God And Infinity, Worlds Without Number Are Numbered To God?

[asbestosman]

This brings up the point I want to discuss. Are God's works truly infinite- his worlds he has created, populated, etc?

I like to think it's countably infinite, but then I'd love to visit Hilbert's Hotel too.

Or does this just mean that His works never cease but in fact they are of a finite order at any given time?

I concede that is a possible interpretation.

When we look out into space we see a seemingly never-ending amount of stars, planets, galaxies, etc. If they are the works of God, then to us it may truly appear to be never-ending and perhaps even infinite.

Never-ending is one possible meaning of infinite such as taking the limit to infinity in integrations in calculus or of metric spaces that do not have a boundary.

I am left somewhat to believe that logically they only appear to us to be innumerable because of our lack of telescope power, technology, etc. and that To God they truly are all numbered being of a finite order.

If you were to argue that things in this universe point towards a finite amount of matter and energy, I would probably have to agree. If the universe we live in had an infinite amount of matter or light, I think it would all collapse in a giant black hole already. Also, there's Olbers' paradox.

I have been often intrigued by Cantor's work in mathematics with "infinity" but I am always drawn to conclude that there is no such thing as an infinity of something because it can't be known or proven, even for God. What say ye?

I'm pretty sure God understands transfinite arithmetic--better than I do.

Edited January 24, 2012 by asbestosman

[asbestosman]

You can belittle my intelligence all you like but I am trying to honestly discuss this matter in a reasonable manner. I don't mind discussing why Cantor was wrong but I would wish to do so in a more civil manner. I don't belittle your intelligence so show me some respect also.

It has more to do with how certain you are about your stance while not seeming to comprehend what Cantor et al are saying than that you're merely mistaken. I don't see Tarski belittling your intelligence--only your apparent ignorance and combined certainty on the topic of infinity. I grant that there is some controversy among mathematicians on the matter of transfinite numbers. Most agree with Tarski, Zeta-flux, and me about Cantor. However, there are some who disagree with Cantor's proofs. If you were using their language and reasoning, I think you'd get a bit more respect for your position. At the very least you should be able to distinguish the different senses in which infinity is used--be it cardinality of sets, behavior in a limit, or whatever.

All that said, I'll always treasure our epic thread from a little over a year ago. I had fun, and I heard others say they learned from it. I made some mistakes in that thread too and learned a few things myself. It's easy to get confused about infinity. It took me longer than I like to admit before I finally understood transfinite numbers. It's just so counter-intuitive.

[inquiringmind]

I thought I should make an addendum to my astronomy lesson, and that is that when you see the word "infinite" being used in the scriptures, it doesn't mean what you might think it means. Even when God makes reference to terms that seem to suggest this, such as "worlds without end" and the like, we see in DC 19:10-12 that Endless is simply one of His names.

God is Endless because He just keeps going on. His creations are Endless because He created them, and He will just continue to create more of them, and will not stop doing so. So Endless is infinite enough.

"Even when God makes reference to terms that seem to suggest this, such as 'worlds without end"?

Doesn't D&C 19:6 kinda imply that "without end" means "without end"?

Is say "Nevertheless, it is not written that there shall be no end...,but it is written endless."

Verse 10 goes on to say that Endless is one of His names, and I get that, but doesn't verse 6 here imply that when the phrase "no end" is "written," it really means "no end"?

Edited January 24, 2012 by inquiringmind

[Rob Osborn]

It has more to do with how certain you are about your stance while not seeming to comprehend what Cantor et al are saying than that you're merely mistaken. I don't see Tarski belittling your intelligence--only your apparent ignorance and combined certainty on the topic of infinity. I grant that there is some controversy among mathematicians on the matter of transfinite numbers. Most agree with Tarski, Zeta-flux, and me about Cantor. However, there are some who disagree with Cantor's proofs. If you were using their language and reasoning, I think you'd get a bit more respect for your position. At the very least you should be able to distinguish the different senses in which infinity is used--be it cardinality of sets, behavior in a limit, or whatever.

