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Math of infinity

 
 
Reply Sat 3 Mar, 2012 03:47 pm
The ideas of infinity and forever are troubling, both underestimated if not unimaginable: If anything that can happen, will happen, then everything happening at this moment must happen again, in minute detail

Incidentally I’m not the first to propose this, it’s very difficult today to come up with an entirely new idea. But maybe I can restate it in different words with the suggestion there’s something more to Intuition than Freudian subconscious ruminations

Suppose the Universe were the size of a pingpong ball and contained only three particles madly bouncing around inside. Once in a while they would assume the very same position they had assumed in the recent past or positions so close as for the difference to be immeasurable: say once a month or even once a year, whatever a year might mean under these circumstances

Anyhow increase the number of particles to four and its size to that of an apple so now it typically takes a century. Yet the condition is inevitable, occasionally taking say, 5000 years. Yet given forever it will of course happen repeatedly

Now incrementally increase the size of the sphere (yes I realize it can’t actually be called spherical), every time decreasing the probability of an “exact” repetition. Perhaps by the time it has grown to the size of a basketball and containing 10 particles the average time between replications mounts to a quadrillion years

Yet near-exact coincidence will continue to happen more or less indefinitely. So let’s expand it to the size of the known Universe, with a proportional increase in the number of particles. Yet forever is a long, long time…..

It strains the credulity and insults the Intuition to assume that someday in a future so many years ahead that we cannot express it with today’s numbers, to assume a universe that a dalehileman will be contributing to an identical a?k at 12:42 PM his time, and that the only difference between then and now is that one hair on Gingrich’s head will be 0.00000000000000012 inch—or one quantum unit—longer

Of course if the Universe is infinite then there must be an infinite number of identical Milky Ways differing each from its nearest neighbor by only that much—simultaneously—this very instant

So, Intuition insists, this just can’t be, maybe (1) my math is wrong, maybe there’s some size so big that above which no near-repetitions can occur. But why should there be such a dividing line

(2) Either forever or infinity are flawed concepts and thus the universe must be finite, a perfectly rational and plausible assertion. But how about forever: the ideas of a beginning and end entail all sorts of contradictions and paradoxes almost as troubling to the Intuition as all those exact copies above

(3) The rules change with each successive Big Bang. Okay but even given an infinite number of each physical constant wouldn’t there still be large numbers of pretty close copies

(4) There’s a God who can do the impossible and incomprehensible, an infinite number of Milky Ways each radically different from the rest
 
georgeob1
 
  1  
Reply Sat 3 Mar, 2012 05:13 pm
Most of the available evidence strongly suggests the universe is finite in both space and time.

There is a cardinality to infinite sets - some are denser than others. The hierarchy starts with so-called "countable infinities" i.e. those that can be put in a one-to-one correspondence with the set of integers. There are many manifold sets of uncountable infinities. For example, the set of real numbers includes infinitely many numbers over any measurable interval, and there is an uncountable number of such intervals. It continues with the set of lines that can be drawn between any two points in a plane which is "larger" or denser still.

The point here is that your musings need to be more precise if you really wish to explore these issues,
markr
 
  2  
Reply Sat 3 Mar, 2012 05:53 pm
@dalehileman,
Your example doesn't account for an ever-expanding universe. If the boundaries (as defined by the extremes of the matter contained within) are continually expanding, repetition is impossible.
JustAnotherGuy
 
  1  
Reply Mon 5 Mar, 2012 12:30 am
@dalehileman,
Another way to sum up what you may be trying to voice is the Many Worlds Theory, the fact that anything that can and possibly will happen will and already has. Many-Worlds implies that all alternative futures have happened, will happen or are happening. The idea that each choice has a branch point which leads to different 'worlds' or 'universe', example is that you come to a crossroads where you can turn left or right, if you believe in the concept or theory of infinity (note the theory of infinity, and it is a theory, can not be proved or disproved), will lead to two different 'worlds'. While you may choose left in this world, life or however you may describe it, somewhere else in universe you have chosen right, and in another you may have chosen left but decided to turn back and go right. At that one moment all possible options or alternative choices have been, will be or are being taken. A better way to explain this is to look at the wiki page as it can explain ten fold better than me and has all the references you can want.

http://en.wikipedia.org/wiki/Many-worlds_interpretation

Hopefully that may be along the same lines as what you were thinking and hopefully has helped,
Cyracuz
 
  1  
Reply Mon 5 Mar, 2012 04:38 am
@dalehileman,
Quote:
Either forever or infinity are flawed concepts and thus the universe must be finite, a perfectly rational and plausible assertion.


I have a few objections to your thinking, but they all center around one thing.
"Forever" and "infinity" are human concepts, useful from a human perspective.

And don't confuse "forever" with "infinity". If something is infinite that doesn't mean it is eternal. It just means it is not finite.

Perhaps a good question to ask at this point is which aspects come from the observed universe, and which aspects are added in the observation. It is becoming more and more clear to us humans that the world we perceive is a world our perception creates.
dalehileman
 
  1  
Reply Wed 7 Mar, 2012 12:13 pm
@georgeob1,
“...is finite in both space and time.” Of course it’s implied to get near reps one or both must be unlimited

"There is a cardinality to infinite sets -…..” Ok but how does this bear upon my prop
dalehileman
 
  1  
Reply Wed 7 Mar, 2012 12:17 pm
@markr,
"If the boundaries…...) are continually expanding, repetition is impossible.” True unless new matter is continually being generated
dalehileman
 
  1  
Reply Wed 7 Mar, 2012 12:26 pm
@JustAnotherGuy,
"Another way to sum up what you may be trying to voice is the Many Worlds Theory,….” Thank you, I knew it had to have a name

