Dimensional Discourse

I agree with you that thought is not limited to three dimensions. In fact, one might even need to use a quadrillion-dimensional space to describe any one human mind. (I believe that there are somewhere around one quadrillion synapses in the human brain. Technically, a single point in this vast hyperspace may represent an entire state of mind, including every conscious and unconscious thought at any one time.)However, although we may use many abstract dimensions in our thought processes, most people cannot form a mental picture of anything with more than three physical dimensions. In other words, we may use many dimensions more than four to think, but we still cannot visualize higher dimensions, in the sense of mutually perpendicular directions. I will have to disagree with you on this point. Math is a very useful tool, especially in dealing with dimensions beyond human comprehension. Certainly it's more interesting to try to visualize higher dimensions than to represent them with mathematical formulas, as true visualization would give us a more intuitive grasp of higher dimensions. But if we use math, we can at least put ourselves on the right track to understanding them, especially since we need math in order to simulate them. no argument there

I know Tony650 stopped posting on this thread way back in 2004, but I still think it would be appropriate to answer his three main questions on dimensions. Yes I do. I believe it is possible to retrain one's brain to be able to conceive 4D, though this would take immense focus and a long time to do. The mathematician Charles Hinton (I believe that's his name) once tried to visualize the fourth dimension by creating a mental 36*36*36 unit cube to represent the 3D retina a 4D creature would have. He then assigned each box in this cube a Latin name, and when he tried to map 3D objects into this "retina," he would recite the name of each cube (voxel) the object occupied. This was a painstaking process, and I think he may have given up this exercise, thinking 4D perception was impossible. I'm sure others have found simpler, though probably just as difficult, methods to "rewire" their perceptions, but I do not know anyone who has done so.Virtual reality is probably a much more efficient way to learn 4D. Just as when you were a baby, you learned to perceive the world as 3D by combining perceptions from different senses (i.e., vision, audition, kinesthetic, vestibular, touch, etc.), full body immersion into a virtual 4D environment should allow faster comprehension of the fourth spatial dimension. A couple of years ago, I came across a project to create "4D Virtual Environments" where participants would wander around a complex four-dimensional spaceship and manipulate objects. Unfortunately, though, as I saw on a demo simulation of the project, the person in the VE can only see a single 3D "slice" of spaceship at a time, though they could still move in the fourth direction. A description of the project is at http://www.cvr.uci.edu/dzmura/4D/ndtech3.pdf. (The URL may be old, so you may need to use a Google cache to view the page.)I think that if you could find a way to transform the picture on the 3D retina of the 4D virtual creature to be able to fit on our 2D retinas without losing any visual information, we could quickly learn to see as a 4D person would see. I would also suggest incorporating "4D sound" to assist in perception of the "4D-ness" of the virtual environment. Anyway, until this technology comes about, I guess we could just keep on trying to visualize the fourth dimension on our own. I haven't thought about this as much, and I would need to be more familiar with quantum mechanics and string theory to get an idea of how to do this. But I believe there is a way, it's just a matter of technology. I read somewhere that if we created super-small, super-temporary doughnut-shaped black holes from a large enough particle collision, it would prove the existance of at least 5 dimensions to our universe, and I heard that scientists are trying right now to build a large particle accelerator to do just just that. Don't worry, though; the black holes would be so small that they would decay almost as soon as they were created. This is a very interesting concept. Of course, it is relatively easy to describe a universe with multiple temporal dimensions mathematically; comprehending it is another story. Several years ago, when I first started thinking about extra dimensions, I hypothesized on the properties of extra tempral dimensions. The first dimension here would be time, composed of the "now" and the two opposite directions of past and future, just as the first spatial dimension has "here" and backward and forward. Are you with me so far? The second temporal dimension, then, would also have the "now," but it would be perpedicular to time. Instead of past and future, it would have two unique directions. You could represent multiple temporal dimensions as perpendicular axes intersecting at "now."With two temporal dimensions, time would no longer look like a line, but rather like a plane. Movement in such a universe would also be different. Instead of moving in a line, you would move in a plane. With 3 temporal dimensions, you could move in a volume. Now imagine a simple universe with only one spacial dimension. Tiny line segments can move only back and forth in their universe. Try to visualize time as a spacial dimension, so that if a point in the 1D universe were to move back and forth repeatedly, it would look like a static zig-zag line on a plane (Remember this plane is a spacetime, so any line drawn on it is actually movement, with the slope of the equalling the speed of the object). If we add another temporal dimension, we can view this simple universe in one of two ways: either as the zig-zag suddenly beginning to move or as a static bumpy plane in a 3D spacetime (Remember, this is still just a single point moving back and forth in a universe with only 1 spatial dimension; it now only looks like a bumpy plane because we are viewing its motion with 2 temporal dimensions). If anyone cannot visualize this, I could try to post a picture of it, as long as someone tells me how to do that.I have read before that a universe with 2 or more temporal dimensions would be inherently unstable, just as would be one with 4 or more spatial dimensions, so life probably could not exist in such a world.

