A layman's questions about universes

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.

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.

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. 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? 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! 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.