Entropy can be reset to initial or previous state

[obsrvr524]

That's what I thought. Liberal minds never commit else they risk losing control of the narrative. Truth means nothing to them because life is all about themselves. They are certainly not interested in seeing their mistakes revealed.

[Silhouette]

Still no content, only claims.

I too could pin this on assumed political leanings and biased stereotypes attributed to them, but it would be equally as vapid as your accusations.

please do get back to the content and let me know what my convenient mistakes are - I've obviously missed them and I'm relying on you guys to point out what I've missed, and likewise you can rely on me to point out if there's anything you've missed in pointing out what I've missed.

I literally asked you what my mistakes are and you say I'm "certainly not interested in seeing my mistakes revealed".

"Truth means nothing to them" is literal psychological projection on your part - confirmed.

Are you going to stop wasting our time now? If so, you have two options only:
Option A) Continue the discussion and reveal my mistakes - I am interested.
Option B) Cease posting. The motion that you have nothing is carried.

If neither are met in your very next post, should you make one at all, that is indisputable proof that you intend only to waste both of our time.

The moment of truth has come, let us see who you really are...

[obsrvr524]

Still no commitment.
Too predictable.

They also have an amazing lack of courage even in debate. It would have been easy enough to just say "yes" and then continue your deny, deny, deny tactic. You were going to do that anyway but at least then you would have been able to learn something if learning about your mistakes was of even the least interest.

I feel like Trump talking to the Pelosi debacle.

[obsrvr524]

Now, while Sil is figuring out how to multiply sets, anyone want to get back to the topic?

I say that the entropy of the entire universe as a whole can never change. James said the universe can never repeat its exact state. Both of those depend upon the universe being infinity in size.

So for the universe to alter and repeat its state of entropy, it must be a finite universe. So the question becomes, "What is outside the finite universe?"

[promethean75]

If you think you can comprehend infinity, you are either giving bounds to infinity or implying your comprehension is infinite. So are you contradicting yourself or professing godlike capabilities?
It's by definition only possible to comprehend the tendency towards infinity, which is why maths deals with tendencies instead of infinities. This shouldn't be hard to comprehend.

i think this might be the crux of the biscuit, 524. there's an ongoing controversy between mathematicians and philosophers regarding the difference between 'actual' and 'potential' infinity. seems to me that mathematicians (as intuitionists, maybe) are assuming some kind platonic numbers that transcend the arbitrary use of numbers as symbols... as if they are 'out there' floating around. if they were, then it wouldn't be a mistake to say it's possible for there to be an infinity of 'things'. but if this isn't taken for granted, mathematics simpliciter would only ever be a rational language that was used to designate observable quantities. this may be what sil means when he alludes to the fact that conceiving of infinity can only always be an 'approach' or a 'tendency'... this making any countable set at the moment of its conception an 'actual' set, and hence only finite.

and this dispute is not for nothing, man. if you take the concept of 'infinity' and apply it to actual, observable terms in space/time, you end up with major problems like trying to find a room at hilbert's hotel. ever been to hilbert's hotel? that place doesn't make any sense, bro.

i think what's happenin here is mathematicians are attributing the fact that a number can be divided and/or added to infinitely, to the notion that therefore things can be divided and/or added to infinitely. but there's quite a bit of evidence that the energy of the universe is finite. entropy, conservation of energy, and the counter-intuitive idea that 'more' energy can be introduced into the whole system from outside of it (which makes no sense because there is no 'outside' the whole system). these are the three biggies.

maybe the confusion lies in trying to reconcile our intuition that space is infinite - on account of there being no conceivable 'boundary' or edge to space/time - with the thought that the stuff in this space/time should also be infinite.

perhaps what we are trying to call 'infinite energy' is not an unlimited quantity of energy - remember we can make numbers unlimited, but numbers aren't things that take up space... they're in our heads - but the impossibility of energy to not exist (for where would it go once all motion stopped?). the only mystery here then is how a system with a finite amount of energy that has reached a local state of absolute entropy 'reset' itself and set into motion again.... as it has perhaps been doing forever.

so if you have the following set of conditions:

infinite space
finite energy
impossibility of 'nothing'

... you end up with a logically forced repetition of the same (or there about) for an eternity, no?

kinda like that snake guy eating his own tail, yeah?

[obsrvr524]

If you think you can comprehend infinity, you are either giving bounds to infinity or implying your comprehension is infinite. So are you contradicting yourself or professing godlike capabilities?
It's by definition only possible to comprehend the tendency towards infinity, which is why maths deals with tendencies instead of infinities. This shouldn't be hard to comprehend.

i think this might be the crux of the biscuit, 524. there's an ongoing controversy between mathematicians and philosophers regarding the difference between 'actual' and 'potential' infinity. seems to me that mathematicians (as intuitionists, maybe) are assuming some kind platonic numbers that transcend the arbitrary use of numbers as symbols... as if they are 'out there' floating around. if they were, then it wouldn't be a mistake to say it's possible for there to be an infinity of 'things'. but if this isn't taken for granted, mathematics simpliciter would only ever be a rational language that was used to designate observable quantities. this may be what sil means when he alludes to the fact that conceiving of infinity can only always be an 'approach' or a 'tendency'... this making any countable set at the moment of its conception an 'actual' set, and hence only finite.

Yes, I have seen some people proclaim the physical existence of numbers. I haven't observed anyone taking them seriously. Space is never short of kooks.

and this dispute is not for nothing, man. if you take the concept of 'infinity' and apply it to actual, observable terms in space/time, you end up with major problems like trying to find a room at hilbert's hotel. ever been to hilbert's hotel? that place doesn't make any sense, bro.

I have heard of that Hilbert's Hotel thing. I don't remember much about it. It seemed at the time to be just a word game more than anything real.

i think what's happenin here is mathematicians are attributing the fact that a number can be divided and/or added to infinitely, to the notion that therefore things can be divided and/or added to infinitely. but there's quite a bit of evidence that the energy of the universe is finite. entropy, conservation of energy, and the counter-intuitive idea that 'more' energy can be introduced into the whole system from outside of it (which makes no sense because there is no 'outside' the whole system). these are the three biggies.

It makes sense that a distance could be either divided infinitely or lengthened infinitely. The quantum people want to argue that there is a minimum length, but they declare it to be far, far to small to ever be verified. And they seem to be basing their theory on gross approximations concerning larger things, extrapolating the vague into the defined. I have never found any reason to believe them.

maybe the confusion lies in trying to reconcile our intuition that space is infinite - on account of there being no conceivable 'boundary' or edge to space/time - with the thought that the stuff in this space/time should also be infinite.

