Analysis of spatiality and time in artistic and visual works

Contents Analysis of spatiality and time in artistic and visual works 1 2 3 4 5 6 7 8 9 10 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 34 35 36 38 39 40 41 42 [43] 44 45 46 47 48 [-50] 51 52 53 54 55 56 57 Time and space 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 Comments Analysis of spatiality and time in artistic and visual works Reality, no matter whether it is nature, technology or art, is naturally divided into separate, relatively self-contained unities. These unities are infinitely full of content: the division of reality into them cannot be called rational knowledge, if by the latter we mean a construction from simple concepts of reason. This simplification of reality is achieved in a completely different way, namely when we try to imagine a mental model of reality, all at once, from some simple and - most importantly - always and everywhere the same mental formations. Space and reality, or instead of it - further decomposition, and reality is built from things and the environment - these are the basic formations of thought. In reality there is neither space nor reality, and therefore there are also no things and environment. All these formations are only auxiliary methods of thinking, and therefore, it goes without saying, they can and should be indefinitely plastic in order to provide the opportunity for thought to adapt each time quite subtly to that part of reality, which in this case is the subject of special attention. In other words, the main auxiliary techniques of thinking - space, things and environment - which have the task of presenting to us a mobile and diverse reality essentially built from unchangeable and homogeneous material; [however] this task is and will always be only a declaration: at the moment when it was actually realized, the death of knowledge would occur, which would from that moment become completely conditional, and, moreover, a consciously conditional transposition of mental constructions, satisfied with their own activity, within themselves, and not at all bearing in mind reality. This is what, in a bad sense, should be called scholasticism; These are precisely the various derivatives of Kantianism. The homogeneity and immutability of these formations of thought should be affirmed only relatively, as slow and small variability, compared with the time and area of ​​reality that occupies us. Expressed mathematically, those mental series with the help of which we depict reality, i.e., its internal law, always converge only within the limits of one or another circle of convergence and, therefore, diverge beyond it. It is possible to depict the same law of reality in rows outside this circle; but this image can no longer be identical with the first, although it is adjacent to the first, constituting it, as they say, an analytical continuation. Likewise, mental formations - space, things and the environment, no matter how we build them, are suitable in one or another circle of convergence and are not suitable outside of it, if only we want to be faithful to actual experience, and not self-confine ourselves into school constructions. But they, these mental formations, can be analytically continued or taken beyond the boundaries of this circle, further and further, by means of constructions adjacent to them, but still different. Functions in the theory of a complex variable are depicted exactly like this, stitched together as patches, and this lack of consistency in one and the same image is not a defect, but the strength of a method that is equal not in itself, but in some mathematical objectivity. In the same way, in general, the mental model of reality, in living thinking, has always been sewn together and continues to be sewn together from separate flaps that analytically continue each other, but are not at all identical to each other. Any other thinking is necessarily scholastic and preoccupied with itself, and not with reality. N.I. A hundred years ago, Lobachevsky expressed a decidedly anti-Kantian thought, which at that time remained only a bold aphorism, namely, that different phenomena of the physical world occur in different spaces and, therefore, obey the corresponding laws of these spaces. Clifford, Poincare, Einstein, Weyl, Eddington revealed this idea and expressed it more clearly in relation to mechanical and electromagnetic processes. Here the dependence of the properties of space on the things and environment contained in this space, that is, on the force field, became quite clear; or vice versa – the dependence of the properties of the force field on the properties of the corresponding space. We can say that things themselves are nothing more than “folds” or “wrinkles” of space, places of special curvatures; you can interpret things or elements of things - electrons, as simple holes in space - sources and sinks of the world environment; one can, finally, talk about the properties of space, mainly about its curvature, as derivatives of a force field, and then see in things the reason for the curvature of space. These and other similar rational decompositions of reality as models, of course, are not at all similar to each other. But their logical equality and pragmatic equivalence are only a consequence of one basic fact that we indicated earlier. This fact is the auxiliary nature of mental constructions, the relationships of which are given a model of reality and each of which, in itself, does not mean anything in relation to reality. The properties of reality, with rational knowledge, must be placed somewhere in a model, that is, in space, things or the environment. But where exactly is not necessarily determined by experience itself, and depends on the style of thinking, and in general on the structure of thinking, and not on the structure of experience. Space, things or environment, any of these mental formations can be considered the first and depart from it; but no matter what is taken as the first, other mental formations will certainly appear in the future, either openly or covertly: each individually, when constructing a model of reality, is fruitless. Geometry is determined by a force field, just as a force field is determined by geometry. The whole point is that geometric constructions and proofs are necessarily based on one or another specific experience, either in the present, when, for example, we measure with a rod, a chain or a light beam, or in the past, when, for example, during theoretical reasoning, we imagine generalized images of past experiences and sometimes imagine that we are dealing with “pure” intuition, only because the memories of past experiences are pale. We can say whatever we want about geometric images, but by really imagining them, and therefore we can really apply them in thinking only when correlating them with certain experiences. And therefore their reliability is entirely related to the same experience used. Meanwhile, private experience, or the totality of private experiences, depends on the experimental background against which it, the experience, or it, the totality, appears and, therefore, depends on their properties. So: in order for the concept of a straight line to be applicable in thinking, we must certainly contact in this regard, that is, in relation to a straight line, with some kind of experimentally observable processes and tell ourselves that to deal with a straight line means to apply the chosen kind of processes in real experience, or in imaginary experience. It depends on us what kind of processes we want to rely on here; but, having made a choice, we are forced, at least within a certain time and a certain area of ​​reality, that is, in a certain circle of convergence, to stick to our choice and be faithful to it. This means that we have doomed ourselves to be carried away by all the currents of reality that carry away our chosen support of thinking. Figuratively speaking, it depends on us what kind of ship we will board; but we still must ascend to one, whatever it may be, because we cannot directly walk on the sea - and this would correspond to thinking without experimental data. But as soon as we have chosen a vessel for ourselves, our arbitrariness ends, and we are forced to sail on it until we meet another vessel on which we could transfer, in order to analytically, that is, coherently, and not by swimming, continue our path, connecting closely two intuitions, and not jumping over with a leap of pure thinking. And, of course, sitting on a ship, we share its vicissitudes - the winds, storms and currents to which it is subject in its voyage. We can define a straight line in different ways: either we associate it with a light ray, or rely on a solid rod, or start from a stretched thread, or imagine a straight line as an inertial trajectory of some mass, or want to see a straight line in the shortest path, etc. But each time we inevitably introduce into the concept of a straight line one or another of the properties of the physical phenomenon taken as the basis and through this property we connect the application of our concept of a straight line with new factors that are separated from our image We are no longer able to do this directly. And therefore the straight line, our straight line, already receives special additional properties, which we must certainly take into account under the threat of otherwise making our concept of a straight line clearly contradictory to experience. So, if a straight line is thought of as a light ray, then no matter how the environment acts on this ray, for example, during refraction, or things, for example, through the attraction of the ray by gravitating masses, we still undertake to call our ray a straight line and attribute the features of its course to the properties of space: we have no criterion by which we could judge the non-straightness of this ray, there is no standard more direct than the ray itself, for it itself there is a standard for everything straight. Consequently, by continuing to insist on its straightness, we are forced to recognize the surrounding space - such an addition that the straight lines in it have the above-mentioned features. It is impossible to construct geometry without recognizing some constitution; but, although it was established freely, it must then be maintained, at least until a new legislative act deliberately puts geometric thinking on a new path. Under no circumstances should the substitution of foundations be carried out unconsciously and tacitly: otherwise, instead of a path there will be wandering, instead of thinking there will be chaos. If a straight line is determined by a rod, and this rod, when the temperature decreases, bends in one direction, and when the temperature rises, in the other, then, moving the rod in a space of variable temperature and looking at the rod through the eyes of a geometer, i.e., having no other concepts other than geometric ones, and completely abstracting from the concept of temperature, which is alien to geometry, we will continue to consider our rod to be straight, but from the features of its behavior in different places we will make the spaces corresponding geometric conclusions regarding the composition of space itself. If you pose the question physically, and not purely geometrically, then you can, of course, argue differently: you can blame the environment, which is differently heated, for everything that happens; one can attribute this to mechanical forces, i.e., postulate certain force centers; Finally, one can see the source of the rod’s peculiarities in the structure of space. But with the first two methods of interpretation, we need to have a standard for the straightness of the rod and be confident in its immutability. The question arises: why did we need to define the direct by means of a solid body, if this definition is unstable, but we have a standard that is truly unchangeable, and why didn’t we take this unchangeable standard from the very beginning? On the other hand, why do we actually renounce the choice we have made and turn with confidence to some other standard? This last one is no more provable than the first one. And the fact that the first standard revealed some features - doesn’t it indicate the value of the standard, and not its worthlessness? If we were confident in him from the very beginning, then the features of his behavior in a certain space expose the properties of this space. Our standard does not want to flatter us to show us the smoothness of the entire space; this is no reason to reject him for his faithful service, if only from the very beginning we considered him trustworthy; otherwise, also from the very beginning, he was subject to recusal. Similar reasoning should be repeated about all other interpretations of the straight line, as well as in general - all geometric images. But this especially applies to the definition of a straight line as the shortest distance. The measure of spatial distance is the work expended to overcome this distance. If reality did not present any obstacles to overcoming distances, and we could move without any effort, even internal, from place to place, then the thought of distance would not arise in us, and we would recognize the individual images of reality as fused. Then, naturally, there would be no measure of distance. The work spent on overcoming space can be different and therefore can be measured differently. This may be mechanical work, or one or another physical process, or, finally, some type of psycho-physical work. And we can measure it in some cases with physical instruments, in others - with a direct feeling of the effort expended, i.e. fatigue. There is no need for space to be overcome necessarily by walking with one’s feet or, on a small scale, moving one’s arm, head, etc.; although, of course, only the space we have traversed on foot is truly conscious. Other expenditures of effort to overcome space are also possible, for example, an effort of attention when seeing glimpses in the window of a carriage, semi-conscious assimilation of the rhythm of knocking and rocking under the same conditions, even an expenditure of effort to fight the overwhelming feeling of danger, etc., etc. But some expenditure is a necessary condition, without which distance turns out to be unappreciated, and space - unconscious. This condition may be fulfilled by economic effort - payment for a ticket, parcel or cargo; but even here the consciousness of space is not given for free. Even during a dream, when the imagination wanders wherever it pleases, we make some effort to imagine, even very superficially, some of the routes of our flights, and we spend money on this: and we get tired of daydreaming. But the insignificance of the work required here corresponds to a vague and indistinct consciousness of the spaces overcome: in the dream there is almost no talk about distances precisely because almost no work has been spent on overcoming them, and then what is far, in one sense or another, from our location seems to be approaching it and almost merging with it. Consequently, if a straight line is defined as the shortest distance, then this definition in itself has no meaning until it is further established how exactly the distance should be measured. And when this additional definition is made, we are logically forced to adhere to the established method and not replace it with any other, supposedly more correct (this should have been thought about from the very beginning), and especially not to check the straightness of the line, since they are assessed by a recognized method as the shortest - not to check this straightness with foreign standards like a rod, a ray, etc. After all, if we, illegally, begin to introduce, along with a purely geometric definition, the assumption of some physical or mental factors that allegedly interfere with the accuracy of geometry, then we violate the very essence of geometry as such and are talking about physics, psycho-physiology, etc., which themselves cannot be constructed without geometry. On the other hand, if doubt arose whether our usual method of estimating distances is appropriate in this case, due to the distorting influence of special conditions of experience, then why would we deny the distorting effect of these very conditions in relation to all other possible ways of estimating the straightness of a certain line. And, moreover, being different, the standards of straightness, of course, inconsistently with each other, will be distorted under the same conditions; It is due to this inconsistency that we will receive data to doubt. But why should an unknown distortion of a new standard be considered acceptable and tolerable, throwing the old standard in the way for distortion and thereby making the results of both tests, old and new, irreducible to each other? Obviously, geometry has no other outcome than stopping with confidence on a certain method of verifying its images, and then not breaking with them and not listening to the whispers of other methods, the impeccability of which itself remains unprovable. Let us explain this with a simple example. Let's imagine that we live in an environment furrowed by streams and have no solid soil under our feet. This would be the case if we were midges in an atmosphere dominated by constant winds and vortices. It would be the same if we were fish in a wide and fairly fast river. Let us further assume for simplicity that we have no vision, or that our environment is opaque or not illuminated. If we now wanted to build geometry, then we would base the definition of a straight line as the shortest distance on the work measured either by physical instruments or by the feeling of fatigue that we need to expend in order to swim from a certain place in the environment to another place. The path on which our fatigue would be the least would be recognized by us as straight. It would not be a straight line of Euclidean geometry. But along with such a definition, another could arise; namely: the definition of a straight line as the fastest way to cross from a place to another place. There is no reason to expect in advance that the paths according to both definitions will always coincide, especially if the flow and vortices of our environment were not steady. Such a discrepancy between the paths according to one and the other definition, perhaps, would prompt a geometer, unsteady in his constitution, to involve in verification new definitions of the straight line and new ways of checking straightness. But all such methods would themselves be subject to the disturbing action of the environment: a material body moving by inertia would move from a rectilinear path according to Euclid to the side, a stretched thread or chain would sag under the pressure of the current, the rod would bend, the light ray would also not go along the Euclidean straight line due to the refraction of differently compacted jets of the liquid medium and due to the very movement of this medium. All paths, initially defined as straight, would be deformed, and, moreover, in different ways, diverging from each other. The question is, where exactly is the straight line and which of these supposed straight lines should be guided when checking straightness, if only we decide to change the formally established definition of a straight line as one, certainly one, of the above methods of definition and verification. But then we will have to, while insisting on the straightness of our line - straight, according to the accepted definition, also recognize a number of special properties of the straight line that do not correspond to Euclid. The set of such properties, in addition, will be different, depending on the definition of which particular line between two points we agreed to call a straight line. But, they will say, there is still a real straight line, i.e. from a geometry textbook. – The fact of the matter is that such a formulation of the objection is meaningless: the direct is not a thing, but our concept of reality. And if we cannot reveal the specific content of this concept, but the scope of its application is zero, then there is no such concept. Meanwhile, in the example taken, as we have seen, the Euclidean straight line finds neither a place nor conditions of application. This reality, as shown, does not provide reasons to apply the concept of the Euclidean line, just as it does not provide experiments that make such a concept meaningful. In other words, there is no Euclidean straight line there. Not a geometrician, but a physicist, and, moreover, standing on solid ground, can, of course, divide fish-like non-Euclidean geometry into the theory of space according to Euclid and the theory of the hydrodynamic field; but to a geometer from that flowing environment, such a division will seem extremely artificial, and he, in turn, will divide the Euclidean geometry of his colleague into his own, non-Euclidean geometry and into the supposed force field, perhaps also the flow of some kind of world fluid; this force field will sufficiently explain why the geometry accepted on earth appears to be Euclidean, although in fact it is not. But simply put, its own geometry, with the supposed worldwide uniformity of physics and psycho-physiology, just as, on the contrary, if you start from things, your own physics and your own psycho-physiology arise everywhere, but with the supposed worldwide uniformity of geometry. The properties of reality are distributed between space and things. They can be transferred to a greater or lesser extent from space to things or, conversely, from things to space. But no matter how we rearrange them, they must be recognized somewhere, since otherwise a picture of reality will not be built. The more that is placed on space, the more organized it is thought of, and therefore the more unique and individual, but accordingly things become poorer, approaching general types. At the same time, a well-known cut-out of reality receives a desire to stand out from the surrounding reality and close in on itself. It is clear that these densely idealized and largely self-enclosed spaces no longer combine well with each other, each representing its own small world. In other words, relying primarily on space in its relationship to reality, and placing the burden of reconstructing reality on it, consciousness moves towards an artistic worldview. The limit of this kind of reconstruction of reality would be the almost complete identification of reality with space, where completely plastic things would obey space until they lose their own form. Such a reality would seem to us to be composed of luminiferous gas, would be clouds of light, submissive to every breath of space. In the field of art, for example, El Greco is close to this limit. On the contrary, by transferring the load onto things, we condense their individuality and at the same time impoverish space. Things, each separately, tend towards self-closure. The connections between them weaken, and at the same time the space fades, losing its distinctive structure, internal coherence and integrity. As forces and organization of reality are attributed to things, each separately, the space that unites them becomes empty and tends toward meon from concrete fullness. Weakening internal coherence and integrity, it thereby becomes separated from external space by a border that is increasingly less reliable. That membrane, which separates a single space within itself, becomes thinner to give room for easy diffusion with the surrounding space. From the whole, space tends to become a cutting out of another, larger space, and things, although each isolated in itself, turn out to be a random heap, the collection of which is not motivated by anything. This reconstruction of the world is characteristic of positivism in science and naturalism in art. Euclidean space and linear perspective are here taken as steps towards the least meaningful and least structural understanding of space. However, this understanding still leaves some traces of spatial organization. The ultimate here would be the complete transfer of all properties of reality to things alone and the deprivation of space of any kind of structure. Such a space, swept clean, would truly be metaphysical space (στέρεσις - deprivation, from the verb στερέω - I deprive, sweep away), i.e. pure non-existence, τὸ μὴ ὄν. A space that was truly strictly universal and truly devoid of the originality of its organization, it would turn out to be pure nothingness, and in the model of reality, as not bearing any explanatory function, it would be useless. So, constructing a picture of reality requires that neither space nor things be brought to their maximum load. But the extent of this load is always determined by the nature and size of the reality under consideration, the style of thinking and the assigned tasks of the work. In general, we can say that it is advantageous to assign to space everything that, within the limits of the analyzed reality, can be considered relatively stable and universal. But both must be taken specifically in relation to this analyzed reality, and not in general, in relation to experiences that lie outside our present consideration. Space can be explained by the force field of things, just as things can be explained by the structure of space. The structure of space is its curvature, and the force field of things is the totality of forces in a given area that determine the uniqueness of our experience here. Euclidean space has zero measure of curvature; This does not mean that the concept of curvature is not applicable to it, but it only determines the nature of its curvature. Before talking about spaces in general, let's take a closer look at the features of Euclidean - features so familiar to us that we take them for granted, although it is not at all like that in reality. So, Euclidean space is characterized mainly by the following features: it is homogeneous, isotropic, continuous, connected, infinite and limitless. These are not all the characteristic features of Euclidean space, and different Euclidean spaces can be subsumed under such a set of features. But for the first approach this is enough. Let us dwell first of all on the homogeneity of Euclidean space as the most hostile to the integrity and self-closure of works of art and living organic forms. A sign of the homogeneity of space in general is the non-individualization of individual places in space: each of them is the same as the other, and they can not be distinguished by themselves, but only in relation to each other. This sign of homogeneity can be divided into more specific ones, mainly into two: the isogeneity of space and its homogeneity. The axiom of isogeneity, the main one of L. Bertrand 1 from Geneva, says: space is homogeneous in all its parts, here it is the same as there 2. Bertrand considers this property to be the simplest and expresses it as follows: “The part of space that a body would occupy in one place does not differ from that which it would occupy in another, to which we also add that the space around one body is the same as the space around the same body placed in another place.” Directly related to this is another property, namely: the ability to divide space into two parts of such a kind that “nothing can be said about one that could not be said about the other.” Consequently, the division boundary applies equally to both parts of space. This boundary is a plane; a transition can be made from a plane to a straight line. The homogeneity of space was noted mainly by Delboeuf 3, also by Rossel 4 and others. This is the property of space or spatial figures to preserve all internal relationships when changing sizes; in other words, the space of the microcosm is the same as the macrocosm. Increasing or decreasing the figure does not violate its shape, even if it goes in one direction or the other indefinitely. In other words, space is characterized by the famous postulate of Wallis: “For every figure there is a similar figure of arbitrary size,” established in the 17th century. and equivalent, according to Wallis, to the fifth postulate of Euclid. The axiom about the homogeneity of space is further adjoined by the definition of a straight line according to Euclid: “A straight line is one that lies equally in its points,” or its equivalent - Delboeuf: “A straight line is a homogeneous line, that is, one whose parts, arbitrarily chosen, are similar to each other, or differ only in length.” So, cuttings of space in any place (isogeneity) and of any size (homogeneity) in itself does not have any distinctive features; it doesn't matter how he is taken. Euclidean space is indifferent to the geometric images in it and, therefore, does not have any holds that serve as supports that hold physical processes in place. The movement in space of some physical system, since there is no other system outside it, remains unnoticed in the first one and cannot be taken into account in any way. Such is the homogeneity of Euclidean space. It is clear that we cannot establish this homogeneity either in direct perception of reality or in art, which is based on this perception, and each place in space has in our experience unique features that make it, this place, qualitatively different from all others. And if this is so, then there is no need to talk about more specific homogeneities, i.e. about Euclidean planes and Euclidean lines. We can, by some complex techniques, force ourselves to understand the space we perceive as containing Euclidean planes and straight lines, but this understanding is bought at a high price and requires very complex mental constructions, which no one wants to do, unless he clearly understands what exactly is required of him. The usual gullible acceptance of Euclidean interpretation, but without corresponding physical and psycho-physical adjustments, testifies to the carelessness of those accepting much more than the actual accumulation of experience. A property of Euclidean space that is close, but not at all identical to homogeneity, is isotropy. Sometimes they tend to insufficiently distinguish it from homogeneity, but this is just as wrong as if someone, from the correlativeness and analogy of the properties of angles and segments, erased the boundary between the two. The isotropy of space in relation to rotations of a ray near a point says the same thing as homogeneity in relation to distances from a point. This means that all straight lines emanating from a point are completely equal to each other, do not have any uniqueness that individualizes them, and, therefore, are not distinguishable by themselves, each separately. There is no sign established in relation to one direction in Euclidean space, which was not at the same time a sign of any other direction. Any rotations of a figure in space do not change anything in its internal relationships: Euclidean space is indifferent to rotation in it, just as it is indifferent to translations in it. Every actual experience shows us the opposite, and immediate consciousness quite clearly notes the qualitative peculiarity of each of the directions. The crystalline medium gives an expressive image of nonisotropy, although it is uniform everywhere: the crystalline axes indicate the directions of greatest expression of one or another property of the medium. Any real perception - we have already seen this earlier - gives each of the main directions a certain absolute quality, which cannot in any way be mixed with another; no one will identify vertical and horizontal, although in Euclidean space it is completely indifferent what is taken as vertical and what is considered horizontal. Direct experience can only be interpreted in this isotropic sense at a higher cost than in a homogeneous sense. In actual experience, it is, of course, possible to be guided by Euclid, but by adhering to the rule: “fiat justitia, id est geometria Euclidiana, pereat mundus, – pereat experimentum.” As has already been said, the above and other properties of space can be completely or largely reduced to one characteristic, namely, to the concept of curvature, and it is stated that the measure of this curvature for Euclidean space is equal to zero. It may be that logically it would not be possible to base the characteristics of Euclidean space on the zero measure of this curvature, just as it would not be possible to formally logically reduce the total characteristic of any other space to the corresponding measure of its curvature. But in any case, the measure of curvature very deeply characterizes space and should be recognized, if not the only, then still the main root of the entire organization of a given space. The initial concept of curvature arises in relation to flat lines. Curvature at a given point is used to evaluate how quickly, or, if you prefer, how intensely, a line deviates from straightness at this point, and the measure of the degree of curvature is taken to be a line whose curvature is the same everywhere, i.e. circle. We select a circle that would merge with a given curve at a given point, which is expressed by the commonality of three infinitely close points. More clearly, we should think of this measurement of curvature as a physical measurement: we have a set of solid circles, and the number on this scale is higher, the more steeply the arc of the circle is curved. If we now place these circles tangentially to the line being measured, then some of them will go on one side of the line, and others on the other, i.e. some are curved in line with this place of our line, while others are steeper. Some intermediate number corresponds to a circle curved no steeper and no more flat than the line being measured, and such a circle goes along with our line for a certain, very small distance, without deviating from it in either direction. This circle, or the degree of its curvature, measures the curvature of a given place on our line. The curvature of a circle is characterized by its radius R, or, better, by the reciprocal value of K₁ to this radius. The curvature K₁ of a line changes from point to point and can become zero in some places, negative when the line bends in the opposite direction, and infinitely large when the line becomes sharpened. A similar concept can be established in relation to two-dimensional geometric images, i.e. surfaces. But this analogy cannot be simplified by replacing the measuring circle with the same sphere and taking the reciprocal of the radius of this sphere as the measure of curvature. In fact, being a two-dimensional manifold, the surface is curved in one direction regardless of its curvature in the perpendicular direction; the example of a sheet of paper, which can be bent in one way or another without remaining bent in the perpendicular direction, explains this property of surfaces. So, the value characterizing the curvature of the surface must take into account the degree of curvature of the surface in two mutually perpendicular directions, i.e. two radii of curvature, as they say - main radii, of which one is the largest - R₁, and the other is the smallest - R₂. This is how the concept of Gaussian curvature of a surface arises at a given point K₂, and The measure of curvature K₂, generally speaking, varies from point to point and can take on all sorts of values ​​between – ∞ and + ∞. The geometric meaning of the value K₂, as one characteristic, is established by Gauss’s theorem on the so-called spherical excess. Let us have a triangle ABC on the Euclidean plane, with sides a, b, c. The sum of its angles is equal to π, so Let us now transfer our triangle, assuming its sides are flexible, but not extensible, to the curved surface under consideration and perhaps stretch its sides so that they do not lag behind the surface. Then each of them will go in the direction of the shortest distance along the surface, or, as they say, along the geodesic line of the surface. Such a line, according to the definition of a straight line as the shortest distance, should be recognized by the inhabitants of this surface as a straight line, or the most straight line - a straight line on this surface and, therefore, the entire triangle - as a rectilinear one. But, of course, the shape of this triangle has now changed and its angles have changed; now they are no longer A, B and C, but A 1, B 1, C 1, and their sum 2q 1 is no longer π, but some other quantity. That's why is no longer equal to zero. This value α, i.e. the amount of deviation of the sum of the angles of a triangle deformed on a curved surface from the same triangle on the Euclidean plane is called spherical excess. It is clear that this excess has a curvature of the surface and, therefore, itself characterizes this curvature. But further, the deformation of the triangle should affect the size of its area. If we imagine that we laid out a triangle on a plane with very small squares and counted the number of them, and then did the same with a triangle on a curved surface, then the number of squares lining its area here and there will be different, and this difference again characterizes the curvature of the surface. Therefore, the idea should arise to connect these three quantities - area, spherical excess and curvature. This is what Gauss' theorem does, according to which where the integral extends to the entire surface of the triangle A 1 B 1 C 1 on the curved surface, and dσ₂ is the area element of this triangle. The meaning of the theorem is that the spherical excess accumulates in total by all elements of the surface, but to a greater extent, the greater the curvature in this element. In other words, we must imagine the curvature of a surface by some formal analogy with surface density, and the total accumulation of this quality of the surface is reflected in the spherical excess of the triangle. Physically, Gauss's theorem can be interpreted using a granular or liquid body. If a certain amount of liquid, conceived as incompressible, were poured in a thin, even layer onto the surface of a flat triangle, and then poured in a layer of the same thickness onto a deformed triangle, then there would either not be enough liquid, or there would be too much. It is this excess, with a positive or negative sign, of the liquid, related to the thickness of the layer, that would be equal to the spherical excess of the triangle. Let's return to Gauss's formula. According to the techniques of infinitesimal analysis, it can be rewritten as: where K 2 is a certain value of the curvature of our surface inside the triangle. Therefore: This average value of curvature is characterized as the spherical excess of the deformed triangle per unit area. In other words, this is the excess liquid during deformation of the triangle, related to its total amount, or, in other words, the relative change in the surface capacity of our triangle during its deformation. Let us now imagine that our triangle is becoming smaller and smaller. Then its area will begin to decrease indefinitely, but at the same time the spherical excess will also begin to decrease indefinitely (unless the point in question is an exceptional one). The ratio of these decreasing causes will tend to a limit that causes a relative change in the surface capacitance at a given point. This is the true Gaussian curvature of the surface at a given point. So, when we discuss a curved surface from three-dimensional Euclidean space, we interpret the transfer of a flat triangle onto it as a deformation and approach the concept of curvature from the idea that its sides have become curved. But this is an assessment of what is happening from the outside and, moreover, when this external world is recognized as unconditionally unchanged; this is an arrogant explanation that would be deeply alien and probably hostile to the inhabitant of the triangle in question. Gaussian curvature as a quantity , for him there is only a formal analytical way of expressing himself, because this inhabitant is not aware of anything outside the surface on which his triangle lies, and therefore is not able to notice the curvature as such. The assessment of what is happening is internal, within the limits accessible to his direct observation, and the corresponding expression of curvature at a given point will be constructed by him in precisely the above manner: the curvature of a surface is the relative change in the surface capacitance at a given point, calculated per unit area. Physically, the change in curvature from point to point could be established by experiments with a thin layer of incompressible fluid. Three-dimensional space is also characterized at each point by a measure of curvature, and a quick transition is made, which is by no means geometrically justified, that just as two-dimensional space can be curved, so can three-dimensional space. Most often, discussions of non-Euclidean spaces are limited to two-dimensional regions. When three-dimensional space is also discussed, its curvature is introduced only formally and analytically, as some expression of differential parameters and has neither geometric clarity nor physical perceptibility. It remains unclear what exactly a physicist must do, at least in a conceivable experiment, in order to have the opportunity to speak out one way or another about the curvature of the space he is studying. Abstractly geometrically, the curvature of space should be expressed by the curvature of the straightest, that is, the shortest, or geodesic, lines. But, as explained above, the physicist, remaining with all his instruments, and even with all his visual representations within the limits of this very three-dimensional world and subject, perhaps, to the same deformation as the geodesic [line] under study, apparently has no way of directly verifying the curvature of the straight line. The concept that is missing in the discussion of non-Euclidean spaces, however, can easily be constructed by referring to the previous one. This concept is a relative change in the capacity of space. The whole point is that the same geometric body, with different curvatures of space, will have different capacities. The change in this capacitance per unit volume will measure the curvature of three-dimensional space. A more precise understanding of the measure of curvature can be approached as follows: Let's imagine a tetrahedron filled with an incompressible fluid. Let the edges of this tetrahedron be flexible, but not extensible, and always stretch, that is, they are straight; We will imagine the edges of this tetrahedron as capable of stretching and contracting. The sum of the solid angles of this tetrahedron is 4π, i.e., four right solid angles. Let us now imagine that our tetrahedron is transferred to non-Euclidean space. Then it will be deformed: its edges will pass along geodesics, the faces will become planes of this new space. Consequently, the solid angles will change, and their sum will no longer be 2π, and therefore the volume of the tetrahedron will also change. Consequently, the liquid contained in it will now become either too little or too much; this excess, understood in an algebraic sense, depends on the degree of deformation of the tetrahedron, therefore, on the excess of the sum of solid angles of the deformed tetrahedron over 4π. But, on the other hand, the deformation of the tetrahedron and all the ensuing consequences depend on the degree of curvature of a given space, and therefore, the relative change in the capacity of the tetrahedron characterizes the curvature of space. Thus, we can state a theorem similar to Gauss’s theorem: Here dσ 3 is the volume element, K₃ is the curvature of three-dimensional space, 2p 3 is the sum of the solid angles of the tetrahedron, and the integral extends to the entire volume of the tetrahedron. This means: an excess of the sum of solid angles over 4π, which can be called a hyperspherical excess, accumulates in the tetrahedron by each element of its volume, but to varying degrees; the intensity of this accumulation in each place is characterized by a measure of curvature. So, the curvature of space is understood here as the specific capacity of the space of a given point. The written relation still gives: where K 3 is the average curvature of space inside the tetrahedron. i.e. the average curvature is equal to the ratio of the hyperspherical excess calculated per unit volume. By making the tetrahedron smaller and smaller and tightening it around a point, we will force the spherical excess, calculated per unit volume, to tend to a certain limit, and this limit is the true curvature at the point around which the tetrahedron contracts. This whole technique can be illustrated with a specific example. Let us transfer the tetrahedron to the hypersphere, so that with all its vertices it is located in a three-dimensional manifold containing the four-dimensional content of the manifold of the hypersphere. – It’s clear that in its intact form it will not coincide with the manifold containing the hypersphere, and for it to coincide it must be curved. Then the edges of the tetrahedron will go along great circles - geodesics of the containing manifolds of the hypersphere; the faces will coincide with large spheres of the same containing manifold, and the volume of the deformed tetrahedron will be part of the volume of the above containing manifold. The result is a hyperspherical tetrahedron, similar to a spherical triangle in two-dimensional space. Measuring the solid angles of this hyperspherical tetrahedron, we would find their sum greater than 4 π. The difference between one and the other value obviously depends on the degree of curvature of the tetrahedron, i.e., on the curvature of the hypersphere, or on the value ; and besides, it depends on the size of the tetrahedron. In fact, a tetrahedron, very small compared to the area of ​​the hyperspherical containing manifold, would be curved very little; and a very small tetrahedron could be considered not subject to deformation. So, if we wanted, conversely, to estimate the curvature of the hypersphere by the value of the hyperspherical excess, then this latter should be attributed to a unit volume. Thus, the specific capacity of a three-dimensional spherical space characterizes its curvature. Similar reasoning could be applied to spaces with more than three dimensions. Here again we would have to talk about specific capacity, but not in relation to volumes, but to hyper-volumes and other n-dimensional contents of the corresponding n-dimensional spaces. Specific capacitance could be taken as a characteristic of curvature. Hitherto, curvature has been defined as specific capacitance with respect to an incompressible fluid, just as length has been assessed with respect to a flexible, inextensible