6
   

Math of infinity

 
 
Cyracuz
 
  3  
Reply Fri 9 Mar, 2012 01:08 pm
@dalehileman,
Quote:
How can its meaning or value have any bearing whatever on the subject of the thread


It is relevant. You see time as a property of the universe. I see it as a property of perception.
dalehileman
 
  0  
Reply Fri 9 Mar, 2012 02:21 pm
@Cyracuz,
Thank you Cyr for that observation but we’re pretty much OT so please see

http://able2know.org/topic/185959-1

Perhaps our evident disagreement is largely semantic
0 Replies
 
carnaticmystery
 
  0  
Reply Wed 16 Apr, 2014 11:28 pm
@dalehileman,
your analogies make no sense. even in the small universe with 3 particles, they will never be in the same locations exactly, especially because no particle in the universe can be localised exactly. furthermore, with every unit of time that passes, the particles themselves undergo qualitative changes, aging, they are no longer the exact same particles themselves. for every particle, the possibility of smaller subparticles exists, and the forces acting on them are unknown. therefore, we are faced with a scenario where there are infinite possible forces acting on any given particle, at all times.

given that a particle can never be in an exact same space as it was before (tiny vibrations move particles a tiny bit), and it can only ever be existing at one point in time, there is never a possibility of repeat scenarios.

dalehileman
 
  0  
Reply Thu 17 Apr, 2014 12:07 pm
@carnaticmystery,
Quote:
...your analogies make no sense. even in the small universe with 3 particles, they will never be in the same locations exactly,
True Car but rereading the OP you'll note,

"...or positions so close as for the difference to be immeasurable…"

Quote:
……. aging, they are no longer the exact same particles themselves……..
Don't have to be. Only so can't tell 'em apart

Quote:
……... there is never a possibility of repeat scenarios.
Suppose however that these three particles are so close in substance and position that after sepoctillion ^ sepoctillion ^ sepoctillion successive Big Bangs their position and appearance is so close to the original as for the difference to be undetectable. So given forever, won't this alignment, a near-identical Universe, will happen an infinite number of times

Thus we have an infinite number of repetitions of Dale sitting here in the Mojave Desert chatting with Car at some distant site; or given an infinite Universe, happening at this very moment

With the closest (however far apart in distance or time), a difference in the foregoing semicolon where the dot is slightly lighter in tone

If you'll return to the OP, Car, you'll note my remark to the effect how unlikely such a scenario to the Intuition, my hope that an arithmetically knowledgeable participant might demonstrate a flaw in my math or reasoning
Ding an Sich
 
  1  
Reply Thu 17 Apr, 2014 08:51 pm
@fresco,
fresco wrote:

Georg Cantor, celebrated mathematician of infinity, ended up in a mental institution. Watch out you guys ! Smile


So? What's your point?
carnaticmystery
 
  0  
Reply Fri 18 Apr, 2014 01:40 am
@dalehileman,
my point is that both space and time can be subdivided infinitely, making the possibility of absolute mathematical equivalence impossible between any 2 objects. whether a human can detect the difference or not is irrelevant, mathematically speaking.

regarding multiple big bangs, my understanding is that multiverse theories suggest that they do not actually occur in linear time successively, because the big bang point lies outside of 'time'. so actually, the complete implosion of the universe would lead to zero matter occupying zero space with zero time happening. then to say it 'happens again' is also assuming some outside observer who is able to view successive universes, but this is not true according to science. so the multiple big bangs are happening 'simulatenously', creating a multiverse of infinite universes with all possible particle locations.

so i don't think its counter intuitive to say that there would be universes with near-exact copies of everything. multiverse theories suggest that a universe exists for every single possibility for particle locations. this means a separate universe exists for every single possible choice you could have ever made in your life, because if that particle movement was possible, then it will happen given infinite 'time', as you say, or infinite universes happening simultaneously.
fresco
 
  1  
Reply Fri 18 Apr, 2014 01:55 am
@Ding an Sich,
Maybe "the point" is merely to provide a catalyst for "Ding to get at fresco" ! Mr. Green
0 Replies
 
fresco
 
  1  
Reply Fri 18 Apr, 2014 02:25 am
@Ding an Sich,
Seriously though, I suggest anyone genuinely interested in the mathematics of infinity needs to consider the proof of Field's Medalist Paul Cohen: that there both IS and IS NOT an "intermediate infinity" between the two infinities defined by Cantor. In my opinion, this finding has philosophical implications for the limits of logic and set theory, and feeds into an ontological discussion about the nature of existence.
http://www.scientificamerican.com/article/infinity-logic-law/
dalehileman
 