I don't think that I have ever heard of anyone claiming that objects are infinite in any way.

perhaps what we are trying to call 'infinite energy' is not an unlimited quantity of energy - remember we can make numbers unlimited, but numbers aren't things that take up space... they're in our heads - but the impossibility of energy to not exist (for where would it go once all motion stopped?). the only mystery here then is how a system with a finite amount of energy that has reached a local state of absolute entropy 'reset' itself and set into motion again.... as it has perhaps been doing forever.

so if you have the following set of conditions:

infinite space
finite energy
impossibility of 'nothing'

... you end up with a logically forced repetition of the same (or there about) for an eternity, no?

You would have to add an infinite past into that list in order to require a cycling.

One thing that I am having trouble imagining is an infinite space extending past known space and with absolutely no energy in it.

If you believe that the entire universe sprang from the big bang then you have accepted the idea of an infinite space with nothing within it. If you believe that time has been infinite then you cannot avoid the fact that light, for example, has had an infinite time to spread throughout the infinite space. So how can you possibly have any space that has never been filled with light, if nothing else? Then in addition you have to ask why energy would be in only one portion of infinite space to begin with. James' proposal was that it is impossible to have space without it being filled with "affectance" (the philosophical form of energy).

I think energy has to be infinite because both space and time are infinite. We don't have to measure it. There isn't any option because there is nothing that we can imagine to prevent it. If there is an boundary to space, there has to be a reason for it to change from what it was and into a boundary. And then the question still remains as to what would be on the other side.

So what is that evidence that energy is finite?

[Jakob]

There seems to have been confusion of what James had put together so far and the rough concepts he was working with.
Anyone who has actually read my posts before responding to me can discern that I and James do not put forth the same propositions.

Ive told James again and again that affectance is too general of a concept and needs to be split up in another infinite ways - qualities of affectance - to do with the fact that things don't only affect, but are also being affected, along with some other concerns. On this level, there is no Newtonean symmetry, but rather a fundamental lack of symmetry which causes growth and diminishing: Nietzsche recognized this as will to power. Symmetry, and Newtonean physics, are a passive result of this on a large scale.

As usual, my concepts here are a well outside of the box of what has already been understood and incorporated by the experts, and I cruelly expect of my readers to make an effort. Cruelty to myself, you see. So let me offer you a fully in the box high school level riddle:

Given a 3 dimensional box which expands in all directions indefinitely and at the speed of light, how does the length of one of the sides of the box equate with the combined length of all of the sides? Is there any point at which they are both the same?

Apply the same thing to the set of Real numbers with respect to the set of Rational numbers.

You cant stop the one set or one of the sides from expanding while you wait for the other set or other side to catch up.

Now apply this to infinite time. Does the spatial infinity of axis x become equal to the spatial infinity of the axes x, y and z combined if t=infinite?

If you take "infinite" as a concrete value, then it is easy. Infinite times infinite is infinite. So the answer would be yes.

This elementary well known example is meant as an indicator of the difference between following rules and thinking.

I salute you gentlemen, may you find a good path.

[Silhouette]

Still no commitment.
Too predictable.

Great, test concluded.
Neither option was taken, therefore the null hypothesis that you intended only to waste both our time is confirmed.
I'll file this away, along with you having nothing to offer with regard to alleged mistakes that I have made, which I've repeatedly asked you to disclose in spite of all your efforts to claim I'm not interested in this, reinforcing my classification of you as a fallacious, disingenuous and slanderous thinker, compromised by your political affiliations and their routine oppositional stereotyping.
Your definition of "commitment" appears to revolve around a willingness to dishonestly debase myself before you. I'm not into prostration and self-humiliation unfortunately, nor am I denying anything except the truth of flawed and/or contradictory argument. I'm just committed to getting to the bottom of as many arguments as possible and determining their truth values - but to you, this is not commitment, the same as my interest in my mistakes not being me being interested in my mistakes. I guess this is why you feel like Trump, constantly contradicting yourself, just "saying stuff" with no justification and making impulsive claims based on popular trending prejudices.

But with that out the way, you have attempted to reignite your disagreement with the second law of thermodynamics for all cases where thermodyanmic equilibrium is not met.
This is in direct violation of your opening post on this thread, quoting James's argument that the universe is infinitely unlikely to be homogenous.

I have no qualms with what you say James says about the universe never repeating its exact state - spacetime has un-curved to the point of curvature no longer being detectable, tending towards flatness and maximum entropy at a slower and slower rate like with the y = 1/x hyperbola, with curvature as the y axis and entropy as the x axis. Therefore it's not expanding into anything, or into nothing, nor is it exactly finite or infinite: the dilemma disappears.

Now we're back to before the infA nonsense you brought up and things can continue as normal, with your dilemma solved just the same as I did the first time around.

Now, while Sil is figuring out how to multiply sets, anyone want to get back to the topic?

I demonstrated how to multiply sets correctly

Perhaps your refusal of relativity, and the laws of thermodynamics, extends to a refusal of arithmetic as well?

(a + b + c + ... + z)ⁿ = n₁aⁿ + n₂aⁿ⁻¹b + n₂aⁿ⁻¹c + ... + n₂aⁿ⁻¹z + n₃aⁿ⁻²bⁿ⁻² + n₄aⁿ⁻²bc + ... + n₄aⁿ⁻²bz + n₃aⁿ⁻²cⁿ⁻² + ... + n₄aⁿ⁻²cz + ... + n₃aⁿ⁻²zⁿ⁻² + n₂abⁿ⁻¹ + n₄abⁿ⁻²c + ... + n₄abⁿ⁻²z + n₄abcⁿ⁻² + ... + n₅abcz + ... + n₄abzⁿ⁻² + n₂acⁿ⁻¹ + ... + n₄acⁿ⁻²z + ... + n₄aczⁿ⁻² + ... + n₂azⁿ⁻¹+ n₁bⁿ + n₂bⁿ⁻¹c + ... + n₂bⁿ⁻¹z + n₃bⁿ⁻²cⁿ⁻² + ... + n₄bⁿ⁻²cz + ... + n₃bⁿ⁻²zⁿ⁻² + n₂bcⁿ⁻¹ + ... + n₄bcⁿ⁻²z + ... + n₄bczⁿ⁻² + ... + n₂bzⁿ⁻¹ + n₁cⁿ + ... + n₂cⁿ⁻¹z + ... + n₃cⁿ⁻²zⁿ⁻² + ... + n₂czⁿ⁻¹ + ... + n₁zⁿ

but when every element a,b,c etc. is 1, and every coefficient n can be broken down into 1s added to together, n can be any value and you still get (1+1+1+...+1)

More ABCs just to prove how stupid your careless and mocking dismissals make you look, to add to demonstrations of how unfounded some of James' basic assumptions are that you're bringing into this thread for some reason. Those predictable <insert presumed group member name here>, never letting you get away with lazy thinking...

