horrible_at_math 0 Posted January 10 I hope it's alright to ask this here. I'm asking about existing theories, so I don't think it counts as speculation (though I could be wrong), also, this is kind of long. I was going to ask this on quora, but I'm way past the character limit, and I might get better answers here anyway. I'm trying to understand how four (or more) dimensions could exist (without math, btw). The fourth dimension is often described is such a way, that I understand it to be an impossible vector. From what I do understand, dimensions are traversable, spatial vectors. A point is non dimensional. A line (x) is one dimensional. Two lines (x, y) intersecting at a right angle is two dimensional (and forms a plane). And three lines (x, y, z) intersecting at a right angle covers three dimensions. That being said, how can there be four dimensions, when three dimensional vectors cover all directions? I know that some people point to time as a fourth dimension, and this may (or may not, idk) make some degree of sense in mathematical terms (perhaps useful in calculations), but not in a literal sense, as “time” cannot actually be described as a dimensional vector. Time, as I understand it, is simply a measurement (for rate of change). There is no spatial, traversable vector known as time. Only the present moment exists. The past is a recording, a memory, which exists in the present, stored chemically, digitally, etc. the future is merely a forecast, based on past experiences (memories), and also exists only in the present moment. There is no time vector. This is the reason that time travel is impossible (unless someone can think of a way to track and reverse the trajectory and compositional/chemical/energetic changes of every particle within a given area, which I think is virtually impossible). I’ve heard somewhere that “higher” dimensions could be the vectors between "points" composed of three dimensions (3d universes like ours); --which, if this is the case, would require the multiverse theory (or something like it)-- basically, this theory stacked all the way up to ten or eleven dimensions, by theorizing (I think) six and nine dimensional points (basically super 3 dimensional points? which are already super points?), and that the highest possible dimension (10 or 11, the master universe, or universal hub) would contain all possible realities. (I do not know the name of this theory, or whether is it reputable... I think heard about it on youtube a year or two ago). This theory makes much more sense to me than the idea that there are impossible spatial vectors making up “higher” dimensions, and that we’re all just too simple do conceptualize them; But a lot of people seem to believe exactly that. There are even these shapes that are supposed to represent fourth dimensional “shadows” or “cross sections”, and an inside-out jar that’s supposed to be continuous if it were fourth dimensional. But I honestly think that this must be the result of a misconception, possibly based on a confusion between reality, and the tools with which we measure it. So am I wrong about this (or right)? If so, why? (and please no equations, I’m not a math guy. seriously, arithmetic is my limit). Share this post Link to post Share on other sites

Strange 2479 Posted January 10 That being said, how can there be four dimensions, when three dimensional vectors cover all directions? Three dimensions cover all directions only in three dimensional space! In space with more dimensions, then more dimensions are required - that is rather a circular argument, but I can't think of any pother way of putting it. Intuitively, we imagine there can only be three orthogonal axes because we exist in a 3D universe. It is hard to visualise more dimensions, and I suspect the only route in is via the mathematics. Time, as I understand it, is simply a measurement (for rate of change). There is no spatial, traversable vector known as time. In relativity, time is a fourth dimension. It is traversable but only in one direction. In special relativity, the effects such as length contraction and time dilation are actually rotations between one of the spatial dimensions and the temporal dimension - an object moving (relative to you) swaps some of its spatial dimension for time. In general relativity, the more complex curvature of the space and time dimensions causes effects such as the thing we call "gravity". Hope that helps a bit. It is a lot to get your head round. Share this post Link to post Share on other sites

swansont 6208 Posted January 10 There are vector spaces with an infinite number of dimensions, all orthogonal to one another. We use "3 space" because it describes a lot of things. Share this post Link to post Share on other sites

DrmDoc 206 Posted January 10 As a novice, I have very little to offer here other than this link to a prior discussion on higher dimensional spheres. This discussion includes a link to a PBS Infinite series video exploring the topic of higher dimensions. I though the video was very interesting and informative. Perhaps you will as well. Share this post Link to post Share on other sites

