Blocks cubes

Hyper-Dimensional Space

back to home pdf share

 

According to the philosopher Rudolf Steiner, the creator of anthroposophy, in his book "The Fourth Dimension", the human being has six dimensions: four in the astral realm, a fifth in the" lower devachan" (lower mental plane), and the sixth dimension in the "upper devachan" (higher mental or manasic plane). Thus, our three-dimensional personality, the only one of which we are habitually conscious, would be nothing but a "shadow" (reflection, or projection), of the four-dimensional aspect of our Being. Such declarations do not pass of being mere curiosities, if it were not, because, as the same author says:

"We will always feel powerless in the higher world if we do not develop faculties that allow us to see here, in the world of ordinary consciousness, the higher world.”

And, on the other hand, as Steiner adds, for ordinary mortals, the higher dimensions exist only as ideas: "Seeing them begins when we enter the spirit world, where we are immediately forced to adapt to more than three dimensions.

    The problem is that unless we are psychic, we cannot consciously perceive what lies beyond the third dimension. It is true that some mathematicians have formulated hypotheses and ideas about the fourth dimension and even about higher dimensions; however, they cannot prove that hyper-dimensional space exists. Nevertheless, we think that, rationally, we can come to intuit the existence of at least the fourth dimension.

 Let us try.

First attempt

 Daily experience shows us that we move in a three-dimensional world, that is, that it is manifested in length, width and height.

    Let us remember, before continuing with our reasoning, the 3 known dimensions:

 - A point (.) has no dimension, it is merely a concept that indicates, from the spatial perspective, a position.

-  A line (---) has only one dimension (length). 

-  A square plane has two dimensions (length and width)  

 

- A three-dimensional object, for example, a cube obviously has 3 dimensions (length, width and height).

 

Let us now try to imagine a one-dimensional being living in a one-dimensional world (an unlimited line). Such a being could "move ", in one direction, within the line, but would never be able to be aware of the dimension it inhabits. In order to do so, it would have to "go out" of its own dimension, that is, become a two-dimensional being.

    Let us imagine now a being of two dimensions, living in a plane. Even this being could not be aware of the dimension in which he lives. It could only be conscious of the beings or objects that move in the plane, that is, of the linear beings or objects (of 1 dimension).

    Following our reasoning, a 3-dimensional being, living in a three-dimensional space (for example, in a cube), could not be aware of its three-dimensionality either, since it could only "see" two-dimensional beings.

    Now, man (and other living beings), is conscious of the third dimension in which he moves, so, necessarily, he must contain in his constitution, at least the fourth dimension and move in a four-dimensional space.

 

Second attempt

Let's approach the problem from another perspective.

If we take, for example, a cube (the simplest three-dimensional shape, formed by 6 folded squares), and we project it orthogonally in a plane (the auxiliary projecting lines are perpendicular to the projection plane), we will obtain a square:

 

If we project the square orthogonally we will get a line, and if we project the line, a point. We could, therefore, say that the point (0 dimensions) is the projection of a line (1 dimension), that the line is the projection of a square (2 dimensions) and that the square is the orthogonal projection of a cube (3 dimensions). Following this reasoning, it is worth pointing out that when we see a line, we are not only observing a one-dimensional shape, but also the edge of a two-dimensional shape (square). In the same way, when we observe a square, we are not only observing a two-dimensional shape, but a face of a three-dimensional object (cube).

    Following the same logic, when we see a cube, we would not only be seeing a three-dimensional object, but a part of a tetra-dimensional   figure; in this case, of a figure formed by 8 cubes, which mathematicians have called Tesseract or Hypercube:

 

Hypercubus

Corpus Hypercubus of Salvador Dali:

 

In this regard, the following question is relevant: If the cube is a part of a larger figure, why don't we encounter "the whole" when we rotate around it? The answer, obviously, is very simple. A two-dimensional being, no matter how much it spins around a square, would never stumble upon "the whole" of the cube, since the "rest" of the cube is in another dimension. In the same way, no matter how much we rotate around the cube, we will never trip over the other 7 "faces" of the Tesseract or Hypercube, since they are in a dimension perpendicular to the third one.

    It is evident that what we have just explained in such a superficial way does not prove that the fourth dimension exists, but that, through reason, we can intuit or glimpse its existence. And if we can intuit that the human being (and other living beings), possesses at least 4 dimensions, it will not be difficult for us to accept that a great part of what we call "human being", exists "hidden" to our perception, in other dimensions.

 

 

 

back to home pdf share