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| In an infinite universe...
Posted: 10/6/2008 12:19:05 PM | | It seems we are erroneous in our attempts at limiting the multiverse to points and spheres and mass and physicality, by assuming it takes up some sort of "space." If we are living within "maya," an illusion comprised of our observation of space-time the closest way to describe this phenomenon is as a geometric "hypothesis." This "maya" (the word hindus used for the world of illusion) is made real by our collective dreaming it into existence. Yet, here on this solid-seeming planet, we are attempting to discuss a dream and trying to lock it down into space/time, which just takes us further down the rabbit hole. We keep stubbornly thinking that the same space/time laws apply to the multiverse. I don't believe they do. | |
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| In an infinite universe...
Posted: 10/6/2008 12:54:14 PM |
The only point I would suggest to intoart would be that it's just a matter of time for physics to catch up with the mathematics. Granted, Cantor's work on infinity has had many critics within the mathematical community (Kronecker, Poincare, Brouwer, etc)
I spent many, many years studying math, and have taken just about every course available. Eventually, it became clear to me that subjects such as Real Analysis which focus on the intricacies of the structure of real numbers (and the various levels of infinity) are about as useful and relevant as the classic philosophical excercise of counting "the number of angels that can dance on the head of a pin".
The combination of the uncertainty principle and the exclusion principle guarantee that the number of any physical unit (photons, say) in a finite volume is finite. The maximum volume of the universe is the speed of light multiplied by the age of the universe. The conclusion is that the number of ANYTHING is finite (though it may approach aleph null as an upper bound.) | |
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| In an infinite universe...
Posted: 10/6/2008 1:05:12 PM | One more time (with feeling): http://www.youtube.com/watch?v=ekGJC5HFDlE.
It seems odd that I should be here while the intricacies of higher mathematics are being discussed by such erudite selves. Be aware that I, too have studied this subject, but from a different approach. The "geometry" of the multiverse was described by ancient mystics long ago. The flower of life is one of the oldest symbols. Please take a look at the video I posted as one physicist has the vision, imagination, mathematics and COURAGE to describe where science and metaphysics intersect. | |
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| In an infinite universe...
Posted: 10/6/2008 1:28:16 PM | | Hmm, maybe I am confused...can you explain. It seems to me that "the eternal" is just a sub class of "the infinite." | |
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| In an infinite universe...
Posted: 10/6/2008 7:01:21 PM | Seems I need brushing up too. But;
The infinite may have a beginning, but the eternal doesn't have a beginning or an end.
So many infinite sets could exist within eternity. | |
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| In an infinite universe...
Posted: 10/6/2008 9:28:50 PM | RE msg 47 by loverofwisdom:
The only somewhat bizarre thing that sounds similar to what you're suggesting is the Banach-Tarski paradox. You can take a sphere, cut it up into a bunch of pieces in a particular way and then put it back together into two spheres identical to the first one. If you want that one explained consult the wiki article on it because I'm not touching that one. The basic idea, I think, is similar to what I mentioned above about the sphere having as many points as a sphere twice its size. This is true. But your two new spheres will still have the same volume as the old one.
The reason is simple.
In order for the paradox to hold, you have to be able to divide the sphere into an infinite number of surfaces.
But the volume of each surface is zero. Now, 0 + 0 + ... infinitely many times, is ZERO!
So the total volume of all spheres would be ZERO!
However, we know that's not true. Why not?
A sphere has volume, because it exists. Even if we split it into 2, 4, or any number of pieces, each piece still exists, and so still has a volume.
If we keep splitting each piece into smaller and smaller pieces, each smaller piece is smaller, but they all exist.
If we kept going forever, we would get to an infinite number of zero-sized pieces. So no pieces wouldn't exist.
But we'd need infinite time to do that, and that would take forever. So we'd never get there.
Infinity doesn't exist, relative to finite pieces. It's a description of something we're heading towards, but never actually achieve.
Because we never achieve infinity, we never find out what happens at infinity.
When we talk about infinity, we are actually discussing infinitely convergent sequences.
We say that if the longer a sequence continues, the more the values of the sequence get closer to a certain point, then we talk about the sequence as if it gets to that point, when it reaches infinity. But it never does. We just use the point as an end approximation.