To end on a positive note, I don't subscribe to any physical existence of numbers either. Sorry, prom - however Hilbert's Hotel is a good analogy to demonstrate the problems of infinity, so it would be good for obsrvr to refresh his memory about it.

Prom, what I mean by approaching/tending towards infinity is in the construction of their mathematical representations by using finites - these are just the standard terms that mathematicians use. I find the philosophy behind it doesn't require Platonic Forms or anything like that. Using my philosophy, Experientialism, numbers arise from treating continuous experience as discrete experiences - as soon as you can distinguish between experiences, and judge relative similarities between experiences as the other side to that coin, you gain knowledge of a thing distinct from a similar enough thing, and using a standard signifier (starting with some value, why not call it 1) to associate with one signified thing, and a different standard signifier (why not call it 2?) when considering both similar things at the same time. Both signifiers and signifieds have real existence, with no necessary real connection beyond the utility of treating them as though they have a real connection. The rest is logical extrapolation on those humble beginnings, such as "keep adding new signifiers to associate with even more than 2 similar things at the same time", and "why not structure the signifiers in a number system and treat them as having their own artificial precision compared to the real world of signifiers that they represent". That doesn't give them platonic form, but at best it's treating them as though they had that. They're still real signifiers in the world e.g. sounds/symbols, but its the association with their signifieds that's "made up": the main function of the brain being to associate real stimuli for the purposes of prediction. The normal passive associations that are "animal" are actively taken over by the conscious "creative" human mind.
The bounding of discrete experiences from continuous experience, that founds this entire process, is an exercise in defining finites. Extrapolating finites beyond this doesn't transcend human conception as dealing in finites, the best discrete experience can do when defining real finite signifiers to associate with real finite signifieds is treat the process as though it was ongoing, and representing the outcome using finites in a finite form, but treating it as if it went on forever - and this is exactly what infinite series does. It's amusing how skeptical obsrvr is over scientists extrapolating experimental data to things like Planck lengths, but he has no problem extrapolating entropy even further than that to infinity.

This explanation should trace the logic right back to the fundaments, which is what Experientialism is for. That way, it should be clear what infinities necessarily have to be to all humans.

We observe from experimentation that energy remains constant, and likewise no matter is gained or destroyed.
An analogy for what is happening in the universe is to drop some dyed liquid into a huge container of water, where the dyed liquid ideally has the same density as water. The dyed liquid, representing matter and energy, doesn't go up or down, it remains constant. It does, however, swirl and eddy turbulently. The same thing would happen if the water had no bounds: the general tendency is for the dye to spread out, but the turbulence can be constructive in the same way as waveforms can constructively interfere, and isolated pockets appear to do the opposite of spreading out the dye. However these constructive interactions get less intense over time, less frequent, and more spread out, just as the rest of the dye appears to lose its colour as it dissipates into the water, which ultimately all of it does.
Entropy isn't resetting or decreasing when the dye interferes with itself constructively.
The dye dispersing (increasing entropy) is slower when the dye is interfering with itself, same as pockets of high temperature in the universe, the entropy increases more quickly the lower this interference and the bigger difference between the dye and the water around it. Entropy increase again slows down as the differences between the dye and the water decrease, and change in entropy tends back to zero as entropy tends to infinity. This is summed up in that change in entropy equation brought up earlier in the thread.

But that's not the whole story, you have to take the analogy away from something everyday and into the extreme conditions found in the wider universe. Under these conditions, instead of imagining whether the water has a container or not (finite or infinite), you can find the water's volumetric dimensions themselves stretching. The water isn't expanding into anything, the dimensions themselves are expanding. Absolute space and time is the everyday life intuition that was assumed at the time of Newtonian physics, but since Einstein and the like, better experimental evidence has shown they are not absolute, they are relative - and they observably change under conditions of extreme gravity and speeds.
A further bit of evidence for this is how visible light from stars has been red-shifted into the microwave spectrum of light by this, and due to the speed of everything moving away from everything else - as is also observed by experiment. Seeing the light from all the stars in every direction, which is red-shifted outside of the visible light spectrum is done by detecting background microwave radiation, which we do see in all directions.

All these assumed paradoxes that get people chasing invalid questions and finding invalid answers disappear if you follow what the experimental evidence shows and figure out how it all makes sense - as has already been done through things like relativity and the laws of thermodynamics.

[promethean75]

So what is that evidence that energy is finite?

i was under the impression that until the curvature of the universe is known - whether it is positive, negative, or flat - we cannot know if the amount of matter in it is infinite or finite. but admittedly i don't understand what any of this means as a physicist would (which i'm certainly not), and i learn this stuff through researching the consensus i find in the literature i read. if i'm fortunate enough i'll find the material put into 'laymens' terms so i can grasp what is going on.

but on the matter of the philosophical problem of infinities, i'm a little more understanding. the most recent resource i've had at my disposal is a book written by william lane craig called 'reasonable faith' - oddly enough a christian apologist. and while i myself am an atheist, i still find the book very compelling in its presentation of the problem of actual infinities... something i don't think gives any evidence of the existence of a 'god' as he seems to believe it does, though. in any case, in the book he explains the various possible models we have of the universe: standard, steady state, oscillating, vacuum fluctuation, chaotic inflationary, quantum gravity, and string scenario, and then applies the problem of actual infinities to each of the models.

prior to this application he demonstrates the philosophical problem by using the ideas of ghazali, hilbert and mctaggert (his a-theory and b-theory of time), and i can get into this when i have more a-theory time (buh dum tshhh!)

quickly though, i don't dispute james's basic premise - before he goes on to draw all these philosophical inferences from it - that to exist means to 'affect', and that essentially there is no 'empty' space. i had believed this myself since democritus and parmenides.

but then i ask myself, if energy is infinite, and an infinite amount of time has existed, why isn't the density of matter perfectly distributed throughout all space by now? if thermodynamics is correct, and both time and energy are infinite, shouldn't this have already happened? on the other hand, if time/space is infinite and energy is not, i can imagine a number of local distributions of energy within particular regions of space that are somehow isolated from others, in which case they running on their own entropy clock, so to speak. but again i'm no physicist so i may not even be posing the problem in the right way.

i'll post more on this problem of infinites as i understand it, later.

