32. Love is the fourth "PA" or GRANDBATMAN! In order to scan this beast, it must be introduced into rigid schematic boundaries from the very beginning. Following the imagery of the GAME, there are four types of love: 1) ROLE LOVE, or DEMONIC, DISCRETE LOVE. 2) LOVE ACTOR, or

Fourth lesson Girls, my dears, good evening! Write to me how you, I hope that everyone today with red roses has not been forgotten. Because we're going to have amazing practice with them. And tell me, how was your week? What did you do? What didn't you do? pamper yourself or

The idea of ​​hidden knowledge. – The problem of the invisible world and the problem of death. – The invisible world in religion, philosophy, science. - The problem of death and its various explanations. – The idea of ​​the fourth dimension. – Different approaches to it. - Our position in relation to the "field of the fourth dimension." – Methods of studying the fourth dimension. - Hinton's ideas. – Geometry and the fourth dimension. - Morozov's article. - An imaginary world of two dimensions. - A world of eternal wonder. - Phenomena of life. – Science and phenomena of the immeasurable. - Life and thought. - Perception of flat beings. - Different stages of understanding the world of a flat creature. – Hypothesis of the third dimension. – Our attitude towards the “invisible”. – The world of the immeasurable is around us. – Unreality of three-dimensional bodies. “Our own fourth dimension. - Imperfection of our perception. – Properties of perception in the fourth dimension. - Unexplained phenomena of our world. - The mental world and attempts to explain it. – Thought and the fourth dimension. – Expansion and contraction of bodies. - Growth. - Phenomena of symmetry. - Drawings of the fourth dimension in nature. – Movement from the center along the radii. - Laws of symmetry. - States of matter. - Relationship between time and space in matter. – Theory of dynamic agents. - The dynamic nature of the universe. “The fourth dimension is within us. - "Astral sphere" - Hypothesis about the subtle states of matter. - Transformation of metals. - Alchemy. - Magic. – Materialization and dematerialization. - The predominance of theories and the absence of facts in astral hypotheses. - The need for a new understanding of "space" and "time".

The idea of ​​the existence of hidden knowledge, superior to the knowledge that a person can achieve by his own efforts, grows and strengthens in the minds of people when they understand the insolubility of many questions and problems that confront them.

A person can deceive himself, he can think that his knowledge is growing and increasing, that he knows and understands more than he knew and understood before; however, sometimes he becomes sincere with himself and sees that in relation to the basic problems of existence he is as helpless as a savage or a child, although he has invented many clever machines and tools that have complicated his life, but not made it clearer.

Speaking even more frankly with himself, a person may recognize that all his scientific and philosophical systems and theories are similar to these machines and tools, because they only complicate problems without explaining anything.

Among the insoluble problems surrounding man, two occupy a special position - the problem of the invisible world and the problem of death.

Throughout the history of human thought, in every form without exception that thought has ever taken, men have divided the world into visible and invisible; they have always understood that the visible world, accessible to direct observation and study, is something very small, perhaps even non-existent in comparison with the vast invisible world.

Such a statement, i.e. the division of the world into the visible and the invisible existed always and everywhere; at first it may seem strange; however, in reality, all the general schemes of the world, from the primitive to the most subtle and elaborate, divide the world into the visible and the invisible - and cannot get rid of it. The division of the world into visible and invisible is the basis of human thinking about the world, no matter what names and definitions he gives to such a division.

This fact becomes obvious if we try to enumerate different systems of thinking about the world.

First of all, let's divide these systems into three categories: religious, philosophical, scientific.

Without exception, all religious systems, from such theologically developed to the smallest detail as Christianity, Buddhism, Judaism, to the completely degenerate religions of "savages" that seem "primitive" to modern knowledge, all of them invariably divide the world into visible and invisible. In Christianity: God, angels, devils, demons, souls of the living and the dead, heaven and hell. In paganism: deities personifying the forces of nature - thunder, sun, fire, spirits of mountains, forests, lakes, spirits of water, spirits of houses - all this belongs to the invisible world.

Philosophy recognizes the world of phenomena and the world of causes, the world of things and the world of ideas, the world of phenomena and the world of noumenons. In Indian philosophy (especially in some of its schools), the visible or phenomenal world, Maya, an illusion, which means a false concept of the invisible world, is generally considered non-existent.

In science, the invisible world is the world of very small magnitudes, and also, oddly enough, the world of very large magnitudes. The visibility of the world is determined by its scale. The invisible world is, on the one hand, the world of microorganisms, cells, the microscopic and ultramicroscopic world; it is followed by the world of molecules, atoms, electrons, "vibrations"; on the other hand, it is the world of invisible stars, distant solar systems, unknown universes. The microscope expands the boundaries of our vision in one direction, the telescope in another, but both are very small compared to what remains invisible. Physics and chemistry give us the opportunity to investigate phenomena in such small particles and in such distant worlds that will never be available to our vision. But this only reinforces the idea that there is a huge invisible world around a small visible one.

Mathematics goes even further. As has already been pointed out, it calculates such ratios between quantities and such ratios between these ratios that have no analogies in the visible world around us. And we have to admit that invisible the world differs from the visible not only in size, but also in some other qualities that we are unable to determine or understand, and which show us that the laws found in the physical world cannot apply to the invisible world.

Thus, the invisible worlds of religious, philosophical and scientific systems are, after all, more closely connected with each other than it seems at first glance. And such invisible worlds of different categories have the same properties common to all. These properties are. First, they are incomprehensible to us; incomprehensible from the ordinary point of view or for ordinary means of knowledge; secondly, they contain the causes of the phenomena of the visible world.

The idea of ​​causes is always connected with the invisible world. In the invisible world of religious systems, invisible forces control people and visible phenomena. In the invisible world of science, the causes of visible phenomena stem from the invisible world of small quantities and "fluctuations". In philosophical systems, the phenomenon is only our concept of the noumenon, i.e. an illusion, the true cause of which remains hidden and inaccessible to us.

Thus, at all levels of his development, man understood that the causes of visible and observable phenomena are beyond the scope of his observations. He found that among the phenomena available to observation, some facts can be considered as the causes of other facts; but these findings were insufficient to understand Total what happens to him and around him. To explain the causes, an invisible world is needed, consisting of "spirits", "ideas" or "vibrations".

Another problem that attracted people's attention by its insolubility, a problem that by the very form of its approximate solution predetermined the direction and development of human thought, was the problem of death, i.e. explanations of death, the idea of ​​a future life, an immortal soul - or the absence of a soul, etc.

Man has never been able to convince himself of the idea of ​​death as disappearance - too much contradicted it. There were too many traces of the dead in him: their faces, words, gestures, opinions, promises, threats, the feelings they aroused, fear, envy, desires. All this continued to live in him, and the fact of their death was more and more forgotten. A person saw in a dream a dead friend or enemy; and they seemed to him exactly the same as they had been before. Obviously they somewhere lived and could come from somewhere at night.

So it was very difficult to believe in death, and man always needed theories to explain the afterlife.

On the other hand, the echo of esoteric teachings about life and death sometimes reached a person. He could hear that the visible, earthly, observable life of a person is only a small part of his life. And of course, a person understood the fragments of the esoteric teaching that reached him in his own way, changed them according to his own taste, adapted them to his level and understanding, built from them theories of a future existence similar to the earthly one.

Most religious teachings about the future life associate it with a reward or punishment, sometimes in an overt and sometimes in a veiled form. Heaven and hell, transmigration of souls, reincarnations, the wheel of lives - all these theories contain the idea of ​​reward or retribution.

But religious theories often do not satisfy a person, and then, in addition to the recognized, orthodox ideas about life after death, there are other, as if not legalized ideas about the afterlife, about the world of spirits, which provide much more freedom to the imagination.

No religious doctrine, no religious system alone can satisfy people. There is always some other, more ancient system of folk beliefs, which is hidden behind it or hidden in its depths. Behind external Christianity, behind external Buddhism, there are ancient pagan beliefs. In Christianity, these are remnants of pagan ideas and customs, in Buddhism - the "cult of the devil." Sometimes they leave a deep imprint on the outward forms of religion. For example, in modern Protestant countries, where traces of ancient paganism have completely died out, systems of almost primitive ideas about the afterlife, such as spiritualism and related teachings, have arisen under the outward mask of rational Christianity.

All theories of the afterlife are connected with the theories of the invisible world; the former are necessarily based on the latter.

All this refers to religion and pseudo-religion, there are no philosophical theories of the afterlife. And all theories about life after death can be called religious or, more correctly, pseudo-religious.

In addition, it is difficult to consider philosophy as something integral - individual philosophical systems are so different and contradictory. It is possible to some extent to accept as the standard of philosophical thinking the point of view that asserts the unreality of the phenomenal world and human existence in the world of things and events, the unreality of the separate existence of a person and the incomprehensibility for us of the forms of true existence, although this point of view is based on a variety of grounds, both materialistic and idealistic. In both cases, the question of life and death acquires a new character, it cannot be reduced to the naive categories of ordinary thinking. For this point of view, there is no special difference between life and death, because, strictly speaking, it does not take as proven a separate existence, separate lives.

No and cannot be scientific theories of existence after death, because there are no facts confirming the reality of such an existence, while science - successfully or unsuccessfully - wants to deal exclusively with facts. In the fact of death, the most important point for science is the change in the state of the organism, the cessation of vital functions and the decomposition of the body that follow death. Science does not recognize any mental life independent of vital functions, and from a scientific point of view, all theories of life after death are pure fiction.

Modern attempts at a "scientific" study of spiritualistic and similar phenomena do not and cannot lead to anything, because here there is an error in the very formulation of the problem.

Despite the differences between the various theories of the future life, they all have one thing in common. They either depict the afterlife like the earthly one, or completely deny it. They do not try to understand life after death in new forms or new categories. This is what makes conventional theories of life after death unsatisfactory. Philosophical and strictly scientific thought require a revision of this problem from a completely new point of view. Some hints that have come down to us from esoteric teachings point to the same thing.

It becomes obvious that the problem of death and life after death must be approached from a completely new angle. Similarly, the question of the invisible world requires a new approach. Everything we know, everything we have thought so far, demonstrates to us the reality and vital importance of these problems. Until questions about the invisible world and about life after death are somehow answered, a person cannot think of something else without creating a whole series of contradictions. Man must construct for himself some kind of explanation, right or wrong. He must base his solution to the problem of death either on science, or on religion, or on philosophy.

