(February 14, 2018 at 1:28 pm)polymath257 Wrote:

(February 14, 2018 at 1:10 pm)RoadRunner79 Wrote: So it would seem that an important part of if a complete set of infinite numbers is to define what it means to be a complete set? We didn’t do very well with defining a point, can we please define this.  How is it complete, but not indicating a stop or an end?

It appears to me, that these sets are just loosely defined, or openly defined but how does that translate to the real world, and how can that be completed if it is open?

Well, to be complete means that we can tell exactly when something is in the list or not. For example, the number 1273749
is in the list 1,2,3,.... but the number 1.34 is not.

It is complete in the real world if everything in the list actually exists and we can tell exactly when something is in the list and when it is not.

I do believe that I was acting more on the second definition prevously.  The first definition to me seems like you are saying a defined set, which seems pretty useless to me.  If you cannot tell what is or is not in the set, then what good is it?   In the end, I don't see that the involvement of sets (completed or otherwise) is really adding anything to the conversation.  You can correct me if I'm wrong. 

So to clarify what I am disputing is an actual infinite.   Which would be completed or ended, on something which is unending.  This is contradictory.  You can not have an infinite.  Even really in the abstract, you don't have an infinite number of things.   You have a concept, which you think gives you an infinite number of things.  But it's a never ending process (here there be dragons) which can never actualize infinity.

(February 14, 2018 at 2:36 pm)SteveII Wrote:

(February 14, 2018 at 2:34 pm)polymath257 Wrote: Actually, it *does* say most believe it is not only possible, but in fact the case.

And yes, it is possible that space is finite. We do not know. Both finite and infinite are possibilities.

Then it shouldn't be hard to cut and paste that section--for both of your points...I'll wait.

I guess you can see where this is going.  Next he'll ask you to bring each sentence to his ear one at a time while making airplane noises.  You're never going to do as much as this twat feels entitled to.

(February 14, 2018 at 4:54 pm)Whateverist Wrote:

(February 14, 2018 at 2:36 pm)SteveII Wrote: Then it shouldn't be hard to cut and paste that section--for both of your points...I'll wait.

I guess you can see where this is going.  Next he'll ask you to bring each sentence to his ear one at a time while making airplane noises.  You're never going to do as much as this twat feels entitled to.

IMO, the subject matter that is being discussed right now is very interesting and presents a nice opportunity for intellectual exploration and mutual learning.  It is unfortunate that it seems to be devolving into a personal contest.

Whoa. When did Steve move his goal posts so far past: ‘Your phrase, “completed infinity” isn’t even a real term?’ I’m guessing right around when you proved he was wrong. Slippery.

If anyone wants to continue this...

https://atheistforums.org/thread-53460.html

I'm bored, so I'll give my two cents worth.

It is typically argued that the universe can't be past eternal because there would be no way to traverse an infinity of time. However, such arguments about being unable to traverse an infinite past up to the present, as implied by such arguments as the one that says you can't count successively to infinity, rely on the A theory of time. The idea of "traversing" an infinite past is incoherent on the B theory of time. If the B theory of time is correct, and the universe is infinite in time, such arguments do not apply and you have the case of an actual infinite existing. This leads to attempts to show that the universe is not past eternal by attempting to directly demonstrate that the universe's past is not infinite because the universe had a beginning. This is done by invoking things such as the Borde-Guth-Vilenkin theorem and the standard interpretation of the big bang model which supposedly indicates that the universe has a beginning. However there are theories such as Penrose's Conformal Cyclic Cosmology (see below) in which neither of these objections apply. Conformal Cyclic Cosmology explains why we would find points "in time" that have the appearance of resulting from a universe that had a beginning in a universe which does not in fact have a beginning. So, to the best I can tell, the idea that the universe is temporally infinite is consistent with a B theory of time and with some models of cosmology. So, ultimately, it doesn't appear that the case that you can't have an actual infinite has been made. (Regarding Hilbert's hotel, supposedly the results are absurd. This can mean several things. It can mean that the result is counter-intuitive, or it could mean that the result is logically impossible. I don't off-hand see that Hilbert's exercise demonstrates anything about logical impossibility so much as it is just showing that such things seem to defy our normal intuitions. I don't see the latter as any kind of argument that actual infinities don't exist so much as a demonstration that we aren't natively well equipped to think about such things. That latter fact is of little consequence. Quantum mechanics presents results that are equally absurd in that sense, that doesn't make quantum mechanics wrong. If you think Hilbert's hotel demonstrates something more substantial than this, I'd appreciate someone drawing out the relevant connections, because I don't see them.)

