Entropy can be reset to initial or previous state

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

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.

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)

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.

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!

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.

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.

Good so far.

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

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.

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.

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

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

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.

So much for it not being turned into a distraction.

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.

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?

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.

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.

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?

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.

You miss the point.

The intention is not to ask you to accept that the rooms are already full, nor to ask you to accept that they aren’t.
It’s to demonstrate that since infinities would require you to accept both at the same time in contradiction with one another, there must be something strange that can occur when you deal with infinities.

It’s not the construction of the analogy that has faulty logic, the analogy is correctly set up to show that if you deal with infinities, you are going to encounter faulty logic.

Getting to infinity, so as to “complete” it requires that it has an end. A completed infinity is a contradiction in terms.

A COUNTABLE infinity is a completed infinity as I am using the term.

There are well ordered sets like the whole numbers

And there are scattered sets like when you count the rationals

I’m sorry, I’m throwing lots of jargon at you …

These are considered complete infinities (countable - meaning: enumerable in 1:1 correspondence)

Now… and I must say this: obsrvr: I don’t like your tone with silhouette. Not only that, but you are wrong that a rational number hotel cannot fit everyone in… if a hotel only has 34 rooms, then if you build a new room for every guest, and move everyone up one room, no contradiction occurs.

The problem is not in the finite, time based logic…

The question is “what happens at infinity?”

There are two possibilities:

1.) Either every room is full
2.) no rooms are full

This is how strange infinity is.

Hilbert didn’t understand the infinities he even claimed to undertstand that he claimed not to understand.

Obsrvr: give silhouette a break, he was very deferential to you

“the infinite is nowhere to be found in reality. it neither exists in nature nor provides a legitimate basis for rational thought. the role that remains for the infinite to play is solely that of an idea.” - david ‘the hitman’ hilbert

maybe try this for thought. when comparing the concepts of ‘finite’ and ‘infinite’ with the use of the terms in this thread, the concept of the infinite is thought of as a possible ‘set’, and therefore a concrete thing, like the concept of finite is being thought of here. but a ‘set’ is a completed object… in the sense that we can know where it begins and where it ends… and in this sense its a conceptual object. now here may be the problem; what you guys are doing is conceiving of a potential infinity… which is a collection that is increasing toward infinity but never gets there… as if it were a collection of definite and discrete members whose number is greater than any natural number. but therein lies the rub. if you can always add 1, you never finish the set of which you speak… and if it remains open, its not a set in the same way a finite set is conceived. the potential infinite set - which you are thinking is an actual infinite set - is really only indefinite, not infinite. the moment you finish it… make it a definitive object… it becomes finite. and yet until you finish it, you’re not speaking of a set or an object, but rather a kind of transcendental idea.

take the typical instance of the division of a distance. a finite distance can be subdivided into potentially infinitely many parts or sections. you can just keep dividing parts in half forever, but you will never arrive at an actual ‘infinitieth’ division or end up with a actually infinite number of parts.

any of you folks familiar with ghazali’s example of one of the absurdities of an actual infinity? it’s a swell thought experiment. kay so let’s assume eternity, and then let’s compare two beginningless series of coordinated events. imagine a solar system consisting of planets with coordinated orbital periods. so for every one orbit planet x completes, planet y completes 2.5 as many. the question is; if they’ve been orbiting for eternity, which planet has completed the most orbits? the correct mathematical answer would be that they have completed precisely the same number. but wtf? the longer they revolve, the greater the disparity between them becomes!

now if you understand what just happened here as a result of trying to construct an actual infinity rather than a potential, you’ll hear the same sizzling sound between your ears that you heard when you visited hilbert’s hotel (though i don’t think anyone so far but sil knows how to get there).

please, for the love of sam sneed, do some reading about ‘actual’ and ‘potential’ infinity. this is an understanding that supercedes what mathematics is telling you. you’ve got to wrap your brain around what the mathematics of infinity necessarily implies in the real world. if an actual infinite number of things were possible, hilbert’s hotel would be possible and not just a thought experiment to demonstrate the utter absurdity of actual infinities.

First I would want to know if you read the prior post and saw the error that you have been making. And if not…

That would depend on who I was trying to prove something to. It seems that James tried something that certainly would have worked on me, but not people who merely dodge the truth for sake of politics or perhaps ego. When debating an issue with me, I suggest two things:

  1. ask for point by point agreement. Avoid long complicated paragraphs where many potential disagreements are possible. Without the effort to prove anything, state one concern at a time and ask for agreement - “agree” or “disagree”. The first time I disagree, ask why.

In that way both parties learn much quicker and also learn ways to word things better. James had set up a forum to handle just that method of debating, “Resolution Debating” - seeking how far people can agree and precisely upon what they actually disagree. James liked to organize things. This one is on his list of “new-to-the-world” concepts although he spelled out much greater detail.