But for a thinking person, both the “scientific” denial of the possibility of life after death and its pseudo-religious assumption (for we know nothing but pseudo-religions), as well as all kinds of spiritualistic, theosophical and similar theories, seem equally naive.

Cannot satisfy a person and abstract philosophical views. These views are too far from life, from direct, genuine sensations. It is impossible for them to live. In relation to the phenomena of life and their possible causes, which are unknown to us, philosophy is like astronomy in relation to distant stars. Astronomy calculates the movements of stars located at great distances from us. But for her, all celestial bodies are the same - they are nothing more than moving points.

So, philosophy is too far from concrete problems, such as the problem of the future life; science does not know the afterlife; pseudo-religion creates it in the image of the earthly world.

The helplessness of man in the face of the problems of the invisible world and death becomes especially evident when we begin to understand that the world is much larger and more complex than we have hitherto thought; and what we thought we knew occupies the least place among what we do not know.

The foundations of our concept of the world must be expanded. We already feel and realize that we can no longer trust the eyes with which we see and the hands with which we feel something. The real world eludes us during such attempts to ascertain its existence. More subtle methods, more effective means are needed.

The idea of ​​a "fourth dimension", the idea of ​​a "multidimensional space" indicates the way in which we can come to the expansion of our concept of the world.

The expression "fourth dimension" is often found in conversations and literature, but very rarely anyone understands and can determine what is meant by this expression. Usually the "fourth dimension" is used as a synonym for the mysterious, wonderful, "supernatural", incomprehensible, incomprehensible, as a general definition of the phenomena of the "superphysical" or "supersensible" world.

"Spiritualists" and "occultists" of various directions often use this expression in their literature, referring all the phenomena of the "higher planes", the "astral sphere", the "other world" to the area of ​​the fourth dimension. What this means, they do not explain; and from what they say, only one property of the "fourth dimension" becomes clear - its incomprehensibility.

The connection of the idea of ​​the fourth dimension with the existing theories of the invisible or otherworldly world is, of course, completely fantastic, for, as already mentioned, all religious, spiritualistic, theosophical and other theories of the invisible world first of all endow it with an exact resemblance to the visible, i.e. "three-dimensional" world.

That is why mathematics quite rightly rejects the common view of the fourth dimension as something inherent in the “other world”.

The very idea of ​​the fourth dimension arose, probably, in close connection with mathematics, or, more precisely, in close connection with the measurement of the world. It undoubtedly was born from the assumption that in addition to the three dimensions of space known to us: length, width and height, there may be a fourth dimension that is inaccessible to our perception.

Logically, the assumption of the existence of a fourth dimension can come from the observation in the world around us of such things and phenomena for which the measurements of length, width and height are insufficient, or which generally elude measurements, because there are things and phenomena whose existence is beyond doubt, but which cannot be expressed in terms of any dimensions. Such, for example, are the various manifestations of vital and mental processes; such are all ideas, all images and memories; such are dreams. Considering them as really, objectively existing, we can assume that they have some other dimension, in addition to those that are available to us, some extension that is immeasurable to us.

There are attempts at a purely mathematical definition of the fourth dimension. For example, they say this: “In many questions of pure and applied mathematics, there are formulas and mathematical expressions that include four or more variables, each of which, independently of the others, can take positive and negative values ​​between +∞ and -∞. And since every mathematical formula, every equation has a spatial expression, from here they derive the idea of ​​space in four or more dimensions.

The weak point of this definition lies in the provision accepted without proof that every mathematical formula, every equation can have a spatial expression. In fact, such a position is completely groundless, and this makes the definition meaningless.

Arguing by analogy with existing dimensions, it should be assumed that if the fourth dimension existed, then this would mean that right here, next to us, there is some other space that we do not know, do not see and cannot go into. From any point in our space, it would be possible to draw a line into this “region of the fourth dimension” in a direction unknown to us, which we cannot determine or comprehend. If we could imagine the direction of this line coming from our space, then we would see the "area of ​​the fourth dimension."

Geometric means the following. One can imagine three mutually perpendicular lines to each other. With these three lines we measure our space, which is therefore called three-dimensional. If there is an “area of ​​the fourth dimension” that lies outside our space, then, in addition to the three perpendiculars known to us, which determine the length, width and height of objects, there must be a fourth perpendicular, which determines some kind of incomprehensible to us, new extension. The space measured by these four perpendiculars will be four-dimensional.

It is impossible to define geometrically or imagine this fourth perpendicular, and the fourth dimension remains extremely mysterious to us. There is an opinion that one hundred mathematicians know something about the fourth dimension that is inaccessible to mere mortals. It is sometimes said, and this can be found even in the press, that Lobachevsky "discovered" the fourth dimension. In the past twenty years, the discovery of the "fourth" dimension has often been attributed to Einstein or Minkowski.

In fact, mathematics has very little to say about the fourth dimension. There is nothing in the fourth dimension hypothesis that makes it mathematically unacceptable. It does not contradict any of the accepted axioms and therefore does not meet with special opposition from mathematics. Mathematics fully admits the possibility of establishing the relations that must exist between four-dimensional and three-dimensional space, i.e. some properties of the fourth dimension. But she does all this in the most general and indefinite form. There is no exact definition of the fourth dimension in mathematics.

In fact, Lobachevsky considered the geometry of Euclid, i.e. geometry of three-dimensional space, as a special case of geometry in general, which is applicable to the space of any number of dimensions. But this is not mathematics in the strict sense of the word, but only metaphysics on mathematical topics; and it is impossible to formulate mathematical conclusions from it - or it can only be done in specially selected conditional expressions.

Other mathematicians found that the axioms accepted in Euclid's geometry were artificial and unnecessary - and tried to refute them, mainly on the basis of some conclusions from Lobachevsky's spherical geometry, for example, to prove that parallel lines intersect, etc. They argued that the generally accepted axioms are true only for three-dimensional space and, based on reasoning that refuted these axioms, they built a new geometry of many dimensions.

But all this is not the geometry of four dimensions.

The fourth dimension can be considered geometrically proven only in the case when the direction of the unknown line going from any point of our space to the area of ​​the fourth dimension is determined, i.e. found a way to construct the fourth perpendicular.

It is difficult even approximately to outline what significance the discovery of the fourth perpendicular in the universe would have for our entire life. The conquest of the air, the ability to see and hear at a distance, the establishment of relations with other planets and star systems - all this would be nothing compared to the discovery of a new dimension. But so far it hasn't. We must admit that we are powerless before the mystery of the fourth dimension - and try to consider the issue within the limits that are available to us.

With a closer and more accurate study of the problem, we come to the conclusion that under the existing conditions it is impossible to solve it. Purely geometric at first glance, the problem of the fourth dimension is not solved geometrically. Our geometry of three dimensions is not enough to investigate the question of the fourth dimension, just as planimetry alone is not enough to investigate questions of stereometry. We must discover the fourth dimension, if it exists, purely by experience - and also find a way to represent it in perspective in three-dimensional space. Only then can we create a geometry of four dimensions.

The most superficial acquaintance with the problem of the fourth dimension shows that it must also be studied from the side of physics.

The fourth dimension is incomprehensible. If it exists, and if, nevertheless, we are not able to cognize it, then, obviously, something is missing in our psyche, in our perceiving apparatus, in other words, the phenomena of the fourth dimension are not reflected in our senses. We must figure out why this is so, what defects cause our immunity, and find the conditions (at least theoretically) under which the fourth dimension becomes understandable and accessible. All these questions relate to, or perhaps to, the theory of knowledge.

We know that the region of the fourth dimension (again, if it exists) is not only unknowable to our psychic apparatus, but unavailable purely physically. It no longer depends on our defects, but on the special properties and conditions of the area of ​​the fourth dimension. We need to figure out what conditions make the region of the fourth dimension inaccessible to us, find the relationship of the physical conditions of the region of the fourth dimension of our world and, having established this, see if there is anything similar to these conditions in the world around us, if there are relations similar to relations between 3D and 4D regions.

Generally speaking, before constructing the geometry of four dimensions, it is necessary to create the physics of four dimensions, i.e. find and determine the physical laws and conditions that exist in the space of four dimensions.

Many people have worked on the problem of the fourth dimension.

Fechner wrote a lot about the fourth dimension. From his reasoning about the worlds of one, two, three and four dimensions follows a very interesting method of studying the fourth dimension by constructing analogies between the worlds of different dimensions, i.e. between the imaginary world on the plane and our world, and between our world and the world of four dimensions. This method is used by almost everyone involved in the question of higher dimensions. We have yet to get to know him.

Professor Zolner derived the theory of the fourth dimension from observations of "mediumistic" phenomena, mainly of the phenomena of the so-called "materialization". But his observations are now considered doubtful due to the insufficiently rigorous setting of experiments (Podmore and Hislop).

A very interesting summary of almost everything that has been written about the fourth dimension (by the way, and attempts to determine it mathematically), we find in the books of K.Kh. Hinton. They also contain many of Hinton's own ideas, but unfortunately, along with valuable thoughts, they contain a lot of unnecessary "dialectics", such as usually happens in connection with the question of the fourth dimension.

Hinton makes several attempts to define the fourth dimension both from the side of physics and from the side. A fair place in his books is occupied by a description of the method he proposed for accustoming consciousness to comprehending the fourth dimension. This is a long series of exercises in the apparatus of perceptions and representations with a series of multi-colored cubes, which must be remembered first in one position, then in another, in a third, and then imagined in various combinations.

Hinton's main idea, which he was guided by when developing his method, is that in order to awaken the "higher consciousness" it is necessary to "destroy oneself" in the representation and cognition of the world, i.e. to learn to cognize and imagine the world not from a personal point of view (as is usually the case), but as it is. At the same time, first of all, one must learn to represent things not as they seem, but as they are, even if only in a simple geometric sense; after which the ability to cognize them will appear, i.e. to see them as they are, and also from points of view other than geometric.

the first exercise given by Hinton: the study of a cube, consisting of 27 smaller cubes, which are colored in different colors and have specific names. Having firmly studied a cube made up of cubes, you need to turn it over and study (i.e. try to remember) in reverse order. Then turn the cubes over again and remember in this order, etc. As a result, as Hinton says, it is possible to completely destroy the concepts in the cube under study: top and bottom, right and left, etc., and know it regardless of the relative position of its constituent cubes, i.e., probably, represent it simultaneously in various combinations. This is the first step in destroying the subjective element in the idea of ​​a cube. Next, a whole system of exercises is described with a series of multi-colored and variously named cubes, from which all kinds of figures are composed, all with the same goal of destroying the subjective element in the representation and thus developing a higher consciousness. The destruction of the subjective element, according to Hinton, is the first step towards the development of higher consciousness and comprehension of the fourth dimension.

