There are more than three dimensions (dimension). The usual Euclidean space studied in elementary geometry is three-dimensional; planes are two-dimensional, straight lines are one-dimensional. The emergence of the concept. . connected with the process of generalization of the very subject of geometry. This process is based on the discovery of relationships and forms similar to spatial ones for numerous classes of mathematical objects (often not of a geometric nature). In the course of this process, the idea of an abstract mathematical space gradually crystallized as a system of elements of any nature, between which relationships are established, similar to certain important relationships between points in ordinary space. Most general expression this idea is found in concepts such as topological space, specifically metric space. The simplest M. spaces are n-dimensional Euclidean spaces, where n can be any natural number. Just as the position of a point in ordinary Euclidean space is specified by specifying its three rectangular coordinates, a "point" in n-dimensional Euclidean space is specified by n "coordinates" x1, x2, ..., xn (which can take on any real values); the distance r between two points M(x1, x2, ..., xn) and M "(y1, y2, ..., yn) is determined by a formula similar to the formula for the distance between two points of ordinary Euclidean space. With the same analogy, they are generalized to case of n-dimensional space and others geometric concepts. Thus, in M. p., not only two-dimensional planes are considered, but also k-dimensional planes (k) geometric representations and methods for the study of functions of any number of variables (and not just one, two, or three).This was the main stimulus for the formalization of the concept of n-dimensional Euclidean space.An important role is also played by other M.p. relativity, they use four-dimensional space, the elements of which are the so-called “world points.” In this case, the concept of a “world point” (as opposed to a point in ordinary space) combines a certain position in space with a certain position in time (therefore, “world points” are given four coordinates instead of three).The square of the "distance" between the "world points" M'(x', y', z', t') and M''(x'', y'', z'', t'' ) (where the first three "coordinates" are spatial and the fourth one is temporal) it is natural to consider here the expression (M' M'')2 = (x' - x'')2 + (y' - y'')2 + ( z' - z'')2 - c2(t' - t'')2, where c is the speed of light. The negativity of the last term makes this space "pseudo-Euclidean". In general, an n-dimensional space is a topological space that has dimension n at each of its points. In the most important cases, this means that each point has a neighborhood homeomorphic to an open ball in n-dimensional Euclidean space. More about the development of the concept of M. p., the geometry of M. p., as well as lit. see Art.
The space of the universe is really multidimensional. Similar to sunlight coexists with pure water in the same space, freely passing through water and at the same time interacting with it little, just as radio waves of different frequencies freely exist in the depths of space outside and inside our bodies - like this everywhere in the multidimensional depths inside and outside of any solid, liquid or gaseous objects there are other worlds - the abode of spirits and God.
The scale of multidimensionality is a special scale of energy states that differ as fundamental ranges. The vector of attention when studying this scale should not be directed up, down, or in some other direction, but deep into. Layers of multidimensional space (in Greek they are called eons, in Sanskrit - loks) differ from one another in their degree. subtlety-roughness.
The layer of the most subtle energies is God in the aspect of the Creator. It looks like the purest, infinite in extent Light, similar to the light of the morning sun - gentle and warm. There are no forms in Him. Once in Him, all forms immediately dissolve.
In different earthly languages, people call Him differently: God the Father, Jehovah, Allah, Ishvara, Primordial Consciousness, Tao, etc. He is the God of the Jewish prophets, and Jesus Christ, and Muhammad, and the faithful of China, India and other countries where there are correct ideas about Him.
And only human ignorance and intellectual primitivism lead to the opinion that, since the “names” are different, then the Gods are also different ...
It is from the Abode of the Creator, from this first, primordial eon, that each new “island” of the multidimensional Creation is created. building material for education solid matter serves, first of all, protomatter (protoprakriti, bhutakasha).
This layer is seen from within - upon penetration into it - as an infinite space filled with Gentle Peace and devoid of glare. It is like a state of warm and quiet gentle southern night with many stars.
It is extremely important that the Creator and the eons of akasha are located in relation to the entire Creation, as it were, on the other side of the “mirror”, in the “Through the Looking Glass”. Yes, as our ordinary mirror has light and dark sides - so it is there, in the multidimensional depth of the universal Ocean.
