multi-dimensional spacetime concept where one universe can easily affect another. This is also one description of strings. Even if the strip were not infinite it could be expanding its spacetime.
Title: Re: Is infinity an illusion?
Post by: dlorde on 24/09/2013 19:21:11
The difference and the interesting thing is that with the infinite mobius strip you have points that are opposite each other on different planes. In this scenario the two points have an interesting property. Gravitational effects experienced on one plane will have an equal and opposite effect on the other. While these can be considered to be an infinite distance apart and to all intents and purposes in a different universe. This results in a multi-dimensional spacetime concept where one universe can easily affect another. This is also one description of strings. Even if the strip were not infinite it could be expanding its spacetime.
Mobius String Theory?
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 25/09/2013 11:52:19
The difference and the interesting thing is that with the infinite mobius strip you have points that are opposite each other on different planes. In this scenario the two points have an interesting property. Gravitational effects experienced on one plane will have an equal and opposite effect on the other. While these can be considered to be an infinite distance apart and to all intents and purposes in a different universe. This results in a multi-dimensional spacetime concept where one universe can easily affect another. This is also one description of strings. Even if the strip were not infinite it could be expanding its spacetime.
Mobius String Theory?
Hey with all the other multi-dimensional string theories around I don't think this is that way out.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 25/09/2013 12:03:07
BTW This could also incorporate particle spin, quantum angular momentum.
Title: Re: Is infinity an illusion?
Post by: Bill S on 29/09/2013 23:10:45
Just "passing through" with a quick question.

What is the nature of Cantor’s “absolute infinity”?

In terms of mathematical infinities, Cantor established not only that there were many infinities, but that there were infinitely many infinities.  He established that there was no overarching infinity that included all other infinities. 

This he seems to have called “Absolute Infinity”.  What this means is that he designated an “Absolute Infinity”, which he proved did not exist. 

Is there a paradox here?
Title: Re: Is infinity an illusion?
Post by: dlorde on 30/09/2013 00:01:34
It gets a bit confusing - he seems to have also equated it with the concept of God. If you google for it, there's lots of articles about it.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 30/09/2013 00:03:56
Just "passing through" with a quick question.

What is the nature of Cantor’s “absolute infinity”?

In terms of mathematical infinities, Cantor established not only that there were many infinities, but that there were infinitely many infinities.  He established that there was no overarching infinity that included all other infinities. 

This he seems to have called “Absolute Infinity”.  What this means is that he designated an “Absolute Infinity”, which he proved did not exist. 

Is there a paradox here?

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.
Title: Re: Is infinity an illusion?
Post by: dlorde on 30/09/2013 00:10:51
There has to be a limit just because of the size of a finite universe, if that is what we are in.
If...
Title: Re: Is infinity an illusion?
Post by: jeffreyH 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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.
Title: Re: Is infinity an illusion?
Post by: scienceguy123 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
Title: Re: Is infinity an illusion?
Post by: syhprum 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
Title: Re: Is infinity an illusion?
Post by: scienceguy123 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.
Title: Re: Is infinity an illusion?
Post by: scienceguy123 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?  ???
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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.
Title: Re: Is infinity an illusion?
Post by: JP 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) 
Title: Re: Is infinity an illusion?
Post by: dlorde 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?
Title: Re: Is infinity an illusion?
Post by: JP 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. 
Title: Re: Is infinity an illusion?
Post by: dlorde 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...
Title: Re: Is infinity an illusion?
Post by: JP on 02/10/2013 21:50:35
You can check out any time you like, but you can never leave?
Title: Re: Is infinity an illusion?
Post by: jeffreyH 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.
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: dlorde 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).
Title: Re: Is infinity an illusion?
Post by: Bill S 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?
Title: Re: Is infinity an illusion?
Post by: jeffreyH 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.
Title: Re: Is infinity an illusion?
Post by: yor_on 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 :)
Title: Re: Is infinity an illusion?
Post by: dlorde 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.
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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?”
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: Bill S 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.
Title: Re: Is infinity an illusion?
Post by: JP 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.
Title: Re: Is infinity an illusion?
Post by: webplodder on 04/10/2013 16:51:29
Infinity may be an illusion caused by our experience of passing through the material world. We do not really understand the fundamental nature of time and it may be the case that a dimension or dimensions underlie the classical world that are non-local in the sense of existing without separation in space or time, therefore, time as we normally define it would not be necessary. It has already been proven mathematically that nature at the quantum level is non-local so time could be simply an emergent property of the macro-world. Actually, this is a more logical approach than to assert infinity exists because how would you ever prove it? It is only because time is a common sense experience that we assume it has to go on forever but common sense is not a good guide to the true nature of reality. People used to think the earth was flat based on common sense or that it was impossible to float about but now we understand how gravity works we are much wiser about things.
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/10/2013 17:00:44
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?
It depends what assumptions you make. If you assume that the lobby can tannoy every room at once to tell them to move to room 2n (or whatever), then the whole move can be done in the time it takes to move one room. Of course, if you insist on the tannoy message travelling at the speed of light or less, it will take an infinite time to complete the whole move (but to each occupant, it will seem as if everyone is moving at the same time). If it takes half an hour to move rooms, you can repeat the whole move every half hour - although the guests might complain - best give them a half-hour rest before moving again if another infinite coachload turns up ;)
Title: Re: Is infinity an illusion?
Post by: webplodder on 04/10/2013 17:06:14
Quote from: alancalverd
The "endless digits" business is irrelevant to infinity.

Would you also apply this to the “endless digits” of number lines?  I look for clarification here because it is so rare to find someone who doesn’t insist that these are examples of infinite series.



I don't think it is very meaningful to say something is infinite, even mathematically speaking, because the mathematics we use today only exists within the context of the material universe we find ourselves a part of with its particular laws. Apparently, there may exist other universes within a multiverse that have no or little resemblance to ours and where our mathematics would simply not apply. In the case of pi this is also true such that even if the value of pi never terminated during the life of our universe it would probably not apply in another future possible one.
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/10/2013 17:06:49
Infinity may be an illusion caused by our experience of passing through the material world. We do not really understand the fundamental nature of time and it may be the case that a dimension or dimensions underlie the classical world that are non-local in the sense of existing without separation in space or time, therefore, time as we normally define it would not be necessary. It has already been proven mathematically that nature at the quantum level is non-local so time could be simply an emergent property of the macro-world. Actually, this is a more logical approach than to assert infinity exists because how would you ever prove it? It is only because time is a common sense experience that we assume it has to go on forever but common sense is not a good guide to the true nature of really. People used to think the earth was flat based on common sense or that it was impossible to float about but now we understand how gravity works we are much wiser about things.
Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/10/2013 17:16:32
Apparently, there may exist other universe within a multiverse that have no or little resemblance to ours and where our mathematics would simply not apply.
Says whom? I can see the laws of physics being different, but mathematics is an axiomatic system; how could it be different in another universe ?

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In the case of pi this is also true such that even if the value of pi never terminated during the life of our universe it would probably not apply in another future possible one.
Can you explain how or why?
Pi is a ratio whose exact value depends on the chosen geometry, but on the Euclidean plane it's irrational, so it seems to me that its decimal representation in any universe will be the same, given a Euclidean plane.
Title: Re: Is infinity an illusion?
Post by: webplodder on 04/10/2013 17:42:59

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Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?

This is not a meaningful question. For a start, how do you define infinity and eternity and what is the difference, if any?
Title: Re: Is infinity an illusion?
Post by: webplodder on 04/10/2013 17:49:49
Apparently, there may exist other universe within a multiverse that have no or little resemblance to ours and where our mathematics would simply not apply.
Says whom? I can see the laws of physics being different, but mathematics is an axiomatic system; how could it be different in another universe ?

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In the case of pi this is also true such that even if the value of pi never terminated during the life of our universe it would probably not apply in another future possible one.
Can you explain how or why?
Pi is a ratio whose exact value depends on the chosen geometry, but on the Euclidean plane it's irrational, so it seems to me that its decimal representation in any universe will be the same, given a Euclidean plane.


Mathematics inevitably reflects the way the laws of our spacetime universe work but not necessarily other kinds of universes where there exist very different laws, if any. What if there existed universes that were like the way the quantum world is, i.e. completely random? Pi only works based on the axioms of maths but such axioms originate from consistent features of nature which may be peculiar to the universe we happen to find ourselves in.
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/10/2013 21:45:39
Quote
Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?
This is not a meaningful question. For a start, how do you define infinity and eternity and what is the difference, if any?
I'll defer to Merriam-Webster:
Infinity
: the quality of having no limits or end : the quality of being infinite.
: a space, amount, or period of time that has no limits or end.
: a very great number or amount.

Eternity
: time without an end.
: a state that comes after death and never ends.
: time that seems to be without an end.

The difference should be obvious - eternity can be considered a type, subset, or instance of infinity, specifically relating to time.
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/10/2013 22:37:12
Mathematics inevitably reflects the way the laws of our spacetime universe work but not necessarily other kinds of universes where there exist very different laws, if any.
The laws of physics are expressed using mathematics. They don't determine mathematics.

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What if there existed universes that were like the way the quantum world is, i.e. completely random?
Ours is a quantum universe - and it has stochastic (probabilistic) randomness; that too can be expressed through mathematics, but doesn't determine mathematics.

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Pi only works based on the axioms of maths but such axioms originate from consistent features of nature which may be peculiar to the universe we happen to find ourselves in.
Which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

Title: Re: Is infinity an illusion?
Post by: Bill S on 05/10/2013 00:35:16
Infinity:

 "the quality of having no limits or end" : the quality of being infinite.  OK.

 "a space, amount, or period of time that has no limits or end."  This definition is so tied to our 3+1D world that it is of very limited value with respect to any thoughts beyond the finite.  However, it does establish a sort of relationship between eternity and infinity, such that it is quite reasonable to use “infinite” when making reference to “eternal”, although this relationship is not necessarily reciprocal.

 "a very great number or amount."  This is simply a mathematical approximation; valuable in mathematics, but not really infinity.

Eternity
 "time without an end."  This is valid only if you accept that an unbounded sequence is really infinite.
 
 "a state that comes after death and never ends."  This is theology/philosophy, not science.

 "time that seems to be without an end."  “seems to be”:  Precisely!
Title: Re: Is infinity an illusion?
Post by: webplodder on 05/10/2013 09:51:31
Quote
Infinity doesn't necessarily have anything to do with time - were you thinking of eternity?
This is not a meaningful question. For a start, how do you define infinity and eternity and what is the difference, if any?
I'll defer to Merriam-Webster:
Infinity
: the quality of having no limits or end : the quality of being infinite.
: a space, amount, or period of time that has no limits or end.
: a very great number or amount.

Eternity
: time without an end.
: a state that comes after death and never ends.
: time that seems to be without an end.

The difference should be obvious - eternity can be considered a type, subset, or instance of infinity, specifically relating to time.

Time and space are inextricably linked, therefore, I cannot see how any separation between them is possible. Matter, and the laws governing the way matter behaves, operate within a space time framework so it seems false to me to attempt to give separate definitions to them.
Title: Re: Is infinity an illusion?
Post by: dlorde on 05/10/2013 10:07:18
Time and space are inextricably linked, therefore, I cannot see how any separation between them is possible. Matter, and the laws governing the way matter behaves, operate within a space time framework so it seems false to me to attempt to give separate definitions to them.
OK, but what has time to do with an infinite amount of something or a numerical (mathematical) infinity - or were you only considering the potential for physical infinities?

Just trying to clear up why you feel time is necessarily involved.
Title: Re: Is infinity an illusion?
Post by: webplodder on 05/10/2013 10:13:54
Mathematics inevitably reflects the way the laws of our spacetime universe work but not necessarily other kinds of universes where there exist very different laws, if any.
The laws of physics are expressed using mathematics. They don't determine mathematics.

Quote
What if there existed universes that were like the way the quantum world is, i.e. completely random?
Ours is a quantum universe - and it has stochastic (probabilistic) randomness; that too can be expressed through mathematics, but doesn't determine mathematics.

Quote
Pi only works based on the axioms of maths but such axioms originate from consistent features of nature which may be peculiar to the universe we happen to find ourselves in.
Which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?



Many physicists regard nature as deeply mathematical in nature so it would indeed appear that maths is determined by the way physical reality works. It is true to say that our universe is finely tuned in a way that permits the development of life and that a slight mathematical shift in the way it works would produce a very different universe. Ask yourself why maths arose in the first place. It arose because it precisely reflects reality and another kind of arrangement would not. What would be the case in a universe with 6 dimensions, for example?

Title: Re: Is infinity an illusion?
Post by: dlorde on 05/10/2013 14:15:45
Many physicists regard nature as deeply mathematical in nature so it would indeed appear that maths is determined by the way physical reality works.
So: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

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Ask yourself why maths arose in the first place. It arose because it precisely reflects reality and another kind of arrangement would not.
So you keep saying. I'm asking for some plausible argument or explanation, preferably with hypothetical examples. 

Quote
What would be the case in a universe with 6 dimensions, for example?
Our universe probably has more than 6 dimensions; but regardless, what would the case be with 6 dimensions? how would that affect mathematics?
Title: Re: Is infinity an illusion?
Post by: webplodder on 05/10/2013 15:08:51
Quote
So: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

Well, for example, 1+1 always equals 2, or the square of the hypotenuse in a right angled triangle is equal to the square of the sums of the other two sides. Pi is another example, although we only have an approximation of it though, for practical purposes, it is predictable enough. So, in the real world adding 2 apples together always results in 3 apples and calculating heights using trigonometry is reliable.



Quote
Our universe probably has more than 6 dimensions; but regardless, what would the case be with 6 dimensions? how would that affect mathematics?

Indeed, but what I meant and should have made clearer is the day to day experience of 4 dimensional spacetime in our universe where classical maths works. In another kind of universe where the surface appearance might be any number of dimensions our maths would fail.

Title: Re: Is infinity an illusion?
Post by: Bill S on 05/10/2013 15:23:01
It is easy to assume that because mathematics seems to be the “language of the Universe”, the Universe is “governed” by mathematics.  Perhaps it is better to reason that mathematics is the best language we have found to enable us to understand the Universe.  There may be a better language, we have just not found it yet.
Title: Re: Is infinity an illusion?
Post by: Bill S on 05/10/2013 15:44:45
Quote from: dlorde
were you only considering the potential for physical infinities?

Just trying to clear up why you feel time is necessarily involved.

Obviously I can’t answer for Webplodder here, but I would like to be clear where I stand. 

Mathematical infinities are approximations for very large numbers, so they can be used with time, space and any numerical quantity.

I have yet to be convinced that something physical can come from nothing; therefore something must always have existed. .this something must, therefore, be infinite/eternal.  To avoid infinite regression, which is infinitely pointless, it becomes necessary to consider a number of possible attributes of infinity. 

Is this science?  In so far as it appears to involve a sine qua non of the existence of everything, I think it must be.  Surely this makes a consideration of the nature of infinity as much a part of physics as, for example, extra dimensions, multiple universes or the reality that might underlie QM.
Title: Re: Is infinity an illusion?
Post by: dlorde on 05/10/2013 16:31:37
Quote
So: which consistent features of nature determine the axioms of mathematics, and in what way could they be different - for example?

Well, for example, 1+1 always equals 2, or the square of the hypotenuse in a right angled triangle is equal to the square of the sums of the other two sides. Pi is another example, although we only have an approximation of it though, for practical purposes, it is predictable enough. So, in the real world adding 2 apples together always results in 3 apples and calculating heights using trigonometry is reliable.
Those are examples of maths in this universe. I'm curious to know how you think it could be different elsewhere. As I mentioned previously, geometric relationships may depend on the topography in which they're used, but given a Euclidean plane, they will always be the same.

Are you suggesting that in another universe 1 + 1 may not equal 2 ? 

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In another kind of universe where the surface appearance might be any number of dimensions our maths would fail.
Why should maths fail? we might find it difficult to express the physical appearance of a strange universe through mathematics, but that doesn't affect mathematics. Also, physicists have already mathematically described a variety of multidimensional universes.
Title: Re: Is infinity an illusion?
Post by: webplodder on 05/10/2013 16:35:12
If the universe or multiverse is non-local then time would not be a necessary property because everything would exist simultaneously, both past and future events and communication would be instantaneous. I'm no expert but aren't there experiments which show that photons can travel back in time to reflect a delayed decision on the part of the experimenter in a variation on the double-slit experiment?
Title: Re: Is infinity an illusion?
Post by: webplodder on 05/10/2013 16:49:54
dlorde, we can only try to conceive of other types of universes in terms of our brain physiology which has been shaped by evolutionary forces peculiar to our planet and the geometry of our spacetime universe. It may be, as far as I know, that if other intelligent forms have arisen in other kinds of universes they would possess an entirely different way of perceiving their environment than us and so their symbolic representation of such could be so bizarrely removed from the way our brains work that we simply could not relate to it. We inevitable are forced to use a three-dimensional brain to describe something outside of our ability to describe. Even our maths are fundamentally three-dimensional since they are the result of electro-chemical processes with the biological brain.

I would like to make another point, however. Notwithstanding the foregoing, it has never actually been proved that consciousness is the result of brain activity, at least, not entirely.  It has been assumed by most scientists that consciousness is an emergent property of the brain's electro-chemical activity but what if this was not correct? That would mean that we would have to introduce the idea that consciousness could exist outside of the brain and possibly beyond physical death. If so, then ideas and concepts might exist in a kind of ethereal 'Platonic' realm which interacts with physical reality.
Title: Re: Is infinity an illusion?
Post by: dlorde on 05/10/2013 18:20:44
dlorde, we can only try to conceive of other types of universes in terms of our brain physiology which has been shaped by evolutionary forces peculiar to our planet and the geometry of our spacetime universe. It may be, as far as I know, that if other intelligent forms have arisen in other kinds of universes they would possess an entirely different way of perceiving their environment than us and so their symbolic representation of such could be so bizarrely removed from the way our brains work that we simply could not relate to it.
Potentially, yes.

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Even our maths are fundamentally three-dimensional since they are the result of electro-chemical processes with the biological brain.
In what way is mathematics 'fundamentally three-dimensional'?

