A layman's questions about universes

But no matter how you cut it, your number analogy doesn't work with the universe. Why? Because your "bound" happens to be a difinitive "bound," in the case of Rrhain's analogy, that difinitive number being "1." With the universe, you have no difinitive boundary which has been observed by anybody. Your imaginary boundary is nothing but space/area, is it not? And beyound your imaginary boundary what do you have? More space! Yet your space is somehow part of your universe, like Rrhains numbers outside of his "1" difinitive boundary do exist.

Buz, remember it was just an analogy in the first place. It was to show you the definition of the terms being used.The universe may or may not be bounded. It may or may not have any number of properties. But when you are attempting to describe what you think it is like you have to choose your words carefully. In fact, you can't use words and have anything more than a weak analogy. You have to use math to attempt to describe differing ideas of the nature of the cosmos. Then it is time to see, through observation, if the universe and the math have any agreement.

I'm just explaining the math. I guess the idea is that since the boundaries aren't in the interval they don't count. But I'm not sure of the reasoning there.Nevertheless finite but unbounded makes perfect sense - the surface of a sphere is the usual example, but the perimeter of a circle works just as well. There are no boundaries on the surface or the perimeter - no matter how they are traversed neither includes an edge. The only "boundaries" are in higher spatial dimensions.

Are you serious, Rrhain? Wow, that is quite possibly the most amazing thing I've ever heard! In case you're wondering who the hell I am, I know I don't post here very often but I'm a frequent lurker and I simply had to reply to this.I've spent an enormous amount of time, over the years, trying to contemplate this very thing! Higher dimensional physics is one of the most fascinating concepts I've ever looked into. But no matter how hard I try, and despite the fact that I understand (at least, in principle) how it works, I've never been able to actually visualize a "hyper-volume" with a forth dimensional axis perpendicular to all other three, let alone a fifth dimensional axis perpendicular to all other four!I realize that I may be asking you the impossible here but is there any way you could elaborate? The closest I have ever come to a true perception of higher dimensions is in researching their mathematical constructs, like the hypercube, for example. The problem with that, of course, is that it is still being viewed from within the "flat" confines of 3D space. A hypercube, as I understand it, is merely the three dimensional "shadow" that we see being cast by a 4D tesseract, the same way that the inhabitants of Flatland would only see the edge-on view of the shadow cast on their two dimensional universe by a 3D "hyper-square" (cube).Unfortunately, I've never been able to get very far beyond this, in terms of actually envisaging higher dimensions themselves. I understand the principle behind them (I even have a 4D version of the Rubik's Cube, on my PC...Lots of fun!), but try as I might, my imagination seems completely unwilling to take the next step and picture them, in my mind.Eventually I came to the conclusion that it just couldn't be done. I figured that it was simply impossible to visualize something that your physical environment absolutely forbade you to experience. I've never rejected their mathematical (or even physical) legitimacy, mind you. I just came to accept the idea that since nobody has ever seen more than the three familiar, spatial dimensions, we lacked the requisite experience to accurately conceptualize any more than that, in our minds.This being the case, I am fascinated that you can do it! Are there any words that can describe what you see, in any detail? Or do you visualize them more in abstract, mathematical terms? If it's too difficult to describe (and believe me, I'll totally understand if you say that it is), perhaps you could suggest a method of approach that would give me a push in the right direction. Maybe I'm just not thinking about it the right way. I would imagine that visualizing the actual configuration of a 4D primitive, or the actual geometry of 4D space, would require a certain amount of "thinking outside the box".Also, if you know of any good internet resources that might help me out, please feel free to post them. I've read a lot of online material relating to this subject but there's always a chance that I've missed something worthwhile. I'll definitely check out anything you recommend.Ack! That was a bit longer than I intended. Sorry about that. I didn't mean to prattle so much but this is a topic that I've always been intensely interested in. And you're the only person I've ever heard say that they can actually perceive higher dimensions. I'm extremely interested in both what your perception of higher dimensions is like and how you go about visualizing them. I would absolutely love to be able to do this, myself! In the end, it may simply be beyond me, but hey, that never stopped me from trying before.Sorry to take up your time, Rrhain. I appreciate your patience.Note to Admins: I hope I'm not getting too far off topic with this post. If I am, please accept my apologies and feel free to move it to an appropriate forum, new thread, etc, at your discretion. Thank you.