[obsrvr524]

So Sil, you really couldn't figure it out.

Now I have to reevaluate. A mere political pundit would have known better than to attempt another display of his ignorance. That means that you must be sincere. And that puts me in a situation where I have to weigh my sympathy.

Do you want to know the truth of your amateurishness, or do you prefer to just feel good about yourself?

Ah to hell with your feelings because you are going to just keep abusing people by trying to always show them up and make endless excuses to dodge the truth and save face. Again, you remind me of the US democrats in congress. This time AOC who might even know less maths than you yet lectures generals and senators on economics. So here is one of the many elementary mistakes you have espoused in the short time I have been reading you:

Perhaps you didn't pass the 3rd grade in elementary school in which case I apologize. But for the rest of us, we learned something called the "Distributive Property of Multiplication". It goes something like this:

a x (b + c) = a x b + a x c

That is the simple form. It gets just a little more complicated when dealing with two sums being multiplied:

(a + b) x (c + d) =
a x (c + d) +
b x (c + d)

Now if all of those variables were 1's, the solution would be easy:

(1 + 1) x (1 + 1) =
1 x (1 + 1) [=2] +
1 x (1 + 1) [=2]
= 2 + 2 = 4

That's what the math experts teach. But using your method for multiplying such sums together would yield:

(a + b) x (c + d) =
a x c [=1] +
b x d [=1]
= 1 + 1 = 2

Now to perform some arithmetic:
infA ^ 2 = (1+1+1+...+1) * (1+1+1+...+1)

Time to sequentially multiply the terms as you do for multiplication of values in parentheses, let's see...
1*1 = 1, ok. 1*1 = 1 as well, let's keep going and what do we get?
(1+1+1+...+1) * (1+1+1+...+1) = (1+1+1+...+1)
infA ^ 2 = infA, huh...

huh?? 2 is equal to 4?

In case you can't follow that, let me explain the process in words.

To multiply two serialized sums, you take the first number from the first set and multiply it times the entire second set. In James' case, that would have been:

1 x (1+1+1...+1) = infA[1]

Then you take the next number in the first set, do the same thing, and add to the previous solution:

1 x (1+1+1...+1) = infA[2]
infA[1] + infA[2] = 2 * infA

Then you take the next number in the first set, do the same thing, and add to the previous solution:

1 x (1+1+1...+1) = infA[3]
infA[1] + infA[2] + infA[3] = 3 * infA

And you keep doing that, in this case infinitely, yielding:

infA[1] + infA[2] + infA[3] + .... = infA * infA = infA^2

That is merely 3rd grade arithmetic and you couldn't figure it out even after being given a second chance.

Maybe consider backing off from calling people "amateurish"?
Probably not. You learn extremely slow that way, but it's your life.

I might get to the rest of your post or mistakes later.

[obsrvr524]

i was under the impression that until the curvature of the universe is known

First I think you need to give the evidence that the universe has any kind of "curve" at all. I think it is an absurd idea lacking any actual evidence. I think that it was proposed merely to try to defend the big bang theory.

but then i ask myself, if energy is infinite, and an infinite amount of time has existed, why isn't the density of matter perfectly distributed throughout all space by now?

The answer to that is that apparently black holes are gathering the energy in the universe back together at the same rate that it is dispersing, merely at different locations. That is what limits the number of black holes in any region and also what limits the degree of distributed energy there is between the black holes. They keep each other in perfect balance because each stems only from the other. Without black holes there can be no dispersing from them and without dispersion there can be no black holes gathering the dispersed energy.

The system is necessarily perfectly balanced because each state is derived only from the other. So the system continues eternally.

if thermodynamics is correct, and both time and energy are infinite, shouldn't this have already happened? on the other hand, if time/space is infinite and energy is not, i can imagine a number of local distributions of energy within particular regions of space that are somehow isolated from others, in which case they running on their own entropy clock, so to speak. but again i'm no physicist so i may not even be posing the problem in the right way.

Apparently at one point James toyed with the idea of "local universes" with vast distances between them. That would allow for the appearance of living in a limited universe even though the space and the amount of energy are both infinite.

Once explained, to me it all seems much too obvious. It really doesn't seem like that big of a thing except that people keep wanted to promote their pet fantasies despite having no good reason to believe them.

People strive to maintain their bubbles of belief because only from those does hope arise and raise up.

[obsrvr524]

Since Sil raised the Hilbert's Hotel thing again, just briefly (please don't make a big distraction of it):

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests.

That scenario seems obviously flawed. If you do as it says, the final n+1 guest gets booted out a window. Of course you can add another guest if you just kick one out. Am I missing something?

EDIT: I found what I was missing. I thought it had said that the first hotel was finite. Instead it said that a finite number of guests were to be added to an infinite hotel. So the dumbness of the first portion is actually identical to the dumbness of the second portion where an infinite quantity is to be added.

The second part seems equally dumb:

It is also possible to accommodate a countably infinite number of new guests: just move the person occupying room 1 to room 2, the guest occupying room 2 to room 4, and, in general, the guest occupying room n to room 2n (2 times n), and all the odd-numbered rooms (which are countably infinite) will be free for the new guests.

The proposal here is that you leap frog guests infinitely through an infinite room hotel then add more. The problem with that is the same. If the infinite room hotel already had an equally infinite occupation, someone would still have to leave from the infinite hotel else all rooms will remain occupied throughout the infinite hotel. You can never take that last guest and move him into a vacant room because all of the infinity of rooms are totally occupied. And since there is no end room anyway, no one can be moved into that last room.

Can you add an inch to an already infinite rope? It has no end to add to and since it is already formed infinitely, there is no space to move one portion to another or to inject another inch into unless an equal portion is removed.

So far, this thing seems dumb, designed to keep simple minded people confused especially when adding the more complex math into the narrative..

Why is that "paradox" even noteworthy?

[Ecmandu]

Obsrvr,

You are correct in stating that infinity transcends time.

Yes, all the rooms are full.

Yes, it is absurd.

[Ecmandu]

Obsrvr,

You are correct in stating that infinity transcends time.

Yes, all the rooms are full.

Yes, it is absurd.

Mathematicians want it both ways, they want their convergent sets, but they also want time paradoxes

[Silhouette]

That means that you must be sincere. And that puts me in a situation where I have to weigh my sympathy.

