A layman's questions about universes

buzsaw responds to me:

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Unbounded, yet finite. There are definitely numbers that are not in the interval, but no matter what number you choose in the interval, you will always find another number that's just a little bit closer to the boundary.

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Gotta get this one in before retiring.

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1. "Unbounded, yet............closer to the boundary??" The unbounded has a boundary??

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Yes.What you seem to be having difficulty with is recognizing that there are three things:The interior points, the exterior points, and the boundary points. Interior points are members of a set for which a neighborhood can be drawn that only includes other members of the set. Exterior points are those for which a neighborhood can be drawn that do not include any members of the set. Boundary points are those for which all neighborhoods necessarily include both interior and exterior points.So when describing an interval, you have a choice: Do you include the boundary or not? You don't have to. And depending upon the geometry, you can even include some parts of the boundary but not others.

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2. This's real confusing, Rrhain.

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I never said it wouldn't be. But I remind you that just because you find it confusing doesn't mean it isn't true. Consider the possibility that the problem is not that the claims are false but rather that you don't understand them.Would you rather I say something like this? Do you really want me going on about: And let's pull it all together: Is that really what you want?

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If you include the numbers outside of the bounded infinity of numbers for your analogy, you must also eliminate the boundary for a true analogy of the universe

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Not at all. The point that I am trying to impress upon you is that it is an equivocation to confuse "infinite" with "unbounded." The two are not the same. Things can be finite or infinite while at the same time being bounded or unbounded. Those two traits are not the same thing.

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It appears to be a bogus analogy for the universe, for the universe is one system.

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Only because you don't understand how infinity works.Time for a thought experiment. For this thought experiment, we need to assume a few things:1) Captain Marvel and Superman both exist.
2) They can move any finite distance in any finite amount of time (even if that means they move faster than the speed of light).
3) There are an infinite number of coconuts, all numbered, and a pit big enough to hold them.Now, Captain Marvel and Superman decide to play a game. At noon, CM tosses coconuts numbered 1 and 2 into the pit. Supes flies in, grabs coconut #1, and tosses it out.They sit around for half an hour discussing the superhero life and at 12:30, CM tosses in #3 and #4. Supes flies in, grabs #2, and tosses it out.Fifteen minutes later, in go #5 and #6 and out comes #3.They continue this process, each time halving the amount of time they wait before tossing their coconuts.When 1 o'clock comes around (and 1 o'clock always comes around), how many coconuts are in the pit?Answer: None. Why? Because for every coconut number you give me, I can give you a time when it was tossed out: #1 was tossed out at noon. #2 was tossed out at 12:30. #3 came out at 12:45. #4 came out at 12:52:30....The next day, they decide to play the game again, but with a twist. This time at noon, Supes throws in coconuts #1 and #2 and Cap tosses out #1. At 12:30, Supes throws in #3 and #4 and Cap tosses out #3. Again, they go faster and faster, halving the amount of time they wait.When 1 o'clock comes around (and 1 o'clock always comes around), how many coconuts are in the pit?Answer: An infinite number. Specifically, all the even-numbered ones.Even though the physical process is exactly the same on the surface (two go in, one comes out), the outcome is quite different.And it's all perfectly logical. It is easy to see why this has to be the case. Even though we might expect identical processes to achieve identical results, we can see that it can't be the same.Why? Because infinity doesn't work like other numbers. It is illogical to treat it the same when we can directly see that it isn't.

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If the system is "unbounded" it cannot have a "boundary"

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Incorrect.If the system is unbounded, it can easily have a boundary...it just doesn't include it.Think of your house. There is the space inside the walls, the space outside the walls, and the walls, themselves. The space inside the walls is not the same as the walls. When we generally think of your house, we include the walls. Thus, "outside" does not include the walls. Your house is bounded and includes the boundary. Outside is unbounded: Though it has the boundary of the walls, it does not include the walls...those are part of the house.I can get as close to your house as I want, but I am not touching your house until I touch the walls. There is a boundary, but the outside does not include it.

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Yes, yes, I know, with science we're not suppose to make any sense, common, that is.

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Have you considered the possibility that the problem is not "common sense" but that you simply do not understand the "common sense" of the situation?It makes perfect sense, buzsaw, and is perfectly logical. There is "inside," "outside," and "edge." The edge is not inherently part of the inside.

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Rrhain
WWJD? JWRTFM!

buzsaw writes:

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Quoting Rrhain:

If you were somehow able to switch off the gravitational field, "space" would disappear as well.

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I never said that. Beercules did (Message 66).