  0  
Reply Fri 18 Apr, 2014 11:28 am
@carnaticmystery,
Quote:
my point is that both space and time can be subdivided infinitely…….whether a human can detect the difference or not is irrelevant, mathematically speaking.
But it isn't. The basic q is, given forever or in an infinite Universe using present mathematical tools, how much alike can two universes be, however far separated in time or distance

Quote:
regarding multiple big bangs,….do not actually occur in linear time…...the big bang point lies outside of 'time'.
Thanks Car for explaining that, and as a sheer amateur in the field I'm at a loss to argue. Nonetheless I don't think we yet know enough to dismiss sequential Universes

Quote:
….so the multiple big bangs are happening 'simulatenously', creating a multiverse of infinite universes with all possible particle locations.
Okay then, but (as I said) the infinite Universe is just as troubling as the sequential one because it suggests an infinite number of nearly identical copies--maybe at this very instant

Quote:
….so i don't think its counter intuitive……...as you say, or infinite universes happening simultaneously.
Perhaps not to you, Car. I'd defend mine but as you're plainly aware, one can't usually rationalize the intuitive

It might be for instance that there's something wrong with the idea of "forever" and/or "infinite", an obscure mathematical error in the realm; maybe as Fres says above,

Quote:
there both IS and IS NOT an "intermediate infinity" between the two infinities defined by Cantor.
,…whatever that means

I have my own very vague theory suggesting that there might be different "sizes" of infinity, leading to the conclusion that two Universes can't even be remotely similar; but again don't ask me to uphold the notion


But thanks Car for another opportunity to shoot off my old mouth
carnaticmystery
 
  0  
Reply Sat 19 Apr, 2014 02:46 am
@dalehileman,
Quote:
The basic q is, given forever or in an infinite Universe using present mathematical tools, how much alike can two universes be, however far separated in time or distance

seems an insignificant question. obviously any 2 universes could be as identical as can be perceived by an observer. but since there is no possible observer who can perceive 2 separate universes, this is not possible anyway. the idea that these alternate universes even 'exist' doesn't make sense, because we can only conceive of existence within this space-time continuum, whereas the multiple universes are in separate dimensions.
Quote:
Nonetheless I don't think we yet know enough to dismiss sequential Universes

i disagree, calling them sequential means you are assuming some other existence, outside it all, which is observing the sequence. if so, what is this existence? nothingness? god? these are all beliefs, but pure science dictates that the big bang point lies outside the space time continuum.
Quote:
Okay then, but (as I said) the infinite Universe is just as troubling as the sequential one because it suggests an infinite number of nearly identical copies--maybe at this very instant

yes, but again, it is trying to conceive of existence outside this space time continuum. all these multiverse ideas are just theories, there is obviously no way to prove other dimensions and universes 'exist'. it is just mathematical extrapolation.
Quote:
I have my own very vague theory suggesting that there might be different "sizes" of infinity, leading to the conclusion that two Universes can't even be remotely similar; but again don't ask me to uphold the notion

i think the very idea of multiple universes is quite irrelevant. it is just scientists trying to push the limits of space and time. the reason intuition goes against understanding infinite, is because intuition is part of your survival mechanism in your brain. if you think you have 'understood infinite', and you know that infinite universes are there with infinite 'yous', you might just kill yourself for fun. haha. so i think some intuition in you tells you that this lifetime is very special, and another like it seems impossible. lol
dalehileman
 
  0  
Reply Sat 19 Apr, 2014 10:55 am
@carnaticmystery,
Quote:
...whereas the multiple universes are in separate dimensions.
However unlikely a prop having no supporting evidence, my speculation requires only a single Universe

"...how much alike can two universes be,…" is misstated. I should have said maybe "two cosmoses" intending them to be separated by time or distance

Quote:
Nonetheless I don't think we yet know enough to dismiss sequential Universes

Quote:
i disagree, calling them sequential means you are assuming some other existence, outside it all, which is observing the sequence.
i disagree. If something isn't sensed that doesn't mean it doesn't exist


Quote:
…... infinite Universe is just as troubling as the sequential one because it suggests an infinite number of nearly identical copies…..

