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Post by Xaa on Sept 23, 2007 14:17:48 GMT -5
Someone wrote and asked for a better explanation of what Marilith meant in book 6 when she was talking about turning Ana or Kata. Well, in trying to come up with an answer, I stumbled across this image on Wikipedia which may help people understand. It's not an inversion or eversion, it's motion through another plane of movement, one at right angles to the three planes we can sense (length, width, height). Viewed three-dimensionally, yes, it resembles eversion, but it's not, it's motion (specifically, rotation) through a fourth dimension of spatial existence. Original image found here: en.wikipedia.org/wiki/Image:8-cell-simple.gifI hope this helps others who have the same question to understand. If it doesnt, however, you might want to consider reading a very old book called "Flatland." In Flatland, the sphere could only be perceived as a circle of varying size (the size changing as it passed through the plane of Flatland), as a single point, or as an invisible voice speaking from somewhere nearby - but yet, from nowhere in their world. This was because the sphere posessed a third dimension that the inhabitants of Flatland (and, indeed, their entire world) did not posess - height - and was able to translate themselves along that axis, in ways the people of Flatland could not, passing through the two-dimensional plane of Flatland at will. Well, Marilith can't pass through this plane like the sphere passed through Flatland - she is encompassed by the plane, and exists within it. To continue the Flatland analogy, it's as though the sphere that visited Flatland was fixed to the plane by it's central point, which would have made it impossible for the sphere to explain the third dimension to the Flatlanders, as they would have perceived it as an unchanging sphere no matter how it turned itself. Visualize, however, the sphere as a US Football or Rugby-ball - an oblate sphere. So long as it travels along the two axes of flatland, it appears as a circle. But, if it rotates along an axis the Flatlanders can perceive, despite that such rotation is impossible for ordinary members of that dimension, then suddenly, it changes shape, becoming an ellipsoid. Actual *translation* (movement) along the third dimensional axis causes them to leave Flatland, and enter... Well, another dimension. So, Marilith has a fourth dimension that ordinary inhabitants of the Prime Material do not, and she can rotate ana or kata (which is not technically correct use of the terms, but it's the only way she can describe it to Corwin) and present a view of herself that ordinarily can only be seen four-dimensionally. In three-dimensional terms, she turns inside out, and if she continues to turn along that axis, she ends up right side out again. But, it's not an eversion, nor is it a translation, since she doesn't actually GO anywhere. It's a four-dimensional rotation. And, like every other inhabitant of every dimension in Eddas' universe, she can't physically leave the plane through translation in the fourth dimension, she can only walk (swim/fly/crawl/etc) along the ordinary axes of movement. And yes, for those of you who already grasped that, the existence of an axis for her to rotate along in turning ana or kata it means there is a higher dimension providing the axis of rotation. That dimension is part of the Void that Eddas keeps nattering on about from time to time - the universal source of everything that exists in his reality. It has more axes to it, as well, but I'll stop before someone's head explodes. I should mention, however, that the movement up the tesseract stairs in Book 4 was, indeed, movement Ana and Kata. However, it was only possible because they were in a place which allowed fourth dimensional movement, because they were in a place which posessed a fourth tactile/spatial dimension they could physically move along. Outside the tesseract/tower, such movement was/is impossible. Having moved ana on the stairs, however, nobody changed physically - they moved to another part of the stairs, and suddenly could perceive it differently. Kind of like walking around to the back of a building, and being able to see the other side. *sound of noisy explosions off-stage* Damn, several of you just did the "Scanners™ Head-Pop™", I'll stop now.
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Post by Kilarin on Sept 23, 2007 16:41:18 GMT -5
wow! what a cool tesseract animation! I've never seen anyone do that with it before.
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Post by Xaa on Sept 23, 2007 16:47:27 GMT -5
wow! what a cool tesseract animation! I've never seen anyone do that with it before. I have. I've also tried to do it myself, but it's not as easy as it looks. I've edited the explanation to try to make it clearer - let me know what you think. ;D
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Post by Kilarin on Sept 24, 2007 7:03:58 GMT -5
I think it's very clear, but then, I thought it was clear before. I may not be the best person to judge this though, since I've been a big fan of flatland since I was in grade school. Not to mention, of course, Wrinkle In Time. I think I occasionally upset my teachers discussing the possibilities of multiple dimensions. I KNOW I upset my parents. It's an idea that can be, somewhat, disturbing.I also found H. G. Wells "Time Machine" explanation interesting: --- You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions.'
'That is all right,' said the Psychologist.
'Nor, having only length, breadth, and thickness, can a cube have a real existence.'
'There I object,' said Filby. 'Of course a solid body may exist. All real things—'
'So most people think. But wait a moment. Can an instantaneous cube exist?'
'Don't follow you,' said Filby.
'Can a cube that does not last for any time at all, have a real existence?'