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... it has never actually been proved that consciousness is the result of brain activity, at least, not entirely.
It isn't something that can be proved, any more than the existence, or otherwise, of god. In these cases, science generally assesses the evidence for and against to generate the most plausible (provisional) explanation. In the case of consciousness, the vast majority (and the most reliable) of evidence is entirely consistent with it being generated by the brain. I'm not aware of any robust evidence to the contrary. This, and the absence of any plausible suggested mechanism (particularly one consistent with the laws of physics), suggests to me that it is beyond reasonable doubt.

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It has been assumed by most scientists that consciousness is an emergent property of the brain's electro-chemical activity but what if this was not correct? That would mean that we would have to introduce the idea that consciousness could exist outside of the brain and possibly beyond physical death. If so, then ideas and concepts might exist in a kind of ethereal 'Platonic' realm which interacts with physical reality.
Or not. If we had some ham, we could have ham & eggs, if we had some eggs...
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 09:47:48
dlorde, Roger Penrose has pointed out the problem with regarding the brain a kind of computer consisting of essentially an immense number of on/off switches when we look at the non-computability of mathematics. What is meant by this is that given a reasonable level of complexity, any set of mathematical rules, or axioms, can be shown to be self-contradictory at some point by anyone expert enough in maths. What this means is that we can no longer regard the brain as a kind of computer operating on strictly logical lines but something more which seems to be produced by consciousness. An ordinary computer would not have the ability to 'see' anything outside of its axioms because a computer does not possess consciousness. This is why it is questionable as to whether we can regard the brain as the seat of consciousness and that consciousness cannot simply be based on a set of simple electro-chemical processes. I'm not suggesting there is compelling scientific evidence to support this view but that things may not be as straight forward as many scientists seem to think.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 09:59:37

Quote
In what way is mathematics 'fundamentally three-dimensional?

Mathematics is produced by a brain that has a three dimensional architecture (or to be pedantic, four dimensional spacetime).

Title: Re: Is infinity an illusion?
Post by: dlorde on 06/10/2013 10:26:32
... given a reasonable level of complexity, any set of mathematical rules, or axioms, can be shown to be self-contradictory at some point by anyone expert enough in maths.
It was Godel who showed that any non-trivial axiomatic mathematical systems can generate statements that are not provable within the system, and cannot include statements of their consistency without being inconsistent.

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What this means is that we can no longer regard the brain as a kind of computer operating on strictly logical lines but something more which seems to be produced by consciousness. An ordinary computer would not have the ability to 'see' anything outside of its axioms because a computer does not possess consciousness.
No one seriously considers the 'brain as computer' to be more than a clumsy and limited analogy. The brain is clearly is not based on an axiomatic mathematical system, and there's no requirement for consciousness to be mathematically complete and consistent.

Also, let's not forget that a digital computer can emulate a neural network, as can any universal Turing machine, and the brain is, basically, a linked assembly of biological neural networks.

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This is why it is questionable as to whether we can regard the brain as the seat of consciousness and that consciousness cannot simply be based on a set of simple electro-chemical processes.
No, it says nothing at all about the brain as the seat of consciousness. Consciousness is neither complete nor consistent in the mathematical sense, so is not, in that respect, different from any non-trivial axiomatic mathematical system, so that doesn't disqualify it from being based on a such a system; however, the brain itself isn't based on such a system. It's nonsense whichever way you look at it.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 11:46:14
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It was Godel who showed that any non-trivial axiomatic mathematical systems can generate statements that are not provable within the system, and cannot include statements of their consistency without being inconsistent.

Yes, I'm aware of that, but I simply wanted to state the case in uncomplicated terms for general understanding.

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Also, let's not forget that a digital computer can emulate a neural network, as can any universal Turing machine, and the brain is, basically, a linked assembly of biological neural networks.

I'm sorry, but a Turing machine is nothing like a biological brain since a Turing machine has no potential for creativity. A Turing machine needs a set of instructions to follow provided by a human programmer.

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No, it says nothing at all about the brain as the seat of consciousness. Consciousness is neither complete nor consistent in the mathematical sense, so is not, in that respect, different from any non-trivial axiomatic mathematical system, so that doesn't disqualify it from being based on a such a system; however, the brain itself isn't based on such a system. It's nonsense whichever way you look at it.

Documented near-death experiences tend to support the idea that consciousness can exist independently of the biological brain. I'm not claiming the case has been proved, however, anyone who cares to look into the evidence would seriously consider the possibility.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 06/10/2013 12:03:36
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It was Godel who showed that any non-trivial axiomatic mathematical systems can generate statements that are not provable within the system, and cannot include statements of their consistency without being inconsistent.

Yes, I'm aware of that, but I simply wanted to state the case in uncomplicated terms for general understanding.

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Also, let's not forget that a digital computer can emulate a neural network, as can any universal Turing machine, and the brain is, basically, a linked assembly of biological neural networks.

I'm sorry, but a Turing machine is nothing like a biological brain since a Turing machine has no potential for creativity. A Turing machine needs a set of instructions to follow provided by a human programmer.

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No, it says nothing at all about the brain as the seat of consciousness. Consciousness is neither complete nor consistent in the mathematical sense, so is not, in that respect, different from any non-trivial axiomatic mathematical system, so that doesn't disqualify it from being based on a such a system; however, the brain itself isn't based on such a system. It's nonsense whichever way you look at it.

Documented near-death experiences tend to support the idea that consciousness can exist independently of the biological brain. I'm not claiming the case has been proved, however, anyone who cares to look into the evidence would seriously consider the possibility.

Consciousness arises out of a particular configuration of matter, the animal brain. This does not entirely constitute life as plants are classed differently. Do plants think? Is thought necessary for something to be termed alive? There may be many other configurations of matter with the ability to generate thoughts. Does this mean that all matter contains life but at differing levels of the definition? Now we are deeply into the philosophical. Something else that has intrigued me for years.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 12:03:51
Back to infinity.

If we assume for a moment that the universe/multiverse is indeed infinite then what of our cherished ideas about cause and effect? It would mean the universe is acausal so that our whole scientific edifice would be brought into question because its foundation of cause and effect would be undermined. How can events which supposedly have a cause originate from something uncaused? There would be no chain of cause and effect to account for the world as we see it today and we might as well settle for the whims of gods in order to attribute an explanation. We might have to question our whole scientific methodology and look for an alternative approach in attempting to explain the way reality works.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 12:37:52
jeffreyH, I do know that there is some evidence that plants use aspects of quantum mechanics in some of their processes of photosynthesis. Using this method the plant manages to solve problems connected to making sensible choices in choosing favourable pathways which promote its ability to survive. The point being that living things may have developed a way of harnessing the 'quantum computing' power of particles, which can be in many places at the same time, thus enabling calculations to be made simultaneously. This, of course, means a plant can save a lot of time in its metabolic processes which imbues it with a evolutionary advantage. I have to wonder if animals and particularly higher animals, like human beings, have evolved to same ability. If this is the case then this seems to link back to the earlier discussion about the role of consciousness in making great leaps of insight in solving difficult problems as for example, the completely groundbreaking work of Einstein in producing an entirely new paradigm of nature. Was Einstein using his ability to think like a quantum computer? Many scientific insights have 'come from the blue' in the past without the apparent need to work them out step by step so does this suggest something over and above the usual idea that ideas originate from the electrochemical actions of the brain? Great artist or musicians have reported that some of their best ideas have come from an 'inspirational moment' completely unbidden, so is this further evidence that the brain has the ability to act as a kind of quantum computer?
Title: Re: Is infinity an illusion?
Post by: dlorde on 06/10/2013 13:20:40
I'm sorry, but a Turing machine is nothing like a biological brain since a Turing machine has no potential for creativity. A Turing machine needs a set of instructions to follow provided by a human programmer.
You're forgetting that you can have multiple levels of complexity with emergent behaviours. So you can program a Turing machine to behave like a neural network. The resulting neural network emulation can be trained (learn) just like a biological neural network, without explicit programming. The explicit programming is at a lower level of complexity, the learning behaviour is an emergent property of a neural network. It's somewhat similar to the way microcode can make one processor emulate another processor, or the way moving, interacting patterns emerge out of the static on-off squares in Conway's Game of Life.

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Documented near-death experiences tend to support the idea that consciousness can exist independently of the biological brain. I'm not claiming the case has been proved, however, anyone who cares to look into the evidence would seriously consider the possibility.
I've looked at the evidence, and it's nowhere near as robust as it's proponents claim - in fact it's almost entirely anecdotal.

None of the major, well-controlled studies, such as the Aware study, have found anything positive to report so far. Lab studies and other monitored environments (e.g. military centrifuge tests) show that it is relatively easy to artificially produce all the reported experiences of NDEs, from white light tunnels, to felt presences (benign or malign), encounters with deceased relatives, and apparent dislocation from the body. Recent studies suggest cause of many such experiences appears to be a burst of neural activity in severe oxygen deprivation (see Nature (http://www.nature.com/scitable/blog/brain-metrics/could_a_final_surge_in) and The Scientist (http://www.the-scientist.com/?articles.view/articleNo/37040/title/Signs-of-Consciousness-in-Dying-Brains/)).

Anecdotal reports of experiences during 'flatlining' have been explained by the known limitations of EEG monitoring (EEG flatline doesn't mean no brain activity), and likely inaccuracies in recall of subjects and medical staff under time pressure.

When every facet of apparently anomalous reports have plausible 'mundane' explanations, and taking them literally would require entirely unknown mechanisms involving entirely novel biology, and physics contradicting known physical laws, a reasonable man will go with the mundane explanation pending definitive evidence.
Title: Re: Is infinity an illusion?
Post by: yor_on on 06/10/2013 14:53:17
Well, that's where I don't know Dlorde. Consciousness as we define it is in deed a a result of linear time, but the idea of a quantum computer exists too. No matter how it reach a outcome. Assuming that those outcomes will be the a best fit to a question, I might formulate it such as whereas humans make both bad and good choices a quantum computer only will make the most probable fit to a question. And that seems ultimately to become a question of free will. In a way it becomes a sort of 'clock work' universe, building on a assumption of there being a 'ultimate answer', for each and any question asked.

Then we have free will itself, statistically we find patterns, probabilities of outcomes, that's our ordered universe and physics. Individually we find indeterminacy, and with consciousness involved also the ability of making 'wrong choices'. So whereas a 'universal quantum computer' might ignore the ability to make a wrong one, meaning that 'free will', it does not imply (to me at least) that it can't have a consciousness, as being self aware.
Title: Re: Is infinity an illusion?
Post by: yor_on on 06/10/2013 14:57:47
As for pure mathematic it's only your imagination and logic webplodder :) that restricts it I think. You can create all sorts of logic, and it does not have to fit this universe, to be self consistent. To make the assumption that theoretical mathematics must be a result of the way we find our universe to work, as coming from that, will need to prove that all mathematics in existence today are subsets of the physics we find. Myself I don't think that is possible to prove.
Title: Re: Is infinity an illusion?
Post by: yor_on on 06/10/2013 15:05:23
What I can agree on though, is that some mathematics fall away, other mathematical definitions and constructs taking their place as we adapt our mathematics to the universe we measure on. And that some mathematics that's purely been a certain kind of theoretical logic historically suddenly become a practical matter fitting a new way of looking at a universe.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 15:42:14
dlorde, how does an artificial intelligent system manage to integrate and synthesise information resulting in completely novel paradigms? I have yet to see this being achieved today, even with the most powerful computers which are really just huge number crunchers. It seems to me that a Turing machine lacks some vital element in processing data which I would call 'thinking.' It is safe to say that so far we have much to learn about how the brain processes information so it would seem over optimistic to assert that a Turing machine would be capable of multi-level operations when we don't even know how this is achieved with people, or indeed, animals. Are you saying a Turing machine is conscious and self-aware? Can Turing machine reflect and make critical evaluations and draw from experience? I tend to doubt it.

I accept that the evidence surrounding NDEs is anecdotal, however, those instances where NDE patients have recounted information they could not possibly have been aware of during the time of their NDE has yet to be explained. Those critics who maintain a NDE patient is just that - near death, but not actually dead so that they might still retain some awareness of their surroundings - overlook the fact that a flatlined brain would simply be unable to experience the rich imagery involved in observing incoming data like images, audio sensations and touch. These are something that require the use of the higher brain functions located in the forward lobes of the brain and other areas which, in a brain that is showing virtually zero EEG activity, would seem implausible.
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/10/2013 16:08:55
It must have occurred to others that there is a striking similarity between QM and thread drift.

Feynman would like it because it takes a topic from A to B by every possible route,

Heisenberg would approve because there is a distinct uncertainty that the topic will ever arrive at B.

Schrödinger would be pleased because the thread, like his cat, remains neither dead nor alive until a Mod takes decisive action.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 16:09:56
As for pure mathematic it's only your imagination and logic webplodder :) that restricts it I think. You can create all sorts of logic, and it does not have to fit this universe, to be self consistent. To make the assumption that theoretical mathematics must be a result of the way we find our universe to work, as coming from that, will need to prove that all mathematics in existence today are subsets of the physics we find. Myself I don't think that is possible to prove.

Funnily enough, I would say this might lend support for the idea that our thinking procesess are not entirely the result of 'linear' thinking based upon binary switching circuits, however complex. What is imagination anyway? Isn't imagination the ability to ignore the obvious, the mundane, the logical, and take a completely new approach to how the world works? If mere plants have evolved the ability to use quantum processes in order to solve certain problems then how much more probable that higher animals have too? Nature has surely had long enough to take advantage of any edge living things can use to survive and today we know that quantum mechanics is the most fundamental and scientifically demonstrated theory we have about the way reality works.
Title: Re: Is infinity an illusion?
Post by: webplodder on 06/10/2013 16:14:51
It must have occurred to others that there is a striking similarity between QM and thread drift.

Feynman would like it because it takes a topic from A to B by every possible route,

Heisenberg would approve because there is a distinct uncertainty that the topic will ever arrive at B.

Schrödinger would be pleased because the thread, like his cat, remains neither dead nor alive until a Mod takes decisive action.


I would call it discussing a topic in depth.
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/10/2013 16:16:30
BTW, is there a forum in TNS for posting science related verse? 

I feel the Schrödingcat  trying to escape, and I think letting it free here would be taking thread drift too far.
Title: Re: Is infinity an illusion?
Post by: dlorde on 06/10/2013 17:39:56
... I might formulate it such as whereas humans make both bad and good choices a quantum computer only will make the most probable fit to a question.
Not so. A computer, quantum or otherwise computes only what it is instructed to. While quantum mechanics may be stochastic in nature, a quantum computer gives definite (non-stochastic) calculation results. What is good and bad in human terms is context and viewpoint dependent and at a much higher level of abstraction than the mechanics of the 'choice' (which is itself a convenient conceptual abstraction).

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And that seems ultimately to become a question of free will. In a way it becomes a sort of 'clock work' universe, building on a assumption of there being a 'ultimate answer', for each and any question asked.
I guess it depends on precisely what you mean by 'free will'. Without wishing to derail again, it seems to me, that the best monist definition is 'The feeling of uncoerced and unconstrained agency' (i.e. that what you do is not constrained or coerced). But this is entirely causal (if not entirely deterministic), as an individual's choice is the result of their state of mind, preferences, emotions, etc., which are a neural result of the unique interaction between their genetics & development and a lifetime of experiences. So the choice is uniquely theirs, but entirely causal. So the answer may be unpredictable, due to the number & complexity of the interacting contributions, a bit of chaos, and some randomness, but whether it is an 'ultimate answer' seems semantically empty - a sequence of events occurs; we call it a choice because we can envisage various circumstances with different outcomes, but in the real world only one set of circumstances occurs, and so one result.

One could argue that quantum mechanics suggests multiple possible outcomes, and could conceivably evade statistical averaging at molecular scales to have an effect at macro-scales; but this doesn't really help free will, as it would imply the perceived choice is either probabilistic (i.e. some randomness) or that every choice is made (in some universe) and you have a well-defined probability of having made a particular choice (i.e. finding yourself in that particular universe).

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Individually we find indeterminacy, and with consciousness involved also the ability of making 'wrong choices'. So whereas a 'universal quantum computer' might ignore the ability to make a wrong one, meaning that 'free will', it does not imply (to me at least) that it can't have a consciousness, as being self aware.
As I mentioned before, what is right or wrong is contextual. I can't make out what you're saying in the rest of that paragraph.
Title: Re: Is infinity an illusion?
Post by: dlorde on 06/10/2013 19:35:10
dlorde, how does an artificial intelligent system manage to integrate and synthesise information resulting in completely novel paradigms? I have yet to see this being achieved today, even with the most powerful computers which are really just huge number crunchers.
You mean computational creativity? I'm not well up on it, but there are a number of ways it can be done, mostly based around selective recombination (e.g. evolutionary algorithms), pattern recognition & matching across unrelated information fields, generating novel combinations of ideas, generating new ideas through rule-driven transformations, and extending conceptual spaces. Googling 'AI creativity' turns up some information.

The difficult part is evaluating the results, i.e. how to assess what is 'good' creativity in some context.

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It seems to me that a Turing machine lacks some vital element in processing data which I would call 'thinking.' It is safe to say that so far we have much to learn about how the brain processes information so it would seem over optimistic to assert that a Turing machine would be capable of multi-level operations when we don't even know how this is achieved with people, or indeed, animals.
A universal Turing machine is really just a programmable computer that can evaluate any computable algorithm. You'll have to define precisely what you mean by 'think' before it's possible to show whether or not it's computable. Bear in mind that a simple microprocessor (UTM), given sufficient memory and appropriate instructions, can emulate (albeit very inefficiently) any other computer or a neural network of arbitrary size, and so can do anything that such systems can already do - learn by example, be creative, intelligently interpret queries & analyse large volumes of data like IBM's Watson, etc.

We know the functional components of the brain and the principles by which they are physically connected and integrated; we know some of the gross architecture and connectivity, and we know in some detail how small neuronal networks, and even cortical columns, function. To the extent that these are switching networks, and they can be used to compute arbitrary algorithms (what's 5 x 4? how many seconds in a minute?), they are Turing machines (they may also be more). We also know a good deal about the gross, high-level functioning of the brain, and we can make informed guesses about how the gross behaviours emerge from the various structures that coordinate them. We can also see echoes of the evolutionary development of the brain from creatures without specialised neural tissue through creatures with simple nerve networks, through to sophisticated central nervous systems. This provides a wealth of information about how brains developed, what they do & why, and how they work.

