LITMIR.BIZ

      And one more nuance: you put a ruler, and it lies, lies to itself, does not touch anyone, and those three lines come out of this “nothing”. They do not lie near the “nothing” they just go out. There is already an element of movement. To show this, sometimes at the end of these lines draw arrows and call them vectors. In general, unusual things begin literally from the first step. Now listen further. I was once again surprised. What are these straight lines themselves? Here’s the mathematical definition of a line: “A line is a collection of points”. Yes, yes! It is a collection of points! It turns out that the line is not something that lasts for some distance, but the points arranged in a row. Lines, it turns out not, but there are only points. Again points, again “nothing.”

      Let’s talk about the point. Although it is denoted by zero on Cartesian coordinates. The point is really zero, really nothing, the complete absence of space, namely: length, width and height. But it is necessary to somehow denote zero, and mathematicians conditionally designated it with a dot. But in reality, all three lines rest on zero, rest in the absence of space. But what is interesting, although it is zero and nothing, it plays a prominent role in the dimensional Universe, at least for contrast. Here is a dimensional Universe with a length, width and height, that is, space. And there is a zero without length, width and height, that is, the absence of space. We will often return to zero as a no-space indication. Zero is present everywhere. He is like a beginning. There is zero – the absence of space, and immediately after it the space begins: length, width and height. And I would say that, really, as in Cartesian coordinates, zero is an inseparable element of space, this is the beginning, this is the point of reference. And, I repeat, in the future we will always rely on this beginning. I came to the conclusion that zero is really the cornerstone of our universe.

      I will say right away: before the start of my investigation, I did not know this. Therefore, when I began to study textbooks, and analyze what I read, each new page brought me new discoveries. I wanted to put everything in its place, but from the very first steps it became clear that in order to put everything in its place or put everything on the shelves, it would be necessary to prepare a new room, and the shelves should be of a different kind. Too unusual opened a new world. And yet, I wanted to understand him, and understand everything.

      It is considered that our space is three-dimensional. It has a length, width and height or in other words: line, area and volume. A point is literally the source, the beginning of three-dimensional space. But while I will not be distracted, thinking about this issue. Continue to deal with the length, width and height. When popular literature describes the properties of three-dimensional space, it also tells you how the two-dimensional and one-dimensional worlds would look like, and how the inhabitants of these worlds would perceive various physical phenomena (unfortunate inhabitants!). It is believed that our three-dimensional world has volume. Accordingly, the two-dimensional world is a plane, and one-dimensional – a line. And again we slipped to the point. The point has no measurements.

      And now mentally we will increase the dimensionless point to the size of the ball and see how it fits into the spatial dimensions. In our three-dimensional space, the ball has volume. If this ball intersected the plane of the two-dimensional world, then the inhabitants of this world would first see a point that would increase in size (a sort of Big Bang of the two-dimensional world) and turn into an increasing circle. Of course, the scientists of this two-dimensional world would begin to guess whether the expansion, about which the “redshift” of their space speaks, will always continue, or the mass of the circle will be large enough, and eventually it will shrink. Meanwhile, the ball crossed the equator and the two-dimensional inhabitants saw that it shrinks and turns into a point again, and finally, it completely disappeared. In this regard, let us ask this question:

      We will return to the problem of the intersection of a plane with a ball and the ball itself, and at the same time a circle. For now, let’s return to the description of two-dimensional and one-dimensional spaces. The hypothetical inhabitants of the two-dimensional world will perceive the ball as a circle. And if their flat world will cross another plane, they will perceive it as a line. Accordingly, in one-dimensional space the ball will be perceived as a line, and the line as a point. We now know how the inhabitants of two-dimensional and one-dimensional spaces would perceive the ball and the plane crossing their limited worlds. And now we call these residents observers. The observer is always outside the observed object, even if it is physically located inside the object, for example, the same ball or examines its insides through a microscope. The observer is different from the observed object. A clear boundary separates him from the observed object, otherwise he simply could not separate himself from what he observes. Since the observer can see with his eyes (in the extreme case, he perceives with the senses), the observed object must be in front of the eyes – outside the observer. I agree that the inhabitants of the flat world would perceive the ball as a circle … to the touch, but they would only see a line – a sizeable segment. It is we, the inhabitants of the three-dimensional world, who see that they are dealing with a circle. And now we ask ourselves: what do the inhabitants of the one-dimensional world see when their line crosses the ball? If they are on both sides of the ball, then they tell each other that some kind of a segment extends, and then a shortening segment obstructs their path, but each of them would see only a point. That is, they both see one dimension less than the space where they live. Then ask yourself this question:

      And the second question:

      So, we see one dimension less than the space in which we live. At first, I thought that I had made a discovery: that we are residents of the three-dimensional world looking from some fourth dimension to our three-dimensional world. But then, having analyzed what we actually see, I came to the conclusion that we do not see the volume, we always see the plane that is, two dimensions. The cube always appears flat to us, and only the stereo effect of the two eyes forms a volume. Well, now let’s think again: maybe our world is two-dimensional? We always walk, go, float on a plane, on the surface of something. What is height? This is gravity. Earth gravity gives us an indication that the flat wall in front of us is the third dimension, that is, height, and if there were no gravity, we would also perceive the wall as a plane and also walk along it. Even man externally represents the plane – this is a skin cover. It turns out that we still do not live in a three-dimensional (time we will not

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