Delta1212 894 Posted January 10 Three dimensions cover all directions only in three dimensional space! In space with more dimensions, then more dimensions are required - that is rather a circular argument, but I can't think of any pother way of putting it. Intuitively, we imagine there can only be three orthogonal axes because we exist in a 3D universe. It is hard to visualise more dimensions, and I suspect the only route in is via the mathematics. In relativity, time is a fourth dimension. It is traversable but only in one direction. In special relativity, the effects such as length contraction and time dilation are actually rotations between one of the spatial dimensions and the temporal dimension - an object moving (relative to you) swaps some of its spatial dimension for time. In general relativity, the more complex curvature of the space and time dimensions causes effects such as the thing we call "gravity". Hope that helps a bit. It is a lot to get your head round. I can kind of visualize a four dimensional object. I start losing the thread at five dimensions, and by six is really more of a concept of what visualizing a six dimensional object should be like than an actual visualization. At seven I give up completely and it just becomes abstract knowledge rather than trying to picture anything. I once spent some time trying to work through how someone could play chess (or at least a chess-equivalent) using a board in 4+ dimensions, which helped a lot with getting the visualization aspect down. Share this post Link to post Share on other sites

ecoli 369 Posted January 10 You may be interested in the book Flatland... the setting is geometrical, though the whole thing is actually an allegory to gender norms in Victorian times. The thing to take away is that, imagine you are a 2d object like a square. You would probably be having just as much trouble imagining a 3d object, such as a sphere, as you are currently having imagining a 4th dimension. For example, take a sphere moving through your 2d plane. All you would see is a point turn into a long line, and then shrinking in length before disappearing. A 4d cube rotating along a plane in 3d would look something like this, to a 3d observer: Share this post Link to post Share on other sites