thread. But just as an inextensible thread is not the only possible visual basis for determining and estimating length, so an incompressible liquid is not the only standard of volume, but admits many others alongside it. Then, consequently, the curvature of space, while maintaining the formal unity of its definition as a coefficient of capacity, will receive different shades depending on the indirect addition to the word “capacity”. What exactly the capacitance coefficient is curvature will be determined differently in different cases, depending on the given application of geometry. The inflexibility of the definition of curvature would make geometry inapplicable in all cases except when we are dealing with incompressible fluids. So, in some cases we will talk about specific capacity in relation to liquid and granular bodies, and in others – about capacity in relation to other physical quantities and characteristics in general. This can be electric or magnetic mass, heat, wave energy, etc., etc. We can attribute the specific capacity of space to the medium, highlighting it, this capacity, as a special independent variety coexisting with space, to which, as such, we do not attribute anything at all except the function of spreading - étendre - the medium, i.e., being étendu, and, therefore, then we prohibit directly combining the concept of capacity with space. Either we do not isolate the variety of the capacitive parameter from space as such, that is, we do not hypostatize the variable, generally speaking, the characteristics of space - the property of having different capacity in different places - into an independent variety. Then we are talking only about space and the physical factor, which we are considering in this case and in relation to which the specific capacity is determined, i.e. curvature of space. When the definition of straightness, or length, or angle, etc. is based on various physical visualizations, then, as we have seen, some agreement between these visualizations is maintained only within one or another limited reality and is upset outside its boundaries - outside the “circle of convergence.” It would be very strange if, according to some pre-established harmony, there were different definitions of straightness, length, etc. everywhere and always would not disagree with each other; if this happened, then everything would convince us that it is only through a misunderstanding that these definitions are considered different, but in fact they are simply identical. In this sense, it is correctly said that curvature, length, angle, etc., defined in relation to different physical visualizations, are generally different and only approximately cover each other. Of course, the situation is no different with the definition of capacitance, and therefore curvature. The capacity of the space of a given point is not a definite quantity until it is indicated by an indirect addition about the capacity of what exactly, which physical agent is being discussed. Generally speaking, only within a small region the curvature of space can be the same in relation to several different agents, and it would be a happy accident if such a coincidence were discovered far beyond the boundaries of the original field of study. If it sometimes seems to us that such agreement in relation to several agents exists everywhere, then this is self-deception: we shift the divergence in the specific capacities of spaces in relation to several agents to the corresponding divergence in the coefficients of the environments in which the physical processes under consideration are played out. These environments here and there are endowed with completely different properties, that is, they are recognized as different. In other words, the different behavior of spaces in relation to different actors is brought as if to complete unity, but because we hypostatize the deviation from unity in the form of special environments, and, moreover, different ones for different actors; It is these media that are responsible for the divergence of spatial capacities. Of course, such hypostatization cannot be prevented; but it is necessary to clearly understand that in fact, overcoming multi-dimensionality is not being done here at all. So, in former times, in order to save Euclidean space at all costs, they came up with many different imponderabilia - weightless liquids, a special one for each person, and they all had special properties. Then they tried to destroy the diversity of these liquids by merging them all into a single ether. But then the diversity of behavior had to return to space, and it turned out to be necessary, in order to save the unity of Euclidean space, to attribute different, contradictory properties to the ether in relation to different figures. The most direct, frank and conscious outcome, accepting geometry as it really is, would be simply geometric, that is, attributing the different behavior of different factors to the curvature of space, which is different in relation to different physical agents. For greater clarity, these considerations should be further clarified with particular examples, however, only relatively particular, for they cover the broadest classes of physical phenomena 6 . “If in the case of a discrete (discontinuous) variety the basis for determining the measure lies in the very concept of this variety, then for a continuous one it must come from outside. Therefore, the real that lies at the basis of space, or should constitute a discrete manifold, or the basis of definitions of measure, must be sought outside the manifold, in the forces acting and connecting it.” This is how Bernhard Riemann spoke about the determination of spatial characteristics by forces acting in space in 1854. This idea, so brilliantly revealed by Einstein, Weyl and others, however, has a meaning that is incomparably deeper and the scope of application is incomparably wider than what is done, and then with significant shortcuts, by modern physics. This narrowness is partly a relic of the mechanical worldview, which accordingly narrowed geometry. Since all processes were reduced to mechanical movements, and forces to mechanical ones, therefore geometry became the science of the space of mechanical movements. Meanwhile, our constant use of the concept of space and spatial relations not only in mechanics alone, and the ability to use geometry in areas other than the group of movements at least in the same physics, forces us to recognize it as deeply erroneous when only mechanics is recognized as the only concrete basis of geometry. As has already been said, there is no geometry without concrete experience; but this experience can be very diverse and is by no means limited to mechanical movements alone. Riemann talks about forces that bind and define space, but the whole question is what exactly is meant by force. In mechanics, force is defined as the cause of acceleration. Acceleration is a change in motion calculated per unit of time. Meanwhile, phenomenologically, among natural phenomena, mechanical movement is not at all the only existing phenomenon. Reality is characterized by mechanical movement, but very one-sidedly and poorly. Along with this characteristic, there are countless others, and therefore, we have to keep in mind their change, that is, movement in a broad, non-mechanical sense, as this word was used in antiquity, for example by Aristotle. Next, we then have to keep in mind the reason for such changes in various characteristics - the spaces of reality. The generally accepted language has always called and continues to call this cause force; the force of gravity, the force of a push, the force of a magnet, the force of light, the force of attention, the force of passion, the force of beauty, etc., etc. Behind this usage [of the word] force there is also a universal human [understanding] of all these and similar figures as the causes of some change. If you like, you can generalize here the law of inertia and the law of proportionality of force and acceleration. In fact, we think of every characteristic of something existing as it is, until it is acted upon by some agent who changes it, just as mechanical speed changes under the action of a mechanical force. The presence of a characteristic in time, and the flow together with time can be understood as speed and called, expanding the meaning of this term, speed. It would also not be justified to call such a change in a characteristic its acceleration, but the cause of the change as force. Moreover, these forces must be of different kinds, just as the characteristics themselves are heterogeneous. There are forces of wider application, and there are also less widespread, i.e., the characteristic that obeys a given force can be characteristic of more or less extensive classes of phenomena. However, there is not a single universal force, and in relation to each one there will be phenomena that are incapable of being accelerated by it. The last circumstance is extremely important to keep in mind when trying to divide phenomena and forces into external, supposedly unconditionally universal, and internal, of a subjective nature, which does not have access to the world taken into account by scientific methods. This division is without sufficient grounds. Let us explain this with an example: a stone released from a hand receives acceleration towards the ground; we call the cause of this acceleration the force of gravity. Flying past the gravitating mass, the stone would deviate from its straight flight, and we explain this curvature of the path by the force of gravity. The same thing will happen with a piece of iron: in terms of gravity, iron and stone show no difference. Neither would each of us show it if we were thrown out of a window, or flying through space past an attracting mass. In all these cases we are talking about one force - universal gravity. However, if in all these cases we replace the attracting mass with a strong magnet, then both the stone and each of us will remain indifferent to it and will not deviate from the straight path, that is, they will not receive any acceleration from the magnet (we will talk about all phenomena roughly and approximately for now). But this is not how a piece of iron will behave under similar conditions: it will undergo acceleration towards the magnet - therefore, the path of its movement will be curved and, up to a certain place or moment, identical with the line of movement of a stone or a living organism, after this place or moment it will diverge from it and go differently. The question is, is there a force in a magnetic field or not? – The answer to this question, positive or negative, depends on the presence or absence of iron capable of moving or exerting pressure on the dynamometers. If there is iron capable of perceiving the action of the field, then we recognize the existence of magnetic force; if there is no iron, then the strength will not be detected. This example explains a thought that should have been understandable by itself and which was clear to the ancient consciousness, but in modern times has fallen out of the principles of science. Here we understand the concept of active passivity, i.e., the correspondence of the object of influence to the force acting on it: nothing is capable of perceiving an efficient cause without being ready for it, i.e. not having in itself certain conditions of perception, correlative with the nature of the acting force. Force causes change, but does not blindly force, and everything that is completely alien to a given force and does not have any conditions for assimilation, thereby does not notice the given force influence at all and behaves as if there were no force at all. But from the ineffectiveness of a given force in relation to a given object of influence, the conclusion can in no way be drawn that there is no force itself. As has already been indicated, living organisms, at least humans, are not susceptible to a magnetic field, even the most intense one. Careful experiments in which the head was pierced by a powerful magnetic flux did not give any results, or, if you like, gave the surprising result of our complete indifference to magnetic force. We do not feel it and are not aware of it, as if there were no magnetic field at all in this space. According to indirect data, we know the known existence of a magnetic force here; but it does not exist directly for us, because we do not have the conditions for its perception. Animals, in particular crustaceans, behave the same way. However, Kreibig showed that if the conditions of perception in the body are artificially caused, then the body is aware of the magnetic field, even if it is not intense, and orients itself in it, adapting all positions and its movements to the direction of the magnetic forces. Kreibig's technique was very simple: for orientation in the force field of gravity and in relation to centrifugal forces, crustaceans have small heavy particles in their ears, or ear stones, atolytes, whose function is reminiscent of human semicircular canals. During molting, crustaceans lose their atolytes and therefore use their claws to place several grains of sand in their ears, which serve as new atolytes. Kreibig let molting crustaceans into a pool, the floor of which was strewn with iron filings, and iron particles fell into the animals' ears instead of ordinary grains of sand. With such iron atolytes, they turned out to be very sensitive to the magnetic field. It is clear that if a liquid of high magnetic permeability were poured into the semicircular canals of a person, then the person would no longer remain indifferent to the magnetic field. Let's now consider the third example. I stand on the street and watch passers-by. They walk straight along the sidewalk, but at a certain point their path bends, although to varying degrees. The immediate impression is that passers-by are pushed away from a certain gate, as if receiving a negative acceleration. I take a closer look and notice a sign above the gate: “Beware of the car.” Another example. Passers-by are drawn to a certain place, lingering here, and some are stuck for a long time: some seller shows various small inventions. As a dense ring forms around it, the attractive effect intensifies, and the paths of passersby deviate more and more noticeably from straightness. Here and there, in both examples, the characteristics of the movement changed and, moreover, through the action of some external cause; here and there passers-by received an acceleration, in one case negative, in the other positive. With all my attention, I cannot discern a significant difference between this deviation from the rectilinear path when gravity or magnetic force acted. And with all the attention, I see no reason to abandon the word “force” in relation to all the cases considered. When they say: “the power of the impression produced such and such,” then there are no obvious reasons to consider this usage more allegorical and improper than the use of mechanics. Impression, of course, is power. Of course, the sign “Beware of the car” will not deflect either an inert mass or a piece of iron from a straight path (we use the word “of course” here for the sake of argumentation, so as not to introduce complicating considerations, which in this case are not important). In the same way, neither inert mass nor iron will be turned aside by a curious sight. Neither a sight nor a word in relation to them is the essence of power; but this does not mean at all that the power of words and the power of spectacle do not exist at all. A piece of iron is not susceptible (as is usually thought) to the power of words and spectacle, just as a man is not susceptible to the force of a magnet, nor is a cobblestone susceptible to it. The absence of an accelerating action in all these cases does not confirm the non-existence of the corresponding force, but only the non-existence of active-passive interaction, which, in itself, leads to one of three possibilities: either to the non-existence of force, or to the non-existence of receptivity, or, finally, to the non-existence of either force or receptivity. So, there are forces in the proper and precise sense of the word, imparting acceleration and producing changes in the characteristics of reality, but nevertheless not mechanical, and not even physical, i.e. unable to be noticed if the perceiving organs respond only to mechanical and physical influences. The power of beauty exists no less than the power of a magnet or the force of gravity. But, probably, objections will be heard that the power of beauty is not capable of directly manifesting its effect and changing the characteristics of reality; that this force must pass through vital and conscious refractions before it affects externally taken into account experience; finally, that we do not know the complex processes and paths along which the action of this force will take place. – We will not go into these arguments in depth, but for now we will only answer the following. We know nothing at all about the processes and ways in which the action of any force, mechanical or physical, is revealed, and we always observe only a ready-made action, unknown how it arose; rather, those actions that pass through our consciousness or our sense of self should be recognized as less incomprehensible. Then, we know nothing about the direct action of mechanical and physical forces, and any attempt to give a model of this kind of influence leads precisely to numerous means. Finally, if in relation to mechanical and physical forces we do not talk and do not consider it necessary to talk about the mental and biological moment, i.e. about the internal reaction, then this is not at all from the knowledge that there are none, but from the inability to clarify this side of the matter. That is why we omit everything that is between the beginning and the end, and are content with establishing the fact of the connection between this beginning and this end. If, in relation to living beings and ourselves, we know something from the middle, then this middle should in no way be an obstacle and in this case phenomenologically connect the beginning with the end, providing some vague knowledge of the middle to those who have a special interest in this. So, to summarize, we note again: everything that is capable of acting, producing changes in the characteristics of reality, i.e. imparting a certain acceleration to their uniform and steady flow in time - all this can rightfully be called force. The forces of reality are numerous and varied, and the activity of each of them manifests itself only with the corresponding susceptibility of the objects of influence, and if this is absent, it remains unknown. There is no dividing line between different forces, on one side of which there would be the objective, and on the other - the subjective: everything objective has its own inner side, just as everything subjective is revealed. There is nothing secret that has not become obvious, just as, on the contrary, everything obvious has a secret in itself. The space of Euclidean geometry has as its physical basis a group of mechanical movements of an absolutely rigid body; at the same time, the absence of force fields and the presence of divine coverage of the entire space by consciousness, in addition to physical media and conditions of knowledge, are tacitly assumed. The group of movement is partly joined by the still poorly thought out and inaccurately taken space of visual perceptions. Usually little thought is given to the much wider use of space, although the auditory and tactile sensations clearly require space. But further: smell, taste, then various mystical experiences, thoughts and even feelings have spatial characteristics and mutual coordination, which forces one to assert their location in space. Externality, i.e. the finding of certain separate entities outside of each other is the main sign of spatiality. Since there is a multitude, then its elements are separate or, as Riemann puts it, they are images of isolation; thus they are outside each other. This is already a sufficient sign that they are in the corresponding space, because, although we do not mix them, we nevertheless consider them not separately, but together, as something connected, and coordinate them with each other. The ability to think and represent them as a set, not connected, necessarily leads to the assertion that there is also a condition for the possibility of this connectedness and coordination of the set. And since we recognize the image as the objective content of thought and space, it is also recognized as such, i.e. objectively forthcoming thoughts, and the condition of the possibility of diversity. This condition is space. We do not confuse it with the images themselves: the reasoning here is the same as that of Georg Cantor, when he proves the existence of an actually infinite line, relying on the fact of the existence of a potentially infinite line. A segment can increase indefinitely, surpassing any given value: this means that there is the very possibility of infinite increase, existing actually, entirely, ready. This opportunity, i.e. this line can no longer be finite, it exceeds any finite value and, therefore, is an actually infinitely large line. Likewise, the presence of corresponding images of isolation presupposes the condition of the possibility of correlation, and this is precisely the space of images of a given perception. There must be many of these spaces, according to the type of perceptions and images of isolation; There is no evidence in advance to consider these spaces identical, although it is natural to expect the relatedness of some of them, and, moreover, different in different cases. Some spaces are very far from each other, others can be very close; The common feature of all is the externality of the images of isolation contained in them and united by them. Each image of isolation is a certain power center. By these centers a given space is connected and determined, as indicated by Riemann in the above quotation; being a condition for the coordination and connection of these power centers, it has a property that corresponds to the nature of the activity of these centers. In other words, the curvature of this space at each point is established by the forces acting at it, of course, in relation to the action of these forces - these, and not any others that are revealed with a different kind of receptivity. If we turn to another receptivity, even if it belongs to the same object of perception, then, according to the assessment of the actions of other forces on this other receptivity, the curvature of space at a given point will turn out to be different, and all space will have a different structure. This is clear by itself: space is the beginning that unites power centers, i.e. allowing the force field to unfold. This means that it must contain forces, or have capacity. There is no reason to expect the same capacity when the forces relative to a given space change. Until now we have talked about centers of force, considering the curvature of space to be something secondary, posited by them; but, as has already been clarified earlier, we can consider the structure of space to be the starting and initial one and see in the centers of force something secondary, foci of curvature, which here becomes very large, or infinitely large, in a positive or negative sense. With equal right, one can resort to one of two methods of description and say either: “the force field bends and thereby organizes space,” or: “space, by its organization, i.e. curvature, determines a certain set of power centers.” So, living on the surface, we would go around some center of repulsion standing in our way and would bend our path: this would be the straightest line, if we are guided by a feeling of fatigue, and we could then talk about the curvature in this area of ​​our plane, with some focus of curvature. But one can also imagine the curvature of the plane, in the usual sense of the word, i.e. some special point on our surface; meeting it on the way, we, too, would begin to go around this sharp point and would also consider our crooked path to be the straightest. Then we would have the right to deny the local curvature of the surface, but we would have to talk about the force center of repulsion. The choice of one or another method of description depends on us, but one of the two must be chosen so that reality itself is not distorted. There is, however, another way of describing it using the changing characteristics of the medium, for example, in this case, using an incompressible fluid spreading from a point. But this third method is very close to the introduction of force centers and, rather, serves as a model of these latter. All culture can be interpreted as the activity of organizing space. In one case, this is the space of our life relationships, and then the corresponding activity is called technology. In other cases, this space is a conceivable space, a mental model of reality, and the reality of its organization is called science and philosophy. Finally, the third category of cases lies between the first two. The space or spaces thereof are visual, like the spaces of technology, and do not allow for vital interference, like the spaces of science and philosophy. The organization of such spaces is called art. Of course, it will not be possible to unconditionally distinguish between these three types of activities, as well as the spaces they organize; Each of the activities also contains the beginnings of other activities subordinate to it, and each of the spaces is, to a certain extent, not alien to spaces of another kind. Thus, technology certainly contains a certain amount of artistry, which is not necessary in order to achieve the goal set by the technology, just as it also contains some philosophical and scientific thought that enriches the theoretical attitude to the world. In philosophy and science it is always possible to discover some artistry and vital applicability, i.e. technical side. In the same way, a work of art contains, to one degree or another, vital usefulness, something technical, and one or another technical relation to reality. In every activity there is everything, and every space has an affinity with the others. Yes, it could not be otherwise, since culture is united and serves one subject, and spaces, no matter how diverse they are, are still called by one word - space. However, these types of activities can be differentiated according to their predominant meaning. And despite this distinction, at the very core they do the same thing: they change reality in order to rearrange space. The force field deployed by them can be interpreted as a producer of space curvature. But it is possible, and logically more expedient, to say that the required space is caused by a force field, manifested - in the photographic sense of the word. A gesture creates space, causing tension in it and thereby bending it. This is one approach to the effect of changing reality. But another approach is possible and more appropriate, when tensions from a gesture mark a special curvature of space in a given place. She was already there, preceding the gesture with his force field. But this invisible and inaccessible to sensory experience curvature of space became noticeable to us when it manifested itself as a force field, which, in turn, posited a gesture. If a piece of cardboard is placed on the poles of a magnet, then to the eye the surface of the cardboard seems no different from the same cardboard not lying on the magnet. This space therefore appears to us to be homogeneous, and in small areas – Euclidean. But this does not mean that it really is like that and will always be perceived as such, but only indicates our insensitivity to the forces acting here, or to the curvature inherent in space. By sprinkling cardboard with iron particles, we manifest a force field or spatial curvature for our perception. At the same time, we can interpret the picture of the force field as produced by a magnet and producing, in turn, the curvature of space, or we can, on the contrary, say that the previous curvature of space in this place (meaning the place in the sense of a place - an event, i.e., as determined by the time coordinate) determines the force field, which, in turn, determines the magnet with its poles. Likewise, in the realities of culture, the change in reality produced can be interpreted both as the cause of the organization of space, and as a consequence of the already existing organization. Then the images of isolation of reality are places of special curvatures of space, its unevenness, knots, folds, etc., and force fields are areas of constant approach to these highest or lowest values ​​of curvature. Then, further, those visual images that art posits, or those devices that a technician builds, or, finally, those mental models that a scientist or philosopher puts into words - all of them are only signs of these folds and general curvatures, together with the areas of approach to these places. The cultural figure sets boundary posts, draws boundaries and, finally, draws the shortest paths in this space, along with systems of lines of equal effort, isopotentials. This matter is necessary for the organization of space to reach our consciousness. But this activity reveals what exists, and is not posited by human arbitrariness: In vain, artist, do you imagine that you are the creator of your creations, They always hovered over the earth, invisible eyes... There are many invisible forms and inaudible sounds in space, There are many wonderful combinations of words and light in it, But only those who can see and hear will convey them. This is the objective, realistic understanding of art and, like it, the understanding of philosophy, science and technology. Another view, according to which an artist and a cultural figure in general organizes what he wants and how he wants, a subjective and illusionistic view of art and his culture, is deeply alien to the first in terms of the well-being of a cultural figure and his worldview. But both views are formally equal, equally possible, isotenic interpretations of the same fact: culture. However, of course, this or that understanding of one’s activity, although capable of being interpreted in one direction or another, cannot but be affected by the special tonality of the activity itself. We will speak more narrowly and more specifically about artistic activity. Is it because the artist saturates certain areas of space with content accessible to the receptivity for which a given work is designed - it becomes distorted and becomes especially strong or especially weak, i.e. organized; or because it is already organized, has special capacities, and therefore is curved and therefore allows for an uneven load with the required content - both are formally one fact. It can be figuratively explained: the artist saturates a certain area with some content, forces the content there, forcing the space to yield and accommodate more than it usually accommodates without this effort. To a geometer who measures spatial extensions - lengths, surfaces, volumes - with a chosen or physical standard, the extent of a given region, and, consequently, its capacity and curvature, will not seem changed by this. This is true, but it means nothing: after all, as a geometer, in terms of his basic physical process, he is not able to notice a work of art at all; the latter is inaccessible to him, just as a magnetic field is inaccessible to someone who has neither iron nor any metallic masses. Of course, without perceiving a work of art, which simply does not exist for a geometer, the latter has nothing to say about the curvature of his space. This is one approach. Another understands space itself as having, in certain areas, a noticeably prominent capacity in relation to the one or those perceptions that a given artist is counting on. These places in space turn out to be greedily absorbing, sucking in the means with which a given artist works; or, on the contrary, these means are accepted by them very poorly. The artist with his means of imprinting moves in a given space, as if in uneven terrain, and by the way these means of his scatter from some places and accumulate in others, he forms an idea of ​​​​the organization of space. He then feels forced by the objective conditions of work - the terrain in which he works - to act this way and not otherwise, not to do what seemed desirable to him, and, on the contrary, to do the undesirable, and even unforeseen. He seems to be rubbing a pencil on paper with a model placed underneath it, while the images appear on their own. This is the realistic approach to art. But, we repeat again, from the formal side, both are only interpretations of one fact. All arts follow the same process. In music, the characteristics of the capacity of the corresponding spaces are tempos, rhythms, accents, meters, with different shades, as dealing with durations, then - melody, using height, harmony and orchestration, saturating the space with coexisting elements, etc. In poetry, such means again serve as the same meters and rhythms, melody and instrumentation, as well as visual, tactile and other images evoked mediocre. In the visual arts, some of the listed elements, such as meter, rhythm and tempo, are given directly, although not as clearly as in music and poetry, others, like melody, are evoked mediocrely, and still others, on the contrary, appear directly and with particular clarity: visual and tactile images, colors, symmetry, etc. Despite the apparently fundamental differences, all arts grow from one root, and once you start looking into them, the unity emerges more and more convincingly. This unity is the organization of space, achieved to a large extent by homogeneous techniques. But precisely because of their homogeneity, what has been achieved is far from the same. Painting and graphics occupy a special place among other arts and, in a certain sense, can be called art par excellence. While poetry and music are somewhat closer, by their very nature, to the activities of science and philosophy, and architecture, sculpture and theater - to technology. In fact, in the organization of space, music and poetry have extreme freedom of action, while music has unlimited freedom. They can and do make absolutely any space they want. But this is because half and even more of the creative work, and at the same time the artist’s current difficulties, is transferred here by the artist from himself to his listener. The poet gives a formula for a certain space and invites the listener or reader, at his direction, to imagine the specific images with which this space should be manifested. This is a multi-valued task, admitting of different shades, and the author declines responsibility if his reader fails to find a solution that is sufficiently visual. Great works of poetry, such as Homer’s poems, Shakespeare’s dramas, “The Divine Comedy”, “Faust” and others, require extraordinary efforts and enormous co-creation from the reader so that the space of each of them is truly represented in the imagination quite clearly and holistically. The imagination of an ordinary reader cannot cope with these too rich and complexly organized spaces for it, and the spaces break up in the consciousness of such a reader into separate, unrelated areas. The material of poetry, words, is too little sensually dense so as not to obey every thought of the poet; but precisely because of this, he is not able to exert enough pressure on the reader’s imagination to force it to reproduce what the poet thinks. The reader retains too much freedom; the unity of space in a work can easily sound to him like an abstract formula, similar to the formula of science. Music uses material even less bound by external necessity, even more malleable to any wave of the creative will. Sounds are infinitely malleable and capable of imprinting the space of any structure. But precisely because of this, a piece of music leaves the listener the greatest degree of freedom and, like algebra, provides formulas that can be filled with almost infinitely varied contents. The task facing a music listener allows for many solutions and, therefore, poses corresponding difficulties for the listener to choose the best. The composer is free in his plans, because his material does not have any solidity in itself; but for this very reason it is not in the power of the composer to force his listener to carry out the images and the corresponding organization of space in a certain sense: a significant share of co-creation lies with the performer of the musical work and then with the listener. Like science and philosophy, music requires a significant share of the listener’s activity, although less than they do. Theater, on the contrary, least involves the activity of the viewer and least allows for diversity in the perception of its productions. This is inferior art, which does not respect those it serves and does not seek artistic consciousness in them. And it does not respect itself, presenting itself to the viewer without difficulty and without initiative. This passivity of the viewer is possible here due to the rigidity of the material, its sensual richness, which holds with the greatest certainty and sensual impressiveness the form that a combination of stage figures managed to impose on it, from the poet and musician to the drayman. But it is not always possible to superimpose on this persistent material - living people, human voices, the sensory space of the stage - the forms conceived by a playwright or musician; in most cases, it is simply not possible at all. Being living bodies, actors are too closely connected with the space of everyday life to be able to transfer them, even temporarily, to another space; in any case, they cannot be transferred to any other space, especially if we take into account that for this they would need to experience something to which they are actually alien. When Shakespeare in “Hamlet” shows the reader a theatrical performance, he gives us the space of this theater from the point of view of the spectators of that theater - the King, Queen, Hamlet, etc. And for us, the listeners, it is not impossible for us, the listeners, to imagine the space of the main action of “Hamlet” and in it - the isolated and self-enclosed, but subordinate to the first, space of the play played there. But in a theatrical production, at least from this side only, “Hamlet” presents insurmountable difficulties: the spectator of the theater hall inevitably sees the scene on stage from his own point of view, [and] not from the same point of view - the characters of the tragedy - sees it with his own eyes, and not through the eyes of the king, for example. In other words, the power of impression from Shakespeare's tragedy as such is achieved by the potentization of space, double isolation, and the reader stops before the second, since he identifies himself, for example, with the king. But in a theatrical production, the viewer sees the scene on stage to a large extent independently, not through the king, but on his own, and the duality of space is not given to his consciousness. In other cases, when the structure of space deviates even further from the usual structure, the stage turns out to not allow such a reorganization of its space, and apart from claims, the actor on the stage does not show anything and, most importantly, cannot show it. These are, for example, visions, phenomena, ghosts. Their spaces are subject to very special laws and do not allow coordination with the images of everyday space. Meanwhile, the sensory density of such phenomena on stage necessarily correlates them with ordinary space, and the ghost remains only a person in disguise. When it is necessary to show the peculiarity of the space of drama, well, at least, for example, in “Faust,” the stage actors, under the pretext of being unstageable, save themselves from the corresponding difficulties by cutting the drama into pieces and throwing out the most essential thing, which gives spatial unity to the work. In these transitions, the most important thing is often, but it really is not stage-like, not in the sense of uninteresting, but because of the powerlessness of the stage to organize itself spatially, as the poet demands. Reading Faust, I can imagine a space that is at first relatively close to ordinary, and then, through the region of the Mothers, transforming into something completely different. But if this transition through the kingdom of mothers were omitted on stage, then absolutely nothing would remain of Faust as an artistic whole. Meanwhile, this transition could have been shown only by a theurgist or magician, and not by any means by a director. Or “The Temptation of St. Anthony." If they decided to stage this work by Flaubert on stage, then nothing but a funny ballet would come out. After all, the whole essence of “Temptation” is the gradual transformation of space, from a closed, very capacious, saturated and whole one - into an expanding, emptying, indifferent one - in the gradual erosion of being by emptiness, chaos and death. In short, this is an artistically visual image of the New Age. To show such a transformation on stage, it would be necessary to gradually reduce the size of the actor playing Anthony, as well as the size of the entire setting, and already close to the beginning of such a play, both Anthony and all everyday objects known to us would have to shrink to a point. As long as Anthony is seen as commensurate with the surrounding space, he will remain the measure of it, and its directions and its scale; and consequently, the result will be a Euclidean-Kantian-astronomical space, i.e., the production of the play will fail. A lot can be said about this sensual rigidity and immobility of the stage, but what has been said is enough to understand the opposition of theater, music and poetry. Architecture and sculpture have a certain affinity with the theater, although, of course, the intractability of their material is incomparably less than that of the theater. In the middle between these and other activities stands painting and graphics, avoiding the difficulties of both poles of artistic culture and at the same time participating, at least in relation to the organization of space, in the advantages of both poles. Is it not because the painter and graphic artist are primarily called artists, for their everyday use they seem to be subdivided, because the epithets “artist” and “artistic” refer to drawing and depiction with paints, as if a musician, poet, sculptor, architect cannot be understood under the general concept of an artist. This, however, is unnecessary, narrowing the concepts of “artist” and “work of art” indicates that, by universal recognition, painting and graphics most clearly and fully represent all art. Indeed, the material of these related arts is in itself not objective and lacks its own form perceptible to the naked eye. This is an almost indifferent opportunity to become everything that will be demanded of him, without resting his own form against the organization imposed on the material by the artist. Like a word or a sound taken separately, paint and ink themselves still express almost nothing - almost like a sound or a word. The intrinsic effect of these materials is almost zero; Moreover, ink or pencil has even less than paint. Thus, being extremely abstract, these materials, nothing or almost nothing in themselves, can become everything or almost everything. In this respect, painting and graphics are close to poetry and music. But, on the other hand, painting and graphics, to one degree or another, provide images in which we recognize objects of the external world, known to us not only as visual images, but also by their functions, and therefore in their way connecting our imagination and preventing it from wandering in uncertainty. By this sensual clarity, painting and graphics differ from the algebraic polysemy in music and partly in poetry and come close to coercive power over the theater audience. Thus, the painter and graphics not only demand from the viewer, but also give him, they give him not a sensory image already known to him, albeit distorted, but not transformed as in the theater, but a truly new one, enriching and representing the organization of spaces unknown to him. That is why what the theater gives always has a taste of deception, illusion, despite the sensual rawness and saturation with everyday elements, which seeps here even beyond the intentions of the stage performer. What music and poetry give is perceived as true reality, but distant, too far from the possibility of direct contact with it. What graphics and painting provide is assessed, in the extreme, as a revelation of a truly different reality, which, having once learned from the artist, we then know on our own, because we now see it with our own eyes. The usual classification of arts takes into account the material of the given art and the tools for using it, but does not take into account the work itself from this material and created through this tool. Thus, the work of painting is, with this classification, a work of the brush, and is characterized by the fact that it is made of paints; The peculiarity of an engraving is that it is worked with a chisel, a graver or a needle, and, moreover, on wood, metal, etc. A work of music is made from sounds caused by the vocal apparatus or some instrument. In the same way, works of architecture are [made of] stone, wood, etc.; works of poetry are made from words. Further divisions of the arts are based on a more specific distinction between the mentioned materials and processing tools. In short, the established classification of the arts takes into account the sensually material conditions of artistic creativity and can be called production. Meanwhile, art is an activity based on goals, not only as technology in general, but [to] a much greater extent; after all, it is not forced by direct everyday necessity and breathes the air of freedom, not depressed by worries about tomorrow. Art sets goals for itself and sees the meaning of its existence in achieving these goals. Obviously, the implementation of precisely these goals must be sought in the very essence of works of art, and, therefore, in the difference in goals is the source of the classification of arts. Then the work of art will be divided into separate categories according to its artistic essence, that is, precisely as art. Then the student is based not on externally received information about how and from what a given work is made, but on what