It is precisely this phenomenon that physicists guess when they try to look into the "Through the Looking Glass" from the world of matter in their theoretical calculations; they call the energy of the eons of akasha... "anti-energy", "anti-matter"...
… In order to create another material “island” in the boundless Ocean of the universe, the Creator first forms a local zone of increased gravitation (attraction) in it. This phenomenon is known in astronomy as "black holes". Thus, it is drawn into the eon of protoprakriti and is transformed to elementary particles, various material space "garbage" - dead planets, meteorites, cosmic dust.
Then the Holy Spirits form a seal from this material. Overpressure and overheating gradually increasing in this clot provoke nuclear fusion reactions; this is how all the elements of the periodic table are formed, molecules are formed, including organic ones. In the latter, clots of protopurusha begin to incarnate. Thus begins the parallel evolution of organic bodies - and the souls incarnated in them. Biologists have studied the evolution of organic bodies quite well, it is only necessary to take into account the leading role in this process of God.
Our - human - task here is to develop ourselves - as a soul, consciousness - to a sufficient extent, to go the way from the Creation to the Creator, refining ourselves as consciousness - in order to merge into Him, enriching Him with ourselves.
This was the “idea” of God when He created our Earth. This is the meaning of our lives.
It is important for us to understand that we are not self-existent, we have no right and no reason to claim our own egocentrism, a sense of our own special “significance”. For self-existent - only the Creator. And He started all this Creation together with us not at all for us, but for Himself, for the sake of His own Evolution.
Hence the quality of our destinies: if we develop correctly, everything goes well in our lives, if it goes wrong, He points it out to us through our pain and failures.
… After a huge, by our earthly standards, time, billions of human bodies and even more souls of different ages and different qualities appeared on our planet. Of these, those who achieve Perfection merge into the Creator and no longer incarnate (except as Messiahs, Avatars). The rest are embodied again and again - until the time of existence of this material "island" ends. When it is destroyed, matter and those souls that have not come close to the Creator are destroyed to the state of akasha, forming construction material for future "islands" and life on them.
… At the opposite end of the scale from the Creator subtleties - rudeness there is a diabolical eon - the world of rough black energies, terrible in emotional state and "sticky" like oil. How to get there - we'll talk about this separately.
But there is also a abode for the righteous - paradise.
Each person, having disincarnated, falls into the eon that he deserved while living in the body on Earth. But we must strive for the higher eons.
It is difficult but necessary for us, brought up in an environment of atheism and dominant religious ignorance, to learn that God the Father does not live high in the sky, not on other planets, not on some mountain, etc. He is everywhere in the whole universe: in depth under our bodies and the whole world of matter, under all Creation.
And the "ladder" to Him does not lead up, but deep into. Its steps are the steps of refinement of oneself as consciousness. And that ladder begins... in our spiritual hearts.
… Everything that was said was actually researched by the author of this book, and is not written off by him from somewhere or is not retold from someone else's words. And everyone should try to pass this Path. At the same time, it is important to know that you should move along it “from step to step”, and not jumping over “flights of stairs”.
… So, the Abode of the Creator exists everywhere, under every molecule of matter. The distance to it, as Jesus said, is no thicker than a sheet of thin paper ...
God the Father is not in heaven, He is everywhere: in and around our bodies, under each of their particles. His Abode is extremely close! But ... - try, step into it!
It can only be crossed with His blessing. And only those who have developed themselves to the proper extent in terms of the parameters of Love, Wisdom and Strength can receive a blessing for this.
The Path to the Abode of the Creator is the Path of gradual refinement of oneself as a consciousness. First you need, in the words of the Apostle Paul, “turn away from evil and cleave to good” [ , ], that is, get out of drunken companies, from among rude and cruel people, find beauty in nature, in true art, let companions along the spiritual Path become friends .
The next stage of strengthening in subtlety will be initial implementation potential of the spiritual heart. Then - cleaning of the chakras and the most important meridians, including chitrini (Brahmanadi). Now, leaving the body through chitrini, we will immediately fall into the Holy Spirit, and meditation Pranava will give the first mergers with Him… Thus, following from step to step of the multidimensional Universe, sometimes making stops to rest and get comfortable, we get to the Abode of the Creator, which is now becoming our Home.