E.g. 1/x tends to 0 as x tends to infinity. We don't mean that 1/x gets to 0. We mean that for any value of 1/x = 0 + e, and as x gets bigger, e gets smaller, and eventually, x will get so big, that e is so small, that we aren't worried about e anymore. But e always exists, because x never gets to infinity.
Put another way, the more pieces of the old sphere we have, the smaller each piece is, but they still always add up to the same volume.
The smaller the pieces are, the more they will fit into becoming 2 new spheres. But they still always add up to the same volume.
Eventually, we get to infinitely small pieces, and we get a perfect fit.
But even when we get to infinitely small pieces, then calculus takes over, which tells us that the volume is the same for all dissections and all recombinations.
Since ONE recombination has the old volume (the old sphere), all other recombinations, including the 2 new spheres, must also add up to the same volume.
RE msg 52 by INTOART:
I spent many, many years studying math, and have taken just about every course available. Eventually, it became clear to me that subjects such as Real Analysis which focus on the intricacies of the structure of real numbers (and the various levels of infinity) are about as useful and relevant as the classic philosophical excercise of counting "the number of angels that can dance on the head of a pin". I can see why. Everything starts to get a bit vague and nebulous once you get to infinity.
But the point of Real Analysis is NOT to get to infinity, and never was. Its purpose is to make observations on what happens as we get more and more accurate, by using greater and greater dissections of the same situations, and so make intuitive leaps to realise of how the universe really is, even if we can never get a truly accurate experiment.
Real Analysis, and it's complements, are all about figuring out the universe without having to resort to experiments that take hundreds of years to develop the technology to make the experiment, and costs billions of pounds. It's a cheap short-cut. The only cost is making effort in thinking, something that Thomas Edison said that most people would do anything to avoid. | |
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| In an infinite universe...
Posted: 10/7/2008 9:17:10 AM | You know, Scorpio? I really value the few times I've come out ahead in debates with you because at times like this, you make me feel like an idiot!
I spent many, many years studying math, and have taken just about every course available. Eventually, it became clear to me that subjects such as Real Analysis which focus on the intricacies of the structure of real numbers (and the various levels of infinity) are about as useful and relevant as the classic philosophical excercise of counting "the number of angels that can dance on the head of a pin". I can see why. Everything starts to get a bit vague and nebulous once you get to infinity. But the point of Real Analysis is NOT to get to infinity, and never was. Its purpose is to make observations on what happens as we get more and more accurate, by using greater and greater dissections of the same situations, and so make intuitive leaps to realise of how the universe really is, even if we can never get a truly accurate experiment.
Plus, it's fun, kills time and exercises the brain. | |
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| In an infinite universe...
Posted: 10/7/2008 9:46:49 AM | My head hurts! I want to go to sleep now!
Gods i hate infinity and math! I really do hope that there aren't an infinite number of universes because then my head won't have to hurt thinking about it.
I will say though, gotapulse :
In an infinite set of universes with all posobilities existing at any one time, there is no need for rules to make two universe identical except for one tiny detail.
The reason being that with an inifinte number of universes, no mater how many posobilities there are, there will always be an infinte number of universes that folow the same set patern as another universe, due to chance rather than rules. For example, if I flip a coin five times, and you flip a coin five times, and everyone on Earth flips a coin five times, then someone out there will have fliped the exact same sequence as either you or I.
I just realised... this also means that there would be an infinite number of universes that were identical to our own in every way!
My brain hurts! | |
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| In an infinite universe...
Posted: 10/7/2008 11:49:26 AM | | Ok, I see where you are going...I can live with that definition. But I still think its best to look at it as one size since it can't be measured anyway. | |
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| In an infinite universe...
Posted: 10/7/2008 12:12:54 PM |
My brain hurts!
The remedy, as I have mentioned before, is to realize that infinity is strictly an abstract concept. Everything in reality is finite (though immensly large in many cases!) If there are multiple universes, the number of them is surely large but finite, not infinite. | |
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| In an infinite universe...
Posted: 10/7/2008 4:49:25 PM |
The remedy, as I have mentioned before, is to realize that infinity is strictly an abstract concept. Everything in reality is finite (though immensly large in many cases!) If there are multiple universes, the number of them is surely large but finite, not infinite.
True enough but only at any given time frame. The nature is to keep going so the further we go, the further it goes... Right? Unless there's a place where there is no more change, but... | |
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| In an infinite universe...