is directly visible, heard, tangible - on what he receives from the work as such. Now he is not looking for someone to tell him about the work, but the work itself tells him about itself and indicates where, in what category it should be included. In a certain sense, it is then indifferent whether this work was made today or thousands of years ago, whether it was created out of self-interest by an artist who sold his soul, or whether it was ready-made brought by angels straight from heaven: the researcher takes into account only what he perceives and is conscious of, and this, perceived and conscious, leads him to further conclusions. The point is the formative purpose realized in the artist’s work. The goal of art is to overcome sensory appearance, the naturalistic cortex of the random, and to manifest what is stable and unchangeable, universally valuable and generally significant in reality. In other words, the artist’s goal is to transform reality. But reality is only a special organization of space; and, therefore, the task of art is to reorganize space, that is, to organize it in a new way, to arrange it in its own way. The artistic essence of an object of art is the structure of its space, or the form of its space; and the classification of works of art must first of all bear in mind this form. Naturally, the question arises about a classification that competes [with the one] that we called production. It is difficult to expect complete identity of the sections of two classifications, proceeding from principles that do not coincide with each other. But, on the other hand, it is impossible to imagine the indifference of the production conditions of creativity in relation to the formative goal. Consequently, there must be some kind of correspondence between both classifications, and the possibility of a break in some production artistic groupings is not excluded, with the distribution of the broken ones into departments that, from a production point of view, seem alien to each other and very far from each other. So, doesn’t poetry fall into divisions, some of which can be related to music, others to architecture, others to painting, and others, finally, have an affinity with sculpture? Or, in painting, especially fresco, rhythm always introduces spatiality of a musical nature, symmetry - of an architectural nature; a very large convexity of volumes, colored, but not playing with external light on them (Picasso, Rousseau), - sculptural spatiality, etc. In short, the classification of objects of art according to their spatiality can lead to regroupings and unexpected divisions and comparisons, although in other cases its categories may well cover the same industrial classifications. However, our business, without extending to the entire field of art, is to focus on the fine arts and, more specifically, on painting and graphics. These two branches of art in the hostel are primarily known as art and are united under the common name of “drawing”. The basis of this common name is purely industrial: the application here and there of a coloring matter, be it oil, watercolor, glue, egg paint or pastel, charcoal, graphite, lead, sanguine and ink, on one or another surface, canvas, paper, gesso, etc. In the order of materials and tools, these two areas, graphics and painting, are really difficult to distinguish, and between them there are, in the order of production, all sorts of intermediate links known under the vague name of “drawings”. Thus, painting is possible with only one color, for example, sepia, like Overbeck; It is possible to paint with charcoal, like Chekrygin, or even with a pencil. No matter how we judge the merits of these and similar links, nevertheless, good or bad, they relate to painting. Graphics, on the contrary, will not become painting if they are made with paints, multi-colors, and at least with the help of a brush. Moreover, even the branch of graphics, which from the production side seems clearly far from painting, when it works with a chisel, a needle or a graver, can wander towards pictorial tasks or take on them deliberately, and then, despite the tools of the engraver or etcher, it becomes a kind of painting. Undoubtedly, the use of black spots and surfaces in engraving, where printing ink already has a blackness not abstract, but colorfully sensual, is of a picturesque nature; This also includes the use of a white stroke, which is so successful and disgusting together - they imitate the stroke of oil painting. In particular, this includes the entire Doré, working with a chisel, a graver, like a brush. In short, neither the surface on which the dyes or coloring matter are applied, nor the type and physical consistency of these substances, nor the instrument for applying them to the surface determine whether the work produced will be a painting or a graphic art. True, in many cases we feel, and even recognize, the unnaturalness of using the production conditions learned by the artist. We then talk about the artist’s unfortunate choice of these production conditions, and perhaps the artist agrees with us. Yes, but this proves that it is not production conditions (which can be quite pronounced here) that determine whether a work belongs to graphics or painting. That is why we are able to judge this affiliation of a work in addition to its production conditions and sometimes even in spite of them, distributing into different departments what was worked under the same production conditions and into one department what was worked under different conditions. It is clear that if it is possible to make an amendment to a production judgment, then it means that there is a fulcrum outside production, that is, the unique essence of a work of art. This is what is called the spatial form of the work. Painting and graphics differ from each other in their approaches to organizing space, and the difference between these approaches here and there is not any particularity, but is rooted in the initial division of spatiality into some two significantly different directions. Each of them can be carried out in different production conditions; but one set of conditions allows this approach to spatiality to be expressed more clearly and purer than another, and among the whole variety of conditions there is a certain selection of them that most transparently shows the space invented by the artist. It is most logical to settle on such a selection, because the logic of things, the very purpose of the work, seeks the means of expression most akin to this purpose. When the artist failed to hear the desire of an imaginary space or, under the pressure of prejudice, did not want to satisfy it, we feel the inconsistency in the work of its purpose and its conditions. The artist’s production means, by their nature, are powerless to realize the conceived space, but they are strong enough to put alongside it, unfinished, in addition to the artist’s intention, a ghostly image of some other space, clouding and confusing the first, already given only by hints. Thus, if there is a discrepancy between the production conditions and the formative goal, there is an interruption of two overlapping spaces: one - intentional, but under-implemented, the other - realized, but contrary to intention. Now it is necessary to more definitely establish the difference in the approach to space and in the understanding of it by the graphic artist and the painter. In his engravings, Dürer is a pronounced graphic artist. It is Dürer who is taken here, since he is not characterized by flatness and contour, which are often considered the proper characteristics of graphics, but, however, do not at all constitute its necessary accessory. So, here we have a characteristic graph, and its images are convex and rich. He is a graph, when he first approaches the matter, because he works as a serger. The surfaces by which his volumes are limited are given to the viewer by a system of lines, strokes, and each of them, in itself, is assessed by us not as a black stripe, even a very narrow one, but as a pictorial symbol of some direction, some movement. It is impossible to say that such and such a place in the engraving is white and such and such is black. There is neither sensually white nor sensually black, but there is only an indication of this or that number of movements of one kind or another. The blackness of the stroke and the whiteness of the paper here is the same external circumstance as the chemical composition of paint and paper: these are conditions necessary for a work to materially exist, but artistic calculation is not based on them, on their sensory reality. This idea can be clarified in the extreme with a clear example: if the required movements were shown not with paint, but in some other way, for example, with sharp edges along the lines, then the impression of such an engraving would remain approximately unchanged. That is why the negative image of an engraving, i.e. white on black, which in the pictorial-visual order represents the complete destruction of the artistic concept, graphically and motorically turns out to be almost unchanged, even despite the psycho-physical phenomenon of irradiation of white on black. It would be complete absurdity to reproduce a painting chromo-photographically in the form of a color negative: i.e. with the replacement of each color with its additional one; but a much deeper, in color, distortion of the engraving, when it is turned into a negative, does not introduce any significant distortion into it. This once again explains the abstraction from color - engravings and graphics in general, and the sensual color of visual means of graphics is not included in the composition of the work itself, like some forms, while it is included significantly in a painting. It is approximately indifferent whether to draw on white, gray or black paper and with a black, colored or white pencil; but replacing these colors with any arbitrary others is unthinkable in a painting. So, in graphics, directions and movements are essential, and it is not important what kind of passively perceived signs these directions and these movements are brought to our consciousness by the artist. In other words, graphics are based on motor sensations and, therefore, organize motor space. Its area is [the area of] active attitude towards the world. The artist here does not take from the world, but gives to the world - he is not influenced by the world, but influences the world. We influence the world with movement, no matter whether it is cutting a stone, with the greatest tension of the muscles and the whole body, or a subtle hand gesture. But even the most convincingly gross and the most subtle manifestation of us in the world, such as a fleeting smile or slightly dilated pupils, is affected by movement, and all movements ultimately begin with the movements of our body. The most complex and powerful movements of machines, after all the intermediate links, lead to the primary wave, which closes the electric current or turns some starting lever. The expression of our will remains internal and inactive until it moves the organs of our body directly subject to will. Thus, an attack on the world is always a gesture, large or small, intense or elusive, and the gesture is thought of as a line, as a direction. It does not consist of individual positions, and the lines it produces are not composed of points. It, like a gesture, like a line, like a direction, is an activity indissoluble in its unity, and by this activity individual points, individual states, as something secondary and derivative, are posited and determined. Graphics, in their utmost purity, are a system of gestures of influence, and they are fixed in one way or another. If you have a pencil in your hand, then the gesture is written with a pencil line; if it is a graver, then it is cut out. If the needle is scratched out. But, whatever the method of recording a gesture, the essence of the matter is always one thing: linearity. The graphics are essentially linear; but not because it is contoural or because these lines are to be perceived in the plane on which they are materially written. The point is not at all about one or the other, but about the construction of all space and, therefore, all the things in it - by movements, i.e., by lines. As soon as dots, spots, surfaces filled with paint appear in a graphic work, this work has already changed the graphic activity of the approach to the world, the motor construction of its space, the gesture of expression of will, i.e. allowed in elements of the picturesque. For, we repeat: passive perception in the world of sensory reality contradicts the very foundations of graphics. In the middle of the last century in England, copper engravings, all done in dots, were very common; such engravings were attached, for example, to the novels of Walter Scott. This granularity gives transparency and subtlety of light and shade. But, despite the lack of paint, the impression of these engravings is clearly not graphic, but pictorial, like lithography or charcoal drawings, but with superior subtlety and detail. This graininess, dottedness, spottiness is the intrinsic property of painting. A smear, a stain, a filled surface is not a symbol of action here, but some givens themselves, immediately present to sensory perception and wanting to be taken as such. Each spot is taken here in its sensual coloring, that is, with its tone, its texture and, most often, its color. It is not a commandment that requires some action from the viewer and a symbol or plan for such, but a gift to the viewer, free and pleasing. Whatever the viewer gets from the work, he later receives without effort the joy of a color spot, which the artist freely received from the world and from the chemist in order to convey to the viewer. This spot is, first of all, part of the thing that is in front of the viewer - part of the picture canvas. In no case should it be thought of abstractly: the entire surface of the picture consists of such spots. Therefore, further, this spot is a material point, some small sensory-visible surface - a smear small enough not to have the shape of a rival with the shape of the whole, the whole picture, but not so small as to be qualitatively foreign compared to the entire surface. Here the artist shows how the world is closing in on him. Individual moments of this passive perception of the world are given by touches, touches. This passive space is built by touch. – Touch presupposes our least possible intervention in the outside world, with the greatest possible manifestation of ourselves by it. When we want to influence the world, we are relatively little interested in its own properties, or more precisely, we take them into account, since they can get in the way of our action, interfere with it or constrain it; they constitute the subject of our attention as a possible passive reaction to the world, and therefore are considered by us only in a general form. In other words, when we actively relate to the world, we take it into account abstractly and consider mainly inertial mass and mechanical hardness. On the contrary, when we try to understand the world itself, we naturally restrain ourselves, as far as possible, from interfering in the order and structure of the reality around us, so as not to distort our own appearance of reality with our intervention. We are afraid to crush it with our pressure or with our swiftness to move things and elements from their natural places. Therefore, we approach them as carefully as possible, as carefully as possible, in order to reach their border, but not accidentally jump over it, i.e. don't give it a new look. The reality of such knowledge is determined by an infinite judgment, in the form of “but not”; this is the smallest possible activity, almost the absence of it. Without activity, knowledge of the world is impossible; open activity is already an intervention in the world. Between one and the other stands touch, as an activity as small as is permissible under the conditions of sensory perception; even less - and we will not at all relate to the object of our knowledge. When in the dark we stretch out our hand to find a wall, a door or an electric light plug, the activity of our search is restrained by a special effort near the threshold, because otherwise we risk hurting ourselves or breaking something in the room. We make a great effort, perhaps much more than with sudden movements, but this effort is directed not at the outside world, but at ourselves, at restraining ourselves, at delaying the impetuosity. A gesture and movement that is more sweeping and faster than required by the given conditions does not indicate an excess of strength of any kind, but internal impotence, when the volitional effort is still enough to swing, but is no longer enough to delay it and limit it. A restrained gesture and a careful touch certainly contain the possibility of sweeping and rapid effort, and, moreover, an effort that limits this possibility: when the will weakens - with drugs, nervous disorders, mental illness, in emotions - then restraint is no longer powerful and movements lead to unforeseen consequences. Thus, touch is an active passivity in relation to the world. It does not want to raise its voice to delve into all the intonations of reality itself. Touch by its very purpose, as a perceptive ability, is aimed at the possible completeness of sensory data. And they take the largest spot-shaped pieces of reality, such parts of it that, due to their smallness, are assessed as not having their own form, and therefore seem to be only material, only bricks of the sensory universe. These pieces, these spots, saturated with sensory content, but in themselves formless and not defining a form, are traces of our contacts with reality: we touch the world with separate touches, and each of them gives a spot in consciousness - an imprint of our active passivity. The line in the chart is a sign or commandment 8 of some required activity. But a tangible spot is not a sign, because it does not indicate necessary activity, but itself gives fruit collected from the world: it itself is some kind of sensory datum. It is from this givenness that the arts of a passive attitude towards the world originate, mainly the purest of them - painting. Initial art creates convex objects, and these are mainly the depiction of bodies, human and animal. If we roughly take into account only this convexity of ancient reliefs, statues, etc., then it is easy to mix them into one genus and call it sculpture or plastic art. But this “or” is a blatant misunderstanding, because sculpture and plastic arts have nothing in common with each other: sculpture is graphics, and plastic arts is painting. Already in the very etymology of both words there is an indication of a deep difference: sculpture - from sculpto - actually means chopped, cut, carved, while plastic, πλάσσω, refers to extruded from a soft material. A sculptural work is a recording of the broad movements of a cutting or beating instrument, and a plastic work is a recording of touches. It goes without saying that cutting and sculpting construct their systems of recordings in matter in different ways; in large and small they lead to dissimilarities. The cutting produces a system of intersecting planes, and the work of sculpture, in its pure form, appears as a faceted and therefore generalizing [record] with its facets. There can be no question of reproducing the surface texture of what is depicted. In addition, the prevailing directions of blows inevitably appear here, determined by the structure of the artist’s body and the type of cutting tool. In the same way, the rhythm of these beats will be captured in the cut-out piece. Sculpture, if it is an imitation of an external object, is an internally musical imitation, responding 9 to the impression of the object with a rhythmic internal leap. This explains the integrity of such a work, its coherence indicating the internal consistency of the will that cuts it down, and, consequently, the predominance of the main concept over the particulars. On the contrary, modeling by touching a soft substance, whether with the hand or with the help of a small tool that continues the hand, gives a system of spots, points, spaces, which we evaluate each separately, at least in extent. They softly transform into each other, because each of these points separately has only a certain place in space, but has no direction. If in sculpture the proximity of certain places to each other is established by the approximate coincidence of the edges that characterize these places and the tangent edges in them (the direction of the edge therefore gives such a place a certain qualitative certainty), then in sculpting it is necessary to somehow characterize the individuality of each point in a different way, and this leads to the reproduction of surface textures. Modeling tends to give a cast and therefore gravitates towards naturalism. It is an imitation of the appearance of an object, and it inevitably transfers the quality of the dots - step by step. Therefore, such a product is forced to imitate all the inconsistencies of the object itself; moreover, it strengthens them, since it loses all functional connections as inaccessible to transfer by modeling. In such a work, the details prevail over the main idea. It is clear that sculpture and plastic arts are taken to the extreme here, but in fact, each branch also uses the techniques of the other in support. And it cannot help but use it, because motor sensations contain to some extent touch, and tactile sensations contain movement. Thus, sculpture is partly plastic, and plastic is sculptural, and sometimes careful analysis is required to decide whether a given work is based on plastic or sculpture. The gap, deep in its internal meaning, between sculpture and plastic art, or more precisely between motor works and tactile works, is usually recognized without corresponding acuteness due to the insufficiently pronounced difference between hard material and soft material. Wax, clay, etc. still not so soft as to mold by pure touch, i.e. without pressure and effort, often significant. Therefore, modeling by touch to a large extent becomes percussive, and the work acquires a motor character. On the contrary, marble, granite, wood and other hard materials are not so hard that they clearly show traces of any impact and do not allow single-impact restrictions. Hence the need arises to split the blow into weak individual blows, no longer very far from the tense touch with pressure. This is how, first, the inevitable and then the deliberate mixture of sculpture and plasticity arises, when clay or wax is unnaturally cut in imitation of blows, and wood or marble is smoothed, as if kneaded from a soft substance. But it is natural to foresee the possibility of both principles, motor and tactile, to manifest themselves more independently of each other if the substance being processed and the processing techniques are more consistent with the needs of movement and touch. This is exactly what graphics and painting are. The first uses movement in its greatest purity in that it does not fix the entire secant plane 10, but only its trace, or projection on the image plane. In this way, graphics relieves the artist from excessive efforts, and the substance from demands that are too difficult for him; That is why the movements here shed their numbness and caution, i.e. are no longer produced by touch, and their rhythm sounds free and undisturbed. In the same way, the painter frees the activity of touch from mechanical efforts by no longer forming volume, but only its projection on a plane, and, moreover, from the most pliable material - liquid or smearable with a semi-liquid. In a certain sense, we can say that the graphic artist cuts the air, and the painter sculpts from liquid. Both now seem to have almost no interference from matter, and therefore each can, if he wants, use either movement or touch in the purest form. But, with this independence from the properties of the substance, the artist also has, on the contrary, a wide opportunity to mix both activities, turning an engraving or drawing into a semblance of painting, and saturating the painting with graphicness. However, the ease of this interweaving of activity at the same time serves as a favorable condition for the intelligibility of each of the elements, and therefore, no matter how mixed the two are, understanding the nature of each is no longer a big task. Everything that has been said so far about mobility and tactility can, however, be rejected with reference to vision. In fact, both plastic and sculpture are seen with the eyes, and if they are felt with the hands, then this is something secondary; The mere fact of the existence of prohibitions on touching statues in museums seems to refute the ideas presented here about touch and movement. But this applies even more so to graphics and painting, the works of which cannot be perceived other than by sight. The fine arts are visual arts, and in the thoughts developed here vision was not even mentioned, and the word itself was never spoken. Meanwhile, there was really no need to mention vision until now, and it was not omitted due to oversight, but was left deliberately, as capable of confusing the still insufficiently developed concept, for vision, although the noblest of the abilities of perception, is in its essence not absolutely new, compared with the fundamental ones - movement and touch. Moreover, vision contains both primary activities, and each in its purest form. Here, both movement and touch are least bound by the inflexibility of matter, and those who rely on the eye for their perceptions are most independent in carrying out their work. The eye is an organ of both passive touch and active movement. Touch: as noted by Aristotle, vision is a widespread and refined sense of touch. The object is felt by the eye through a light beam. Until recently, the physiology of the sense organs imagined an object reaching the eye with its light energy and thereby touching the eye; There is no significant difference here from touch in the usual sense of the word, because it is not the object itself that acts on the touching hand, but certain of its forces and energies. Fractions of a millimeter in one case and meters in another separate the object and the organ that touches it, but in both cases they still separate. The ancients interpreted the process of perception differently, and they were followed by the Middle Ages, Roger Bacon and, unconsciously, all those who geometrically construct optical images in the eye. Namely, the ancients did not imagine an object reaching the eye, but the eye, through the rays emitted by it, coming close to the object and its touch. There is neither room nor need to choose one or the other of these explanations: basically, i.e. in recognizing that an object is touched by the eye, both of them agree with each other, and the discrepancy between them is only on an unimportant question for us, where exactly, a little closer or a little further, is the very contact of internal and external energies, as the meeting place of the eye and the object. The idea of ​​vision as a sense of touch has been expressed more than once and, in particular, is supported comparatively anatomically and embryologically: the eye, along with other organs of perception, comes from the same germ layer as the skin, the organ of touch; in this regard, both the eye and the skin appear to be organs of the nervous system that have reached the surface of the body. To make things somewhat rougher, we can say that the body is dressed in one continuous nerve, clothed in an organ of perception, i.e. into a living soul. The eye is then a kind of node of refinement, a particularly sensitive place of the skin with a particular, but especially subtly solved task. While the skin is capable of touching primarily near, although it is not alien to touching at a distance, the eye, on the contrary, is little susceptible to direct touch, is somewhat more sensitive at very close distances, is best suited to touch at a distance of 33 centimeters, and then again becomes less and less sensitive as the object moves away. Along with this increased sensitivity to touch, the ability to perceive the property of a surface, i.e. its texture, also becomes more refined. The finest texture is chromaticity, if we understand this word as a designation of the intrinsic property of the object itself, which characterizes not its relationship to the surrounding space, but the internal property of the substance. As is known, the color of natural bodies is determined by the finest structure of these bodies, their dispersion, but not molecular, but coarser (Wolfgang Ostwald). Therefore, perceiving this color, we essentially subconsciously recognize the structure of bodies, i.e. unconsciously tangible, just as when listening to music, “the soul,” according to Leibniz, “unconsciously engages in algebra.” Small tactile impressions, Leibniz's petites perceptions, give the consciousness of color. In other words, if we already have the ability to touch, then this is vision, and the organ of touch is the eye. Of all the organs, it has the greatest ability to grasp things with active passivity - to touch them without distorting, without pressing, without crushing. If it says: With fingers as light as a dream he touched my eyes, then these lightest fingers were not just a touching organ, but also a transforming one: The prophetic eyes have opened... But there is a sense of touch even easier than with these fingers, as light as a dream: vision. However, another line of abilities, motor perceptions, also ends with vision. Ordinary touch, no matter how essentially opposite it is to motor perception, is actually accompanied by it and relies on it: in order to feel an object, we slide along its surface with our fingers and palm, move our hand, move our whole body, even move from place to place. Movement contributes to the sense of touch. The eye, which brings the ability of touch to the greatest refinement, also brings mobility to its pinnacle: when palpating with the eye, as is well known, we certainly move the eye, move the head and even the whole body, and when we want to examine an object more carefully, we move from place to place. In short, visual perception is very similar to tactile perception. Moreover: with ordinary touch, if it is not accompanied by movements, reality is not divided and not formed; and if this motionless touch lasts longer, then the consciousness of reality will weaken, and we will fall into drowsiness, even into sleep. But vision, insofar as it can be freed from movement, gives a visual image that is indistinct, undifferentiated, and vague. It is like a fog that does not yet have a specific place, either close or far from us, sometimes as if directly approaching the eye, unstable and ultimately ugly. We are not able to perceive it for a long time without plunging into sleepiness, unless we allow movement within ourselves. Complete immobility leads, as is well known, to numbness not only of the body, but also of the mind, and extinguishes thought in us. What is given by touch is qualitatively incomparable with what we receive through movement; but nevertheless, it, in itself, cannot become our property, it is not assimilated by us. On the other hand, movement, taken separately from touch, turns out to be not embodied and therefore flows away: its recording in a substance requires the touch of this substance as resisting the change introduced into it. Here we involuntarily recall Kant’s words: “concepts without sensation are empty, and sensations without concepts are blind.” And this is not an external comparison, because according to Kant, our activity is affected by concepts, and passivity by sensations. So, movements without touch are empty, and touch without movements are blind. Our ability to perceive the world is led by vision; and in vision, therefore, tactility and mobility, each brought to the utmost expression and possible independence, contribute to each other to the highest degree. The perfection of the eye is the freedom to use at will either one of these primary abilities, or the other, or both together, or, finally, to make any of them the main one, and the other to accompany the chosen one, and, moreover, to the desired extent. Vision is the most flexible ability, the most ready at any moment to serve as pure touch, as pure movement, or as a plexus in any proportion of both. The most delicate sculpting is accessible to the eye, no longer paint-sculpting, but simply light-sculpting, but the most daring cutting is also accessible to the eye, dissecting space with pure activity, bordering reality with a lightning-fast glance. If the eye lays the most delicate spot, then it is the eye that cuts the line most boldly. Then, on these two paths, painting and graphics arise. The first, in the extreme, goes to passivity, to textured spots, to colorful strokes, to color dots that have no form; Such an extreme painter, like his viewer, does not notice the lines that actually arise through the contact of spots, and are distracted from them. Here visual images, or, more precisely, the visual field, unfolds from the inside, because from the very beginning, every stroke is already part of the plane, a certain seed of the visual field. The image here does not have a contour, in any case, the defining image does not have a contour, but, on the contrary, it itself posits with its spread, its spread across the plane, a certain contour, as something secondary and passive. Here this contour, if it affects itself, is only the limit of exhaustion and weakening of the colorful spot. Thus, in emanative philosophy, matter is thought of as the lower limit of successively and correspondingly drying up emanations, as something already defined by pure negation and equal to nothing. Pure painting, as it strives to be on the path of neo-impressionism, destroys the contour, or at least deprives it of activity; here he is already deprived of the power to tighten a certain part of the surface, to increase the elasticity of its energies; it simply exists - if only it exists - because it comes out from the interaction of spots. On the contrary, graphics come from a contour, and what it does within a certain general contour turns out to be itself a contour, a private contour. Here the plane is built with contours, more contours and more contours. The spot is alien to pure graphics and therefore the texture inseparable from it and its accompanying texture is alien. If, however, in the graphics, which have somewhat yielded to the beginning of the pictorial, a spot and the corresponding texture nevertheless appear, then as expected by the activity of the contours, i.e. as something secondary and passive in relation to the contour. Such a stain and such a texture indicate a certain powerlessness of life, which can no longer fill the plane with the links of its elasticity, leaves voids and gaps, and therefore there is a need to fill them with sensual texture. Here the abstract line is no longer able to be everything, and therefore color, tone, texture, and then straight spots are introduced into it. If pure painting leads to the philosophy of emanation, then pure graphics is akin to the philosophy of creation, for the artist wants to create the fullness of its images from the nothingness of the plane, doing without the sensuous at all. Brought to final purity, the arts of visual touch and visual movement are themselves destroyed; the first - as incomprehensible, the second - as imperceptible. In fact, although the graphic is abstracted from the sensory properties of the lines it draws and from the texture and color of the surface it uses, be it wood, metal or paper, the perception of these lines and this surface is still possible only in the presence of the sensory, and completely non-sensory graphics can only be an object of abstract reasoning. Thus, each of these basic arts actually uses not one, but two primary abilities. The qualitative difference between the arts is in which of the abilities the artist acts as the main and which as an auxiliary, i.e. Whether movement serves touch or touch serves movement. If in painting, with the dominance of the spot-dot, there is also a line, then in graphics the dominant principle, the line, does not unconditionally exclude the spot and its limit, the point. But in painting, the spot and, accordingly, the point are logically the first, and the line is the second, whereas in graphics it’s the other way around. The duality of passivity and activity in relation to the world, i.e. touch and movement, leads, as has been shown, to the fundamental duality of the initial elements of fine art: the point and the line are irreducible to each other and irreducible from each other, but at the same time they do not exist in complete isolation from each other. These are elements interconnected, and therefore the artist is given the opportunity to start with any of them in order to come to the other. However, it would be hasty to consider this conjugation of point and line as belonging only to the aesthetics of fine art and to deny the logical legitimacy of this conjugation. On the contrary, it is from the logical side that this conjugacy has long been known and is well substantiated in projective geometry, which is also higher, or also synthetic. But here the psycho-physiological substratum of this conjugation remained unexamined and therefore it remained unclear what the meaning of this conjugation, formally established in art, was. We are talking here about the so-called principle of duality in geometry. Depending on the two- or three-dimensionality of the space under discussion, this principle of duality is formulated differently; but the essence of the matter in both cases is the same. It can be further formulated even more generally, in relation to the topological consideration of space. But even here the essence of the matter will not change. Let us briefly outline the principle of duality in its successive extensions. Geometric formations are given in modern geometry, as is known, not in the form of visual images, but by logical definitions, and these latter are built not according to Aristotle, through the nearest genus and species difference, but through the relationships and connections of some initial logical symbols. Thus, the visual difference between geometric formations does not in any way ensure the difference in the corresponding definitions. And if so, then two identical definitions or two identical systems of definitions in the entire further course of geometric thought will give completely identical conclusions, although these conclusions will relate to two dissimilar visual areas. They will sound differently when expressed differently, but will be identical in their formal and logical structure; this last circumstance will be expressed in the identity of logical formulas expressing in signs both types of conclusions. As long as the initial relationships are identical, and the formal rules for handling these formulas, the purely logical rules, are the same, then no matter how far our conclusions are drawn, we are confident in advance of the constant and complete parallelism of both series. And if so, we don’t need to do the same work twice and derive one and the other series separately; it is much easier to expand one of the series and then replace in it the original visual samples and their basic relationships with the corresponding ones from another series. What will be obtained by such a substitution will turn out to be correct, of this we are sure in advance. Generally speaking, in any given area several such series can be expected; at least these series will appear and increase in number as the conclusions and corresponding geometric formations become more complex. But two such series are known in space, going back to the very beginnings and foundations of geometry. These two series are rooted in the principle of duality. Namely, on a plane, a straight line and a point, from the side of formal relationships, behave quite symmetrically and completely replace each other. Formally and logically, this is connected with an arithmetic fact that is identical for a point and a line. Each of these elements, in the singular, is precisely established or given by two elements of a different kind. Two points completely define a straight line, and two straight lines completely define a point. In addition, a straight line is the geometric locus of an infinite number of points lying on it, and a point is the geometric locus of an infinite number of straight lines passing through it. Each point on a line can be linearly expressed through any two of them; in the same way, each straight line of a bundle can also be expressed linearly, through any two straight lines of the same bundle. Thus, any logical relation, or logical function of points and lines, if true, will not change its truth after replacing the sign of a point with the sign of a line and the sign of a line with the sign of a point: since the basic properties of a straight line and a point are formally identical, then, consequently, in any complex relationship of points and lines, nothing will formally change if by the sign of a point and the sign of a line we everywhere mean the opposite of what was understood earlier. On the contrary, if the relation thus transformed was false, then even after the transformation it cannot become true. The formal relationships thus obtained, or geometry in signs, are essentially diplomatic language; being completely true, he, however, avoids responsibility for the visual side of the matter and expresses every position in two, equally pleasing both those who accept the point as the initial element of the plane, and the straight line as the derivative, and their opponents, who see the originality in the line, and the derivative in the point. For this very reason, this diplomatic speech into the ordinary language of visual images can be translated in two ways in each of its statements, and, moreover, in completely different ways. Both translations will each be completely true, but like a theorem about visual images, they will have nothing in common with each other. Thus, each theorem can be doubled without the slightest labor; one cannot count as labor the mechanical replacement of several words by others, according to precisely defined requirements. Simply put, a formal logical construction of geometry must also be accompanied by a dictionary of ten and a half to two words (of which the words of the first ten are especially needed). This dictionary is arranged in three columns: the first column contains alphabetic symbols and logistics signs, the second contains the corresponding concepts of point geometry, and the third contains the corresponding concepts of linear geometry. Then any statement in one of the three languages ​​can be easily translated into both other languages: the formal-logical relationship of signs is interpreted in the language of visual point or visual linear formations, and the statement of one or another visual area is transformed into a corresponding statement of another area or raised to its formal-logistic scheme. This dictionary, if we leave now the little occupied column of the logistics language, is structured something like this: To illustrate with an example exactly how these translations are made, let’s take four points. Connecting them in all possible ways, we get six straight lines: four sides and two diagonals of the quadrilateral. If we now draw a straight line connecting the intersection points of opposite sides of the quadrilateral, then the diagonals will mark two points on this line, and they, as is proven, will be harmonic with respect to the points of intersection of the sides. From this theorem it is easy to derive the dual conjugate theorem. Namely: let's take four straight lines (instead of four points) and all six points of their mutual intersection (instead of six straight lines connecting them). Let us now connect the opposite vertices with straight lines (instead of: taking the points of intersection): they will intersect at one point (instead of connecting the points with one straight line). Then the other two intersection points of opposite sides together with this point will define two straight lines (instead of intersecting at two points). These two lines, together with the previous diagonal lines, form a beam, and this beam will be harmonic. Or here's another example: two extremely important theorems, Pascal's and Brianchon's, were discovered independently of each other and approximately two hundred years apart; meanwhile, with a simple verbal translation, each of them turns into the other. Pascal's theorem applies to a hexagon: if there are six points on a plane, then by connecting each of the adjacent pairs with a straight line (and which pairs are considered adjacent depends on our arbitrariness), we get six sides of the hexagon - although it may not at all resemble what is called by this name in elementary geometry. Let us now consider the points of intersection of pairs of opposite sides, i.e., in the agreed order of vertices - separated by one vertex. Thus there will be three points of intersection. Pascal's theorem states that they lie on the same line. Let us now translate everything said into the language of linear geometry. So, we take six straight lines (instead of six points) and agree on the order of their sequence. Then we intersect them in the order of their sequence (instead of connecting) and find six vertices (instead of six sides). We now connect opposite vertices (i.e., separated by one side) (instead of: intersecting the sides) with straight lines; then there will be three straight lines (instead of three points). Brianchon's theorem is that all three lines pass through one point (instead of: lying on the same line). Similar examples, as indicated above, can be given literally as many as you like, because any theorem of point geometry can be subject to such a translation into the language of linear geometry. But even from these two examples it is quite clear that we are not talking here about some kind of tautology or even about the transformation that is given by the converse theorems; the principle of duality leads to an essentially new geometric truth, and the property it establishes of geometric images, as visually represented, has nothing in common with the original one from which it was originally obtained. Without knowing the principle of duality, this new property could in no way be guessed, and it would have to