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Are you saying a Turing machine is conscious and self-aware? Can Turing machine reflect and make critical evaluations and draw from experience? I tend to doubt it.
We are self-aware and conscious (by definition), and our brains are, at least in part, Turing machines. If they don't seem like what you think of as a Turing machine, remember that a Turing machine is a hypothetical device, and the hardware usually described (tape, printer, scanner, etc) is only a simple example. Consider also, that if we can consciously emulate a UTM (e.g. cooking a meal from a recipe involves scanning a sequence of symbols, interpreting them, and acting on the instructions) we are not only UTMs at a neuronal level, we're UTMs at a high level of abstraction too, since any UTM implementation can, in principle, emulate any other.

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I accept that the evidence surrounding NDEs is anecdotal, however, those instances where NDE patients have recounted information they could not possibly have been aware of during the time of their NDE has yet to be explained.
It's true enough that there is probably not enough information available for these cases ever to directly demonstrate beyond reasonable doubt what happened. This means that we can't verify how accurate the reports are (e.g. we can't verify they couldn't have known the information they recounted, or that they actually recounted information they couldn't have known). What we do know is that there are a raft of potential mundane explanations; subconscious knowledge, exaggeration, confabulation, imagination, confirmation bias, misinterpretation, errors of perception, errors of recall, errors of timing, etc., etc. Subjective (e.g. eye-witness) reports are notoriously unreliable, and one of the most consistent findings of neuroscience & psychology in recent years is the fallibility of our perception & recall.

As I mentioned before, controlled studies have given no positive results, and to take the reports at face value also means abandoning tried and tested biology & physics without even a hypothetical mechanism. I don't know about you, but that makes me skeptical.

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Those critics who maintain a NDE patient is just that - near death, but not actually dead so that they might still retain some awareness of their surroundings - overlook the fact that a flatlined brain would simply be unable to experience the rich imagery involved in observing incoming data like images, audio sensations and touch. These are something that require the use of the higher brain functions located in the forward lobes of the brain and other areas which, in a brain that is showing virtually zero EEG activity, would seem implausible.
That, of course, assumes that the 'rich imagery' is actually experienced at the time of 'virtually zero EEG activity', but given that (arguable) assumption, EEG is not know for it's sensitivity in this context (e.g. New Scientist (http://www.newscientist.com/article/dn24228-mysterious-bursts-of-activity-in-flatlining-brain.html#.UlGFdxthB8E)), and the generation of rich perceptual imagery is a function of the early sensory cortices for vision, hearing, somatic sensation, taste, & smell, supported by the thalamic relay and associative nuclei, not the frontal lobes (see Damasio's 'Self Comes To Mind', ch.3, 'Making Maps & Making Images').

If the subjects were actually dead, they would be unable to report their NDEs  ;)
Title: Re: Is infinity an illusion?
Post by: dlorde on 06/10/2013 19:40:56
It must have occurred to others that there is a striking similarity between QM and thread drift.

Feynman would like it because it takes a topic from A to B by every possible route,

Heisenberg would approve because there is a distinct uncertainty that the topic will ever arrive at B.

Schrödinger would be pleased because the thread, like his cat, remains neither dead nor alive until a Mod takes decisive action.

Excellent!

Dawkins would like it because it evolves according to the selective pressures of the participants and (to a limited extent) the forum rules.

Hawking would like it because such topics eventually collapse into a black hole of apathy, and it's not clear whether all the information supplied is actually lost to the universe or not...
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/10/2013 22:02:39
Einstein would like it because it is a relatively simple process, and changes with your frame of reference.
Title: Re: Is infinity an illusion?
Post by: Pmb on 07/10/2013 00:52:31
Bill - What exactly is it about infinity that bothers you so much?
Title: Re: Is infinity an illusion?
Post by: Bill S on 07/10/2013 16:11:18
Pete, infinity doesn't bother me.  There was a time when I felt I needed to take issue with the use of the term infinite for things that were obviously not infinite, but that is no longer the case.

I have tried on a few occasions to clarify my position, but either I don't do a very good job, or others are reluctant to pick up the idea.  As this thread demonstrates, discussion diverges into all kinds of other things.  There may be a link between NDEs and infinity, but I wonder about its scientific pedigree. :)

Perhaps, if I state my starting position as three simple points it might help.

1. There can never have been nothing, otherwise there would still be nothing now.

2. If there has always been something, that something must be infinite/eternal.

3. If there has always been something, what is the relationship between that something and the Universe we observe?
Title: Re: Is infinity an illusion?
Post by: webplodder on 07/10/2013 17:53:19
It seems to me that the reason we get into difficulties surrounding this subject is that we treat the concept of time as real. If you eliminate time as a fundamental aspect of the universe then you do not have to answer questions such as what existed before our universe and what existed before that, ad infinitum. Time " appears" to exist to us in the way we navigate our way through reality but is this just really an illusion? Perhaps we inhabit a level of reality where time is really just an emergent property of a fundamentally timeless and spaceless universe. Why is it that "spooky action at a distance" seems to violate our classical ideas about time and space? Is this phenomenon telling us there is something more profound we have not yet understood?

If this is true then all "moments" exist simultaneously and there is no "now" so that the Big Bang, for example, is still happening somewhere as is your birth or the events of 9/11. If you count up to and beyond the number 15 it does not mean the number 15 suddenly stops existing. It may "appear" to be in the past but that is only relative to us.
Title: Re: Is infinity an illusion?
Post by: Pmb on 07/10/2013 18:12:08
Quote from: Bill S
Pete, infinity doesn't bother me.  There was a time when I felt I needed to take issue with the use of the term infinite for things that were obviously not infinite, but that is no longer the case.
Thanks Bill. I wanted to let you know how much I admire your interest in this and your pursuit to find the truth. It's very heart warming to me to see people such as yourself blessing physics forums with your presense. Thank you. :)

Quote from: Bill S
I have tried on a few occasions to clarify my position, but either I don't do a very good job, or others are reluctant to pick up the idea.  As this thread demonstrates, discussion diverges into all kinds of other things.  There may be a link between NDEs and infinity, but I wonder about its scientific pedigree. :)

Perhaps, if I state my starting position as three simple points it might help.

1. There can never have been nothing, otherwise there would still be nothing now.

2. If there has always been something, that something must be infinite/eternal.

3. If there has always been something, what is the relationship between that something and the Universe we observe?
Unfortunately I've been ill for a while and my attention span is gone, which I'd need to follow your line of reasoning. When I'm better I look foward to discussing this with you. :)
Title: Re: Is infinity an illusion?
Post by: dlorde on 07/10/2013 19:21:11
1. There can never have been nothing, otherwise there would still be nothing now.

2. If there has always been something, that something must be infinite/eternal.

3. If there has always been something, what is the relationship between that something and the Universe we observe?
I agree with your logic here, and the question you're asking.

My only concern (I don't have any answers to this) is how one might take account of the possibility that time might have 'started' a finite period ago - what might that mean for infinity/eternity, and how one deals with the idea of there potentially being no temporal 'before' (e.g. what does it mean? would it be the nothing of point 1? etc).

p.s. apologies for the earlier derail - I can get carried away at times ;)
Title: Re: Is infinity an illusion?
Post by: JP on 07/10/2013 20:07:24
Bill, I'll voice my objections again, but I feel like I'm a broken record at this point. ;)

Quote from: Bill S
1. There can never have been nothing, otherwise there would still be nothing now.

2. If there has always been something, that something must be infinite/eternal.

3. If there has always been something, what is the relationship between that something and the Universe we observe?

These are all making way too many assumptions about how the universe would be created.  You seem to be enforcing the physics within this universe onto whatever existed that created the universe. 

For example, could the creation of the universe involve a creation of infinite amounts of space and time instantaneously?  You could argue that would violate causality, but causality is something that exists within the universe in our space and time--it isn't defined and shouldn't be expected to hold for an event that occurred outside our space and time. 

You're coming into asking these big questions with a lot of preconceptions.  You may be right and your view is certainly one way of looking at it, but it certainly isn't the only way of looking at it.
Title: Re: Is infinity an illusion?
Post by: Pmb on 07/10/2013 20:09:47
Bill, I'll voice my objections again, but I feel like I'm a broken record at this point. ;)

Quote from: Bill S
1. There can never have been nothing, otherwise there would still be nothing now.

2. If there has always been something, that something must be infinite/eternal.

3. If there has always been something, what is the relationship between that something and the Universe we observe?

These are all making way too many assumptions about how the universe would be created.  You seem to be enforcing the physics within this universe onto whatever existed that created the universe. 

For example, could the creation of the universe involve a creation of infinite amounts of space and time instantaneously?  You could argue that would violate causality, but causality is something that exists within the universe in our space and time--it isn't defined and shouldn't be expected to hold for an event that occurred outside our space and time. 

You're coming into asking these big questions with a lot of preconceptions.  You may be right and your view is certainly one way of looking at it, but it certainly isn't the only way of looking at it.

I agree with JP, of course. I understand where Bill is coming from but it's not a logical conclusion, just one based on everyday experience and that doens't always work.
Title: Re: Is infinity an illusion?
Post by: JP on 07/10/2013 20:18:20
By the way, if "way of looking at it" in my above post doesn't sound scientific--it isn't!  Thinking about what might have created the universe is such a big question and so far beyond what we can measure in physics, that it's very hard to be grounded in science.  Remember, science involves advancing testable hypotheses.  If you're playing with ideas like "something can't come from nothing" without grounding them in testability that's metaphysics and doesn't necessarily have any relation to science.
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 07/10/2013 22:39:50
We can see by looking at black holes and the speed of light that infinities arise when considering extreme situations. The black hole has a past as well as the photon. We can draw an analogy between the collapse of the black hole and the big bang. It is only a directional difference. One is collapsing whilst the other expanding. The past of the black hole involves a system before it's collapse and in theory a future in which it evaporates. If we run this backwards we can imagine a condensation being the past of the big bang which would reflect the evaporation phase of the black hole. This could be an infinity away or it could have some finite time under a different frame of reference. This 'condensation' could be another way of expressing a prior collapsing phase.

As an additional point, what would be the Schwarzschild radius for a singularity with a mass the size of the universe. Would it be the Hubble sphere?
Title: Re: Is infinity an illusion?
Post by: Bill S on 07/10/2013 22:43:18
Two naïve questions:

1. Would I be right in thinking that science maintains that matter and energy cannot be created or destroyed?
2. If so, on what is this claim based?   
Title: Re: Is infinity an illusion?
Post by: jeffreyH on 07/10/2013 22:49:40
Two naïve questions:

1. Would I be right in thinking that science maintains that matter and energy cannot be created or destroyed?
2. If so, on what is this claim based?

The law of conservation of mass
http://en.wikipedia.org/wiki/Conservation_of_mass
Title: Re: Is infinity an illusion?
Post by: Pmb on 08/10/2013 02:33:55
Two naïve questions:

1. Would I be right in thinking that science maintains that matter and energy cannot be created or destroyed?
2. If so, on what is this claim based?   
Scientists don't often use the term "matter" in a precise way so what you said is too vauge to comment on. I would say that mass cannot be created or destroyed. Energy is not a thing that can be created or destroyed like a golf cart. What can be said about it is that its constant, i.e. conserved.

So mass being conserved is taken as an axiom which means that it's assumed to be true but it cannot be proven to be so. All laws of physics are axioms. That's why they call them laws.
Title: Re: Is infinity an illusion?
Post by: lean bean on 08/10/2013 16:57:39
You could argue that would violate causality, but causality is something that exists within the universe in our space and time--it isn't defined and shouldn't be expected to hold for an event that occurred outside our space and time.
That reminds me of the faster than light inflation period in the early universe. :)
Title: Re: Is infinity an illusion?
Post by: JP on 08/10/2013 20:20:30
Two naïve questions:

1. Would I be right in thinking that science maintains that matter and energy cannot be created or destroyed?
2. If so, on what is this claim based?   
Scientists don't often use the term "matter" in a precise way so what you said is too vauge to comment on. I would say that mass cannot be created or destroyed. Energy is not a thing that can be created or destroyed like a golf cart. What can be said about it is that its constant, i.e. conserved.

So mass being conserved is taken as an axiom which means that it's assumed to be true but it cannot be proven to be so. All laws of physics are axioms. That's why they call them laws.

To add to what Pete is saying here and to head off attempts to use this to justify that the universe can't be infinite...  :p

All these laws are assumed to be true only within our universe, since that's the only place where we can look to see if they're true.  We have no idea what happens outside of our universe--if there is an outside.  If our universe was created from "nothing" it's possible this law doesn't hold. 

Similarly, causality can't be violated within our universe, but outside our universe it might be---in particular, the concept of causality probably wouldn't have meaning, since it describes how things interact within the space-time of our universe, which presumably doesn't extend outside of it.
Title: Re: Is infinity an illusion?
Post by: JP on 08/10/2013 20:22:40
You could argue that would violate causality, but causality is something that exists within the universe in our space and time--it isn't defined and shouldn't be expected to hold for an event that occurred outside our space and time.
That reminds me of the faster than light inflation period in the early universe. :)

That's a good point!  One thing that puzzles people until they learn a bit about how causality works is that distant stars can recede from each other at apparently faster-than-light speeds.  In other word, the distance between them can increase faster than the speed of light. 

But this isn't a violation of light speed travel since the light speed limit only applies to things moving within space-time, but if space-time itself grows, two points can separate at apparent faster than light speeds. 
Title: Re: Is infinity an illusion?
Post by: webplodder on 09/10/2013 09:26:59
dlorde, it has been shown that certain aspects of human thinking is of a non-computable nature, as was mentioned in an earlier post, so once again, we have the problem of trying to understand how this occurs which, as far as I am aware, has eluded cognitive science. The problem with a Turing machine is that it is bound by its axiomatic nature so it does not have the ability to make sudden jumps of insight. In effect, it's like someone having a chain of thought but is prevented to reflect and modify the implications of it because it is written in stone. In other words, human beings are able to play about with ideas and explore novel relations that cannot be predicted so it would not be possible to incorporate this into a Turing machine. How can an algorithm be designed that predicts the unpredictable? For example, how would it have been possible to design an algorithm that eventually produced the theory of relativity? In short, people possess imaginations, computers do not.

Another aspect to this is that while people can discuss and debate about ideas with other people (which might lead to new a insight) a Turing machine, as far as I am aware, is stuck with its own internal processes not being able to benefit from interactions in the form of natural language. Mathematics only goes so far in trying to describe the world. This is crucial, of course, because language has the ability to generate ideas out of the blue due to the flexibility of words which allows new relations to be formed. Can computers understand jokes? This is important because through jokes we can see how human beings make ridiculous relationships, which are not found in the real world, yet may have some value in forming new ideas about reality. An artificial intelligent system is just that - artificial - and can never represent the real world unless and until it becomes a conscious entity which has experienced real-world interactions.

Today's most powerful computers are very good within narrow parameters of application but every time they are required to be used in others fields require new algorithms to be created. Never forget that they are basically number crunching but you can only achieve so much using this method. Human beings are not designed this way so there must exist more effective methods to deal with reality that have been evolved over millions of years.
Title: Re: Is infinity an illusion?
Post by: dlorde on 09/10/2013 11:45:08
it has been shown that certain aspects of human thinking is of a non-computable nature, as was mentioned in an earlier post
I'm sorry, I can't find that post (searching for 'computable' or 'non-computable'); can you post a link to it, or explain what was shown to be non-computable, or link to a reference?

Quote
The problem with a Turing machine is that it is bound by its axiomatic nature so it does not have the ability to make sudden jumps of insight. In effect, it's like someone having a chain of thought but is prevented to reflect and modify the implications of it because it is written in stone. In other words, human beings are able to play about with ideas and explore novel relations that cannot be predicted so it would not be possible to incorporate this into a Turing machine.
No. You're confusing the hardware with the algorithms. From the time the first computers were built people have been writing self-modifying code, learning algorithms, evolutionary algorithms, etc. One advantage of evolutionary algorithms is they can come up with novel and unexpected results. There are also systems explicitly designed to generate creative solutions. Have a read of VS Ramachandran's work (or watch his videos) where he describes how creativity an insight is generated in the brain; it's basically a form of pattern matching and metacognition - applying principles & ideas from one area to a unrelated area (this is also how simile and metaphor work). In the brain, this is done subconsciously; in a computer, it's usually an emergent product of explicit algorithms (e.g. iterative feedback, recursion, etc).

Quote
How can an algorithm be designed that predicts the unpredictable? For example, how would it have been possible to design an algorithm that eventually produced the theory of relativity? In short, people possess imaginations, computers do not.
It is, by definition, impossible to predict the unpredictable, so you'll need to clarify that thought. The theory of relativity didn't come out of the blue, it was based on the work of Michelson, Lorentz, Poincare and others, dropping certain assumptions. A great piece of work, but a mix of derivation and synthesis. Algorithms have already been written that can generate novel mathematical theorems and proofs, and novel artwork and music, so be careful not to confuse what has not yet been done with what is impossible.

But this is all off-topic. I suggest if you want to discuss this stuff further, you create a new thread for it.
Title: Re: Is infinity an illusion?
Post by: webplodder on 09/10/2013 16:05:13
dlorde:

http://www.technologyreview.com/view/511421/the-brain-is-not-computable/
Title: Re: Is infinity an illusion?
Post by: webplodder on 09/10/2013 16:11:32
Quote
Algorithms have already been written that can generate novel mathematical theorems and proofs, and novel artwork and music, so be careful not to confuse what has not yet been done with what is impossible.
dlorde, ultimately this is not an independent consciousness acting by itself but simply a set of instructions that has anticipated certain conditions, in which case it is all the result of human intelligence, not machine intelligence. A machine cannot learn, only blindly follow its algorithm. A truly intelligent machine would be able to actually understand the subject matter it is analysing but so far, this is not the case. A calculator has the ability to add 8 and 12, for example, but has no clue what numbers are aside from a series of electronics signals generated within its circuits so cannot draw generalisations from mathematical operations. Computer artwork is more in the eye of the human beholder rather than in the eye of the "artistic" algorithm. Are you seriously suggesting a computer knows what art is? Even the most powerful chess computer relies on huge number crunching algorithms with which to analyse variations and this is because the external world can only be represented by binary representations due to the architecture of its internal workings.