I am sincere, but never wanted you to weigh or do anything with any sympathy in the first place, hence repeating over and over the truism "Arguments either hold or don't hold completely irrespective of their author and anyone's emotions."

You chose not to anyway, so good. We can continue discussing the actual content of the thread and finally bring an end to this whole ad hom charade of bringing in personal issues, emotions and political persuasion.

But using your method for multiplying such sums together would yield:

(a + b) x (c + d) =
a x c [=1] +
b x d [=1]
= 1 + 1 = 2

Not my method.

My method:

Now to perform some arithmetic:
infA ^ 2 = (1+1+1+...+1) * (1+1+1+...+1)

Time to sequentially multiply the terms as you do for multiplication of values in parentheses, let's see...
1*1 = 1, ok. 1*1 = 1 as well, let's keep going and what do we get?

Sequentially multiply the terms:
1st term in set one multiplied by 1st term in second one = 1
1st term in set one multiplied by 2nd term in second set = 1
1st term in set one multiplied by 3rd term in second set = 1
which would go on infinitely to get you (1+1+1+...) as you add each result - no need to add James' extra "+1" to give the illusion of a finite end to an infinite, endless sequence.
We could pretend the sequence reaches an end or just skip at any point to the next stage of:
2nd term in set one multiplied by 1st term in second one = 1
2nd term in set one multiplied by 2nd term in second set = 1
2nd term in set one multiplied by 3rd term in second set = 1
and so on, but this would also continue you on the same infinite addition (1+1+1+...) however you structure your approach.

Now, I actually predicted this wording could be misconstrued by somebody who wanted to misread it, so I clarified as much in my next post on the topic:

(a + b + c + ... + z)ⁿ = n₁aⁿ + n₂aⁿ⁻¹b + n₂aⁿ⁻¹c + ... + n₂aⁿ⁻¹z + n₃aⁿ⁻²bⁿ⁻² + n₄aⁿ⁻²bc + ... + n₄aⁿ⁻²bz + n₃aⁿ⁻²cⁿ⁻² + ... + n₄aⁿ⁻²cz + ... + n₃aⁿ⁻²zⁿ⁻² + n₂abⁿ⁻¹ + n₄abⁿ⁻²c + ... + n₄abⁿ⁻²z + n₄abcⁿ⁻² + ... + n₅abcz + ... + n₄abzⁿ⁻² + n₂acⁿ⁻¹ + ... + n₄acⁿ⁻²z + ... + n₄aczⁿ⁻² + ... + n₂azⁿ⁻¹+ n₁bⁿ + n₂bⁿ⁻¹c + ... + n₂bⁿ⁻¹z + n₃bⁿ⁻²cⁿ⁻² + ... + n₄bⁿ⁻²cz + ... + n₃bⁿ⁻²zⁿ⁻² + n₂bcⁿ⁻¹ + ... + n₄bcⁿ⁻²z + ... + n₄bczⁿ⁻² + ... + n₂bzⁿ⁻¹ + n₁cⁿ + ... + n₂cⁿ⁻¹z + ... + n₃cⁿ⁻²zⁿ⁻² + ... + n₂czⁿ⁻¹ + ... + n₁zⁿ

but when every element a,b,c etc. is 1, and every coefficient n can be broken down into 1s added to together, n can be any value and you still get (1+1+1+...+1)

Perhaps I should have added the bold and underline when I originally posted it, just to be sure, but it appears you were determined to miss this too.
See all those n terms with subscripts?
They're the result of simplying like-terms, which in the case of (1+1)(1+1) could have you representing (1+1+1+1) as (2+2), but they're all like-terms so you might as well fully combine like-terms and write (4) by what your example demonstrates, and both your example and mine would be equally correct, and in the case of (1+1+1+...)(1+1+1+...) you could also represent the result as either (n₁1+n₂1+n₃1+...) OR (1+1+1+...) and pretend the former is "a different order of infinity" or "deeper" than the latter, but in both finite and infinite cases they are just different representations of the same thing, one with some simplification and one without. As with the finite example, the representation does not affect the actual result nor does it affect the same failure to get a result because it infinitely diverges away from one.

But you know what, fuck it. Taking blame is the only language you understand that translates to "commitment" to having my mistakes pointed out if and when they are made, so I'll take full responsibility for my misleading wording making you think I made a 3rd grade elementary school mistake.

I shouldn't have even tried to back up my wording with quotes and demonstrations to prove the truth, because now you'll think I'm trying to dodge the truth because I'm dodging an opportunity to lose face in the wake of one of your accusations.

I would like to point out that providing proof to prove truth is not making excuses to dodge the truth, and the more losing of face is not lessening the degree to which you're dodging truth, but I am becoming increasingly aware that too many of my words are being wasted trying to manage your hunger to slander and debase me to "prove my commitment" rather than simply asking:

"Did you make this mistake? There is a chance you didn't and I misread, but the way I read it brought to my attention the possibility that you did."

I will try to lead by example, and hope you respond in kind.
So, I apologise for making you think you had to point out a 3rd grade elementary school mistake. It's my fault entirely. To continue this reformed approach, I hope it is to your liking:

Since Sil raised the Hilbert's Hotel thing again, just briefly (please don't make a big distraction of it):

I will endeavour to help keep this tangent as brief as possible, please accept any incompetence on my behalf should I fail to live up to your polite request.

You found the issue with your first objection, so we can move straight to the second objection:
The someone you say "would still have to leave from the infinite hotel" would always have another room to "leap frog" to, because it is infinite - this is the intention behind the analogy. There is no "last person in the hotel who would get "boosted out a window" for the same reason you realised about your first objection. There is no "all of the infinity of rooms", because would imply the encompassing of the "unencompassable".

I will refrain from addressing your accusations of dumb as this is unproductive.

You are correct that you can't add an inch to the end of an already infinite rope because it has no end.
You could cut the rope and move it apart to add an inch, because there is no end of the rope to bump up against any edge any more than there was before you cut it.

I humbly request you re-evaluate your analysis of both the hotel and rope paradoxes. You can be assured I will offer no ill will if you do. I would politely request in return you do not insist I have been making mistakes before respectfully asking and gracefully receiving explanation either for against any possible mistakes of mine, which I am sure are highly likely.
Ecmandu I also humbly request you do the same.

[Ecmandu]

Silhouette,

An infinity can be counted (all the rooms can be full) just not by a single person.