All that said, I'll always treasure our epic thread from a little over a year ago. I had fun, and I heard others say they learned from it. I made some mistakes in that thread too and learned a few things myself. It's easy to get confused about infinity. It took me longer than I like to admit before I finally understood transfinite numbers. It's just so counter-intuitive.

I don't think one has to use the exact language of "math" in order to be understood. Tarski knew what I was talking about. As for Cantor, he, in my opinion, is best known for his diagonal argument- his proof that the real numbers are larger in cardinality than whole numbers. His proof seemingly shows that one can make a list of real numbers of infinite length and he can, from that list make a new number not already in the list. But, I can show how this is a false theory and that he couldn't really do this.

For instance- Let's put some principle in place first. when making a list of numbers, one must include all possibilities for every column- all numbers between 0-9 in sequential rows. Next we must also include that for every shift in column we would also have every possible combination. So, for the next shift it would include every possibility between 0-99. The next colum would be thus- 0-999 and so on forever. Now when we look at this list in this manner knowing that for every possible column (because they can be countable and do truly go on without end), there is already every possibility, no new number could be written from the list because we would already recognize that there are no new possibilities for each new column. Cantor's list does not follow this principle even though it certainly must be in place. It kind of tricks the mind by allowing us to just pick random numbers such as .84762429048 and then us not comprehending basic math operations and why we have columns and rows. For instance, if we made a new list and started it like this- .0, .1, .2, .3, .4, .5, etc and utilyzed every possibility before moving on and then used Cantor's diagonal argument only after each possibility was exhausted for every new column you could never make a number that wasn't already in the list. This shows a coulpe of facts. The first fact is that something infinite in number has an endless cardinality- it can't be known. The second fact is that there is no such thing as one infinity being larger or smaller than another infinity because once again- how can you prove somthing that must be counted, yet has an endless count.

[thesometimesaint]

I don't believe the number of worlds is infinite in the absolute sense of the word. They are numbered unto God. But whatever that number is it is a VERY large number.

[Rob Osborn]

I don't believe the number of worlds is infinite in the absolute sense of the word. They are numbered unto God. But whatever that number is it is a VERY large number.

I agree.

[asbestosman]

I don't think one has to use the exact language of "math" in order to be understood.

I agree. However, from the language you do use it's still obvious that you don't know what you're talking about. Now granted, there are some tricky things there. Tarski could say more about spaces like in your example which do not contain every point that a series of points converges to, but contains points arbitrarily close. Your particular example contains only some of the rational numbers between 0 and 1. It doesn't even contain 1/3 although it gets arbitrarily close. Whatever language you use, you need to demonstrate that you understand this distinction--even if ultimately you disagree with it. At the very least I would expect you to explain why irrational numbers cannot be represented as a ratio of integers and then go on to explain how that does or does not relate to your example.

Let's say there's a hypothetical professor of Middle Eastern studies. We'll call him Peter Danielson. Let's say that a hypothetical critic comes by and starts off ranting about middle-eastern religions and history. I would imagine that this hypothetical professor after attempting to offer a few corrections would soon grow tired of the combination of hubris and ignorance regardless of whether the hypothetical critic was using the academic language of Middle Eastern studies. Just a guess.

Edited January 24, 2012 by asbestosman

[Rob Osborn]

I agree. However, from the language you do use it's still obvious that you don't know what you're talking about. Now granted, there are some tricky things there. Tarski could say more about spaces like in your example which do not contain every point that a series of points converges to, but contains points arbitrarily close. Your particular example contains only some of the rational numbers between 0 and 1. It doesn't even contain 1/3 although it gets arbitrarily close. Whatever language you use, you need to demonstrate that you understand this distinction--even if ultimately you disagree with it. At the very least I would expect you to explain why irrational numbers cannot be represented as a ratio of integers and then go on to explain how that does or does not relate to your example.