There have been many things in science that were once not thought to be possible yet have materialised, so we cannot always predict what will happen in the future and the reason for this is because human thinking itself is often unpredictable, something that is non-computable and creative. This is what I meant when I said it is impossible to produce an algorithm that anticipates original and novel ideas since such ideas have first to be thought of. Otherwise, you might as well say it's possible to produce an algorithm to cure cancer or predict the weather for years to come. Even if a computer algorithm had been fed with all the knowledge and data available at the time connected with physics I am very doubtful it would have come up with the theory of relativity. It required a leap of insight not at all suggested by the then current data.
Title: Re: Is infinity an illusion?
Post by: Bill S on 09/10/2013 19:10:22
Quote from: JP
All these laws are assumed to be true only within our universe, since that's the only place where we can look to see if they're true.  We have no idea what happens outside of our universe--if there is an outside.  If our universe was created from "nothing" it's possible this law doesn't hold.

One of the objections to God and creationism raised by scientists is that such beliefs constitute a barrier beyond which we cannot speculate or reason. 

Surely you are not saying that because we have no proof of what might be beyond our Universe (if anything), it is meaningless to consider possibilities that might be relevant to the origin of the Universe.

If it is reasonable to speculate, wouldn’t Ockham’s  razor  lead us to start our speculations with a minimum of wild assumptions?
Title: Re: Is infinity an illusion?
Post by: Bill S on 09/10/2013 19:43:42
Quote from: JP
Similarly, causality can't be violated within our universe, but outside our universe it might be---in particular, the concept of causality probably wouldn't have meaning, since it describes how things interact within the space-time of our universe, which presumably doesn't extend outside of it.

You seem to be assuming that I am saying that the principles of causality must be the same within, and outside the Universe.  This is not so; in fact I would be quite surprised if that were the case. 

What I am saying is that science is able to lead us to such a deep understanding of the Universe, and to interpret so many of the underlying laws, that it seems reasonable to speculate that even the origin of the Universe might be understandable using the same rational tools.

Causality may well be different outside the Universe, but without making assumptions like "God created everything", or "everything suddenly appeared from nothing without cause", we have only those guidelines which are known to us on which to base our thoughts.
 
Title: Re: Is infinity an illusion?
Post by: JP on 09/10/2013 20:16:51
This is a hard topic to discuss because we're burdened with ideas like "cause" which imply time.  However, there's no reason to believe time exists outside our universe.  If it does, then it probably isn't a simple extension of the timeline within our universe or it would be a part of our universe.

So let me put it this way: why, scientifically speaking, couldn't our universe be infinite and have always been infinite?
Title: Re: Is infinity an illusion?
Post by: dlorde on 09/10/2013 20:35:49
http://www.technologyreview.com/view/511421/the-brain-is-not-computable/
Nicolelis is using a restricted sense of computable, i.e. direct algorithmic simulation:
Quote
... human consciousness (and if you believe in it, the soul) simply can’t be replicated in silicon. That’s because its most important features are the result of unpredictable, nonlinear interactions among billions of cells, Nicolelis says..
However, you can (as the Human Brain Project (https://www.humanbrainproject.eu/web/public/home) is partially attempting) emulate the brain by modelling neurons and their connections (Neuromorphic Computing Systems), so that you can have unpredictable, nonlinear interactions among billions of cells emulated neurons. It's coming.

p.s. wrong thread.
Title: Re: Is infinity an illusion?
Post by: Bill S on 09/10/2013 21:35:37
Quote from: JP
  So let me put it this way: why, scientifically speaking, couldn't our universe be infinite and have always been infinite?

The Universe could be infinite – even I haven’t been around long enough to know that. :) – but there do seem to be some reasons for thinking otherwise; like the Big Bang, entropy etc.  Perhaps you were thinking more along the lines of eternal inflation, and an infinity of bubble universes; or bouncing universes?  These are things I would be happy to discuss, with a view to learning more about them.
Title: Re: Is infinity an illusion?
Post by: JP on 09/10/2013 21:40:43
Quote from: JP
  So let me put it this way: why, scientifically speaking, couldn't our universe be infinite and have always been infinite?

The Universe could be infinite – even I haven’t been around long enough to know that. :) – but there do seem to be some reasons for thinking otherwise; like the Big Bang, entropy etc. 

Why are those reasons for thinking otherwise?
Title: Re: Is infinity an illusion?
Post by: yor_on on 10/10/2013 00:11:48
The point, to me dlorde, with a quantum computer is that if you find a way to formulate your question it will give you a answer. The assumption behind it being that this answer will be the most probable. In effect, as in using it for cracking 2056 bits pgp. the possibilities inherent for finding one right solution there are more than we imaginatively can go through.

"AES supports a 256-bit key. How many keys does AES-256 have? See if you can find some number in physics, chemistry, or astronomy of about the same size. Use the Internet to help search for big numbers. Draw a conclusion from your research.

Answer:
The equation we need to solve is 2256 = 10n . Taking common logarithms, we get n = 256log 2, so n = 77. The number of keys is thus 1077 . The number of stars in our galaxy is about 1012 and the number of galaxies is about 108 ,so there are about 1020 stars in the universe. The mass of the sun, a typical star, is 2*1033 grams. The sun is made mostly of hydrogen and the number of atoms in 1 gram of hydrogen is about 6*1023 (Avogadro’s number). So the number of atoms in the sun is about 1.2 *1057 . With 1020 stars, the number of atoms in all the stars in the universe is about 1077 . Thus, the number of 256-bit AES keys is equal to the number of atoms in the whole universe (ignoring the dark matter). Conclusion: breaking AES-256 by brute force is not likely to happen any time soon."

From http://210.43.188.28/jpkc10/wangluo/Course/skja/ywxt/enCh-8.html

So, the 'attack' by a quantum computer would have to work outside a linear time line, and assuming the principles are correct it is presumed to do the calculation 'instantly'.

(and if we could stretch the time allowed for a edit somewhat, I would be much obliged. Got a slow connection invariably ending up it that ugly 'edit comment' as soon as I correct my spelling etc)
Title: Re: Is infinity an illusion?
Post by: webplodder on 11/10/2013 10:11:36
If the universe has always existed then where does that leave causality? If there is no initial cause then it seems to me there cannot exist a chain of cause-and-effect leading to the situation today. Possibly, an alternative interpretation might be that instead of one thing causing another, events exist as a set of pre-existing ensembles so that causality is an illusion and we exist in a kind of computer program where things are already pre-determined. Admittedly, this sounds far fetched but how else can we avoid the problem of a causeless universe giving rise to an apparent chain of events?
Title: Re: Is infinity an illusion?
Post by: webplodder on 11/10/2013 10:37:36
http://www.technologyreview.com/view/511421/the-brain-is-not-computable/
Nicolelis is using a restricted sense of computable, i.e. direct algorithmic simulation:
Quote
... human consciousness (and if you believe in it, the soul) simply can’t be replicated in silicon. That’s because its most important features are the result of unpredictable, nonlinear interactions among billions of cells, Nicolelis says..
However, you can (as the Human Brain Project (https://www.humanbrainproject.eu/web/public/home) is partially attempting) emulate the brain by modelling neurons and their connections (Neuromorphic Computing Systems), so that you can have unpredictable, nonlinear interactions among billions of cells emulated neurons. It's coming.

p.s. wrong thread.

One important aspect that should be addressed here is that very often we learn by our mistakes. In the history of science there have been many instances of experiments that have yielded important information that was unexpected so by "playing about" with ideas human beings have learnt new things that could never have been predicted by any algorithm.
Title: Re: Is infinity an illusion?
Post by: dlorde on 11/10/2013 10:40:48
The point, to me dlorde, with a quantum computer is that if you find a way to formulate your question it will give you a answer.
...
Sorry yor_on; as usual, I don't have the foggiest idea what you're on about. I haven't mentioned quantum computing on these forums since April.
Title: Re: Is infinity an illusion?
Post by: dlorde on 11/10/2013 10:53:06
... there have been many instances of experiments that have yielded important information that was unexpected so by "playing about" with ideas human beings have learnt new things that could never have been predicted by any algorithm.
Computing can't yet match the human brain in this respect, but computing systems can be creative using similar principles, and evolutionary algorithms regularly come up with unexpected, unpredictable ideas (e.g. Evolving Soft Robots (http://creativemachines.cornell.edu/soft-robots/) - not the best example around, but I just happened to be watching it). Neuromorphic systems have even greater potential.
Title: Re: Is infinity an illusion?
Post by: webplodder on 11/10/2013 11:03:47
... there have been many instances of experiments that have yielded important information that was unexpected so by "playing about" with ideas human beings have learnt new things that could never have been predicted by any algorithm.
Computing can't yet match the human brain in this respect, but computing systems can be creative using similar principles, and evolutionary algorithms regularly come up with unexpected, unpredictable ideas (e.g. Evolving Soft Robots (http://creativemachines.cornell.edu/soft-robots/) - not the best example around, but I just happened to be watching it). Neuromorphic systems have even greater potential.

dlorde, as fascinating as this discussion is, I think we should stop now because we are way off topic and must be trying the patience of the mods.
Title: Re: Is infinity an illusion?
Post by: Bill S on 11/10/2013 14:52:14
Quote from: JP
Why are those reasons for thinking otherwise?

My thinking there was that if the Universe started at the BB, and progressed towards a predictable end, it would most likely be finite.  One would have to think outside this Universe to find infinity.  Similarly, the one-way progression of entropy might point towards the same conclusion.

These thoughts are probably naïve, but it is the nature of this naivety that I am trying to understand.
Title: Re: Is infinity an illusion?
Post by: JP on 11/10/2013 15:48:19
Quote from: JP
Why are those reasons for thinking otherwise?

My thinking there was that if the Universe started at the BB, and progressed towards a predictable end, it would most likely be finite.  One would have to think outside this Universe to find infinity.  Similarly, the one-way progression of entropy might point towards the same conclusion.

These thoughts are probably naïve, but it is the nature of this naivety that I am trying to understand.


That is one possible answer, but there isn't a reason to assume the universe didn't start off infinite (aside from intuition, which isn't scientifically credible).  To be scientific, you'd have to tie it into observation or measurement somehow.  I think nearly every human has the intuition that if the universe "started" it must have been tiny and that since then it has grown at a finite rate so that now it can't be infinite.  But our intuition is a dangerous guide to dealing with modern physics, especially with such fundamental questions as the nature of the universe's creation, so it can't be relied upon alone to give us answers.

If we stuck to intuition, we wouldn't have quantum mechanics, black holes, inflation of the universe, relativity, etc.

I think the best way to approach the answer to give it some scientific credibility is to note that mathematics is extremely useful in physics, and to ask what kind of mathematically allowed states the universe might be in currently and eliminate states which are disallowed by observation.  For example, we know that space-time has certain properties, which eliminates many possibilities.  We know that the universe's expansion appears to be accelerating, so that eliminates more.  What we have no evidence for either way is the size of the universe, since we're limited to only seeing a patch of the whole and we don't see any sign of finiteness as we look out.  Of course, we don't see a sign of infiniteness either--what we see could be compatible with finite or infinite universes.  To rule out infinite universes, we'd presumably need to know how the universe was created and that would tell us, but we haven't figured that out yet.  Intuition just isn't a good reason to rule something out, though it's fair to say that you prefer finite models because your intuition finds them more comfortable--just realize that's an argument people used to oppose quantum mechanics, relativity, etc.
Title: Re: Is infinity an illusion?
Post by: webplodder on 11/10/2013 16:39:32
Quote from: JP
Why are those reasons for thinking otherwise?

My thinking there was that if the Universe started at the BB, and progressed towards a predictable end, it would most likely be finite.  One would have to think outside this Universe to find infinity.  Similarly, the one-way progression of entropy might point towards the same conclusion.

These thoughts are probably naïve, but it is the nature of this naivety that I am trying to understand.


But what caused the BB?
Title: Re: Is infinity an illusion?
Post by: Bill S on 11/10/2013 23:11:31
Quote from: JP
there isn't a reason to assume the universe didn't start off infinite

I’m delighted that you mentioned that, JP, its something I have come across in discussions on other forums.  I always ask for an explanation as to how some infinite object can come into existence; especially something that is often described as infinitesimally small.

Those who don’t just ignore the question have so far failed to produce a convincing answer.  Perhaps its just that I don’t understand the answers.  However, I usually find that your explanations make sense, so perhaps I’m in luck at last.
Title: Re: Is infinity an illusion?
Post by: JP on 12/10/2013 03:53:01
I don't think you'll like the answer.  ;)  There's a couple of parts to it, and I'm not an expert--someone who deals with "theories of everything" could probably tell you more, but I don't think there's someone like that on this forum. 

The first part is that you're basically asking for the answer to "how does a universe come to be?"  The problem with that is that there are very few ways to approach that question--all our scientific measurements take place within the universe and all our models deal with measurements within the universe.  One hope is that if we can come up with a theory that describes everything in the universe in simple terms (string theory being one candidate) that it would tell us about the allowed structure of the universe or universes and perhaps how they came to be.  String theory does indeed do this to an extent--predicting that an infinite number of universes exist all with different parameters.  (I don't know what it says about finite vs. infinite universes, but if I had to guess, it would allow both.)  Is this useful?  Is this even science?  I'm doubtful.  It may explain our universe very well, but can we ever test its predictions about other universes? 

The second part is to ask yourself why you prefer a finite universe or why you feel an infinite universe is impossible and check if there's a scientific reason to think so.  The usual reason is that nothing we can measure of starts off infinite, so why should the universe?  And everything that we know of that starts off finite and grows does so at a finite rate, and so can never become infinite in any of our measurements.  That's a logical reason to say that nothing can be infinite, including the universe.  That would also be an erroneous conclusion.  Why?  Everything we measure is within the universe.  In fact, everything we measure is within the observable universe, which is certainly smaller than the entire universe.  So we can apply this logic only to the class of objects "things within the (observable) universe."  Since that class does not include the universe itself, it's flawed reasoning to try to apply these limitations to the whole universe.  This doesn't help us come up with a plausible reason why the universe could be infinite, but it demonstrates that there's no plausible reason why it couldn't be and that the usual arguments are flawed.

So what is a model that might work?  One that I've heard of and that makes some sense to me is that all possible universes at all possible times exist as a set of states.  We say there is time and space because our brains and bodies work in a certain way to put ordering to these states.  We process information by moving "forward" in time (converting energy to entropy) so we see an arrow of time.  Various parameters of our particular universe define what we can interact with as we move in time, so we experience causality, etc. 

So what might we see if we could step outside our human brains and look at the set of states making up our "universe"?  It might just be that each universe is completely generated from a small set of parameters.  From those parameters, you can imagine generating an entire set of states of the universe, which when placed in order by things living within the universe, form the entire universe from start to finish.  From the outside however, you'd just have a list of parameter values for each potential universe from which you can generate an infinite set of states.  Some of these values might make observers within the universe measure it as infinite and some might make them measure it as finite.

One last comment: theories of everything are pretty far out there and I take them with a huge grain of salt--I view most of them as philosophy with a lot of math rather than physics, since they don't make testable predictions.  They also veer alarmingly close to what we see in New Theories where promoters of crackpot ideas will say "you have to free your mind for a paradigm shift" or somesuch nonsense.  But the important difference is that while you do have to be willing to consider "really out there ideas" when thinking about the origin of the universe, all ideas are going to be about as far out there, since they all deal with the creation of the universe, which is something we don't have a good way of scientifically probing.  As I mentioned at the start, you have just as much scientific evidence and justification to back up your "common sense" ideas as you do to back up the idea that the universe started off infinite or even that there's an infinite number of universes, some of which are finite and some of which are infinite.
Title: Re: Is infinity an illusion?
Post by: Pmb on 12/10/2013 07:05:03
Quote from: JP
there isn't a reason to assume the universe didn't start off infinite

I’m delighted that you mentioned that, JP, its something I have come across in discussions on other forums.  I always ask for an explanation as to how some infinite object can come into existence; especially something that is often described as infinitesimally small.

Those who don’t just ignore the question have so far failed to produce a convincing answer.  Perhaps its just that I don’t understand the answers.  However, I usually find that your explanations make sense, so perhaps I’m in luck at last.

This would make an excellant FAQ question. Don't you think?
Title: Re: Is infinity an illusion?
Post by: Bill S on 12/10/2013 14:03:45
JP, thanks for that response.  There's a lot there to think about, and I shall have to come back to it a few times to get the most out of it.

I may have missed it, but so far I have not found the much sought after answer to the question: How can something that did not previously exist come into being in an infinite state?

There are other things to come back to when time permits, but, for now, thanks again.
Title: Re: Is infinity an illusion?
Post by: lean bean on 12/10/2013 15:57:58
Quote from: JP
there isn't a reason to assume the universe didn't start off infinite
I always ask for an explanation as to how some infinite object can come into existence; especially something that is often described as infinitesimally small.
Bill, I don’t know why you assume the universe was  infinitesimally small to begin with?  Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?

I may have missed it, but so far I have not found the much sought after answer to the question: How can something that did not previously exist come into being in an infinite state?
Answering from what JP has already said, the processes of the origins of a universe or universes maybe a unique process with no comparison processes/laws within a universe. Smacks of philosophy... but I like it.
How can something that did not previously exist come into being in an infinite state?
the bb was the beginning of a determinable space and time, and as such, could be a regional happening following from the density of matter/energy within that region. In other words, our understanding of spacetime (determinable) may be a regional property not happening at the 'same' time everywhere in an infinite universe.
Title: Re: Is infinity an illusion?
Post by: Bill S on 12/10/2013 16:18:55
Quote from: LB
Bill, I don’t know why you assume the universe was  infinitesimally small to begin with?

That is not an assumption at which I just arrived.  As a hitch-hiker, I have to place some reliance on what scientists say when they write books for the edification of non-scientists.