As a single person, there's no way I can count all the counting numbers BUT! With an infinite number of people counting one number each, yes, its countable (yes, all the rooms are occupied)

All +1 is a contradiction

[Silhouette]

i was under the impression that until the curvature of the universe is known - whether it is positive, negative, or flat - we cannot know if the amount of matter in it is infinite or finite. but admittedly i don't understand what any of this means as a physicist would (which i'm certainly not), and i learn this stuff through researching the consensus i find in the literature i read.

Learning by researching the consensus is nearly all a physicist can do, too - except they might also research what the consensus is not, and experimental physicists may even have access to the means to conduct their own tests to back up or disprove either consensus, non-consensus, or any new compelling hypotheses as yet not considered.

Like everyone else here, I'm not an experimental physicist, and I too am interested in deviating from the consensus just like obsrvr, as I sum up in this previous post from this thread, in the paragraph before I quote myself.
The consensus is that the universe is flat, following extremely precise measurement, and concluding that if it is perfectly flat now then it was always flat. As with all experimental data, there is a margin of error, and I understand there is a limit to the scope of the measurements taken.
I am interested in and arguing in favour of something that recently occurred to me to be parallel to debunking flat-earthers, but instead of having all evidence in my favour, I only have logical argument and only some evidence in my favour. I contend that the extrapolation of experimental evidence of "everything moving away from everything else" back to a singularity, with all matter and energy maximally condensed at some previous point in time (as is the scientific consensus), formerly fulfilled the conditions of maximum spacetime curvature (which experiment confirms to occur under the highest gravitational forces and under conditions of the highest velocities e.g. at the "big bang"). I am unaware of why these two pieces of experimental evidence aren't considered to be in conflict with one another, hence my hypothesis that the singularity had maximal spacetime curvature and the universe wasn't always flat, even though it appears to be now, a ridiculously long time after the event itself.

This is no doubt due to my own ignorance, but do you see the reasoning behind my point of interest? Not only does it seem justified to me, it also does away with the paradoxes of infinity and finitude, which Jakob and obsrvr are chasing. From the James quotes it reads as though he was too. I think they each go too far with the experimental evidence that they have to reject in order to justify their directions - including not least the rejection of the laws of thermodynamics and relativity. It appears their struggles are in part made harder by their respective treatments of infinity - which would be why the topic has been so prevalent so far in this thread. I think if these struggles are resolved, some progress could be made on the main topic of the thread.

The most fascinating part of my line of inquiry to me is the topology of extra dimensions. Spacetime curvature can be modelled as curving around at least one extra dimension to what people popularly understand as what we can see of spacetime. My guess is that mass is at least part of how we perceive this extra dimension, since mass curves spacetime along its axis (and not along spacetime axes - though this is how it is represented in drawing aids to help people conceive of the effect). Orbits are in fact moving straight relative to spacetime, but spacetime itself is curved around the mass to make the orbiting mass "go around" the mass it's orbiting.

I suspect not only the gravitational fundamental force, but also the electromagnetic force and its cousins the strong and weak nuclear forces are further dimensions that curve spacetime - but that seems to be the next step after fully comprehending the effect of mass on spacetime.
I also suspect that getting to the bottom of this will explain away notions of dark matter and dark energy. Perhaps antiparticles and the like will be explainable as some symmetry of the same particles curved back on themselves - but this really is getting into speculation as far as my knowledge goes.

if energy is infinite, and an infinite amount of time has existed, why isn't the density of matter perfectly distributed throughout all space by now? if thermodynamics is correct, and both time and energy are infinite, shouldn't this have already happened? on the other hand, if time/space is infinite and energy is not, i can imagine a number of local distributions of energy within particular regions of space that are somehow isolated from others, in which case they running on their own entropy clock, so to speak. but again i'm no physicist so i may not even be posing the problem in the right way.

KT pointed out the obvious in his post here, that if energy was infinite, everything would hurt rather a lot.

We can confirm without doubt that energy is not infinite by the very fact we are alive at all.
All experimental evidence shows that energy is conserved, as in the first law of thermodynamics.

So with infinite energy easily disproven, whether or not time could go on infinitely from now is not the same question as whether it has been going on infinitely so far.
Whether you go down my line of inquiry, or stay with the consensus, the universe can be determined to have a finite age so far.
So the universe hasn't had enough time to get to the point where matter is "perfectly distributed throughout all space by now".

Experimental evidence shows that all matter in the universe appears to be evenly distributed in all directions this far in. As such, the evenness of forces probably won't result in "local distributions of energy within particular regions in space that are somehow isolated from others"

Another reason why I like my position is because representations of the size of the universe so far show that it kind of "eased into" its current rate of expansion (which is actually still accelerating apart) in its early stages. This also fits with the curvature of spacetime infinitely easing into what seems to be the start of the universe. As such, time has been going on infinitely so far in a way, it's just been dilated so much while in the conditions of the singularity that it tended towards "taking forever" to actually "begin", and also without having to have stretched back in "absolute measurements of time" before a zero point of entropy. This is why I've been modeling such beginnings on the y = 1/x hyperbola, where y is spacetime curvature and x is entropy.

An interesting piece of experimental evidence is that it's speeding up its expansion. This disrupts the simplicity of my hyperbola modelling, but doesn't necessarily rule out its applicability to our humble beginnings as far as I know.

i don't dispute james's basic premise - before he goes on to draw all these philosophical inferences from it - that to exist means to 'affect', and that essentially there is no 'empty' space. i had believed this myself since democritus and parmenides.

I think it would be more accurate to say that "to experimentally detect" an affect confirms the existence of something, subject to our abilities to detect affect. A kind of Verificationism, that doesn't necessarily work the other way around: such that all that exists has affect. However, Falsificationism prevents this avenue from being explored, so existence being treated as affect and vice versa is merely "all we have to work with".

So any philosophies or ontologies based on "affect" presuppose Pragmatism. And why not, eh? Interesting how ancient greeks already considered such an approach.

[Ecmandu]

Silhouette,

An infinity can be counted (all the rooms can be full) just not by a single person.

As a single person, there's no way I can count all the counting numbers BUT! With an infinite number of people counting one number each, yes, its countable (yes, all the rooms are occupied)

All +1 is a contradiction

We crossed posts within seconds, so I don't know if you caught this.

I'd use it as a direct refutation of james INF^1+1 concept

[Silhouette]

Silhouette,

An infinity can be counted (all the rooms can be full) just not by a single person.

As a single person, there's no way I can count all the counting numbers BUT! With an infinite number of people counting one number each, yes, its countable (yes, all the rooms are occupied)

All +1 is a contradiction

All the rooms are full at the beginning of the thought experiment, so yes "all the rooms can be full".

