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Carborendum

Eternity, infinity, and limits

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Once upon a time I mused about the rate of improvement I was making in overcoming my weaknesses and faults.  Yes, I actually spend some time pondering "what lack I yet?" and how much further I have to go, what I need to repent of.

I had made a meaningless calculation that I could possibly achieve perfection in another 400 years.  But that was really off because of a simple mathematical thing known as "asymptotes."  I believe our improvement in this life is largely asymptotic.  That is why it is so difficult to be perfect.  Yes, the scriptures speak of "perfect men" who have been purified in Christ.  But I'm still wondering what that means.

It seems almost paradoxical that as our improvement in this life is asymptotic, the progression in eternity is not limited in any way.  And I'm beginning to wonder if that is so in the lower kingdoms as well. 

Pondering the three kingdoms, I wondered: Are the Telestial and Terrestrial really "limited"?  The "progression between kingdoms" crowd speak of the lower kingdoms trailing behind the engine of the celestial. They get to the same point, just a bit later.  I rejected that notion.  But what is the alternative?  Either there is a cap on where the other kingdoms go, or...

Bruce R. McConkie says that "they don't even go in the same direction."  Still not sure what that means.  But when thinking of it from a mathematical perspective, I considered: What if

  • Telestial = infinity.
  • Terrestrial = infinity^2.
  • Celestial (lower levels) = infinity^3.
  • Celestial (highest degree) = infinity^infinity.

Then even the Telestial is not "damned" because there is still no cap.

I'm fairly certain that most people won't see the difference because they don't understand the nature of the exponential infinities that I just posited.  Beyond that, there are higher levels of infinity (beyond infinity^infinity) that I was recently introduced to (a few years back) that I'm still having trouble wrapping my head around.  But regardless of the nature of these infinities, it is interesting that such concepts are talked about in math, but don't quite make it into gospel discussions.  I wonder if any of this could clarify some doctrinal questions.

Edited by Carborendum

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I don't know that I have any answers but I do have some thoughts I think are relevant. First off, I don't think God would ever deny one of His children the chance to progress if they are willing to whether it be in this life or a billion years from now. But the question is will they want to (speaking of those in the lower kingdoms). We existed for however many eons of time before coming to this earth and I think our trajectory was already pretty well defined by then. Though perhaps this life could act as a "scared straight" experience for some. But when we consider that our ultimate destination is truly of our own choosing and that choosing took place over who knows how long of time it makes me wonder what could happen in the eternities that would all of a sudden make someone say "okay, now I'm willing to live a higher law." There is so much that hasn't been revealed like what will the inhabitants of the lower kingdoms be doing with their time? I don't know. We do know they will be happy with their allotment and perhaps that will breed contentment. But if progress between kingdoms was a real thing it would be a truth that would work against God's purposes in this life. 

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3 hours ago, Carborendum said:

I had made a meaningless calculation that I could possibly achieve perfection in another 400 years.  .

This is interesting.  Personally I don't think that any mortal could obtain perfection even with an unlimited lifespan.

It seems almost paradoxical that as our improvement in this life is asymptotic, the progression in eternity is not limited in any way.  And I'm beginning to wonder if that is so in the lower kingdoms as well.

I have the same thought.  I have heard in Seminary/Institute that God the Father presides over the Celestial, Christ presides over the Terrestrial, and that the Holy Ghost presides over the Telestial.

To me that means that the inhabitants of each place will still be learning/progressing.  For example, what is the Holy Ghost' purpose of presiding over the Telestial unless there is teaching?  There must be some type of progression.

Quote

 

Edited by Scott
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I find this subject to be interesting.  I thank @Carborendum for creating it and @laronius for their very thoughtful contribution.   However, I would take our thinking in a very different direction with the principle of Agency.  As we ponder eternity most think in modern concepts that involve time.  The ancient Egyptians had a very different concept of things eternal that had nothing to do with time.  Perhaps I should amend this slightly because "nothing" is perhaps not quite the way to be thinking.  In essence, the ancient Egyptians thought in terms of something that could not be altered or changed.  Our modern thinking of eternal is what changes over time - but as I have tried to express - time distorts our understanding of eternity.