Most here refuse to even acknowledge the highest dimension so evidenced in the universe and especially on earth. That is the spiritual realm/dimension, the invisible, the wonderful. Amazing how some will make soooo much of a supposedly wonderful math dimension vision or whatever and reject so much of that high dimension. I'm interested in Rrhain's own explanation of his post in question.For the purpose of our discussion do these other dimensions solve anything?

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The immeasurable present is forever consuming the eternal future and extending the infinite past. buz

1. The problem is that the universe is not a circle or a flat 2d volumnless disk. The analogy of a 2d flat circle or disc in any discussion about the universe is bogus and essentially says nothing as to the questions at hand about the universe.
2. How is the surface of a disk or circle or the disk or circle itself analogous to the universe, pray tell?

The disk or sphere-surface are lower dimensional analogues of our 4D universe. They are embeded in our 3 spatial dimensions just as our universe could be considered to be embedded in a higher dimensional mathematical construct.How "real" that higher dimensional construct is I don't really know. It does allow the cosmologists to describe possible forms of the universe though.The analogy isn't "bogus" if we are using it to explain some ideas about bounds and topologies. It is just simplified so it is possible to get a picture of it in your head. I'm sure not like Rrhain and able to picture higher dimensions (though I've tried to picture a tesseraact and get fuzzy things formed but not a real visualization).The statments made about boundaries and limits that we make about sphere surfaces or disks is, I think, very analogous to things we can say about the higher dimensioned universe.

The OP was asking questions that have to bring up some of these issues to really attempt to answer.These extra dimensions will only "solve" anything if they can produce predictions which will be testable. That is the job of the cosmologists. It is an example of how these areas of science progress. Some theoreticians construct what may be truely outlandish speculations. Then these are examined to see if there are any observations which they might suggest. Experiments are performed and a lot of the speculations end up in the rubbish heap.

Well then:
1. What is space?
2. What properties in space are affected by gravity?

So what you seem to be saying is that they really serve no purpose here and now. We have to wait and see. In the mean time we back off and try to hash out this matter about the analogies as to what works and what doesn't.

It's nuts, imo to distract ourselves with these so called higher dimensions. Heck, I can't get you people onto either my dimensionless model or your own 3d model yet, not matter what I say. You all keep insisting on a useless 2d volumnless flat circle or disk. It's like trying to get the few flat earth folks left to think in a 3d sphere and they refuse. As I said, the 2d so called explanation is not for the layman atol. Imo, it's for the physicists
to justify belief in the theory (rather hypothesis) of a curved closed system universe.

Just an anlogy? So since it's just and analogy, the objections I've raised don't matter anyhow, so why worry about the answer to them? That's the message I'm getting.
The universe may or may not be bounded. It may or may not have any number of properties. But when you are attempting to describe what you think it is like you have to choose your words carefully. You sure do, especially when you discount logic and common sense.So Rrhain says it's both bounded and unbounded. Now you say it may or may not be either. Sorry, my friend, but it appears you guys are sinking deeper and deeper into the quick sand bog of where the math has led you. Imo, it's time for logic and common sense to come, rescue you. Mmmm, observation. I'm afraid you need my protruding strait edge models already given for that, since there's nothing out there within view looking like a boundary -- nothing but more galaxies, etc. Btw, nobody's attempted to refute either of my straight edge models. Why not?