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I get the implication here that Rrhain has it in his mind that given the right conditions, space would have the capacity to disappear. Where'd I go wrong??

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By confusing gravity and space as separate things rather than being the same thing.

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Rrhain
WWJD? JWRTFM!

NosyNed responds to me:

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I'm pretty sure that Rrhain did, in fact, word that wrong.

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Unbounded, yet finite. There are definitely numbers that are not in the interval, but no matter what number you choose in the interval, you will always find another number that's just a little bit closer to the boundary

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Should have ended with ... just a little bit closer to the limit.

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No, I said "boundary" and I meant "boundary." That is what it is called in point-set topology.An interior point of a set is defined as all points where there exists a neighborhood such that all points in the neighborhood do not contain the boundary or any exterior points.Limits and boundaries are very similar. However, limits are for functions. Boundaries are for sets.

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Rrhain
WWJD? JWRTFM!

buzsaw writes:

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For the purpose of our discussion do these other dimensions solve anything?

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Yes. From string theory, the universe has 10 dimensions.

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Rrhain
WWJD? JWRTFM!

Tony650,No, I can't really describe it. How do you describe "red" to someone who hasn't seen it? It's really hard and I don't know how. The closest I can come is to artificially add a fourth dimension such as the temperature gradient of a solid object, but there's still the visual leap required to convert that non-spatial dimension into a spatial one.

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Rrhain
WWJD? JWRTFM!

No. Actually, the mathematics fits right in with "common sense". We use the mathematics because it allows one to make clear, precise statements about the physics. As you are discovering, verbal analogies are insufficient.With relativity, one can make testable predictions of physical observations, that have in fact been verified. With string theory, the same is true. Certain elementary particles of certain mass should exist. Experimental tests of this are in the future, e.g. may need larger particle accelerators than current.It is getting difficult to escape the conclusion that you are slamming something simply because you don't understand it.

Yeah, I was afraid you'd say that.Just to clarify, you are saying that you can actually visualize true four dimensional topology, aren't you? You're not referring to their 3D analogues? To be clear, I don't doubt your word. I just want to confirm that I'm not misreading you. For the time being, I'll assume that I've understood you correctly.I've always read that it's impossible to represent true 4D in a two dimensional image, like on a piece of paper. Is this true? Is there any way you could show me what you see in your mind, by sketching it, perhaps? Or is this also not an option?Unfortunately, I'm guessing that it isn't because believe it or not, I've tried. I've sat for hours at a time, trying to figure out "which way" a fourth perpendicular axis would go. And herein lies my problem, I believe. I'm still thinking in 3D.A fourth axis doesn't go anywhere that exists within three dimensional space. By definition, it sits outside of it, the same way that the z-axis has zero length within a two dimensional plane. Perhaps I simply lack the necessary understanding of axes or Cartesian co-ordinates themselves.Since it's too difficult to describe directly, could you perhaps describe what led to your perception of higher dimensions? Obviously it was your mathematics, but was it the dimensional equations and such themselves, or more of an intuitive understanding of the properties of 4D objects/spaces and how they are affected by specific types of manipulation?For example, a cumulative feel for the way the three dimensional cross-section of a tesseract is altered by sliding it along its 4D axis, and passing it through a 3D "plane"? Something like this, which allowed you to gradually combine all of the individual pieces of data which, while only observable separately in 3D, eventually allowed you to see the "big picture"? Perhaps it was a combination of both, or something else altogether?I guess what I'm asking is; can you tell me what I'll need to do in order to come to something even approaching your ability to visualize higher dimensions? Yeah, I know...I'm not asking much, am I?I'm just hoping that it won't require a perfect understanding of advanced calculus, dimensional equations, etc. It's quite obvious from your posts (I've been reading your posts on EvC for a long time) that your mathematical prowess is well and truly beyond anything I'm ever likely to attain. So I would like to think that achieving your level of mathematical comprehension isn't my only hope of ever perceiving higher dimensions. If it is, I think I'm screwed!Sorry to keep bothering you with this. It's just that you can do something that I've wanted to do very badly, for a long time. Visualizing higher dimensions has been one of my holy grails for years. Then after giving up and assuming that it was simply impossible, I come across someone who can do it! Argh!Anyway, I talk too much. Thanks again for your time, Rrhain.