be discovered completely anew, as, for example, happened with Brianchon. In three-dimensional space, the principle of duality turns out to be different. Here, one of the ways to understand space is to approach space as a point, and the dual approach to it considers the plane to be the original element of space. Then in the above dictionary the word “straight line” should be replaced everywhere by the word “plane”, and the derivative of “straight” or “side” - with the corresponding derivatives of “plane” or “face”; So, instead of “multilateral” you should put “polyhedron” in the dictionary, etc. As for the straight line, it is always a secondary formation and is determined either by the connection of two points or the intersection of two planes. Therefore, when translating from the language of point geometry to the language of plane geometry and vice versa, the word “straight line” and its derivatives remain without translation; without changing their phoneme, they suffer changes in sememe due to the translation of other words. Thus, in spatial duality the straight line corresponds to itself. As has already been indicated, the principle of duality can be generalized to such an understanding of space in which there are no straight lines, but only ways to connect certain areas, called here points. But what has been said above is enough to give an understanding of the formal-logical meaning of the dual approach to space. Thus, the main task of fine art on the surface - the organization of space - can be solved by two approaches, close to each other formally, but deeply alien in the sensations underlying both approaches. On one path, the depicted space is thought of tactilely and is constructed by dots or specks, and they in turn define a line, but the lines are thought of here as possible paths of movement, and it is more or less indifferent whether these movements are carried out or not. On the contrary, with a motor approach to space, it is organized by lines, and lines here are the primary elements, active and themselves defining certain points as places of possible meetings, and therefore stops, for the sense of touch. But it makes no difference whether the sense of touch actually uses these points or not. In other words, surfaces and volumes are clearly presented here as motor images, but with an indication to a certain extent of possible touch; and with another approach, on the contrary, the surface and volumes are presented as tactile images, but with an indication of possible movements. But now things are tangible, and space gives scope for movement, just as vice versa, space is not tangible, and in things as such it is impossible to move. This explains the dominance in each of the two named branches of art of one of the two related aspects of reality: painting deals primarily with things, and graphics deals with space. Painting is akin to substance, while graphics is akin to movement, But we have already seen the inseparability of things and space and the impossibility of giving either things or space separately. Both sides of reality are certainly present in each of the works of both one and the other branch of fine art. The inclination of this branch towards one side or the other is reflected in the corresponding interpretation of the other side of reality. Thus, painting can strive to dissolve individual images as a whole, subordinating them to composition, deforming and intertwining. Then the images of reality lose their strict separateness; but not because the space of the work has truly become tightly connected and inseparable. On the contrary, here the internal, organically constructive coherence of each thing, in itself, is only weakened; Until now there was still movement in them, but now these last lines of connection have been pulled out of the images and instead of many individual things, a countless number of individual things have turned out. Now every part of a thing itself claims to be a thing, every spot, every stroke, every point exists on its own, without being connected by movement with another point, with another spot. They are all approximately equally effective, at least of the same order of effectiveness, and since there is a certain uniformity of their distribution over the plane, it seems to us, with a superficial assessment, as if we are looking at a work in which space has absorbed things. But no, rather, things, having finally become reified and having lost their organic structure, spread throughout the entire space and captured it. There are no things here now, but the beginning of materiality fully dominates. In other words, before us is not space, but environment. Hardness, in the sense of preserving form, exists mainly for motor perceptions, because touch, if we take it as extremely careful, both soft and hard are equally not amenable to touch. Therefore, the art of pure touch, which claims to give space, actually gives porridge, or liquid, or steam, or air - anything you like, but filled with substance, and, moreover, precisely as filled. This medium can be the subtlest - fire or simply light, but whether stones or spirits are depicted in this way, they are still presented here from the side of their materiality. While this distribution of matter over all space had not yet occurred, tactile points were the content of the interior of things, the substance of which things are composed; and the surrounding space was empty and weak. When the shell of things is completely weakened, things stretch out in space like ghosts of smoke. And these tactile points, the material filling of things, spread throughout space, the substance spreads throughout it. But that doesn’t make the space stronger. Translating everything that has been said into the language of general physics, let's say: the organization of space is achieved here by some continuous distribution of sources and sinks, or some point masses, positive and negative. This is the use of the Poisson equation - the last term containing the mass distribution density at each point. The artist plays here on this last member, and the force field and the corresponding structure of spaces are then established by themselves as something secondary and reflected. In this kind of art you have to work with a dot and stroke. As tactile to the last degree, such a point must be removed from a thing by pure passive vision: it is like a peeling scale of the visible surface of things, and not even the things themselves, but their projections. The artist here passively takes what is presented to him at the moment, and consciously strives to understand the thing, regardless of the random environment of present perception. If a line is characterized by its individual shape, then the point is devoid of shape, and therefore – individuality. Hence the need to individualize a point in painting by the size of its surface, tone, color, that is, to give it sensual characteristics in addition to the geometric characteristics - a known place on the plane. From here, the tendency of painting to further and even more crudely sensually individualize its points is understandable: this leads painting to the search for textures, and even further, it encourages us to borrow these textures as ready-made ones, from various works of technology. This is how stickers, paddings, inlays, etc. appear. If it were necessary to give examples of this direction of art, in its purer form, then, of course, this includes, first of all, everything directed towards impressionism, whether this impressionism is called by its proper name or not. Tintoretto, El Greco, partly Rembrandt, Delacroix and his school, neo-impressionism in the person of Paul Signac and others, pointillism, etc. - all this strives to provide a color environment that is passive, incoherent, devoid of structure and therefore, due to its sluggishness, easily subordinated to composition. If we call this environment space, then in any case it is not room for movement, because it is dense and overcrowded. This is the space of Descartes, completely filled with countless parts of matter, with which it is, logically erroneously, but naturally psychologically, completely identified. Painting extends materiality to space and therefore tends to transform space into environment. On the contrary, graphics bring spatiality to things and thereby interpret the things themselves as certain possibilities of movements in them, but different movements in different cases. In other words, it interprets things as a space of special curvatures, or as force fields. Painting, therefore, deals with the substance itself, that is, with the content of a thing, and according to the model of this content it builds the entire external space. And graphics are occupied with the space surrounding things and, using its model, interpret the interior of things. Space, in itself, is inaccessible to touch; but painting still wants to interpret it as tactile and for this purpose places a substance in it, even the subtlest one. This is how the light environment arises. On the other hand, matter as such does not give scope for movement. Therefore, the interior of a thing is inaccessible to motor perception. The graph, constructing space from movements, wants to approach the inside of a thing with the same perception and therefore depicts the volume of a thing, making mental movements inside it, i.e., imaginary motor experiences. If he had resigned himself to the inaccessibility of this volume to touch and had not carried out these experiments, then the inside of the thing would have remained a deep secret to him and could not be depicted graphically. After all, a painter, touching a thing, conveys its substance, starting at the border and extending into the depths, and graphics can only move around the thing and the substance of it does not know at all during its movement - in exactly the same way as a painter, by touching a thing, does not know at all the space surrounding it. And therefore, if the painter extrapolates his experience, extending in his imagination the substance he has cognized into external space, then the graphic artist extrapolates his motor experience relative to this external space to the inside of the thing, that is, in his imagination he introduces there movements that are experimentally inaccessible to him. Then the inside of the thing is interpreted as a force field. Mathematically speaking and remembering the Poisson equation, let's say: the graph considers its last term to be zero everywhere, but takes the left side of the equation not in Euclidean space, but in some other space of variable curvature. Formally, mathematically, both methods lead to similar results, because it makes no difference whether the non-identity of the resulting equation is attributed to Laplace’s equation due to a variable density in space, a variable curvature, or a variable coefficient of the medium. But physically and visually, these techniques are profoundly different from each other 12 . The organization of the space of a work of art would each time be a unique, already more unique case, if the organizing means did not include the method of using them. It is not enough to write a book: it is necessary to imprint in it the order of its reading. Otherwise, the reader will not be able to perceive the words of the book in their actual sequence, and the work will remain unsolved. But this also applies to any work, including fine art. Moreover: the more abstract art is, the fewer crude pieces of reality and crude connections of reality it assimilates to itself, the more definitely the guiding principle or the basic scheme of works should appear in its affairs. The elements that construct space in the artist’s mind arise systematically, and the systematicity of their reproduction by the viewer, this same or some other, the artist must command the viewer. Otherwise, the viewer would feel as if the artist, instead of the finished work, kindly offered him a blank canvas, paints, paper, etc., and then left him alone to do whatever he wanted with them. And the artist himself must consolidate in one way or another the sequence he intends, risking not understanding himself without this. This scheme or this plan of the work is composition. The plan is not the content, as when we talk about the plan of a verbal work, but the plan for the organization of space, which has no direct relation to the plot. Composition is, therefore, a diagram of the spatial unity of a work. It is not yet unity in itself; it foretells this unity and then represents it for it. Only in the work is it realized and clothed in artistic flesh, and therefore only if it is present will it be a representative of some space. In itself, it is only an element or several elements that are completely homogeneous with those that construct the entire work. In fact, nothing foreign can be introduced into a work, and if such an attempt were made, this heterogeneity would separate like oil mixed with water. Such a scheme would remain unembodied, and the work itself would remain without a guiding plan for its perception. Obviously, the composition can only be given by the same elements from which the entire composition of the work is made, but especially accentuated, especially highlighted and put forward as primarily perceived. These elements are grasped by perception, in addition to the viewer’s intentions, first of all and most definitely, and then the perception of other elements is already located on them, and, moreover, in a certain sequence and with a certain coefficient of their hierarchical place in the work. Having perceived the composition, we, regardless of conscious efforts, have already figured out the hierarchical plan of artistic organization, and therefore in our consciousness will now appear not just any elements of the work, but certain ones at certain times. If, before mastering composition, we, wanting to understand the work correctly, would unwittingly break his artistic organs, now, having mastered composition, we will not be able to deliberately examine the work as we please. In a sense, we are now forced to understand it correctly, that is, according to the artist’s intentions, and trying to do the opposite is difficult and even painful. Plato says of dialectic that he is like a good cook who divides rather than chops the links of a fish. Likewise, the viewer, having a composition in front of him, dismembers and does not tear the work apart. As an expression of unity, composition is necessarily connected every time with the fundamental activities of a given art. At first glance, it may seem that the compositions can be anything and that there are countless of them. Indeed, with their combinations, compositions are woven in a variety of ways, but this variety refers to secondary and tertiary formations. The primary compositional schemes, deserving the name of the first composition, are very few, not to say simply poor. The most complex plans fit into one of these few primary schemes, and it further predetermines the entire structure of the plan. So far we have used the term composition in the general sense of the basic scheme according to which a given work is constructed. But along with the term “composition” one can often hear another, namely construction, which sometimes appears almost as a synonym for the first, sometimes in opposition to it. In some cases the whole discussion of objects of art is conducted with the help of these two terms, composition and construction, taken to be terms of primary importance; but nevertheless, their exact relationship is not indicated clearly enough. Let us try to establish this relationship, if not quite clearly, then at least with a preliminary sketch. Both of these terms are extremely far from each other, and when you realize how great the degree of their divergence is, not to say complete opposites, even the psychological motives for confusing both become incomprehensible. But on the other hand, both terms are equally necessary when discussing art, and the very attempt to deal with only one of them, or even to associate a certain direction of art with one or the other term, with a composition or design, taken separately, is surprising. In fact, a work of art is always dual, and in this duality lies the need for a double approach to the work, and, consequently, a double scheme for it, the corresponding duality of the term needed here. A work of art is something about itself, as an organized unity of its visual means; in particular, it is an organized unity of colors, lines, points and geometric shapes in general. This unity also has a basic diagram of its structure; this is what is called composition. Thus, the diagonal division of Rubens’s paintings or the central symmetry of Tintoretto, Botticelli, etc., the dominant vertical axis of icons or the equality of vertical and horizontal in Greek relief, etc., all these and similar primary schemes, according to which a certain work of fine art is constructed, they relate directly to the artist’s visual means: according to one or another plan they are located on the pictorial plane lines, dots, color spots and surfaces. You can understand nothing about the subjects of Rubens’s paintings, and yet, with complete confidence, establish the indisputable fact that the most noticeable, most arresting color spots in Rubens fall on one side of the diagonal dividing the rectangle of the picture, while on the other side of the same diagonal are less effective color spots. Moreover, even if the person looking at these paintings had never seen people and had no idea about the human body, he would still have established with the same degree of confidence the fact of their diagonal composition. One can even imagine that this fact is analyzed and identified by some kind of photo machine, for which the plot and, in general, the objectivity of the work, that is, one or another of its meanings, simply does not exist. In the same way, it is quite possible to imagine an automatically produced recognition of which direction predominates in a given painting or engraving, what are the axes and centers of symmetry, etc. When setting up a composition, knowing the meaning of a work is usually not only unnecessary, but rather harmful; after all, knowing this meaning, it is difficult to then abandon it and discuss the work from the perspective of the visual means present in it and the plan of their unity. And this is the composition. But, in addition, the work has a certain meaning, the organized unity of all media serves to express this meaning. The work depicts something. What it depicts, its subject, is not identical with the work as such and is not even at all similar to the organized set of means depicting it. He is outside these environments, although he is given to consciousness by them. And it obviously, since the work must be integral, has its own unity; it is one in itself, just as the totality of visual means is one in itself. But, of course, the unity of what is depicted cannot in any way be confused with the unity of the image. This means that the first must be internally connected by its scheme of unity, its plan, uniting the depicted object into something whole. This diagram, or this plan of a work of art, from the point of view of its meaning should be called construction. Thus, the composition, speaking as a first approximation, is completely indifferent to the meaning of the work of art under discussion and deals only with external visual means; the design, on the contrary, is aimed at meaning and is indifferent to visual means as such. What these latter are is clear; the meaning of the work can be interpreted from different sides, and therefore a more precise explanation is required. With a superficial approach to artistic creativity, it seems self-evident that the understanding of the word meaning, which identifies it with the plot. Indeed, the plot is part of the structure, if we take the last word broadly. But the plot is only a more superficial one and therefore is an external moment of construction, some secondary or tertiary formation, while what is primary is some first-construction, still very far from the plot, or some first-plot, the first withdrawal of consciousness beyond the boundaries of the unity of visual means. Here the consciousness is given the relationship of forces, elements, elementary things to which consciousness is brought by pictorial means, but which, i.e. forces and so on, are not directly given by the image. Thus, one cannot talk about the severity of a stain of any earthy paint, because, taken directly, this stain gives only a visual sensation, for example, brownness, and not a feeling of heaviness. But such a spot can take our consciousness beyond the limits of purely visual sensation; and then the consciousness is prompted by the idea of ​​heaviness. This idea can take shape even more when the spot is limited not in some arbitrary way, but in some specific way, for example, a square, with horizontal and vertical sides, and when it is correlated with another spot, for example, with a horizontal stripe under the square, of an even more material, earthy color. When we see such spots, we will imagine some heaviness pressing on the support. However, this will by no means be the idea of ​​a heavy body and any bodily support. No, in our consciousness the sensation of color and geometric form will be joined by the idea of ​​abstract heaviness and abstract pressure, not yet complicated by physicality, but lying on the other side of the visual sensations directly given to us and therefore undoubtedly objective. This, that is, the struggle of abstract gravity and abstract opposition to it, will be some of the meaning of such an image; one can say that this relationship of forces will be depicted by the indicated system of color spots, will be its subject, or primary subject. And the diagram of this relationship will be the design of this object. The composition, one must think, will be carried out here by a vertical axis and an equal horizontal axis, and by the distribution of the increasing materiality of colors in a downward direction, while the design will be carried out by the simplest relationship of gravity and counteracting force. If you like, such a construction could also be called a plot, a natural-philosophical myth in the spirit of Schelling or Hoffmann. But it is also clear that the plot in the more ordinary sense of the word is formed as a complex whole, dominating over a multitude of such elementary primary plots. And this dominant whole in a work of art can be present or absent, without its absence violating the artistic and creative character of the given work, while the primary plot, i.e., some initial departure beyond the realm of visual means, is an indispensable condition of art itself. Lines, dots, spots, etc., which do not lead anywhere due to their sensory reality, in any case, are not art. But going beyond oneself is a condition of art, necessary but not sufficient: the area into which one goes must be objective, that is, whole in itself, and not a random accumulation of inconsistent and ununited elements. Only in this case, with its integrity, can it be called the meaning of this work. In other words, this area should be constructive. A work without a structure is not a work of art. But this construction does not necessarily lead to the idea of ​​bodily reality, and therefore, even more so, should not be plot-based at all. The usual misunderstanding here is the confusion of objectivity with physicality and meaning with plot. Meanwhile, a work of art, while necessarily objective and meaningful, does not necessarily have to be physical and subject-matter. One might even say that too much physical density and too definite and coherent a plot can destroy a work of art, weakening its harmonious duality and damaging the composition for the sake of an inappropriately strong construction. So, a work of art necessarily has both composition and construction; when the work is harmonious, both of these principles, compositional and constructive, are balanced; and in most cases, when instantaneous balance, this heavenly integrity of creativity, is lost, then either a compositional scheme or a constructive scheme gains predominance. Apart from Hellenic art and icon painting, it seems that it will not be possible to give other examples of such balance. We can now simply explain the meaning of both of these principles. The artist says something about reality with his work, but in order to be able to say something about it, it itself must contain some meaning, declare itself with some word about itself. Thus, in the work, two words, the word of reality and the word of the artist, are combined into something whole. But even having united, they do not each lose their own nature. What reality itself speaks about itself through a work is a construction in the work; and what the artist says about this reality is the composition of the work. Here it was said “construction in the work” and “composition of the work”, because it is not the work that is subordinate to the construction, but the reality depicted by the work, while the work itself is subordinate to the composition. And on the contrary, the work, as such, is completely independent of the structure of reality, just as reality, in itself, has nothing to do with the composition of the work. In other words, construction is a way of relating the elements of reality itself, no matter whether it is physical or abstract, the structure of reality about itself; and composition is a way of relating the elements by which reality is depicted, that is, the structure of the work. It is clear that there is no direct connection between the structure of reality and the structure of the image, and there cannot be, at least when approaching this issue for the first time. And here it must be affirmed with all our might that there is nothing in common between design and composition. After all, construction characterizes reality in itself, in its internal connections and relationships, in the struggle and cooperation of its forces and energies. And the composition characterizes the inner world of the artist himself, the structure of his inner life. That is why, no matter what the subject and, more broadly, the artist’s subject, he is inclined, if only he is strong and internally stable, to express every subject and every plot with the same composition. The most diverse constructions of reality are expressed by works of compositions that are almost identical; as is known, authorship is established by the composition no less than by the direct signature of the artist’s name. On the contrary, the same object and plot, while having its own specific structure, is depicted by different artists in completely different compositions. However, despite all the variety of compositions, in all these works we recognize their subject, their plot and do not doubt its self-identity. This means that we capture a single design of a diversely depicted object, i.e. we do not at all confuse the designs in the work with its composition. Construction is what reality itself wants from production; and composition is what the artist wants from his work. These two demands, one emanating from the external world, the other from the internal, are expressed independently of each other, at least in the first approach to this issue; and it goes without saying that it cannot happen that an artist would want to eliminate himself from creativity and not express anything from himself, because then the presence of reality itself would be enough. On the other hand, there is no reason to assume that reality will somehow be lined up or rearranged to please the artist. Thus, the two requirements cannot be assumed to be consistent with each other. But they converge in the work and by their interpenetration they form the work, like the warp and weft that weave a fabric. However, as in fabric, it is possible for one of two principles to predominate, either the warp - the design, or the weft - the composition of the work. Then a work arises that is either one-sidedly objective, or, on the contrary, one-sidedly subjective. You can go further in weakening one of the principles. The first way consists in the artist's self-elimination. The artist is concerned here only with the correlation of forces in reality itself, and therefore the figurativeness of his work weighs on him. The actions depicted must turn into simply actions, and, consequently, the depiction of things into the things themselves. The unity of artistic contemplation, that is, composition, weakens more and more and finally, exhausted, comes to naught. But at the same time, the unity of the work as depicting something is lost: its space ceases to be delimited from the surrounding space, and becomes only a corner of it. Then the frame of the image, virtually inevitable due to the limitations of any material plane, loses its meaning of aesthetic isolation and becomes only the end or segment of the work, not aesthetically motivated: such a canvas or such paper could be cut off anywhere, or, on the contrary, an arbitrarily large piece could be added here. In extreme naturalism this is precisely the problem of space. But even naturalists still do not dare to abandon representation and therefore do not have the courage to complete the functional unity of the work to the reality it depicts. In other words, by running away from compositional unity, they do not provide constructive unity. They do not dare, however, to take a thing in its own relations and really completely eliminate itself. Thus, instead of the functional unity of the thing in itself, an image of this unity is depicted, distorted by the subjective gaze of the person looking at it. But at the same time, the subjective unification introduced here is accidental and fleeting; it is not formed into a natural and necessary unity capable of characterizing the artist’s mind as such; in short, being peripherally subjective, it does not achieve subjectivity. This is a half-hearted and flabby direction, hardly even worthy of the name of art, even a bad one. It places its dignity in truthfulness, although it is precisely this that does not take into account either the mind of reality or the mind of man. It comprehends things just as little as photography; but, on the other hand, it is also soulless, like the glass lens of a photographic camera. Its truthfulness is fidelity to chance, in its randomness. Eradicating from the perception of the world everything eternal and valuable, this direction wants to retain and consolidate only what depends on everything that is not internally connected with either a given thing or a given mind. The pursuit of random highlights and scrupulous capture of color reflexes seems important to this direction, although highlights, reflexes and the like do not characterize the thing as such, but only its environment, changeable and random, moreover, not depicted in the work. Thus, what seems to be explained in the work is not depicted there, and what is depicted remains without explanation. In other words, instead of a thing, an empty space is given here, on which functions belonging to things outside the image field converge. These nihilistic techniques also include direct perspective, which is similar in meaning to them: after all, its job is not to let the eye rest in contemplation on a single thing, but always to go past each of them, the infinity of emptiness, where all concrete visual images are gradually destroyed and every something evaporates into nothingness. Both perspective and other favorite techniques of naturalism, like the above, are similar to greed, which encourages one to neglect everything that is present for the sake of something else, and this other thing is to be abandoned again for the sake of a third, etc. This is the eternal languor of the spirit falling in the void. But humanity cannot hold on to artistic nihilism for long, and therefore the transition to such conclusions is inevitable, which clearly destroys representation and takes the thing as such and its function as such, but not their representation. This is how the inevitable transition to technology arises in naturalism. The artist now wants to give not an image of a thing containing the depicted function, but the thing itself with its action. In other words, he wants direct access to his work in practical life. What he does claims to be not a painting or a graphic, but a thing. Abstractly, three solutions to the problem posed can be envisaged; as we will see now, the artist is unlikely to want to follow any of them. The first solution: to create natural objects - organisms, landscapes, etc. Clearly, this would not only be impossible, but also absolutely unnecessary. Nature already exists, and doubling it would be a futile exercise. The same thing that is not useless and possible here is done on ways independent of art; in these areas, the artist would only take bread from the livestock specialist, gardener, agronomist, etc. Another solution is the creation of things that do not exist in nature: these are machines. And here again an artist can successfully or unsuccessfully compete with an engineer, but in both cases he works as an engineer, not an artist, and does not open up any new field of art. Finally, the third solution is when creation is aimed at things of a non-physical order. Then such a work is also a kind of machine, but a magical machine. This is a kind of weapon of magical influence on reality. Such tools really exist: for example, advertising and propaganda posters are intended to force everyone who looks at them to take certain actions and even force them to look at them. Here the effect on others and the change in their mental life should be not the meaning, but the direct presence of colors and lines. In other words, such posters are machines for suggestion, and suggestion is the lowest level of magic. Pantacles and other magical images, as well as techniques of imitative magic, precisely relate to the above-mentioned third solution to the problem of naturalism to find a way out beyond the limits of representation. Now there is no value in discussing how satisfactorily these and similar magical machines actually perform their service. This discussion is required here no more than that of the technical qualities of mechanical machines invented by the artist. Whether a machine is good or bad, it is a machine, not an image. Even if it has no effect at all, it will still not be an image, but only a machine, but an unusable one. In the same way, whether active or inactive, magical machines give the right to their inventor to be called a magician, strong or powerless, but not an artist. Suprematists and others of the same trend, without realizing it themselves, are making attempts in the field of magic; and if they had been more successful, then their works would probably have caused spiritual whirlwinds and storms, sucked in and twisted the spiritual organism of everyone who entered the sphere of their action and would have turned out to be the centers of powerful associations. You can in any way increase in thought the effectiveness and power of this kind of magical machines and imagine them as infernal machines in the non-physical realm; but nevertheless, these will be machines, and not works of art, and the activity that creates them will be magical technology, and not art. 05/10/1924 Art. Art. 15, Friday 16 So, the design is the form of the depicted work, or, in other words, the way of relationship and interaction of the forces of reality, transfused with the help of the work, perceived through it. On the contrary, composition is the form of the image itself, as such, i.e. the way of relationship and interaction of visual means used in this work. One can also say: by construction, insofar as it is expressed in a work, it is given to the viewer (or listener, if we are not talking about a visual work) the unity of a certain part of reality, as a result of which a corner of the world is perceived and understood as some kind of whole, closed in on itself, albeit relatively; in this way it is likened to an organism. But to perceive and convey the organic self-closure of a certain reality does not yet mean the same unity of the work itself, i.e. images of this reality. Thus, a photograph of a beautiful representative of some animal species, with all the typicality of the animal depicted, i.e., therefore, with the vivid expression of its organically constructive unity, is still not at all a work of art: the image, as such, is devoid of integrity. Thus, the image itself must have its own unity, and, showing us the organism of reality, must itself be an organism. So, firstly, organicity and, secondly, also organicity: firstly, the whole and, secondly, the whole again. But these, firstly and secondly, relate to different, in no way comparable areas of existence: there is nothing in common between a bull under a tree and P. Potter’s canvas called “Young Bull,” no less than [between] Kern and a piece of paper with “I Remember a Wonderful Moment.” However, both unities, relating to significantly different areas and leading to the integrity of completely heterogeneous areas, are nevertheless connected to each other in a mysterious knot called a work of art. Both unities, constructive and compositional, are combined in one work, although one does not follow from the other, or vice versa, by any direct dependence. Moreover, you need to think ahead of time about their mutual exclusion of each other, because it is by no means clear how there can be constructive unity in a work if this work is subject to its own, and, moreover, not resulting from the first, compositional unity. On the other hand, if we have already gone to convey the constructive unity of reality itself, then it is incomprehensible to introduce yet another unity, compositional. It would seem that the new unity will necessarily distort and destroy the one that was accepted as the original one. But the presence of both of these unities in a work not only exists - contrary to the abstract thought of impossibility - but also determines the very possibility of the work: both unities are antinomically conjugate poles of the work, inseparable from each other, as well as irreducible to each other. The formula of the Perfect Symbol - “unmerged and indivisible” - extends to every relative symbol, to every work of art: outside of this formula there is no art. But here an objection arises, the closest reason for which is a branch of art, apparently tertiary, but which is capable of growing with an influx of new comparisons and raising doubts, if not about the correctness, then at least about the universality of everything previous). This branch of fine art is ornament. When they want to condemn a work for being pointless, it is equated with an ornament. This should indicate its lack of representation; as they say in such cases: “It’s beautiful, but it doesn’t mean anything - a carpet.” Thus, ornament turns out to be a typical example of non-objective painting or graphics and, therefore, only by misunderstanding is classified among the fine arts. Perhaps the archaeologist will try to justify this long-standing attribution of ornamentation to fine art by reference to the historical past of ornament. Not being an image in the proper sense, the ornament was, however, originally an image, and only ever-deepening stylization erased from it the resemblance to objects of nature, the images of which were elements of various ornaments. This is where, they will say, from old memory, the place of ornament among the fine arts is preserved. Even if the above archaeological consideration were justified in itself, it still would not justify in the present attributing ornament to fine art: no matter where ornament originated in the past, i.e. as a stylized image of human and animal figures, utensils and tools, trees, flowers, fruits and leaves, it cannot be called an image now if its connection with the depicted is already broken and can only be established archaeologically for indirect reasons, abstractly asserted, but not visually perceived. However, this archaeological statement of the objectivity of the ornament is more than doubtful. The history of ornament, at least in many particular cases, is characterized not by simplification and schematization, but, on the contrary, by complication and condensation. The ornament is initially constructed by geometric lines, and only later they are clothed in flesh, in accordance with the given geometric pattern of the ornament, and then individual pictorial elements appear in the ornament, as an attempt to interpret the original non-objective in an objective manner. Perhaps this attempt is not entirely arbitrary; but nevertheless, the interpretation of some lines as a diagram of a given image, and not some other, can be carried out in various ways, and the images selected to emphasize a given ornament are varied. The objectivity of an ornament, with this interpretation, is something secondary, added to the ornament by a special act of creativity, although the ornament does not force, but does not necessarily follow from it. Thus, the basis for doubting whether it is correct to classify ornament as a fine arts is given even stronger. So, ornament, generally speaking, does not depict the external world and does not have its own models in objects of nature; in any case, figurativeness in this sense is not necessarily inherent in ornament, and when it is, it should be considered as something secondary and secondary 17. This can be considered established. But from here it would be too hasty to conclude that the ornament is pointless, for the object, in the sense of the content transcendental to the image - the depicted content must not necessarily be one of the sensual images of nature. Indeed, along with sensory images and above them, there also exist non-sensory, but quite real types and types of relationships between the sensory, rhythms and patterns of the sensory (as well as the supersensible), which themselves are no longer represented by sensory images. These rhythms of existence, laws of world life and types of concreteness may well be the subject expressed or transmitted through a work of art; they are even the most worthy subject of art. “Poetry,” Aristotle once said, “is more philosophical than history.” This is due to the greater generality of the images of poetry, compared with the images of history, which are private, fractional and therefore of little value. And in general, art is more philosophical than the depiction of reality. But the same should be repeated in relation to art, which expresses the rhythms and laws of reality in a much more general, and therefore integral and compacted way, than the images of individual things and beings that make up the subject of ordinary art. Thus, the ornament is by no means pointless, i.e. is not devoid of the antinomy inherent in the symbol, but, on the contrary, it significantly enhances the contradiction between composition and design and thus extremely strains the antinomic tone between the image and the depicted. Ornament is more philosophical than other branches of fine art, because it depicts not individual things, nor their particular relationships, but conveys with clarity certain world formulas of existence. If the ornament seems to be devoid of transcendental content, then this is due to the low accessibility of its subject to consciousness, which is not accustomed to eagle soars above the particular and fractional. Thus, a book of deep truths may seem either incomprehensible or empty to a reader who has not matured enough to understand it - as if everything is said as if it is the same thing with minor changes, the meaning and value of which seem elusive. But the moment comes, and the book’s own subject emerges from the fog as a majestic massif, before which all the recent pleasures of the surrounding clearing are nothing. In the same way, the ornament created in other times, of monumental thinking and monumental world feeling, is inaccessible in its world sense to the petty consciousness of modernity, and it uses these mysterious patterns of existence, saturated with majestic thought, as an external decoration or remplissage of voids where there is not enough creativity for sensual images. Isn’t it true to the saying, “they cover pots with icons,” obviously not seeing anything in them other than boards? However, this board is an imprinted phenomenon of the spiritual world, and the ornament is the deepest penetration into the rhythm and structure of life. But neither the spiritual world nor the Pythagorean music of the spheres is accessible to the embodied modern eyes and ears. This is where the judgment about the pointlessness of ornament comes from. The above thoughts can be confirmed by what is now known about the origin of this branch of art. In fact, the original purpose of the ornament relates to theurgy and magic. Abstract decoration, considered as such, arises only in cultures that are fragmented and devoid of organic integrity, and, moreover, is characteristic only of social strata that have lost a living connection with the people's consciousness and therefore cannot justify themselves ontologically. This is where modern ornament appears, i.e. in a peaceful, decorative sense. And in entire cultures, ornament has always been an applied art, if by such we mean any art that is directed not directly at abstract and independently taken beauty, but at the whole of culture, where beauty serves only as a criterion of embodied truth. If we delve further into the even more organic historical basis of culture, then ornament is definitely used as a sacred protection of things and all life in general from the attack of evil forces, as a source of strength and vitality, as a sanctifying and cleansing means. In short, ornament is here a sacramental, theurgic, or, on the contrary, magical tool. In our impoverished and faded culture, the conscious use of theurgic ornamentation was retained only by the sign of the Cross, and, perhaps, some shade of the mysterious power of the ornament is felt in the initials of the owners placed on things. But even the last refuge of theurgic ornament - the Cross - has largely lost its original strength, and the marking of a cross on things is partly considered conventional, and partly it is completely falling out of use. In ancient times, we find many such sacred ornamental structures - double axes, swastikas, meanders, etc., and even any ornamental combination of lines and dots and various colors was drawn for the sake of communicating special powers to a thing or being, as, for example, in a tattoo. Of course, a more