I wonder however if you agree that intuition objects most vigorously to the idea of reps, esp an infinite number of them, doubly so if the Universe is infinite so if they can exist simultaneously; if so agree then why; and if reason plausible then doesn’t intuition deserve more attention as a powerful force of reason
dalehileman
 
  1  
Reply Wed 7 Mar, 2012 12:34 pm
@Cyracuz,
"I have a few objections to your thinking,…” Thank you, a response rare in this diriment of procrustean devolution

'…..but they all center around one thing. "Forever" and "infinity" are human concepts, useful from a human perspective.’ We have to work with what we’ve got

'And don't confuse "forever" with "infinity". Forever is an infinite length of time
0 Replies
 
dalehileman
 
  1  
Reply Wed 7 Mar, 2012 01:05 pm
@dalehileman,
For some reason I am denied permission to edit my own post so herewith apologize where in para 2 of post #4920819 please delete the third “if"
0 Replies
 
north
 
  1  
Reply Wed 7 Mar, 2012 04:08 pm

I have as of yet come across the equate mathematics of infinity to the energy and matter of infinity

math of infinity is one thing , to equate this as the same as the infinity of energy and matter is another , they are NOT the same
georgeob1
 
  1  
Reply Wed 7 Mar, 2012 05:29 pm
@dalehileman,
dalehileman wrote:

“...is finite in both space and time.” Of course it’s implied to get near reps one or both must be unlimited

"There is a cardinality to infinite sets -…..” Ok but how does this bear upon my prop

It isn't clear just what your proposition is. Moreover your openingf statement contains a number of self contradictory assertions that make it fairly clear that you have not thought (or learned) enough about the concepts you are discussing.

Here's a simple example. Consider the molecules of a gas in a large container. The number of these molecules is quite large, but certainly not infinite. The thermodynamic state of the gas is completely specified by extablishing the three spatial coordinates for each moleculke, as well as the three coordinates of its velocity vector at that instant. This is called the "microstate" of the gas in statistical thermodynamics. The macrostate or thermodynamic state of the gas at any instant is determined by the average momentum (mass times velocity) of all the molecules impinging on the container surface (the gas pressure) ; the average kinetic energy (the particle mass times the square of the velocity divided by two times the gravitational constant) (the gas temperature) ; the particle mass times the number of particles divided by the container volume (the gas density); and finally the number of individual microstates that yield the same values of pressure, temperature, and density at that instant (the gas entropy). With N gas molecules and six distinct coordinates for each molecule, the number of possibilities and permutations for a microstate is very large indeed. While the probability of the exact reoccurrence of a particular microstate is clearly non zero, it is, for a reasonably sized container, very small indeed. One might have to wait several billion years for such a reoccurrance to take place. Even then you couldn't be sure because you can't measure it without changing the microstate.
markr
 
  1  
Reply Wed 7 Mar, 2012 09:17 pm
@dalehileman,
If new matter is continually being generated, then repetition is also impossible. How can you repeat a previous state which is a proper subset of the current state? Perhaps (relatively large) subsets are what you have in mind.
fresco
 
  1  
Reply Thu 8 Mar, 2012 01:40 am
Georg Cantor, celebrated mathematician of infinity, ended up in a mental institution. Watch out you guys ! Smile
dalehileman
 
  1  
Reply Thu 8 Mar, 2012 09:56 am
@north,
, to equate this as the same as the infinity of energy and matter is another , they are NOT the same

I didn’t realize that’s what I had done but if so I apologize most profusely
0 Replies
 
dalehileman
 
  1  
Reply Thu 8 Mar, 2012 10:10 am
@georgeob1,
"It isn't clear just what your proposition is."

Alas it’s somewhat manifold

“…..fairly clear that you have not thought (or learned) enough about the concepts you are discussing.”


Clearly that’s the case else no need for my OP

“…….simple example. Consider the molecules of a gas in a large container. ………...as well as the three coordinates of its velocity vector at that instant……. the "microstate” ……….the average kinetic energy (the particle mass times the square of the velocity divided by………... finally the number of individual microstates that yield the same values…….…….possibilities and permutations for a microstate is very large indeed…….. …….. several billion years for such a reoccurrance……...without changing the microstate.”

I absolutely agree in every respect and apologize most profusely if my OP wasn’t clear but you might continue by addressing its intuitional aspects
0 Replies
 
dalehileman
 
  1  
Reply Thu 8 Mar, 2012 10:21 am
@markr,
"Perhaps (relatively large) subsets are what you have in mind.”

Indeed so. Given the endless expansion with continual generation of new matter of course a rep of the entire Megillah is impossible. However once in a long while given the same set of parameters wouldn’t you get a near rep; for instance another Milky Way differing from the present one only by the length of one hair on Mom’s head and possibly the Pacific Ocean containing one additional water molecule; and eventually wouldn’t this very rep be repeated an infinite number of times according to my general assertion that the size of infinity and the duration of forever are grossly underestimated

And wouldn’t you agree with the intuitional assertion that such a Universe is absurd, along with the implications therewith concerning the value of said subconscious reasoning

Somebody help me
0 Replies
 
JLNobody
 
  1  
Reply Thu 8 Mar, 2012 12:44 pm
@Cyracuz,
Bingo (from my perspective).
Off to have a root canal.
Cyracuz
 
  1  
Reply Thu 8 Mar, 2012 12:56 pm
@JLNobody,
I did that last year. Most uncomfortable part was having to keep my mouth open for so long. The joys of living. Wink
dalehileman
 
  1  
Reply Thu 8 Mar, 2012 01:01 pm
@Cyracuz,
Come on fellas I’m perfectly serious. What can I explain to clarify
 

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