You don't, of course. Trig and Calculus were also part of the package.Back when I was in high school we really didn't have too many choices. We could select which languages we were going to study (I sucked at all of them) but that was about it in terms of subject choices.At that time the school was both a day school and boarding and so they had us poor boarders more or less 24/7. Since I left it has become a day school only. Looks like it's still pretty small.Just because I was curious, I went to their website and today it is much like you state. You are required to have so many credits in each subject area. It looks like Calculus, Trig, Analytical Geometry are still offered but I can't tell if everyone has to take them or not.

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Aslan is not a Tame Lion

Tony650 responds to me:

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Just to clarify, you are saying that you can actually visualize true four dimensional topology, aren't you?

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Yes, but without an actual four-dimensional object to show you that you could look at and verify for yourself, I have no way to prove it to you. I think I can. It certainly feels like I can. My work in mathematics seemed to follow intuitively from the visual models that I had in my head.Until we perfect that telepathy thing and I can project the image into your head, it's something you'll just have to agree that I claim.

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I guess what I'm asking is; can you tell me what I'll need to do in order to come to something even approaching your ability to visualize higher dimensions?

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I'll tell you what did it for me:Fundamental Concepts of Mathematics (often called "Real Analysis"), Differential Geometry, and Topology. When you spend six to eight hours a day, every day dealing with mathematical constructs of more than three dimensions, you brain starts coming up with ways to organize it. I don't know if there are other ways to do it...I only know that about midway through sophomore year, I realized that I was working through multi-dimensional problems visually in my head.

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Rrhain
WWJD? JWRTFM!

It appears that you're talking two systems here, not one. The house, I assume is your analogy of the universe. Right? So according to your universe analogy of the house, the space outside the house is not included in your house universe because of the wall. The problem is that the universe has no wall/boundary. If you think it does what does it look like? What does it consist of? The wall of your house analogy consists of lumber, etc. What does the wall of the universe consist of? What in the universe separates the space inside your alleged boundary from the space outside of it?

Well then, please define space. My understanding of it is that it's nothing but area into which things can be either created into or expanded into. Until something is in it such as rays, force (like gravity, for there is no gravity unless something is near enough to gravitate) so if you get far enough away from everything the space would contain nothing, absolutely nothing including the force of gravity as I see it.If you think gravity and space are one and the same, why couldn't you say the same for light rays and a brick for that matter? Just because these things are in space does not make them space.

Well, ya see they are the same. It is under our current conditions that the similarity (symmetry) is wrecked and the similarity isn't apparent. The current leading edge of physics is trying to understand the way in which they are connected. It's been a century since we understood that matter and energy are manifestations of the same thing. The light and brick are transformable into each other.(ok, now let's get practical, turning light into a brick isn't something that is going to be done. Nor is turning a brick into energy. However, light can be turned into the material constituents of atoms and that's all a brick is. And if you mistreat the brick atoms appropriately you can get energy out. It's just that to bring them back together you might have to recreate the big bang or something close to that. )

Like we keep telling you, you need more mathematics to truly understand how space is defined. If we tell you that in relativity, space is a 4 dimensional Riemann manifold with the Minkowski metric tensor, and where coordinates transform according to the Lorentz equation,and then go on to show, mathematically, how this connects to gravity...well, this is all graduate level mathematical physics.
There's probably someone on the boards who does this for a living. I just had the one graduate course in relativity, so I'm not an expert.It's not just mathemaitcs without physics, however. We can make testable predictions that have been observed. The precession of the perihelion of the planet Mercury was explained by relativity.
If relativity is true, starlight should be bent by gravity, and light should be redshifted when leaving a gravitational source. Both have been observed many times.And thats just for starters, in the string theory there are more dimensions...Intuition and "common sense" just don't cut it. It is what it is.Brian Greene (who does string theory for a living) has some books out on string theory for the popular reader. I highly recommend them e.g. "The Elegant Universe".

Well, as NN said (somewhat cryptically IMHO), you can in some sense consider light rays and a brick as the same; they're both mass-energy and E = mc².But saying that gravity and space are one and the same is not an arbitrary decision; it's a conclusion forced on us by the evidence. The only thing anybody has come up with that fits all the evidence (and fits it exceptionally well) is relativity, in which time and space are inherently different-appearing aspects of one thing: space-time. [joke]It's kind of like the Trinity[/joke]

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Well then, please define space

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You can define spacetime as a 4D coordinate system. To locate any event that takes place in the universe, you need this coordinate system. Finding this event requires 3 spatial dimensions, and one temporal. That is a simplified way to put it, but it gets the idea across.Moreover, this coordinate system is contingent upon matter/energy or any gravitational source. That means if all the mass in the universe were to disappear, spacetime would disappear with it. Note: I am not saying the mass can disappear.