The analogy is simple. Like the circle or the sphere (NOT a "disk" as you seem to think I said) the universe is curved in a higher spatial dimension. Thus the idea of the finite but unbounded universe states that the universe is curved back on itself in a higher spatial dimension, just as the one-dimensional perimeter is curved in a second dimension or the two-dimensional area is curved in a third. Where is the problem ?And by the way might I suggest that the implication that analogies only apply to things that are identical to the objects in the analogy - rather than, well, analagous - negates the whole concept of an analogy. I trust that you never ever attempt to use analogies even to try to explain ideas since you think that they say nothing.

buzsaw responds to me:

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am fully aware that my logical arguments are to you very contrary to what you've been taught and sincerely believe.

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Incorrect.While I was certainly taught relativistic physics, it isn't something I "believe." It is something that I have directly experienced. There are actual experiments that you can do that directly show the predictions made by the theories of relativity.This isn't something I "believe." I can actually make it manifest right in front of everybody's eyes. Don't take my word for it: Run the experiments yourself. If you come up with something different, we'd all love to hear about it.

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You asked about how you could have infinity in a finite object. And I showed you. The sponge has a finite volume but an infinite surface area.

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1. Here again, logic and common sense says anything having finite volumn capacity must needs have also bounds inclusive of a finite surface and is in no way analogous to 2d.

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Incorrect. Your logic is obviously false because there it is, right in front of you: An object that has infinite surface area yet finite volume.I have to ask you again: Are you seriously saying that we should stick with a "common sense" that is obviously [I][B]WRONG[/i][/b] simply because you don't like it? Because it requires more effort to understand the more accurate model?Have you considered the possibility that the problem isn't a violation of logic or "common sense" but that you simply do not understand? Why should anybody follow your "common sense" when we can directly prove it to be fallacious?

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2. Using a sponge analogy seems to be adding a new dimension to our discussion about an alleged 3d universe isn't it?

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Not at all. A sponge is a 3D object. And yet, it has an infinite surface area contained in a finite volume.There was a wonderful Scientific American Frontiers on PBS last night that was about all of this: Origins of the universe, the concept of the universe being "infinite," and how can the universe be expanding when there is nothing for it to expand "into"?Alan Alda had a wonderful statement about it as he was talking to the physicist: We think of the Big Bang as something that happened at a point and expanded outward, so if we were going to look backward in time [from me: which is what we do when we look at the sky given the nature of light...when you see a star, you do not see it as it is now but rather how it was years ago because it takes the light that long to reach here], we should be looking toward the center. You're telling me that what we really do is look in every direction?And that was the point the physicist was making: That's exactly right. The idea that the Big Bang happened at a point and expanded outward is completely wrong. As Hawking pointed out, the Big Bang did not happen at a point: It happened everywhere at once.

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Thanks to all for your patience and indulgence to ole Mr Logic's intrusion here into your lab.

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Um, when all the people who actually study this thing for a living are telling you that you're wrong, don't you think that you should at least consider the possibility that you might be mistaken?In other words, what on earth makes you think you're "Mr. Logic"?

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Rrhain
WWJD? JWRTFM!

jar asks:

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Way back when I was in high school we had to have Plane Geometry, Analytical Geometry, Eucledian and Non-Euclidian Geometry as requirements for graduation.

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None of the high schools I attended had a requirement for a specific level of mathematics. Instead, they all simply required that you had a certain number of credits in it. Thus, if you came in having a year of Pre-Algebra and a year of Algebra I, you were good to go.And to satisfy my curiosity, how does one do Analytical Geometry without Calculus? Perhaps what I'm thinking of (where you do things like derive the formula for the surface area of a sphere by integrating the formula for a circumference) isn't the same as what you are thinking of.I handily admit that it has been a couple decades since I had Geometry, so I can't recall if we had a section that was called "Analytical Geometry" that was more of a simple algebraic representation of geometrical concepts. Instead, "Analytical Geometry" was part of Calculus...all of my basic Calculus texts are titled "Calculus with Analytic Geometry."

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Rrhain
WWJD? JWRTFM!