Quote:The conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicists Roger Penrose and Vahe Gurzadyan. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next. Penrose popularized this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.

Wikipedia || Conformal Cyclic Cosmology

Quote:The basic point is this. The very early universe is smooth. The universe right now is lumpy, with stars and galaxies and black holes all over the place. But the future universe will be smooth again — black holes will evaporate and the cosmological constant will disperse all the matter, leaving us nothing but empty space. (Just wait about 10100 years.) So, Penrose says, we can map the late universe onto a future phase that looks just like our early universe, simply by a conformal transformation (a change of scale). Do this an infinite number of times, and you have a cyclic cosmology — the universe goes through a series of “aeons” that start with a smooth Big Bang, get lumpy as structure forms, smooth out again, and then gets matched onto another smooth Big-Bang-like phase, etc.

Penrose’s Cyclic Cosmology

(February 14, 2018 at 6:44 pm)Jörmungandr Wrote: I'm bored, so I'll give my two cents worth.

It is typically argued that the universe can't be past eternal because there would be no way to traverse an infinity of time.  However, such arguments about being unable to traverse an infinite past up to the present, as implied by such arguments as the one that says you can't count successively to infinity, rely on the A theory of time.  The idea of "traversing" an infinite past is incoherent on the B theory of time.  If the B theory of time is correct, and the universe is infinite in time, such arguments do not apply and you have the case of an actual infinite existing.  This leads to attempts to show that the universe is not past eternal by attempting to directly demonstrate that the universe's past is not infinite because the universe had a beginning.  This is done by invoking things such as the Borde-Guth-Vilenkin theorem and the standard interpretation of the big bang model which supposedly indicates that the universe has a beginning.  However there are theories such as Penrose's Conformal Cyclic Cosmology (see below) in which neither of these objections apply.  Conformal Cyclic Cosmology explains why we would find points "in time" that have the appearance of resulting from a universe that had a beginning in a universe which does not in fact have a beginning.  So, to the best I can tell, the idea that the universe is temporally infinite is consistent with a B theory of time and with some models of cosmology.  So, ultimately, it doesn't appear that the case that you can't have an actual infinite has been made.  (Regarding Hilbert's hotel, supposedly the results are absurd.  This can mean several things.  It can mean that the result is counter-intuitive, or it could mean that the result is logically impossible.  I don't off-hand see that Hilbert's exercise demonstrates anything about logical impossibility so much as it is just showing that such things seem to defy our normal intuitions.  I don't see the latter as any kind of argument that actual infinities don't exist so much as a demonstration that we aren't natively well equipped to think about such things.  That latter fact is of little consequence.  Quantum mechanics presents results that are equally absurd in that sense, that doesn't make quantum mechanics wrong.  If you think Hilbert's hotel demonstrates something more substantial than this, I'd appreciate someone drawing out the relevant connections, because I don't see them.)

Quote:The conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity, advanced by the theoretical physicists Roger Penrose and Vahe Gurzadyan. In CCC, the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next. Penrose popularized this theory in his 2010 book Cycles of Time: An Extraordinary New View of the Universe.

Wikipedia || Conformal Cyclic Cosmology

Quote:The basic point is this. The very early universe is smooth. The universe right now is lumpy, with stars and galaxies and black holes all over the place. But the future universe will be smooth again — black holes will evaporate and the cosmological constant will disperse all the matter, leaving us nothing but empty space. (Just wait about 10100 years.) So, Penrose says, we can map the late universe onto a future phase that looks just like our early universe, simply by a conformal transformation (a change of scale). Do this an infinite number of times, and you have a cyclic cosmology — the universe goes through a series of “aeons” that start with a smooth Big Bang, get lumpy as structure forms, smooth out again, and then gets matched onto another smooth Big-Bang-like phase, etc.