careful review of life will note numerous cases where ornament continues to mean more than simple decoration. Semi-consciously, this more decorative moment in such ornaments is recognized, and moreover, not only as some meaning of them, but also as another, more directly acting and inaccessible to rational analysis force, sometimes beneficent, sometimes, on the contrary, hostile. But nevertheless, all these are pitiful and random fragments of the enormous art of metaphysical schemes of being, once powerful, and now huddling in the corners and outskirts of culture, not cleaned by rationalism. There is another industry where vestiges of sacred ornament are observed. This is precisely a mixture of vague but deep traditions of ancient esotericism with a superstitiously fearful clinging to a letter that is no longer understood, and with outright charlatanism - a mixture that is called modern occultism. Here, in the so-called pentacles, an attempt is made to condense groups of ornaments and signs with activities directed in one direction into separate images. Such pantacles are, according to the teachings of occultism, condensed formulas for influencing certain elements and certain spirits. Leaving aside the question of the actual effectiveness of pentacles, which is not subject to discussion here, we only note that from the side of graphic pentacles they clearly refer to the time of the decline of sacred ornament: when the direct feeling of the mystical power and metaphysical significance of the ornament, as achieved precisely by art, is largely lost, then they grab hold of quantity and heap fragments of ornaments into some almost unorganized heap. This heap is called a pentacle. Each of the ornamentally composing it in itself no longer enjoys trust; but then the accumulation of such ornamental motifs is all the less trustworthy, in which cluster not a single one of the motives is allowed to unfold and organize space. It’s the same as if someone, having lost the feeling of the power and saving power of the Cross, decided to build something like a machine for grace, piling up many crosses of different types. These are precisely the pentacles. So, modern ornament, even in its applied application, is indeed considered to be of little objectivity, and therefore of little constructive value. He has lost the balance of compositionality and constructiveness; but precisely because of this, holding on only out of old memory, among the fine arts it lost the rank of serious art and became something insignificant and almost falling out of the realm of creativity. The design is the point of application of the compositional concept. Free in itself, as an expression of the artist’s will, the composition adheres to itself for this very reason, that is, because of its freedom; however, this would not have happened if her chosen point of support had changed. And therefore, for the integrity of the composition, a design must be chosen every time that does not have an internal movement that can lead the composition astray from its own path. Reality is not passive, and if it were, it would not provide a solid point of support. For this very reason, it must be chosen by such a direction of forces that strengthens the artist in his chosen decision, keeps him with his plan and returns him to it in case of internal instability. Probably these thoughts, expressed in this way, seem somewhat vague. But they can be easily expressed more definitely if we temporarily abandon formal reasoning. Things, as a certain unity, also have a certainty of their relations to space: in other words, different directions in space are formed and organized by the different activities of a thing. And since by its activities a thing manifests itself as a certain unity, but manifests itself in different ways, then from different sides of the thing, geometrically speaking, we see different sides in it, already in the ontological sense. A thing speaks about itself, but in its different turns it says different things, expressing different aspects of its single essence. We are talking here, however, not about the self-evident fact that, changing the point of view, we will not see identical projections of a thing. No, a qualitative difference and even deeper - different planes of understanding are characteristic of different turns of a thing. There is no normally assumed continuity with changes in rotation; a small twist can express a thing in a completely new way, i.e. in a significantly different manifestation than it was. On the contrary, there are turns that are simply underexpressed, ontologically unstable positions that tend to move to either one or another of the stable turns. Just as in a living body there are places where the pulse can be easily felt, and there are places that are inaccessible to such research, and having found this place, which is less transparent, one might say, the hand tends to move to one of the places that clearly shows the movement of blood, so the internal unity of a thing is easily accessible to perception from some places in space, while others, on the contrary, are not conducive to it. In other words, the thing cannot be taken by the artist in any random turn, because then it will either be mute, or it will say something completely different about itself and not in the sense required by the compositional plan. Renaissance artists, abandoning ontology, introduced the word foreshortening and boasted about the boldness of their foreshortenings. But what is a bold angle? – This is some completely unexpected, unusual and even unnatural turn of the depicted object, i.e. one in which we never see this object and, most importantly, do not want to see it. We deny these unexpected turns in the knowledge and contemplation of an object, as impoverishing the object, depriving it of the most essential in it and characterizing not it, in any case, not so much it as the point of view of the artist or contemplator. Such a point of view, since it provides the least knowledge of the subject, is obviously random in relation to the subject, and random means passive. If the artist, by force of circumstances, found himself in a place unfavorable in terms of knowledge, showed his will, then he would naturally change his place and look for another that would satisfy him. But the artist described has no need for reality, because he does not believe in its own meaning and reality; and in relation to himself, he also does not feel in himself a real agent of the world and therefore does not seek knowledge. To such an artist, all places and turns seem equal in value, but not equally meaningful, and equally meaningless: he equates them in nihilism. And therefore, as the only truth that he still values, he recognizes the truth about the absence of truth, and as the only cognitive activity, he recognizes the affirmation of his passivity. The Renaissance artist needs a random perspective as an expression of his will to passivity, as evidence that he does not recognize ontology and is not interested in it. But in fact, reality is not at all random and things usually relate to each other in such a way that they turn to each other with their cognitively valuable sides. Therefore, with sincere passivity, i.e. without being deliberate, the artist has the majority of chances to vitally encounter a turn of events that is significant in relation to cognition. Hence, in a deliberately passive artist, who elevates passivity to the rule, a search for random turns arises, a planned and conscious use of such points of view in which randomness is expressed especially clearly. In other words, the artist wants to express his non-recognition of true reality, and, therefore, his true subject is now no longer the thing depicted, but he himself, as denying it. In reality there are turns, but there are no angles; camera angles come from subjectivity, as gestures of hostility against reality. Meanwhile, things have their own turns, and each of these turns expresses a special relationship of a thing to the whole world, a special ontological moment of it and, therefore, predetermines a special approach to understanding this thing. The artist cannot convey a thing from any side, because this particular turn of it may turn out to be either an unstable balance, an unclear and ambiguous self-evidence of the thing, or organize the space in a completely different way from what was imagined by the artist. And then the thing depicted in this way will disorganize the space of the work and will come into conflict with the composition that it should serve. Thus, random turns of things destroy compositional unity. The design of a thing is understood through a comparison of the thing with our own organism, or, what is the same, through the transfer of our self-consciousness and well-being into the thing, so that we feel and think about its parts, while we assimilate the organs and functions of the thing to ourselves. Hence it is clear that the most important turns in things are related to our own turns. But, however, this discussion about things in general in the present analysis of works of art is not so important, because the subject that takes precedence over all subjects, immeasurably superior to them and even exceptional in great art, was, is and, of course, will remain man himself. The rotations of things come down almost exclusively to the rotations of the human body and, partly, the bodies of animals. At these human turns, it is especially easy to understand the ontological meaning and types of turns in general: Man is the measure of things. The main ways of relating to the world, or the main turns, are fixed by language in grammatical persons: that which is addressed to the world and exhibits a corresponding way of perceiving the world or influencing it is a person. The face can be threefold: either contemplation, which embraces all of Being; either an object of someone else's contemplation and, as such, embraced by the world, or, finally, a principle correlated with the world and balanced with it. Grammatically it will be: I, He and You. As an I, the face is given by a straight turn. Being complete and embracing everything, it is the engine of everything, itself motionless. This is self-sufficient completeness, and therefore clarity, equanimity and bliss. It is not in space, but space in it. This is a person par excellence - a substance. In the order of mental activities and abilities, this is reason. As from all that has been said, it is clear that a truly worthy object, the proper object of a frontal image, can only be an absolute Person, only He who can truly say about himself: I. This is I, which, containing everything within itself, is determined through Itself and is comprehended through Itself. The face image befits only God alone. But God revealed, i.e. depicted is Christ. The supreme prototype of frontal images is the Image Not Made by Hands, as well as the Almighty Savior, the All-Merciful Savior and the Child on the icons of the Mother of God. All other faces can be depicted in a straight turn only insofar as the reflection of divine absoluteness is seen and should be expressed in them, i.e. since the artist’s compositional plan allows and presupposes a contemplative-reasonable and dispassionate, disinterested, unperturbed Self: Gods, Saints, Righteous, Sages, Infants... In this sense, every face portrait compositionally belongs to the category of icons and, therefore, the artist’s plan should include the idealization of the depicted, raising it to the divine norm, to God’s thought about it. Here the face is brought to the face, and, therefore, such a portrait should be considered as gratification, apotheosis. This is obvious in Christian church icons and in general cult images of Buddhism, Lamaism and other religions. This also includes ancient Greek and Roman funeral masks, Egyptian funeral portraits, etc., the purpose of which is to reveal in the cult the deified, rested in eternity and therefore the blessed face of the deceased, which has now become a face. It has already abandoned everything random and passionate; it has become normative through and through. This ideal appearance, considered in itself, as an object of veneration, of course, cannot be represented in any direction other than the direct one. But on the contrary, a direct image is internally contradictory, since it does not allow a halo around the face. The frontal image represents the subjectivity of a person, which should be strictly distinguished from subjectivity. Its objectivity, when it is a means and not a goal, when it is moved, but does not move, when it is a part of the world, incommensurable with it and embraced by it - such an approach to man is expressed by a rear turn. From behind, a person is thought of and perceived as defenseless, without the power of resistance and not even aware of the impending danger. Then man is only He, in whom we forget about the moment of I; in this aspect, a person is thought of only as a representation of someone else’s consciousness, but not in himself. Such a person does not require a face, it is even required that he not exist: otherwise the beginning of possible opposition would be artistically introduced into his passivity. The front image stands, it certainly stands, and it would be artistically unbearable to see it emerging from contemplation and moving forward, as if emerging from the frame: then the composition would contradict the design. On the contrary, the rear image cannot stand, because it does not have its own point of support and its own place in the world, and it goes deep under the pressure of the forces acting on it, driven by a will external to it. To stop it would mean to force the structure to fight the composition. Yes, that is from the back, servants, slaves, in general, all those in whom the artist denies personality and independent activity, should be depicted - whom he wants to present as a thing [or as] an impersonal instrument of someone else's will. For a spiritual worldview, which affirms freedom in everyone and even comprehends things from the angle of freedom and spirituality, a dorsal turn is excluded. Here both the slave, the servant, and the messenger are considered as freely determining themselves to submission and therefore, therefore, in their actions and movements, drawn towards the goal, and not pushed by reason. But Renaissance art, with the general bias of the entire Renaissance worldview towards the despiritualization of the world, mechanization and determinism, was not alien to the spinal turn. You are placed between I and He. This is an ontological turn in which the personality is a center that interacts with what is outside it, and therefore goes out of itself, heading towards something else. This is how action arises on the outside, at its source called will. In contrast to internal balance, active with subjectivity and passive with objectivity, the will is characterized by dissatisfaction and movement, although coming from within, but directed towards an external object. And only in this object is the fulcrum of the will; or, rather, together with this object the will receives balance, is balanced by the object and, therefore, puts this object before itself as something of its own kind. In other words, the will puts the object towards which it is directed, also as will, and enters into relationship and struggle with it. Thus, in this volitional aspect, the personality is no longer a whole, is not self-closed about itself, but forms a whole together with the object to which it is directed. What is depicted here, therefore, is not the person as such, but the function, his, his activity, and activity includes its beginning - the initial will - and its end - the perceiving will. With such a balance of two wills, or, in particular, two persons, a force field arises between them and movement flows; but the energy in the work moves, but the work itself is motionless and therefore calm. As soon as one of the poles of the action is weakened, or, moreover, completely destroyed, the balance is destroyed and the flow of force begins to move the work itself. Here the face, proceeding from itself by will, as if flowing from the organs of manifestation of the will, moves by itself, like a Segner wheel; but without movement relative to the environment depicted around it, i.e. being motionless relative to the entire image, it moves itself and it. If this work is written on something physically mobile and, moreover, moving in the sense to which its image leads, then such an image may be appropriate. This could be, for example, the painting of locomotives, steamships, airplanes, cars, flywheels, etc. moving parts, all kinds of crews, guns that have a certain meaning in their movement; then such a painting would contribute to the very function of the object, like a directional arrow or a hand with an outstretched finger. But if the surface on which the image is written is assumed to be motionless and has no motor function, then images of this kind would do violence to it, contrary to its nature and unbearable to the eye. The meaning of the movement that a person receives during such a turn depends, firstly, on the turn to the right or left, and secondly, on the meaning of the direction of action, i.e. depends on whether this will is active or perceptive. Grammatically, such a turn corresponds to You as a subject becoming objective (active will, i.e. active-active), or an object considered as a subject (perceiving will, i.e. active-passive, as opposed to passive passivity or pure passivity of the He aspect). I and He are each of only one kind, but You are of two kinds, and if the work is balanced, both of its aspects must be given conjugately. When demonstrating our will or perceiving someone else’s will, we turn our face to the object to which the will is directed or where it comes from. In other words, a volitional turn is expressed by a profile. Graphically, this alignment of the will specifically with the profile is clear, since it requires an imbalance in the contour itself. Of all possible turns, the profile one gives the greatest possible axial asymmetry and is therefore the most unbalanced. This leads to the need for him to balance himself with something outside himself, i.e. something that would be a mirror reflection of himself, that is, another profile. The facial and dorsal turns, already in their design, as symmetrical about the axis, are self-sufficient and do not imply an active contour outside of themselves. Here, in these turns, all the tensions and pressures of the visual force field are directed towards each other and mutually balance themselves, so that the drawing is perceived to the highest degree as a whole, in itself, without needing addition. The liberated energy flows here freely, not deflected by any center of gravity, and fills the entire remaining space, like the manifestation of a face, or its glory; in icon painting this is called “light”. The area filled with this energy, this “light”, is located physically, i.e. as a section of canvas or paper, outside the drawing, outside the contour of a given face, and, therefore, physically the face is part of the world. But the radiant energy is perceived and recognized by the glory of the face and only one of the moments of its existence; and graphically the visual energy of the contour is seen after the contour, as a consequence of the drawing. And therefore the area filled with it is understood as a whole of the work as part of the space of the contour itself, i.e. this latter is assessed as space, the whole space, and “light” is assessed as a region of the same space. In other words, the entire area physically located outside the contour in the organized space of the work is wrapped up and refers to the interior of the contour, while the contour is perceived as the limit of the entire space of the work. The above applies equally to both facial and dorsal rotations. But the meaning of the spread of glory here and there is the opposite: with a facial turn, the energy is directed from the contour, and with a dorsal turn, towards it. In the first case, the person gives, and in the second, he absorbs. In the first, it brings beyond itself, and in the second, it introduces into itself. If the facial turn is compared to the sun, then the dorsal one begs to be compared with a gaping hole in which the energy flowing there fades away; this is the black sun and the center of destruction. But in both cases there is no need for the external, and therefore no direction towards it. The ancients recognized this lack of need, and therefore selflessness and envy, as the highest ontological property, a sign of existential perfection, and attributed it to the divine world; on the contrary, constant hunger, dissatisfaction and darkness betray, according to the same worldview, metaphysical incompleteness, non-existence. Thus, here again a connection is established between worldview and graphic dynamics. In the depiction of the divine, the holy and then everything that is considered along this line of ontological perfection, the dorsal turn, naturally, has no application, cannot and should not be. And since art in general is normative, there is hardly a lot of place for the spinal turn in art in general. In its pure form, such a turn, that is, with the general withdrawal of being into emptiness, a dorsal turn, could not at all provide material for the construction of art. However, Renaissance art loved to introduce the dorsal turn, although, of course, it could not, while remaining art, stop only at it. This tendency to such a turn is a particular manifestation of perspective, which leads from each given place to another more distant one and does not give peace and clear satisfaction in any one. A rush into the distance, an eternal rush, although the distance itself is recognized as completely homogeneous with every other place. Thus, the Renaissance, having extinguished Heaven, a reality other than Earth, in the consciousness, instead infinitely expands the earth and drives it across the face of this earth, declaring in advance that nothing new will be found anywhere in comparison with its surroundings. And therefore, the aimlessness and futility of this incessant tedious wandering through boundless worlds, everywhere equally unsatisfying, is announced in advance. Whether this wanderer is called Faust (without the second part), Don Juan or the Eternal Jew, he is still the same person of perspective. The work of such a spirit, always receiving and yet always hungry, will show every being as a promising hole, that is, as a departure into an infinite space, united only by a vanishing point, or an illusory, unattainable and non-existent point in reality, with which the distance lures in order to destroy, pulling every form and dismemberment into a point of non-existence, no longer having any parts. The facial turn as such counteracts perspective. Even with the usual, i.e. Without an artistic look at a group of people facing us, we introduce a correction of judgment into physical perception and affirm the sizes of the faces as equal. On the contrary, a photograph from a group, where one of the participants would stand much further than the others and would therefore be very small compared to the others, is assessed by us not as a prospectively correct representation of distances, but from a comic or, if there is no reason to laugh, then strange and disgusting: a very small face next to a large one seems not only distant, but also somehow humiliated and deprived. Moreover, this applies not only to different people, but also to different organs, also considered like faces of one person: not a single portrait painter, the most convinced supporter of perspective, will ever dare or be able, without making the person depicted funny, to depict him with an outstretched hand or with a raised leg, according to the requirements of perspective; it will certainly increase the size of the more distant parts of the body and reduce the size of the closer ones, bringing both to what they would have been if they were in the same plane. When a photographic lens, regardless of faces and mechanically indifferent to what it conveys, shows in a photograph a huge leg or arm, or a wide knee, we are indignant at this “distortion,” although this “distortion” is the perspective projection that we have just theoretically defended. In short, even from a photograph, let alone from a work of art, we demand that it comply with the law of frontality. The hieratic art of antiquity strictly adhered to this law, and deviations arose each time only when the sacred meaning of art was lost. Similar to the law of frontality, one could also establish the law of dorsality, as the continuity of a vertical plane through the axis of the body. As has already been indicated, the dorsal image has mobility into the depths of space and carries out this removal, unless it is paralyzed by reverse perspective. In a frontal image, unless extraneous contours are introduced that disturb the internal balance, the facial image is at rest; but this is subject to its hieratic nature. However, as soon as the image loses its blissful satisfaction and self-containment, the image, even if graphically balanced in its contour, becomes accessible to the influence of the physical reality located in front of the image, and tends to go out of itself, with its energies, into physical space. He comes to life, looks, moves towards the viewer, leaving the image plane, and tries to destroy the integrity of the work and enter the world as part of the physical world. Gogol's living portrait is a type of this kind of strong, but anti-artistic images, and it cannot but be assessed as a sin against artistic truth. Moreover, the more illusory such an image is, the more convincingly it shows itself emerging from the canvas, the more definitely the viewer’s connection with it is established, the more sinful is this skillful perversion of art. Graphically balanced, such an image, if it moves, is obviously still not balanced, and it is not difficult to understand that this imbalance already relates to expression. An expressive gesture, an expressive look, if it is directed in the plane of the picture, but is not balanced by the corresponding object, this absorbing gesture moves, as indicated above, in the plane of the image and carries the image itself with it. When a gesture or gaze is directed perpendicular to the designated plane, then the graphic balance of images turns out to be powerless to delay the convergence of images from the pictorial plane, since there cannot be an object in this plane that perceives the energy of the gesture. An image that is not closed by itself and in relation to gesture is inevitably devoid of a certain plane. And it is clear that such a gesture certainly arises, since in the image of a facial turn the artist did not comply with the basic requirement - that in a direct turn gods or god-like beings should be depicted: after all, the burning of the will, the unquenched passions and therefore the greed and suffering that characterize unholiness, invariably seek an external object; and this quest is revealed by an expressive gesture. And if such an object is not located in the space of the image itself, on its plane, then, since there is unquenched lust or another passion and a corresponding gesture, the viewer inevitably assumes passions on this side of the pictorial plane, in physical space. Thus, the depicted image is associated with physical space, that is, it loses its aesthetic isolation from the outside world and therefore cannot be artistic. Nevertheless, reality is not entirely holy, and the volitional undesirable aspect of it exists, can be depicted artistically and is depicted as such, but only if one basic requirement is met. Namely: the expressive meaning of images, their functions must find their outcome in the composition of the work, but not be independent, compositionally not expressed, and even more so - violating it. In other words, the design of the work, although foreign to the composition, must be artistically clothed and expressed by the latter in such a way that nothing from the content of the work is given to consciousness apart from the visual means of the artist himself, i.e. regardless of the composition. No one can forbid an artist to depict the volitional aspect of a person, in particular, any of the passions and any of the aspects; but everyone has the right to demand that the image intended in this sense be additionally depicted, i.e. embodied by artistic visual means. In other words, the artist, having taken up the image of whatever design he pleases and freely chooses it for himself, further undertakes to be an artist to the end, and only one. Feelings and thoughts, gestures and functions, in general the entire structure must be carried through the composition and justified compositionally. In particular, the artistic integrity of a work requires that any imbalance of the image in itself find a counterweight and a fulcrum in some other image, so that the work as a whole remains motionless, no matter how rapid the movements plowing through its spaces. If an image has expression - gesture, gaze, passion, movement, etc., then this expressiveness must be expressed graphically and find a counterbalance, justified not only by the meaning of the image, but also compositionally, in particular graphically. In view of this, a profile image, where it is appropriate and corresponds to the internal makeup of the person depicted, is not in the proper sense a portrait, if by the latter we mean an image of a person or, in general, a face in itself. On the contrary, the profile conveys the action of a given person on the outside world, and, therefore, it requires somehow showing this outside world. In other words, the profile image is characterized rather by the interaction of the face and the environment. Here it can no longer be said that everything outside the contour contained by a special act of contemplation must be introduced inside the designated contour: it cannot be said that the face here is equal to the space of the entire image. No matter how significant it is, it is still only a part of this space, because the significance of a person can only be revealed with a corresponding significance of the environment it conquers. On the contrary, a strong movement into the void, a gesture or pressure without an object, as indicated above, would only disturb the balance of the work itself, and its energy would be self-destructive in the work, but it could not show the given person as a bearer of power. From what has been said, it is clear what kind of faces should be profiled in the image. Everyone understands that a soft profile, little expressed by outstanding facial features or strong movements of the will, is not interesting in the visual arts. On the contrary, direct rotation of images of faces with strong, anatomical or spiritual aspiration is unprofitable; unusual turns devalue faces, depriving them of what is in them and showing the appearance of what is not in them, i.e. making them pretentious. Regarding the profile, it is clear that it becomes appropriate wherever it is necessary to express the victory of the will over the environment. And this is power. The Tsar, Emperor, commander, leader, when they are depicted not by themselves, in their inner essence, but as rulers, should be taken in profile. These are the same heroes in the modern sense of the word, orators and public figures. The same can be the rulers of thoughts, writers, moralists, partly artists, when it is right to consider them not as heralds of truth, but humiliatedly - as usurpers of power, which, in essence, does not belong to them. However, the responsibility of the profile image is well known; and therefore, without expressing real strength, the profile simply becomes a face turned to the side, without the internal closure of the latter. Most of the existing profile images are indeed taken without sufficient expression and strength and therefore involuntarily invite comparison with a flounder, which in profile turns out to be only a crooked face. Unbearable when it comes out accidentally, this crooked face was beautifully used in icon painting of the 14th and 15th centuries. In fact: according to the meaning of iconographic images, they are required to turn a straight line (later on, special mention will be made about a three-quarter turn). And besides, this direct turn expresses the holiness of the person to whom it is given. Meanwhile, the plot of the icon may require the introduction of non-holy persons, for example, some non-holy participants in some event, for example, its spectators. To give them in a direct turn would mean to distort their assessment. But turning them in profile would lead to the need to balance them, and this would introduce pieces of foreign, unwanted and therefore earthly space into the icon. And besides, a profile turn would give them too much strength and power, which the entire meaning of the icon not only does not recognize, but even directly denies. And then those gristly, shapelessly soft profiles, like those of a baby, appear on the icons of the 14th and 15th centuries, which at first glance so strangely contradict the amazing elasticity of other iconographic lines. At first it seems incomprehensible how an icon painter, who had just drawn perfect lines, could make these profiles sculpted as if from meat, and if we assume the complicity of inexperienced apprentices here, then it is not clear why they were allowed there. But a closer look forces us to recognize the axial symmetry of these profiles. Although they are profile in the sense of a hint, they, however, have a straight line in their contour. Thus, the main compositional task of the icon is not violated by these private intrusions of persons who, by their nature, are incapable of bearing the high responsibility of a direct turn. If this same profile is drawn more expressively and more elastically, then local tension will arise, and the space of the icon - the light - will go beyond the frontal contour and destroy the spatial integrity of the icon. Everything that has been said can be verified, for example, in the icons of St. George the Victorious slaying the serpent 18. There is, however, one area of ​​art in which the requirement of a balanced profile is not respected. And moreover, this non-compliance can be noted not in isolated special cases, in simple failures and blunders of this field of art, but all the time, so that there is almost not a single example where the opposite is true. Moreover, it is in these latter cases, i.e. where the profile is balanced or where a direct or other turn is introduced, the work of this branch of art is perceived as clearly unsuccessful, sluggish, devoid of sharpness and meaningfulness. In short, there is a branch of art in which profile and, moreover, unbalancedness turns out to be the main requirement. This industry is the art of coins, medals, and partly snuff making and cameo art. It willingly depicts profiles that, through the expression of their points, act in one direction and do not have the object of this influence near them. What the profile represents here is clear, for the person depicted is a ruler and, moreover, in this case, taken precisely as a bearer of power. The coin represents state power; The medal enshrines one or another historical moment of the state or power in general. In those cases when the anniversary memory of a great person is immortalized on a medal, he is taken as a hero of a given people, and, moreover, not at the discretion of the artist-medalist, but by the collective decision of the people, state, etc.; in other words, the authorities declare him in some sense to be theirs, and the nationalized great man becomes, if not a bearer of power, then a screen for them. In the same way, a snuff box with a profile depicted on it is a gift from someone in power and represents him: the image on it does not just decorate it and is not even just interesting in itself, but is valued primarily because the person in power himself gave this snuff box and thereby handed over some ray of his power. Undoubtedly, a coin from a country far from us, a medal in memory of a person whose greatness and right to nationalization we do not recognize in any way, as well as a snuff box with a royal profile, but bought from an antique dealer or simply made to a special order, are deprived in our minds of something most essential and seem to be dead skins of a former life - internally incomplete, even if their primary master worked. In their meaning, they are manifestations and representatives of power; and when we are not aware of this latter behind them, or do not want to be aware, then something disharmonious inevitably appears before us in such things. But this disharmony is not only our subjective displeasure: it cannot be compared, for example, with the theological disapproval that we can express to the icons of a religion alien to us, but without in the least denying the internal integrity and artistry of such icons. No, we are talking about an objective assessment of the above-mentioned works with a profile, and it is objective because these works, in their very design, do not belong to pure art and, therefore, give the legal right to involve known living conditions in judging them. This functionality of these works also contains the answer to the question about the unbalanced profile. These works cannot at all be considered as images on a coin, medal, snuff box, etc. The work of art here is not a profile, no matter how perfectly it is executed, but the thing as a whole, the object as such, i.e. coin with profile, medal with profile, snuff box with profile. The profile here is only a certain moment of the whole thing, as opposed to a portrait, for example, about which it cannot be said that the image in it is only a moment of the whole thing. While for a portrait there is a frame, canvas, stretcher, etc. are only the material conditions of the work and without the image itself - everything loses its meaning, in a coin, etc. depicted in profile is one of the conditions for the function of the coin, but it cannot be said that the coin exists only for him and for his sake. In the same way, if there remains any evidence that the medal was knocked out in honor of a given person, and the snuff box was received from the hands of the sovereign, these things will retain their value, even if the image on them is erased: what is important, first of all, is the fact of nationalization or the fact of the sovereign's favor. Thus, in all the above-mentioned things we are not dealing with objects of artistic contemplation as such, but with material evidence, or, more precisely, evidence of some power. But by their very meaning they must pass from hand to hand: otherwise they cannot fulfill their function. A coin, a medal, or a snuff-box placed under glass clearly does not fulfill its purpose: it should proclaim some power from which it came, and make of its owner some secondary or tertiary center of the same power. Money exists for purchase, and only in this way is the power that the state gave me, in the form of money, revealed. The medal exalts the person depicted on it, and in reflection – me, the owner of this medal, because meaningfully, i.e. not collector's, they have medals in honor and memory of people or events to which they consider themselves somehow involved: “our sovereign”, “our commander”, “our Pushkin”, etc. - this is what every non-collector who values ​​a medal thinks and says, and when “ours” cannot or does not want to say this, then the medal retains for him only the value of the metal. The true meaning of this relationship to the medal is, of course, a feeling of expansion of one’s being through a connection with someone great and invested with power. “I own this medal not as an accidental owner, but legally, i.e. at the behest of the authorities, as a subject of his state, a member of his people, etc. And so, the greatness immortalized by the medal belongs to one or another collective “we”, and I am proud and happy that I am greater than myself, because I participate in this “we”. Similar feelings are associated with all cases of this type of profile art. Even a profile image of a dear person, especially in the form of a cameo or intaglia, contains the vesting of this person with power, even at least over the person wearing this cameo. "Ruler of my heart!" In fact, it would hardly occur to anyone to wear a cameo, even of the best work, if it depicts a profile unknown to a given person or someone alien or hostile: this shows that in a cameo we do not want to see only a beautiful thing, the further meaning of which is indifferent to us. So, the profile of the image in all of these cases is significantly determined by the objective nature of the thing on which the profile is inscribed, and, therefore, serves the function of this type of object. And their function is to proclaim the power of the depicted. In other words, resting is alien to these objects: they want to move, this is their life and purpose, but to stagnate in place is death to them. And therefore, pointed, characteristic of medals, etc. the expressiveness of the profile, unbalanced by anything, gives an impulse to movement to the entire object, and this, in view of the function of the object itself, should be recognized not only as not discrediting it as a work of art, but, on the contrary, showing the sensitivity of those who developed the coin and medal profile. In graphical order, this coin-medal profile can be considered as an arrow indicating movement. Let us pay attention: a coin lying in the hand in front of us most often gives a profile facing to the right. This means she wants to move in the direction of the profile, i.e. to the right, which corresponds to giving it back when paying with the right hand. There is one more circumstance that must be noted in relation to coins, medals, etc., and this again relates to the mobility of these things. Namely, one can ask oneself what faculty of perception these things are primarily designed for. The correct answer can only be given here when we turn to the most original and at the same time the most artistically perfect examples of medal art. And these are precisely the Greek and Roman coins. Modern coins, as is known, are minted from a flat sheet and thus assume a main plane of their image, both sides of which are separated from each other by a rim and sharp edges. Thus, both sides of the modern coin and medal exist largely independently of each other. This indicates the visual nature of modern coins and medals, which is reflected in the complexity of their composition, the fine detail of decoration, often even landscape and, terrible to say, even perspective. Modern coins and medals require viewing with the eye. On the contrary, ancient works of the same kind were minted, as is known, from a metal ball or round spool; it was crushed, and its edges continued to retain elastic and rich roundness even after minting, so that, despite being crushed, the antique coin is perceived as limited to one closed surface, i.e. as if it came from a ball. The cracks that necessarily break the edges during such minting emphasize the continuous transition of individual sections of the surface delimiting the coin. The concentration of the main mass of metal precisely in the middle part leads to a flat-shaped or lenticular shape of the entire coin and at the same time allows and even forces the image to be given a very large convexity. But the character of the surface of these reliefs is still the same - pleasantly oily, flowing, soft, without dry and sharp edges and lines, without small solitary irregularities, calmly moving from place to place and from one side of the coin to the other. More precisely, there are no two sides, just as there are no isolated sections at all, but there is a common calmly wavy and gently, albeit forcefully, dissected surface enveloping the coin. This is the complete opposite of the analytically fragmented, harsh and callous, but at the same time devoid of force, plane of the modern coin. The entire character of an antique coin clearly indicates the tactility of its space - motor tactility, and a coin can be artistically understandable only when it is perceived by the muscular sense. But the muscular feeling required here is unique: architecture involves movement with the whole body, sculpture - movement with the hand, ceramics - movement with the hand, and coin-medal making - only with the fingers. The body of touch here is not the hand as a whole, but only the ends of the fingers, where, as is known, the endings of the nerve fibers are most concentrated. So, the corresponding way of perceiving a coin or medal is the same gesture that characterizes passionate misers, moneylenders, and especially ghetto dwellers, when they enthusiastically rub gold between their fingertips. Indeed, the coin is felt here like a ball crushed between the fingers, as if melting under warm fingers, and its substance is absorbed by the organ of touch with its energies. Here there really is no thought about two separate planes of the coin, but there is a consciousness of one continuous surface, dissected in such a way that it has the desire to constantly circulate, successively passing through its sections under each sensitive point of the finger. A coin is unthinkable lying motionless in the hand or simply squeezed between the fingers: it certainly turns, and, moreover, repeatedly, moves under the fingers, we want to turn it, but it wants to be turned; and the profile of the image on it is an artistic device to impart a certain compulsion to this movement and show its intentionality and meaning. About modern coins and medals, everything that has been said could only be partially repeated. A modern coin is taken into the hand not lovingly and artistically, but only utilitarianly and out of external necessity. In contrast to the joy of touching an ancient coin, a new one leaves us cold and indifferent, and most often causes disgust. It’s hardly just a matter of the possibility of dirtiness (yes, copper coins, especially the nasty ones, are not that dirty at all, in the sense of infection); then a deeper feeling of the unkindness of a modern coin, some deep discrepancy between its surface and the touch of the fingertips. This coin doesn’t go into your fingers any more than a chemical drug that looks like food doesn’t go down your throat. On the contrary, an ancient coin, dirty at least on a par with a modern one, and even covered with a hardened crust of dirt and oxides, clings to our hands, and when it gets there, we don’t