The point is that even when they're full, they can counterintuitively still accomodate more people.

Counting doesn't appear to affect the thought experiment. Let's say an infinite number of people count one number each, counting up their one counted number that they each have is exactly the same as counting all the rooms without infinite people counting to 1 in the first place.

Think about what you're doing here. You're ready to claim addition even of finites as a contradiction before you'll claim that dealing with infinites is problematic...
You can add up a couple of finite things right now, go on try it - I think you've reversed your priorities here: with noble intent no doubt, you wish to explore the counterintuitive in counterintuitive ways, yes? But beware of incurring obsrvr's disfavour if you pursue these tangents too much.
James' infA has already been refuted by myself here by staying within perfectly intuitive realms - have you checked it out? obsrvr thinks he's found mistakes because of how I worded things, but I straightened them out here.

[Ecmandu]

Silhouette,

I already explained this when I said that people want their infinities both ways...

People want their convergent theories and they want their time paradoxes.

The slots that Hilbert is moving to in time, are already full through convergence.

Like I stated before:

All + 1 = a contradiction

You should always watch yourself when you use the word "counter intuitive", as it means: believe my contradiction (most of the time)

[Silhouette]

The slots that Hilbert is moving to in time, are already full through convergence.

Is there a way for you to better explain this "convergence" issue?

The point is that the new slots at Hilbert's Hotel are never actually full even though the hotel is supposed to be full, because each former occupant simultaneously moves from their room "n" to "2n". That person who was in "2n" has already simultaneously moved to the new occupant's "4n" and so on. The counter-intuition here isn't that the analogy is contradictory, it's that it reveals the contradictions that arise when dealing with infinities more easily when they're analogised.

I'm probably getting the wrong end of the stick with this guess, but are you suggesting that since you can't realistically coordinate actual guests to simultaneously time their movements that there's a time paradox? Perhaps you don't even like this simultaneity when dealing mathematically with the number line that the hotel is supposed to analogise? Needless to say, each occupant has to empty their hotel room before occupying the next (so they're temporarily definitely not full) or to abandon the hotel analogy that's just an aid to visualise the number line anyway, you could just acknowledge each point on the number line half way between each integer and optionally then double them all to get the same effect and keep things relating to integers only. Time is irrelevant unless you're trying to visualise the physical acting out of these processes, which misses the whole point, so both time paradoxes or time non-paradoxes have nothing to do with it.

Again, let's not take too long here, or all the non-tangential posts will get buried. If it's not clear to me what you mean in the next post, I might wait for others to catch up and respond first before getting back to you.

[Ecmandu]

What I mean, is that in Hilberts thought experiment, the rooms are already full. A completed infinity, a convergence.

Even by his own wording this is true.

But he ignores the implied convergence (that all the rooms are already full) and assumes a time paradox where it's impossible to exist.

So... it's not really a paradox, just faulty logic.

Think about it this way... hilbert makes the argument using odds and evens, but what's he supposed to do after that?!?!

Every three, every four!?!?

Now extend this to infinity!!

How are all the rooms not already full?? A completed infinity!

[obsrvr524]

Sil, my first thought was "wow, is this guy just way too dense or what" but on second thought I realized that you are another of those guys who changes his story once caught. But then on a third reading, I thought maybe he really did mean to do it right but he just doesn't realize that he has to add his iterative products, which gets me back to the "dense" notion. We will shortly find out.

But using your method for multiplying such sums together would yield:

(a + b) x (c + d) =
a x c [=1] +
b x d [=1]
= 1 + 1 = 2

Not my method.

Well that is exactly what you did unless you instead just didn't add your products. Since you didn't fully explain your method I don't know which screwup you enacted.

My method:

Now to perform some arithmetic:
infA ^ 2 = (1+1+1+...+1) * (1+1+1+...+1)

Time to sequentially multiply the terms as you do for multiplication of values in parentheses, let's see...
1*1 = 1, ok. 1*1 = 1 as well, let's keep going and what do we get?

Sequentially multiply the terms:
1st term in set one multiplied by 1st term in second one = 1
1st term in set one multiplied by 2nd term in second set = 1
1st term in set one multiplied by 3rd term in second set = 1
which would go on infinitely to get you (1+1+1+...) as you add each result

Good so far.

2nd term in set one multiplied by 1st term in second one = 1
2nd term in set one multiplied by 2nd term in second set = 1
2nd term in set one multiplied by 3rd term in second set = 1
and so on,

Still good (although I still suspect a switchup to hide the 1st mistake)

but this would also continue you on the same infinite addition (1+1+1+...) however you structure your approach.

And that is where you screwed up this time.

After your first sequence you had one infA derived as the product. After the second sequence you had another infA derived. And after each of the following infinity of sequences, you will have another infA.

When you sum those products, as you must do but didn't, you get infA * infA = infA^2.

Now, I actually predicted this wording could be misconstrued by somebody who wanted to misread it, so I clarified as much in my next post on the topic:

(a + b + c + ... + z)ⁿ = n₁aⁿ + n₂aⁿ⁻¹b + n₂aⁿ⁻¹c + ... + n₂aⁿ⁻¹z + n₃aⁿ⁻²bⁿ⁻² + n₄aⁿ⁻²bc + ... + n₄aⁿ⁻²bz + n₃aⁿ⁻²cⁿ⁻² + ... + n₄aⁿ⁻²cz + ... + n₃aⁿ⁻²zⁿ⁻² + n₂abⁿ⁻¹ + n₄abⁿ⁻²c + ... + n₄abⁿ⁻²z + n₄abcⁿ⁻² + ... + n₅abcz + ... + n₄abzⁿ⁻² + n₂acⁿ⁻¹ + ... + n₄acⁿ⁻²z + ... + n₄aczⁿ⁻² + ... + n₂azⁿ⁻¹+ n₁bⁿ + n₂bⁿ⁻¹c + ... + n₂bⁿ⁻¹z + n₃bⁿ⁻²cⁿ⁻² + ... + n₄bⁿ⁻²cz + ... + n₃bⁿ⁻²zⁿ⁻² + n₂bcⁿ⁻¹ + ... + n₄bcⁿ⁻²z + ... + n₄bczⁿ⁻² + ... + n₂bzⁿ⁻¹ + n₁cⁿ + ... + n₂cⁿ⁻¹z + ... + n₃cⁿ⁻²zⁿ⁻² + ... + n₂czⁿ⁻¹ + ... + n₁zⁿ

That self aggrandizing bit is just nonsense, a poor attempt. Now you're reminding me of James Comey who really should have kept his self aggrandizing mouth shut when he had the chance.

you still get (1+1+1+...+1)

only if you leave out the adding of the iterative products as I and your third grade teacher explained:

1 x (1+1+1...+1) = infA[1]

Then you take the next number in the first set, do the same thing, and add to the previous solution

1 x (1+1+1...+1) = infA[2]
infA[1] + infA[2] = 2 * infA

When you add those iterative products, as you must do but didn't, you get infA * infA = infA^2.