Hinton argues that if there is the ability to see in the fourth dimension, if it is possible to see the objects of our world from the fourth dimension, then we will see them in a completely different way, not as usual.

Usually we see objects above or below us, or on the same level with us, to the right, to the left, behind us, or in front of us, always on the same side facing us and in perspective. Our eye is an extremely imperfect apparatus: it gives us a highly incorrect picture of the world. What we call perspective is, in essence, the distortion of visible objects, produced by a poorly constructed optical apparatus - the eye. We see objects distorted and we imagine them in the same way. But all this is solely due to the habit of seeing them distorted, i.e. due to habit caused by our defective vision, which has weakened our ability to imagine.

But, according to Hinton, we have no need to imagine the objects of the external world necessarily distorted. The faculty of representation is by no means limited to the faculty of sight. We see things distorted, but we know them for what they are. We can get rid of the habit of representing things as they appear to us, and learn to imagine them as we know they are. Hinton's idea is that before thinking about developing the ability to see in the fourth dimension, you need to learn to imagine objects as they would be seen from the fourth dimension, i.e. not in perspective, but from all sides at once, as our "consciousness" knows them. It is this ability that Hinton's exercises develop. The development of the ability to imagine objects from all sides at once destroys the subjective element in representations. According to Hinton, "the destruction of the subjective element in representations leads to the destruction of the subjective element in perception." Thus, the development of the ability to imagine objects from all sides is the first step to the development of the ability to see objects as they are in a geometric sense, i.e. to the development of what Hinton calls "higher consciousness".

In all this there is much that is true, but there is also much far-fetched, artificial. First, Hinton does not take into account the differences between different mental types of people. A method that is satisfactory for himself may not produce any results or even cause negative consequences for other people. Secondly, the very basis of Hinton's system is too unreliable. Usually, he does not know where to stop, his analogies lead too far, thereby depriving many of his conclusions of any value.

From the point of view of geometry, the question of the fourth dimension can be considered according to Hinton in the following way.

We know geometric figures of three kinds:

one dimension - a line, two dimensions - a plane, three dimensions - a body.

At the same time, we consider a line as a trace from the movement of a point in space, a plane as a trace from the movement of a line in space, a body as a trace from the movement of a plane in space.

Imagine a line segment bounded by two points, and denote it by the letter a. Suppose this segment moves in space in a direction perpendicular to itself and leaves a trail behind it. When it has traveled a distance equal to its length, its trail will look like a square, the sides of which are equal to the segment a, i.e. a2.

Let this square move in space in a direction perpendicular to two adjacent sides of the square and leave a trail behind it. When he has traveled a distance equal to the length of the side of the square, his trail will look like a cube, a3.

Now, if we assume the movement of the cube in space, then what form will its trace have, i.e. figure a4?

Considering the relations of figures of one, two and three dimensions, i.e. lines, planes and bodies, we can deduce the rule that each figure of the next dimension is a trace of the movement of the figure of the previous dimension. Based on this rule, we can consider the figure a4 as a trace from the movement of the cube in space.

But what is this movement of the cube in space, the trace of which turns out to be a figure of four dimensions? If we consider how the movement of a figure of a lower dimension creates a figure of a higher dimension, then we will find several general properties, general patterns.

Namely, when we consider a square as a trace from the movement of a line, we know, we know that all the points of the line moved in space; when we consider the cube as a trace of the movement of the square, then we know that all the points of the square moved. In this case, the line moves in a direction perpendicular to itself; a square is in a direction perpendicular to its two dimensions.

Therefore, if we consider the figure a4 as a trace from the movement of the cube in space, then we must remember that all the points of the cube moved in space. At the same time, by analogy with the previous one, we can conclude that the cube moved in space in a direction not contained in itself, i.e. in a direction perpendicular to its three dimensions. This direction is the fourth perpendicular, which does not exist in our space and in our geometry of three dimensions.

The line can then be viewed as an infinite number of points; square - as an infinite number of lines; a cube is like an infinite number of squares. Likewise, figure a4 can be thought of as an infinite number of cubes. Further, looking at the square, we see only lines; looking at the cube - its surfaces or even one of these surfaces.

It must be assumed that the figure a4 will be presented to us in the form of a cube. In other words, the cube is what we see when we look at the figure. a4. Further, a point can be defined as a section of a line; line - as a section of the plane; plane - as a section of the volume; in the same way, a three-dimensional body can be defined as a section of a four-dimensional body. Generally speaking, when looking at a four-dimensional body, we will see its three-dimensional projection, or section. A cube, a ball, a cone, a pyramid, a cylinder - may turn out to be projections, or sections, of some four-dimensional bodies unknown to us.

In 1908, I came across a curious article about the fourth dimension in Russian, published in the journal Modern World.

It was a letter written in 1891 by N.A. Morozov* to fellow prisoners in the Shlisselburg Fortress. It is interesting mainly because it very figuratively sets out the main provisions of the method of reasoning about the fourth dimension by analogy, which was mentioned earlier.

* ON THE. Morozov, a scientist by education, belonged to the revolutionaries of the 70s and 80s. He was arrested in connection with the assassination of Emperor Alexander II and spent 23 years in prison, mainly in the Shlisselburg Fortress. Released in 1905, he wrote several books: one about the Revelation of the Apostle John, another about alchemy, magic, etc., which found very numerous readers in the pre-war period. It is curious that the public in Morozov's books liked not what he wrote, but what about what he wrote. His real intentions were very limited and strictly corresponded to the scientific ideas of the 70s of the XIX century. He tried to present "mystical objects" rationally; for example, he announced that in the Revelation of John only a description of a hurricane was given. But, being a good writer, Morozov expounded the subject very vividly, and sometimes added little-known material to this. Therefore, his books produced completely unexpected results; after reading them, many became interested in mysticism and mystical literature. After the revolution, Morozov joined the Bolsheviks and remained in Russia. As far as is known, he did not take a personal part in their destructive activities and did not write anything else, but on solemn occasions he unfailingly expressed his admiration for the Bolshevik regime.

The beginning of Morozov's article is very interesting, but in his conclusions about what could be in the area of ​​the fourth dimension, he departs from the method of analogies and refers to the fourth dimension only the "spirits" that are called up at spiritualistic sessions. And then, rejecting spirits, he also denies the objective meaning of the fourth dimension.

In the fourth dimension, the existence of prisons and fortresses is impossible, and this is probably why the fourth dimension was one of the favorite topics of conversations that were conducted in the Shlisselburg fortress by tapping. Letter to N.A. Morozov is the answer to the questions posed to him in one of these conversations. He's writing:

My dear friends, our short Shlisselburg summer is ending, and mysterious dark autumn nights are coming. In these nights, descending like a black veil over the roof of our dungeon and enveloping our little island with its ancient towers and bastions in impenetrable darkness, it involuntarily seems that the shadows of the comrades who died here and our predecessors invisibly fly around these cells, look into our windows and join us. , still alive, in mysterious intercourse. And are we ourselves not shadows of what we once were? Haven't we already turned into some kind of knocking spirits that appear at seances and invisibly talk to each other through the stone walls separating us?

All this day I have been thinking about your dispute today about the fourth, fifth and other dimensions of the space of the universe that are inaccessible to us. I tried my best to imagine in my imagination at least a fourth dimension of the world, the very one through which, according to metaphysicians, all our closed objects can suddenly be open, and through which beings can penetrate them, capable of moving without only according to our three, but also according to this fourth dimension, which is unusual for us.

You demand from me a scientific treatment of the question. For the time being, we will talk about the world of only two dimensions, and then we will see if it will not give us the opportunity to draw any conclusions about the other worlds.

Suppose that some plane, well, at least the one that separates the surface of Lake Ladoga on this quiet autumn evening from the atmosphere above it, is a special world, a world of two dimensions, inhabited by its own creatures that can only move along this plane, like those the shadows of swallows and seagulls that run in all directions on the smooth surface of the water surrounding us, but never visible to us behind these bastions.

Suppose that, having escaped behind our Shlisselburg bastions, you went swimming in the lake.

As beings of three dimensions, you also have those two that lie on the surface of the water. You will take a certain place in this world of shadowy creatures. All parts of your body above and below the water level will be imperceptible to them, and only that contour of yours, which is surrounded by the surface of the lake, will be completely accessible to them. Your contour should seem to them the object of their own world, but only extremely amazing and wonderful. The first miracle, from their point of view, will be your unexpected appearance among them. It can be said with full confidence that the effect that you have produced by this is in no way inferior to the unexpected appearance between us of some spirit from an unknown world. The second miracle is the extraordinary variability of your species. When you sink to the waist, your shape will be almost elliptical to them, since only that circle will be noticeable to them, which on the surface of the water covers your waist and is impenetrable to them. When you begin to swim, you will take on the shape of a human outline in their eyes. When you come to a shallow place, so that the surface they inhabit is bordered only by your feet, you will seem to them turned into two round-shaped beings. If, wanting to keep you in a certain place, they surrounded you on all sides, you could step over them and find yourself free in a way incomprehensible to them. You would be omnipotent beings for them, inhabitants of a higher world, like those supernatural beings about which theologians and metaphysicians narrate.

Now, if we assume that in addition to these two worlds, flat and ours, there is also a world of four dimensions, higher than ours, then it is clear that its inhabitants in relation to us will be the same as we were now for the inhabitants of the plane. They should just as unexpectedly appear before us and arbitrarily disappear from our world, leaving for the fourth or some other, higher dimensions.

In a word, a complete analogy so far, but only so far. Further in the same analogy, we will find a complete refutation of all our assumptions.

Indeed, if the beings of the four dimensions were not our invention, their appearance among us would be ordinary, everyday occurrences.

Further, Morozov analyzes the question of whether we have any reason to think that such "supernatural beings" really exist, and comes to the conclusion that we have no reason for this if we are not ready to believe the stories.