To illiterate lets us consider the concept and doctrine of Agency.  If we define agency primarily as a choice or choices in time we begin to get confused over what appears to be conflicting principles.  Such conflicts have already been expressed.  One thought is - if our agency or choice could be altered and the choice changed - was the previous choice really an expression of our agency?  If we ever change our kingdom of glory which change exhibits the "true" exercise of our agency?  Then we are faced with why a choice or agency changed?  Was something missed the previously "time" we exercised our choice through our agency?  If something was "missed" were we really exercising true agency?  But this line of thinking leaves us with the notion that once agency is exercised - it is lost and we no longer can ever exercise our agency again.  The only conclusion to such thinking is that G-d's plan of salvation is flawed - severely flawed and unjust. 

I suggest that although agency is a choice that there is much more to agency than choice - however, when I have suggested such in the past I am not sure it is understood and I am not that good at explaining things.

 

The Traveler

 

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13 minutes ago, Traveler said:

I suggest that although agency is a choice that there is much more to agency than choice - however, when I have suggested such in the past I am not sure it is understood

Well, it is good to see that some things never change. :crackup:

Quote

and I am not that good at explaining things.

No comment.

Edited by Carborendum

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2 hours ago, Traveler said:

 I suggest that although agency is a choice that there is much more to agency than choice - however, when I have suggested such in the past I am not sure it is understood and I am not that good at explaining things.

I think a key element in all this is knowledge. To the degree knowledge is lacking so is agency and yet we are required to make choices all the time with incomplete knowledge. But this is a saving grace for us as it is far worse to screw up knowing verses only believing or only knowing in part.

We are familiar with the doctrine that we cannot be saved in ignorance. It can likewise be said that we cannot be damned in ignorance as well. Sons of perdition have lost this excuse because they really do KNOW and still reject it.  

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When we think on our mortality, will a human body ever be able to exist inside the sun on it's own.  If we were left on our own, as we are, would our bodies ever be something other than what they are now?

We hypothesize, we think, and conjecture, but perhaps physically it is impossible for our mortal bodies to do certain things no matter how much time is given.  We can advance forever in our own sphere, but we cannot exceed our sphere.

A comparison would be that of ants.  Could an ant ever be a human in this mortal world?  Could they ever construct a space ship?  They can advance and increase in their own kind and way, but their own limitations prevent them from exceeding what man can do.

What if we took a higher level animal such as a Dog or Monkey.  They can emulate what a man can do, they can even imitate, but they will never be able to be or do what man is able to do today.  Unless they changed (evolved as science would put it) into something greater, they will never be able to accomplish what men do today, a thousand years ago or even two thousand years ago in architecture, buildings, or science.

In a similar vein I imagine the differences in the degrees of glory.  Nothing prevents one from advancing in learning and experiences in the Telestial or Terestrial Kingdoms, each in their sphere, but much like ant or a dog or a monkey, they are limited by their own physical being.  There are bodies telestial, bodies terrestrial, and bodies Celestial.  They each can increase in their own way, but they are all different as well, with the greater have greater potential as a consequence of it's fabric of creation than those that are lesser.

In my opinion.

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On 9/16/2020 at 8:07 AM, Carborendum said:

But when thinking of it from a mathematical perspective, I considered: What if

  • Telestial = infinity.
  • Terrestrial = infinity^2.
  • Celestial (lower levels) = infinity^3.
  • Celestial (highest degree) = infinity^infinity.

Then even the Telestial is not "damned" because there is still no cap.

I'm not sure what you mean by [infinity]n, so I'm going to propose a few models and we can discuss them.

