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Author | Topic: A layman's questions about universes | |||||||||||||||||||||||||||
Tony650 Member (Idle past 4032 days) Posts: 450 From: Australia Joined: |
Rrhain writes: 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. Oh don't misunderstand my question. I believe you. My concern was that I may be misunderstanding. I was just looking to confirm that you were saying what I thought you were saying. From your reply, it seems that you were.
Rrhain writes: 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. So to clarify a little further, you can (for example) plot points in true 4D space, in your head? Or solve problems by "seeing" the actual figures, in your mind? I'm not sure if I'm making sense so, once again, I'll come down a level (for my own benefit, not yours). Also, I'm not familiar with multi-dimensional equations so you'll have to forgive the crudeness of this example. What you're saying is that you're like Flatland's resident mathematician, who doesn't have to rely on his understanding of the properties of the visible (two dimensional) slice of a "hyper-square" to make calculations, predictions, etc about the rest of it. Because he has such a grasp of its characteristics that he can actually picture, in his mind, the hypothetical "cube". Is this correct? I have no problem visualizing and understanding (within reason) the three dimensional cross-section of a tesseract, but that seems to be as far as I can go. No matter how much I try, I just can't seem to imagine its vertices extending "up" along the fourth axis. If I've understood you correctly, you actually know what a tesseract looks like. Not just a three dimensional "slice" of it but the whole thing; a tesseract. You can "see" its four perpendicular axes, its eight cubical "surfaces", and so on. Is this correct?
Rrhain writes: 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. Believe me, if I ever discover that I can reach into other people's minds, you're the first one I'll contact. That is assuming, of course, that I haven't figured out four dimensional topology, on my own, by then. Ha! Not likely!
Rrhain writes: 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. So it does come more from a familiarity with the physical constructs, than the math itself? Do you think, then, that I have any hope of perceiving it as you do, without having your depth of understanding of the complex equations? In other words, do you think that "hands on experience" (for want of a better term) with the constructs, and an overall "feel for" how they work when manipulated, will be enough to teach me how to perceive them as you do? Or is my only chance, to understand the theory as well? To work with the mathematical aspect of multi-dimensional constructs? I understand the fundamental principles of dimensionality but I haven't looked, in any depth, into the actual mathematics underlying hyper-dimensional construction. Do you think this is a necessary part of what I'm trying to achieve, or is it possible without it? I hope I'm not annoying you with my constant questions. You're probably the most mathematically proficient person I've ever discussed this with and it's an area that I've always found absolutely fascinating. Thanks again for your time, Rrhain. I really appreciate your help.
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Buzsaw Inactive Member |
Like we keep telling you, you need more mathematics to truly understand how space is defined. I'm not asking for understanding of how you define it. I'm asking for a statemnet defining space, the area in which things exist. I'm not asking about the things which exist in apace like gravity and light. I'm asking about the space itself, that area in which things like light gravity and bricks [i]may or may not exist.[i] My dictionary's #1 definition goes as follows: "Distance extending without limit in all directions; that which is thought of aa a boundless, continuous expanse extending in all directions or in three dimensions, within which all material things are contained. Where has my dictionary gone wrong?
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Eta_Carinae Member (Idle past 4375 days) Posts: 547 From: US Joined: |
because dictionaries are not physics texts!
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NosyNed Member Posts: 8996 From: Canada Joined: |
Your dictionary is not a physics text. That's what's wrong with it.
You've been given what we can give you in words. At this point to avoid giving you a confused or wrong answer we do need a real physicist to try to give an answer. I'm fairly sure though that the real definition of space would (as others have suggested) have to be given in a mathematical form. This may be because I don't understand this well enough to give a valid simplified description in words though. I'd sure like to see Eta drop in and up date us on this at this point.