horrible_at_math 0 Posted January 19 Three dimensions cover all directions only in three dimensional space! In space with more dimensions, then more dimensions are required - that is rather a circular argument, but I can't think of any pother way of putting it. Intuitively, we imagine there can only be three orthogonal axes because we exist in a 3D universe. It is hard to visualise more dimensions, and I suspect the only route in is via the mathematics. In relativity, time is a fourth dimension. It is traversable but only in one direction. In special relativity, the effects such as length contraction and time dilation are actually rotations between one of the spatial dimensions and the temporal dimension - an object moving (relative to you) swaps some of its spatial dimension for time. In general relativity, the more complex curvature of the space and time dimensions causes effects such as the thing we call "gravity". Hope that helps a bit. It is a lot to get your head round. Relativity is an equation, a mathematical approximation used for calculations, and cannot be trusted as an accurate description or definition of reality. There is no dimension such as time. we do not "move" through "time". Changes in the composition an location and trajectory of objects in three dimensional space occur. "Time" is an illusion created by memory and mathematics (physics). We can remember or calculate the past state of the universe, and we can estimate the future state of the universe (The trajectory of an object in motion, for example). There is no evidence to support the idea that time exists as a dimension. It is merely a factor. A measurement used to compare the rates of change in various objects and substances within the universe. Also, though I am not well versed in the details of relativity, I am under the impression that the theory refers to spacetime, not space and time, and that Einstein himself considered time --as some people think they know it-- to be an illusion. (this is not to say that time "travel" is entirely impossible either. But it is mostly impossible. Although time is not a traversable dimension, it is a physical phenomenon. Time is all of the ongoing change within the universe. if someone could find a way to reverse all of that change, even in a local area, that would count as time travel. but reversing all of the chemical, energetic, compositional, and trajectorial changes at once, even in a small space, with 100% accuracy, seems like an insurmountable task, and would likely be fairly dangerous if it could somehow be accomplished) [also, I am aware that I am possibly contradicting myself by stating that time cannot be considered a dimension, while also stating that time manipulation is possible. I guess it could be considered a dimension if we ever develop the technology to time travel, but time cannot be considered a naturally occurring dimension, as we'd really just be manipulating space and the contents within it, or in other words, we'd be manipulating three dimensions at once, and in a very substantial way, which would create the illusion of a dimension of time] As for dimensions, I cannot imagine four dimensional space --if it exists-- could work in the same way as the first three dimensions. As I said before, three dimensions cover all possible spatial directions. The only way that I can imagine more dimensions is using probability, multiple realities, and maybe Schrodinger's cat. That is, I can imagine that reality may branch of into multiple possibilities, and possibly a near infinite number of realities. These multiple realities would make up the points which, when connected, could make up higher dimensions. there are some videos on youtube which sort of demonstrate this concept. and Other realities may naturally exist alongside our own, or may only be possibilities that could theoretically be created. Even if these other realities do exist, there would be no easy way to access them. though personally, I don't believe that they can naturally exist, and I think that the only way to create or traverse them would be time manipulation. But even then, I'm not sure that a universe could be made to split into two distinct realities existing simultaneously. For example, if I created a spacetime manipulation device, which could effectively reverse all processes within the universe, while isolating myself and the device from these changes, I would simply be changing the state of the universe around me. a new timeline would be created, but the old timeline simply would never have occurred. The only evidence that the old timeline existed would be myself and the device. This is because I have not traveled through a dimension known as time, I have simply manipulated the state of the universe around me, while leaving myself and my device unchanged. If there were two of these devices, and both were used at the same time, at different rates or directions ("foreward" or "backwards"), well, I don't have enough information to accurately predict the results, but I can guess that either one or both devices would break (likely creating an explosion or explosions of unimaginable magnitude), or the universe would rip itself apart. The latter could possibly create a new universe or multiple universes, but there would be little to no continuity of the old universe. These would be brand new(ish) universes, so there would be no branching of our original timeline. Now, if I happen to be wrong, and multiple universes can or do exist simultaneously, and can be traversed, then I imagine that higher dimensional life would evolve from beings who initially learned to travel between different realities, then began to exist simultaneously in multiple realities, and then to exist as an amalgamated entity with components of itself located in several different realities, the way our cells are located in different 3d locations in our body, and that these entities could be the links that create higher dimensional structures. That is how I imagine higher dimensional structures and objects could come to form. You may be interested in the book Flatland... the setting is geometrical, though the whole thing is actually an allegory to gender norms in Victorian times. The thing to take away is that, imagine you are a 2d object like a square. You would probably be having just as much trouble imagining a 3d object, such as a sphere, as you are currently having imagining a 4th dimension. For example, take a sphere moving through your 2d plane. All you would see is a point turn into a long line, and then shrinking in length before disappearing. A 4d cube rotating along a plane in 3d would look something like this, to a 3d observer: I'm fairly positive that two dimensional life is not possible; that life needs at least three dimensions to exist. This is because life is the result of an interaction of chemicals and compounds, atoms and molecules, etc. None of these things exist on a two dimensional level. In fact, as far as I know, nothing exists or can exist on a two dimensional level. Even the things that we perceive as two dimensional, such as drawings, are actually 3 dimensional. Share this post Link to post Share on other sites

MigL 511 Posted January 22 (edited) Higher dimensions were postulated in string theories as 'compacted' dimensions. They don't need to be infinite in extent like length, width, height an ( possibly ) time. Rather they can be a compact/finite, orthogonal dimension which curves back on itself,at each point in space-time. So compact ( Planck scale possibly ) that we would never notice or detect them, but they could possibly affect gravity, allowing it to 'leak' into these compacted dimensions such that it 'seems' weaker than it actually is. Only at the compact scale ( Planck ? ) would gravity have equivalent strength as other forces. These compacted dimensions take the form of Calabi-Yau spaces or manifolds, have been an important tool for theoretical physics and are an active area of study. You should look them up. Don't be so dismissive of Flatland. While a fantasy, it is a useful reduced dimensional analogy which gives insight into 3D and 4D spaces. Edited January 22 by MigL Share this post Link to post Share on other sites