want to part with it. We value this layer of dirt that has accumulated on it over the centuries, this age-old dirtiness, these traces of countless touches, we experience direct pleasure from them and call them “the noble patina of the ancients.” It is noble because it has clothed itself with a noble surface; but a modern coin, even if it lies in the ground for however many centuries, will never be covered with a noble patina and will always be disgusting: it will not have patina layered on it, but simply dirt. Between the will and intellectual contemplation lies the area of ​​feeling. Emotions lead the personality out of self-enclosed integrity and dispassionate and disinterested worldview and lead to a volitional influence on the world, i.e. to making the individual a part of the world. But emotion as such, leading the mind out of dispassion, only inclines it towards expression of will, although it does not yet lead to this. In other words, emotion is a nascent expression of will, which, however, may not be destined to reveal itself in the world. By its very essence, as a mediator between contemplation and action, emotion is a fluid mental process, something sliding, unstable and changing. A healthy personality does not allow long-term emotions within himself, because he either refuses the corresponding actions or carries them out. On the contrary, flabbiness of character is expressed in the accumulation of emotions; such a personality has neither the power of self-concentration in pure mental contemplation, nor the power of invasion into the external world: it has neither an impassive eye nor a strong hand, and therefore gets stuck halfway, half-manifested. Ancient man, mentally healthier than modern man, knew little about emotion apart from the action that developed from it. And the ancient Hellene, relying on the structure of his own personality, developed only a dual anthropology. What is meant here is the division of mental life, common to all ancient psychology, into a rational principle and a desirable principle, i.e. on the mind and will. Feeling, as an independent coordinate of mental life, manifests itself in psychology much later, and this circumstance should be explained, of course, not by the crudeness of psychological analysis, but by the transience of the emotional stage in the development of volition: ancient man contemplated an object for a long time and dispassionately, and then, if he was inclined to action, he carried it out without hesitation and delay, without looking back and thinking, already belated. Therefore, the action of ancient man, whether good or bad, is always distinct and integral. On the contrary, the man of modern history has no conviction in the truth of his thoughts and does not trust it; and therefore, not interested in contemplation, he rushes to take action, but hesitantly and, constantly looking back, paralyzes his will. This is a person with double thoughts, and therefore with a delayed will. His dispassionate thought and powerless will thus limit his wildly growing emotions. This connective tissue of the soul structure grows here and dominates. It thus becomes the main subject of mental analysis, especially attracts literature and, being in fact a disease of the soul, is cultivated and artificially grown. Maybe sometimes she is beautiful; but the pearl is still a disease of the mollusk. It is quite understandable that figures in the fine arts were carried away by the general flow of the entire culture of modern times and, for their part, focused their attention on the emotional aspect of the individual. This is precisely how the three-quarter turn, so characteristic of the new fine art and especially the new portrait, arises. Just as emotion is a transition from contemplation to action, so a three-quarter turn is precisely a turn from front to profile. This is an internal balance that has already come out of itself, but has not yet been balanced by an external object - a person who has the desire to become profile, but is powerless to realize this desire to the end. In this sense, the three-quarter turn gives some anxiety, some uncertainty and therefore excites us, forcing us to unconsciously find out how this movement will go further. Thus, a three-quarter turn makes us accomplices of some mental process, evokes a sympathetic emotion and, thereby, the depicted person approaches us, and we approach him, as an interlocutor, like-minded person and like-minded person. A three-quarter portrait gives an impression of intimacy. This is the most clear transmission of what our time considers to be its own sign of humanity: not the truth proclaimed and not the will manifested, but feelings, i.e. subjective beginning, an area where there is no longer a self-sufficient truth, just as there is no victorious will. Modern man fell in love with his weakness, his hesitations, his infirmity, and tried to express them and show them as beautiful. Perfection, holiness, wisdom, the generally completed state of personality is not accepted by people of modern times because it requires either “yes, yes” or “no, no.” The new person prefers the search for truth to truth and methodology to achieved knowledge. Therefore, a direct turn seems too strict, not allowing one to play with itself, and the new art deviates from a direct turn not only in portraiture, but even in icon painting, introducing subjectivity and evasiveness into religion. For a new person, we repeat, it is important not to have the perfect in front of him as some norm, but to admire himself, his subtle spiritual movements, for which the truth serves only as a pretext and stimulant. “To suffer”, “to strive”, “to have ardent feelings” seems to a new person to justify life, regardless of the presence of truth or lies as the sources of all these states. And therefore the new person does not want a direct turn either for himself or for others. But on the other hand, he does not have the power to directly express his will. He is poisoned by passions driven inside. He does not dare to be openly profile: a rapist of someone else’s personality in his lusts, a new person does not want to admit his desires to himself and hides behind the haze of daydreaming, allowing desires to arise, but not allowing them to culminate in action. And he is afraid of the profile as too frank in its onslaught and therefore requiring clarity and strength. If a direct turn exposes the selfishness of the attitude towards the world, then the profile reveals the internal flabbiness and lack of integrity of the will. From this, as from the other, the new man hides behind a three-quarter turn, behind an ambiguity for which an excuse is ready: if the face is reproached for the lack of dispassion, they will say that this is not an icon, but a beginning action; if they note the delay, and therefore the powerlessness of this action, then they will refer to the non-core image. Different shades of feeling also correspond to different three-quarter turns, of which some are more objective, others are more subjective, some are more dreamy, others are more lustful. There can be four of these subtypes of three-quarter turn, and it would not be difficult to establish more definitely the meaning of each of them in particular. But questions of this kind would be too specialized for the present work. A three-quarter image, as has been said, expresses the proximity of what is depicted to the viewer and, one might say, their commensurability with each other, and the space of such an image is most akin to the space of sensory perceptions. Hence, it is clear that such a turn is used in all those cases when the artist is required to give an intimate portrait, to express a feeling, especially a tender feeling - in general, to take the pole directly opposite to monumentality. If a straight image belongs to saints, and a profile image to rulers, then the three-quarter turn rightfully belongs primarily to beauties, and, moreover, in the understanding of modern times, i.e. with a wealth of spiritual movements. This turn is primarily feminine and, more precisely, female, because emotionality develops in the female soul in particular. Of course, not only a woman can be depicted in three-quarter view, just as not only a saint or a sage can be depicted upright and not only an emperor in profile. But when depicting anyone in a certain turn, the artist by the very turn brings the depicted person, whoever he is, under a certain ontological aspect, and as a result, if he wants to remain true to himself and maintain artistic integrity, he is forced to bring forward in this person elements of the corresponding psychological type, emphasize them and, conversely, abstract as much as possible from all the others that do not correspond to the chosen ontological aspect. If so, if a turn of the line has already been chosen, then the artist needs to show as much as possible the internal integrity, contemplation and self-sufficient dispassion of a given personality; otherwise, instead of a portrait, you will end up with a caricature, which actually acts as a kind of deliberate internal contradiction. But it may happen that the artist will not be able to grasp eternity in his face, or this side of reality is expressed here too vaguely. Then the direct image is doomed to failure in advance, because a different turn was required. In other words, although not only a saint can be depicted in a straight turn, he is also depicted as a saint, idealized in the direction of holiness, and the artist’s job is to show the legitimacy of such idealization. In the same way, a profile image can be not only an emperor, or another ruler, but also many others. However, whoever is depicted in this way, since he is turned in profile, it is necessary to give this profile strength, expressiveness and clarity, to give him energy and power, without which profile would be only a ridiculous pretense. Here the facial features should also be idealized, but along a completely different line than in the case of the front. The same face, when depicted straight and in profile, is worked out by the artist in a directly opposite sense, as if split into two polar opposite faces. And if the artist does not understand the need for this, then it would be more useful for him to work on signs. So, like what was indicated, faces can be depicted, generally speaking, in three-quarters. And this turn, like others, is not an irresponsible external form that can be applied, leaving in the future the complete arbitrariness of all one’s actions. The artist is not forced to stop at this turn. But if he stops, he, by the logic of things, undertakes to remember that this turn makes its own demands on him, which must be satisfied. Otherwise, he would have looked like a painter smearing with his elbow what he painted with a brush. In this case, the three-quarter turn suggests and requires a forward movement of emotions, some dreaminess, and especially combines well with tenderness or melancholy. Cuteness or generally pleasantness, in one sense or another, should not be absent from such an image. A face strong and with strong impulses of will, when depicted in three-quarters, should be softened and, so to speak, inhibited in its impetuosity. Children's faces ask for a three-quarter turn. On the contrary, the application of a certain specific twist in the case where the aspect of the personality is established in advance by the purpose of this application leads to a struggle between two forces, the own strength of the given twist and the strength of the work as a whole where this twist has found its application. Such a struggle between two forces mutually weakens them and makes the work sluggish. A striking example of such a failure is the anniversary Romanov ruble, or the actual medal in memory of the tercentenary of the House of Romanov in the form of a ruble. It is clear that the purpose of this medal is to condensedly express the greatness and power of the royal family, which gathered and governed the great power. This is a clot of power, more powerful than what each of the kings of this family had and can have separately. This is the power of the clan as a whole, which held by its will a three-hundred-year section of Russian history. This power was powerful; but even if it were not such, then the very meaning of knocking out a medal should have led to the expression of precisely this side of the matter. If the artist does not feel the power of Russian statehood and the power of the House of Romanov, if he does not see the power center of Russia in this House, then he cannot and should not take on such a medal, because the medal, by its very purpose, expects this very word from the artist; In this case, the artist has no choice at all to say this or that word, but only the opportunity to say a certain word, but more or less expressively, more or less vividly, and the more expressively and vividly it is said, the more successful the work itself will be. Everyone remembers to what extent the meaning of this medal is actually distorted. First of all, the very character of the sculpting, which claims to be tender, is flat, barely visible, blurring like a ghost. If these two portraits, of Tsars Mikhail Fedorovich and Nikolai Alexandrovich, were supposed to depict a melancholy dream of the dearly loved dead, then it would be possible to discuss how successful they were. But in this case, these foggy ghosts, bloodless and powerless, can only ironically be passed off as images of kings. Moreover, there are two of them, but they remain just two, neither compositionally nor even plot-wise showing their unity, as representatives of a single clan and a single power. The most unfortunate thing is the three-quarter turn of both faces, giving them the appearance of weakness, inner lethargy and daydreaming. Perhaps such images have their merit as a home portrait, for example, for a medallion. But, of course, they distort the meaning of the medal and talk about the Russian state as an empty ghost. There is no doubt that if the rulers of Russia had only the aspect depicted on the medal, the Russian state would not have existed not only for three hundred years, but also for three months. The function of different turns of the face and figure in the image is determined directly - by the very form of what is depicted, i.e. on the plane by the direction and curvature of the lines. The front and rear, as indicated, are on their own, i.e. with their essays, give the impression of balance and therefore self-closure, while the profile is also in itself, i.e. by the asymmetry of its outline and the sharpness of its unbalanced protrusions, it gives a forceful onslaught in one direction and thereby creates a force field outside itself. But it would be one-sided and poor to dwell only on this formal graphic approach and limit the design of the human face and human figure to the relationships of lines in the image. After all, a face does not become constructive only from the work of the artist, but also has its own design in itself. The geometric design of the face and of a person in general, its spatial form, expresses outwardly the complex relationship of all the internal forces and activities of the body. The geometric surface of the body is the final resultant and the result of everything that happens inside a person, analytically, physiologically, mentally, and even spiritually. Thus, this or that expressiveness of the known lines of the drawing, although it speaks for itself in the drawing, however, this does not prevent it from repeating at the same time a certain self-testimony about itself of the organism. If a certain organ or gesture expresses something with its graphic design, then this does not destroy the inner word of the organ or gesture itself, as a manifestation of life. Artistically, these two languages, which coincide in their meaning, the language of lines and geometric forms and the language of organic processes, support each other and mutually reinforce each other. In other words, the graphic significance of different turns is at the same time expressed in the language of physiognomy. Each of the organs, especially the face, is connected, as everyone knows, primarily with one side of inner life and testifies especially to it. The turn lies in the fact that some organs are emphasized and the energy of others is weakened. In physiognomic order, each turn is a special characterological section of the personality, bringing forward a certain group of abilities and activities that is complete in itself and shadowing others. We can say that every turn is a certain idealization of the human appearance, and the direction and meaning of this idealization is exactly what is indicated above when considering different turns. It would be possible to analyze in detail the order of organs, facial features and facial expressions, from which elements the holistic meaning of each turn is formed. But this would lead us away from the direct task of our presentation, and therefore we will only explain the general considerations expressed with two or three particulars. Let's turn to the face. It is clear that with a straight turn, the oval of the face, the shape and size of the forehead, eyebrows and, most importantly, the outline of the eyes and mouth become especially clear. There is no other turn that would give better visibility to these organs. On the contrary, the nose is flattened by a frontal turn, loses its definition, and, looking only straight, it is impossible to give oneself an accurate account of the shape of this organ. In the same way, the shape of the chin, the protrusion of the jaws and lips, the degree of development of the brow ridges, the facial angle and the entire position of the head remain completely unclear and, as it were, erased. But all these facial features are established with the greatest confidence when the face is viewed in profile, while features that are advantageously observed when turning straight are hidden by the profile and become indistinct. – A three-quarter turn does not provide the greatest visibility either to what is seen from the front or clearly seen in profile; but, yielding each individual organ separately to both previous turns, this turn has an advantage over them in the breadth of its scope: here, although not in the greatest expressiveness, the greatest number of individual features and organs speaks about itself. The three-quarter turn is not the most typical cut of the human personality, but it best conveys the average and therefore the most common everyday impression of it. Added here is some of the own content of this turn, inaccessible to others, but essential in understanding a face, especially a gentle one, rich in possibilities that have not yet been revealed, and not worked through life to a poorer, but more defined coinage. This is precisely a line, the anatomical meaning of which, it seems, has not yet been clarified, but which is assessed by immediate consciousness as giving a lot for understanding tender and difficult to name character traits and manifestations of inner life due to their fluidity. This line could be approximately defined as an edge formed by the intersection of the frontal plane of the head with the side; it runs along the church, touching the outer end of the eyebrow, passes close to the corner of the eyelids, then through the top of the cheek bone and along the cheek to the mandibular bones. It can be more clearly characterized as the boundary along which the face itself would have to be cut out if one wanted to take it out as a mask. When turning three-quarters, the shape of the face is given precisely by this line. Now, even from what has been lightly sketched here, it is not difficult to calculate the physiognomic composition of the different turns. In fact, the general outline of the face, which determines the dominance of the upper or lower part of it, the forehead, eyes, together with its addition - the eyebrows, are associated primarily with the ability of contemplation and express the life of the mind. This is visible when turning straight. Here is added an outline of the lips, the calm of which and equanimity with passion constitute a necessary condition for the spiritual balance of intellectual life. Seeing the lips in this case is necessary to ensure oneself confidence in the unshakability of the mind by those impulses that are expressed through the mouth. It is necessary to see them in order to be convinced of their obedience, and eyes without a mouth, by themselves, do not give anything solid and reliable. On the contrary, the organs of will and passion - the nose and jaws, the organ of volitional self-determination - the chin, the lower intellectual functions expressed by the superciliary arches - all this is erased, hidden, obscured to the point of invisibility by a face turn. The position of the head, expressing the strength of self-affirmation, is hidden in the same way. The profile, as indicated, emphasizes all these organs. Its width is hidden in the forehead, but the brow ridges are visible. In the eye, its contemplation becomes invisible, but the gaze is more expressively shown, as some kind of action. The mouth is again represented in its movement, and the nose and chin reveal will. Finally, the entire position of the head characterizes a strong-willed attitude towards the outside world. If the movement of the hand is also added here, then its offensive moment can only be given in profile with the greatest expressiveness. With a three-quarter turn, the organs of contemplation and the organs of will are visible to varying degrees, and in this sense this turn can be called balanced. But, being organs of opposing mental activities, they turn out to be weakened by their equal expression. That is why spiritual movements, barely perceptible in themselves and not clear, not drowned out by stronger and more defined ones, now become intelligible and receive an organ of expression in the above-described temporo-buccal line, like the boundaries between the front and the profile. As such, this line expresses subtle spiritual properties and, easily changing along with a person’s current state, is capable of conveying the ebb and flow of his emotional life. Until now, we have discussed the force fields of works of art as independent of time. This made it possible to approach the question of fields in a simplified manner, and the conclusions obtained can now be expanded and deepened by new data that have been deliberately omitted so far. We are talking about time as the fourth coordinate, or the fourth dimension of reality; Of course, this fourth coordinate should not be completely omitted in works of fine art. But on the other hand, this fourth coordinate should not be considered indifferently similar to the other three, especially since they themselves, each separately, have their own uniqueness and are not at all confused with each other. Both in reality itself and in its images, certain coordinates can be predominantly expressed, and different historical centuries and different artistic styles tend to notice and put forward a certain or specific coordinates. One can even say that the most important basis for the stylistic originality and artistic spirit of the century is determined by the choice of the dominant coordinate. Thus, in Egyptian art and especially in the art of the Stone Age, length and horizontal were clearly dominant, and Egypt began to introduce, but very subordinately, height. Greek art is characterized by a complete balance of length and height, i.e. horizontal and vertical, and the depth is outlined, but subordinately. Christian art advanced the vertical and gave it a significant predominance over other coordinates (we are not talking about the time coordinate at all yet); The Middle Ages strengthened this stylistic feature of Christian art and gave the vertical a complete predominance, and this process is observed in Western medieval architecture and in Eastern medieval fresco. Renaissance art, having made an attempt to return to the Hellenic balance of vertical and horizontal, does not stay here and gradually makes it dominant - depth, which grows into immensity and evil infinity, gradually clogging up all other coordinates, initially among them there is, as a relic of Gothic, a certain predominance of the vertical over the horizontal. So, each coordinate has one or another expression in this or that art and manifests this or that spiritual aspiration of the era. This one circumstance alone should suggest different ways of perceiving, understanding and depicting time, depending on the spiritual character of the era. But before discussing these methods, let us understand to what extent time is actually connected with reality and our perception and assessment of it. Everyone, of course, knows that reality is in time, just as we ourselves are in time, and that, therefore, all our perceptions and assessments of reality are connected with time. But, although this is known to absolutely everyone, the essentiality of this penetration of all reality by time eludes almost everyone. The connection with time seems to be some kind of accident, from which, with the proper effort, one could, if necessary, get rid of it, just as one can wipe off a layer of dust that has settled on it from a thing. Time seems, unlike the other three coordinates of reality, to deny which would mean moving away from reality - time seems to be some kind of misunderstanding, and an attempt to abstract from it is an approach to a more accurate knowledge of reality. Everyone knows that the measurement of quantities occurs in time, but almost no one thinks about the significant consequences that follow from this. Everyone also knows that the perception of reality and the thought of reality take place in time, and knows about the time of mental reaction and other durations that characterize the life of our psycho-physical organism. But it seems to everyone in immediate self-awareness that this slowdown occurred only this time, due to some kind of weakness, absent-mindedness, and in general - reluctance to make an effort, but that he has another time in reserve for the future, when he does not fail and will perform the same action without the slightest slowdown, i.e. untimely. This recognition of oneself and in general of the reality of timelessness, if not actual, then at least possible, expresses some deep truth, but vaguely felt. Taken literally, this self-consciousness is false and arises from the transfer of spiritual truth into an area alien to it. Now we are discussing precisely this latter, and therefore we will talk not about the truth of this self-consciousness, but about its falsity. This falsity lies in the reinterpretation of the processes of our cognition as knowledge of the divine: although no one will formally attribute to themselves divine omnipresence and, resulting from this, omniscience, as a direct holding in their minds of the entire world reality, they half-consciously accept the premise about the metaphysical nature of their cognition, and evaluate the physical processes involved in cognition, although without fully realizing it, as something allowed by weakness, as a crutch of cognition, fundamentally speaking, can be eliminated. If this were really so, then we could indeed make instant mental views of the universe, sections of it perpendicular to the direction of time (assuming a single time for the universe to exist), and give, as it were, instant photographs of the world. In other words, we could then construct differential equations of the world. But the fact of the matter is that this entire circle of premises and thoughts is fundamentally false and, contrary to the religious understanding of life, is at the same time incompatible with direct evidence of reality. Every real process occurs in time and has its own duration. Every measuring and other instrument has its own, in a broad sense, inertia and therefore its own delay time: the readings of no instrument can be considered instantaneous, and the instrument certainly lags behind the process it measures. Every observer has what astronomers call a personal equation, i.e. in its perception, in its consciousness and in its required reaction is delayed in comparison with the readings of the instrument. True, the processes of nature can be accelerated by the creation of certain conditions; the delay of instruments by improving them can be limited, just as the personal equation of the observer can be reduced by a favorable physiological state, the cultivation of receptivity and efforts of will. But the limit of this reduction in duration in all the indicated cases is by no means zero, but each time a certain finite value that follows from the essence of the matter and therefore cannot in any way be neglected as infinitesimal. Whether it is large or small in each individual case is indifferent in a fundamental discussion of duration, as an essential and irreducible feature. When we talk about physicality, i.e. three-dimensionality, every thing of the external world and we fundamentally deny the physical reality of things of one or two dimensions, then there is no limitation at all introduced here, as if the size of a body in one or another dimension must be no less than some value: whether a given dimension of a thing is large or small, it exists and is not reducible to the other two. We consider things about one or two dimensions to be abstractions. The situation is exactly the same with the fourth dimension - in time: every real object certainly has its own duration, large or small - it doesn’t matter. But it certainly exists, it is thickness in the fourth coordinate, in time, and the object is only three-dimensional, i.e. zero duration, zero thickness in time, is an abstraction and cannot in any way be considered part of reality. But such, in addition to the impossibility of being actually perceived in experience, could not be conceivable, since the very processes of thought, i.e. real thoughts, flow in time and themselves have their own duration and sequence of their elements. Various physical processes that serve to understand the world occur at different speeds. Where the speed of the process is very low, we inevitably take it into account; but, annoyed by the slowness, we do not bring to our consciousness the essential participation in knowledge - time, because we usually have in reserve some other process, faster and, moreover, at a speed that no longer tests our patience; and if we don’t actually have it, then we calm down at the thought of the possibility of such a thing. In other words, we are accustomed to the idea of ​​​​the possibility of significantly speeding up our cognition, and the processes at our disposal usually turn out to be quite fast in practice. But this sufficiency, correlated with the requirements that we impose on experience, can always turn out to be unsatisfactory. Thus, at a certain pace of life, the slow communication between countries, which is achieved by rare embassies, is also satisfactory: here the dialogue between states stretches out for years. The post and railway greatly speed up this exchange of thoughts and desires, but the satisfaction or unsatisfactoriness of this speed, like any other, depends on the distance. So, an ordinary conversation, i.e. Sound signaling is assessed in everyday life as having no slowdown on the part of the signaling itself: we do not take into account the time required for the passage of sound from the speaker to the listener. Perhaps we would not take it into account when using an acoustic telephone. Echo and resonance already give us a sense of the duration of the sound process. And if acoustic signaling, for example, by shots or corresponding amplification of sound during transmission and reception, were applied to negotiations between cities, then even relatively close cities, like Moscow and Petrograd, would lose patience with the slowness of such a conversation. To the above question from Moscow, the Petrograd answer could have been heard no earlier than after (...) 19 hours. And therefore, the shortest conversation would last about a week. Sound transmission is the fastest process we use in everyday life. However, as we see, even the spread of this method of communication within one state shows its complete unsatisfactoryness. We are usually not afraid of this slowness of the sound message, because we have in stock the telegraph and telephone, the time delay of which we consider negligibly small. The transatlantic cable undermined this abstraction about the instantaneity of telegraph signals: each individual signal required (...) 20 minutes to communicate across the ocean, and therefore the transmission of telegrams occurs with intolerable slowness. However, even here, those who want to think of the duration of the processes of cognition as something insignificant and removable, do not give up and point to an incomparably faster process, to electromagnetic waves propagating at a speed of 300,000 kilometers per second. Consequently, at the service of cognition there are light, infrared, ultraviolet and all kinds of electromagnetic signals in the narrower sense of the word, i.e. waves of relatively long length. Indeed, it is so. But with this speed of 300,000 kilometers per second, the limit of signaling speed has been reached, and we not only do not know any faster processes and cannot assume the possibility of such, but, on the contrary, as the most essential foundation of modern physical knowledge, we must deny even the most remote possibility of discovering physical processes faster than the spread of electromagnetic perturbations. Of course, their speed seems quite sufficient in everyday life; however, even she is like this only with a certain scale of desires. If we take into account in a businesslike manner the conversations about interplanetary and interstellar communications and see in such plans not only fantasies from idleness, then the speed of light will suffer the same fate as the speed of sound. Already communication with the Sun, i.e. receiving a response from there to the sent request would have required more than a quarter of an hour, and a similar response from the nearest star (let’s pretend that we believe the astronomers) would have been received only after seven years. Communication with most other stars requires thousands and even millions of years. As we see, the thickness in time of even the fastest phenomena is clearly reflected here, and there is no possibility of thinking about it as negligibly small. Thus, every part of reality, even purely physically, has its own thickness in time and cannot in any way be discussed as three-dimensional. What has been said will be strengthened immensely if we take into account the physiological, psycho-physiological and psychological aspects of reality, as perceived in genuine experience. Here, all the more, reality must be recognized in all its parts and individual formations as four-dimensional. Perhaps the general idea of ​​the abstractness of timeless objects is quite easily accepted. But it does not meet with opposition, partly because the specific meaning of this type of reasoning is not sufficiently weighed. Meanwhile, he is far from indifferent. After all, then individual perceptions of this or that object, i.e. those in which the temporary thickness, duration, is vanishingly small, do not correspond to the true image of the object just as much as the cross sections of a tree trunk do not give the image of the tree as a whole. True, from microtomic slices of some object one can imagine an image of the object itself, but this requires the presence of a third dimension in consciousness, and even then such a restoration of a three-dimensional image from its thin slices is very difficult. If the representation of the third dimension is absent, or, what is the same, if spatial imagination is not developed at all, then no effort can be taken to unite all the slices into one integral spatial image, and many of them will remain scattered, and each slice will be in the representation - on its own. This is precisely how every concrete image of reality in the consciousness of the majority is split into slices, cut perpendicular to time, and they do not even bother to collect in their consciousness all such slices, or at least many, but snatch out at random or arbitrarily this or that cut. And the idea of ​​reality turns out to correspond to its true image no more than if we replaced the image of an oak tree with the image of its sawing, or the human body with the sawing of a frozen corpse. Here the word “inaccurate” would be completely inappropriate, because visually there is simply no direct transition from the view of a section of an object to the view of the whole object. The same should be repeated about the section in time. Let us make one clarification, however. The cut of a tree, speaking quite strictly, is not a two-dimensional image: the unevenness of its surface and some transparency of its substance give us a third dimension of the tree trunk, but very weakly, so that in comparison with other dimensions we can consider the section only two-dimensional and neglect the third dimension. In exactly the same way, the cross-section of reality in time, according to our very perception, cannot be exactly contemporary or simultaneous, i.e. necessarily has different time characteristics at different points, we consider and are aware of different parts of the image not at the same instant. But, compared with the duration of the entire object as a whole, these temporary irregularities in our perception are very insignificant, and we neglect them and consider all perceptions to be contemporary in all their parts. There would be practically no obstacle to considering these fluctuations in the time coordinate to be infinitesimal, but logically they should not be overlooked if we do not want to significantly distort the understanding of reality. So, all reality is extended in the direction of time no less than it is extended in each of the three directions of space. Every example of reality, once it is actually perceived or truly accepted, has its own time line, and each point of its abstract statistical section is in fact a point - an event. In other words, every real image has four dimensions and is, if we talk about it as a whole, a certain formation of four-dimensional geometry, i.e. not a body, but a super-body or, in the terminology of N. A. Gulak, a body-body. This body-body has its own geometric shape, which is just as significantly different and even incomparable from what we usually call the shape of a body, just as, for example, a cube or octahedron does not resemble a parallelogram obtained by cutting them, or an ellipse does not resemble a cone. It is necessary to be fully imbued with the thought of the decisive dissimilarity of the image of the real, i.e. its four-dimensional and three-dimensional cross-section, usually taken as the shape of an object. The microscopist, cutting his preparation into slices, tries to determine their possible fineness, i.e. about the possible weakening of the third dimension. And the analytical scientific and everyday consciousness of an intellectual, when clarifying the image of reality, tries in every possible way to abstract from duration or possibly limit it in order to possibly exclude its fluidity from the image; the subject of research is nailed down in order to at least approximately delay its processes. The microscopist needs his efforts in the indicated sense under the conditions of modern microscopic technology; but he does not delude himself with the hope that the true structure of the object will be represented most accurately by such a technique. On the contrary, when they try to eliminate the fourth dimension, what is meant is not only and not so much the research technique, unfortunately, currently irremovable, as the truth of the image obtained by such a technique. These three-dimensional sections, like two-dimensional microscopic preparations, with regard to their shape, we repeat, do not have anything similar to the image of a solid object, and there is no direct visual transition from the first to the second. But the cuts undoubtedly provide material for abstract conclusions about the shape of the whole image and in this sense can serve as a basis for knowledge of the latter. In some cases, this basis turns out to be sufficient or approximately sufficient for a complete understanding of this latter - when the time lines of all points of this image are identical to each other. This means that the subject under consideration does not change over time, and, as they usually say, does not depend on time. But from this it would be too hasty and downright false to conclude that the true form of such an object should be considered its three-dimensional image. Such a conclusion would be as false as if its cross section were recognized as the true shape of the cylinder, since it is the same everywhere. Objects of this kind, unchanging or, more precisely, practically unchanged over a certain period of their existence in time, we repeat, can be compared in the region of three-dimensional space - with cylinders and prisms, and in four-dimensional geometry they are called (...) 