Posted: 10/7/2008 5:51:34 PM |
If there are multiple universes, the number of them is surely large but finite, not infinite.
Speculative, since there is no way to effectively do a census. That's not to say that physics won't, at some point, be able to place an upper or lower limit on the number of possible universes. It is safe to say that the range is anywhere from one to infinity. However, until that time when the physics are sufficient to the task, it is impossible to make definitive statements either way. | |
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| In an infinite universe...
Posted: 10/7/2008 9:04:56 PM | There is serious investigation taking place into the possibility that all we see is only a small part of a much greater whole, specifically that our universe is only one of perhaps an infinite number of universes. It's part of a matrix of continuous "creation" for lack of a better, less religiously-charged phrase.
If that is the case, don't all probabilities begin to approach 100 per cent? Somewhere, somehow, a species of "pig" actually evolved the capacity to fly? There's actually an honest car salesman? The government is really there to help someone?
Silly examples, I know, but you see my point. What are the implications of it?
This depends on the means by which you define universe. If you define a universe as a cluster of galaxies, stars, and other bodies encompassing mass (AKA defining that galaxies are clumped into universes much like how stars are clumped into galaxies), then the answer is no, pigs cannot evolve to fly. The reason is they would still have to follow the laws of physics in a three dimensional space. As to an honest car salesman or a government that's there to help someone, it really depends on you. If you believe that our planet was created with a unique purpose by a greater power, then no...God didn't create intelligent life on other planets. If you believe that it's purely random chance, then yes in an infinite number of universes, the probability doesn't approach 100%, it actually becomes 100% The only barrier that exists then is the barrier of physical laws.
Now if you define a universe by the multi-dimensional geometric space, then you're saying that there are an infinite number of other dimensions greater than ours. While it is physically impossible for us to see these dimensions because they are defined as perpendicular to every pre-existing dimension of the previous magnitude (4th dimension would include a direction that we cannot comprehend that is perpendicular to length, width, and depth) then yes, pigs would be able to fly, even in our own dimension assuming that there is some sort of intersection between dimensions. What I mean here is that even though we cannot understand the 4th geometric dimension, we can make correlations based on patterns we see in our dimension and the second dimension and how they interact. For example, we can see that a shadow is an area of a lack of light projected onto a lesser dimension. Therefore, in the 4th dimension, a shadow becomes a 3 dimensional space that lacks light. If you take other examples like a direct intersection of a 3 dimensional object and the second dimension, you can see that a 3 dimensional object does not need to obey the laws of 2 dimensional physics when intersecting that space. Take for example a fork and a sheet of paper. Lets assume for a moment that the paper has no width and is actually 2D. Lets also assume that there's a living 2D being standing on that sheet of paper. Now if you push the fork through the sheet of paper in front of the living being's eyes, from his point of view, he only sees where the fork intercepts the paper, and so as you push the fork through the paper, not only does it ignore the laws of 2D gravity, it ignores the laws of 2D physics. Since matter cannot be created or destroyed, the 2D being is watching as matter appears out of nothing and the amount of matter grows and shrinks depending on where the fork is. This all being said, yes a 4 dimensional object which intersects the 3rd dimension in the shape of a pig will be able to fly because it is not bound by 3 dimensional gravity.
Edit: Previously, I mentioned the idea of having a God that governs the creation of humans. I just want to point out that while proving God exists is impossible, proving that there is an infinite number of universes vs a very large uncountable finite number is just as impossible, so you might as well flip a coin and make a 50-50 guess at this point. | |
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| In an infinite universe...
Posted: 10/7/2008 9:32:17 PM | | It looks to me like a lot of you believe yourselves to be observing a thing from outside of it. The whole point of understanding the concept of the multiverse is to place you in the center of it and what that implies. | |
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| In an infinite universe...
Posted: 10/8/2008 5:31:26 AM |
However, until that time when the physics are sufficient to the task, it is impossible to make definitive statements either way.
Good point. Also, it is likely that the physics will never be sufficient to the task. If there are other universes, the fact that we live in this universe effectively prevents us from ever observing them. | |
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| In an infinite universe...
Posted: 10/8/2008 8:13:10 AM |
You are observing it all the time! You just don't realize it.
By definition, an "alternate universe" must be different than the one we observe. If it weren't, it wouldn't be "alternate"! | |
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| In an infinite universe...