Quote:
yes, but again, it is trying to conceive of existence outside this space time continuum.
Again Car I apologize for having conveyed that impression. A single Universe provides enough complexity for now

Quote:
... so i think some intuition in you tells you that this lifetime is very special, and another like it seems impossible. lol
As I've implied, it seems reasonable to conclude that the least evidence for a prop the less likely, and no evidence at all, most
Ding an Sich
 
  1  
Reply Sat 19 Apr, 2014 01:01 pm
@fresco,
fresco wrote:

Seriously though, I suggest anyone genuinely interested in the mathematics of infinity needs to consider the proof of Field's Medalist Paul Cohen: that there both IS and IS NOT an "intermediate infinity" between the two infinities defined by Cantor. In my opinion, this finding has philosophical implications for the limits of logic and set theory, and feeds into an ontological discussion about the nature of existence.
http://www.scientificamerican.com/article/infinity-logic-law/


I'll check it out. Busy right now finishing up my Physics BS (I graduate this semester), so I can't take any real time to investigate this stuff. Thanks for the link. Very Happy
0 Replies
 
Krumple
 
  2  
Reply Sat 19 Apr, 2014 01:06 pm
@dalehileman,
If you are getting infinities in math or physics, generally you have made an error somewhere. Infinities really shouldn't exist and more than likely they don't exist. I know cosmologists like to say black holes have infinite density but it doesn't make any sense if black holes can have various masses. I think it's an error in understanding what the black hole is and I bet the problem will be solved in the future.

There was a time when the speed of light was assumed to be infinite. That was proven not to be the case.

There was a time when the size of the universe was assumed to be infinite but that was also proven not to be the case.

Infinities really only exist as an abstract concept without the human imagination.
dalehileman
 
  0  
Reply Sat 19 Apr, 2014 04:27 pm
@Krumple,
Quote:
If you are getting infinities in math or physics, generally you have made an error somewhere.
I'm sure you're right Krump though not sure what you mean

Quote:
Infinities really shouldn't exist and more than likely they don't exist.
I'd agree though only on basis of intuition

Quote:
I know cosmologists like to say black holes have infinite density but it doesn't make any sense if black holes can have various masses.
At the start of the Big Bang we might have had a particle of infinite density but zero diameter

Quote:
I think it's an error in understanding what the black hole is and I bet the problem will be solved in the future.
Yes I think we'll get closer to the answers

Quote:
There was a time when the speed of light was assumed to be infinite. That was proven not to be the case.
An infinite light speed, or at least one much greater than c easily explains almost all the mysterious relativistic effects, suggesting an alternative way of interpreting our measurements based on another way of looking at time-at-a-distance

Quote:
There was a time when the size of the universe was assumed to be infinite but that was also proven not to be the case.
That's news to me Krump. Wonder if you might have a link to this discovery

0 Replies
 
carnaticmystery
 
  2  
Reply Sun 20 Apr, 2014 03:54 am
@dalehileman,
Quote:
i disagree. If something isn't sensed that doesn't mean it doesn't exist

it is not about sensing. you are talking about the entire universe, which is by definition 'all of existence'. if it is all gone, then there is no more existence. anything you can define as existence is by definition GONE. but you want to say that something still exists, time is still going on in nothingness? existence is still there, if it is all gone?

you are trying to separate the ideas of matter and awareness. you believe that awareness is a separate concept, and because of it, you can use your awareness to predict what would happen if there was no matter. but awareness evolved out of matter, and it is likely a property of all matter.
Quote:

I should have said maybe "two cosmoses" intending them to be separated by time or distance

again, doesn't make sense. cosmos is synonymous with universe, and is just meant to define all of existence. anything separated by time or distance is necessarily within this one single cosmos or universe. to 'try' and go beyond this, you need to go beyond space and time obviously. so the theorists decide that a multiverse may 'exist' beyond this.

if you are trying to say is there a clone milky way galaxy out there, or will there ever be within this universe? i would say definitely not, although similar galaxies may be possible. but think about it, each single form of life on our planet was created by unique conditions. the chances of it all happening the same way to create exact copies is basically impossible. it would require much longer than the estimated life of the universe, to happen. and again, this is just for a 'similar galaxy'. an absolutely mathematically exact copy is scientifically impossible, just like no 2 particles or objects can ever be exactly the same even within our observation. any atom, if observed at a single point in time, would have a unique electron configuration and therefore be a unique particle in the entire universe.



dalehileman
 
  0  
Reply Sun 20 Apr, 2014 11:44 am
@carnaticmystery,
Quote:
by definition GONE. but you want to say that something still exists, time is still going on in nothingness?
By no means Car. But I don't remember having endorsed the idea of nothingness, you'll have to refresh an old fella's mem

Quote:
you are trying to separate the ideas of matter and awareness. you believe that awareness is a separate concept,
I didn't realize that was what I was trying to do

Quote:
and because of it, you can use your awareness to predict what would happen if there was no matter. but awareness evolved out of matter, and it is likely a property of all matter.
Yes Car I'm sure it is but still don't comprehend what it was I asserted to which you take exception