Usually when we talk about different infinities we are talking about the cardinalities of some infinite set. We start with all Natural numbers [1, 2, 3, ...] and we know there's infinitely many of them [inf]Nat. We compare that against a set that only contains even numbers [2, 4, 6, ...] and our instincts say this should have 1/2 the cardinality of [inf]Nat, but it turns out that for every element in [inf]Nat there's a matching element in [inf]Even.[inf]Even[k] = 2*[inf]Nat[k]. So the cardinalities are exactly the same. This is expressed as Aleph0. (Hebrew - for when your math exceeds Greek notation). Similarly, sets of odds, squares, and primes all have this same cardinality. Even the set of all rationals (Natural + fractions) have this same cardinality. It's all Aleph0. The set of all irrationals, on the other hand, does not map back to the set of Natural numbers so it has a different Aleph (I couldn't tell you what it is, as I've reached the limit of my knowledge on this subject) as does the set of all Reals which subsumes it.

A models come from this knowledge. First, we can say that when you say infinity you really mean Aleph0, infiinity2 is Aleph1, and so on. In this case I'm not sure what infiintyinfinity means. This model suggests that Telestial progress is unbounded as far as formal limits go, but vastly smaller than any others. I'm unfamiliar with other Alephs so I can't add anything further here.

Second, we could say that when you say infinity, you mean the infinity of a specific infinite set. We'll say that's [inf]Even and infiinty2 is [inf]Nat and infinity3 is [inf]Rational.Additionally, we'll say infinityinfinity is [inf]Real. Again, the implication is that Telestial progress is infinite, but now each kingdom's elements (or experiences, or achievements, or glory) is a subset of the kingdom above it. Additionally, this shows some commonality between the first three (all are countably infinite) and a special state of the highest degree (uncountably infinite). If you want to bring immortality and eternal life into the discussion it would work well. An additional implication is that the lower kingdoms move "faster" than the higher. The kth even element when charted on a number line is farther along than the kth natural which is farther along than the kth rational and so on. You can tease some meaning out of that, but don't know how relevant it would be.

A third way we could view it (similar to the 2nd in implications) that lines up more with what you cited to McConkie is to use a number graph. Every degree adds another axis. The x-axis (Telestial) progresses infinitely, and go move along however fast or slow you want it to. But it never enters the y-axis (Terrestrial). y=0. Always. But that's okay, because x- knows nothing of y. A 2-D graph is quite literally infinityso it matches up with your naming convention. The Celestial then is 3-D. The advantage of this model is that it's probably more approachable to the (mathematically) lay person than the others.  For the highest degree of the Celestial Kingdom I would perhaps model it as having Dimensions upon Dimensions added upon it because, as God offers another Dimension the Celestial person never says no.

The next 2 don't apply to your model but I mention them just for completion.

A fourth way that your modeling is contrasting (but which I'm going to include since that's the one sometimes used for this discussion so it gives a baseline to the discussion) is asymptotic progression. In this one you can view the positive quadrant for 

1 - 1/(x + 1)

and then just change that first 1 value for Kingdom Max. The first 3 all have some max that is ever approached but never reached, while Exaltation is not asymptotic.

A fifth model which this stands in contrast with is the one that seems to come to mind simply because of math ignorance. It has Telestial = x, Terrestrial = x2, and Celestial = x3, (and maybe Exaltation is nx?). These are unbounded, but their differences are simply the rate of progression.

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39 minutes ago, mordorbund said:

Even the set of all rationals (Natural + fractions) have this same cardinality.

How is this possible? How can you map the integers onto the rational numbers? I'm not mathematically sophisticated, but I understand mapping the integers onto any subset of the integers. I don't see any strategy to map the integers onto something like the rationals. Can you explain? Preferable if you use small words that I can easily understand, but if you need to get fancy, that's fine, too. Or if you'd rather just point me to a reference, that works.

