3 Answers

  1. A meter in 4 dimensions can? Here you can find descriptions and visualizations of a 4-dimensional cube. wikipedia.org

    You can also try this: A point is an object without dimensions. We continue the point in the 1st direction and get a straight line of a 1-dimensional object. Now we draw a line in the other direction-we get a 2-dimensional object plane. Then, by analogy, we draw a plane – we get a 3-dimensional cube. Now it is more difficult – we pull the cube into the 4th dimension, see the link here)

  2. Christina,

    a computer is just a digital tape recorder.

    At serious studios, they don't write in analog for a long time.

    Even ABBA, in its darkest years, already wrote the last records in numbers.

    Accordingly, you need exactly the same thing as for normal sound recording.

    And start with the essay 😉

  3. If we are talking about generalizing the concepts of square and cubic meter to spaces of dimension higher than 3, then the simplest thing is to add time. Next, I will not talk about units of measurement and just tell you how to represent a four-dimensional cube.

    To understand how this works, let's analyze the transition from a two-dimensional square to a three-dimensional cube. So, how do I get a cube out of a square by adding time?

    The square is located in a plane and each time point corresponds to its own version of the plane. If, for example, we move a square with acceleration, take a picture of the plane at each moment, and then add the images of the planes one on top of the other, we get something like this picture:

    Here, each section of the resulting shape with a horizontal plane is our square at some point in time. It's as if we recorded the movement on video with an infinite number of frames, and then put all the frames in a stack.

    Now, to get a cube, you need to do the same, but do not move the square. Moreover, the time should pass exactly 1. That's all. A three-dimensional cube is built. For a better understanding, it is useful to think about how the sections of such a cube with the x = 0 and y = 0 planes will look in our model, as well as what the edges and faces are made of.

    A four-dimensional cube is obtained similarly to their three-dimensional one. That is, a four-dimensional cube is a set of states of a three-dimensional cube at rest for a single time.

    With this construction, you can imagine the situation and answer some questions.

    • What, for example, will be the vertices of such a cube? All vertices of the original three-dimensional cube at the start and end times.

    • What kind of ribs will it have? The edges of the source cube at the start and end moments, plus edges connecting each vertex at the start moment to the same vertex at the end moment.

    • What will be the cross-section of such a cube with the x = 0 plane? The projection is obtained by fixing one coordinate – in this case, the x coordinate. If we fix x, then the original three-dimensional cube that we move turns into a square x = 0, 0 < y < 1, 0 < z Adding time 0 < t Putting the planes on top of each other, we get a three-dimensional cube in the space y, z, t.
      For illustrations, color is often used instead of time. The general approach is to associate an additional numeric property with each point in space. Another good example of this property is temperature.

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