Quote
Answering from what JP has already said, the processes of the origins of a universe or universes maybe a unique process with no comparison processes/laws within a universe.

Isn't that a bit like saying "God created the Universe, so there is no point in even thinking beyond that"?
Title: Re: Is infinity an illusion?
Post by: Bill S on 12/10/2013 16:35:09
Quote from: JP
So what is a model that might work?  One that I've heard of and that makes some sense to me is that all possible universes at all possible times exist as a set of states.  We say there is time and space because our brains and bodies work in a certain way to put ordering to these states.  We process information by moving "forward" in time (converting energy to entropy) so we see an arrow of time.  Various parameters of our particular universe define what we can interact with as we move in time, so we experience causality, etc.


Apart, perhaps, from some of Barbour’s work, this is the closest I have seen to the basic outline of what I have in mind.  However, it does seem to make one assumption that I would consider has an alternative.  It appears to assume that existence necessarily takes the form of universes.  Such an assumption robs the idea of much of its potential explanatory power.
Title: Re: Is infinity an illusion?
Post by: lean bean on 12/10/2013 16:47:47
Cor Bill, that was quick.
Quote from: LB
Bill, I don’t know why you assume the universe was  infinitesimally small to begin with?
That is not an assumption at which I just arrived.  As a hitch-hiker, I have to place some reliance on what scientists say when they write books for the edification of non-scientists.
Where does it say for sure the 'whole' universe was infinitesimally small at 'a' beginning. Remember the bb was a beginning of determinable space and time. That could be a regional state (because of mass/energy density) in an infinite universe.
Quote
Isn't that a bit like saying "God created the Universe, so there is no point in even thinking beyond that"?
True, but if you want to go beyond, you have to remember things that can't happen within our universe can happen with 'objects' like universes, faster than light inflation for instance.

Title: Re: Is infinity an illusion?
Post by: dlorde on 13/10/2013 13:17:52
dlorde, as fascinating as this discussion is, I think we should stop now because we are way off topic and must be trying the patience of the mods.
As I said, if you wish to continue it, start a new thread :)
Title: Re: Is infinity an illusion?
Post by: dlorde on 13/10/2013 13:32:06
Quote from: LB
Bill, I don’t know why you assume the universe was  infinitesimally small to begin with?
That is not an assumption at which I just arrived.  As a hitch-hiker, I have to place some reliance on what scientists say when they write books for the edification of non-scientists.
I'd be surprised if a knowledgeable scientist would describe it in those terms. I suspect it's a misinterpretation or misunderstanding. The 'initial' (earliest we can describe) state is generally described as very hot and very dense and expanding very rapidly. Intuition would suggest that the currently observable universe would then have been infinitesimally small, but the observable universe is (almost certainly) not the whole universe, so could conceivably have started as an infinitesimally small part of an infinitely large, hot, dense, expanding universe.
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/10/2013 18:49:37
Quote from: LB
Where does it say for sure the 'whole' universe was infinitesimally small at 'a' beginning. Remember the bb was a beginning of determinable space and time.


 Once again we run into difficulties arising from the use of “universe” in various ways.  This is why I prefer to reserve “Universe” what we can observe, or to which we can reasonably extrapolate our observations; and use “cosmos” for the bigger picture.

Quote
That could be a regional state (because of mass/energy density) in an infinite universe.

Or a finite Universe in an infinite cosmos.  It seems very much to be a matter of terminology.
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/10/2013 19:00:44
Quote from: dlorde
Intuition would suggest that the currently observable universe would then have been infinitesimally small, but the observable universe is (almost certainly) not the whole universe, so could conceivably have started as an infinitesimally small part of an infinitely large, hot, dense, expanding universe.

To avoid falling into the “misinterpretation trap” I must ask for more clarification before responding to this. 

Do you mean that the “infinitely large, hot, dense, expanding universe” came into being at the BB, or was it just the “infinitesimally small part”?

If the former, what is the relationship/difference between the infinite part and the infinitesimally small bit?

If the latter, is the infinitely large part eternal?

 What are your grounds for thinking that the infinitely large part is expanding?
Title: Re: Is infinity an illusion?
Post by: Bill S on 13/10/2013 19:30:04
JP, although this is a (part) response to your last post, it is very general, so I am not starting with a quote. 

I am aware that intuition is a poor guide where modern scientific concepts are concerned, but if an idea seemed to provide some insight into aspects that were poorly understood, or not really understood at all, might it not be worth investigating? 

I am certainly not saying “Look, I have the answer”.  I lack both the scientific background and the maths to make such a claim, but I have some (crackpot?) ideas in my head.  Obviously, it would be gratifying if they turned out to be well founded, but I’m not really that naïve, so having them laid to rest would be quite acceptable, and much more likely.

Basically, the idea is that a re-think of the concept of infinity could explain much of the weirdness of quantum theory.  That would include things like wave/particle duality, the ability of quons (sensu Herbert) to appear to be in more than one place at a time, entanglement and action at a distance.     
Title: Re: Is infinity an illusion?
Post by: Pmb on 13/10/2013 22:28:32
Quote from: lean bean
Bill, I don't know why you assume the universe was  infinitesimally small to begin with?  Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?
That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do. Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.
Title: Re: Is infinity an illusion?
Post by: Pmb on 13/10/2013 22:42:02
Quote from: webplodder
But what caused the BB?
Nobody knows.
Title: Re: Is infinity an illusion?
Post by: dlorde on 14/10/2013 00:30:28
Do you mean that the “infinitely large, hot, dense, expanding universe” came into being at the BB, or was it just the “infinitesimally small part”?
As far as I'm aware, it's not known whether anything 'came into being' at the BB, just that the earliest state we can infer was a hot, dense, expanding one. This may have been finite or infinite in extent. If it was infinite, the observable universe would be a part of it.

Quote
If the former, what is the relationship/difference between the infinite part and the infinitesimally small bit?
Not sure I understand what you're asking - it would be the same as for any finite part of something infinite. 

Quote
If the latter, is the infinitely large part eternal?
I have no idea. Pace concerns about the meaning of eternity and whether time began at the BB, how could we possibly know or guess? (and what difference would it make?).

Quote
What are your grounds for thinking that the infinitely large part is expanding?
The Cosmological Principle (http://en.wikipedia.org/wiki/Cosmological_principle) (homogeneity) & Ockham's Razor. The observable universe is expanding; if it is part of a larger universe, the simplest assumption is that it too is expanding. Otherwise we'd have to find some explanation for why the observable universe is not representative of the greater whole.
Title: Re: Is infinity an illusion?
Post by: Pmb on 14/10/2013 17:23:18
Quote from: dlorde
Intuition would suggest that the currently observable universe would then have been infinitesimally small, but the observable universe is (almost certainly) not the whole universe, so could conceivably have started as an infinitesimally small part of an infinitely large, hot, dense, expanding universe.

To avoid falling into the “misinterpretation trap” I must ask for more clarification before responding to this. 

Do you mean that the “infinitely large, hot, dense, expanding universe” came into being at the BB, or was it just the “infinitesimally small part”?

If the former, what is the relationship/difference between the infinite part and the infinitesimally small bit?

If the latter, is the infinitely large part eternal?

 What are your grounds for thinking that the infinitely large part is expanding?

Bill, You might find some of the answers to your questions here
http://superstringtheory.com/cosmo/
Title: Re: Is infinity an illusion?
Post by: lean bean on 14/10/2013 17:25:08
Quote from: LB
Where does it say for sure the 'whole' universe was infinitesimally small at 'a' beginning. Remember the bb was a beginning of determinable space and time.

 Once again we run into difficulties arising from the use of “universe” in various ways.  This is why I prefer to reserve “Universe” what we can observe, or to which we can reasonably extrapolate our observations; and use “cosmos” for the bigger picture.

I prefer to reserve "observable universe" to that which we observe... it's in the name :)  If I have been using the term infinite universe, then I would guess that's what you call the Cosmos and for what we can 'conjecture' about ,as you say, the bigger picture...Mulitverse ideas and infinite Universe.

bill
Quote
Or a finite Universe in an infinite cosmos.  It seems very much to be a matter of terminology.
Yes, our observable universe as part of a larger infinite Universe.
Quote from: lean bean
Bill, I don't know why you assume the universe was  infinitesimally small to begin with?  Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?

That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do.
So who is it  coming up with ideas like mulitverse and eternal inflationary Universe, If not cosmologists ?  And can you rule out the idea of an infinite Universe?
 
Quote
Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.
Yes, that’s why I said a determinable space and time began at the bb, If you want to be precise then 10-34s after the bb a determinable space and time arose.
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/10/2013 21:23:36
Quote from: LB
you have to remember things that can't happen within our universe can happen with 'objects' like universes

Do you mean there may be other universes in which things could happen that cannot happen in our Universe, or do you have concrete examples?
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/10/2013 21:29:00
Quote from: dlorde
The Cosmological Principle (homogeneity) & Ockham's Razor. The observable universe is expanding; if it is part of a larger universe, the simplest assumption is that it too is expanding. Otherwise we'd have to find some explanation for why the observable universe is not representative of the greater whole.

Delightfully put.  I hope you won't mind if I hang on to that, and quote it later.  :) 
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/10/2013 21:44:50
Quote from: LB
This is why I prefer to reserve “Universe” what we can observe, or to which we can reasonably extrapolate our observations

What I said was:
"This is why I prefer to reserve “Universe” what we can observe, or to which we can reasonably extrapolate our observations"
Obviously there should be "for" between "Universe" and what, but even allowing for any confusion that might have arisen from that omission, your addition of bold type is tantamount to miss-quoting me. 

"Universe", as I defined it, and "observable universe" are not quite synonymous.

I guess discussions would be less fun if we all used a rigidly defined terminology.  :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/10/2013 22:55:16
LB, its not going anywhere other than to note that "the Universe we can observe, or to which we can reasonably extrapolate our observations" is not quite the same as the "observable universe". Just an observation.  :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 14/10/2013 23:00:17
Quote from: LB
Cor Bill, that was quick.

I'm working on getting responses in before the questions are posted, but my time machine is being difficult.
Title: Re: Is infinity an illusion?
Post by: lean bean on 14/10/2013 23:11:54
LB, its not going anywhere other than to note that "the Universe we can observe, or to which we can reasonably extrapolate our observations" is not quite the same as the "observable universe". Just an observation.  :)
Bill, my last post. I can't get the quote boxes looking right?? It seems the whole post is from you..I have given up trying to get it right..

Quote
LB, its not going anywhere other than to note that "the Universe we can observe, or to which we can reasonably extrapolate our observations" is not quite the same as the "observable universe". Just an observation.  :)
what's not going where? I'm usually asleep by now...I have had me milk and biscuits and teddy's tucked in

Ps late add on. if you mean the galaxy is going nowhere, yes I know it's expanding spacetime taking it for a ride. did you mean something esle?

Title: Re: Is infinity an illusion?
Post by: dlorde on 14/10/2013 23:46:54
Delightfully put.  I hope you won't mind if I hang on to that, and quote it later.  :) 
Thank you; you're welcome to quote it any time.
Title: Re: Is infinity an illusion?
Post by: lean bean on 15/10/2013 11:22:54
Do you mean there may be other universes in which things could happen that cannot happen in our Universe, or do you have concrete examples?

To give a quote from John Barrow's book 'The Infinite Book' page 197....The bubbles are universes .
Quote
As in the chaotic inflationary process, each of the bubbles may carry a different number of forces of Nature,different vaues for some (or even all) constants of Nature,and different  numbers of dimensions of space and time.
Same page
Quote
if it is infinite in size, without us having to appeal to metaphysical notions like 'other' universes existing in parallel realities.  One infinite universe contains enough room to contain all these possibilities.This is the conserative multiverse option.
His italics


Same book page 192.
Quote
It is this impressive agreement between the simple predictions of the inflationary universe theory and a large number of high-precision observations that provokes us to take seriously the wider consequences of the inflationary universe for infinite universes.



Quote from: lean bean
Bill, I don't know why you assume the universe was  infinitesimally small to begin with?  Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?
That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do. Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.
pete, are you saying within that 10-34s the universe was infinitesimally small, how do you know the size for certain within the period of undeterminable space and time.
Title: Re: Is infinity an illusion?
Post by: Bill S on 15/10/2013 21:16:45
Quote from: LB
Bill, my last post. I can't get the quote boxes looking right

I hope you are not asking me for technical advice; I'm a certified and practicing luddite.

Title: Re: Is infinity an illusion?
Post by: Bill S on 15/10/2013 21:21:28
Quote from: LB
what's not going where?

Strange! I was sure you had asked "Where's this going".  Now I can't find it; I guess it must have gone, whatever it was. :)
Title: Re: Is infinity an illusion?
Post by: dlorde on 15/10/2013 21:35:19
... I can't get the quote boxes looking right??
Make sure each start-quote tag has a matching end-quote tag. Nest them to go back to previous posts:

current post
[q...]
   recent post
   [q...]
      earlier post
      [q...]
          even earlier post
      [/q...]
      earlier post again
   [/q...]
   recent post again
[/q...]
current post again

Title: Re: Is infinity an illusion?
Post by: Bill S on 15/10/2013 23:02:15
Thanks, dlorde.  I shall enjoy trying that and seeing what sort of mess I can make.
Title: Re: Is infinity an illusion?
Post by: Pmb on 15/10/2013 23:17:35
Quote from: lean bean
Bill, I don't know why you assume the universe was  infinitesimally small to begin with?  Just because the equations of running the observable universe backwards ends with those equations breaking down/singularity, Why do you assume that means the whole of the universe was once infinitesimally small?
That's what modern cosmology says so its no surprise that Bill accepts that as it is. I do. Cosmologists and most physicists know that the big bang theory is an extrapolation running back wards. But it works that way. Only when we run things back to 10-34s or so do we see things working out to what we observe today.
pete, are you saying within that 10-34s the universe was infinitesimally small, how do you know the size for certain within the period of undeterminable space and time.
[/quote]
I can’t recall where I got that from so let’s ignore that comment. I’m not sure what LBs problem was above either. However Infinitely small is not a real term. It has no meaning. And we don’t know what happened at  t = 0 and we can’t take the universe back to a size of zero. The term infinite quite literally means unbounded. So the term infinitesimally small means unbounded smallness which is meaningless.

Our understanding of physics today only allows us to run the equations back only so far.

Note: Please understand that when it comes to the early universe and cosmology that I’m a beginner. I do not profess to be an expert or even fully versed.

Let me quote Gravitation and Spacetime – Third Ed. by Ohanian and Ruffini. From Chapter 10 Early Universe page 445
Quote
Entirely new physics needs to be introduced to deal with the behavior of the universe at earlier times, at about 10-32s and earlier, when the universe apparently suffered a quick and very large inflation. Strong circumstantial evidence consistent with such an inflation has now been discovered by analysis of miniscule temperature fluctuations in the observed distribution of the cosmic background radiation over the sky. But the mechanism underlying inflation remains purely conjectural, and a large variety of possible theoretical scenarios are still under investigation.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/10/2013 04:15:40
Quote from: Pete
  Infinitely small is not a real term. It has no meaning.

If I were not already in bed (4.15am) I would open a bottle to celebrate that one! :D
Title: Re: Is infinity an illusion?
Post by: Pmb on 16/10/2013 04:36:34
Quote from: Pete
  Infinitely small is not a real term. It has no meaning.

If I were not already in bed (4.15am) I would open a bottle to celebrate that one! :D
I'm so glad to hear that. I'm here to please. :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/10/2013 14:30:30
Quote from: Pete
So the term infinitesimally small means unbounded smallness which is meaningless.

This is probably nit-picking, but surely "unbounded smallness" would be the definition of infinitely small; whereas "infinitesimally small" means so small it cannot be measured, but not zero.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/10/2013 15:18:17
One of the things that emerges in this thread is the thought that I am basing arguments on unwarranted assumptions. 
I asked myself the following questions, and made a stab at answering them.

Q1.  Given that there is something now; can there ever have been nothing?

A1.  Possibly.

Q2.  How could that be possible?

A2.  Outside our observable universe the laws of physics, including the laws of causality, could be different.  It is possible that something could come from nothing as a result of a process unknown in this Universe.

Q3.  Is there anything we can observe in our Universe that would point to such differences? 

A3. Not to my knowledge.

Q4.  Is there anything we can observe in our universe that would negate such differences?

A4.  Not to my knowledge.

Q5.  If one needs to make an assumption about what conditions might be outside the Universe, is it better to assume that conditions are essentially as we observe them in the Universe, or that that they are different?

A5.  Ockham’s razor would tend to point towards the former.  Also, James Hutton started a revolution in geology with his assertion that “The present is the key to the past”.  One might extrapolate this to “The known is the key to the unknown”.   

Q6. How reasonable is it to make assumptions in order to try to move from the known to the unknown?
 
A6.  Science in general, and cosmology in particular, would be severely hampered without a few very basic assumptions.

Cosmologists assume that the Universe is both homogeneous and isotropic, even beyond the horizon of our observations.

The laws of physics are assumed to be the same everywhere in the Universe, including those parts we cannot observe.

Even the second law of thermodynamics is based on an assumption - that the Universe began its life in an ordered state.

Q7.  Can anyone make assumptions about the unknown, or should only experts do this?

A7.  Obviously, experts are in a better position to make reasonable assumptions than are non-experts.  Non-experts would be wise to run their ideas past experts to test validity.  However, there is often disagreement among experts, so the extent to which ideas are validated may depend on the choice of expert.

Conclusion:  Thinking outside the box is hard work.  :)
Title: Re: Is infinity an illusion?
Post by: JP on 16/10/2013 15:38:56
Quote from: Pete
So the term infinitesimally small means unbounded smallness which is meaningless.

This is probably nit-picking, but surely "unbounded smallness" would be the definition of infinitely small; whereas "infinitesimally small" means so small it cannot be measured, but not zero.

Just to be the grumpy dissenter--infinitely small is a bit of an abuse of the term "infinitesimally small" as you noted, Pete, but it does certainly have meaning mathematically.  If it didn't, we'd have no calculus!