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6 minutes ago, Vort said:

How is this possible? How can you map the integers onto the rational numbers? I'm not mathematically sophisticated, but I understand mapping the integers onto any subset of the integers. I don't see any strategy to map the integers onto something like the rationals. Can you explain? Preferable if you use small words that I can easily understand, but if you need to get fancy, that's fine, too. Or if you'd rather just point me to a reference, that works.

I found a reference that explains an example demonstrating that the rationals are countably infinite, and thus aleph-naught. It's not mathematically rigorous, so if you want to use it on your Math Ed Master's thesis, you're out of luck. But it's convincing. I admit I chuckled out loud when I saw it. Clever.

https://www.homeschoolmath.net/teaching/rational-numbers-countable.php#:~:text=A set is countable if you can count its elements.&text=In mathematical terms%2C a set,the set of natural numbers.

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1 hour ago, mordorbund said:

Additionally, we'll say infinityinfinity is [inf]Real.

Or perhaps [inf]complex. (Don't mind me. I'm just getting caught up in the irrelevant details of the comparison.)

Edited by Vort

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One of the classic differences between a mathematician and an engineer is that an mathematician is greatly disappointed if there is ever any real applications that can be applied to mathematical theories - engineers, on the other hand believe mathematical theories are useless unless there is an application to the real world.  One of the great criticism of Black Hole theory is that theoretical infinity has never been proven to exist in nature.  Mathematics is a great representation of our universe of "things" but the universe is not comprised of anything mathematical.  

I find it most interesting that G-d says that his creations and works are not countable (thus infinite) to man but that they are (finite) to him.  I interpret this to mean that G-d is involved with mathematics at levels we have not encountered yet.  We keep developing new mathematical theories to explain stuff we encounter that does not fit the old system.  For example the real number system is but a subset of the imaginary number system.  A thousand years ago no one knew that imaginary numbers could be defined and have purpose.  Anciently the number zero was not understood and causes a lot of confusion in ancient scriptures to modern thinkers.  For example: many think that 1/3 of heave followed Satan.  What we are told is that a third part followed Satan - which means that Heaven was divided into 3 parts - the assumption that the 3 parts were equal parts and thus 1/3 of heaven is a flaw in the understanding of ancient number theory.

I do not believe we are quite ready to compare our number theory to G-d's or use our current theories to accurately explain G-d and his creations and works - but it is fun to try.

 

The Traveler 

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4 hours ago, Vort said:

I found a reference that explains an example demonstrating that the rationals are countably infinite, and thus aleph-naught. It's not mathematically rigorous, so if you want to use it on your Math Ed Master's thesis, you're out of luck. But it's convincing. I admit I chuckled out loud when I saw it. Clever.

https://www.homeschoolmath.net/teaching/rational-numbers-countable.php#:~:text=A set is countable if you can count its elements.&text=In mathematical terms%2C a set,the set of natural numbers.

That's the standard mapping for it. Guess what that means for the following scenario: stand in a regularly ordered grid of 1-D trees that extends in the plane, with each tree placed some unit length along two axes (glad @zil isn't around to read this), and then point your 0-D laser out into the woods. Will your laser hit a tree?

 

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When thinking about progression and the eternities I love the following verses of scripture:

Doctrine and Covenants 77: 3

3 Q. Are the four beasts limited to individual beasts, or do they represent classes or orders?
A. They are limited to four individual beasts, which were shown to John, to represent the glory of the classes of beings in their destined border or sphere of creation, in the enjoyment of their eternal felicity.

Doctrine and Covenants 93:30

30 All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence.

In both verses of scripture we are informed ( @JohnsonJones hinted to this also) that all of God's creations are able to progress according to the "sphere" which God has placed them within. According to scripture, as it stands now (until more is revealed), the telestial, terrestrial, and lower stations of the Celestial kingdom have their limits. As scripture is clear, "he cannot have an increase."

