Universe - Size . . . something doesn't compute !

Actually if the universe was closed in the fourth spacial dimension - as a globe is closed in the third dimension - the universe could be both finite in volume and have no boundary in the third dimension. Then it would never be possible to travel to to the boundary of the universe, because you could never get there - just as you can never get to the end of the line when you're travelling on a circle.

If you're an organism limited in experience to two dimensions, then for all practical purposes, yes, there's nothing outside the globe. You'll never know what's out there, anyway. No, I'm saying that the universe is finite in volume, but has no boundary in three dimensions. So that if you took off in one direction in a straight line, eventually you'd return to your starting point, even if you never turned. I don't think the universe is infinite. I don't see how an infinte space could be expanding. But that's just me. (We assume space expands, but it could very well be that it's matter that's shrinking at an incredible rate. Who knows?) On the net? Not really. But if you stop into your local bookstore's science section, you'll likely find any number of books on hyperspace and higher dimensions, etc. Yeah, it's hard to talk about higher dimensions except through analogy. What he was trying to show you was probably a hypercube. Just as a cube has a square for every face, a hypercube has a cube for every face.

If there's no way that it could affect you or the universe, and no concievable way to test it, Occam's Razor says "throw it out."There's no way that what is outside the universe could be opened to our inquiry. If it could, then it would by definition be inside the universe. So why try to guess what's out there? You'll never be able to be right about it. Um, think about a globe. Start at Africa and trace your finger around the equator, heading west. Eventually you'll come back to Africa from the east. At what point did east become west? At what point did you turn around and head back? The answer is, at no point. You never turned around.In a universe closed in the 4th dimension, all straight lines return to their origins. There's no point where they "turn around". Yes, but we're also talking about non-Euclidian geometry. Straight lines aren't exactly "straight", if you get my meaning. On a globe, the equator (or any other "great circle") is a straight line in two dimensions, but it curves in the third. In a hyperspherical universe, all lines that appear straight to us are still curved in the fourth spacial dimension.I don't know if there's any way that we could determine the volume of the universe, or its potential curvature in any dimension. So we may just be shooting the breeze, here. Glad to hear you're having fun, though.

Well, what you found was kind of a simplistic summary - the version I'm familiar with says "it is undesirable to needlessly multiply untestable entities." So, if you have a theory or model that contains entities that cannot affect the things we observe and cannot themselves be observed - as anything proposed to be outside the universe would be - then throw them out, because they're pointless. It's not so much a theory, Occam's Razor, as it is a rule of thumb for the formulation of scientific thought.Things outside of the universe by definition cannot affect us nor be observed, so no scientific model can make reference to entities outside the universe. Now, I'm not adverse to speculation, but know that it will always be fruitless. There's just no way to know what's outside the universe. Well, in an infinite universe, no. On the other hand, in a universe that's truly infinite, if you traveled in a straight line long enough, you'd eventually come to a place that was exactly like the place you started from. You would even encounter a copy of yourself. (Similar to how, given an infinite string of random digits, like pi, any arbitrary finite string of digits can be found within it.) Hey, as far as I'm concerned, we're both laymen. (Laypeople?) I have absolutely no professional training or education in this, just a lot of popular-press math/science books.

That's not mathematically correct. You can always add to infinity. And subtract, as well. (I once heard an analogy about "the Hotel Infinity" that may make this more clear for you. I'll tell it to you, if you like.)

Sure thing. My apologies to it's original author, whom I cannot remember.Basically, it's like this. You work the night desk at the prestigious Hotel Infinity, which has an infinite number of non-smoking, single-queen-sized-bed rooms. It's a busy night, so it's full. That is to say there's an infinite number of guests at the hotel.A customer comes up and wants a room. "Sorry," you tell him, "we're full." "Nonsense," he replies. "This is the Hotel Infinity. You have an infinite number of rooms." He's right, of course. "Well, I guess you could have the room at the end of the infinitely long hall..." you say. "Won't work - I'll never get there. Humans can only walk a finite distance."Then it comes to you. You can use the P.A. system to tell every customer that they'll have to move to the room immediately down the hall. Each customer only has to walk a distance of one room. And voila! One more customer at the Hotel Infinity. In fact you can do this for any number of guests - just have each guest move that many rooms down the hall. Each person only walks a finite distance, so it doesn't take you infinite time to complete the move (which is good, because you hate working overtime.)The next night, you're full again, but oh-no! A convention has just pulled into town. It's the largest convention ever - in fact, it has an infinite number of people, none of whom made reservations. And they're all in your lobby.Well, you can't shift every person an infinite distance, after all. Humans can only walk a finite distance. Luckily it's a mathematicians convention, and they tell you what to do: tell everybody in the hotel the following:1) Look at your room number.
2) Multiply it by 2.
3) Go to the room with that number.And there you go. You've just put another infinite amount of people into the already full Hotel Infinity. Infinity isn't a number so much as a concept derived from the simple fact that there's no number so large that you can't add to it. Even infinity. You just get infinity every time. Even infinity + infinity is still infinity. (infinity times infinity is actually larger than infinity, however. Doesn't that just bend your noodle?)[This message has been edited by crashfrog, 09-13-2003]