The only worthy indications of such beings can be found, according to Morozov, in the teachings of spiritualists. But his experiences with "spiritualism" convinced him that despite the presence of mysterious phenomena that undoubtedly occur at seances, "spirits" do not take any part in this. The so-called "automatic writing", usually cited as evidence of participation in the sessions of the intelligent forces of the unearthly world, according to his observations, is the result of mind reading. The "medium" consciously or unconsciously "reads" the thoughts of those present and thus receives answers to their questions. ON THE. Morozov was present at many sessions and did not meet the case that in the received answers something unknown to everyone was reported, or that the answers were in a language unfamiliar to everyone. Therefore, without doubting the sincerity of most spiritualists, N.A. Morozov concludes that the spirits have nothing to do with it.

According to him, his practice with spiritualism finally convinced him many years ago that the phenomena he attributed to the fourth dimension did not really exist. He says that in such seances, the answers are given unconsciously by those present and therefore all assumptions about the existence of the fourth dimension are pure fantasy.

These conclusions of Morozov are completely unexpected, and it is difficult to understand how he arrived at them. Nothing can be objected to his opinion about spiritualism. The psychic side of spiritual phenomena is, of course, quite "subjective". But it is completely incomprehensible why N.A. Morozov sees the "fourth dimension" exclusively in spiritualistic phenomena and why, denying spirits, he denies the fourth dimension. This looks like a ready-made solution offered by that official “positivism” to which N.A. Morozov and from which he could not move away. His foregoing reasoning leads quite differently. In addition to "spirits", there are many phenomena that are quite real for us, i.e. habitual and daily, but not explainable without the help of hypotheses that bring these phenomena closer to the world of four dimensions. We are only too accustomed to these phenomena and do not notice their “wonderfulness”, we do not understand that we live in a world of eternal miracle, in a world of the mysterious, inexplicable, and most importantly, immeasurable.

ON THE. Morozov describes how wonderful our three-dimensional bodies will be for flat creatures, how they will appear from nowhere and disappear from nowhere, like spirits emerging from an unknown world.

But aren't we ourselves the same fantastic creatures that change their appearance for any immovable object, for a stone, for a tree? Don't we have the properties of "higher beings" for animals? And do not phenomena exist for ourselves, such as, for example, all manifestations of life, about which we do not know where they came from and where they go: the appearance of a plant from a seed, the birth of living beings, and the like; or natural phenomena: thunderstorm, rain, spring, autumn, which we are not able to explain or interpret? Isn't each of them, taken separately, something of which we grope only a little, only a part, like the blind in an old oriental fairy tale, each defining the elephant in his own way: one by the legs, the other by the ears, the third by the tail?

Continuing the reasoning of N.A. Morozov about the relation of the world of three dimensions to the world of four dimensions, we have no reason to look for the latter only in the field of "spiritualism".

Let's take a living cell. It can be absolutely equal - in length, width and height - to another, dead cell. And yet there is something in a living cell that is not in a dead cell, something that we cannot measure.

We call this something "life force" and try to explain it as a kind of movement. But, in essence, we do not explain anything, but only give a name to a phenomenon that remains inexplicable.

According to some scientific theories, the vital force must be decomposed into physical and chemical elements, into the simplest forces. But none of these theories can explain how one passes into the other, in what relation one stands to the other. We are not able to express the simplest manifestation of living energy in the simplest physical and chemical form. And while we are not able to do this, we strictly logically have no right to consider life processes identical with physical and chemical ones.

We can recognize philosophical "monism", but we have no reason to accept the physico-chemical monism that is constantly being imposed on us, which identifies vital and mental processes with physical and chemical ones. Our mind can come to an abstract conclusion about the unity of physical-chemical, vital and mental processes, but for science, for exact knowledge, these three kinds of phenomena stand completely apart.

For science, three kinds of phenomena—mechanical force, vital force, and psychic force—only partly pass one into the other, apparently without any proportionality, without yielding to any calculation. Therefore, scientists will only then have the right to explain life and mental processes as a kind of movement when they come up with a way to translate movement into vital and psychic energy and vice versa and take this transition into account. In other words, to know how many calories contained in a certain amount of coal are needed for the emergence of life in one cell, or how much pressure is needed to form one thought, one logical conclusion. While it is not known, the physical, biological and mental phenomena studied by science occur on different planes. One can, of course, guess about their unity, but it is impossible to assert this.

Even if the same force acts in physicochemical, life and mental processes, it can be assumed that it acts in different areas, only partly in contact with each other.

If science possessed the knowledge of the unity of at least only vital and physico-chemical phenomena, it could create living organisms. There is nothing excessive in this statement. We build machines and apparatus much more complex than simple unicellular organism. And yet we cannot build an organism. This means that there is something in a living organism that is not in a lifeless machine. There is something in a living cell that is not in a dead one. We can rightly call this "something" equally inexplicable and immeasurable. Considering a person, we may well ask ourselves: what is more in a person - measurable or immeasurable?

“How can I answer your question (about the fourth dimension), says N.A. Morozov, - when I myself do not have a measurement in the direction you indicate?

But what does N.A. Morozov's reason to say so definitely that he does not have this dimension? Can he measure everything in himself? Two main functions life and thought of man lie in the realm of the immeasurable.

In general, we know so little and so poorly what a person is, there is so much in us mysterious and incomprehensible from the point of view of the geometry of three dimensions, that we have no right to deny the fourth dimension, denying "spirits", but on the contrary, we have every reason to look for the fourth dimension exactly in yourself.

We must tell ourselves clearly and definitely that we absolutely do not know what a person is. This is a mystery to us - and we need to recognize it.

"The Fourth Dimension" promises to explain something in it. Let us try to understand what the "fourth dimension" can give us if we approach it with the old methods, but without the old prejudices for or against spiritism. Let us imagine again the world of flat creatures, having only two dimensions: length and width, and inhabiting a flat surface.*

* In these discussions of imaginary worlds, I partially follow the plan proposed by Hinton, but this does not mean that I share all Hinton's opinions.

On a flat surface, let us imagine living beings that look like geometric shapes and are capable of moving in two directions. Considering the conditions of life of flat beings, we will immediately encounter one interesting circumstance.

These creatures can move only in two directions, remaining on the plane. They are not able to rise above the plane or move away from it. Similarly, they cannot see or feel anything that lies outside their plane. If one of the creatures rises above the plane, it will completely leave the world of other creatures similar to it, hide, disappear to no one knows where.

If we assume that the organs of vision of these creatures are located on their edge, on the side that has a thickness of one atom, then they will not see the world that is outside their plane. They are only able to see lines lying on their plane. They see each other not as they really are, i.e. not in the form of geometric figures, but in the form of segments, and in the same way, in the form of segments, all their objects will be presented to them. And what is very important: all lines are straight, curved, broken, lying under different angles- will appear to them the same, in the lines themselves they will not be able to find any difference. At the same time, these lines will differ for them from each other by some strange properties, which they will probably call the movement or oscillation of the lines.

The center of the circle is completely inaccessible to them, they are not able to see it. To reach the center of the circle, a two-dimensional being would have to cut or dig its way through the mass of a flat figure one atom thick. This process of digging will appear to him as a change in the line of the circle.

If a cube is attached to its plane, then the cube will appear to him in the form of four lines that limit the square that is in contact with its plane. Out of the entire cube, this one square exists for him. It is not even able to imagine the whole cube. Cube will not exist for him.

If many bodies are in contact with the plane, then in each of them for a flat creature there is only one plane. She will seem to him the object of his own world.

If its space, i.e. flat surface, crosses a multi-colored cube, then the passage of the cube will appear to him as a gradual change in the color of the lines that limit the square lying on the surface.

If we assume that a flat creature has acquired the ability to see with its flat side facing our world, then it is easy to imagine how distorted the idea of ​​our world will be.

The whole universe appears to him as a plane. It is possible that it will call this plane the ether. Phenomena occurring outside the plane, it will either completely deny, or consider as occurring on its plane in the ether. Unable to explain the observed phenomena, it will surely call them miraculous, surpassing its understanding, being out of space, in the "third dimension".

Noticing that unexplained phenomena occur in certain sequence, in a certain dependence on each other, and also, probably, on some laws - a flat being will cease to consider them miraculous and will try to explain them with the help of more or less complex hypotheses.

The first step towards a correct understanding of the universe will be the appearance in a flat being of a vague idea of ​​another parallel plane. Then all the phenomena that the being cannot explain on its own plane, it will declare to occur on a parallel plane. At this stage of development, our entire world will seem to him flat and parallel to his plane. The relief and prospects for it will not yet exist. The mountain landscape will turn into a flat photograph. The idea of ​​the world will, of course, be extremely poor and distorted. The big will be mistaken for the small, the small for the big, and everything, both close and far, will seem equally distant and unattainable.

Recognizing that there is a world parallel to his flat world, a two-dimensional being will say that he knows nothing about the true nature of the relationship of these worlds.

AT parallel world for a two-dimensional being there will be many inexplicable things. For example, a lever or a pair of wheels on an axle - their movement will seem incomprehensible to a flat being (whose ideas about the laws of motion are limited to movement along a plane). It is quite possible that it will consider such phenomena as supernatural, and then call them "superphysical".

Studying superphysical phenomena, a flat being can attack the idea that in the lever and in the wheels there is something immeasurable, but nevertheless existing.

From here it is only a step to the hypothesis of the third dimension. The flat creature will base this hypothesis on facts inexplicable for him, such as the rotation of wheels. It may wonder if the inexplicable is not, in fact, immeasurable? And then he will gradually begin to establish the physical laws of the space of three dimensions.

But it will never be able to mathematically rigorously prove the existence of a third dimension, because all its geometric considerations refer to a plane, to two dimensions, and therefore it will project the results of its mathematical conclusions onto a plane, thus depriving them of any meaning.

A flat being will be able to get the first concepts about the nature of the third dimension through simple logical reasoning and comparisons. This means that by examining everything inexplicable that happens on a flat photograph (which is our world for him), a flat creature can come to the conclusion that many phenomena are inexplicable because, perhaps, there is some kind of difference which it does not understand and cannot measure.

It can then conclude that the real body must be something different from the imaginary one. And having once admitted the hypothesis of a third dimension, it will be forced to say that a real body, unlike an imaginary one, must, at least to a small extent, have a third dimension.

In a similar way, a flat being may come to recognize that he himself has a third dimension.