These kingdoms though are subject to the "sphere" God has placed upon them in each kingdom. Each kingdom will have their ability to progress throughout eternity. They can reach whatever point, height, available in each kingdom. At that point, there isn't any increase. So, I would agree with the following statement, if I am understanding asymptotic correctly, "And I'm beginning to wonder if that is so in the lower kingdoms as well." Appears to be accurate according to the sphere the lower kingdoms are given.

I'm not sure though I agree that we are asymptotic though in this life. I would say Christ's life proves that we could have achieved it, but through Christ it still can be achieved but the refiner's fire isn't all to appealing to become what Christ became in this life through him.

 

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On 9/17/2020 at 1:41 PM, mordorbund said:

I'm not sure what you mean by [infinity]n, so I'm going to propose a few models and we can discuss them.

 

Quote

Usually when we talk about different infinities we are talking about the cardinalities of some infinite set. We start with all Natural numbers ... This is expressed as Aleph0.

Yes, this is what I had heard about before.  I understand Aleph0.  I don't get what comes next.

Quote

it has a different Aleph (I couldn't tell you what it is, as I've reached the limit of my knowledge on this subject)

I see you had the same problem I had.

Quote

A models come from this knowledge. First, we can say that when you say infinity you really mean Aleph0, infiinity2 is Aleph1, and so on. In this case I'm not sure what infiintyinfinity means. This model suggests that Telestial progress is unbounded as far as formal limits go, but vastly smaller than any others. I'm unfamiliar with other Alephs so I can't add anything further here.

I was actually told differently.  I was told that all those things I spoke of were all Aleph0. And there were more things in Aleph1.  But as I said, I have no idea what that means.  The person telling me all this struggled to explain it himself. And the example he gave me was something I disproved in a couple minutes.  Maybe he didn't know either.

I'm essentially saying something along the lines of...

Quote

Every degree adds another axis. The x-axis (Telestial) progresses infinitely, and go move along however fast or slow you want it to. But it never enters the y-axis (Terrestrial). y=0. Always. But that's okay, because x- knows nothing of y. A 2-D graph is quite literally infinityso it matches up with your naming convention. The Celestial then is 3-D. The advantage of this model is that it's probably more approachable to the (mathematically) lay person than the others.  For the highest degree of the Celestial Kingdom I would perhaps model it as having Dimensions upon Dimensions added upon it because, as God offers another Dimension the Celestial person never says no.

That is what I was saying about the various infinity^n.  I don't know how it could be ineterpreted any other way.

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1 - 1/(x + 1)

This is how I was describing achieving perfection in this life, where x = time in mortality.  Some argue that this is also how we progress eternally through the Telestial and Terrestrial.  I'm toying with the idea that this notion is not correct, hence, my three dimensions and infinite dimensions pradigm. I did not realize that McConkie agreed with me.

Quote

A fifth model which this stands in contrast with is the one that seems to come to mind simply because of math ignorance. It has Telestial = x, Terrestrial = x2, and Celestial = x3, (and maybe Exaltation is nx?). These are unbounded, but their differences are simply the rate of progression.

I don't see this as much different than the original 3-d and infinite-D model.  Sure there is a numerical difference.  But conceptually, they're pretty much the same.

BTW, I liked the Numberphile link you provided.  I've been a fan of that channel. But I never saw that video before.  One thing that he brought up, but didn't get into much: Something I believe to be at the root of why sealing is so important.

When you add dimension to the trees or the laser, it really doesn't really matter how much dimension it is.  The original analysis was based on the trees and laser being of zero dimension.   But once you give both of them any measurable dimension at all, then anywhere you point will eventually hit a tree.

I believe that this concept is why we need to be sealed.  I believe sealing is the "dimension" of eternity.  I know that makes no sense as a point-for-point allegory.  But conceptually interpreting the math, that is the closest thing to where sealing falls into eternity (off the top of my head postulate).