Let's say there's a hypothetical professor of Middle Eastern studies. We'll call him Peter Danielson. Let's say that a hypothetical critic comes by and starts off ranting about middle-eastern religions and history. I would imagine that this hypothetical professor after attempting to offer a few corrections would soon grow tired of the combination of hubris and ignorance regardless of whether the hypothetical critic was using the academic language of Middle Eastern studies. Just a guess.

So, did you understand what I was saying or not? That's all that matters. If you didn't understand then let us reason together so that we have understanding. Yes, it's true i don't speak in "mathematical" language but that doesn't meran I don't understand the concepts or that they can't be spoken of in everyday laymen terms.

[asbestosman]

So, did you understand what I was saying or not? That's all that matters.

Understand you about what? See post 26 for the general idea of God and infinite worlds (the topic of the OP), or #32 first paragraph where I try to shed some light on why your list of numbers example is problematic. I even avoided technical jargon unless the words "converge" and "irrational" should be better explained. Let me know. Indeed it's not just a matter of me understanding you. You need to understand what I'm saying too if we're going to get somewhere.

[Zeta-Flux]

Rob,

I think that another scripture will shed light on your conundrum. Alma says, "...all is as one day with God, and time only is measured unto men." So if as you say God's work never ends, and He will continue to create forever, then when viewed as "one day" by God there are an infinite number of creations. So, in any given era, there may only be a few new creations, but in the grand scheme His works never end, and He sees them all. You may be correct that in any slice of time there are only finitely many creations.

As for your argument against Cantor, let me echo that you are wrong. I think I understand your argument, so I hope I can help you understand your mistake. Real numbers are not like what I talked about in the first paragraph. Some real numbers have finite expansions, but some go on forever. If you picked one it may have an infinite decimal expansion. Numbers like 1/3= 0.333333... and Pi= 3.1415926535.... are examples. So, by analogy, this would be like the case if God had infinitely many creations all at one time (which may or may not be the case).

You gave a rule which you think listed all of the real numbers. Where in your list, using the specific rule you gave, does 1/3 (or Pi) occur?

[Analytics]

His proof seemingly shows that one can make a list of real numbers of infinite length and he can, from that list make a new number not already in the list. But, I can show how this is a false theory and that he couldn't really do this....

Are you sure, really sure, that you understand Cantor's argument? A lot of really, really smart people who have spent a lot of time studying this agree with it.

Your counter-proof rests upon the assumption that one couldn't come up with a number not on the list. The beauty of Cantor's argument is that not only is it possible to come up with a number not on the list, it's actually easy to do so. That result is counterintuitive, but that doesn't mean it isn't true.

Edited January 24, 2012 by Analytics

[Cold Steel]

One thing that interests me is entropy. Stars that we're watching go through birth, life and then death. God speaks of eternal worlds, but in this universe everything we see is going through the same process we are. But if stars and planets "die," then where are the "eternal" worlds, and where will the Earth go when it is resurrected in a celestial state (and thus becomes the habitation of the faithful)?

Everywhere we look, even with the Hubble, we see entropy. This means that there is another place and time where entropy does not exist. Certainly the Lord spoke truly when he said his works are without number...to us. But to an eternal being with and eternal mind, they are numbered. And they continue to grow. Plus he is mindful of his children on each world.

It's my personal belief that if one were to go beyond the boundaries of this universe that one would see other universes spiraling off in space. I recall Hugh Nibley quoting an ancient work that stated, "Everything is a system in the midst of like systems." I don't know where he got it, but it was something that has stuck with me for years. It's a wise truism, and profound, and it applies to astrophysics as well as microphysics. We also have quantum physics which changes everything we thought we knew about the universe. And we can be sure there are many other things the Lord knows that would change everything we thought we knew about nearly everything. It is absolute nonsense to discuss scriptures like this when God views us as infants in our understanding of what we can see and deduce. (I saw a recent documentary about black holes that revealed that supermassive black holes exist throughout the universe, and that the one in the center of our galaxy was 4.1 million times the density of our sun; and it was compressed into the size of ten diameters of our sun. I don't know about you, but I just can't wrap my head around something like that, especially when similar supermassive black holes existed in the centers of all galaxies.)