We can debate whether it has meaning physically in the sense that it may or may not make sense to talk about infinitesimally small regions of space.  The Planck length, as I understand it, isn't the smallest possible distance--it's simply where we need a better theory.  (That better theory may very well end up telling us that the Planck length is the smallest unit of distance, but we don't have it yet!)
Title: Re: Is infinity an illusion?
Post by: JP on 16/10/2013 16:45:32
One of the things that emerges in this thread is the thought that I am basing arguments on unwarranted assumptions. 
I asked myself the following questions, and made a stab at answering them.

...

Q5.  If one needs to make an assumption about what conditions might be outside the Universe, is it better to assume that conditions are essentially as we observe them in the Universe, or that that they are different?

A5.  Ockham’s razor would tend to point towards the former.  Also, James Hutton started a revolution in geology with his assertion that “The present is the key to the past”.  One might extrapolate this to “The known is the key to the unknown”.   

Q6. How reasonable is it to make assumptions in order to try to move from the known to the unknown?
 
A6.  Science in general, and cosmology in particular, would be severely hampered without a few very basic assumptions.

Cosmologists assume that the Universe is both homogeneous and isotropic, even beyond the horizon of our observations.

The laws of physics are assumed to be the same everywhere in the Universe, including those parts we cannot observe.

Even the second law of thermodynamics is based on an assumption - that the Universe began its life in an ordered state.

Q7.  Can anyone make assumptions about the unknown, or should only experts do this?

A7.  Obviously, experts are in a better position to make reasonable assumptions than are non-experts.  Non-experts would be wise to run their ideas past experts to test validity.  However, there is often disagreement among experts, so the extent to which ideas are validated may depend on the choice of expert.

Conclusion:  Thinking outside the box is hard work.  :)


I thought I responded previously but I can't find it, so maybe I got distracted and forgot to post.  (Just got a new puppy, so I tend to get about 30 seconds at a time at the computer before he chews on something he shouldn't!)

In light of what you're saying here, I think my main contention with your argument is your assumption that extrapolation to the unknown is always the best option.  It isn't!  Extrapolation is fair when you have reason to believe your models are continuously connected to the unknown cases in some way.  For example, we observe large-scale homogeneity and isotropy in the visible universe, and we expect the universe as a whole to be a large, connected region of space-time.  Therefore, it's reasonable to assume that isotropy and homogeneity hold for the universe as a whole. 

Similarly, physical laws seem to be consistent over space and time, so it's natural to assume that the same laws which hold today also also held back near the birth of the universe. 

Both of these may be false, but since we can continuously extend our models to cover these regions we don't have access to, it's most natural to assume that this extrapolation holds.

However, when you can't continuously extend your models to cover the new cases, Occam's razor doesn't hold.  You're essentially saying "I'm going to apply what I know to an unrelated system."  The simplest explanation is not to enforce the unrelated model to hold.  I'd argue that the simplest model is to say "I can put bounds on how this system behaves in terms of measurements I've made, but I have to assume I know little about the model at work."

For example, a lot of people mistakenly assume that "photons don't experience time."  This is based on erroneously extending special relativity, which says that if a clock moves past a stationary observer, the clock appears to run slowly as measured by the observer.  The closer the clock moves to the speed of light, the slower it appears to run.  In the limit as it's speed approaches the speed of light, its clock slows down without bound.  It's natural to say "well, that observer sees all photons as flying past him at the speed of light, so photons must experience that limiting case and so their clocks don't move at all as measured by that observer."  (By the same logic, an observer riding on a photon would see the entire universe as static, since he/she would measure all external clocks as static).  This immediately leads to a paradox, since we know photons are emitted an absorbed, interacting at 2 points in time, so clearly they do somehow "experience" time. 

The problem here is that special relativity is defined over a set of states (observers moving with constant speeds) that can be connected continuously to each other by accelerations (Lorentz boosts).  We've only tested special relativity in a small range of cases, but we can safely extrapolate it to all inertial (constant speed) reference frames because they're all continuously connected to each other within the framework of the theory.  However, no amount of Lorentz boosting will take you to the reference frame of light, so this case isn't connected in any way to the rest of the theory, including cases we've tested.  There's no justification for extrapolating to this unconnected case and here it provides answers that are both paradoxical and useless (and wrong in the sense that they have no meaning).

I'm arguing throughout that your ideas of finite-sized objects growing at finite rates makes a lot of sense, but only within our universe, since that's where all the examples we know of live.  Moreover, finite objects must exist in space, and rates of increase in size occur over time, so we're justified in extrapolating these ideas to any region in space and time that's connected to the region we've observed--in other words, the entire universe (possibly excepting black holes and other singular objects).  In other words, these ideas make sense so long as your object is bounded in some region of space and time within our universe. 

The problem is that you're asking us to extrapolate this idea to our entire universe, which clearly doesn't live in a region of space and time within itself!  Whatever set it's a part of (if it is a part of any larger set) is not in any way we know of continuously connected to the space and time of our universe (since anything connected to our universe would be part of our universe.)

I'd go further and argue that extrapolation is useless when performed to unconnected cases.  I'd also suggest that the best way to tackle the problem of an infinite universe is to return the fundamentals of science: can we come up with a theory that makes a testable prediction based on the size of the universe.  Then we can apply Occam's razor to boil down these theories to the simplest ones and experiment or observation should then be the judge of which one is best.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/10/2013 21:20:34
Once again, thanks for the detailed response, JP.  What you say makes very good sense to me. 

I must point out that I didn’t intend saying, or implying, “that extrapolation to the unknown is always the best option”.
What I was saying was that if one were speculating about the unknown one would have the choice of assuming that the situation there would be essentially as it is in the known Universe; or that it would be essentially different.  Assuming (without a sound reason) that it is different introduces an additional level of “unknown”.  This is where I was applying Ockham’s razor. 

Correct me if I’m wrong, but you seem to be saying something more like “We don’t know what, if anything, is outside our Universe, so there is no point in trying to think about it.”

That’s a perfectly valid point of view, but, to me it seems much like saying “God created it; end of speculation.”  While this may also be a valid point of view, it too seems a bit restrictive.
Title: Re: Is infinity an illusion?
Post by: Bill S on 16/10/2013 21:23:47
BTW, JP, what sort of puppy?
Title: Re: Is infinity an illusion?
Post by: JP on 16/10/2013 23:14:31
2 points, Bill:

1) Boiled down, my point is basically that your idea is based on things we view within the space-time of our universe.  You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.  How would you even go about doing this?  It seems a bit contrived to try to force our models into a case that's probably completely alien to them just for "simplicity."

2) I wouldn't say it's not worth questioning what's outside the universe, but I would say that as scientists it's our duty to make every possible effort to come up with testable models.  This is where much of this does go into the domain of experts (and I'm not an expert on this!)  Sure, these models will likely have a lot of speculation, but we should be speculating towards testable answers.  I see two possible ways forward on this front: 1) we can work entirely within the universe and try to figure out testable consequences if the universe is finite vs. infinite or 2) we can work on models outside the universe with testable predictions.  This second vein of work contains string theory and other similar theories of everything which are generally criticized because they don't provide testable predictions.  I also don't find them terribly convincing for that reason.  But there are plenty of scientists who are convinced that the theory is heading in the right direction towards testability and I trust them, since I don't know enough of the area to judge otherwise.  :p

But hey--you may be right.  I just don't think it's the most fruitful way to approach the question.

Title: Re: Is infinity an illusion?
Post by: JP on 16/10/2013 23:16:26
3) Pembroke Welsh Corgi
Title: Re: Is infinity an illusion?
Post by: Pmb on 17/10/2013 09:33:25
2 points, Bill:

1) Boiled down, my point is basically that your idea is based on things we view within the space-time of our universe.  You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.  How would you even go about doing this?  It seems a bit contrived to try to force our models into a case that's probably completely alien to them just for "simplicity."
I thought that string cosmology was doing something very similar. Is this not the case? They'e using that to formulate the Pre-Big Bang scenario

See http://www.ba.infn.it/~gasperin/
Title: Re: Is infinity an illusion?
Post by: JP on 17/10/2013 12:55:41
From what I understand of string theory, its not a matter of simply extending known physics to pre-big-bang times.  String theory has a bunch of new parts (11 dimensions, for example, in M-theory). 
Title: Re: Is infinity an illusion?
Post by: Bill S on 17/10/2013 14:05:00
Quote from: JP
You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.

In this sort of discussion it is easy to divert to side issues which, although relevant to some extent, detract from the main point, or even give a wrong impression.

In fact, the only concept I would seek to apply to anything beyond our Universe is that if there had ever been nothing, there would be nothing now.  I certainly have no wish to argue that space and time exist outside the Universe.  I would not even join the multiverse advocates in assuming that whatever might be beyond our Universe would need to be composed of universes.

I like the look of the puppy and hope you and he/she have many enjoyable years together.
Title: Re: Is infinity an illusion?
Post by: JP on 17/10/2013 14:33:51
Quote from: JP
You're trying to extend this idea to regions outside of our universe, where space and time as we know them probably don't exist.

In this sort of discussion it is easy to divert to side issues which, although relevant to some extent, detract from the main point, or even give a wrong impression.

In fact, the only concept I would seek to apply to anything beyond our Universe is that if there had ever been nothing, there would be nothing now.


That goes to a bigger side issue--what is nothing?  Do you mean a complete vacuum, or do you mean "absolute nothing," e.g. no space, time or anything else?  (We did have a lengthy argument elsewhere that showed the difficulty in defining absolute nothing.) 

Again, it seems like a simple requirement to say "if there ever was nothing, there will be nothing now," but that's far from simple once you step outside the bounds of our universe.
Title: Re: Is infinity an illusion?
Post by: lean bean on 17/10/2013 16:38:52
... I can't get the quote boxes looking right??
Make sure each start-quote tag has a matching end-quote tag. Nest them to go back to previous posts:
current post
Thanks dlorde, I will keep that in mind. I have removed the post to keep the thread neat. :)
Title: Re: Is infinity an illusion?
Post by: Bill S on 17/10/2013 19:20:36
Quote from: JP
Do you mean a complete vacuum, or do you mean "absolute nothing,"

I mean "absolute nothing", which does seem somewhat tautologous. 

Quote
it seems like a simple requirement to say "if there ever was nothing, there will be nothing now," but that's far from simple once you step outside the bounds of our universe.

Other than saying that something could come from nothing outside the Universe, what would be the complications?
Title: Re: Is infinity an illusion?
Post by: JP on 17/10/2013 22:36:27
Quote from: JP
Do you mean a complete vacuum, or do you mean "absolute nothing,"

I mean "absolute nothing", which does seem somewhat tautologous. 

Quote
it seems like a simple requirement to say "if there ever was nothing, there will be nothing now," but that's far from simple once you step outside the bounds of our universe.

Other than saying that something could come from nothing outside the Universe, what would be the complications?

Define "nothing."  Define "come from."  Keep in mind that we're outside the universe which contains all (known) space and time.
Title: Re: Is infinity an illusion?
Post by: Bill S on 17/10/2013 23:06:16
Quote from: JP
Define "nothing."  Define "come from."  Keep in mind that we're outside the universe which contains all (known) space and time.

Nothing:  Complete absence of anything, known or unknown to us.

Comes from (as used here):  Is caused, created or otherwise brought into existence by.
Title: Re: Is infinity an illusion?
Post by: JP on 18/10/2013 15:36:31
Quote from: JP
Define "nothing."  Define "come from."  Keep in mind that we're outside the universe which contains all (known) space and time.

Nothing:  Complete absence of anything, known or unknown to us.
I think the result of the previous thread on nothing was that isn't a scientifically useful definition, since science deals with measurable which are necessarily tied to "somethings".  If you think "nothing" is scientifically useful, I suspect the burden of proof is on you that it can be so before we start using it to make predictions about the universe.

Quote
Comes from (as used here):  Is caused, created or otherwise brought into existence by.
That seems to imply that there was a time at which something didn't exist and a time at which it did, which means there is time outside of the universe.  What justification do you have for assuming this, since the universe presumably contains all time?  If that's not what you mean, created/caused/brought into existence are problematic to use in a definition, since all imply time passing.
Title: Re: Is infinity an illusion?
Post by: webplodder on 18/10/2013 16:35:38
Quote from: JP
Define "nothing."  Define "come from."  Keep in mind that we're outside the universe which contains all (known) space and time.

Nothing:  Complete absence of anything, known or unknown to us.



Comes from (as used here):  Is caused, created or otherwise brought into existence by.


What this seems to imply is that we can never know or define nothing since any 'idea' of nothing is itself not nothing as it is an idea. Now, as we know, an idea is really the electrochemical activity of the brain (at least we will use that as a working definition unless and until we know better) so it must be something. No doubt, there are ideas or concepts that have yet to be experienced, however, it seems to me that for any meaningful purposes nothing cannot exist. Even if you talked about a complete vacuum containing no atoms, quarks, virtual particles and the rest, you will still be left with the ideas of space and time and dimension, which are not nothing. Science cannot exist within a framework of nothing because it needs to measure things and nothing cannot be measured! A puzzling question to me is: do things already exist before we think about them or do they come into being by the processes of consciousness? The reason I pose this question is because it is always possible to ask "what went before?", but an eternal universe, with no beginning or end, doesn't seem to make much sense to me since it seems to defy cause-and-effect. If something is uncaused how then does it give rise to causality? How can causality suddenly spring from nowhere? A more logical, if more startling, conclusion would be that it is consciousness itself that defines reality because this way we only have to worry about stuff we can think about rather that what might or might not already exist. The problem about an eternal universe then disappears because it is only as 'real' as our ideas.
Title: Re: Is infinity an illusion?
Post by: dlorde on 18/10/2013 18:43:15
... A more logical, if more startling, conclusion would be that it is consciousness itself that defines reality because this way we only have to worry about stuff we can think about rather that what might or might not already exist. The problem about an eternal universe then disappears because it is only as 'real' as our ideas.
That sounds too much like solipsism. I don't see that it helps at all; apart from the philosophical cul-de-sac of solipsism, you still have to account for consciousness itself, and you've now removed any causal material basis for it. You also have the problem of how we can discover new things and be surprised by them if they're defined by our consciousness...
Title: Re: Is infinity an illusion?
Post by: Bill S on 18/10/2013 20:00:35
Quote from: JP
since science deals with measurable which are necessarily tied to "somethings"

Does science deal with infinities?

Are infinities measurable? 

Quote
If you think "nothing" is scientifically useful, I suspect the burden of proof is on you that it can be so before we start using it to make predictions about the universe.

I am certainly not saying that “nothing” is scientifically useful.  In fact I am trying to investigate what might be the effect on science – and everything else – if there had ever been nothing.  So far no one has convinced me that, had there ever been nothing, there would now be scientists to discuss what might or might not be scientifically useful. 
Title: Re: Is infinity an illusion?
Post by: Bill S on 18/10/2013 20:12:55
Quote from: Webplodder
What this seems to imply is that we can never know or define nothing since any 'idea' of nothing is itself not nothing as it is an idea

Of course an idea is something; but having an idea of "nothing" does not make it something, any more than having an idea of Mount Everest upside down would actually invert that geological feature.
Title: Re: Is infinity an illusion?
Post by: webplodder on 18/10/2013 20:59:53
Quote
That sounds too much like solipsism. I don't see that it helps at all; apart from the philosophical cul-de-sac of solipsism, you still have to account for consciousness itself, and you've now removed any causal material basis for it. You also have the problem of how we can discover new things and be surprised by them if they're defined by our consciousness...

But how can we similarly account for any causal basis for an eternal universe? The concept of an eternal universe removes any causal chain leading to what we see today because, by definition, there can never be any original cause. The only way out is to reject such a notion and accept that 'classical' ideas about time and space are merely illusions - illusions created by the mind. Is this not itself "a new thing?"

If it turns out that consciousness is the only basis of reality then it cannot obey the same rules of cause-and-effect that we see in material objects, despite giving rise to it.
Title: Re: Is infinity an illusion?
Post by: webplodder on 18/10/2013 21:03:32
Quote from: Webplodder
What this seems to imply is that we can never know or define nothing since any 'idea' of nothing is itself not nothing as it is an idea

Of course an idea is something; but having an idea of "nothing" does not make it something, any more than having an idea of Mount Everest upside down would actually invert that geological feature.

Is it not a truism that any scientific theory one can name began only as an idea? All of reality is, in the final analysis, an idea. Even using the word " nothing" is, in a sense, producing "something" that attempts to describe an idea.
Title: Re: Is infinity an illusion?
Post by: JP on 18/10/2013 21:25:14
Let me address your points in reverse order:

I am certainly not saying that “nothing” is scientifically useful.  In fact I am trying to investigate what might be the effect on science – and everything else – if there had ever been nothing. 

I'll go one further, then. "Nothing" in the sense you're using it is a scientifically vacuous term: it has no useful meaning.  It in no way relates to any measurements we can or ever will make.  This is different in one important respect from the concept of infinity.  Regardless of whether infinity can exist or not in nature, we can approximate certain things as infinite if they are simply very large in order to simplify our calculations, so it serves some purpose in physics.  We can never approximate anything as "absolute nothing" since that term is meaningless to physicists.

Quote
So far no one has convinced me that, had there ever been nothing, there would now be scientists to discuss what might or might not be scientifically useful. 
This is a loaded statement: one doesn't need to convince you of this, since the statement "had there ever been nothing, there would now be scientists to discuss what might or might not be scientifically useful" is meaningless in a scientific sense.  We can't convince you of this because we can't talk about nothing and what might arise from it in a meaningful way.  This is very similar to someone saying "No one has convinced me that god didn't make the universe."  Sure, you can hold that opinion, and a god defined in the right way can never be disproven by science, so it's a scientifically useless statement.


Quote from: JP
since science deals with measurable which are necessarily tied to "somethings"

Does science deal with infinities?

Are infinities measurable? 
First, I'd like to point out that we could have the case where your argument holds no water and infinity isn't physical.  I'm not arguing that infinity exists.  I'm arguing against the logical fallacies being brought up in the thread to provide reason to believe that it doesn't exist.  My claim is that these arguments, in particular yours about something being unable to come from nothing, have no meaning and can't be used to tell us about the existence or nonexistence of physical infinity.