Penrose’s Cyclic Cosmology

Regarding Hilbert's Hotel, I wouldn't say the results are absurd (even if counterintuitive, as you suggested), rather that this is what is to be expected with infinity. If infinity is an actual thing in the real world, then this sort of thing is what is to be expected. Otherwise, it would be absurd if actual infinities led to intuitive results instead. That said, Steve's handpicked equations are nevertheless partly incorrect and otherwise misleading. Not that it matters anyway, because infinity is regardless not a number (and so doing operations on infinity is different from doing the same operations on numbers, and is very contextual).

And (back to Steve) of course, we don't see actual infinities in this local universe, but it doesn't mean that it's not a thing in the part of reality beyond finite (and probably discrete) universes. The universes themselves might be finite and discrete, but they may still be part of an infinite and continuous cosmos/reality.

First quote:

"First, the Standard Model of particles and forces is one of the best tested and most successful theories in all the history of physics. So are the theories of relativity and quantum mechanics. All these theories imply or assume that, using Cantor’s technical sense of actual infinity, there are infinitely many infinitesimal instants in any non-zero duration, and there are infinitely many point places along any spatial path. So, time is a continuum, and space is a continuum.

The second challenge to Hilbert’s position is that quantum theory, in agreement with relativity theory, implies that for any possible kinetic energy of a free electron there is half that energy−insofar as an electron can be said to have a value of energy independent of being measured to have it. Although the energy of an electron bound within an atom is quantized, the energy of an unbound or free electron is not. If it accelerates in its reference frame from zero to nearly the speed of light, its energy changes and takes on all intermediate real-numbered values from its rest energy to its total energy. But mass is just a form of energy, as Einstein showed in his famous equation E = mc2, so in this sense mass is a continuum as well as energy."

Second quote:
"Disagreeing, the theoretical physicist Roger Penrose speaks about both loop quantum gravity and string theory and says:

...in the early days of quantum mechanics, there was a great hope, not realized by future developments, that quantum theory was leading physics to a picture of the world in which there is actually discreteness at the tiniest levels. In the successful theories of our present day, as things have turned out, we take spacetime as a continuum even when quantum concepts are involved, and ideas that involve small-scale spacetime discreteness must be regarded as ‘unconventional.’ The continuum still features in an essential way even in those theories which attempt to apply the ideas of quantum mechanics to the very structure of space and time.... Thus it appears, for the time being at least, that we need to take the use of the infinite seriously, particular in its role in the mathematical description of the physical continuum. (Penrose 2005, 363)"

---

(February 14, 2018 at 3:18 pm)RoadRunner79 Wrote:

(February 14, 2018 at 1:28 pm)polymath257 Wrote: Well, to be complete means that we can tell exactly when something is in the list or not. For example, the number 1273749
is in the list 1,2,3,.... but the number 1.34 is not.

It is complete in the real world if everything in the list actually exists and we can tell exactly when something is in the list and when it is not.

I do believe that I was acting more on the second definition prevously.  The first definition to me seems like you are saying a defined set, which seems pretty useless to me.  If you cannot tell what is or is not in the set, then what good is it?   In the end, I don't see that the involvement of sets (completed or otherwise) is really adding anything to the conversation.  You can correct me if I'm wrong. 

So to clarify what I am disputing is an actual infinite.   Which would be completed or ended, on something which is unending.  This is contradictory.  You can not have an infinite.  Even really in the abstract, you don't have an infinite number of things.   You have a concept, which you think gives you an infinite number of things.  But it's a never ending process (here there be dragons) which can never actualize infinity.

Yes, a defined set that has an infinite number of elements. For example, the set of integers.

What it adds to the discussion is precision. Whether something 'ends' or 'is complete' is, at best, ambiguous. But putting things in correspondence with natural numbers (Cantorian equivalence of size) is precisely defined.

So, does the collection of integers end? not in the sense that for every integer there is a larger and a smaller integer. Is it complete? yes. It is *one* collection of things. It isn't a process. It is one thing: the collection of integers.

And, there are differing sizes of infinity (in the Cantorian sense). These are actual sets (like the set of real numbers).

And this shows the concept if NOT logically contradictory.