What is "numberless" to us and the greatest supercomputers we have is not numberless to God, for he has numbered them and they are his.

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Edited January 24, 2012 by Cold Steel

[Tarski]

So, did you understand what I was saying or not? That's all that matters. If you didn't understand then let us reason together so that we have understanding. Yes, it's true i don't speak in "mathematical" language but that doesn't mean I don't understand the concepts or that they can't be spoken of in everyday laymen terms.

You are making errors in reasoning. On top of that, you don't get it when it is explained even though the errors are simple and basically everyone but you gets it.

This is interesting from a cognitive science or psychological perspective but not mathematically. Your errors are either trivial or the result of just plain old conceptual fuzziness.

So if you are the same guy we tried to explain this to before then I have to say I that it is almost as if there were a very spooky and rather specific deficit in abstract reasoning together with a corresponding anosognosia.

I don't know of course. I don't pretend to diagnose. It is just "as if".

Maybe it is simpler; stubbornness, a conceptual rut, a mental block or bad habit?

I don't think there is a problem with your overall intelligence.

The math of the infinite, on the other hand, is in good condition. There remains a few subtle foundational and meta-mathematical issues of course but I don't think that is where your problem is.

Oh, and it is next to impossible to talk about the notion of infinity effectively and precisely enough to settle these issues while using only layman's term. They aren't up to the job.

But the job has basically been done.

Edited January 24, 2012 by Tarski

[Rob Osborn]

Are you sure, really sure, that you understand Cantor's argument? A lot of really, really smart people who have spent a lot of time studying this agree with it.

Your counter-proof rests upon the assumption that one couldn't come up with a number not on the list. The beauty of Cantor's argument is that not only is it possible to come up with a number not on the list, it's actually easy to do so. That result is counterintuitive, but that doesn't mean it isn't true.

I am positive I understand Cantor's argument. If One were to make a list as I have previously suggested and just modify the rule to how it should be- having lists of each possibility for each column and then one were to try to make a new number off of one not already in each column possibility it is therefore impossible to ever come up with any length of sequence not already in the list- even if that number were to be infinitly long (if it were possible). In simpler terms, One couldn't make any number sequecne possibility, no matter how long he proceded to do so, that wasn't already in my list I proposed..

[Rob Osborn]

You are making errors in reasoning. On top of that, you don't get it when it is explained even though the errors are simple and basically everyone but you gets it.

This is interesting from a cognitive science or psychological perspective but not mathematically. Your errors are either trivial or the result of just plain old conceptual fuzziness.

So if you are the same guy we tried to explain this to before then I have to say I that it is almost as if there were a very spooky and rather specific deficit in abstract reasoning together with a corresponding anosognosia.

I don't know of course. I don't pretend to diagnose. It is just "as if".

Maybe it is simpler; stubbornness, a conceptual rut, a mental block or bad habit?

I don't think there is a problem with your overall intelligence.

The math of the infinite, on the other hand, is in good condition. There remains a few subtle foundational and meta-mathematical issues of course but I don't think that is where your problem is.

Oh, and it is next to impossible to talk about the notion of infinity effectively and precisely enough to settle these issues while using only layman's term. They aren't up to the job.

But the job has basically been done.

I would like to advance your statement to say that "the philosophy of the infinite..." I don't really see how mathematical constructs can say anything positive or in "proof" about the concept of infinity. There is no math that man has ever used in mathematical proofs that use anything other than a finite number. Even though anumber may repeat itself endlessly like 1/3 expressed like ".3333333333..." and we may say it has infinite length, there are no proofs to show what that number would actually end in. All we can use are finite limits with abstract numbers to make proofs with. One doesn't have to have a degree in math to understand the concept of infinity and how or if it can be properly looked at in all realms of philosophy and science.