Note in the last post I examined and agreed to each step of your process until I found an error. That way you could know what to NOT argue with me about (although perhaps someone else). It brings focus on the “devil in the detail” to straighten out the disagreement or at least point to where more investigation is needed. If wording was the issue, now both parties would know it. “Light is the best disinfectant”.

It is like climbing a mountain. If you can make certain of each footing along the way, you are far more likely to get to the top, more quickly as well. And if either party makes a mistake it is far more quickly resolved before pride gets too involved.

Pride, politics, and stupidity forbids people from doing that, but you asked what I would do if I were you debating with me. When any of those 3 concerns are present, the other person simply refuses to respond and instead gives some distractive lecture. That’s when you know the kind of person you are dealing with.

So, in like kind, do you agree with the correction that I pointed out?
This one:

If you don’t agree, simply say, “I disagree”. If you have a simple reason, state it and ask for agreement. If the reason is complex, state only the beginning of it and ask if I agree.

It would save a whole lot of wall paper.

  1. When you start an ad hom battle, stop it by just taking your hits realizing that you started it.

I would have to disagree with that. Since he clearly did not understand the concept “infinity”, of course he would conclude that it doesn’t apply to reality.

I think that I have detected that to be where all of the confusion about infinity began.

Teachers describe infinity as a list that can always be added to, “no matter the number, you can always add 1”. But when they say that, some people think that infinity is this idea of always being able to add one. That isn’t really what the teacher meant. The teacher meant that if you try to get to the end, you can’t get there because there are always more numbers already accounted for, already there. You can always add 1 to whatever number you pick in order to find the next number that was already in the “set” of numbers. You are not adding to the set. You add to your position within the set. The set already includes ALL numbers potentially involved.

With an infinite set, 1 more cannot be added.

The hyperreals begin at infinity+ 1.

The correct mathematical answer would have been “2.5 times as many”. And of course that means 2.5 * infA.

It only doesn’t make sense to those to don’t understand infinity. And that seems to be a great many despite the math proofs.

Discuss!

A better, more precise word would have been “a filled infinity”, then he would have been right. The author stated that the hotel was completely filled.

I think in the maths, “countable” just means no irrational or endless numbers. The real numbers between 0 and 2 are not countable.

deferential?

I’m not sure what he meant by that but it seems to me that the value 2/3 is something that exists in reality and also has a precise mathematical extension = 0.666… So I don’t see the contradiction.

Again “0.666…” is a proposition that seems to “have sense”.

The whole thing appears to be someone wrongly criticizing someone who was wrong. But since I don’t really know those players nor some of the words they use, I’m just guessing.

That’s not what Wittgenstein is talking about.

Even 0.666… can only be expressed finitely

That’s what he’s talking about.

He only says we can believe what we can see, and discards the entire human experience of inferential proofs.

This is what I mean by that:

To Wittgenstein, the counting numbers are not infinite, they are only as far as we actually count them.

If we never counted it; it doesn’t exist, even in imagination.

Of course, all of our inferential proofs of infinity are derived from imagination.

Wittgenstein has no discourse on imagination.

believe me, bro, i’m not either, but i’m trying to figure this shit out.

yes, ‘2/3’ is a symbol extended in space, and if included in a closed series of calculations, it would be part of a finite set. this statement has mathematical extension. the difference is, you can’t call a set ‘infinite’ and at the same time give it extension, because in performing the infinite, i.e., endless divisions, all you’re giving extension too are the rules of calculation, recursively; divide, and again, and again, and again, etc. being open ended like this it is only intensional and a concept that is categorically different from extension. i can see more than just a rule extended when i see a finite set; i see the form of calculation and the product of it. but in conceiving an infinite set, i only observe the rule and not the product… for there can’t be an infinite set to observe… only the endless process of division, which is only the expression of a rule.

of course, but that’s not an infinite mathematical proposition.

consider this question. a math student performing the task of dividing, hands his paper to the teacher and asks; ‘is it infinite yet?’

how does the teacher answer? he cannot say ‘yes, the set is infinite’ and produce from that statement the same syntactical meaning as he would had he looked at a completed set of calculations and answered ‘yes, the set is finite’. now he could say ‘no, but it would become infinite if you divided forever’. here, it is theoretically and logically possible to divide forever, so the rule of division is extensional insofar as it is sensible, but the product of following that rule would never be extensional. only intensional and recursive.

infinite calculation could never produce a list. it only expresses a mathematical law by intension. one doesn’t observe infinity, but one can do it… or i should say, ‘approach’ it. thus lies the distinction between actual and potential infinity. one mistakes the process of listing with a list itself… one does the rule and then mistakes it as being a product. that erroneous dualism mentioned above that’s to blame for the battle between realists and anti-realists in mathematics.

I have no education on Wittgenstein (even have trouble getting his name spelled correctly) but if what you say is a correct representation of what he actually meant (and I will never have the time to find out), I would say that he seems to be missing the point in having a mind. And I do know that to be a common problem. It is something politically promoted to ensure an ignorant population. And that tactic is as old as the hills.