21. The visual comparisons that arise here are rocks confections, Venetian beads, cut from cylinders, the contents of which are built in parallel with stretching colored threads and fibers. One can also compare such hypercylindrical forms with wooden blanks in the form of complex cylinders, the cross-cut of which produces figures of people and animals - a common method of production for handicraft toy makers. Beautiful patterns and even pictures obtained in the cross-section of sweets and beads, and the familiar views of people and animals when cutting wooden blocks make all these sections closer and more understandable to us than the cylinders from which they are cut. But this does not yet mean the actual primacy of sections over cylinders, for cylinders exist on their own, and sections exist only in them and could only be taken from there abstractly. More precisely, every section, taken by itself, is still only a piece of a cylinder, and itself is a cylinder, even a very low one, so the structure of the piece, or its shape, can in no way be reduced to a qualitatively foreign and qualitatively more elementary type of flat pattern. In the same way, the true form of any image of reality, even if we consider it unchangeable, is a super-cylinder, and not its three-dimensional base. And, in particular, a person, at short intervals of his biography, when he has not yet had time to noticeably change, should be compared in appearance to the aforementioned wooden block, and not to its cross-cut. Generally speaking, cylinders are an exception among three-dimensional bodies, and, taking a body at random, we have no reason to assume the identity of all its sections parallel to each other. Moreover, taking at random some image of reality, i.e. four-dimensional, we, without sufficient data, would begin to count on an exception here, namely, on the identity of all its three-dimensional sections, and the probability of such an identity understandably decreases with an increase in the number of dimensions. Over time, this three-dimensional section changes, and its time lines converge and diverge from each other. Here, a solid four-dimensional image can not only be constructed from a separate section; in order to even abstractly understand a whole four-dimensional image, it is necessary to know many sections of it at different times. Usually we do not think about this difficulty, because most often we isolate from a holistic, in a four-dimensional sense, image only that part of it where it changes relatively little over time; and we neglect areas of significant change and areas of turbulent process, mentally disengaging from them as something external and not belonging to the image itself. True, each process may have the most significant stage, and then we recognize this segment of the process as dominant over all others, in a certain sense - the purpose of the existence of all others, and then this stage is assessed by us as the entelechy of the entire process, as a symbolic representative of the four-dimensional essence. In the language of the ancients, we may apply here in an extended sense the term ἀκμή, flourishing, originally applied to human life. Ἀκμή of a person comes, according to the views of the ancients, approximately at the age of forty and expresses the greatest fullness of strength, bodily and mental, achievable by this person, the greatest harmony of the personality, the most magnificent and complete disclosure of its capabilities. Just as in a three-dimensional cross-section of a person, his face expresses him most, i.e. In comparison with other organs and parts of the body, it can most fully represent the whole person; just as in a four-dimensional holistic image, a person represents a certain period of time, about forty years, according to the ancients, for his entire life as a whole. In a plant, the flower is perceived by us as the pinnacle of its organization, a symbolic substitute for the entire plant, and the classification of plants takes into account primarily the flower among all organs and parts of the plant. But the fact that in a three-dimensional spatial image there is a flower in relation to the entire plant - in a holistic four-dimensional image of the same plant as having a duration in time should be recognized as the time of flowering: and it symbolically replaces the entire development of the plant. This substitutive symbolism of a certain stage of development is reflected even more clearly in the four-dimensional image of a butterfly, with all its transformations. Gren and the caterpillar, and the pupa, and, finally, the fluttering butterfly - these are not four different images, but one image, with very bizarre time lines. But, no matter how [incompatible] a fluttering flower is with the appearance of a voracious worm, it is nevertheless one image, the temporal sections of which are extremely dissimilar from each other, but, however, are inseparable from each other no less than the front and back parts of the same butterfly. The time coordinate is at least as unifying as the other three; You cannot cut a caterpillar along its length, but you cannot divide it according to its temporal depth. But even here, with this indivisibility of the integral four-dimensional image, the lepidanthera stage is perceived by us as ἀκμή of the entire image and symbolically represents the entire image. And so - not only in the everyday consciousness or in the assessment of poets and painters, but also biologically, for the classification of these creatures refers almost exclusively to the winged stage. The butterfly is the entelechy of these creatures, their soul, which has appeared openly. Not only a person has ἀκμή, and, moreover, about each of the coordinates, but also an animal and a plant. Every thing has its flowering, the time of its most magnificent opening, its ἀκμή. when she especially fully and especially completely represents herself, in her four-dimensional integrity. Everything has its own peak in time, just as there is a maximum size in each of the other three dimensions. Nothing has infinite dimensions, neither in length, nor in width, nor in height, and absolutely everything, no matter how large it is, ends somewhere, just as it has a beginning somewhere. This statement is acceptable to everyone, because everyone knows about the extent of everything visible - in space. But time is often not recognized as a necessary condition of everything that exists in the world, and therefore the possibility of boundless existence seems natural, which, if it ends, is only an unfortunate accident: in fact, since the coordinate of time is not necessarily included in the characteristics of a given image, then it does not have duration in the proper sense of the word, and therefore there is no internally determined process in it, with its temporal divisions, with its ascents and descents, with its beginning and end. Relatively recently, in the sciences of inorganic nature, the expression “preserves indefinitely” was constantly encountered, the true meaning of which indicated infinity and possible infinity, unless something external happens that destroys a mineral, rock, chemical preparation or some thing. This idea of ​​​​indefinite duration was also carried out in biology, when the infinite longevity of many trees was proven, and in any case this longevity was implied when discussing the life of the species, plant and animal, and generations were represented as repeating the same cycle to infinity, since there were no external agents of change. Just as all mechanics ignored duration, so did natural science not take it into account. As the most striking teaching about the timelessness of the world, i.e. denial of the process as such, one should call Darwinism: here the life of the species, in itself, seems absolutely independent of time and the species has no history, for every change occurs by the force of an external impulse, not connected with the life of the species and therefore random, i.e. may or may not exist. There is nothing to say about the falsity of such constructions. A biological genus has its own history, i.e. its own time line, just as it is characteristic of an individual member of the clan. External conditions can cause a distortion of an internally intended time line of a given kind, they can bend it, just as a tree trunk is bent by a protruding rock or a plant stem by a stone pressing down on it. But the law of development, i.e. the form of time lines has its own invariant, and the race will not give it up and will not be able to abandon it, except at the cost of its own death. The law of time is characteristic not only of the phenomena of life, but also of everything that exists in the world. The words “indefinitely long” actually mean “very long compared to the duration of the experiment, so that the law of time has not yet been clarified for this phenomenon.” There is no need to talk about colloids and dispersed matter in general: it is well known that these substances are in a constant process and, with an internal necessity determined by their very structure, go through successive stages. But crystals are also subject to time, first growing and folding, and then slowly decomposing, just as any substance decomposes and disintegrates. But, since in all beings and things of reality some kind of fall, some kind of decomposition and, in general, a movement towards the border in time can be established, the necessity of the existence of a point of flourishing, the top of the line of time, to which there was its rise, its growth, from some beginning, is also established. This is the ἀκμή of a given thing or a given image, and it, as said, represents to us the thing as a whole. The flourishing of a certain process represents the whole process. That's true. But it is necessary to firmly keep in mind the symbolic nature of this representation and the decisive falsity of the simple substitution of the entire image as a whole by it, even if it is the most significant, temporary section. Already the classification of plants by flower suffers from one-sidedness, which may not be distorting and harmful in the modern way of natural science, but undoubtedly deprives the holistic image of the plant of proper specificity and completeness. A rose, the most lush one, is not like a whole rose bush, and even less so is a cut-out rose. But a blooming rose bush is not like the whole life of a bush, from seed to degeneration, and finally drying up, with its growth, the change of leaves, the appearance of buds opening, and then falling off and the ripening of new seeds. Everyone understands how one-sided and meager the idea of ​​a plant organism would be if we knew nothing about its growth and drying out and if the plant were an operatic, invariably flowering bush. The rhythm of its life, its greening and hibernation, the appearance and disappearance of flowers, this whole process, like the music of an image, is infinitely fuller and more beautiful than a flower taken in isolation. What has been said about the holistic image of a rose bush must be repeated about any process, about any development. A single moment captured separately does not show us a complete image of a thing, and many such moments will not show it to us, as long as each of them is taken separately and the form of the phenomenon along the fourth coordinate is not captured. Just as a three-dimensional image will become a spatial form for us only when its parts or, more precisely, sections of it are perceived not each in itself and located only outside the others, but when they are permeated by a single law of structure that we recognize, connecting them, so a process in time must be formalized by a single law, which is, in its specific application to a given sequence, a form in time. Thus, trying to imagine the image of a certain person, we would act falsely, snatching out a single moment of his life, but it would be no less false to tell his biography as a chronological sequence of individual events. If the description of an ear or nose does not yet provide an image of a face (although it does provide an experienced physiognomist with material from which he can draw abstract conclusions about the face), then a consistent description of the organs will also not show us the face as a whole: here it is necessary to grasp the single law of a given face. The same must be repeated [about] three-dimensional biographical images, whether to take just one of them or take many of them, simply following each other. The appearance of a person can be shown only through the single law of his life, from the cradle to the grave, i.e. form of personality over time. And here, no matter how important the flourishing of the personality is, it only symbolically hints at the whole, but does not at all cancel its entire growth, as well as its decline. Each state itself is directly related to the holistic image of the personality, and not at all through the medium of ἀκμή; and each age in itself is valuable, as demonstrating integrity, and only service value does not matter, as a condition or stage of flourishing. Each age in itself, and not only in relation to tomorrow, expresses the four-dimensional fullness of personality, and expresses it in its own way: no matter how expressive another age is, it cannot express what is given to this one. And therefore, no age is canceled out by another. There are days of our life that are more important, more responsible and more characteristic biographically than others; There are also ages that are more noticeable in various respects than others. And yet we live today not for tomorrow, but for today, or more precisely, today, and tomorrow, and the day after tomorrow, we live for the sake of wholeness, not exhausted by a single day, but at the same time symbolically signified by every day. The task of the biographer is to show this integrity. In a three-dimensional image, certain lines and surfaces can diverge, and in some cases, voids, cavities and recesses are formed in a three-dimensional body, making the surface and volume of a given body a multi-connected space. This partial separation of the regions of a given body can go further, so that the voids themselves become multi-connected volumes. But the existence in the body of areas not occupied by the body itself does not yet destroy the three-dimensional unity of the body, although its two-dimensional sections will break up into two-dimensional sections disconnected from each other. In fact, in a solid three-dimensional image, from any point of it there are ways of communication with any other point that do not lead into the void beyond the boundaries of the medium that fills the given body. And therefore, being only an accumulation of scattered slices, if we talk about a given body, remaining in the plane of a two-dimensional section, this body, with three-dimensional contemplation, is a single image, one whole, and we do not experience any obstacles in seeing and thinking like that, for we are clearly aware of the unity of its forms. As a clear example of what has been said, let us again take a plant, let’s say a tree. We see it as an integral spatial image and recognize it as a single organism, a phenomenon of one organic form. Does the existence of an internal void or hollow in the trunk interfere with this? Does dividing the trunk into many roots and roots in one direction and into branches, twigs and leaves in the other prevent this? Meanwhile, a flat section of a tree in the area of ​​the roots or at the height of the crown produces separate round and elliptical slices that are in no way connected with each other. Even if we don’t talk about a two-dimensional cross-section or a cross-section, albeit three-dimensional, but still thin, then even then staying only in the region of the end of the roots or at the top of the crown would give an idea of ​​​​many organic formations, very similar to each other, but not a complete image of a single organism. Perhaps, by studying the structure of bark and wood and establishing the identity of the chemical composition of the substances of these individual formations, and noticing the simultaneity of life processes in them, a researcher in these areas would begin to guess about the essential unity of the organic world he observed. Perhaps, with insight, he would have developed the concept of a single organism of roots, trying to explain to himself the biological and physical basis of its interactions between these individual parts, their interdependence and mutual necessity, due to which the organic world he observed should be understood as one whole. But, it should be foreseen in advance, this whole would be an abstract concept, and not a concrete image of the tree as a whole; achieved through a significant effort of research and thought, it still remained vague and somewhat conditional, so that the unity of the tree would be spoken of in a not entirely proper sense. What an abyss would separate even the most brilliant scientist of this limited field of research in the third dimension from the last fool who actually sees a whole tree with his own eyes. And in the end, this brilliant botanist, right in his premonition of unity, would not only be abstract in his constructions of this unity, but also simply wrong: after all, the signs of unity that he establishes are only secondary manifestations of life activity, and the organic unity of the tree as an integral form is reflected by them, but is not at all built by them. Moreover, they could be a consequence of the collective life of individual organisms, so that a non-genius researcher could with [full] formal right deny the vital unity of individual roots. The analyzed example is not as invented as it might seem at first, and almost before our eyes the thoughtful botanist G.F. worked in exactly the same sense and with similar failure. Morozov. Only his intuition and his research related not to individual roots and branches, but to individual trees, and that felt of roots in which he saw a single organic form was a forest. Morozov literally rebelled against belonging to the group of “those who cannot see the forest for the trees” and wanted to see it, the forest, as a single plant form. And he showed extraordinary insight and great industry to prove this unity. But he proved this unity primarily by the biological interdependencies of various factors of the plant formation he studied and only as a conclusion noted the ensuing dynamics of this formation, i.e. the process of its development over time. Despite his depth, Morozov showed indecisiveness in the most essential thing, in recognizing his own formative unity behind the forest, and expressed his main intuition vaguely, leaving the opportunity to think in both directions. But the real clarity of the statement would require him to make a leap, openly by virtue of intuition and no longer hiding behind external necessity based on observations. This ambiguity and reticence of Morozov’s constructions and his indecisiveness in the most important things were a consequence of the abstractness of his concepts about the forest and his lack of a concrete image of the entire forest. This abstraction is psychologically understandable, because the forest is a four-dimensional form with a strongly expressed duration, and the experience of human life, and even generations, is excessively subtle in the fourth coordinate compared to the extent of the forest in time. Morozov was forced to observe only a three-dimensional cross-section of the forest and did not see its biography as a whole. There was still a way left then, but it is almost impossible for a scientist of our time to enter upon it, having lost the necessary skills and abilities. This is precisely the mystical contemplation of the same forest, but in the symbolic form of a special creature, outwardly unlike the forest, but representing the forest itself, just as a smell can be the sensation of the whole flower, landscape, or even a person. Simply put, Morozov was unable to see the forest over the centuries and did not want or was also unable to see it in an instant, for example, in the form of a goblin. Five winding prints of typographical ink on a sheet of paper will not give a concrete idea of ​​​​a person as a whole being to someone who does not already know him directly, and it is impossible to imagine the degree of mental giftedness and spiritual courage that would allow one to move, even abstractly, from these five ink curls to an understanding of the whole person. But another transition is incomparably more accessible to us and immeasurably shorter, from the relatively short-term organs of the four-dimensional essence to this essence itself: from relatives to the clan. Here the lines of time continually diverge and the multiplicity of space increases. In relation to the time coordinate, something very similar to the divergence in space of the branches of a tree, in the direction of height, occurs here. When talking about a family tree, they use an image that is much more appropriate in this case than the speakers themselves usually think. The genus is really a tree, and it really branches, but not in height, i.e., in the third dimension, but in time, i.e. into the fourth dimension. But even here, this difference outlined here is not at all as significant as it might seem at first. The tree branches in height or, if we take a creeping plant, in the plane of the soil. But the branches themselves appear over time, diverge from the main trunk and from each other sequentially, not only as we move away from the beginning of the trunk, but also as we move away from the beginning of it in time, i.e. from the moment of seed germination. We think little about this, partly because the previously formed parts of the branches are not destroyed, and thus the spatial three-dimensional image of the tree accumulates the entire temporal process and pushes it out of our consciousness with its completeness. But imagine a plant that dies as it grows, something like the sacred fig tree, for example. Then the spatial image clearly no longer replaces the four-dimensional image of this fig tree as a growing organism. If we now turn to the genus, then we see its spread along one of the dimensions of space, namely the settlement of the genus and its occupation of an increasingly larger area (while it is growing; and an increasingly smaller one when it declines). But in this distribution along a plane, similar to the growth of a sacred fig tree, one cannot see an absolutely necessary property of the genus: if the family nest were a high tower, then the branching of the genus would go upward. Along with this divergence of relatives in space, either horizontally or vertically, the branching of the genus occurs in time. At the same time, the last process especially attracts attention, because, in contrast to a tree, the previous generation quickly dies out and in each three-dimensional section of the genus there are rarely more than three generations at a time. Thus, if the oak retains all previous generations of branches, and they continue to live, forming to a certain extent the image of the entire history of the tree, then in the genus the past does not leave its traces, and the spatial picture of the genus is disproportionately poorer than its four-dimensional image. In life and socially, this circumstance teaches the absolute need for a person to know, represent and synthesize in his knowledge the past of his kind, to consolidate it in possible ways, while the branches of a tree, if we imagine it as conscious, are much less in need of such consolidation, because there the past itself remains fixed, and as long as the organism of the tree is alive, the memory of its entire past is alive. The genus is a single organism and has a single holistic image. It begins in time and ends. It has its peaks and its declines. Each time of his life is valuable in its own way; However, the race strives for some definite, especially complete expression of its idea; it faces a historical task assigned to it, which it is called upon to solve. This task must be finally completed by special organs of the clan, one might say, the entelechy of the clan, and to give birth to them is the immediate goal of the life of the entire clan. These are fragrant flowers or tasty fruits of this genus. They end some cycle of ancestral life, they are the last or some penultimate manifestations of the genus. Whether there will be offspring from them or not is no longer a significant question, at least in the life of this family, for in the person of these flowers it has already fulfilled its task. If there are offspring here, then this can only be the development of the species by inertia, and in the near future, i.e. in three, four, etc. generations (and what do three or four generations mean in the history of a clan!), the vital energy of the clan is destined to dry up. In other cases, it is possible, with the influx of proper blood, to give birth to stable offspring. But this most often comes from one of the younger branches of the clan, junior in carrying the generic idea. This is, as it were, the vegetative emergence of a new offspring, if you will, a new genus, with a new generic idea and a new historical task. But the more fully and perfectly the historical meaning of the family is expressed in a famous representative, the less reason there is to expect further growth of the family branch to which he belongs. There is no doubt that the life of the race is determined by its law of growth and passes through certain ages. But there is also no doubt about the freedom that belongs to the clan - a freedom that, in the power of its creativity, is just as superior to the freedom of an individual representative of the clan on average, as the fullness of life of the clan as a whole is superior to that of individual relatives on average. In addition, at some time and in the person of some individual representatives of the clan, this self-determination receives extraordinary opportunities. The family then stands at the door of its own destiny. If in general, at other times and in the person of his other members, he is given some carelessness and clear decisions and insight into the life and task of the whole are not required from him, then, on the contrary, in such times and in the person of such of his members, he acquires the opportunity to pull himself up, to strain himself spiritually and at these turns to make a choice, to say either yes or no to the highest decision about him. This happens in the life of an individual; but these nodal points in the life of an entire race are immeasurably more responsible. And here the race is free to say no to its own idea and tear out the source of life from itself. Then, after this fatal event, the race itself no longer has any reason to exist and it dies in one way or another. The life task of everyone is to know the structure and form of his species, its task, the law of its growth, critical points, the relationship of individual branches and their particular tasks, and against the background of all this - to know one’s own place in the family and one’s own task, not one’s individual task set for oneself, but one’s own - as a member of the family, as an organ of a higher whole. Only with this ancestral self-knowledge is it possible to have a conscious attitude towards the life of one’s people and to the history of mankind, but usually they do not understand this and ancestral self-knowledge is neglected, considering it at worst as an object of empty vanity, and at best as a legitimate, historically earned reason for pride. However, neither one nor the other captures the main thing: the qualitative superiority and qualitative completeness of the clan over relatives. But the current, quantitative understanding of it as a simple sum of changeable generations, as an eternal eadem sed aliter, as the boring performance by each generation of all the successive duties of age - this understanding is fundamentally false, and it leads to the desire for a generation to isolate itself within itself, not to see anything behind and not to take into account the future. From the genus, as an integral four-dimensional image, the transition is already relatively easy, at least in thought, to the tribe, people, state, pace, and finally to the whole humanity, the concrete unity of which was understood and felt in an almost mystical experience, contrary to the rational structure of all thinking, by Auguste Comte. All these entities, extending four-dimensionally, each have their own form, their own integral appearance, and in appearance he is perceived as a genius or as a guardian angel of a tribe, people, state, race and all humanity. Auguste Comte called the total humanity as a single organism the Great Being - Grand Être and symbolized it with the image of the Madonna. But, apparently, he did not understand his own guesses in their literal sense and pushed the concrete image of humanity into indefinite distances, not taking into account the possibility of vision. Only later, when he suffered a mental disorder and thereby unchained the shackles of French rationality, in his cult of Clotilde de Vaux, greater concreteness of the same ideas flashes. The Living Idea of ​​the collective creation, it is the Eternal Church, or Sophia - God's Wisdom in creation, this divine Prototype and Form of all created being completes the considered series of ascending images, as they ascend, more and more general and at the same time more complete, concrete and meaningful. In icon painting, this Great Being, this eternal, unfading purity, integrity and innocence of the Prototype of God's World, fully expressed in the Heart of the World - the Mother of God, it is represented in the form of an winged, fiery, royal female figure. So, all reality extends four-dimensionally and is isolated into an image of four dimensions. And time, the fourth coordinate of this image, is organized in it, as its own, of this image, time, which has its beginning and its end in it. This time is not external time, by which we mean the time of lifeless things devoid of bright individuality. And therefore, the time of a given image cannot be judged from the time of others, strangers to it, and approach it with the measure of this latter: it is necessary either to enter into the own time of a given image and consider it as a unity closed in itself, or to rise through contemplation to an image that specifically unites that image and others from which we would like to depart. Then this new image in relation to those private ones will be their common space, with its own special time, i.e. four-dimensional space, and they, these particular images, in relation to the general image, will be things in it, connected to each other by force and energy interaction. Here, with regard to time, we would have to repeat everything that was said about the first three dimensions 23. Until now we have been talking about the reality being depicted, regardless of the perception of its image. For those who understand art realistically, such consideration of the temporal organization of images of reality is necessary as the basis for a theory of the very image of this reality. But it is not absolutely necessary within the theory of art as such: after all, those who understand art subjectively do not care about the organization of reality, and the question can only be raised about the consciousness of reality and, in particular, the transmission of artistic intent. Thus, whatever reality may be in itself, we are now faced with the question of perception and consciousness of it, and precisely in relation to time. How is time organized in consciousness? A preliminary answer would refer to the synthesis of temporal succession. However, it is important for us to know exactly what stages this synthesis goes through and what exactly each of them contributes to the treasury of art. For it is clear that the features of artistic style, manner and techniques should be associated with different types and methods of temporal synthesis. The synthesis of time, of course, requires a special activity of perception, and everything that facilitates the activity thereby prepares the ground for an easier synthesis. Thus, the opportunity opens up to apply free energy to a new set that has not yet been united, i.e. expand and deepen your synthesis. Everyone is familiar with the contrast between passive and active attitudes towards time. It can be especially clearly noticed in musical impressions, for in this art the coordinate of time is dominant and, therefore, the synthesis of time in perception is everything. We are forced to recognize this opposite as the consciousness of our powerlessness when we first listen to a difficult and intense piece of music, especially when we are tired. Here the music we listen to passes before us phrase by phrase, or even bar by bar; the play falls apart in the mind into pieces of more or less duration, each of which lies on its own, without any connection with the others. In the extreme case of very great difficulty and very great fatigue, the piece simply breaks down into individual sounds or their groups, and instead of a musical form, it comes to consciousness just sound noise. This difficulty in grasping the play as a whole and perceiving it from the first hearing does not at all testify against its objective integrity, although taken in itself, it does not, of course, provide objective coherence. Thus, from the very first time Beethoven is perceived in rather wide stripes, and the clearly perceived present moment only gradually, through a series of penumbras, turns into the darkness of what is already forgotten or not yet predicted. In other words, although the coherence of the whole is not given without effort, the premonition of this coherence is obtained relatively easily. On the contrary, Mozart is heard for the first time in the same way as a picture is seen, which we would view through a thin slit passing over different areas of the picture. The visible here would be sharply demarcated from the invisible. So here is Mozart: the perceived is sharply separated here from the no longer perceived or not yet perceived; here the gospel is musically realized: to her, to her - neither, nor, and he does not allow any half-yes. At first, Mozart, no matter how much he delights with the crystal murmur, is not embraced, even approximately, as a closed whole. But after hearing it once, and twice, and three times, the piece comes together. With Beethoven this happens gradually, and each new time tightens the connections of the whole. For Mozart, the understanding of integrity suddenly comes: a musical form crumbled, and then suddenly emerged. Beethoven thickens in consciousness, and Mozart suddenly opens up, like a snowy peak in a gap in the fog. When this unity in consciousness is, one way or another, established, music ceases to be only in time, but also rises above time. Musical tones or their combinations, physically sounding one after another, become combined in the consciousness of the whole, without, however, losing their order: thus, the ratio of quantities, even if they tend to zero, remains during this transition to the limit as an internal law of their relationships. Through the activity of attention, the time of a musical work is overcome, because it is already overcome in creativity itself, and the work stands in our soul as something single, instantaneous and at the same time eternal, as an eternal moment, although organized, and even precisely because it is organized. This is a single point, a single monad, containing an organized fullness of sounds, but the world of this diversity is condensed here by a creative act, and then secondarily by the perceiving consciousness into one point, into one perception, into one act of apperception. This is exactly how things are created that are actually created, and not put together and glued together - both in music, and in poetry, and in philosophy, and in science, not to mention the visual arts. One could string together a long series of self-testimonies about this subject given by the creators. But such material is easy to find in the relevant psychological literature, and therefore we will limit ourselves to one, especially expressive in its childlike purity. This is Mozart's description of his own work. “When I am alone with myself - and am in the mood of the spirit, when I, for example, travel in a carriage, or walk, or do not sleep at night, then musical thoughts are born in abundance and of the best quality. Where and how they come to me, I don’t know, and I have nothing to do with it. The ones that come to my mind, I keep in my head and sing them to myself, as at least others have told me so. If this state continues longer, then one thought comes to me after another, so that it would be worth it for me to make a tiny effort to prepare a pate of sounds, according to the rules of counterpoint, instrumentation, and so on. And so, if nothing bothers me, my soul becomes inflamed. Then what comes to me grows and brightens, and now the play, no matter how long it is, is almost ready, so that I look at it with one glance, like a beautiful picture or a dear person, and listen to it in my imagination, not at all successively, as is the case later, but as if simultaneously. This is true pleasure! Everything that was born in me passes like a beautiful vision of deep sleep: no other listening can compare with such listening to everything at once.” Such is the acquisition of time, which has reached high levels, although not the highest. But even below there is a compression of time, its saturation: when listening to someone else’s music, for example, the same Mozart. This applies, however, not only to music, but also to any creative work that emerged from the sole discretion of its creator and was so cognized that consciousness took possession of every part of it and can therefore, by an effort of attention, overcome the separation of sensory time. This happens especially clearly with drama and, above all others, with ancient tragedy. Recognized and assimilated in its successively appearing scenes, actions and individual phrases, ancient tragedy with irresistible force begins to be pulled together into a transtemporal unity, and its successive elements grow into each other and germinate each other, intertwining more and more closely and forming a single, more and more inseparable, in which everything is correlated with everything and every particular is determined by the whole. But of all the tragedies accomplished as only human works can be perfect, Sophocles’ “Oedipus the King” has long been recognized as exceptional perfection. And this tragedy is especially integrally compressed in consciousness, forming the archetype of any tragedy, the tragedy itself par excellence. It contracts to a point, dazzlingly shining and, like any dazzling light, it appears black. This is a dazzling black sun, the night sun of Dionysus’s passions, full of content, complexly organized and, however, point-like, one and indivisible, having no parts outside of each other and after each other. The condition for the synthesis of time, as well as the synthesis of space, has long been recognized, both everyday and scientifically, as the activity of consciousness. And the more capable the consciousness is of activity, the wider and deeper it carries out the synthesis, i.e. the more united and integral they take their time. Coverage here is possible as wide as desired—as long as time periods, as well as spatial extents; in the same way, the compaction of what is united into one object of thought and contemplation - time - is possible as deep as desired. Time can acquire an arbitrarily large share. The activity of art works precisely at this compaction of space and time, which is why fleeting and scattered impressions across the face of the earth and in the changing years acquire through art the weight of a precious ingot: This leaf that withered and fell, Burns with eternal gold in song, - but not only burns with gold, but is also as heavy as gold. After all, it brings together countless sheets that have faded and fallen all over the world and throughout history, and not only in the past, but also in the future. They are collected because time itself is compacted here. Art always makes this condensation, either by trying to permeate a given, relatively short period of time with forces in order to unite it as completely as possible, or by turning to larger periods. The department of biography and even the duration of an entire life, a historical period, the cycle of a people, and finally, geological and even astronomical space and times can be successively the areas to which the artist’s synthesizing activity extends. But the abstract possibility of such syntheses does not mean their actual existence. Usually, when trying to cover very large periods of time artistically and visually, the combined time turns out to be loose and even falls apart, so that the work does not show the synthesized period as a single, self-contained time, but only proclaims it as such: integrity remains here only an abstract requirement presented to the viewer, but not shown in reality. However, activity is also required from the viewer in order to see the temporary unity, if such were realized. In this sense, the viewer himself, who cannot see and has not cultivated a sufficiently strong ability of synthesis, can easily be to blame. Then, no matter how deeply a given time in a work is imbued with integrity, such a viewer will not understand the latter, with all his internal effort, just as someone who did not make the corresponding symbols the tools of his mind would not understand a mathematical formula. But nevertheless, for ease and even the possibility of perceiving this unity, a certain commensurability is required between the time being synthesized and the time of personal experience. Beyond these limits, the perception of wholeness becomes difficult and vague, and even further - simply impossible. Just as perception, the most habitual one, loses its ability to directly embrace hundreds of individual representations, so it does the same with the coverage of too many individual events in time. However, the first difficulty does not mean the complete impossibility of coverage at all. To do this, it is worth carrying out the unifying activity of perception by several successive ascents, introducing units of higher orders and thus making the disordered and incomprehensible set a relatively simple collection of units, each of which has its own organization. In the same way, time, incommensurate with our experience in its vastness, can still be made observable by dividing it into separate times, which themselves unite other temporal unities. Thus, the history of the state is divided into dynastic periods, and the history of the dynasty, as a generic unit of time, is itself divided into biographical unities, already commensurate with direct experience. In relation to this division in time, a construction is made in all art; the same basic technique of processing time is also necessary in the visual arts. Time is built by the activity of consciousness, but by passivity, on the contrary, it is disrupted: disintegrating, it gives separate, self-sufficient parts, and each of them is only externally adjacent to the other, but from the perception of one it is impossible to foresee what the other will tell us. This is precisely the everyday consciousness of the majority in relation to even their own lives. It breaks up here into separate pieces, successive to each other only by contiguity, but not derived from the single integral time of the entire biography, as it unfolds the internal diversity and rhythm of the personality. Only prayerfully and in moments of soaring one’s own life is embraced in the consciousness of ordinary people as an internally coherent whole, as an artistic unity, where everything, large and small, is presupposed by each other 24 and serves to reveal and express the self-contained form of a given personality. The consciousness, relaxed by the bustle of the city, gets used to even greater passivity and covers only small pieces of time from one push to the next. These snippets of time usually do not extend even to one day. And then, with severe fatigue, with twitchiness, neurasthenia, etc. these segments are further shortened until, finally, they are reduced to the time of a single impression. Then consciousness no longer has a basis for comparing it with another, i.e. has no basis for thought. This state, as we know, is close to unconsciousness: this mastery of thought by one impression, in which diversity is not seen, leads to a hypnoid state, a kind of half-sleep, where the will is inactive and movement freezes. At extreme degrees of such passivity, the assessment of time ceases, as it is overcome, although for the opposite reason, by the higher activity of spiritual soaring. Whether this delay of consciousness on one impression lasts long or short - a person does not know from direct experience and only later, guided by indirect signs, will he estimate the period of his half-asleep. He is carried away here along with time, or almost along with it, and therefore, although he still knows that there is time, he no longer understands its structure at all and takes it as a formless possibility, as the limitless, standing on the border between is and is not and, just about, threatening to drown in the darkness of oblivion. Finally, with complete inaction, the synthesis of time completely ceases, and with it the consciousness of time itself extinguishes. Here a person, like a thing among the things of the world, rushes along with others along the river of time. But he knows nothing about it, because he has no consciousness at all of what is happening to him. Time has decomposed, and each moment of it in consciousness completely excludes all others. Time has become for consciousness only a point, but not a point of completeness, which has absorbed all time, but a point of devastation, from which all diversity, movement, and form have been extracted and driven away. The question of the transmission of time by a pictorial work and, therefore, the organization of time is no more difficult, but also no easier, than the questions of the transmission and organization of other space coordinates. Perhaps even the transfer of time is more understandable than the transfer of depth, for the contemplation of a work of art certainly requires some psychological processes occurring in time, while the third coordinate, depth, is in no way clearly connected with the pictorial plane of the work. If we talk about a work as a thing, then, of course, it has its own duration; but this duration applies equally to all parts of the work and is not at all organized by them. The time in which the work is located as a thing has nothing in common with the time that is in the work as a pictorial work. Obviously, the conditions for the transmission and organization of this internal time should be sought in the dismemberment of the image itself. Obviously, further, time can be in the image if its individual organs and elements, although they coexist with each other, like physical parts, i.e. like strokes or strokes of ink, but they have a known order, a known internal sequence, or their sequence numbers are written on them, as it were. This order makes it aesthetically compulsory for individual elements to appear to the beholder in a certain temporal order. The work is aesthetically forced to unfold before the viewer in a certain sequence, i.e. along certain lines that form a certain scheme of the work and, when contemplated, give a certain specific rhythm. Aesthetic compulsion here is opposed to psychological arbitrariness. Nothing prevents me from tearing apart a ball of thread anywhere or opening a book anywhere. But if I want to have a solid thread, I look for the end of the ball and from there I go along all the turns of the thread. In the same way, if I want to perceive a book as a logical or artistic whole, I open it on the first page and proceed according to the page numbering sequentially. A work of art, of course, is accessible to my inspection from any place, starting in any order. But if I approach it as an artistic endeavor, then with an involuntary instinct I find the first thing to start with, the second thing to follow, and, unconsciously following its guiding pattern, I straighten it with an internal rhythm. The work is structured in such a way that this transformation of pattern into rhythm occurs by itself. If it is not done, or has not yet been done, either because of the difficulty of such a transformation, or because the viewer is unprepared, then the work remains incomprehensible. There is no impenetrable boundary between the visual arts, which are quite mistakenly considered to be the arts of pure space, and music in its various forms, which are considered to be the art of pure time. After all, works of fine art, until they are read and implemented in time, do not become art for us at all. In this sense, they are no more understandable than a musical score if it, being in itself only a kind of flat ornament, does not sound rhythmically instrumental or internal reading. And according to the instructions of the composers, the graphic design of the symphony, its visual beauty or ugliness, gives an experienced person a basis to judge the musical value of this recording. So, a visual work is nothing more than a recording of a certain rhythm of images, and the recording itself provides the keys to reading it. The difference from ordinary musical recordings is mainly in the rationalization and analytical nature of the latter, with each element of the recording having a pre-agreed meaning. And in the visual arts, the meaning of individual elements is not always determined in advance, in relation to them in their individuality, but for the most part is given directly in the very process of contemplation. This can be compared, perhaps, with the instructions of a conductor's baton, which continues and intensifies the expressive pointing gesture. This latter can be understood to a certain extent by an unprepared person, although only preparation, i.e. knowing what exactly is being indicated makes it possible to have clear and quick reactions to it. The signs of rhythmic movements in a work of fine art are even easier to understand directly; but nevertheless, even here, mastering a complex system of them, such as, for example, a painting or an engraving, requires habituation to known signs and preliminary familiarity with their content. Continuously flowing homogeneous time is not capable of producing rhythm. The latter involves pulsation, condensation and rarefaction, deceleration and acceleration, steps and stops. Consequently, visual means that give rhythm must have a certain dismemberment in them, with some of their elements delaying attention and the eye, while with others, intermediate ones, promoting both from element to another. In other words, the lines that form the basic scheme of a pictorial work must penetrate or subdue the alternating elements of rest and jump. The elements of peace are contemplative and observed, each on its own, at once and with a resting gaze. This is the fragmented matter of the work. It is timeless, in the sense of the indifference of these elements to duration: the eye can rest on them longer or shorter, but, of course, no less than an atom of time required for the perception of a single element. The elements of the leap are not contemplated in themselves, and in aesthetic perception both attention and gaze are unable to consider them. Their purpose is to separate two adjacent elements of rest and deprive the work of continuity. The eye skips past them, they are not noticed by them and that is why they perform their service. They are also timeless, but not in the same way as the elements of rest, because their consideration requires a time of zero duration. However, in combination with elements of rest, they create rhythm and thus shape time. These are non-sensual