Here - true path to God. And not vicious rallies calling for reprisals against "infidels", not anathemas (curses) against individual "dissenters" or neighboring sects or even entire nations! That is the path of devilization, the path to hell.
What's happened spatial And time coordinates? There are four explicit ones: three spatial and one temporal. Are additional, unknown to us, hidden spatial and temporal dimensions possible in our world?
Physicists say yes. In 1921 in the journal "Sitzungsberichte der Berliner Akademie" an article by Theodor Kaluza appeared under the title "On the problem of the unity of physics" (the article was recommended by A. Einstein). In it, the researcher proposed to supplement the four dimensions of space-time with a fifth, spatial dimension. The introduction of the fifth dimension made it possible to describe all fundamental dimensions known at that time (gravitational and electromagnetic) through spatial categories.
A few years later, the Swedish physicist Oskar Klein expanded this theory by considering other multidimensional variants of the Universe and checking their compatibility with already known fundamental physical laws. In modern physics, the Kaluza-Klein theory is any quantum theory that attempts to unify the fundamental interactions in a space-time that has more than four dimensions. There is currently a large number of theories considering our World as 5, 6 and even 12 dimensional, and additional coordinates can turn out to be both spatial and temporal.
However, there are a number of strong arguments “against” multidimensionality. First of all, it is not observable. And no matter how many theories physicists invent, not a single fact has been found in our world that confirms the theory of multidimensionality. Except, of course, the human mind.
Moreover, it turned out that if there is surrounding us world additional dimensions, some existing natural phenomena would be impossible (in particular, the existence planets, stars, atoms and molecules).
Clearly, although not quite right, it can be represented as if there were additional spatial dimensions in our world, then something would definitely fall in there, fall out, arch out (atoms, planetary orbits, waves or particles). But this is not happening!
Naturally, multidimensional theories take into account the limitations imposed by reality. There are several ways to bridge the tension between the rigid demands of our world and the dream of multidimensional realities.
First way.
Offered at work A. Einstein And P. Bergman“Generalization of Kaluza's Electricity Theory”, it assumed “that the fifth coordinate can vary only within certain limited limits: from 0 up to some value T, i.e. The 5-dimensional world is enclosed, as it were, in some layer of thickness T”. This value is so small that even an elementary particle (an electron, for example) exceeds it as much as Earth- a pea. And it is impossible to place anything in this more than narrow layer of an additional dimension.
If we imagine all of our visible world with its 4 dimensions as a plane, for example, a sheet of paper, then the fifth dimension will appear as the thinnest layer of space applied to this sheet. In all directions, the leaf is infinite, and upwards (into the 5th dimension), its length is limited by the microscopic size of the layer. It is impossible to fall into such a dimension, not only for a person, even for an elementary particle. And you can't see him. Even the most powerful microscopes will not help.
Method two.
The extent of space in the fourth dimension can be arbitrarily large (in principle comparable to almost infinite length, width and height). However, this space is "curled into an exceptionally small circle." And this folded 5th direction (coordinate axis) is connected to the 4-dimensional world that we see only by a narrow neck, the diameter of which is comparable to the size of the 5-dimensional layer described above. “In order to detect this circle, the energy of the particles illuminating it must be large enough. Particles of lower energies are distributed evenly around the circle and it cannot be detected. The most powerful accelerators create particle beams with a resolution of 10-16 cm. If the circle in the fifth dimension is smaller, then it is impossible to detect it yet.”
The adoption of one of these provisions explains the unobservability of extra dimensions (by the way, that is why they are called hidden) and why they do not affect our world.
But, besides physicists, representatives of other natural sciences also turned to multidimensional theories of space, in particular V.I.Vernadsky, which assumed that physical space is not a geometric space three dimensions”
How, in general, could these multidimensional spaces come to a person's head if they are not in the surrounding reality? And can we invent, imagine something that has no analogue in the outside world (until now, only the wheel has been proposed as such, and even then it had analogues - moving rounded disks - the moon and the sun).