steveupson 18 Posted January 24 From what I do understand, dimensions are traversable, spatial vectors. A point is non dimensional. A line (x) is one dimensional. Two lines (x, y) intersecting at a right angle is two dimensional (and forms a plane). And three lines (x, y, z) intersecting at a right angle covers three dimensions. That being said, how can there be four dimensions, when three dimensional vectors cover all directions? I know that some people point to time as a fourth dimension, and this may (or may not, idk) make some degree of sense in mathematical terms (perhaps useful in calculations), but not in a literal sense, as “time” cannot actually be described as a dimensional vector. First, let me know if this response is off topic or if I’m hijacking your thread. My only intention here is to actually have a grown up discussion of the issue you raised (I think) in your question. I agree that there does seem to be something that is slightly off about either the accepted terminology or about the fundamental concept, or both. We can easily see that time isn’t like anything else, certainly it isn’t equivalent to a length, or, more correctly, it isn’t like two lengths that are oriented perpendicular to one another. When we start talking about dimensions there is an arbitrary explanation or understanding that has been agreed upon. As some of the experts here have already pointed out, dimensions can be different things (both conceptually and mathematically) depending on the application. The way it is mathematically expressed, Euclidean 3-space actually comprises three sets of 2D planes. It would be more meaningful to call it 2D^3 rather than 3D. That’s the reason why Euclidean 3-space has octants… 2X2X2=8. There is a deeper understanding of what a 2D plane is, though. It is two lengths perpendicular to one another, sure, but what does that really mean? The concept of orthogonality brings direction (or orientation) into the picture, along with the length which is the first dimension. So, what is direction, really? We can call it angular position, and we can call the change in angular position angular velocity, and we can call the change in angular velocity angular acceleration. In case it isn’t obvious, there is a stunning symmetry with length here, where we call the change in length speed, and the change in speed acceleration. Even more stunning is the fact that when we add direction to length we get position, when we add direction to distance we get displacement, and when we add direction to speed we get velocity. Still, even in light of all these facts, there seems to be a winning argument (for reasons no one can explain other than the old "we've always done it that way") that direction isn’t really a base quantity, like time or length. It’s supposed to be a thing that isn’t really a thing, whereas the other two are things that really are things. I think that this approach is rather arbitrary, especially when direction can be quantified as a scalar value exactly like time and length are both quantified. Time, as I understand it, is simply a measurement (for rate of change). There is no spatial, traversable vector known as time. Only the present moment exists. The past is a recording, a memory, which exists in the present, stored chemically, digitally, etc. the future is merely a forecast, based on past experiences (memories), and also exists only in the present moment. There is no time vector. This is the reason that time travel is impossible (unless someone can think of a way to track and reverse the trajectory and compositional/chemical/energetic changes of every particle within a given area, which I think is virtually impossible). A more correct approach would be to identify time, length, and direction as three different dimensions. We already see time and space as separate, so all that is necessary is to recognize that space is the combination of direction and distance. It does make much more sense to view it this way because the math supports this view, and it doesn’t really support the other mainstream view, whatever that is (no one seems to be able to say exactly what the mainstream view is, only that it isn't this). So am I wrong about this (or right)? If so, why? (and please no equations, I’m not a math guy. seriously, arithmetic is my limit). I'm not a math guy either, but I do see what I think are the same issues as what you're asking about. Personally, I think that the higher dimensional spheres are one of those mathematical oddities that has very little to do with our physical universe. When we look at spacetime mathematically we see it as time orthogonal to a backdrop of hyperbolic space. I do think that this mathematical "trick" has usefulness and it does represent a major aspect of the natural universe. Everything else (string theory, etc.) must lie somewhere between these extremes. Share this post Link to post Share on other sites