Second, science does deal with infinities, in the sense I've pointed out several times: as approximations to very large things.  This is very important because it at least gives us some reason to think a physical infinity (if it exists) might have some bearing on reality (unlike "absolute nothing").  Are they measurable is an open question.  Clearly we are finite constructs, so I doubt we can ever measure infinity directly.  The critical point is that those scientists who do or don't believe it is physical are making arguments based on what we can measure to test their ideas.  The no-infinity camp is looking for consequences if space is discretized (so no infinitesimals) or the universe is finite.  Similarly, the infinite-universe camp is looking for measurable consequences as well.


-------

By the way, I'm intending this as friendly debate--when I reread it, I saw that "scientifically meaningless" might come across sounding overly critical, but it's not a bad idea to have.  I just think it is an idea that ends up leading nowhere useful when you try to develop testable, scientific models based on it.

And I to tend to agree with you that in the end, physical infinity is probably not real, but I don't think anyone has figured out a way to test for its existence one way or the other yet!  I feel that it's important as a scientist to distinguish between what you feel is true and what you can back up with scientific rigor as true.
Title: Re: Is infinity an illusion?
Post by: Bill S on 19/10/2013 16:16:35
Quote from: JP
I'll go one further, then. "Nothing" in the sense you're using it is a scientifically vacuous term: it has no useful meaning.  It in no way relates to any measurements we can or ever will make.

Is this tantamount to saying “if we can’t measure it, it doesn’t exist”?  That would be a bit dogmatic for my taste, but I would be very happy with the idea that “nothing”, or perhaps I should say “the state of nothingness”, cannot exist. 

OK, someone is going to say: “You can’t have a state of nothingness, because a state is something.”  However, I’m more interested in the discussion than the semantics.  I acknowledge the difficulty of discussing infinity when our language is based in the finite, and discussing nothingness when our existence is essentially something-based.  I think it’s worth trying, though.

Quote
we can approximate certain things as infinite if they are simply very large in order to simplify our calculations

As I have said before, I have no problem with this as long as we accept that these are approximations that cannot actually be infinite.     

The way in which scientists use “nothing”, e.g. “a universe from nothing” seems very much like using “nothing” as an approximation for “something ethereal”.
Title: Re: Is infinity an illusion?
Post by: Bill S on 19/10/2013 16:30:59
Quote from: JP
This is a loaded statement: one doesn't need to convince you of this, since the statement "had there ever been nothing, there would now be scientists to discuss what might or might not be scientifically useful" is meaningless in a scientific sense.

If "nothing"  is meaningless in a scientific sense, does this mean that science maintains that there must always have been something, or is “eternal something” scientifically meaningless as well?

NB. I’m not being deliberately awkward here, but if I feel something is within my ability to understand, it is not in my nature to let go of it until I come as near to understanding as I can.  This is probably why, years ago on a geology trip to Arran, I became known as “Bloody Bill”.  I’ve not changed much.  :)

Title: Re: Is infinity an illusion?
Post by: Bill S on 19/10/2013 16:38:06
Quote from: JP
And I to tend to agree with you that in the end, physical infinity is probably not real

Are we at cross purposes here?  I am certainly not saying that physical infinity is unreal.  In fact, logically, I see no way to escape its reality.  This is one reason for my persistence; I need to know if/how my logic might be flawed. 
Title: Re: Is infinity an illusion?
Post by: webplodder on 19/10/2013 17:47:13
Quote from: JP
This is a loaded statement: one doesn't need to convince you of this, since the statement "had there ever been nothing, there would now be scientists to discuss what might or might not be scientifically useful" is meaningless in a scientific sense.

If "nothing"  is meaningless in a scientific sense, does this mean that science maintains that there must always have been something, or is “eternal something” scientifically meaningless as well?

NB. I’m not being deliberately awkward here, but if I feel something is within my ability to understand, it is not in my nature to let go of it until I come as near to understanding as I can.  This is probably why, years ago on a geology trip to Arran, I became known as “Bloody Bill”.  I’ve not changed much.  :)



I'm probably way off beam here but I have an inkling we might eventually be forced to accept a model of the universe and reality that is both infinite AND finite, both eternal AND otherwise depending on how we wish to explain phenomena. This does sound crazy but bear in mind it is the job of science to provide supportable evidence to account for what is observed, not to make religious proclamations about who or what made the universe and why we are here. We only have to turn to the strange behaviour of quantum mechanics to realise things are far from what our common sense would have us believe. This may seem like giving up on any possibility of answering the really big questions but to seek scientific answers to perplexing questions leaves us in such a position.
Title: Re: Is infinity an illusion?
Post by: JP on 19/10/2013 19:23:43
Bill, to address your points:

1) We don't have to directly measure something to render it scientific, but we have to have a model which makes testable predictions and depends on that "something."  For example (and without any basis in fact here), let's say we find out that there's a constant that will have one value if the universe if infinite and another if it is finite.  We could measure that parameter to answer the question "is the universe infinite?" without having to measure the size of the universe directly. 

1a) Therefore, to answer whether there was ever "absolute nothing" we'd have to have a model that discriminates in terms of measurables between a scenario in which there was at one point "absolute nothing" and one in which there was not. 

1b) My claim is that neither you, nor anyone else can come up with such a model.  The arguments you've given so far which are along the lines of "something cannot come from nothing" is basing a model on opinion with no connection to physics--at least until you define what processes are available for things to "arise" and define precisely "absolute nothing" in a form that plugs usefully into that model.  "Arising from" in the context of the universe not yet existing is hard enough, but "absolute nothing" is a metaphysical concept without physical utility.  I don't think it's worth going into "nothing" again in this thread.  It was pretty clear from the thread about "absolute nothing" that it's a nebulous metaphysical concept that no one could really nail down except by saying it was the absence of everything. 

2) I agree that "the universe from nothing" is very poorly chosen phrasing that confuses laypersons.  When physicists say "nothing," they mean something specific, for example vacuum, which is certainly "something," if perhaps a very empty something.  The impetus to sell books can make scientists jazz up their titles for laypersons a bit more than should probably be done.

3) I think we both agree that "infinity" is useful mathematically, and that we both agree that we do not yet know if it's real or not in a physical sense (the size of the universe, for example). 

4) Your question:
Quote
If "nothing"  is meaningless in a scientific sense, does this mean that science maintains that there must always have been something, or is “eternal something” scientifically meaningless as well?
I think your first problem is "eternal," which assumes time always existed and therefore makes this a bit circular.  I suspect science is always going to deal with "somethings" though, since everything eventually has to tie back to measurable quantities and this always requires defining models.  The minute we define a model about anything, it becomes a "something."  So scientific answers probably will always avoid "absolute nothing" because it can't plug into a model in any useful way.  This places limits on what science can describe, but we already know that to be the case.  We can always define a god such that science can't answer questions of its existence, for example.  Absolute nothing is a similar concept.

4b) Let's say we do come up with an ultimate theory that explains everything in existence.  Let's say also that it describes that the "initial" (again, we're limited by terms dealing with time) state of things was that nothing in existence was there--it was a blank slate from which some processes occurred to generate everything.  Even then, this blank slate is not absolute nothing, since it has the potential to generate everything, which is a property.  "Absolute nothing" could not have properties.

5) Logically, infinity doesn't have to exist.  Let's say we prove we can never go beyond the universe in any experiments and we also find the universe is finite and that space and time consist of discrete units on a fundamental level.  Then physics will never have a real infinity present in it.  We can speculate philosophically or religiously about what is outside the universe, and whether infinities could exist there, but it's not a scientific question since we can't ever address it. 

6) It strikes me as I write this, that part of the problem is that you're looking for absolute answers, whereas physics is only capable of generating answers to a certain set of questions that can be scientifically framed.  A lot of ideas of infinity or absolute nothing are simply outside of this set of questions.
Title: Re: Is infinity an illusion?
Post by: grizelda on 19/10/2013 19:36:59
I once had a theory that the universe reconfigured itself randomly every planck instant, and our experience was those instants which made that experience valid, all other instants not figuring in consciousness, i.e. nothing. Since most random reconfigurations of the universe would not work for us, there would be an eternity between instants which figured in our experience. So our experience would be finite but spread out over infinity.
Title: Re: Is infinity an illusion?
Post by: lean bean on 20/10/2013 10:34:21
Are we at cross purposes here?  I am certainly not saying that physical infinity is unreal.  In fact, logically, I see no way to escape its reality.
Bill, is this where I came in...http://www.astro.ucla.edu/~wright/infpoint.html (http://www.astro.ucla.edu/~wright/infpoint.html)
Quote
The Universe was not concentrated into a point at the time of the Big Bang. But the observable Universe was concentrated into a point.
Here is a cosmologist  Prof.(Ned) Wright not requiring an infinitesimally small beginning.

About the 'infinitesimally small' thing...
I maybe be wrong ,but I thought the extrapolation of equations backwards, only make ’sense’ back to the end of the Planck era…10^-43 sec after bb.  So, before 10^-43 sec I would ask,where’s the evidence to say it started infinitesimally small?

Ps, it is I, lean bean :)

Title: Re: Is infinity an illusion?
Post by: Pmb on 21/10/2013 07:50:52
Quote from: JP
1b) My claim is that neither you, nor anyone else can come up with such a model.  The arguments you've given so far which are along the lines of "something cannot come from nothing" is basing a model on opinion with no connection to physics--at least until you define what processes are available for things to "arise" and define precisely "absolute nothing" in a form that plugs usefully into that model. 
This is the best point that I’ve seen anybody make in this entire thread. It’s a shame that more people never took the lesson that quantum mechanics taught us much more seriously. QM taught us that its dangerous to attempt to use our physical intuition in areas where we have no experience. We have no experience with times that short and distances that small. We never have and we never will. Therefore using the intuition we’ve developed billions of years after the big bang on a scale of human dimensions (give or take factors of many tens) is not using very good logic.

Thanks JP. :)
Title: Re: Is infinity an illusion?
Post by: webplodder on 22/10/2013 13:46:51
I believe time is really just an illusion caused by our conscious experiences in order to allow us to exist as organisms. Fundamentally, time has no meaning and, therefore, when we examine our material universe we are faced with perplexing questions about how old the universe is and what gave rise to it and what gave rise to that, ad infinitum. It is assumed that our sense experiences are reflecting the true nature of reality but in making such an assumption we inevitably run into problems about causality which can have no meaning in an eternal multiverse. Some people put forth the view that time, space and causality were introduced at the time of the big bang but this is little better because we are then immediately faced with the question of how causality can be uncaused ; it is little better than saying God did it! Although very difficult, we have to ditch the idea of time and space and try to embrace a model of reality that does not follow regular rules but is actually very schizophrenic in nature and that the parameters we place on our experiences are just artificial illusions, being simply special cases of a much greater truth.
Title: Re: Is infinity an illusion?
Post by: dlorde on 22/10/2013 14:10:15
I believe time is really just an illusion caused by our conscious experiences in order to allow us to exist as organisms.

This implies that time doesn't exist (which needs a thread to itself), and that if we weren't conscious, we wouldn't exist as organisms - which doesn't sound plausible, given the multitudes of organisms that appear to exist quite happily despite not being conscious...
Title: Re: Is infinity an illusion?
Post by: webplodder on 22/10/2013 15:38:56
I believe time is really just an illusion caused by our conscious experiences in order to allow us to exist as organisms.

This implies that time doesn't exist (which needs a thread to itself), and that if we weren't conscious, we wouldn't exist as organisms - which doesn't sound plausible, given the multitudes of organisms that appear to exist quite happily despite not being conscious...

You seem to be making a distinction between people being conscious and other organisms as not being conscious. Why should it be all or nothing? Surely we can see that animals such as chimps and other primates possess awareness and consciousness, though not to the same degree as us, therefore, they too experience the passing of time as a unidirectional experience. In my view, every organism possesses SOME consciousness because it is through being able to be conscious that organisms can adapt to their environment. We all evolved on this planet and so had to find solutions to the problems of survival which has favoured those species who hit upon the correct solutions, i.e., things like sight, hearing, smell, touch and so on. Even an amoeba has to have the ability to feed and sense its surroundings to some extent and this, I believe, is how consciousness developed.
Title: Re: Is infinity an illusion?
Post by: Pmb on 22/10/2013 17:38:10
Quote from: webplodder
I believe time is really just an illusion caused by our conscious experiences in order to allow us to exist as organisms.
I strongly disagree. When physicists use the term time they have something very specific in mind. Time is a measurable phenomenon and is defined according to the change in things that are not related to different locations in space. E.g. think of a room with four boxes in it, one box sitting on the floor in each corner of the room. Now think of the same room and the same boxes but where the boxes are no longer in the corner but are stacked on top of each other in the middle of the room. This is a obviously a measurable phenomenon. We define time to denote the two configurations. We say that the rooms only differ in “time.”

Quote from: webplodder
Fundamentally, time has no meaning and, ..
Why would you say that? It’s clearly a well defined term whose meaning is also well defined. So in what sense are you claiming that it has no meaning?

If you want a very clear and precise definition of the concept please see
http://users.wfu.edu/brehme/time.htm

It’s very well done. The author was a GR expert in his day. He’s retired now.

Quote from: webplodder
It is assumed that our sense experiences are reflecting the true nature of reality but in making such an assumption we inevitably run into problems about causality which can have no meaning in an eternal multiverse.
I believe that you’re confusing physical time with personal time.
Title: Re: Is infinity an illusion?
Post by: Pmb on 22/10/2013 17:50:49
The Foundational Questions Institute[/i] as a category for this under their website which is located at http://www.fqxi.org/community/forum/category/10

Consider the tact that someone else took on this subject, i.e. Space does not exist, so time can. by Fotini Markopoulou
Quote
I argue that the problem of time is a paradox,
stemming from an unstated faulty premise. Our faulty assumption is that space is real. I propose that what does not fundamentally exist is not time but space, geometry and gravity. The quantum theory of gravity will be spaceless, not timeless. If we are willing to throw out space, we can keep time and the trade is worth it.
Yikes! I've heard it all now.
Title: Re: Is infinity an illusion?
Post by: dlorde on 22/10/2013 18:00:17
You seem to be making a distinction between people being conscious and other organisms as not being conscious.
No, not really. Plenty of other organisms are conscious; I was pointing out that the capability for conscious experience is not of existential importance, as demonstrated by trillions of organisms not capable of conscious experience.

Quote
Why should it be all or nothing? Surely we can see that animals such as chimps and other primates possess awareness and consciousness, though not to the same degree as us, therefore, they too experience the passing of time as a unidirectional experience.
Yes, of course.

Quote
In my view, every organism possesses SOME consciousness because it is through being able to be conscious that organisms can adapt to their environment.
That looks like an equivocation of 'consciousness'; you were talking about time being an illusion caused by conscious experience; which suggests a nervous system capable of mapping & interpreting. But simple responsiveness is rather different.

But that's OK, I'm just trying to discover what you meant by our conscious experiences causing the illusion of time to allow us to exist as organisms.

If conscious experience causes the illusion of time which is necessary to exist as an organism, then all existing organisms must cause the illusion of time. Which suggests that bacteria, plants, fungi, etc., have conscious experience that can cause the illusion of time.  I'm not sure that's what you meant, so I was hoping you'd clarify.
Title: Re: Is infinity an illusion?
Post by: Bill S on 22/10/2013 18:24:34
my absence does not mean I have lost interest, or that I don't appreciate the efforts of others.  Time is short - as usual - but last Sunday I managed to take part in a geology field trip in Suffolk, and hope to fit in another next weekend.  Splashing around in the mud will always take pride of place over the computer keyboard.  Having said that, there are always the notes to write up. 

As someone once, famously, said:  "I'll be back."
Title: Re: Is infinity an illusion?
Post by: webplodder on 24/10/2013 12:35:45
Quote from: webplodder
I believe time is really just an illusion caused by our conscious experiences in order to allow us to exist as organisms.
I strongly disagree. When physicists use the term time they have something very specific in mind. Time is a measurable phenomenon and is defined according to the change in things that are not related to different locations in space. E.g. think of a room with four boxes in it, one box sitting on the floor in each corner of the room. Now think of the same room and the same boxes but where the boxes are no longer in the corner but are stacked on top of each other in the middle of the room. This is a obviously a measurable phenomenon. We define time to denote the two configurations. We say that the rooms only differ in “time.”


Yes, but my problem with this approach is that although this model of time seems to work well within specific frames of reference, when you try to apply it to an eternal universe it does not seem to work. What do I mean? Well, we ask the question: what caused the Big Bang, ok? Now, let us assume we manage to come up with a workable theory about that (which may or may not be correct). Sooner or later, we have to confront another question about what gave rise to that particular model and this process has the potential to go on forever, never reaching any final solution. What this means is that we can never find any original cause, so we then have the problem of trying to answer how causality can arise from an apparently causeless universe! I don't think we can because it seems to destroy the legitimacy of causality since it is based on an irrationality (i.e. an eternal universe) and the underpinning of this difficulty is the concept of time itself as being a forward flowing aspect of reality. In view of this it seems inevitable to me that we need to adopt a new model of reality which avoids such a huge contradiction where time and, therefore, space are fundamentally unseperated and where time does not "flow" but is actually static and it is only our conscious attention to the incredibly complex interwoven fabric of the universe that seems to make time real. So, what it comes down to is when we think about time it is not that a thing called "time" really exists but as a result of the mechanisms of consciousness which can switch its attention, leading to the illusion of time.
Title: Re: Is infinity an illusion?
Post by: webplodder on 24/10/2013 13:05:06
Quote

If conscious experience causes the illusion of time which is necessary to exist as an organism, then all existing organisms must cause the illusion of time. Which suggests that bacteria, plants, fungi, etc., have conscious experience that can cause the illusion of time.  I'm not sure that's what you meant, so I was hoping you'd clarify.


Exactly, that is my point.