If the psyche is a reflection of the macrocosm, then it reflects all spatio-temporal properties universe, including some that we don't yet know about. This applies to any concept of space. The more complex the World around us is, the more complex the display is. Any mirror is two-dimensional, but it is capable of reflecting three-dimensional objects, just as there is a three-dimensional world behind an absolutely flat TV screen; and if you try a little, then the landscapes shown can acquire depth. And if the psyche is still not a reflection, but an elusive higher substance, then, in this case, a person created “in the image of likeness” initially carries the Highest plan of the Universe structure. And, of course, if this plan provides for higher dimensions for space-time, a person carries them in himself.
Reflected (can they be reflected) in sensual images hidden dimensions the outside world, if of course there are any in it?
A person can perceive and visualize only three-dimensional objects, images of a higher dimension are fundamentally inaccessible to either perception or imagination, i.e. we cannot only see them, but also imagine them.
We have developed "organs" only for those aspects of Being-in-itself that were important to take into account in order to preserve the species.
Yes, but... And if the perception or imagination of multidimensional structures has meaning and significance for the survival of the species? If we do not realize this, but the multidimensionality of space-time plays an important role in the organization of our mental life? Then it is possible that we somehow reflect the multidimensional structure of the Universe inside us, although we are not aware of this, because the fish, reflecting the hydrodynamic properties of water by the structure of its body, is also unaware of this and, moreover, is not familiar with the laws of thermodynamics.
Research has established empirically that images of altered states of consciousness can be multidimensional.
In LSD sessions, subjects “familiar with mathematics and physics sometimes report that many of the concepts of these disciplines, which elude rational understanding, can become more comprehensible and can even be experienced in altered states of consciousness. Insights that promote comprehension include such theoretical systems as non-Euclidean geometry, the geometry of n-dimensional space, space-time, Einstein's special and general theory of relativity” ...
If the hidden dimensions of space-time exist in any form, then their presence must be reflected in the structure of the internal space, i.e. under certain conditions (perhaps in altered states of consciousness) a person can visualize visual images with dimension greater than three. If this happens, then we can talk about the multidimensionality of the inner space of a person. If this turns out to be beyond the power of a person, then his inner space is at best 3-dimensional.
Hypnosis. The subjects were put into a state of deep hypnosis.
1 experience - after waking up for a while (until receiving the final signal), they will no longer see everything that is to their right, it does not matter where they look and with which eye (right-sided agnosia);
2 experience - after waking up for a while (until receiving the final signal), they will stop seeing everything that is to their left, it does not matter where they look, and with which eye (left-sided agnosia).
In the second series of experiments, visualization of images was called 4th spatial dimension. Before the experiment, the subjects did not know what exactly they were to visualize. Before the experiment, the subjects were reminded of certain provisions school course geometry. A straight line, a right angle, coordinate axes were drawn; from matches and plasticine it was composed: a straight line, an angle, two straight lines at an angle of 90 degrees, three straight lines intersecting at 90 degree angles - Cartesian coordinate axes, an example of a three-dimensional right angle was shown - the corner of a room in which three walls intersect at a right angle. It was unobtrusively mentioned that the 4th line cannot be drawn in this way (“how to draw one more line at a right angle to all the others - it doesn’t work, okay”).
1. Visualization in a state of hypnosis. The subjects were introduced into a similar state of deep hypnosis. They were then asked to imagine:
1) straight line,
2) two lines intersecting at an angle of 90 degrees,
3) three lines intersecting at an angle of 90 degrees.
Then we proceeded to the visualization of the 4th spatial dimension. The subjects were asked to mentally draw another line (the fourth) at an angle of 90 degrees to all the others. Another option was to imagine a corner of the room and try to imagine a fourth wall, at right angles to the others. Next, the subjects were asked to mentally “look” in the direction of this line and verbally describe everything they see.
2. Post-hypnotic visualization. In a state of deep hypnosis, the subjects were suggested that after waking up for a while (until receiving the final signal), they would retain their ability to visualize the 4th straight line and be able to look in its direction from anywhere in the room. Next, they were taken out of the state of hypnosis, and the safety of the suggestion was checked. The subjects described the features of their vision of the world. At the end, the final signal was given.
7 people took part in the experiments.
Results of the second series. The phenomenon of visualization of the 4th spatial dimension was very easy to cause. All seven people completed the task.