Having come to the conclusion that a real two-dimensional body cannot exist, that it is only an imaginary figure, a flat being will have to say to itself that since a third dimension exists, then it must itself have a third dimension; otherwise, having only two dimensions, it turns out to be an imaginary figure, existing only in someone's mind.

A flat being will reason like this: "If the third dimension exists, then I am either a being of three dimensions, or I do not exist in reality, but only in someone's imagination."

Arguing about why it does not see its third dimension, a flat being can come to the conclusion that its extension in the third dimension, as well as the extension of other bodies in it, is very small. These reflections may lead a flat being to the conclusion that for him the question of the third dimension is connected with the problem of small quantities. When examining a question from a philosophical point of view, a flat being will at times doubt the reality of all that exists and its own reality.

Then he may have the idea that he imagines the world wrong, and sees it not as it really is. From this reasonings about things as they appear and about things as they are can flow. The flat being will decide that in the third dimension things must be as they are, i.e. that it must see much more in them than it saw in two dimensions.

Checking all these arguments from our point of view, from the point of view of three-dimensional beings, we must admit that all the conclusions of a flat being are absolutely correct and lead him to a more correct understanding of the world than the previous one, and to comprehension of the third dimension, even if at first purely theoretical.

Let's try to use the experience of a flat being and find out if we are not in the same relation to something as a flat being is to the third dimension.

Analyzing the physical conditions of human life, we find in them an almost complete analogy with the conditions of life of a flat creature, which begins to perceive the third dimension.

Let's start with an analysis of our relationship to the "invisible".

At first, a person considers the invisible to be miraculous and supernatural. Gradually, with the evolution of knowledge, the idea of ​​the miraculous becomes less and less necessary. Everything within the sphere accessible to observation (and, unfortunately, far beyond it) is recognized as existing according to certain laws, as a consequence of certain causes. But the causes of many phenomena remain hidden, and science is forced to confine itself to classifying such inexplicable phenomena.

Studying the nature and properties of the "inexplicable" in different areas of our knowledge, in physics, chemistry, biology and psychology, we can formulate the problem as follows: is not this inexplicable the result of something "immeasurable" for us, firstly, in those things that we think we can to measure, and, secondly, in things that cannot be measured at all.

We come to the thought: does not the inexplicability itself arise from what we consider and try to explain within the limits of three dimensions of a phenomenon that passes into the region of higher dimensions? In other words, are we not in the position of a flat being trying to explain how the phenomena observed on the plane occur in three-dimensional space? Much testifies to the correctness of this assumption.

It is quite possible that many of the inexplicable phenomena are inexplicable only because we want to explain them entirely on our plane, i.e. in three-dimensional space, while they flow outside our plane, in the region of higher dimensions.

Recognizing that we are surrounded by the world of the immeasurable, we come to the conclusion that until now we had a completely wrong idea about our world and its objects.

We already knew that we see things not as they really are. Now we affirm more definitely that we do not see in things from a part immeasurable for us, which is in the fourth dimension. This consideration leads us to think about the difference between the imaginary and the real.

We have seen that a flat being, having come to the idea of ​​a third dimension, must conclude that there cannot be a real body of two dimensions, it is only an imaginary figure, a section of a three-dimensional body or its projection in two-dimensional space.

Assuming the existence of the fourth dimension, we are also forced to admit that there cannot be a real body of three dimensions. A real body must have at least the smallest extent in the fourth dimension, otherwise it will be an imaginary figure, a projection of a four-dimensional body in three-dimensional space, similar to a "cube" drawn on paper.

Thus, we come to the conclusion that there can be a three-dimensional cube and a four-dimensional cube. But only four-dimensional cube will be real.

Considering a person from this point of view, we come to very interesting conclusions.

If the fourth dimension exists, then one of two things is possible: either we have a fourth dimension, i.e. are four-dimensional beings, or we have only three dimensions, in which case we don't exist at all.

For if the fourth dimension exists, and we have only three dimensions, this means that we are deprived of real existence, that we exist only in someone's imagination, that all our thoughts, feelings and experiences occur in the mind of some other, higher being that represents us. We are the fruits of his imagination, and our entire universe is nothing more than an artificial world created by his imagination.

If we do not want to agree with this, then we must recognize ourselves as four-dimensional beings. At the same time, we must agree that we know and feel our own fourth dimension very poorly, as well as the fourth dimension of the bodies around us, that we only guess about its existence, observing inexplicable phenomena.

Our blindness to the fourth dimension may be due to the fact that the fourth dimension of our bodies and other objects of our world is too small and inaccessible to our sense organs and apparatuses that expand the scope of our observation, just as the molecules of our bodies and other objects are inaccessible to direct observation. . As for objects that have a greater extension in the fourth dimension, under certain circumstances we sometimes feel them, but we refuse to recognize their real existence.

The latter considerations give us sufficient reason to believe that, at least in our physical world, the fourth dimension must belong to the region of small quantities.

The fact that we do not see their fourth dimension in things brings us back to the problem of the imperfection of our perception in general. Even if we do not touch on other shortcomings of our perception and consider it only in relation to geometry, then even then we will have to admit that we see everything very little like what it is.

We see not bodies, but only surfaces, sides and lines. We never see a cube, only a small part of it, we never perceive it from all sides at once.

From the fourth dimension, one can probably see the cube from all sides at once and from the inside, as if from the center.

The center of the ball is not available to us. To reach it, we must cut or dig our way through the mass of the ball, i.e. act exactly like a flat creature reaching the center of the circle. And the cutting process will be perceived by us as a gradual change in the surface of the ball.

The complete analogy of the relation of man to the ball with the relation of a plane being to a circle gives us reason to think that in the fourth dimension the center of the ball is just as easily accessible as the center of the circle in the third dimension, i.e. that in the fourth dimension, the center of the ball can be penetrated from somewhere unknown to us, in an incomprehensible direction, and at the same time the ball remains intact. The latter seems to us some kind of miracle; but by the same miracle it must seem to a flat creature that it is possible to reach the center of the circle without crossing the lines of the circle, without destroying the circle.

Continuing to explore the properties of vision and perception in the fourth dimension, we are forced to admit that not only from the point of view of geometry, but also in many other respects from the fourth dimension, much more can be seen in the objects of our world than we see.

About the human eye, Helmholtz once said that if an optician had brought him such a mediocre instrument, he would never have taken it. Undoubtedly, our eye does not see very much of what exists. But since we see in the fourth dimension without resorting to such an imperfect apparatus, therefore, we must see much more, see what we do not see now, and see without that cover of illusions that covers the whole world and makes its appearance completely different from what is actually there.

The question may arise: why in the fourth dimension we must see without the help of the eyes, and what does this mean?

It will be possible to give a definite answer to these questions only when it becomes definitely known that the fourth dimension exists and what it is; but so far we can only talk about what could be the fourth dimension, and therefore the enumerated questions cannot be answered definitively. Vision in the fourth dimension should not be associated with the eyes. We know the limits of seeing with the eyes; We know that the human eye will never reach the perfection of a microscope or a telescope. However, these tools, by multiplying the power of vision, do not bring us any closer to the fourth dimension. From this we can conclude that vision in the fourth dimension is something different compared to ordinary vision. But what could it be? Probably, with something similar to the “vision” with which a bird, leaving northern Russia, “sees” Egypt, where it flies for the winter; or at the sight of a carrier pigeon, which “sees” its dovecote hundreds of miles away, from where it was taken away in a closed basket; or to the vision of an engineer who makes the first calculations and preliminary sketches of the bridge and at the same time “sees” the bridge and the trains running along it; or the sight of a person who, looking at the timetable, “sees” his arrival at the departure station and the arrival of the train to the appointed point.

Now, having outlined some of the features that vision in the fourth dimension should have, we will try to more accurately describe what we know from the phenomena of the world of the fourth dimension.

Using again the experience of a two-dimensional being, we must ask ourselves next question: Are all the "phenomena" of our world explainable in terms of physical laws?

There are so many inexplicable phenomena around us that, getting used to them, we cease to notice their inexplicability and, forgetting about it, we begin to classify these phenomena, give them names, put them in different systems, and, in the end, even begin to deny their inexplicability.

Strictly speaking, all equally inexplicable. But we are accustomed to consider some orders of phenomena more explicable, and others less so. We separate the less explicable into a special group, we create a separate world out of them, as if parallel to the “explainable”.

This applies primarily to the so-called "mental world", to the world of ideas, images and representations, which we consider as parallel to the physical.

Our relationship to the psychic, the difference that exists for us between the "physical" and the "psychic", shows that it is the psychic that should be attributed to the area of ​​the fourth dimension.*

* The expression "psychic phenomena" is used here in its only possible sense - those mental, or mental, phenomena that constitute the subject of psychology. I mention this because in spiritualistic and theosophical literature the word "psychic" is used to designate supernormal or superphysical phenomena.

In the history of human thought, the relation to the psychic is very similar to the relation of a flat being to the third dimension. Psychic phenomena are inexplicable on the "physical plane", so they are opposed to physical ones. But the unity of both, nevertheless, is felt and attempts are constantly made to interpret the mental as a kind of physical, or the physical as a kind of mental. The separation of concepts is recognized as unsuccessful, but there are no means for their unification.

Initially, the mental is recognized as completely separate from the body, a function of the “soul”, not subject to physical laws: the soul lives on its own, and the body on its own, one is incommensurable with the other. This is the theory of naive dualism, or spiritualism. The first attempt at a no less naive monism regards the soul as a direct function of the body, asserting that "thought is the movement of matter." This is the famous formula of Moleschott.

Both views lead to a dead end. The first is because there is an obvious relationship between physiological and mental acts. The second is because movement still remains movement, and thought remains thought.

The first is analogous to the denial by a two-dimensional being of the physical reality of phenomena that are outside its plane. The second is an attempt to consider phenomena occurring on this plane that occur outside it, above it.

The next step is the hypothesis of a parallel plane, on which all inexplicable things happen. But the theory of parallelism is a very dangerous thing.

A plane being will understand the third dimension when he clearly sees that what he thought was parallel to his plane may actually be at different distances from it. Then the idea of ​​perspective and relief will arise in him, and the world will take on the same form for him as it does for us.

We are more correct understand the attitude the physical to the psychic only when we make it clear to ourselves that the psychic is not always parallel to the physical and may be completely independent of it. And the parallel, which is not always parallel, is obviously subject to the laws of the four-dimensional world that are incomprehensible to us.