Filby became pensive. 'Clearly,' the Time Traveller proceeded, 'any real body must have extension in four directions: it must have Length, Breadth, Thickness, and—Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.'--- I find it interesting, and significant, but not entirely satisfactory. so anyway, having been fascinated by the concept of multiple dimensions for quite some time, none of these ideas were new to me, but they still seemed to be presented in a very clear and simple format. And certainly increased my interest in the Mage series!
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Post by Xaa on Sept 24, 2007 7:14:03 GMT -5
I think I occasionally upset my teachers discussing the possibilities of multiple dimensions. I KNOW I upset my parents. It's an idea that can be, somewhat, disturbing.I tried that on my parents when I was a kid, and my father quickly disabused me of the notion. 1) He already knew the basic theories of there being more than one dimension. 2) When I tried to discuss it, he simply said "point at it." I was like "point at what?" He said "point in a fourth direction." "I can't," I replied. "There you go. Unless you plan on becoming a mathematician or nuclear physicist, don't bother thinking about things like that - they have no bearing on reality." Well... I was, of course, rather miffed. Here I thought I had this really cool thing I had learned, and he basically blew it off as nothing. Now, however, I'm forty-five, and I realize he was right. You can hurt your brain trying to wrap your mind around concepts like this, and in the end, it serves no useful purpose to anyone other than a mathematician and a nuclear physicist. His explanation, though a very good one from a layman's perspective, has only one problem in this case: Everything he said only applies when the fourth dimension being discussed is time. In physics, time is not a dimension - it's a fundamental property of the universe that defines existence (hence the term 'spacetime'). All other properties of matter and energy are defined in terms of time. Thus, it's not a dimension, it's a property. Certainly, in Eddas Ayar's universe, time *is* a fourth dimension (as he explains in book 4 - it's not *the* fourth dimension, it is *a* fourth dimension). But, Eddas is a fictional character living in a fictional universe where magic works. In our universe, time isn't a dimension, it's a fundamental property of existence. ----------------------- And for anyone who doesn't quite get that and thinks that we are all constantly travelling forward through time, my response is this: Turn right. If time is a dimension instead of a property, then you can move in that dimension at right angles to it. Nevermind whether or not you can speed up, slow down or go backwards. Get up out of your chair, and turn right in time. See? You can't. It's not a spatial axis you can move along, rotate along, or move at angles to. Time is a fundamental property of existence. Well... Technically, time is an alternative form of space which allows the transformation of the absolute motion of light to the relative motion of quantum particles, and thereby the transformation of acausal space to causal history via the transmission of quantum information and systemic entropy, but let's not split hairs - it still boils down to a fundamental property of existence. Another example of what I mean, just to make this clearer: Gravity, as you know, is a force that is constantly accellerating you downward. This provides an axis starting from the center of the earth and passing through your body, upwards to infinity. You can move at right angles to this axis (by getting up and walking around) and you can rotate along this axis (by turning around). You can even move along this axis very easily (try jumping up and down). But, you can't do the same with time - not even at the quantum level. There is nothing you can do to "jump up and down" in Time, walk at right angles to it, or turn around relative to your 'motion'. Thus, time is not a dimension you are travelling forward through (as in HG Wells' explaination, above), it's a fundamental property of reality. For similar existential reasons, time machines don't work. You can't travel through time in the same sense you travel through space. Time is a fundamental property defining your existence, not a dimension a machine/vehicle can move you through. And that's long before get into causality and conservation of energy. And yes, at the quantum level, particles can theoretically bounce backwards and forwards in time. But, that's only theoretically. This isn't an observable phenomenon, it's simply a shortcut that is used to resolve certain quantum physics formulas that rely on quantum properties we do not completely understand at this point. Moreover, you are a lot bigger than a quantum particle, and quantum physics doesn't apply at macroscopic scales - only at the quantum scale (hence the name 'quantum physics'). I like time-travel stories, but I don't fool myself into thinking they're anything other than stories read for entertainment. ----------------------- Glad you enjoyed it. ;D
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Post by wellsy007 on Jul 30, 2009 16:50:47 GMT -5
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Post by grobblewobble on Dec 9, 2009 15:38:17 GMT -5
Thinking about a hypothetical fourth dimension has long been a hobby for me (even before I discovered and read Flatland). I like your explanation above, but would like to say something about rotation. And yes, for those of you who already grasped that, the existence of an axis for her to rotate along in turning ana or kata it means there is a higher dimension providing the axis of rotation. Rotation in higher-dimensional spaces does not occur along an axis. In flatland, things rotate within a plane, around a point. In our world, things rotate "within" a plane, around (perpendicular to) an axis. In 4-D, things rotate "within" a plane, around (perpendicular to) another plane. So in N-D it is more convenient to think of rotation as occuring in a plane of rotation, rather than around an axis. In flatland there is one plane you can rotate in. In our world there are three perpendicular planes to rotate in. In 4-D there are six perpendicular planes to rotate in (every combination of two perpendicar direction constitutes one of them). I hope this explanation is clear. By the way, something that I think is pretty cool about 4D: In flatland you can't tie a knot. In our world you can tie a knot in a rope. In 4-D a knot in a rope falls apart, but you can tie a knot in a sheet.
