11 Answers

  1. With a lot of training, I'm sure a person will be able to understand four-dimensional space. In other words, they will be able to effectively navigate it, answer “tricky” questions, and so on.

    If it is considered that a person “imagines” a four-dimensional space, then the answer is “yes, it is possible”. Another thing is that they won't be able to draw it clearly for you so that you can understand it too.

    What is the mechanism that makes it difficult for people to understand four-dimensional space? Plain. Four-dimensional space was completely unnecessary for humans to evolve successfully. People live in three dimensions. To perform all the daily tasks, get food, and avoid hazards, you need a very good understanding of three-dimensional space. So in a billion years, the brain has become an expert in three-dimensional space. This is a necessity. The brain also knows how to keep the body in balance (and this is very difficult, if you think about it), is able to distinguish many tastes, is able to recreate the picture of what is happening, looking at the world with two-dimensional vision. The brain can do a lot of things that you need.

    He would have been able to understand four-dimensional space. But-why?

    Why four-dimensional space cannot be visualized. Because a person has absolutely no tool for interacting with four-dimensional space. None of the senses work in four dimensions. In order to “visually imagine” a four-dimensional space, you must first mentally imagine that you are a four-dimensional being living in a four-dimensional world, that you have four-dimensional eyes. I think that with the right amount of practice, you can put all this in general terms in your head and understand the four-dimensional space. But you will be able to explain and describe it to another person only when they, too, first imagine themselves as four-dimensional. You need some basic experience, basic feelings. Just as a child learns to see, navigate, and walk as a child.

    And, of course, all this will be much more difficult and slower. Because the brain is evolutionarily optimized for three dimensions.

    P. S. Since the question is relegated to the mathematics section, I did not address the question of the depth of the 4th space, the shape of the space, etc., which might be relevant in physics. I took the 4th dimension without any curvatures and restrictions: an infinite straight line orthogonal to the other three.

  2. You can always draw a three-dimensional shape on a plane, such as a cube. This will, of course, be a jumble of some intersecting lines, but if you understand with your mind or intuition what is depicted in the drawing, which line is closer, which is further from the observer, what intersects with what and what intersects, then two dimensions are quite enough to operate with three-dimensional images. Similarly, in three-dimensional space, you can imagine projections of 4-figures. First, of course, you need to understand everything at the level of reason. Study theorems for N-space that are analogous to those of stereometry. And be sure to think about it a lot, then your intuition will develop.

    Various mathematical methods such as stereographic projection or analytical geometry can be of great help.

  3. Yes, it is possible and necessary when we want to find out what has become through TIME t with a point in this space The fact is that an orthogonal metric space has 3 ordinates and when the 4th dimension of TIME t is included, I represent it as a square of hypotenuses between 3 orthogonal metric and time coordinates. In short, how quaternions are constructed. That is, in other words, we find out where the point has moved in Time t in complex space. For example, in economics, when you need to find out where the cash point has moved during TIME t.

  4. as a rule, the overwhelming majority of people can not imagine what was not a practical opt-out.

    what is a 4-dimensional space to explain to an ordinary person is as difficult as a blind person from birth to explain what color is. that is, almost impossible.

    it is possible that there are those who have the gift of abstract thinking so much that they are able to understand what it is, because in the novels of some science fiction writers certain inventions are predicted, which neither they nor the existing society at that time had ever encountered.

    However, I doubt that they will be able to give a sufficiently clear explanation of 4 or more dimensions.

  5. You can represent a space of any dimension, but the method of representation will not be the same as we are used to. Place the coordinate axes parallel to each other. The point of an n-dimensional space is a polyline that connects points on the axes (of course, the point is only in points on the axes, they are connected by a polyline, just for visual representation). For example, a tesseract looks like a collection of all polylines with vertices on 4 segments of the same length, lying on 4 parallel lines “under each other”. �A straight line in a four-dimensional space is defined as: any polyline with 4 vertexes on parallel lines, and points on each axis “go” in both directions at constant speeds (on each of the 4 axes, the speed may be different). Having a certain imagination, you can imagine any shape in this way, both in four-dimensional and in space of any dimension. This representation of an n-dimensional space allows us to graphically solve many problems that we are used to solving only for 2 variables. For example (just for those who know about it), this is how you can graphically solve a linear programming problem with any number of variables (which, of course, is much more efficiently done by the simplex method), but I'm only talking about the ability of a person to represent a space of ANY dimension.

  6. Our perception of the world is limited by our senses, and perhaps there is a lot that we do not see, do not feel, do not understand. And since this is the case, there is no point in speculating about it. You can only make assumptions and guesses. But I am sure of one thing for sure-the human brain and mind are not perfect and cannot grasp and understand everything that exists in the universe. Yes, here on earth, living in a civilization, we can amuse ourselves with how far our science has progressed and how intelligent we are. But who are we on a universal scale? Just stupid little bugs.. as stupid as insects are to us.