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sidelined Member (Idle past 5908 days) Posts: 3435 From: Edmonton Alberta Canada Joined: |
buzsaw
Well then, please define space. I am at this moment reading a book. Relativity: The Special and the General Theory. It is published by Three river press and sells for 8.95 U.S. In it you will find the proper understanding of how things like position and space are best defined in order to clarify how science is able to learn things that give real insight into the nature of the universe. It is not a hard book and the math is kept to a minimum. The author does his best to explain in clear terms just what is meant by each of the equations used and allows you to gain a grasp of the physical picture behind it. Give it a try and see if it helps.
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Beercules Inactive Member |
quote:I just posted a simple definition. So have others.
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
buzsaw responds to me:
quote:quote: No, I'm talking about THREE. I even directly said so: The the space inside the walls, the space outside the walls, AND THE WALLS, THEMSELVES.
quote: Wrong. You are missing the entire point. I am not trying to make a direct comparison between a simple mathematical example of the Real number line and the universe. Instead, I am pointing out that your use of the term "infinite" as a synonym for "unbounded" is not accurate as can be seen by this mathematical example of the Real number system. I am not trying to get you to think that the universe is like the Real number line. I am trying to get you to think that "infinite" and "unbounded" are two different things and need to be treated separately.
quote: How do you know? What is your definition of "boundary"? Again, you are confusing "infinite" with "unbounded" and the two are not the same.
quote: Nothing.
quote: Nothing.
quote: (*sigh*) There is no space outside of it. The empty set is just as much of a set as the universal set. And yet, the universal set is closed, which means it includes its boundary. And yet, what on earth is this "boundary" of the universal set? You need to learn the math, buzsaw.
[qs]DEFINITION Let S subset-or-equal R. If bd S subset-or-equal S, then S is said to be closed. if bd S subset-or-equal R\S, then S is said to be open. If none of the points in S are boundary points of S, then all the points in S must be interior points of S. On the other hand, if S contains its boundary, then since bd S = bd (R\S), the set R\S must not contain any of its boundary points. The converse implications also apply, so we obtain the following useful characterizations: THEOREM A set S is open iff S = int S. A set S is closed iff its complement R\S is open. The interval (0,5) is open and the interval [0,5] is closed. Thus our present terminology is consistent with our inteval notation. That is, an "open inteval" (a,b) is an open set and a "closed interval" a,b is a closed set. In particular this means that any neighborhood is an open set, since it is an open interval. The interval [0,5) is neither open nor closed, and the unbounded interval [2,infinity) is closed. The entire set R of real numbers is both open and closed! It is open since int R = R. it is closed since it contains its boundary: bd R = empty set and empty set subset-or-equal R. PRACTICE Is the empty set open? Is it closed? Analysis: An Introduction to Proof[/i] by Steven R. Lay, page 106 - 107, "Topology of the Reals"][/qs] [Note: I did not misspell "if" in the theorem. I really did mean to write "iff." It has a specific meaning in mathematics.] Now, you tell me, buzsaw: What in the Reals separates the reals from the empty set? You simply do not understand the concept. You are stuck in a simplistic view of how space is supposed to behave. It does not look the way you want it to look. The only reason I brought up the house analogy was to get you to comprehend the idea that there is a difference among a set, its complement, and the boundary between them. It was not to imply that the universe is exactly like a house. A house is finite and the universe is infinite. The universe, however, has a boundary. That boundary is what separates it from nothing. Edited to replace the font symbols for infinity and the empty set with the words since the system doesn't seem to like the extended character set This message has been edited by Rrhain, 06-27-2004 04:08 AM Rrhain WWJD? JWRTFM!
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RingoKid Inactive Member |
bout time I chimed in with my nothing but bubbles again...
nothing is perfectin the space where nothing exists will one find perfection the perfect nothing ...in the meantime Imagine, if you will bubbles...expanding as they float around bumping into other bubbles and inside of these bubbles is another bubble expanding and so on... ...and if all these bubblesmade a musical note, as they bumped and merged and expanded, they created chords and melodies and so on... In other words, beyond the boundary of our bubble membraned like universe exists something that we will probably never see and therefore will probably never have an accurate term of reference for likewise for the pre big bang singularity so let's call it nothing and accept nothing as factquestion everything determine your own truth define your own reality and be most excellent to each other...or else !!!
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