***********

The orchard problem also brings up another interesting point.The fact that the zero dimensions will only hit on rational numbers says something.  We mortals try to fit everything into neat little rational boxes.  We have a mind, we therefore must be able to understand all the things of God with using our intellect alone.

Ha-hah.

Compared with the Lord, our intellect is infinitesimal (i.e. has zero dimensional width).  So, we limit ourselves when we depend entirely on our rational mind alone.  Certainly the rational mind focuses and provides some framework.  But if we are to understand eternity and infinity, we must look at and make use of the irrational numbers.  By the orchard analogy, we know there are infinitely more irrational numbers than rational numbers.  And some of the most important numbers like pi and e are irrational. And they govern the design and intent of so much in this universe alone.

Why do we limit ourselves when the Spirit is right there waiting for us to simply listen?  Listen, and we had some dimension to our being.

Edited by Carborendum

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On 9/18/2020 at 3:33 PM, Anddenex said:

So, I would agree with the following statement, if I am understanding asymptotic correctly, "And I'm beginning to wonder if that is so in the lower kingdoms as well." Appears to be accurate according to the sphere the lower kingdoms are given.

I'm afraid you may have misinterpreted.  I was beginning to wonder if that asymptotic behavior in the lower kingdoms was incorrect.  I had been taught this for a long time.  But I'm not so sure anymore.

On 9/18/2020 at 3:33 PM, Anddenex said:

I'm not sure though I agree that we are asymptotic though in this life. I would say Christ's life proves that we could have achieved it, but through Christ it still can be achieved but the refiner's fire isn't all to appealing to become what Christ became in this life through him.

Of course there are exceptions to such rules.  Christ was an exception in far too many ways to discount a theory by pointing to the one man who was OBVIOUSLY an exception.

For example: How many people have been translated?  Even if we count the cities of Enoch and Salem, we're not even talking about 1 million people of all the billions who have lived on this planet.  Even the people of Ammon who by most people's estimation were perfect in keeping the commandments, were not translated.

So, what does perfection mean in this life?

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On 9/17/2020 at 4:43 PM, mordorbund said:

 

That's the standard mapping for it. Guess what that means for the following scenario: stand in a regularly ordered grid of 1-D trees that extends in the plane, with each tree placed some unit length along two axes (glad @zil isn't around to read this), and then point your 0-D laser out into the woods. Will your laser hit a tree?

 

I haven't watched this Numberphile (yet—great channel, btw), but given the assumptions that the trees extend infinitely in both directions on a perfectly Euclidian plane and that the tree trunks and the laser beam are all infinitesimally narrow (and that the tree branches, leaves, etc. aren't part of the question), I'm going to say yes, you will always hit a tree. My sense is that such a problem is like saying, "If you pick any real number at random, will you get a rational or an irrational?" The set of irrationals is so much larger than the rationals that it becomes infinitely improbable that you would end up with a rational. Similarly, I'm guessing it's infinitely improbable that you point the laser in exactly a "rational" direction such that you avoid all the infinite tree trunks.

But if it's infinitely improbable, isn't that the same as saying it's impossible? Yet we can see that e.g. if you point the laser exactly parallel to a row of trees, that it will never hit a tree trunk. So what does "impossible" mean in this case? What do probabilities mean? It becomes practically a philosophical conundrum, at least for someone as tender and innocent in the arcane ways of mathematics as am I.

EDIT: Wow. I was exactly, 180° wrong, and for exactly the reasons I discussed. I wonder how I missed that. The trees represent, in effect, the rational set of numbers, so as long as you pick an effectively "irrational" direction, you'll miss the trees. So with infinitely thin trees and an infinitely narrow laser, it is in effect impossible to point the laser in any direction on the plane and hit a tree.

Edited by Vort

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40 minutes ago, Vort said:

EDIT: Wow. I was exactly, 180° wrong, and for exactly the reasons I discussed. I wonder how I missed that. The trees represent, in effect, the rational set of numbers, so as long as you pick an effectively "irrational" direction, you'll miss the trees. So with infinitely thin trees and an infinitely narrow laser, it is in effect impossible to point the laser in any direction on the plane and hit a tree.