Posted: 10/8/2008 8:51:35 AM | | Perhaps the universes intersect all the time, like a big ball of string? Isn't that one of the current theories? | |
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| In an infinite universe...
Posted: 10/8/2008 9:22:33 AM | I have a saying; Knowing a lot about the unvirese is like knowing a lot about dinosaurs.
Bothn are very interesting and awesome to comtemplate but, to borrow a phrase from Bob Dylan, it is all "pointless and useless knowledge." Children who know a lot about either , know nothing.
Even if all your sececulations are true .... so what? How does that effect the price of baloney? It has no practical application except maybe furthering the cause of atheisim which, in strickly secular terms, is folly | |
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| In an infinite universe...
Posted: 10/8/2008 9:50:53 AM |
It has no practical application
Study of the universe is useful because it can lead to quite unexpected practical applications. For example, the scientists who developed quantum mechanics thought that it was of purely theoretical interest. Instead, it is the basis of all modern electronics! | |
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| In an infinite universe...
Posted: 10/8/2008 10:56:19 AM | | Here's another fun fact to know and tell: Renee Descartes, thought by many to be the father of modern science, derived his philosophies through a visitation he had in a dream state while he was a soldier. The angel announced that the future of science will be obtained through weights and measures. Pretty ironic that the whole of what many of you believe to be beyond the esoteric was founded on an apparition. | |
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| In an infinite universe...
Posted: 10/8/2008 10:58:18 AM |
It seems we are erroneous in our attempts at limiting the multiverse to points and spheres and mass and physicality, by assuming it takes up some sort of "space." If we are living within "maya," an illusion comprised of our observation of space-time the closest way to describe this phenomenon is as a geometric "hypothesis." This "maya" (the word hindus used for the world of illusion) is made real by our collective dreaming it into existence. Yet, here on this solid-seeming planet, we are attempting to discuss a dream and trying to lock it down into space/time, which just takes us further down the rabbit hole. We keep stubbornly thinking that the same space/time laws apply to the multiverse. I don't believe they do.
At this point we're talking just infinity, not multiple universes which are both separate discussions which may or may not have overlap.
With respect to multiple universes, it will depend on what motivates that hypothesis. In the case of Everett's many world model, for example, the laws of physics are the same in every world.
Another motivation for a multiverse postulate has to do with the constants of our fundamental laws. Many equations in physics have constants, numbers introduced into them and there's no rhyme or reason to their introduction; they are just experimental facts. A classic example is the "gravitational constant" found in Newton's law of gravitation. What this multiverse postulate has to do with is universes which utilize different values for the constants. So in this universe the gravitational constant is 6.673 (with respective units... I have no idea how to code some of this stuff on these forums). In some other universe it might be a different value. | |
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| In an infinite universe...
Posted: 10/8/2008 11:02:46 AM | | Thank you for responding, loverofwisdom, I enjoy your posts although I admit that my higher mathematic skills are deplorable. Is it safe to assume, from what you state, that alternate realities exist on these universes as well? For instance, in one universe, time may run backwards? Sorry if my question is simple, but I really am curious. TIA | |
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| In an infinite universe...
Posted: 10/8/2008 11:07:15 AM | intoart wrote:
The combination of the uncertainty principle and the exclusion principle guarantee that the number of any physical unit (photons, say) in a finite volume is finite. The maximum volume of the universe is the speed of light multiplied by the age of the universe. The conclusion is that the number of ANYTHING is finite (though it may approach aleph null as an upper bound.)
I don't have qualms with quantization as such but I would imagine you are familiar with renormalization techniques which attempt to rid infinite results from physics. While there aren't any applications of Cantor's work on transfinite numbers I'm not going to say that they can't be applied in physics. Many things have become essential to physics. Consider the number "i" dubbed "imaginary" which now is an essential part to understanding our world.
The remedy, as I have mentioned before, is to realize that infinity is strictly an abstract concept. Everything in reality is finite (though immensly large in many cases!) If there are multiple universes, the number of them is surely large but finite, not infinite.
As a side note I take issue with your usage of "abstract concept" as you seem to be using it as "nonexistent". Abstract concepts may very well exist and they may exist independent of minds (Plato, Frege, et al). I would contend they are fundamental to any scientific realist view but most nominalists will disagree with me on this (and be wholly wrong). The honest nominalists have moved more towards some sort of social constructivism. | |
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