So, I apologise for making you think you had to point out a 3rd grade elementary school mistake. It's my fault entirely. To continue this reformed approach, I hope it is to your liking

You need to apologize for making the actual 3rd grade mistake and trying to demean others because of it. Stop being so arrogant and maybe you will learn past 3rd grade maths.

Since Sil raised the Hilbert's Hotel thing again, just briefly (please don't make a big distraction of it):

I will endeavour to help keep this tangent as brief as possible, please accept any incompetence on my behalf should I fail to live up to your polite request.

So much for it not being turned into a distraction.

All + 1 = a contradiction

That is exactly the point.

You can also realize the fallacy of the paradox by starting with a finite hotel size that is fully occupied. Then by making the hotel larger and larger, you can see that no matter how large it gets, there is never a way to shift all of the guests. That doesn't magically change just because the hotel became infinite.

You could cut the rope and move it apart to add an inch, because there is no end of the rope to bump up against any edge any more than there was before you cut it.

No you cannot. You are right that you don't have an end to bump against. Instead you always have an infinity of rope to bump against when you try to move it apart.

Apparently you just can't comprehend what infinity means. There is no end that you can freely add to. And "no end" does NOT mean that there is nothing past the end. Is this like a genetic thing with you? Clearly you aren't German, French maybe?

I humbly request you re-evaluate your analysis of both the hotel and rope paradoxes. You can be assured I will offer no ill will if you do. I would politely request in return you do not insist I have been making mistakes before respectfully asking and gracefully receiving explanation either for against any possible mistakes of mine, which I am sure are highly likely.
Ecmandu I also humbly request you do the same.

You need to be seriously far more humble and take your own advice. But I'm sure that you will never change.

I'm beginning to sense what James must have felt like. It's hard to believe that he did this for years.

[Silhouette]

Sil, my first thought was "wow, is this guy just way too dense or what" but on second thought I realized that you are another of those guys who changes his story once caught. But then on a third reading, I thought maybe he really did mean to do it right but he just doesn't realize that he has to add his iterative products, which gets me back to the "dense" notion.

Guy, I am going to ask your advice, because I don't seem to be able to get around a certain conundrum that I am in, and you present yourself so prestigiously that I figure you may know the answer.

What would you do if you presented a proof to somebody, any proof - doesn't matter what - and it was sound and valid but you wrote it in such a way that it was misconstrued by someone else.
This other person read the proof, and due to misconstruing the wording insisted that the proof was flawed at a basic level that only a poor and ill-advanced student would have made at the time they learned about it and still make to this day, when you, the author, aced this level of education and continued to ace the same subject far, far beyond that level.
Remember that this is you, and you're on the internet and you have no way to prove how wrong this other person's conclusions are about your past.
You recognise what's gone on and attempt to straighten things out, but this other person insists that are in fact at this low level of education, or at the very least that you made the error of someone at this low level of education and that this is reflective of the standard of other things you have also been saying on the topic. They insist that you are in fact attempting to cover up your mistake and that this is simply a reflection of the political leanings that they assume you have.
Again - you, as the person to whom I am asking this advice, are the person to whom these events are happening - what would you do when you have already tried to take the blame on yourself that you didn't sufficiently word the proof well enough?
Bear in mind that to this person, anything you say seems to be taken as more proof that you are denying the mistake you didn't make that they have judged you to have made, and your only intention is to advance a conversation that this proof is linked to.

Would you regard this person with respect? Would you continue to play their game of self-deprication just to get interesting content from them? Change the subject? Would you leave the thread and cease all contact with this person, reasoning that it has become impossible to gain intellectually honest interaction from them?
You are the one in this predicament - what would you do? Just out of interest.

[Silhouette]

things don't only affect, but are also being affected, along with some other concerns. On this level, there is no Newtonean symmetry, but rather a fundamental lack of symmetry which causes growth and diminishing: Nietzsche recognized this as will to power. Symmetry, and Newtonean physics, are a passive result of this on a large scale.

As usual, my concepts here are a well outside of the box of what has already been understood and incorporated by the experts, and I cruelly expect of my readers to make an effort.

What do you make of the kind of genius most famously associated with Feynman? "The great explainer" found a way to translate even the most complex of concepts into a language that anyone could understand. Do your abilities stretch this far too?

It would be cruel to yourself indeed to move to a foreign country where nobody knew your language, and insist only on speaking your own language.

Regardless of Newtonian physics, I don't find that modern physics neglects the fact that things are being affected as well as affecting other things. Is your quarrel only with Newton then?

If you take "infinite" as a concrete value, then it is easy. Infinite times infinite is infinite. So the answer would be yes.

This elementary well known example is meant as an indicator of the difference between following rules and thinking.

I salute you gentlemen, may you find a good path.

Well there's your issue right there - the "concrete" is defined as the real where the "infinite" is a hyperreal number.

You can distinguish between following the rules and thinking, but does this in the context of your example imply that logic is "following the rules" and "thinking" can be distinct from following the rules of logic?
Afterall, treating the infinite as no different from the finite is a logical contradiction.

Your substitution relies on the transfer principle, but the reals and hyperreals do not have identical behaviour.
It is true that you can operate on hyperreals the same as you can with reals, but statements about sets "may not carry over" as wikipedia says. Infinite series, as in your "inside the box" example, are sets.

Your intention is obviously to illustrate how 12l tends towards infinity "12 times quicker" than "l" - and it does, for however long you track the finite progression.
For all finite, non-zero values of "l" (the length of the edges of your box), regular boxes have 12 edges. At no point does 12l = l, i.e. 12 = 1.
The thing about infinite progressions is that you can't track them to the end, because there is no end.
With no end, neither is bigger nor smaller than the other, and neither "deeper" nor more shallow because infinities represented in two dimensions are just as undefined as those in one or more than two dimensions.
You can't compare the sizes of different things that are each undefined, because they have no size by defintion.

Obviously I'm just another idiot in the presence of your vastly superior, outside-the-box intellect, so I await for you to apply this ability to communication as Feynman did, and enlighten the student of their mistakes.