I just felt I should elaborate on how one might retrain himself to be able to visualize 4D without the aid of virtual reality since I may have focused too much on VR in my last post.First of all, a hypothetical 4D analog of a human would have a basically 3D retina, just as a normal human's retina is basically 2-dimensional. The trick is to be able to form a 3D image in your mind where you can "see" every point in the image, including the back, the front, and every internal point, all simultaneously. This should take a while to master, though. It might help at first if you make the image "transparent" so you can see all the points at once, or maybe just imagine one slice at a time of the image. As for depth perception, you could either try to picture 2 individual 3D retinas and try to apply parallax shift, or just use something like color-coding to assign depth (This is all still in your mind).Now, about rotating objects in 4D. There are actually 6 rotational "axes" in the 4th spatial dimension, not 5. It's probably better to think in terms of planes of rotation rather than in terms of rotating around an axis, as an "axis" is 2D in the 4th dimension. You can find the number of rotational planes with the formula r = (n^2-n)/2, where r is the number of rotational planes and n is the number of dimensions.I'll try to help you visualize 4D rotation.

      __________        /|     |     |\        __________
|          |      / |     |     | \      |          |
|          |     |  |     |     |  |     |          |
|          |     |  |     |     |  |     |          |
|          |     |  |     |     |  |     |          |
|__________|      \ |     |     | /      |__________|
\|     |     |/

Above is as good a picture I can do of a square rotating in the 3rd dimension. As you can see, one side "grows" as the other "shrinks," and they appear to come closer together until you're seeing the square on edge; then the process reverses. Keep in mind that this is only an apparent distortion of the square.For rotation of a cube in 4D, first imagine just a plane cube. Now distort it similar in fashion to how I distorted the square, only "shrink" one face while "enlarging" the opposite face, at the same time, bringing the two opposite faces closer together. This should look like the cube distorting into a frustum and finally flattening into a square, the square being the "edge-on" view of the cube.I hope this helps.

Many people, when they first hear that a fourth spatial dimesion means a space that can include 4 mutually perpendicular lines, think that it is impossible because neither can they visualize it, nor can they point in this new direction. One reason you cannot visualize such a space is that you have never directly experienced anything like it, so you assume direction is not applicable.Visualization is not intrinsic to 3D. Imagine a Flatlander; he could only see a line in front of him. He would not be able to visualize 3D because he had never experienced it, nor could he ever consider shapes like circles or squares to be flat, since they have both width and depth. Similarly for us, we might not be able to imagine a 4th spatial dimension, but that does not make one impossible. I believe an intuitive grasp of higher spatial dimensions is only a matter of training. Of course. It's not impossible to conceive that there could exist an extra "spiritual" dimension. However, as I believe someone else has mentioned before on this thread, we would not call it a fourth dimension if it had nothing in common with the three below it. For instance, even though time is a dimension, we do not call it the fourth dimension because it is so different in nature from the three spatial dimensions. Thus, even if there is another dimension "beyond physical," I would not call it the fourth dimension; it would be just another dimension in its own category. I would not dismiss the existance of higher dimensions so quickly. String theory, which has mathematically reconciled relativity and quantum mechanics, may very well be true, though scientists are still not sure whether they can test for it. If it does turn out to be true, then there are actually higher dimensions, only curled up very tightly so as to be shorter than the width of a proton.Now don't think I believe there is an actual fourth spatial dimension of macroscopic scale "somewhere out there." Probably very few people believe one actually exists. But being able to visualize higher dimensions would certainly be useful in the real world, especially when trying to understand the relationships between many variables and to more intuitively see trends among them. Economics, for instance, often involves many more variables than three, so being able to visualize higher spatial dimensions would allow an economist more readily to notice trends in the data than by simply looking at numbers (think about graphing on a 4D coordinate system).Again, a macroscopic fourth spatial dimension probably doesn't exist, but a theoretical fourth dimension certainly has its applications.