My hiccups with the philisophical theories of infinity is in saying that one infinity can be larger or smaller in count than another. There are certain principles about constructing numbers in abstract form on paper that perhaps Cantor overlooked and theus why there are problems with his theory and philosophy of the infinite.

[Rob Osborn]

Rob,

I think that another scripture will shed light on your conundrum. Alma says, "...all is as one day with God, and time only is measured unto men." So if as you say God's work never ends, and He will continue to create forever, then when viewed as "one day" by God there are an infinite number of creations. So, in any given era, there may only be a few new creations, but in the grand scheme His works never end, and He sees them all. You may be correct that in any slice of time there are only finitely many creations.

As for your argument against Cantor, let me echo that you are wrong. I think I understand your argument, so I hope I can help you understand your mistake. Real numbers are not like what I talked about in the first paragraph. Some real numbers have finite expansions, but some go on forever. If you picked one it may have an infinite decimal expansion. Numbers like 1/3= 0.333333... and Pi= 3.1415926535.... are examples. So, by analogy, this would be like the case if God had infinitely many creations all at one time (which may or may not be the case).

You gave a rule which you think listed all of the real numbers. Where in your list, using the specific rule you gave, does 1/3 (or Pi) occur?

In principle 1/3 expressed like .33333333... would be already expressed in my list. Here one must show where it wasn't in the list. Of course this is an impossible feat as one could never see the end to the length of my list just containing the list with just the number 3 in it. But, I can assure you that in "principle" it certainly must be in the list. "Pi" would also be in the list using that same principle.

[Rob Osborn]

Understand you about what? See post 26 for the general idea of God and infinite worlds (the topic of the OP), or #32 first paragraph where I try to shed some light on why your list of numbers example is problematic. I even avoided technical jargon unless the words "converge" and "irrational" should be better explained. Let me know. Indeed it's not just a matter of me understanding you. You need to understand what I'm saying too if we're going to get somewhere.

All numbers are, are abstracts- nothing more and certainly nothing less. they mean nothing ina real physical tangible world other than a way for us to relate those things in mathematical constructs for solving unknowns or representing things known. Our philosophy of the numbering system in principle shows that some things like 1/3 can't be properly and perfectly expressed with a numbering system like .3333333....

[asbestosman]

Even though anumber may repeat itself endlessly like 1/3 expressed like ".3333333333..." and we may say it has infinite length, there are no proofs to show what that number would actually end in.

What do you men here by the number it ends in? Do you mean what digit the decimal expansion of 1/3 ends in? That's a nonsensical question because the decimal expansion of 1/3 does not end. Do you mean what the sequence 3/10 + 3/100 + 3/1000 + . . . = .3 + .03 + .003 + . . . = .333... converges to? The proof that this converges to 1/3 is pretty straightforward. It's a geometric sequence with a simple proof for the converging formula.

[Zeta-Flux]

Rob,

You said: "But, I can assure you that in "principle" it certainly must be in the list."

My response: Your assurances do not assure me. You seemed to claim that you had a concrete way to list all of the real numbers. I asked you the simple question of where 1/3 fell in your list.

I'll make it even easier. What are the first 10 numbers that occur in your list?

[asbestosman]

Our philosophy of the numbering system in principle shows that some things like 1/3 can't be properly and perfectly expressed with a numbering system like .3333333....

Nonsense. We can express 1/3 perfectly by typing 1 divided by 3 as we both did. If you mean we can't express it as a sum of integers divided by powers of 10, that's not necessarily true either. We can express it perfectly well as the limit of such a sequence. That's all we really need.

[thesometimesaint]

Cold Steel:

Entropy is only for closed systems. With the discovery of dark matter and especially dark energy. We might have to rethink what we believe about entropy.

[Rob Osborn]

What do you men here by the number it ends in? Do you mean what digit the decimal expansion of 1/3 ends in? That's a nonsensical question because the decimal expansion of 1/3 does not end. Do you mean what the sequence 3/10 + 3/100 + 3/1000 + . . . = .3 + .03 + .003 + . . . = .333... converges to? The proof that this converges to 1/3 is pretty straightforward. It's a geometric sequence with a simple proof for the converging formula.