Now it is often said that we know nothing about the exact nature of the relationship between the physical and the psychic. The only thing that has been more or less established is that every mental act, thought, or sensation corresponds to a physiological act, expressed at least in a slight vibration of the nerves and brain fibers. Sensation is defined as the awareness of a change in the senses. This change is a certain movement, but we do not know how the movement is transformed into feeling and thought.

The question arises: is it possible to suggest that the physical is separated from the psychic by the space of the fourth dimension, i.e. that a physiological act, passing into the area of ​​the fourth dimension, causes there effects that we call feeling and thought?

On our plane, i.e. in the world accessible to our observation of vibrations and movements, we are not able to understand and define thought, just as a two-dimensional being on its own plane cannot understand and determine the movements of a lever or a pair of wheels on an axle.

At one time, the ideas of E. Mach, set forth mainly in his book "The Analysis of Sensations and the Relationship of the Physical to the Mental", enjoyed great success. Mach completely denies the distinction between the physical and the mental. The whole dualism of our worldview was created, in his opinion, from the metaphysical idea of ​​the "thing in itself" and from the idea (erroneous, according to Mach) of the illusory nature of our knowledge of things. Mach believes that we cannot cognize anything incorrectly. Things are exactly what they appear to us. The concept of illusion must be discarded altogether. Elements of sensations are physical elements. What we call "bodies" are only complexes of sensations (light, sound, pressure, etc.), images of representations are the same complexes of sensations. There is no difference between the physical and the mental, and both are made up of identical elements(sensations). Molecular structure Mach accepts bodies and the atomistic theory only as symbols, denying any reality behind them. Thus, according to Mach, our mental apparatus creates the physical world. A "thing" is only a complex of sensations.

But speaking of Mach's theory, it must be remembered that the psyche builds the "forms" of the world (i.e. makes it the way we perceive it) from something else that we can never get to. The blue color of the sky is unreal, the green color of the meadow is also. Obviously, in the "sky", i.e. there is something in the atmospheric air that makes it appear blue, just as there is something in the grass of a meadow that makes it appear green.

Without this addition, a person, based on the ideas of Mach, could easily say: this apple is a complex of my sensations, which means that it only appears, and does not exist in reality.

This is not true. The apple exists, and a person can be convinced of this in the most real way. But it is not what it seems to us in the three-dimensional world.

The psychic (when considered as the opposite of the physical or three-dimensional) is very similar to what must exist in the fourth dimension, and we can rightly say that thought moves in the fourth dimension.

For her there are no barriers and distances. She penetrates impenetrable objects, imagines the structure of atoms, the chemical composition of stars, the population of the seabed, the life of a people who disappeared ten thousand years ago ...

No walls, no physical conditions restrict our fantasy, our imagination.

Didn't Morozov and his comrades leave the Shlisselburg bastions in their imagination? Didn't Morozov himself travel in time and space when, reading the Apocalypse in the Alekseevsky ravelin of the Peter and Paul Fortress, he saw thunderclouds flying over the Greek island of Patmos at five o'clock in the evening on September 30, 395?

Don't we live in a dream in a fantastic, fabulous realm, where everything is capable of transforming, where there is no stability of the physical world, where one person can become another or two at once, where the most incredible things seem simple and natural, where events often go in reverse order, from end to beginning, where we see symbolic images of ideas and moods, where we talk to the dead, fly through the air, pass through walls, sink, burn, die, and yet remain alive?

Comparing all this, we see that it is not necessary to consider as four-dimensional beings only spirits that appear or do not appear at seances. With no less reason, we can say that we ourselves are four-dimensional beings and are turned to the third dimension with only one of our sides, i.e. just a small part of your being. Only this part lives in three dimensions, and we are aware of only this part. The greater part of our being lives in four dimensions, but we are not conscious of this greater part. Or it would be even more correct to say that we live in a four-dimensional world, but we are aware of ourselves in a three-dimensional one. This means that we live in conditions of one kind, and imagine ourselves in others. The conclusions of psychology lead us to the same conclusion. Psychology, although very timidly, speaks of the possibility of awakening our consciousness, i.e. about the possibility of its special state, when it sees and feels itself in the real world, which has nothing to do with the world of things and phenomena - in the world of thoughts, images and ideas.

Considering the properties of the fourth dimension, I mentioned that the tessaract, i.e. a4, can be obtained by moving the cube in space, and all points of the cube must move.

Therefore, if we assume that from each point of the cube there is a line along which this movement occurs, then the combination of these lines will form a projection of a four-dimensional body. This body, i.e. tessaract, can be considered as an infinite number of cubes, as if growing out of the first.

Now let's see if we know examples of such a movement, in which all points of a given cube would move.

Molecular motion, i.e. the movement of the smallest particles of matter, which increases when heated and weakens when cooled, is the most suitable example of movement in the fourth dimension, despite all the erroneous ideas of physicists about this movement.

In the article "Can We Hope to See Molecules?" YES. Goldhammer says that, according to modern views, molecules are little bodies with linear dimensions between one millionth and one ten-millionth of a millimeter. It is calculated that in one billionth of a cubic millimeter, i.e. in one micron, at a temperature of 0 degrees Celsius and at normal pressure, there are about thirty million oxygen molecules. Molecules move very fast; For example, most oxygen molecules normal conditions has a speed of about 450 meters per second. Despite such high speeds, the molecules do not scatter instantly in all directions just because they often collide with each other and change the direction of movement from this. The path of the molecule looks like a very tangled zigzag - in essence, it marks time, so to speak, in one place.

Let's leave aside the tangled zigzag and the theory of molecular collisions for now ( Brownian motion), and try to establish what results molecular motion produces in the visible world.

To give an example of movement in the fourth dimension, we must find such a movement in which the given body would actually move, and not remain in one place (or in one state).

Considering all the types of movement known to us, we must recognize that we are best suited to the conditions set. extension and reduction tel.

The expansion of gases, liquids and solids means that the molecules move away from one another. The contraction of solids, liquids and gases means that the molecules approach each other and the distance between them decreases. There is some space and some distance. Doesn't this space lie in the fourth dimension?

We know that when moving through this space, all points of a given geometric body move, i.e. all the molecules of a given physical body. The figure obtained from the movement in the cube space during expansion and contraction will look like a cube for us, and we can imagine it in the form an infinite number cubes.

Is it possible to assume that the combination of lines drawn from all points of the cube, both on the surface and inside the lines along which the points move away from one another and approach one another, will constitute a projection of a four-dimensional body?

To answer this, you need to find out what are these lines and what is the direction? Lines connect all points of the given body with its center. Therefore, the direction of the found movement is from the center along the radii.

In the study of the ways of movement of points (molecules) of the body during expansion and contraction, we find a lot of interesting things in them.

We cannot see the distance between molecules. In solids, in liquids and gases, we are not able to see it, because it is extremely small; in highly rarefied matter, for example, in Crookes tubes, where this distance probably increases to sizes perceptible by our apparatus, we cannot see it, because the particles themselves, the molecules, are too small and inaccessible to our observation. In the article cited above, Goldhammer says that under certain conditions molecules can be photographed if they can be made luminous. He writes that when the pressure in the Crookes tube is reduced to one millionth of an atmosphere, one micron contains only thirty molecules of oxygen. If they glowed, they could be photographed on a screen. Whether such photography is possible is another question. In the given reasoning, the molecule, as a kind of real quantity in relation to the physical body, is a point in its relation to the geometric body.

All bodies have molecules and, therefore, must have some, at least a very small intermolecular space. Without this, we cannot imagine a real body, but perhaps imaginary geometric bodies. A real body consists of molecules and has some intermolecular space.

This means that the difference between the cube of three dimensions a3 and a cube of four dimensions a4 is that the cube of four dimensions consists of molecules, while the cube of three dimensions does not really exist and is a projection of a four-dimensional body onto a three-dimensional space.

But, expanding or contracting, i.e. moving in the fourth dimension, if we accept the previous reasoning, the cube or ball always remains a cube or ball for us, changing only in size. In one of his books, Hinton quite rightly remarks that the origin of a cube of a higher dimension through our space would be perceived by us as a change in the properties of its matter. He adds that the idea of ​​a fourth dimension can arise from observing a series of progressively larger or smaller balls or cubes. Here he comes close to the correct definition of motion in the fourth dimension.

One of the most important, clear and understandable types of movement in the fourth dimension in this sense is growth, which is based on expansion. Why this is so is not difficult to explain. Every movement within three-dimensional space is at the same time movement in time. Molecules, or points, of an expanding cube do not return to their original place during contraction. They describe a certain curve, returning not to the point in time from which they left, but to another. And if we assume that they do not return at all, then their distance from the original point in time will increase more and more. Imagine this internal movement a body in which its molecules, moving away from one another, do not approach each other, and the distance between them is filled with new molecules, which in turn diverge and give way to new ones. Such an internal movement of the body will be its growth, at least the geometric scheme of growth. If we compare a tiny green ovary of an apple with a large red fruit hanging on the same branch, we understand that the molecules of the ovary could not create an apple by moving only through three-dimensional space. In addition to continuous movement in time, they need continuous deviation into space, which lies outside the three-dimensional sphere. The ovary is separated from the apple by time. From this point of view, an apple is three or four months of movement of molecules in fourth measurement. Imagine all the way from the ovary to the apple, we will see the direction of the fourth dimension, i.e. the mysterious fourth perpendicular - a line perpendicular to all three perpendiculars of our space.

Hinton comes so close to getting the fourth dimension right that he sometimes guesses where the "fourth dimension" is in life, even when he can't pinpoint it. So, he says that the symmetry of the structure of living organisms can be explained by the movement of their particles in the fourth dimension.