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Post by Zesvotzashni Sinkunndai'Jari on Dec 10, 2009 1:00:02 GMT -5
I think I occasionally upset my teachers discussing the possibilities of multiple dimensions. I KNOW I upset my parents. It's an idea that can be, somewhat, disturbing.I tried that on my parents when I was a kid, and my father quickly disabused me of the notion. 1) He already knew the basic theories of there being more than one dimension. 2) When I tried to discuss it, he simply said "point at it." I was like "point at what?" He said "point in a fourth direction." "I can't," I replied. "There you go. Unless you plan on becoming a mathematician or nuclear physicist, don't bother thinking about things like that - they have no bearing on reality." Well... I was, of course, rather miffed. Here I thought I had this really cool thing I had learned, and he basically blew it off as nothing. Now, however, I'm forty-five, and I realize he was right. You can hurt your brain trying to wrap your mind around concepts like this, and in the end, it serves no useful purpose to anyone other than a mathematician and a nuclear physicist. Er. What. I'm really trying real hard to understand how, exactly, does said professions find such concepts paticularly "useful"? If such concepts "have no bearing in reality" because we cannot therotically "point" in a 4th dimension (Would it even count as pointing anymore?) then why would they suddenly find it useful? And more so, how is it making it "useless" to the rest of us? Especially somebody like me, a Tennahjauhn, who's nearly entire life revovles around totally bizarre, really disturbing, completely deranged, incredibly stupid, twisted and backwards, seemingly impossible concepts which are closer to home than the house I live in right now. The entire thing smells like a plothole. I mean, you made a story about it (Or contains it in some form), and people actually bought it, well, they didn't just BUY it, they loved it, sounds like it DID have a useful purpose to you. AND to the readers (Even if it made their heads explode). And it's one of the few things that makes me happy and treats my homesickness, so it has a useful purpose to me, too. And on the time machine thing, (Warning: Insane theories ahead)actually I believe you can indeed make a machine to "browse" around time AKA the "Grand Organizer", you can't think about the data (Space) you must think about the base (Time) and figure out a way to access a paticular section of data in said base. It cannot REALLY be travelled through then, because you have nowhere to go except into the data, so I think when people say "jump through time" they actually mean browse through time inorder to "jump" to a specific point of data.
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Post by grobblewobble on Dec 10, 2009 6:40:40 GMT -5
The reason high-dimensional spaces are particularly useful to mathematicians and phycisists is that they represent a natural and convenient way to formulate theories and make calculations.
Just like points and lines and perfect circles. Those are all hypothetical objects that do not actually occur in the real world, but nonetheless help us in understanding and predicting phenomena that do occur in the real world.
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Post by Kilarin on Dec 11, 2009 10:16:07 GMT -5
grobblewobble:
cool info, thanks!
Zesvotzashni Sinkunndai'Jari:
grobblewobble:
And many physicists believe that our universe really DOES have more than 3+1 dimensions. String theory is built upon this idea. It's VERY speculative, but there are several features of the universe that it would help to explain. For example, the rate at which some natural forces drop off would make perfect sense if they were spreading along more than 3 dimensions, with some of the dimensions curved in upon themselves.
It's complicated, and its been a long time since I looked at it. But it IS rational to believe that dimensions exist beyond those that we can observe.
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Post by grobblewobble on Dec 11, 2009 11:33:21 GMT -5
For example, the rate at which some natural forces drop off would make perfect sense if they were spreading along more than 3 dimensions, with some of the dimensions curved in upon themselves. Wow, that is some cool info as well, thanks. Since you seem interested, I will try to explain how a knot in a sheet works. Imagine you have a large (4D) sheet of cotton, and imagine you are capable of moving into the ana and kata directions. Since it is a 4D "sheet", it is thin in two directions and large in two other directions. Now let's say you hold one end of the sheet in your hands and someone else (say, Marilith) holds the other end. Together you are keeping the sheet stretched. Now Marilith moves her end of the sheet into the kata direction. The sheet is now diagonally stretched into kata, and you would only see a small piece of cloth that you are holding. This piece of cloth that still remains in your, 3D slice of space has a long and thin shape: in other words, it looks a bit like a rope. If someone else would hold the end of the sheet for you and you would move kata, you would see another piece of the sheet, which also looks like a rope. Now, imagine that a 4D creature would simultaneously take all these ropes in his hands and would simultaneously tie identical knots in all of them. This would be possible without tearing the sheet, since all connected parts of the sheet can stay connected during this operation. And now we have a knot in the sheet. If you would try to rotate the entire sheet back into your 3D world, that would not be possible. This is the same as trying to fit a knot in a rope into a plane. Part of the sheet would always remain ana or kata, until the knot is untied.
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Post by Kilarin on Dec 11, 2009 16:37:12 GMT -5
thank you, absolutely fascinating, and now my brains have melted.
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