Mordred 886 Posted January 24 (edited) Pretty good post fairly on target to the OP. Mathematically think of these extra dimensions as additional degrees of freedom. So you can add as many dimesions to describe the possible degrees of freedom. Each interaction counts as a degree of freedom ie in string theory or Kaluzu-Klien. So for example a complex object such an electron I need three dimensions to describe its volume aspects 1 for time an an additional one for its charge behavior Edited January 24 by Mordred Share this post Link to post Share on other sites

steveupson 18 Posted January 24 Pretty good post fairly on target to the OP. Mathematically think of these extra dimensions as additional degrees of freedom. So you can add as many dimesions to describe the possible degrees of freedom. Each interaction counts as a degree of freedom ie in string theory or Kaluzu-Klien. So for example a complex object such an electron I need three dimensions to describe its volume aspects 1 for time an an additional one for its charge behavior Thanks Mordred. Yes, that is the understanding of how the math works in the conventional scheme of things. Since each of these degrees of freedom that is being added is orthogonal, then their direction is axiomatic. It's the same (mathematically) as adding more length axes that are orthogonal to the normal three. That's very different than what I was talking about. Once again, the terminology that we're stuck with isn't very specific. Your use of degrees of freedom has a meaning that is much more specific than just using the term dimensions. The point I was making is that time isn't a length at all. It does add a degree of freedom, but not in the same way that adding another orthogonal length does. They are two distinctly different processes, both mathematically and conceptually. Time is added to 3-dimensional Euclidean space by a different method, specifically we're talking about Minkowski space. "Because it treats time differently than it treats the three spatial dimensions, Minkowski space differs from four-dimensional Euclidean space." Also, direction isn't a length at all, either. It comes to the party wearing its own ensemble, too, just like time does. Because of the mathematical treatment we use in order to add these additional degrees of freedom, it's difficult to visualize exactly what is happening when we start piling up more and more orthogonal axes. Because of the way we do the math, length and direction get conflated in a very subtle fashion (it has to be extremely subtle because it hasn't been recognized until now.) If we zoom in on this subtle conflation then we can actually separate direction completely from the base quantity of length. When we do that, direction becomes another base quantity. In case you haven't understood what I've been saying all along (which I'm fairly certain no one has understood completely) let me try and say it once more, with some clarity this time. We currently only express direction or orientation as a relationship between two (or more) lengths. It never stands alone, without being associated with at least two lengths. These can be perpendicular xyz lengths or they can be the diameter and circumference of a circle. In either case we express direction by explicitly defining two lengths. There's another method for expressing direction, one that doesn't rely on any lengths at all. It expresses direction based on the relationship between three orthogonal objects. This relationship only occurs with three orthogonal dimensions. It doesn't have any existing analog since all of our expressions for direction are based on two-dimensional relationships that occur between lengths. Share this post Link to post Share on other sites

Mordred 886 Posted January 24 (edited) Just to clarify vectors are orthogonal but not all degrees of freedom are. example being a spinor Just to clarify vectors are orthogonal but not all degrees of freedom are. example being a spinor. Though we model spinor rotations under orthonormal basis. ie some of the groups involved are orthogonal but other groups can be unitary ie (SU) is special unitary while SO groups are orthogonal. Not all symmetry groups fall under orthogonal groups. Thats more on how the symmetry groups are constructed than on the required dimensions. I mention that simply to be aware not all groups are orthogonal groups Edited January 24 by Mordred Share this post Link to post Share on other sites

steveupson 18 Posted January 24 That's a very good point. It helps to illustrate how a huge variety of different kinds of information can be represented this way. That's sort of the whole point behind defining direction as a base quantity. It can represent a lot more information than what we would normally ascribe to it doing it the simple way. Share this post Link to post Share on other sites

studiot 1156 Posted January 24 Please note there is no reason to suggest that the basis vectors or axes have to be orthogonal. Calculation convenience often dictates this but skew axes are also sometimes useful as in shear transformations. Share this post Link to post Share on other sites

steveupson 18 Posted January 25 Yes, of course. This is even more support for the thesis than any other proof that's been offered. Direction must contain information in order for this to be true. In the case of the skew axis, direction encodes useful information, thereby making the calculation more manageable. Share this post Link to post Share on other sites