Everyone knows, says Hinton, a way to get insect-like images on paper. Ink is dripped onto the paper and folded in half. It turns out a very complex symmetrical figure, similar to a fantastic insect. If a number of such images were seen by a person completely unfamiliar with the method of their preparation, then he, logically speaking, would have to come to the conclusion that they were obtained by folding paper, i.e. that their symmetrically located points were in contact. In the same way, we, considering and studying the forms of the structure of living beings, reminiscent of figures on paper, obtained by the described method, we can conclude that the symmetrical forms of insects, leaves, birds, etc. created by a process similar to folding. The symmetrical structure of living bodies can be explained, if not by folding in half in the fourth dimension, then, in any case, by the same arrangement as when folding, the arrangement of the smallest particles from which these bodies are built. In nature, there is a very curious phenomenon that creates a completely correct drawings the fourth dimension - you just need to be able to read them. They are seen in fantastically varied, but always symmetrical figures snowflakes, in drawings of flowers, stars, ferns and laces of frosty patterns on glass. Droplets of water, settling on cold glass or ice, immediately begin to freeze and expand, leaving traces of their movement in the fourth dimension in the form of bizarre patterns. Frosty patterns and snowflakes are figures of the fourth dimension, mysterious a4. The imaginary movement of a lower figure in geometry to obtain a higher one is carried out here in practice, and the resulting figure is really a trace of the movement due to the fact that frost preserves all the moments of expansion of freezing water droplets.

The forms of living bodies, flowers, ferns are created according to the same principle, although more complex. General form tree, gradually expanding in branches and shoots, is, as it were, a diagram of the fourth dimension, a4. Bare trees in winter and early spring are often very complex and extremely interesting diagrams of the fourth dimension. We pass by them without noticing anything, because we think that the tree exists in three-dimensional space. The same wonderful diagrams can be seen in the patterns of algae, flowers, young shoots, some seeds, etc. etc. Sometimes it is enough to enlarge them a little to reveal the secrets of the Great Laboratory, hidden from our eyes.

In the book of prof. Blossfeldt* on the art forms in nature, the reader can find several excellent illustrations of the above points.

* Karl Blossfeldt, Art Forms in Nature. London, 1929.

Living organisms, the bodies of animals and people are built on the principle of symmetrical movement. To understand these principles, let's take a simple schematic example of symmetrical movement: imagine a cube of twenty-seven cubes, and mentally imagine that this cube expands and contracts. When expanding, all twenty-six cubes located around the central one will move away from it, and when contracted, they will approach it again. For convenience of reasoning and for greater similarity of our cube with a body consisting of molecules, we assume that the cubes of measurement do not have, that they are just points. In other words, let's take only the centers of twenty-seven cubes and mentally connect them with lines both to the center and to each other.

Considering the expansion of a cube consisting of twenty-seven cubes, we can say that each of these cubes, in order not to collide with others and not interfere with their movement, must move away from the center, i.e. along the line connecting its center with the center of the central cube. This is the first rule:

During expansion and contraction, the molecules move along lines connecting from to the center.

Next, we see in our cube that not all lines connecting twenty-six points to the center are equal. Lines that go to the center from points lying on the corners of the cube, i.e. from the center of the corner cubes, longer than the lines that connect with the center of the points lying in the centers of six squares on the surfaces of the cube. If we assume that the intermolecular space is doubled, then all the lines connecting the twenty-six points to the center double at the same time. These lines are not equal, therefore the molecules do not move at the same speed - some are slower, others are faster, while those that are farther from the center move faster, those that are closer - slower. From this we can deduce the second rule:

The speed of movement of molecules during the expansion and contraction of the body is proportional to the length of the lines connecting these molecules with the center.

By observing the expansion of the cube, we see that the distance between everyone twenty-seven cubes increased in proportion to the former.

Let's call a- segments connecting 26 points with the center, and b- segments connecting 26 points to each other. Having built several triangles inside the expanding and contracting cube, we will see that the segments b elongate in proportion to the elongation of the segments a. From this we can deduce the third rule:

The distance between molecules during expansion increases in proportion to their distance from the center.

In other words, if the points are equidistant from the center, they will remain equidistant from it; and two points that were at an equal distance from the third will remain at an equal distance from it. Moreover, if you look at the movement not from the side of the center, but from the side of some of the points, it will seem that this point is the center from which the expansion occurs - it will seem that all other points move away from it or approach it. her, maintaining her former attitude towards her and among themselves, while she herself remains motionless. "Center everywhere"!

The last rule underlies the laws of symmetry in the structure of living organisms. But living organisms are not built by extension alone. This includes the element of movement in time. As it grows, each molecule describes a curve resulting from the combination of two motions in space and time. The growth is going in the same direction, along the same lines as the expansion. Therefore, the laws of growth must be similar to the laws of expansion. The laws of expansion, in particular, the third rule, guarantee strict symmetry to freely expanding bodies: if points that were at an equal distance from the center will always remain at an equal distance from it, the body will grow symmetrically.

In the figure obtained from spreading ink on a piece of paper folded in half, the symmetry of all points was obtained due to the fact that the points of one side were in contact with the points of the other side. Any dot on one side corresponded to a dot on the other side, and when the paper was folded, these dots touched. From the third rule it follows that between the opposite points of a four-dimensional body there is some kind of relationship, some kind of connection, which we have not noticed until now. Each point corresponds to one or more others, with which it is somehow incomprehensibly connected. Namely, it cannot move independently, its movement depends on the movement of the points corresponding to it, occupying similar places in an expanding or contracting body. These will be the opposite points. It is as if in contact with them, in contact in the fourth dimension. The expanding body precisely folds in different directions, and this establishes a mysterious connection between its opposite points.

Let's try to consider how the expansion occurs the simplest figure. Consider it not even in space, but on a plane. Let's take a square and join four points lying in its corners with the center. Then we connect with the center the points that lie at the midpoints of the sides, and, finally, the points that lie at half the distance between them. The first four points, i.e. points lying in the corners are called points BUT; points lying along the midpoints of the sides of the square, dots AT; finally, the points lying between them (there will be eight of them), the points FROM.

points BUT, AT and C lie at different distances from the center; therefore, when expanding, they will move with unequal speed, maintaining their relationship to the center. In addition, all points A are connected to each other, as points B and C are connected to each other. There is a mysterious internal connection between the points of each group. They must stay on equal to distance from the center.

Let us now assume that the square expands, i.e. all points A, B and C move away from the center along the radii. As long as the figure expands freely, the movement of points occurs according to the specified rules, the figure remains a square and retains symmetry. But suppose that on the path of movement of one of the points C there suddenly appeared some kind of obstacle that forced this point to stop. Then one of two things happens: either the rest of the points will move as if nothing happened, or the points corresponding to point C will also stop. If they move, the symmetry of the figure will be broken. If they stop, this will confirm the conclusion from the rule of the third, according to which points that were at an equal distance from the center, when expanding, remain at an equal distance from it. And indeed, if all points C, obeying the mysterious connection between them and point C, which met with an obstacle, stop while points A and B move, our square will turn out to be a regular symmetrical star. It is possible that this is exactly what happens during the growth of plants and living organisms. Let us take a more complex figure, in which the center from which the expansion occurs is not one, but several, and they are all located on the same line - the points moving away from these centers during expansion are located on both sides of the central line. Then, with a similar expansion, not a star will be obtained, but something like a jagged leaf. If we take a similar figure not on a plane, but in three-dimensional space and assume that the centers from which the expansion comes lie not on one axis, but on several, then we will get a figure during expansion that resembles a living body with symmetrical limbs, etc. And if we assume that the atoms of the figure move in time, then we get the "growth" of a living body. Laws of growth, i.e. motion, starting from the center along the radii during expansion and contraction, put forward a theory that can explain the reasons for the symmetrical structure of living bodies.

The definitions of the states of matter in physics are becoming more and more arbitrary. At one time, in addition to the three known states (solid, liquid, gaseous), they also tried to add "radiant matter", as the highly rarefied gases in Crookes tubes were called. There is a theory that considers the colloidal, jelly-like state of matter to be a state different from solid, liquid, and gaseous. According to this theory, organic matter is a kind of colloidal matter or is formed from it. The concept of matter in these states is opposed to the concept of energy. Then came the electronic theory, in which the concept of matter almost does not differ from the concept of energy; later, various theories of the structure of the atom appeared, which supplemented the concept of matter with many new ideas.

But it is precisely in this field, more than in any other, that scientific theories differ from the concepts everyday life. For a direct orientation in the world of phenomena, we need to distinguish matter from energy, and also to distinguish three states of matter: solid, liquid and gaseous. At the same time, we have to admit that even these three states of matter known to us differ clearly and undeniably only in such "classical" forms as a piece of iron, water in a river, the air we breathe. And transitional forms are different and coincide with each other; therefore, we do not always know exactly when one passed into the other, we cannot draw a clear dividing line, we cannot say when solid turned into liquid and liquid into gas. We assume that different states of matter depend on different strength adhesion of molecules, on the speed and properties of molecular motion, but we distinguish these states only by outward signs, very unstable and often intermingling with each other.

It can be definitely stated that each finer state of matter is more energetic, i.e. containing, as it were, less mass and more movement. If matter is opposed to time, then we can say that the finer the state of matter, the more time and less matter in it. There is more "time" in a liquid than in a solid; there is more "time" in gas than in water.

If we allow the existence of still finer states of matter, they must be more energetic than those recognized by physics; according to the above, they should have more time and less space, more movement and less time. Logically, the necessity of energy states of matter has long been accepted in physics and is proved by very understandable reasoning.

What is, in essence, a substance? - writes C. Freycinet in "Essays on the Philosophy of Science". - The definition of substance has never been clearer and has become even less clear after the discoveries of modern science. Is it possible, for example, to call that mysterious agent, to which physicists resort to explain the phenomena of heat and light, a substance? This agent, this environment, this mechanism - call it what you like - exists because it manifests itself in irrefutable actions. However, it is devoid of those qualities without which it is difficult to imagine a substance. It has no weight, it may not have mass either; it does not make a direct impression on any of our senses; in a word, he does not have a single sign that would indicate what was once called "material." On the other hand, it's not a spirit, at least it never occurred to anyone to call it that way. But is it really just because it cannot be subsumed under the category of substance that its reality should be denied?

Is it possible, for the same reason, to deny the reality of the mechanism by which gravity is transmitted into the depths of space at a speed incomparably greater than the speed of light (Laplace considered it to be instantaneous)? Great Newton thought it impossible to do without this agent. The one who owns the discovery gravity wrote Bentley:

“For gravitation to be innate and inherent, characteristic of matter in the sense that one body could act on another at a distance through empty space, without the mediation of anything by means of which and through which action and force could be transmitted from one body to to another, it seems to me so absurd that I don't think any person capable of philosophical reasoning would fall into it. Gravity must be produced by an agent that exhibits its continuous influence on bodies known laws; but is this agent material or not material? This question is presented to the judgment of my readers” (3rd letter to Bentley, February 25, 1692).