Well, yes. They did laugh at Einstein. But be careful - they also laughed at Bozo the Clown.

True, but then, are you and I?

Nonsense. A hotel is full when the number of guests equals the number of rooms (roughly speaking). In the Hotel Infinity, the number of rooms is infinite, and the number of guests is infinite. Guests = rooms, so the hotel is full. This is pretty simple logic. Well, the number of points on a line is infinite. And there's an infinite number of lines in a plane. Therefore the number of points in a plane is larger than the number of points on a line. They're both infinite, but one of those infinities is larger than the other.Another way to think about it would be to compare the whole numbers (1,2,3) with the real numbers (1.3, pi, 4.3434... etc.). No matter how you try to line them up, you'll always have more real numbers than whole numbers, because between any two whole numbers there's infinitly more real numbers.Cantor proved this a lot simpler in his famous "Diagonal proof", but as I'm not a mathematician - only the least bit mathematically capable, in fact - I dare not attempt to repeat it here. Doubtless Rrhain could do it, if you asked him to. But you don't have to give it a value in order to add to it. You're still thinking about infinity like it's the largest number or something. It isn't - it's a concept we use to describe the fact that there is no largest number.You can add to infinity as much as you like. You still get infinity. Nothing prevents you fron doing the addition, though. If you had a bucket of infinite size filled with an infinite amount of water, nothing prevents you from adding another glass, or even another infinite amount. The amount of water in the bucket is still infinity. Not so. There's nothing magic about infinity, or for that matter, anything really that weird. It fits right into mathematics. You don't need to try to grok it, because infinity is very well explained through mathematics. In fact that's the only place infinity does (or could) exist, in my opinion.

Well, if you were a cosmologist, you'd have done the math. Science isn't done by analogy, those are just tools to aid comprehension for the layperson. But believe me when I tell you that every theory you've heard here so far is pretty well supported by the math.But cosmology isn't done by sitting around and having a beer and wondering what the universe is like. Cosmologists work like all scientists - a rigorous process of collecting data, doing the math, and constructing explanitory models.Not that we can't play around, and wonder about space without Ph.D's, but I just want to make it clear that what we're doing here is as far removed from real cosmology as playing "Halo" is from serving in the Marines.

No, it's science. In this particular science we infer the larger structure and nature of the universe from the nature of the observable universe.I don't see that there need be something ineffable about that. It's pretty simple, really. You don't have to shrug your shoulders and say "we may never understand" when you can just look up and observe.I have no problem with a finite universe, because the question "well, what's beyond it, then?" is predicated on a misassumption: that the concept of space extends beyond the universe. There's simply no "there" there.I do have a problem with a universe that is infinite in time and space, simply because it's contrary to observation.

It's the bolded part of your statement that I disagree with. There's no requirement for there to be "something large enough" in the idea of an expanding finite universe, because there's no such thing as "space" or "volume" outside the universe. "Size" and even "time" are concepts that end at the universe's edge.

Oh. Well, in that sense, I suppose the universe is infinite. But I'm working from a definition that most cosmologists seem to take: that the universe is the set of all coordinates that it is possible to travel to. That's why we can talk about mutilple and finite universes, for instance. I guess I'm of the opinion that my definition is a little more useful.

Seriously, a good attempt, but it doesn't work - the Hotel Infinity only has rooms labeled with whole numbers. So, there's less rooms than if you labeled every one with real numbers (one order of infinity less, in fact) but it's still infinite. It would if there weren't a restriction on what rooms can be in the Hotel Infinity.

You've misunderstood me.Not the part that we can travel to now. The parts that we could travel to theoretically. After all, there's no place in the universe I couldn't go to with sufficient time. On the other hand, there's no concievable Newtonian propulsion that could take me out of the universe.So, what I mean to say is that the universe consists of all possible places I could get with Newtonian motion.