An amusing fact occurred to me. If you aim the beam by physically pointing the laser, it is impossible to hit a tree. But if you aim the beam by punching in a set of [necessarily rational] coordinates on an aiming mechanism, it is impossible not to hit a tree.

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1 hour ago, Vort said:

An amusing fact occurred to me. If you aim the beam by physically pointing the laser, it is impossible to hit a tree. But if you aim the beam by punching in a set of [necessarily rational] coordinates on an aiming mechanism, it is impossible not to hit a tree.

And yet by sweeping the beam from side to side even just a little will allow you to hit an infinite number of trees. Maybe the point is to just keep moving. 😀

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3 hours ago, Carborendum said:

I'm afraid you may have misinterpreted.  I was beginning to wonder if that asymptotic behavior in the lower kingdoms was incorrect.  I had been taught this for a long time.  But I'm not so sure anymore.

I assume then you would have to then define the limit. Is the limit we are discussing "Exaltation" >> becoming one with God the Father and receiving all he hath? Is the limit you are then expressing simply "perfection" that necessarily doesn't mean to become like God is?

Each kingdom is placed in a sphere of truth/creation. Each sphere has its limit. The Telestial kingdom will come close to, but never reach the Terrestrial kingdom glory, as the Terrestrial kingdom will come close to but never reach a oneness with the Father and Christ (receiving all the Father hath). The scripture specifying they have no increase I would think supports this.

What is it that causes you to believe that the Telestial will reach, surpass the limit, placed upon it? Do you feel now it actually doesn't have a limit, is that why you aren't sure anymore?

3 hours ago, Carborendum said:

Of course there are exceptions to such rules.  Christ was an exception in far too many ways to discount a theory by pointing to the one man who was OBVIOUSLY an exception.

For example: How many people have been translated?  Even if we count the cities of Enoch and Salem, we're not even talking about 1 million people of all the billions who have lived on this planet.  Even the people of Ammon who by most people's estimation were perfect in keeping the commandments, were not translated.

This is where we would find disagreement. If one person reaches -- in this life -- a supposed limit the limit can no longer be in place as it has been surpassed. I'm unsure how a limit that has been surpassed can no longer be surpassed by anyone else. The possibility is there. It can be reached. Again, I may be misunderstanding something regarding asymptotic behavior, which I find this definition for, "Your function may approach this limit, getting closer and closer as you change the function's input, but will never reach it."

Does the possibility that all could have reached it discount the theory? The number of people who didn't doesn't seem to be what asymptotic behavior is representing. It appears to simply state that they never will reach it. So, in order for asymptotic behavior to be true, the limit must never be reachable by anyone. That appears to be more of what Protestant Christians teach. We can do all we can but we will never reach the limit (Godhood, becoming one with the Father).

I don't think being translated is the only reason for not being perfect. Abraham was never translated but I would think Abraham was just as just as Alma. Joseph in Egypt was never translated but was definitely just as just/perfect as Alma (if not more so, seeing his life is symbolically an archetype of Christ) but was never translated. As a people all would need to be in a position to be translated as it only takes one individual to have the city remain. So, there could have been many of the people of Ammon who were worthy of translation, but like Abraham, Isaac, Jacob, and Joseph the Lord kept them upon the earth. It could also mean they simply never asked for it.

I misunderstood previously, so I am trying to morefully understand your thoughts here and why you think it may not be correct anymore.

3 hours ago, Carborendum said:

So, what does perfection mean in this life?

Godly. I think Nephi's promise by the Lord regarding anything he said would happen. Nephi, in this life, achieved a oneness of mind with God.