The difficulty of making room for these agents is so great that some physicists, namely Hearn, who masterfully developed this idea in his book The Structure of Celestial Space, consider it possible to imagine new genus agents occupying, so to speak, the middle between the material order and the spiritual, and serving as a great source of the forces of nature. This class of agents, called dynamic by Hearn, from which he excludes any idea of ​​mass and weight, serves, as it were, to establish relations, to cause actions between different parts of matter at a distance.

Hearn's theory of dynamic agents can be based on the following. In fact, we have never been able to define what matter and force are. Nevertheless, they considered them opposite, i.e. They defined matter as something opposite to force, and force as something opposite to matter. But now the old views of matter, as something solid and opposed to energy, have changed to a large extent. The physical atom, previously considered indivisible, is now recognized as complex, consisting of electrons. Electrons are not material particles in usual meaning the words. Rather, they are moments of manifestation of force, moments or elements of force. In other words, electrons are the smallest divisions of matter, and at the same time, the smallest elements of force. Electrons can be positive or negative. It can be considered that the difference between matter and force lies in the different combination of positive and negative electrons. In one combination they give us the impression of matter, in the other of force. From this point of view, the distinction between matter and force, which continues to form the basis of our view of nature, does not exist. Matter and force are one and the same thing, or rather, different manifestations of the same thing. In any case, there is no essential difference between matter and force, and one must pass into the other. From this point of view, matter is condensed energy. And if this is so, then it is quite natural that the degree of condensation can be different. This theory explains how Hearn could imagine semi-material and semi-energetic agents. Subtle, rarefied states of matter should indeed occupy a middle place between matter and force. In his book The Unknown Forces of Nature, K. Flammarion writes:

Matter is not at all what it appears to our senses, touch or vision... It represents one whole with energy and is a manifestation of the movement of invisible and weightless elements. The universe has dynamic nature. Guillaume de Fontenay gives the following explanation dynamic theory. In his opinion, matter is not an inert substance, as it is imagined. Take the wheel and put it horizontally on the axle. The wheel is stationary. Let the rubber ball fall between his backs, and the ball will almost always pass between them. Now let's give the wheel a slight movement. The ball will often hit behind the back and bounce. If the rotation is accelerated, the ball will not pass at all through the wheel, which will become for it, as it were, an impenetrable disk. Can be done similar experience by placing the wheel vertically and pushing the stick through it. A bicycle wheel will do this well, as its spokes are thin. When the wheel is stationary, the stick will go through it nine times out of ten. When moving, the wheel will more and more often repel the stick. With an increase in the speed of movement, it will become impenetrable, and all attempts to pierce it will break like steel armor.

And now, having considered in the world around us everything that corresponds to the physical conditions of the space of higher dimensions, we can put the question quite definitely: What is the fourth dimension?

We have seen that it is impossible to prove the existence of the fourth dimension geometrically and find out its properties, and most importantly, determine its position in relation to our world. Mathematics only allows possibility the existence of higher dimensions.

At the very beginning, defining the idea of ​​the fourth dimension, I pointed out that if it exists, this means that, in addition to the three perpendiculars known to us, there must also be a fourth. And this, in turn, means that from any point in our space a line can be drawn in a direction that we do not know and cannot know; and further, which is very close, near us, but in some unknown direction, there is some other space that we are not able to see and which we are not able to penetrate.

Next, I explained why we are not able to see this space; I established why it should lie not near us, in some unknown direction, but inside us, inside the objects of our world, our atmosphere, our space. But this is not the solution to the whole problem, although it is a necessary step on the way to the solution, for the fourth dimension not only within us, but we ourselves are inside it, i.e. we exist in a four-dimensional space.

Earlier I mentioned that "spiritualists" and "occultists" of various schools often use the expression "fourth dimension" in their literature, attributing to the fourth dimension all the phenomena of the "astral sphere".

The "astral sphere" of the occultists, which permeates our space, is an attempt to find some place for those phenomena that do not correspond to our space. Therefore, to some extent, it represents the extension of our world inward that we are looking for.

From the usual point of view, the "astral sphere" can be defined as subjective world, projected outward and taken for objective world. If someone really managed to prove the objective existence of even a part of what is called the "astral", this would be the world of the fourth dimension.

However, the very concept of "astral sphere" or "astral matter" in the occult teachings has changed many times. On the whole, if we consider the view of the occultists of various schools on nature, we find that it is based on the recognition of the possibility of studying other conditions of existence than our physical ones. "Occult" theories are for the most part based on the recognition of one basic substance, the knowledge of which provides the key to understanding the secrets of nature. But the very concept of substance is conditional. Sometimes it is understood as principle, how existence condition and sometimes like substance.

In the first case, the basic substance is the basic conditions of existence; in the second case - the main matter. The first concept, of course, is much more subtle and is the result of a more developed philosophical thought. The second is much grosser and is usually a sign of the decline of thought, a sign of ignorant handling of deep and subtle ideas.

Philosophers-alchemists called this basic substance Spiritus Mundi - the spirit of the world. But the alchemists - gold seekers - already considered it possible to enclose the Spiritus Mundi in a flask and perform chemical manipulations on them.

This must be remembered in order to appreciate the "astral hypotheses" of modern theosophists and occultists. Saint Martin, and later Eliphas Levi, still understood "astral light" as principle, as conditions of existence that differ from ordinary, physical ones. But among modern spiritualists and theosophists, the "astral light" has turned into "astral matter", which can be see and even take pictures. The theory of "astral light" and "astral matter" is based on the hypothesis of "subtle states of matter". The hypothesis of subtle states of matter was still possible in the last decades of the old physics, but it is difficult to find a place for it in modern physical and chemical thinking. On the other hand, modern physiology is increasingly deviating from physical and mechanical explanations of life processes and comes to recognize the colossal influence traces of matter, i.e. matter, inaccessible to perception and chemical definition, which, nevertheless, are revealed by the results of their presence, such as "hormones", "vitamins", "internal secretions", etc.

Therefore, despite the fact that the hypothesis of subtle states of matter has nothing to do with modern physics, I will try to give a brief explanation of the "astral theory" here.

According to this theory, the particles that are the result of the fission of physical atoms produce a special kind of subtle matter - "astral matter", subject to the influence of physical strength, but forces that do not affect physical matter. Thus, this "astral matter" is subject to the influence of psychic energy, i.e. will, feelings and desires, which are real forces in the astral sphere. This means that the will of a person, as well as the reactions of his feelings and emotional impulses, affect "astral matter" in the same way that physical energy affects physical bodies.

Further, it is recognized as possible the transition of physical matter, which makes up visible bodies and objects, into an astral state. It - dematerialization, i.e. the absolute disappearance of physical objects to no one knows where, without a trace or a trace. Reverse transition, i.e. transition of astral matter into physical state, or physical matter, is also recognized as possible. It - materialization, i.e. the appearance of things, objects and even living bodies from nowhere.

Then it is recognized as possible that the matter that is part of some physical body, having passed into the astral state, can “return” to the physical state in a different form. So, one metal, having passed into the astral state, “returns” in the form of another metal. Thus, alchemical processes are explained by the temporary transfer of some body, most often metal, into an astral state, where matter is subject to the action of the will (or spirits) and under the influence of this will completely changes, and then reappears in the physical world. in the form of another metal; in a similar way, iron can turn into gold. It is considered possible to transfer matter in this way from one state to another and to transform one body into another by means of mental influence with the help of rituals, etc. Further, it is considered possible to see in the astral sphere events that have not yet taken place in the physical sphere, but should take place and affect the past and the future.

All this, taken together, constitutes the content of what is called magic. Magic in the ordinary sense of the word means the ability to do what cannot be done by ordinary physical means. Such, for example, are the ability to influence people and objects at a distance, to see the actions of people and know their thoughts, to make them disappear from our world and appear in unexpected places, the ability to change their appearance and even physical nature, incomprehensibly transported over long distances, penetrate walls, etc.

"Occultists" explain such actions by the acquaintance of magicians with the properties of the "astral sphere" and their ability to act mentally on the astral substance, and through it on the physical. Some kinds of "magic" can be explained by the message inanimate objects special properties, which is achieved by psychic influence on their astral substance, a special kind of psychic magnetization of them, through which magicians can impart any properties to things, make them executors of their will, force them to bring good or evil to other people, warn of impending misfortunes, give strength or take away her, etc. Among the magical actions is, for example, the "blessing of water", which has now become a simple rite in Christian and Buddhist worship, but originally consisted in the desire to psychically saturate the water with some kind of radiation or emanations in order to impart to it the desired properties, healing or otherwise.

In theosophical and modern occult literature there are many very imaginative descriptions of the astral realm. But nowhere is any evidence of its objective existence given.

"Spiritual" evidence, i.e. séance phenomena and "mediumistic" phenomena in general, "messages," etc., attributed to spirits (i.e., disembodied souls) are in no sense evidence, because all these phenomena can be explained much more simply. In the chapter on dreams, I establish the possible meaning of spiritual phenomena as the results of "impersonalization." Theosophical explanations based on clairvoyance require, first of all, proof of the existence of clairvoyance, which remains unproven despite big number, in which the authors describe what they have achieved, or what they have found, with the help of clairvoyance. Not everyone knows that in France there is a prize established many years ago, which promises a significant amount of money to anyone who reads a letter in a sealed envelope. The premium remains unpaid.

Both spiritualistic and theosophical theories suffer from a common defect which explains why the "astral hypotheses" remain the same and receive no evidence. In both spiritualistic and theosophical astral theories, "time" and "space" are taken exactly the same as in the old physics, i.e. separately from each other. "Disembodied spirits" or "astral beings" or thought forms are understood as spatial bodies of the fourth dimension, but in time like physical bodies. In other words, they remain in the same conditions of time as physical bodies. But this is precisely what is impossible. If "subtle states of matter" created the bodies of another spatial existence, these bodies would have to have a different temporal existence. But this idea does not penetrate into theosophical and spiritualistic thinking.

This chapter contains only historical materials related to the study of the "fourth dimension", or rather, that part of them that leads to the solution of the problem, or at least to its more precise formulation. In the chapter “A New Model of the Universe” of this book, I show how the problems of “space-time” are related to the problems of the structure of matter and, consequently, the structure of the world, how they lead to a correct understanding real world - and avoid a whole series of unnecessary theories, both pseudo-occult and pseudo-scientific.