Unless you have reference to my particle of infinite mass but zero diameter and yes, that's a pretty wild idea, I was merely advancing it half-facetiously

Quote:
I should have said maybe "two cosmoses" intending them to be separated by time or distance

Quote:
again, doesn't make sense. cosmos is synonymous with universe,
Point well taken Car, I should have said something like "the Visible Universe" the logic of which which of course you can still contest. What I was trying to get across was the q whether in a single infinite Universe one might find an infinite number of these huge collections of matter essentially identical

Quote:
if you are trying to say is there a clone milky way galaxy out there, or will there ever be within this universe?
Not just the Milky Way but an infinite number of very nearly identical other collections of galaxies like the one we can presently see most of, each with a Car and a Dale discussing their existence

Quote:
i would say definitely not
Me too tho of course I can't defend the notion

Quote:
it would require much longer than the estimated life of the universe,
That's if there's only one Big Show. In the case of repeated Bangs as I mentioned somewhere above, eventually we should get an exact copy, then if we wait long enough, another, etc ad infinitum

On the other hand if there's only this single production but it's infinite, then (forgive some repetition) all those nearly identical copies are occurring simultaneously

Quote:
the chances of it all happening the same way to create exact copies is basically impossible.
Precisely the q before the house: Why


Infinity is underestimated. Thus if anything that can happen, will happen……..

My point being that intuition objects to the idea, suggesting a sort of subliminal reasoning process either (1) rejecting our mathematical assumptions about infinity or (2) showing that the Universe probably can't be infinite
carnaticmystery
 
  1  
Reply Mon 21 Apr, 2014 04:05 am
@dalehileman,
Quote:
By no means Car. But I don't remember having endorsed the idea of nothingness, you'll have to refresh an old fella's mem

to endorse the idea of a big bang, you must endorse the idea of nothingness, or as you put it, infinite mass contained in zero space.
Quote:
Point well taken Car, I should have said something like "the Visible Universe" the logic of which which of course you can still contest. What I was trying to get across was the q whether in a single infinite Universe one might find an infinite number of these huge collections of matter essentially identical

again, i feel that you have a visual idea of infinite space, and our 'universe' being just the collection of matter within it. but science points to the fact that space is also included within this universe, ie, space can never be separated from matter, and it also implodes with the matter, leaving actual 'nothingness'. any collections of matter within infinite space are by definition, part of this single universe.
Quote:
Not just the Milky Way but an infinite number of very nearly identical other collections of galaxies like the one we can presently see most of, each with a Car and a Dale discussing their existence

Quote:
That's if there's only one Big Show. In the case of repeated Bangs as I mentioned somewhere above, eventually we should get an exact copy, then if we wait long enough, another, etc ad infinitum

i feel you misunderstand the idea of the big bang, theoretical as it is. there is no possibility of repeat big bangs within one universal cycle! the entire universe is one event, including all of space and time. the very idea of 'repeat' big bangs is as i said a multiverse theory which goes beyond time, and is all happening simultaneously. ie. the single nothingness has the potential to explode into infinite combinations of particles, and always does this infinitely.

from this perspective, of course there could be billions of universes exactly like ours, differing by maybe only one particle. but none are existing within this space time continuum.

Quote:
On the other hand if there's only this single production but it's infinite, then (forgive some repetition) all those nearly identical copies are occurring simultaneously

yes, i agree with this. but in my consciousness, at least, i am unable to ever access any other dimension than this one! haha. so it doesn't matter that theoretically there are infinite other universes with clones of me and you.

dalehileman
 
  0  
Reply Mon 21 Apr, 2014 12:14 pm
@carnaticmystery,
Quote:
to endorse the idea of a big bang, you must endorse the idea of nothingness,
I don't see why. I can easily suppose the Big Crunch gives us a shrinking "ball" of increasing density ending with very small but very massive blob of uniform composition for the next Big Bang

But now let me see if I can summarize what you [Car] seem to be asserting: (discounting other simultaneous parallel dimensions) That it all starts with nothing, then nothing becomes something; but it only happens once, our Big Crunch ending in nothing

Quote:
again, i feel that you [Dale] have a visual idea of infinite space…...space can never be separated from matter, and it also implodes with the matter, leaving actual 'nothingness'…….
Yes Car, no, you're obviously more deeply into this sort of thing. By "implodes" am I right you mean the Big Crunch, and have I guessed correctly you maintain Science has now confirmed that it finally vanishes entirely

(Almost everyone else assures me there won't be a Big Crunch; you and I seem to be alone with it; such a sad state of affairs my intuition anyhow can't support)