  7. The brain can't imagine more than 3 dimensions of space. There are several reasons, first, from our point of view, 4D space does not exist, this is the main problem – you can't just invent it, describe its laws, when we don't use them. Second, we don't know what the fourth axis [W] describes, if it exists. Talking about the time t and so on is certainly good, but this and the like cannot [yet] be applied physically and is even difficult to imagine.

    When we think of a two-dimensional space, such as a notebook sheet, we mean drawings on points on it, both two-dimensional and three-dimensional. For example, we can draw both an ordinary line and a [three-dimensional] cube, resorting to the formulas of [orthogonal vector] projection, as is often done in the 9th grade when drawing a cube on the blackboard. We construct composite lines using vectors projected from three-dimensional space onto the plane [of the board]. By inviting a shadow artist, we can turn our wireframe into a full-fledged 3D drawing by simulating light reflections on the cube's surface (for example, using Lambert's formula).

    But if we take a three-dimensional space – a box of balls-we don't have the slightest idea of what the [three-dimensional] points describing these shapes (bodies) are a projection of. There are several theories, the most popular of which are “string theory”, the theory of four – dimensional Calabi-Yau space (wikipedia.org), which are part of string theory. These theories attempt to describe the structure of our [theoretically four-dimensional] world…

    The answer to the question “what mechanisms prevent us from representing a four-dimensional space” is a lack of information. Imagine that the author compressed our world into an absolute plane, and everything became two-dimensional. Then we will [never] be able to discover three-dimensional space, because we will have no proof of its existence, and accordingly, we will not be able to deduce its laws. But is it true that our world is three-dimensional and no more? Scientists still need to prove what space looks like in practice, if it is more complex than three-dimensional.

    We understand three-dimensional space only because it is tangible. Even if there are other “axes” (planes, etc.) in space, we have no perceptual organs associated with it, we do not receive such data.

    Do not confuse four – dimensional, five-dimensional and other figures from mathematics with the physics of real space-these are different things.

  8. yes it is possible!!!!and the mechanism of sequence interferes, as it is impossible to understand one without the other.And the fourth point will prove that teleportation is possible and if it is possible then … I think you guessed it.

  9. I believe it is possible, but it requires some training. By analogy with sports: a person from the street will not be able to lift a heavy barbell, but this can be achieved by training. In this case, training may consist of systematic (preferably professional) work with a mathematical four-dimensional space. I heard it (but couldn't find any confirmation) about a software simulator where a person controls arrows and moves a three-dimensional cross-section of various four-dimensional shapes on a computer screen. It seems that after a long game with such a simulator, four-dimensional intuition can develop and a person begins to imagine it. Well here is another link from one forum about this:�http://dxdy.ru/post1135112.html#p1135112

  10. The previous answers were good and detailed, and I agree with them. I want to share my knowledge and ideas in this area and answer the question is it possible to present. I'll answer right away, YES-IT's POSSIBLE.

    We are trying to imagine the 4th dimension (we will omit time) physically (that is, to reach into it, look into it, and so on…), and thereby feel and” taste ” it. And as it was correctly said, this is impossible (or is it still possible???) since we live and are limited to 3 spaces. A good example: make a beetle live and run on a Moebius sheet (With a double Moebius sheet, it's even more interesting). The beetle will spend its entire life thinking that it lives on a flat sheet and will never get to the other side of it. No matter how much he wants to, he will not see or feel the opposite side. But we know that he lives and runs on both sides of the Mobius leaf. And that the Mobius leaf is not 2D but 3D.

    Go to 4D. Further, purely hypotheses and fantasies, but answering the question of whether we can imagine it.

    What if the 4th and subsequent dimensions are, how would you put it, not physical but spatially deeper.

    Well, for example, the 4th dimension can be our life. Living our lives, we measure the next milestone on the 4th dimension and everything repeats again, but of course with changes. I can easily imagine it and imagine it in my head. It's just that we are limited in our lives to prove it (remember the beetle – he can also imagine it if he comes up with a Mobius leaf, but he can never prove it)

    Or the 4th dimension can be realized (I don't remember where I heard or read this) from quantum theory. At every moment of time, our space for each of us is bifurcated and we exist in infinite numbers of copies of ourselves. And this is all along the X, Y, and Z axis. Thus, the 4th, 5th, and 6th dimensions are formed. That is, in one 3D dimension, I am now answering this question, but in another, I am not. Personally, I can easily imagine that, too.

    Well,in order to please the opponents of this answer, I will answer the opposite. Perhaps we can't imagine more than three dimensions because we created these dimensions ourselves and they don't exist at all. There is no X Y and Z in nature. And in general, it is possible that there is only one dimension in the universe. Or maybe it doesn't exist at all. After all, if, for example, the world is 100% deterministic, then all our actions determine the future, just as our present was predetermined by the past, and so on and so forth. And maybe it's the Big Bang dimension or God himself.

    Or if you really fantasize, then perhaps (if you take into account the quantum neglect and non-determinism of the world) dimensions do not exist at all (or their infinity) and everything is subject to chaos and the inability to measure and know anything.

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