Moderator: Flannel Jesus
Silhouette wrote: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.
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.
promethean75 wrote: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.
promethean75 wrote: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.
promethean75 wrote: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.
promethean75 wrote: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.
promethean75 wrote: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?
obsrvr524 wrote:Still no commitment.
Too predictable.
obsrvr524 wrote:Now, while Sil is figuring out how to multiply sets, anyone want to get back to the topic?
So what is that evidence that energy is finite?
Silhouette wrote: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...
promethean75 wrote:i was under the impression that until the curvature of the universe is known
promethean75 wrote: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?
promethean75 wrote: 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.
wikipedia wrote: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.
wikipedia wrote: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.
Ecmandu wrote:Obsrvr,
You are correct in stating that infinity transcends time.
Yes, all the rooms are full.
Yes, it is absurd.
obsrvr524 wrote:That means that you must be sincere. And that puts me in a situation where I have to weigh my sympathy.
obsrvr524 wrote: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
Silhouette wrote: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?
Silhouette wrote:(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)
obsrvr524 wrote:Since Sil raised the Hilbert's Hotel thing again, just briefly (please don't make a big distraction of it):
promethean75 wrote: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.
promethean75 wrote: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.
promethean75 wrote: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.
Ecmandu wrote: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
Ecmandu wrote: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
Ecmandu wrote:The slots that Hilbert is moving to in time, are already full through convergence.
Silhouette wrote:obsrvr524 wrote: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.
Silhouette wrote:My method:Silhouette wrote: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
Silhouette wrote: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,
Silhouette wrote: but this would also continue you on the same infinite addition (1+1+1+...) however you structure your approach.
Silhouette wrote: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:Silhouette wrote:(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
Silhouette wrote: you still get (1+1+1+...+1)
obsrvr524 wrote: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
Silhouette wrote: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
Silhouette wrote:obsrvr524 wrote: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.
Ecmandu wrote:All + 1 = a contradiction
Silhouette wrote: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.
Silhouette wrote: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.
obsrvr524 wrote: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.
Jakob wrote: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.
Jakob wrote: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.
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