When visualizing under hypnosis, most of the subjects in the direction of the 4th axis "saw" or abstract geometric figures or found it difficult to describe what they saw
In the next group of experiments, an attempt was made to physically penetrate the 4th dimensions in a situation of post-hypnotic suggestion. In this group of experiments, the well-known fact was confirmed that, alas, it is impossible to penetrate physically into the 4th dimension. Even if a person sees images of this dimension, the physical body still imposes restrictions on the freedom of its movements. Thus, almost all of our subjects, "looking" into the 4th dimensions, visualized abstract geometric shapes. And only in one case, the subject imagined real pictures. By the way, this was the only left-handed subject in this series of experiments.
The question that arises. Or maybe all this imagination game? Maybe the subjects did not really represent Fourth dimension but only imagine what they imagine? But it was precisely the space of the imagination that was studied; Not physical world how it works (after all, the study of the physical world is a matter of another science - physics), A dimension our space of imagination. And if Human only imagines that he imagines the fourth change, maybe this means that he can imagine higher dimensions in his inner space.
The fact draws attention. Ease of completing the task “imagine the fourth dimension” by the subjects. It can be assumed that the multidimensionality of the space of imagination is the natural state of the human psyche, which has a completely material under itself - the brain substrate.
Indeed, if multidimensionality is not alien to our world, then shouldn’t the psyche that has arisen in its image and likeness reflect it with the depths of its being? It should be noted that such a definition of the internal space does not violate any of the laws of physics.
Let us now turn to the verbal realm. The ideas embodied in the word are brought to consciousness and thus are realized by us. The display of the multidimensional aspects of the universe occurs through the embodiment of relevant ideas in the achievements of culture (from myths and fairy tales to formulas and theories). And it is in such forms that these ideas are realized by mankind - as myths and legends, as fantasies and works of art; embodiment in the form of formulas and theories.
At first, of course, the display of the multidimensional structure of the universe was in myths. The idea that our universe consists of several worlds, communicating or almost not communicating, is quite common in mythology. different peoples. For example, in the myths of the ancient Slavs, there was an idea of the three main substances of the world. The idea of the multidimensionality of the structure inner peace human is found in Egyptian mythology. This is a fairly common division of the universe into three worlds (earthly, heavenly and underworld).
man displayed multidimensionality of our world and hidden space-like dimensions from time immemorial. But the question of how to penetrate into the higher dimensions of the space of our Universe remains from the breed of the eternal. Answers to it, of course, exist, it's just not entirely clear how to use them.
Most often, for the transition to higher dimensions, it is recommended to present one's internal space as external, and the external space of multidimensional reality as internal. In terms of the topology of high-dimensional spaces, this is really a great way to imagine the fourth spatial dimension, being in the third.
Even in the apocryphal Gospel of Thomas, it is precisely in such words that the path of man to the kingdom of God is described. “When you make two one, and when you make the inside as the outside, and the outside as the inside, and the top as the bottom, /.../ when you make the eyes instead of an eye, and a hand instead of a hand, and a foot instead of feet, an image instead of an image - then you will enter the [realm]. Usually these words are interpreted in a figurative sense: a person must completely change, understand himself, realize the complex nature of his inner world, change it into better side etc. But perhaps these words can be understood in their literally, as another description of the transition to higher dimensions. Well, the “kingdom of heaven” is a classic representation of other realities in the mythology of many peoples.
Our psyche has additional dimensions, as a kind of higher (in spatio-temporal sense) reality that is not reducible to everyday life.
Or maybe otherwise, only due to the presence of additional dimensions in our Universe, the very possibility of mental reflection appeared, the psyche arose and the mind developed.
One of the main tasks of theoretical physics today is to find an answer to the question of whether there are higher dimensions. Does space really only consist of length, width and height, or is it just a limitation of human perception? For millennia, scientists strongly rejected the idea of the existence of a multidimensional space. However scientific and technological revolution changed a lot, and today science is no longer so categorical on the issue of higher dimensions.
What is the essence of the concept of "multidimensional space"?
Man lives in a world that consists of three dimensions. The coordinates of any object can be expressed in three values. And sometimes two - if we are talking about what is on the surface of the Earth.
By means of length, width and height, one can describe both terrestrial objects and celestial bodies- planets, stars and galaxies. They are also enough for things inhabiting the microcosm - molecules, atoms and elementary particles. The fourth dimension is considered to be time.