Allow me to approach this from a different direction. A piece of wood, for example, it not alive and so does not possess any consciousness. Since a piece of wood is not conscious it has zero ability to experience the passing if time and has zero ability to be aware of its environment, let alone the universe in which we live. It is only the possession of consciousness that permits its owner to experience the passing if time and history and, indeed, the concept of cause-and-effect. So, I suppose I'm reaching the conclusion that the essential difference between a human being and a piece if wood is complexity! It is complexity that allows us to be observers but that is not to imply we are passive observers but dynamic observers in that we collate, arrange, organise and analyse the myriad instances of our consciousness enables us to make. The same argument can be made for the difference between a piece of wood and a bacterium, say, because although a bacterium is nothing like a human being it is even less like a piece of wood!
Title: Re: Is infinity an illusion?
Post by: dlorde on 24/10/2013 13:34:22
The same argument can be made for the difference between a piece of wood and a bacterium, say, because although a bacterium is nothing like a human being it is even less like a piece of wood!
I'm aware of the varying complexities of wood, bacteria, and humans. But it's not just complexity that's relevant. A dead person is far more complex, yes, and dynamic, than a bacterium. But which has conscious experience (if either) ?

So, to repeat the question, are you saying that bacteria, fungi, plants, etc., all have conscious experience and can use it to generate the illusion of time?

If so, can you explain precisely what you mean by 'conscious experience' ?
Title: Re: Is infinity an illusion?
Post by: webplodder on 24/10/2013 13:59:47
The same argument can be made for the difference between a piece of wood and a bacterium, say, because although a bacterium is nothing like a human being it is even less like a piece of wood!
I'm aware of the varying complexities of wood, bacteria, and humans. But it's not just complexity that's relevant. A dead person is far more complex, yes, and dynamic, than a bacterium. But which has conscious experience (if either) ?

So, to repeat the question, are you saying that bacteria, fungi, plants, etc., all have conscious experience and can use it to generate the illusion of time?

If so, can you explain precisely what you mean by 'conscious experience' ?


A dead person is actually decomposing and is inactive, so on that level there is no complexity at all in terms of living processes. I think we have to make a distinction between an organism's parts and the ability to be greater than the parts due to conscious awareness.

Lower lifeforms certainly have the ability to organise how they eat, avoid predators and other dangers, mate and so on, so, yes one would have to attribute at least this degree of consciousness to them. Now, as you can imagine, the concept of time is crucial to being able to achieve all of this since time is crucial in reacting to stimulii which promotes the chances of an organism's survival. Cause-and-affect is equally crucial because otherwise an organism would not be able to distinguish between what is danger and non-danger. So you can see that the ability of living things to navigate their way through their environments demands that they have the ability to experience time and space. When you ask me, however, to define exactly what a consciousness experience is you are asking me something philosophers, scientists and poets have been trying to answer from time immemorial! There is no simple all-defining answer to that question since it depends on the perspective the question is framed in.
Title: Re: Is infinity an illusion?
Post by: Bill S on 27/10/2013 18:32:33
A lot of interesting points have been raised in this protracted thread, and a lot of re-capping would be necessary to be able to summarise it, so I think I might pass on that.

I appreciate the efforts of other posters, and would like to make a start on some feedback.  Experience teaches that a little at a time is the best way forward.

It is important to note that I distinguish between the Universe and the cosmos in an attempt to avoid confusion as to what I am trying to say.  It is also important to note that references to nothing mean “absolutely nothing” unless otherwise qualified.

In this thread, by applying rigorous scientific terminology and reasoning, we seem to have established that it is scientifically meaningless to state that “had there ever been nothing, there would be nothing now”, because nothing is not defined in science. 

To apply this reasoning to the Universe, or to the cosmos, by extrapolation from the Universe; and thus to reason that the cosmos must be eternal, is also scientifically meaningless.  The basis on which this is seen to be scientifically meaningless is that because our knowledge is predicated on our observations of the Universe, we cannot know if, outside the Universe, the laws of physics which we observe would still apply.  Therefore, it might be possible for something to come from nothing, either without cause, or by some process of which we have, and can have, no knowledge.  To reason from such a standpoint would not be science. 

Title: Re: Is infinity an illusion?
Post by: JP on 28/10/2013 15:40:00
Yep, that's basically my view of it, which I think is valid (and my credentials are a Ph.D. in physics and years of work and study in the field). 

This could all be overturned in an instant if someone were to come along and figure out how to measure "absolutely nothing," but I can't even imagine a way that could happen. 

This discussion might benefit from some professional philosophers who crack open the concept of absolute nothingness.  As a scientist, it's an idea that's very alien to me...
Title: Re: Is infinity an illusion?
Post by: lean bean on 28/10/2013 16:21:00
This discussion might benefit from some professional philosophers who crack open the concept of absolute nothingness.  As a scientist, it's an idea that's very alien to me...
Perhaps the concept of absolute nothingness is an unique trait of intelligence, with no such 'state' (want of a better word) as absolute nothingness found anywhere in an infinite universe. And those which talk of it should be made to explain why it should be part of science.
Ps, As you can see I'm no philosopher.
Title: Re: Is infinity an illusion?
Post by: dlorde on 28/10/2013 17:10:45
... those which talk of it should be made to explain why it should be part of science.
I don't see how it can be part of science - by definition it isn't there, & by inference it doesn't exist!
Title: Re: Is infinity an illusion?
Post by: lean bean on 28/10/2013 18:34:09
... those which talk of it should be made to explain why it should be part of science.
I don't see how it can be part of science - by definition it isn't there, & by inference it doesn't exist!
Yes, I agree.
I did have Bill's post in mind
Quote
To apply this reasoning to the Universe, or to the cosmos, by extrapolation from the Universe; and thus to reason that the cosmos must be eternal, is also scientifically meaningless.  The basis on which this is seen to be scientifically meaningless is that because our knowledge is predicated on our observations of the Universe, we cannot know if, outside the Universe, the laws of physics which we observe would still apply.  Therefore, it might be possible for something to come from nothing, either without cause, or by some process of which we have, and can have, no knowledge.  To reason from such a standpoint would not be science.

Bill, If there are laws and processes which we don’t know of or can know of, why do you reason that it automatically follows that somewhere there must  be laws or processes requiring the concept of absolute nothing? 
 Something like the up side down Egyptian pyramid here.

Title: Re: Is infinity an illusion?
Post by: AndroidNeox on 29/10/2013 00:15:15
Within a causal system, infinity isn't observable. Consider Feynman diagrams... events happen one at a time. For any observer to see/interact with an infinite amount of information would require infinite time and infinite energy and the observer would have to have infinite information capacity. Observation isn't special, either. No interaction, event, can include an infinity.

Simple rules of causality are sufficient to explain why no infinities are observable though QM suggests they exist.
Title: Re: Is infinity an illusion?
Post by: JP on 29/10/2013 14:50:33
The hope for those trying to measure if the universe is infinite or not would be that there would be some finite parameter(s) that could be measured that might tell us if the universe is infinite.

Of course, it might also be that we can never distinguish between "really, really big" and infinite.
Title: Re: Is infinity an illusion?
Post by: Bill S on 29/10/2013 19:37:28
Quote from: Beany
Bill, If there are laws and processes which we don’t know of or can know of, why do you reason that it automatically follows that somewhere there must  be laws or processes requiring the concept of absolute nothing?

I don’t have time to check back to see if I really did say that.  If I did, I was playing devil’s advocate.  It has been known.   :)

The fact is that I cannot, logically, see how there can ever have been nothing, which seems to be tantamount to saying I believe there is no such “thing” as nothing.  OK, that’s not science, that’s a belief.  In my own defense I would add that the reverse of this would be to assume that nothing is “something real”.  Manifestly, there is something now, so if nothing is a real concept it must have existed in what we perceive as the past.  Ergo, there was nothing, but now there is something.  Nothing became something.  To argue that this could have happen would necessitate making an assumption which, as far as I am aware, has no basis in any known reality.

On the other hand, if nothing is not a real concept, there can never have been nothing; thus there must always have been something.  Something is eternal.  Since we cannot measure, or even really imagine eternity, this also involves making an assumption. 

At this point we have to make a decision; either we decide which assumption is likely to be the more valuable to follow, or we have to say “don’t know – can’t think about it".  How far would science have progressed over the past 300 years if scientists adopted the latter position?
 


Title: Re: Is infinity an illusion?
Post by: lean bean on 30/10/2013 18:58:52
On the other hand, if nothing is not a real concept, there can never have been nothing; thus there must always have been something.  Something is eternal.  Since we cannot measure, or even really imagine eternity, this also involves making an assumption.
I can see where your coming from.
When I think of laws or unknown processes, there is a 'something' to be covered by a law or 'something' to be part of a process, even if that process is unkown or can't be known to us.

My starting point was asking the question: “Can there ever have been a time when there was nothing?”
When running the equations of the Universe backwards the contents and spacetime become undeterminable, but, there's still something, even though it's undeterminable.
The person who wants to add an absolute nothing to the mix should explain where that fits in.
Title: Re: Is infinity an illusion?
Post by: Bill S on 30/10/2013 19:11:53
Quote from: Beany
  The person who wants to add an absolute nothing to the mix should explain where that fits in.

Agreed, but the way to avoid that sort of difficulty is to argue that there might have been nothing, and that there could have been a mechanism, of which we have no knowledge, which might have made it possible for something to appear spontaneously.  Come back God, all might be forgiven.  ;P

Title: Re: Is infinity an illusion?
Post by: lean bean on 30/10/2013 19:40:14
Quote from: Beany
  The person who wants to add an absolute nothing to the mix should explain where that fits in.

Agreed, but the way to avoid that sort of difficulty is to argue that there might have been nothing, and that there could have been a mechanism, of which we have no knowledge,
A mechanism is a 'something'/process existing.

To play the devil's advocate,  I would ask...If it makes sense to say there is an unknown mechanism to get a Universe from an absolute nothing,then it makes the same kind of sense to say... there could be an unknown mechanism to make a Universe into an absolute nothing, what happens to your idea of eternity then?
Title: Re: Is infinity an illusion?
Post by: Bill S on 31/10/2013 21:35:09
Quote from: beany
A mechanism is a 'something'/process existing.

Absolutely!  The more one thinks about nothing, the less likely it seems that there could ever have been nothing.
Title: Re: Is infinity an illusion?
Post by: lean bean on 01/11/2013 16:57:04
Quote from: beany
A mechanism is a 'something'/process existing.

Absolutely!  The more one thinks about nothing, the less likely it seems that there could ever have been nothing.
I did make the point about unknown laws and unknowable processes having to be for a ‘something’ here...
When I think of laws or unknown processes, there is a 'something' to be covered by a law or 'something' to be part of a process, even if that process is unknown or can't be known to us.

Your next post went on to introduce an argument for an unknown mechanism.
Didn't you think a mechanism needs a 'something' to be a mechanism for?

Agreed, but the way to avoid that sort of difficulty is to argue that there might have been nothing, and that there could have been a mechanism, of which we have no knowledge, which might have made it possible for something to appear spontaneously.  Come back God, all might be forgiven.  ;P
My bold.

Title: Re: Is infinity an illusion?
Post by: Bill S on 01/11/2013 18:10:47
Quote from: Bill S
Agreed, but the way to avoid that sort of difficulty is to argue that there might have been nothing, and that there could have been a mechanism, of which we have no knowledge, which might have made it possible for something to appear spontaneously.

I think I wasn’t very clear here.  I cited that line of argument as the sort of counter one often meets; not necessarily as an argument I would use.  However, if scientists use it, it is best to be aware of it and to factor it into one’s thinking.

Quote
Come back God, all might be forgiven.  ;P

This was intended to draw attention to the similarity between arguments based on unknown/unknowable factors and some arguments founded on religious beliefs.
Title: Re: Is infinity an illusion?
Post by: Bill S on 01/11/2013 18:19:48
Quote from: beany
Didn't you think a mechanism needs a 'something' to be a mechanism for?

I would go further and say that a mechanism is something, as is a potential or a possibility.  Your point that “a mechanism needs a 'something' to be a mechanism for” is correct, but it is step 2 in the chain of reasoning.
Title: Re: Is infinity an illusion?
Post by: lean bean on 03/11/2013 10:14:50

I would go further and say that a mechanism is something, as is a potential or a possibility. 
Further??
I also made that point too...check it out
A mechanism is a 'something'/process existing.
Title: Re: Is infinity an illusion?
Post by: Bill S on 03/11/2013 23:40:15
Quote from: beany
I also made that point too...check it out

You did indeed.  I was responding only to the specific quote. 

It would be interseting to make a comparison to see to what extent we are "on the same page".
Title: Re: Is infinity an illusion?
Post by: dlorde on 04/11/2013 09:32:08
Those of us interested in the idea of 'nothing' from a science point of view, might be interested in a new book from New Scientist magazine (http://www.newscientist.com/article/dn24442-nothing--the-new-book-from-new-scientist.html#.UndpXPm-18F) called, appropriately, 'Nothing'.
Title: Re: Is infinity an illusion?
Post by: Bill S on 04/11/2013 17:09:34
Those with access to the venue may also be interested in:

Nothing is the intriguing theme of the latest book from New Scientist, to be published on
7 November. Take zero, a critically important number to our modern world with a difficult birth. Anaesthetics that take our consciousness to the brink of nothingness. Or the nocebo effect, where just a few words can kill.

Discover more by joining the team from New Scientist and our panel of guest speakers (including Marcus Chown & Helen Pilcher) for an entertaining evening of amazing insights into nothingness:

When?
Wednesday 13th November from 6:30pm - 8:30pm (doors open at 6pm)

Where?
Conway Hall, 25 Red Lion Square, London, WC1R 4RL

Tickets:
£10 (inc. booking fee & copy of Nothing book) in advance from NSnothing.eventbrite.co.uk
or £10 on the door if available (not including book)*.

Make sure you don't miss this fascinating event, and if you know someone who may be interested in attending, share this link with them: NSnothing.eventbrite.co.uk
Title: Re: Is infinity an illusion?
Post by: Bill S on 04/11/2013 17:11:33
Sorry folks, I've just checked and they are sold out.
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/11/2013 00:08:17
Quote from: JP
This could all be overturned in an instant if someone were to come along and figure out how to measure "absolutely nothing,"

Arguing that there can never have been nothing seems tantamount to asserting that "nothing" does not "exist".  I fail to see why this calls for a precise definition of "nothing".  Other than as "the absence of anything"; how could we define something that does not exist?
Title: Re: Is infinity an illusion?
Post by: JP on 06/11/2013 01:29:38
Quote from: JP
This could all be overturned in an instant if someone were to come along and figure out how to measure "absolutely nothing,"

Arguing that there can never have been nothing seems tantamount to asserting that "nothing" does not "exist".  I fail to see why this calls for a precise definition of "nothing".  Other than as "the absence of anything"; how could we define something that does not exist?

It depends if you want to discuss science or metaphysics.  Science involves the measurable, whereas metaphysics involves ideas, which may not be measurable. 
Title: Re: Is infinity an illusion?
Post by: Bill S on 06/11/2013 18:44:19
This may seem to be off topic, but it should find its way back, so I’m not starting a new thread. 

I would appreciate comments on my reasoning.

Where does the energy for the formation of virtual particles come from? 
Does this process violate the law of conservation of energy?

1. Energy is borrowed from the vacuum energy.

2. Repayment of the energy is to the vacuum.

3. The vacuum is an integral feature of the universe.

4. If it were possible to observe the energy while it was being borrowed, it would not be where classical physics says it should be.  However, it must still in the Universe.

5. At no time does energy leave or enter the universe; therefore, conservation of energy is not violated.
Title: Re: Is infinity an illusion?
Post by: woolyhead on 06/11/2013 20:45:44
I have no quarrel with infinite sets/series as mathematical tools.  As far as the extremely small is concerned, I am fine with “infinitesimally small”.  I wish scientists would use it instead of “infinitely small”, which, in my opinion, is tantamount to saying it cannot be further divided, even in principle.  If space is continuous, this must be the same as saying it is nonexistent.

Unfortunately, there seems to be no term, equivalent to “infinitesimal”, to cover things that are “sort of” infinitely large.     

I would certainly not “jump into the no-infinity boat”.  Without infinity, what would I argue about?  :)

Seriously, though, I see no realistic way round the idea that something must be eternal/infinite, otherwise we would not be here.  This has caused me to do a lot of thinking about infinity, which might well be considered as being philosophy rather than science.  I would not argue with that, except to say that if it is something so fundamental to our existence, then perhaps it has as much right to a place in scientific thought as does the underlying “reality” of QM.
In one of the very few theories that successfully combine quantum theory with relativity, Rovelli's "loop quantum gravity" sets a minimum dimension of space as being the Planck length. Space is seen as consisting of discrete loops. Time is viewed in the same way, ie separate loop from space loops on this scale. Thus space and time are separated on this scale. Whatever you may think about it going against Einstein's idea of spacetime, his theory works. So space is not infinitesimal. I would suggest that through symmetry considerations it looks as if it not infinitely big either. Indeed, if space was created at the big bang 15 billion years ago, it is 15 billion light years across. That's big but it's not infinite.
Title: Re: Is infinity an illusion?
Post by: dlorde on 06/11/2013 21:48:58
, if space was created at the big bang 15 billion years ago, it is 15 billion light years across. That's big but it's not infinite.
Seems to me that's true if only the universe expanded from a point (or, perhaps, it's only true of the observable universe). As I understand it, we don't know if the universe was a 'point source' at the big bang or not. It was extremely hot and extremely dense; but, for all we know, could have been infinitely large. But if it was larger than a point source, it could well be that most of it is outside our observable cosmic horizon.

I understand that the current cosmological proper distance (i.e. the comoving distance (http://en.wikipedia.org/wiki/Comoving_distance)) for the diameter of the observable universe is actually about 93 billion light years (i.e. 46.5 bl from here to the observable 'edge').
Title: Re: Is infinity an illusion?
Post by: Bill S on 11/12/2013 18:17:42
Sorry to dig this one up again, but I would like to pick up on one of JP's points.

Quote from: JP
1a) Therefore, to answer whether there was ever "absolute nothing" we'd have to have a model that discriminates in terms of measurables between a scenario in which there was at one point "absolute nothing" and one in which there was not.

As you have pointed out elsewhere, "absolute nothing", if it can be said to exist, would be outside our Universe.  The only material we have from which to construct our model would be from within the Universe.  Would it not be impossible to construct a model that said anything about "absolute nothing"?