Quote:
any collections of matter within infinite space are by definition, part of this single universe.
Yes I had understood that space was included within the Big Crunch, that there's nothing outside it because there simply isn't any outside

Quote:
ie, space can never be separated from matter, and it also implodes with the matter, leaving actual 'nothingness'.
Yes I had always understood the inseparability of space and matter, as you say, but the notion that its final state truly is "nothingness" leaves me wondering

Quote:
any collections of matter within infinite space are by definition, part of this single universe.
….and wondering if this last phrase possibly a typographical, it seems somehow contradictory

Quote:
theoretical as it is. there is no possibility of repeat big bangs within one universal cycle!
Again Car you're 'way ahead of me. While I'll agree time slows down during the Big Crunch and resumes at the next Big Bang, I don't see why two successive Universes can't be called sequential

Quote:
could be…... universes exactly like ours, differing by maybe only one particle. but none are existing within this space time continuum.
Still, once more again, forgive any repetition, it seems so far that the less evidence for something the less likely; and no evidence at all, the least

So far all the evidence seems to point to a single finite Universe, and I can only speculate in addition to what's known by suggesting successive productions forever. I have to admit however this still suffers the speculation of near-identical reps

…..countering with a yes perhaps weak contention that there's something wrong with our concept of the math, the original purpose of my OP

Quote:
On the other hand if there's only this single production but it's infinite, then (forgive some repetition) all those nearly identical copies are occurring simultaneously

Quote:
yes, i agree with this. but in my consciousness, at least, i am unable to ever access any other dimension than this one…..
Again, at some risk of repetition, once more, revisiting, I see no need for "other dimensions"



dalehileman
 
  0  
Reply Mon 21 Apr, 2014 12:15 pm
@dalehileman,
Car can I possibly infer from the lack of participation that we're both terribly screwed up
carnaticmystery
 
  1  
Reply Tue 22 Apr, 2014 04:00 am
@dalehileman,
Quote:
(Almost everyone else assures me there won't be a Big Crunch; you and I seem to be alone with it; such a sad state of affairs my intuition anyhow can't support)

even i am not 'with it', haha, i told you these are just mathematical extrapolations. no human can predict what will happen to the universe in such huge time scales, when they will only ever exist for a hundred odd years.
Quote:
any collections of matter within infinite space are by definition, part of this single universe.

Quote:
….and wondering if this last phrase possibly a typographical, it seems somehow contradictory

why? i am simply saying, any matter existing in any time scale is still part of this single universe. when i talk about big bang/crunch theories, they are necessarily outside of this dimension, they cannot possibly occur as an event in time, but must be a more primary causative factor for both space and time. if something caused matter and time to exist, can it be said to happen 'at a time'? the mind can't conceive of it.
Quote:
While I'll agree time slows down during the Big Crunch and resumes at the next Big Bang, I don't see why two successive Universes can't be called sequential

time slowing down is only the points near the big bang/crunch. the actual point of it lies outside of space and time, and cannot be assumed to just be a normal point of time, where infinite mass exists in zero space. that is impossible obviously, and this is why something beyond space/time must be considered to make it possible.
Quote:
So far all the evidence seems to point to a single finite Universe, and I can only speculate in addition to what's known by suggesting successive productions forever.

there is no evidence of our universe being finite. all are theories only. successive productions forever is not at all what maths or science points to. advanced maths and science points to the fact that infinite 'space time continuums' exist on a background of infinite nothingness, which is beyond space and time.

now in this nothingness, beyond space and time, you cannot say that a sequence of events are occurring, because they are not. there is no space for events to occur, or time for them to happen. as soon as space and matter is 'created', time starts. now, the argument for how 'something' could come out of 'nothing', is again endless, but if you want to follow what science points to, then that is it.

Quote:
then (forgive some repetition) all those nearly identical copies are occurring simultaneously

Quote:
yes, i agree with this. but in my consciousness, at least, i am unable to ever access any other dimension than this one…..

Quote:
Again, at some risk of repetition, once more, revisiting, I see no need for "other dimensions"

there is a need for them. you are talking about identical copies of universes existing simultaneously, ie right now, then 'where do they exist'?. they cannot exist in any of the 'space' coming from this universe. so if they do 'exist', they must be in a space in another dimension of existence, which doesn't apply to our experience.

you are simply saying that time is the ultimate dimension, and anything that can ever 'happen', or 'exist', is all under the one infinite time. and therefore, it is all a sequence of infinite universes. but science does not really point to this at all, thats why time is simply identified as the fourth dimension, with many more possible.

 

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