A multidimensional space must have at least five dimensions. Modern theoretical physics has developed many theories for spaces with different dimensions - up to 26. There is also a theory that describes a space with an infinite number of dimensions.
From Euclid to Einstein
Physicists and mathematicians of Antiquity, the Middle Ages and Modern times categorically denied the possibility of the existence of higher dimensions. Some mathematicians even deduced justifications for the limitation of space by three parameters. Euclidean geometry assumed only three dimensions.
Before the advent general theory In relativity, scientists generally considered multidimensional space to be a subject unworthy of study and advancement of theories. When Albert Einstein formulated the concepts of space-time, combining three dimensions with the fourth, time, certainty in this matter immediately disappeared.
The theory of relativity proves that time and space are not separate and independent things. For example, if astronauts board a ship that moves at high speed for a long time, then upon returning to Earth they will be younger than their peers. The reason is that less time will pass for them than for people on Earth.
Kaluza-Klein theory
In 1921, the German mathematician Theodor Kaluza, using the equations of the theory of relativity, created a theory that for the first time combined gravity and electromagnetism. According to this theory, space has five dimensions (including time).
In 1926, the Swedish physicist Oskar Klein provided Kaluza's rationale for the invisibility of the fifth dimension. It consisted in the fact that the higher dimensions are compressed to an incredibly small value, which is called the Planck value and is 10 -35 . Subsequently, this formed the basis of other theories of multidimensional space.
String theory
This area of theoretical physics is by far the most promising. String theory claims to be what physicists have been looking for since the advent of general relativity. This is the so-called theory of everything.
The point is that two fundamental physical principle- theory of relativity and quantum mechanics are in irresolvable conflict with each other. The theory of everything is a hypothetical concept that could explain this paradox. In turn, string theory is more suited to this role.
Its essence is that at the subatomic level of the structure of the world, particles vibrate, similar to the vibration of ordinary strings, for example, a violin. This is where the theory got its name from. Moreover, the dimensions of these strings are extremely small and fluctuate around the Planck length - the same one that appears in the Kaluza-Klein theory. If an atom is enlarged to the size of a galaxy, then the string will only reach the size of an adult tree. String theory only works in multidimensional space. And there are several versions of it. Some require 10-dimensional space, while others require 26-dimensional space.
At the time of its inception, string theory was perceived by physicists with great skepticism. But today it is the most popular, and many theoretical physicists are engaged in its development. However, it is not yet possible to prove the provisions of the theory experimentally.
Hilbert space
Another theory describing higher dimensions is the Hilbert space. It was described by the German mathematician David Hilbert while working on the theory of integral equations.
Hilbert space - mathematical theory, which describes the properties of the Euclidean space in infinite dimension. That is, it is a multidimensional space with an infinite number of dimensions.
Hyperspace in fiction
The idea of multidimensional space has resulted in many science fiction plots - both literary and cinematic.
So, in Dan Simmons' tetralogy "Songs of Hyperion", humanity uses a network of hyperspatial null-portals capable of instantly transporting objects over a long distance. In Robert Heinlein's Starship Troopers, soldiers also use hyperspace to travel.
The idea of hyperspace flight has been used in many space opera films, including the famous saga " star Wars and TV series "Babylon 5".
The plot of the film "Interstellar" is almost entirely tied to the idea of higher dimensions. In search of a suitable planet for colonization, the heroes travel through space through wormholes - a hyperspace tunnel leading to another system. And towards the end main character falls into the world of multidimensional space, with the help of which he manages to transfer information to the past. The film also clearly shows Einstein's connection between space and time: for the astronauts, time passes more slowly than for the characters on Earth.
In Cube 2: Hypercube, the characters find themselves inside a tesseract. So in the theory of higher dimensions is called a multidimensional cube. In search of a way out, they find themselves in parallel universes, where they meet their alternate versions.
The idea of a multidimensional space is still fantastic and unproven. However, today it is much closer and more real than a few decades ago. It is quite possible that in the next century scientists will discover a way to move in higher dimensions and, therefore, travel to parallel worlds. Until then, people will fantasize a lot on this topic, inventing amazing stories.