We both understand each other on this. I do mean "what digit the decimal expansion of 1/3 ends in". That was my point, we both agree. Numbers like that of 1/3 can't be perfectly expressed in this format- .33333333333...

Edited January 25, 2012 by Rob Osborn

[Rob Osborn]

Rob,

You said: "But, I can assure you that in "principle" it certainly must be in the list."

My response: Your assurances do not assure me. You seemed to claim that you had a concrete way to list all of the real numbers. I asked you the simple question of where 1/3 fell in your list.

I'll make it even easier. What are the first 10 numbers that occur in your list?

The fraction "1/3" can be expressed as .33333.. although it will always be imperfect. And yes, that number would be in my list.

The first twenty numbers in my list would be (in this list it is all the numbers between .0-1.0) as follows. From the pattern one could continu this list forever always moving over one more column for every new sequence and thus- no new number could possibly be generated from going through this list. Here are the first 20 numbers (note that .1 and .2 repeat but this is just to show the sequence).

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

.10

.11

.12

.13

.14

.15

.16

.17

.18

.19

.20

Edited January 25, 2012 by Rob Osborn

[Stargazer]

One thing that interests me is entropy. Stars that we're watching go through birth, life and then death. God speaks of eternal worlds, but in this universe everything we see is going through the same process we are. But if stars and planets "die," then where are the "eternal" worlds, and where will the Earth go when it is resurrected in a celestial state (and thus becomes the habitation of the faithful)?

Everywhere we look, even with the Hubble, we see entropy. This means that there is another place and time where entropy does not exist. Certainly the Lord spoke truly when he said his works are without number...to us. But to an eternal being with and eternal mind, they are numbered. And they continue to grow. Plus he is mindful of his children on each world.

Entropy scares me. Basically, it means that the ball rolls only downhill, and it only rolls uphill using momentum is has gained from rolling downhill. Eventually it reaches the bottom.

The Universe is running down, at least as far as we know. I'll say why I thinkj it might not be running down in a moment, but as far as we know it, it is.

And the very interesting thing is this: we are at about the time in the Universe where it is most probable that life can develop. At the moment the Big Bang happened, the composition of the Universe was exclusively hydrogen -- no helium or any heavier elements to speak of. No carbon to base life on, no gold to use for currency, and no uranium to make bombs, either. It has taken billions of years for heavier elements to accumulate, and this accumulation has made it possible for life. But I have heard astronomers say that as more and more billions of years go by, this accumulation will stagnate as energy itself streams out into the void and is lost forever. And eventually the Universe will run down and burn out. This will take perhaps one or two hundred billion years, but eventually the Universe will consist of white dwarfs and black holes, each billions of light years away from any others.

But in the meantime there are lots of opportunities for life to develop, at least in those galaxies which are metal rich. And there's lot of them, so Father has lots of places to put His children.

But the thing we don't know is: has the Big Bang finished? Or is it still happening? If it is still happening (my guess), the Universe could still be moving from that point from which it emerged into this space-time continuum and will continue to expand.

That 3 degree K signature of the Big Bang suggests that it might have been a one-time event, but I don't think it is possible to prove that it isn't still ongoing.

[asbestosman]

I propose a slightly better numbering system Rob since your pattern will never get numbers between 0.0 and 0.1. It is as follows:

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

.01

.11

.21

.31

.41

.51

.61

.71

.81

.91

.02

.12

.22

etc.

Note that there are no repeats. Also note that it reaches .01 which your list never will reach. That said, even this list never reaches 1/3 although it gets arbitrarily close. Even you admit that, "Numbers like that of 1/3 can't be perfectly expressed in this format- .33333333333... " Actually, that's not entirely true. You can express 1/3 in that format as a limit of a sequence. However the sequence itself would not contain 1/3.