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2 hours ago, Anddenex said:

I assume then you would have to then define the limit. Is the limit we are discussing "Exaltation" >> becoming one with God the Father and receiving all he hath? Is the limit you are then expressing simply "perfection" that necessarily doesn't mean to become like God is?

I think the basis of disagreement is founded in conflating an asymptotic limit vs a dimensional limit.

I had thought the limit of a Telestial was like a really, really big box.  The Terrestrial is just a much bigger box.   I'm thinking this is wrong.

I'm now thinking the Telestial is more like being stuck on a line that goes on forever.  A train track on a long journey that goes on forever.  As long as you keep moving along that train track, you can continue to improve.  But you only have one dimension, the track.  An infinitely long track.  But a single dimension.

The Terrestrial would be infinitely wide plane or even a universe.

The celestial would not only have an infinite universe.  You'd have infinite numbers of infinite universes. 

(I'm shorthanding my more complete explanation above).

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On 9/21/2020 at 11:39 AM, Carborendum said:
On 9/17/2020 at 2:41 PM, mordorbund said:

First, we can say that when you say infinity you really mean Aleph0, infiinity2 is Aleph1, and so on. In this case I'm not sure what infiintyinfinity means. This model suggests that Telestial progress is unbounded as far as formal limits go, but vastly smaller than any others. I'm unfamiliar with other Alephs so I can't add anything further here.

I was actually told differently.  I was told that all those things I spoke of were all Aleph0. And there were more things in Aleph1.  But as I said, I have no idea what that means.  The person telling me all this struggled to explain it himself. And the example he gave me was something I disproved in a couple minutes.  Maybe he didn't know either.

Thanks for clarifying that you're working off a dimensional model. I want to revisit this just so it can be closed cleanly. infinityn has cardinality of Aleph0. This can be shown using the same argument that's used for INFRational having cardinality Aleph0. You line up all the whole numbers on one axis and all the whole numbers on another axis and you cleanly map the 2D to 1D with zigzags. A special zigzag you can use for this is the Hilbert curve. This is useful because there's a 3D analog that maps cleanly to 1D. I haven't done anything rigorous, but given the nature of nD cubes, I imagine you have that mapping for any infinityn. I'm not sure if it applies to infinityinfinity. and all bets are off if you intend to use INFReals for your axes (since just the first axis alone is in Aleph1).

On 9/21/2020 at 11:39 AM, Carborendum said:
On 9/17/2020 at 2:41 PM, mordorbund said:

A fifth model which this stands in contrast with is the one that seems to come to mind simply because of math ignorance. It has Telestial = x, Terrestrial = x2, and Celestial = x3, (and maybe Exaltation is nx?). These are unbounded, but their differences are simply the rate of progression.

I don't see this as much different than the original 3-d and infinite-D model.  Sure there is a numerical difference.  But conceptually, they're pretty much the same.

The difference is that for any given y, x12 = x23. This is essentially the math equivalent of eat, drink, and be merry. God will be us with a few stripes, but eventually we'll have all the same experiences as Celestial people. It just takes longer. And who really cares about longer when we're talking about eternity? In contrast, the dimensional model says you will never experience "up, but not North".

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On 9/25/2020 at 10:47 PM, mordorbund said:

The difference is that for any given y, x12 = x23. This is essentially the math equivalent of eat, drink, and be merry. God will be us with a few stripes, but eventually we'll have all the same experiences as Celestial people. It just takes longer. And who really cares about longer when we're talking about eternity? In contrast, the dimensional model says you will never experience "up, but not North".

The flaw in their thinking is that they're using finite thinking for infinite concepts.  e.g. x12 = x2wouldn't make sense if you substituted (infinity1) and  (infinity2) for the bases using their respective exponents because there is no such thing.  There is no difference between the two.  It completely misconstrues the nature of infinity. 

So, they're basically saying the Lord took the time to make a very important distinction where there was none.  Wouldn't that make Him a liar?  

He's not a liar.  So, there IS a difference.  And the finite equation simply wasn't it.

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