elements and are in the service of the form of the work as a whole; they can be called formal. They give movement. Thus, time is introduced into the work using a cinematic technique, i.e. by dividing it into separate moments of peace. This is a general technique of the fine arts, and none of them can do without it. But it is not enough to divide time into moments at rest: it is necessary to connect them into a single series, and this presupposes some internal unity of individual moments, which makes it possible and even the need to move from element to element and during this transition to recognize in the new element something from the element just abandoned. Dismemberment is a condition for facilitated analysis; but a condition for facilitated synthesis is also required. Speaking very generally, this last condition is realized by the directly perceived qualitative relatedness of individual elements or known groups of them. The method of establishing this relationship can be very different, and, according to this, the synthesis itself can be given to consciousness with more or less difficulty. When thinking is synthetic in its basic structure, related groups can be large, and then transitions between them are correspondingly difficult. On the contrary, thinking, which is analytical in its basic nature, is not able to master unity when the elements of movement are too difficult and is lost, not understanding the integrity of such a work. In the first case, unity is contemplative and intelligent, and in the second it is close to sensory-visual. And therefore this is assimilated by the activity of the spirit, while this itself is imposed on sensory perception. In both cases, unity cannot be sensual in the proper sense of the word; but in analytical thinking unity has to be given the appearance as if it were sensory. We can say it another way: the organization of time is always and inevitably achieved by division, i.e. discontinuity. With the activity and synthetic nature of the mind, this discontinuity is given clearly and decisively. Then the synthesis itself, if only it is within the capabilities of the viewer, will be extremely complete and sublime, it will be able to cover great times and be filled with movement. But, if you are unable to embrace these groups as a single whole, no rhythm of images will emerge in your consciousness at all and the majestic music will crumble into separate sounds. That is why the mind, prone to analyticity and the resulting passivity, is afraid of obvious discontinuity and tries to hide it by fragmenting related groups and facilitating transitions between them. Essentially, such a work will remain discontinuous; but in sluggish perception it will pass for something continuous and not requiring a spiritual form over a sensory reality. When the deviations of this false continuity from the real continuity of the sensory are revealed, the unthinking viewer will explain them to himself as random errors of the artist, or a kind of poetic liberties, and will forgive them to the artist, but still will not understand that it is precisely through them that his life is realized in the work. To such a viewer, these breaks in sensory coherence noticed by him, more visible than many others, unnoticed by him, will seem like random defects of insufficiently experienced production, similar, for example, to seams on a casting. But he will not think that such seams are formed necessarily and that, therefore, rubbing them out with greater dexterity would not change anything in the essence of the matter. Such a viewer will not want to ask himself the question of what exactly is the expediency and internal necessity of these and other similar seams, i.e. what is their aesthetic function in the organization of the entire work. The simplest and at the same time the most open method of cinematic analysis is achieved by a simple sequence of images, the spaces of which physically have nothing in common, are not coordinated with each other, and are not even connected. If you like, this is the same cinematic tape, but not cut in many places and therefore in no way condoning the passive connection of images with each other. In cinema, this binding occurs on the basis of the physiological inertia of the retina, which retains the received irritation for some time and thereby forcibly merges it under certain conditions with the subsequent one. Therefore, the movement conveyed by cinema is psycho-physiologically identical with the movement transmitted, i.e. there is not a spiritual image of it, but an illusory substitution, and, therefore, completely naturalistic. In art, consistent naturalism would be a simple destruction of art itself, for it first of all presupposes freedom. But the cinematic technique, as such, does not necessarily lead to a naturalistic obsession with illusory imitation of reality and, under certain conditions, can, on the contrary, require the greatest spiritual effort, and the unity conveyed by it will be contemplated by the eye of the intelligent, but not at all sensual. The simplest example of using this technique is given in the book. The majority of those handling books have not realized that, along with the literary unity of the printed work, there exists and must necessarily exist the unity of the book as such, and the first unity, i.e. the work is included in this, i.e. the unity of the book as one of the sides, or rather as the original grain. Once a work is read with the eyes, those visual means by which this reading is made possible cannot in any way be regarded as an external appendage to the work, accidental and indifferent; undoubtedly, they serve to embody it and therefore participate in its unity. The book, as a whole, must itself be a work of art and, therefore, have its own composition and its own design. The existence of non-fiction books does not at all refute what has been said, but only testifies to the ill-conceived or mechanical nature of their composition and design. The book, however, must be integral, and its structure and entire appearance are determined primarily by its internal design. Its dimensions, the nature of its paper and binding, font, its division through the placement of text, the sequence in the use of various fonts for the names of parts, chapters, paragraphs, ways to begin and end departments of one order or another, placement of drawings, diagrams, tables, formulas, etc., etc. – all this has its own expressiveness and can be used as successfully as possible, i.e. in accordance with the intention of the book itself, it was unsuccessful, i.e. contradicting him and hindering him. This applies to every book. But the question of the composition of a book arises especially acutely when its existence is not justified by its usefulness alone. The further the concept of a work is from direct utilitarianism, the more urgent is the artistic elaboration of the corresponding book. The occasional appearance of an accounting textbook is still somewhat tolerable; but a book of poetry that does not satisfy some of the initial requirements of artistry not only causes a certain disgust, but also clearly interferes with the perception of its poetic content. Its pages, successively passing before the reader, should by their very appearance, the type of their construction, contribute to the consistently unfolding, but internally coherent unity of the work. Margins, white space, page numbering, etc. – all this gives rhythm, and it must convey the internal rhythm of the idea itself and visually maintain the impression of its unity. If it destroys it or if its rhythm does not correspond to the internal rhythm, then this will bother us and interfere with reading. The simplest case: poems visually divided into groups corresponding to meter and rhythm. It is worth imagining a book of poetry, printed entirely or, even worse, divided into lines that do not coincide with the verse, in order to understand the essential necessity of a certain book form. Further - the same about the division into chapters, parts and so on. It would be unbearable to see the beginning of a new part at the very end of the page, just as the page division of octaves would be unbearable. Self-evident examples are taken here deliberately so as not to talk about things that need clarification. A similar example of visual integrity can be, for example, the need to maintain one font throughout a book for all homogeneous parts of its content. It would be unbearable to see a book in which the font suddenly changed without internal motivation from the content. This art-book alphabet gains new weight when the art of a draftsman or engraver joins the art of a poet. Vignettes, headpieces, endings, and especially illustrations, along with other visual and artistic elements of the book, such as the cover, frontispiece, title, etc. cannot in any way be considered as a decoration of a book, and a book “with decorations” is always an abomination, making the perception of the work itself unbearable. “Luxury editions” are most often just like this (for example, Brockhaus editions of world poets). All these elements of representation either form a single whole, entering into the fabric of the book itself and, therefore, into the work and thereby becoming organs of increased expressiveness for the design, or they reside in the book by themselves, and then, whatever their self-sufficient artistic merit, they interfere with the book, drown out the bare work, instead of supporting and enriching it, and are decidedly intolerant, we repeat again, regardless, perhaps, of the great significance of their own to yourself. There should be no “pictures” in the book. The variety of illustrations, each of which may be excellent, turns the book into a junk shop. Here the visual elements draw attention to themselves, separating it from others and from the entire unity of the book. The internal movement, the unfolding of the book in time, is destroyed. These elements only mechanically follow each other, not being spiritually united into a holistic image and therefore not providing rhythm. On the contrary, in an artistically organized book, its individual graphic or illustrative elements appear in the mind sequentially, as parts of one whole, which is organized along the fourth coordinate, even, perhaps, predominantly along the fourth. This whole unfolds as one picture, like a landscape viewed from a train. Here the sequence of impressions is conceived by the viewer not as a simple “after”, but serves as a condition for greater richness and inner life of this landscape. I remember my travels on foot, on horseback or in a carriage, when they began a few hours before sunrise and ended in complete darkness: everything seen during the day is then combined into one picture, over which the sun reigns in motion. The usual perception of the sun is instantaneous, fixing it in a certain place and in a certain shade, and this impoverishes the 25 sun and deprives it of life. On the contrary, the sun royally and divinely unites everything and unites everything, the sky, when its arc across the firmament is caught. The advantage of poetry over fine art is generally recognized in this ability to unfold events to the listener. But we must remember: this unfolding primarily occurs before the inner gaze, which, although internal, is nevertheless by its nature a gaze and, therefore, thereby gives the impressions of poetry a pictorial character, at least in some cases. On the other hand, the unity of a pictorial work, organized in time, is also given to internal contemplation, and not sensually, and, therefore, for its part again approaches the impressions of poetry. In other cases, the impression of poetry develops so clearly with the character of figurativeness that after reading the book there remains an almost irresistible conviction that you yourself saw what was described there, or that the book was illustrated. And vice versa, the sequence of pictorial images sometimes gives an internal movement and rhythm that is forcedly poetic and dramatic, sometimes even purely musical. As an example of the first, I recall Walter Scott's amazing story about Quentin Dorward's journey through the Parana Gorge. This is not an analytical verbal description of this or that individual landscape, but rather a picture of the entire journey in its movement, which Walter Scott really shows to the reader, or, better said, to the viewer. Something similar, although not as powerful, is Georges Sand's painting of Consuelo's journey with Joseph Haydn. And here again the unfolding landscape is shown, and not served as the subject of verbal analysis, and, moreover, it is shown in its movement. You can give examples of the opposite, i.e. poetic development and musical sound of visual works. Books, in the sense explained above, can undoubtedly be like this. But whether it’s because our time doesn’t produce really good books, or I just don’t remember any now, I would find it difficult to name a printed music book. The manuscript knew this integrity of the artistic organization of the book - in time, and in the ancient manuscript one can actually sometimes see a musical structure. Such, for example, is the life of St. Sergius, kept in the Trinity-Sergius Lavra, which has an illustrative miniature on each page. The strict uniformity of the composition, techniques, general character of the colors and even the particular colors of all these miniatures draws them together with a single thread so that, when flipping through the book, one gets in one’s mind not many separate illustrations, but one, but a living one - one image of the life of St. Sergius, holistic and united, having absorbed the beat of time. The miniature, as it has been mentioned here, is cohesive throughout the book much more closely than the usual book illustration. But our book, like our manuscript, introduced a division that was not present in the ancient scroll. A Chinese book, made of one continuous paper strip and printed on one side, is a historically frozen transitional stage between a scroll and our book, and in this sense it can make the perception of its organization in time even easier than a face manuscript. A Chinese book embroidered and pulled out at the ends produces a scroll in which cohesion in time is perceived with even greater ease. And transferred to the wall, the same book gives a fresco or other type of mural painting. The mural painting obviously must have internal unity, because otherwise the architecture would suffer direct damage. The single meaning of this architectural monument is revealed by its mural painting. And no matter how numerous and varied the individual wall images are, they must be perceived as a single whole. The mural must necessarily have a unified composition. This also includes that easel painting, which, separated from the stone wall, stands in the air as an objectified vision - i.e. iconostasis. The church charter establishes the basic schemes for wall painting and iconostasis as a single composition. Where these principles are somewhat consistent, the church really sounds like incessant music, the rhythmic fluttering of invisible bells, which fills the entire space. When you are alone in such a church, then this sound of its painting, a sacred insensible sound, is heard with objective compulsion and it becomes absolutely certain that it comes from the images as a whole, and is not imagined by us. The entire church beats with the rhythm of time. This elaboration of it along the fourth coordinate, further, is perceived with even greater ease when individual images and numerous groups of them are uniform not only in their general stylistic unity, techniques, manner and colors, but, in addition, represent the development of one legend and are built, each separately, according to one compositional scheme. This is what usually happens in ancient churches, that the main theme of a given monument unfolds throughout all the walls especially richly and consolidates the diversity of all other images. Such, for example, is the Assumption Cathedral in the Trinity Lavra, where the theme of the end of life and the Dormition of the Mother of God dominates all others. Each of these others is given here by a single image, while the Dormition of the Mother of God is represented by very many, giving the course of this event a majestic, heavy tread and thus involving other events and persons of church history in this movement. In the painting of this cathedral as a whole, time is organized and brought to unity precisely by the event of the Assumption; everything else is relatively motionless, like stars between which the ether flows. We can say that here time is the Assumption. This compositional technique is more or less common to all wall paintings, whether it be the life of St. Francis by Giotto, or Byzantine paintings. On the contrary, the paintings of the recent past are characterized by a lack of understanding of this principle: such is the absurd St. Vladimir Cathedral in Kyiv, where there is no unity of theme, no common compositional principle, no dominant event unfolding in time, no sequence of colors, no unity of an art school or direction, or even an approximate adaptation of the manner of one artist to another. No matter what you think about each of the images separately, their incompatibility in one church is undeniable, because the church is not a museum where Vasnetsov and Kotarbinsky gather indifferently, but a single work. It is easier to collect individual moments along the fourth coordinate when the private spaces of individual subordinate compositions are not delimited from each other. Here the image has visual integrity, and at first glance, its individual groups and sections are perceived as physically different and coexisting with each other. Only upon closer examination of these groups and sections does it become clear that they all depict one person or the same persons, one landscape, one event, but in some consistent development. Then these groups, although physically coexisting, receive different time coordinates and give some depth. The visual work comes to life and flows: currents and streams plow its space. It is clear that some sign or some signs must establish in our consciousness the numerical identity of the object or objects depicted in their different time coordinates by different groups: otherwise there would be no impetus for synthesis along this coordinate. This sign can be given, in addition to the implied unity of style and manner, by the identity or similarity of facial features, figures, some of the furnishings, etc. Compared with pre-Christian religion, Christianity greatly increased interest and sensitivity to organized time, and therefore also the understanding of it as a certain unity: this was a consequence of the clarified consciousness of eternity. And therefore, in Christian art there was an acute need to convey movement and development. The technique under discussion, which combines several successively developing compositions, was used many times in catacomb art, and then in medieval miniature. Thus, in the catacomb paintings the story of the prophet Jonah is depicted, and its successive moments are presented in one space: the prophet Jonah is riding on a ship. He is thrown from the ship, he is swallowed by a whale, the whale throws him ashore, the prophet sits under a canopy, he mourns a withered plant, etc. - all of these are separate groups, but they are connected in one space, and at first glance could be understood as an image of different persons. Travel, dramatic events, in general, everything that, of all the coordinates of space, most needs the fourth, is usually conveyed in medieval miniatures with just such a technique 26. But in the technique under consideration, individual compositions, although not spatially separated from each other, nevertheless have some relative delimitation: it is achieved by fields surrounding each particular composition, the space of which has a curvature much less than the space in the sections of the compositions themselves. Further facilitation of synthesis is achieved by filling or, more precisely, compacting these framing fields. Then the spatial unity of the work becomes even more sensually visual, and at the same time, above the plot developing in time, another one grows, spreading and multiplying in space. The art of modern times, being much more sensual than ancient and medieval art, strives for the indicated concealment of the seams between individual compositions. In this way, an image is given, the inner life of which and the initial plot developing in it are only felt, but are not established with complete necessity by consciousness. Time here plays rather on three-dimensional images rather than entering into their very composition. There are many works of this kind, and they arise especially often when the artist tries to express something large and complex, but thinks of it in a largely analogous way, without having before him an idea of ​​it in the proper sense of the word. Such is, for example, “The Soul of the People” by M.V. Nesterova. The idea of ​​this painting is to show how the best things that united the Russian people and comprehended their existence in the world lived throughout history, manifesting themselves most clearly in their own way in each century. But the artist wants to present the various moments of this manifestation not in their obvious sequence, but in a somewhat hidden sequence. In other words, he needs to present individual people and groups of them, who in their time were the primary bearers of the soul of the Russian people, as existing and acting unitedly and simultaneously, although with a hint of their temporal continuity. And for this it is necessary, of course, not just to put them side by side, but to motivate their presence together with some plot, i.e. get them to participate in one action. Some internal consistency of this general action, although extending over a short period of time, can then provide favorable soil for the transition to the historical period of time. It is clear that in order to unite people of different times in one action without exaggeration, it is necessary to take it as suitable for all centuries covered: an action characteristic of one century would clearly exclude from the group everyone who does not belong to this century, and the plot unification would become impossible. Nesterov unites his group in a religious procession, and the mood common to all its participants is hope and expectation, confident expectation. From here the location of the picture is naturally determined. The religious procession descends along the spring hillock to the lake, probably with a hint of Svetloe Yar-Ozero. On the other bank, like a golden vision, there are some (re)buildings, again with a hint of the sacred Kitezh. The procession seemed to suddenly stop, perhaps because it had come to a place, or perhaps it was struck by the light coming towards it. In the allusion - the lake is Yar-Ozero, the building is Kitezh, the light is Christ the Coming, and the Procession itself is the Russian people in their history. Directly, all this has an ordinary meaning, although not so definitely as to be called everyday. In exactly the same way is the composition of the group, which is not capable of being pinned down with complete accuracy to some specific moment in Russian history and in this sense hints at its symbolic-collective meaning, but at the same time is not so obviously contradictory as to become completely ahistorical. This was achieved by depicting representatives in clothes characteristic of their time, which at the same time were valid in other times, in particular in our 20th century. A boy with a birch bark bucket runs ahead of the entire course. This is the Russian people in their adolescence, at the very dawn of their Christianity. But the boy, although from that time, could have been at any other time: he is dressed like a peasant, just as boys in the north are dressed now. Next is a group of women surrounding the blessed one, completely naked. This is the initial feat of the people, the feat of complete renunciation. But this feat and a similar group, although most characteristic of its time, are nevertheless conceivable in any other. Even further to the right: a feat that is already receiving internal organization is monasticism. There is a schema-monk, like Anthony of Pechersk, but not that specific Anthony, but in general Anthony, living among the Russian people, although he flourished especially brilliantly in his age. Next - an even more organized feat - the consolidation of the church and the embodiment of the soul of the Russian people; its representative is a Metropolitan or Patriarch, in the type of Moscow saints, but not one of them, but a saint in general, appearing among the people from time to time, such as, for example, Filaret of Moscow. After him - the further embodiment of the soul of the people - church-state construction, represented by the Grand Duke or Tsar and the soldiers behind him. And again, this Autocrat, either Vasily or John, is possible in any age. In the same way, it is necessary to repeat about the priests, merchants, townspeople, sisters of mercy leading a wounded soldier, standing next, and finally about the writers, already taken in portraiture - Dostoevsky, Solovyov and Tolstoy, and the latter enters the canvas only halfway, gloomily and heavily closing the group from which he cannot be separated and with which he cannot merge. Walking through the figures from left to right, we survey the different layers and spiritual currents of the Russian people, which historically embodies their soul, and this relates to the historical moment of painting the entire canvas, at least when combined it does not seem contradictory. But at the same time, we survey the entire course of Russian history according to its inner meaning, and then each of the images becomes incomparably more significant and brighter. This is how time is conveyed on the canvas, without leaving anyone who is unable to cover such a large extent of the fourth coordinate unsatisfied. In the picture under consideration, the adhesions of images belonging to different time coordinates are erased to a certain extent, but are nevertheless visible: although the entire group is united by a common action, there is no direct connection between the individual characters, either plot-wise or pictorially: nevertheless, the space of the picture breaks up into a number of separate areas, very loosely connected with each other, although according to the concept of the picture, this disintegration should not have been and can hardly be motivated. Therefore, it is worth noting an example of further visual unification of space along the fourth coordinate, where the seams have already been completely destroyed. This is, for example, Watteau’s “Ride to the Island of Cythera”. It depicts a holiday in the middle of nature, walking couples - some are talking in the grove, others are rising, others are going to the seashore, others are boarding a boat, others have finally left and are covered in the haze of humid sea air. All these pairs are completely united both in plot and picturesquely, so that all this movement from right to left seems to be a continuous flow - the movement of both the images and the people represented by them. Understood as an image of a celebration, as a collection of different types of gallantry, the picture has a certain extent in time. But at the same time, more deeply, it can be interpreted in time. Then the magnificent holiday ends, the brilliant society falls somewhere, and before us is a secluded grove - the refuge of a secret meeting. This whole gallant crowd turns out to be just one, depicted in a series of successively unfolding love [couple]. It is she, the only couple, talking in the grove and then gradually leaving to hide in the luminiferous fog on the island of Cythera. Another example where the cohesion of successive states and ages of feeling is given without any seams. This is a little-known work by Michel Angelo (...) 27 In the examples considered, different moments of a developing event are given in separate images. The images are weakly or closely united with each other; in any case, the unification occurs against the background of the general landscape, and not within the images themselves. In this sense, the landscape turns out to be seams in the depiction of a temporal process, seams that are decorated, but which therefore gain even greater visibility. Uniting the process as a whole, the landscape at the same time separates images expressing individual moments, processes, as such. Thus, although the unity of the image is given here visually, its unity in time requires more mental effort for its comprehension than in other coordinates. Therefore, it is necessary to talk about the further visual consolidation of time, when different moments of the process are presented within one image, and by the clarity of this image they themselves are visually united. It’s clear that here the entire image can no longer serve to depict a single moment; but this is not required, because we, perceiving this or that process, this or that movement, are not able to view the moving image, at every moment, in all its aspects. Observing the process, at each stage we pay attention to a relatively small number of elements of the changing image, namely those that most clearly characterize the dynamics of the image at this particular stage: these are the guiding features that give our consciousness this particular image, and, moreover, as a moving one. In further stages of the process, the guiding significance from these features can, and even in most cases should, gradually move to some other features: when the image moves, some movement occurs within the image itself, which serves as the focus of attention. But this movement of the supporting area of ​​attention within, as said, the image itself, is already a movement of the second order, so to speak, a movement of movement, and therefore it usually occurs much more slowly than the first. When a new process must be presented in one way, then the means of conveying the entire process is cinematic fragmentation, but not of the process itself directly, but of a second-order movement, i.e. moving the reference area of ​​the image. In other words, from each stage of the process the artist takes only this supporting area, in that place and in that state that corresponds to his given state. And having thus chosen throughout time the most important thing with which this process is characterized at different moments, the artist combines this most important thing into one image. Instant photography of a moving image provides images of simultaneous positions and states of all organs. In this way, one moment is captured, with all the present circumstances that do not interest us at all and do not reach our consciousness; but this moment is taken outside of its relation to the subsequent one. The consequence of this is well known: instant motion photography is unable to convey movement and presents an unbearable spectacle of instantly frozen bodies and a fairy-tale sleeping castle. The raised leg remains forever, showing no desire to lower itself back; and frozen laughter, which does not arise from anything and does not turn into anything, becomes a mask of a dead soul. Here the moment is snatched from the process and taken on its own, without a past and without a future, in its stupid opposition of itself to everything else. He is self-sufficient, exactly according to the rational law of identity. In relation to time, instant photography does not contain a contradiction, but precisely because of this it has no relation to the images of reality, concretely perceived and thought, and is pure abstraction. On the contrary, the life of the image in a work of art is achieved by the fact that it is certainly a coincidentia oppositorum, a clear combination of contradictions, a clear overthrow of the law of identity. If we were to compare an artistic depiction of a moving object with an instant photograph of it, then in the first we would see numerous anatomical and physical contradictions and absurdities between individual organs and parts. A given part or a given organ cannot be in the depicted position if some other organ is assumed to be depicted correctly. Here, anatomically and physically speaking, there must certainly be one or the other, but not both together. Instant photography does not suffer from this contradiction; but the galloping horse hung in the air forever. The artistic depiction of the same galloping horse is full of contradictions; but that is precisely why we see the horse’s jump itself, and we visually perceive how it galloped and how it will stand on the ground again. This contradiction is not really a contradiction, and the identity of a photograph is not really an identity. After all, we do not look at the entire image at once, but consider it, i.e. we take in parts with our gaze, and, moreover, moving our attention along the leading parts in a certain order, if only the artist managed to clearly enough draw out our visual route for us. Thus, we encounter anatomical and physical contradictions during the aesthetic contemplation of an image not at one moment, but at different ones, and, accordingly, we attribute the areas we see to different objective times. If anyone feels their inconsistency, then this simply means an inability to contemplate aesthetically, or, in particular, powerlessness in this particular case. On the contrary, the consistency of photography in aesthetic perception will inevitably turn out to be contradictory. After all, the contemporaneity of the positions of individual members, which is imprinted on a photosensitive plate, is not observed by us in direct perception, and, therefore, the photograph does not correspond to what we actually see. Moreover, we will begin to examine the photograph itself sequentially, so that its individual sections will appear in consciousness precisely as belonging to different times, and in this multi-temporal position they will turn out to be unbearably contradictory in their temporal content. If the natural way of perceiving external reality gives sequential impressions, and the image of reality is again considered sequentially, then we are not able to take into account the formal requirement of the simultaneity of all its parts and during perception we will attribute different parts of the image to different times. And if this circumstance is not provided for by the image, then the image itself will be assessed by us as internally contradictory. The deeper the image is along the fourth coordinate, i.e. the more noticeable the movement in it, the more clearly the anatomical and physical inconsistency of the depicted images should appear, since these images, with a non-aesthetic approach to the image, are considered as modern in all their parts. The stronger the movements of people, the more the angles of individual parts must contradict each other, if only the artist wants to create an image that is internally consistent. But here it is necessary to reveal somewhat more precisely the very concept of anatomical and physical inconsistency, which is used when approaching the image in a non-aesthetic way. Here we are not talking about anatomy or physics as such, but exclusively about the method of projection, and the use of some method of projection that is unusual for a given connoisseur is judged as a contradiction. But, let us repeat, this is not a contradiction of reality, but only of one or another habitual method of projecting reality onto a plane. Anyone who does not understand this has not even gone through the most preliminary chapters of the philosophy of art. After all, reality in itself cannot stand in any direct relation to its projection, and therefore no projection can stand in contradiction with reality. The contradiction of a given projection relates to some other projection, according to another technique. In this sense, any image can be declared contradictory, as soon as a certain method of projection has been learned, but this one does not agree with it. Thus, for an engineer, a perspective image is already contradictory, just as it is even more contradictory in the assessment of a Persian miniaturist. In the same sense, any image of an object moving in its motion will certainly turn out to be contradictory to those accustomed to linear perspective. After all, visually, the very essence of movement is that a single point of view, a single horizon and a single measure of scale are not respected; and yet these three unities are assumed at the very basis of the perspective projection of the world. Naturalism, as starting from a passive worldview, tends to take images simultaneous in all parts and thus naturally leans towards perspective in projection, although even here perspective is not the only possible solution. Of course, since the artist, even the most naturalistic one, is still guided to a certain extent by a living perception of reality and, therefore, cannot completely exclude temporal depth, he certainly introduces multi-temporality of individual parts into the images he creates. Thus, he too will, to one degree or another, violate the dictates of perspective. But, in any case, programmatically, in the spirit of his worldview, he will fight for perspective and against time - both are almost the same thing. Historically, naturalism, perspective and the struggle with temporal depth appear together. We read a very interesting passage in this regard from Leon Battista Alberti, one of the most prominent leaders of naturalism with perspectivism, namely in his treatise “On Painting,” dating back to (...) 28. Here it is: “Some depict such sudden movements that on the same figure both the chest and back are visible at the same time - a thing as impossible as it is obscene. They consider this commendable, for they have heard that such pictures, where individual figures wildly throw their limbs about, seem very alive, and make of them fencing teachers and magicians without any artistic dignity. But this not only deprives the painting of all charm and grace, but such a course of action also reveals the artist’s excessively unbridled and wild temperament.” So, the question discussed in the next paragraphs is quite old and arose already on the threshold of Renaissance art, in connection with perspective and naturalistic aspirations. We don't know who exactly Alberti is referring to; but since he himself proclaims hitherto unrecognized techniques for depicting the perspective, obviously we are talking about artists who retained something from the medieval traditions. And in fact, this non-perspective combination of profile and frontal images, the front and back planes of the body, in particular the chest and back, at every step serves iconography and miniature in conveying movements. Thus, in the front Gospels there is often an image of the Evangelist John the Theologian with his disciple Prokhor; a similar translation is often found on the icons of the same Evangelist. Prokhor is depicted here sitting in a cave and writing down the words of the Evangelist. He is bent and directed towards the right side of the image, so that his body is presented in profile. But the face is given in an almost straight turn, turned to the left and raised upward, towards the Theologian. Thus, in Prokhor’s drawings, at least two contradictory angles are combined, as a result of which the back and chest are visible in the image at the same time, just as in the drawing of the head, much more surfaces are connected than can be seen in a perspective image. To an inattentive glance, the figure of Prokhor will seem at first hunchbacked and inverted. A closer look characterizes her rather as spread out. Artistic perception also gives understanding: at a certain moment of visual synthesis, the humps, the flatness, and the anatomical inconsistency of angles instantly disappear: the image comes to life. We now see a slender figure, but with strong movement, the figure of a mediator between the word of the Evangelist and the charter on which this word is written. Prokhor is turned with his attention, and therefore his face, to the Evangelist, with his executive will - to the record, and therefore here - with his whole body, serving to embody in writing a non-sacred narrative. The meaning of the figure of Prokhor is precisely in his mediation, in his service as an instrument, and therefore the movement towards the Evangelist and towards paper, both are absolutely necessary in order to convey the meaning of this figure through the means of fine art. Prochorus, calmly writing, would be on his own, would disappear in artistic perception from John the Theologian, and the connection would then be given not by the perception itself, but literary, i.e. conditionally in relation to the image itself, external in relation to its plot knowledge of this icon. We could then know abstractly that Prochorus is a disciple of the Theologian and that he does not write his own, but testifies to John’s; but we would not at all see this with our own eyes, but would see just the opposite. In its present form, the icon, regardless of how much we know its plot, testifies to us, to our vision, that the Gospel of John was written by John, and not by Prochorus, although by Prochorus’s hand; and then it would testify to the opposite, contrary to its plot. True, dexterous, but not thoughtful, i.e. not feeling the reality of what is depicted, the artist could compositionally link the figures of John and Prokhor, i.e. hide their gaping gap under the unity of lines and colors as such. Then you will get a solid spot, something solid in the decorative sense. But the composition here will be in conflict with the design of the image; and as soon as the eye stops outwardly sliding along these lines and colorful spots and the viewer begins to wonder about the artistic completeness of the image, then this discrepancy between the composition and design in the image will become an unbearable falsehood. The humps and “anatomical contradictions” of the figure of Prokhor very accurately carry out the design of this icon as an artistic expression of its plot, or, more precisely, its name. One more case of similar humps should be noted. Here a uniform design technique is used many times, which gives a special rhythm, which in terms of the power of artistic impression is superior to that of the rhythmic declinations and turns of the writing Prokhor. Here we mean the rank of the Deesis row of our ancient iconostasis. Right in the middle, unshakably vertical, like the absolute axis of the world - Savior Almighty. On either side of Him are those present, according to their rank, bent over and with, as it were, huge humps. They are standing. But if they only stood as independent verticals, then the Almighty would be such only according to the conventional proclamation of the icon painter, but would not be perceived by our eyes as the axis of the world, holding the world, as the foundation of both being and truth. Despite the dogmatics and good intentions of the artist, we would see the One sitting on the throne as nothing more than the first among equals, the first vertical in a row, but not the only one in essence, not the first vertical, which determines and sets all the others in itself. At best, the Savior would then be the Emperor, and those present would be courtiers, but in no way would this be the original Father's Word, by which everything became and by which everything is enlightened, and by which the world is judged. We, the spectators, do not care about the artist’s verbally declared piety: it must be evidenced by the deed itself, in this case – visually. And if we do not see a known idea with our own eyes, and even more so if we see the opposite, then no assurances have any force and should not have any. This is exactly how things would have stood if the Deesis order had been built on a number of independent verticals: each of them would have affirmed something divine, in the sense of pantheism, but independent of the One Person, of God; and then the Savior would only be Christ, in the sense of Khlysty. But, on the other hand, the absence of verticals, except for one and only one, would violate the idea of ​​the Deesis order, for here the possibility of sanctification and straightening by the Divine Logos would be denied to man. Thus, the structure of the Deesis rank is revealed as a series of verticals, of which the middle one is motionless and autocratic, and the lateral ones adhere to the middle one, are directed towards it, although they remain in their places, and through their movement are identified with this fundamental principle. There are many verticals here, but in essence there is only one, and all the others are perceived as rhythmic repetitions of the main one. They should gravitate back towards this main one and move towards it. But this movement is a single movement, a single process emanating from the middle vertical, the rhythm of the entire structure as a whole, the law of movement imposed on the verticals in their very placement. This rhythm comes from the main vertical and is therefore united. This implies the need for a rhythmic and symmetrical structure of the entire order. The direction of the verticals to the main vertical is achieved in the design by the inequality of both sides of each vertical, i.e. manifestation of the difference between their right and left sides. Figuratively, this is achieved by rotating the corresponding figures about the vertical axis of their bodies, so that all the figures look with their faces towards the main vertical. But in addition to the direction, which expresses the dependence and derivativeness of these verticals, there must also be their movement towards this vertical. This movement is achieved by the humps of the people ahead, or more precisely, by the flatness of the upper part of their figure. The lower part is not spread out, because it is motionless: the feet of those present should stand, and not walk. The movement of those approaching the Savior is a spiritual movement, not a mechanical movement in space, and the merging of their verticals with the fundamental principle has nothing to do with the denial of the physical impenetrability of bodies. On the contrary, while maintaining their physical stability and independence, those of the Deesis rank spiritually move towards the middle vertical. The flatness of their torso is not flattened, but a turn: passing by us, they are visible first from the chest, then from the side, finally from the back; depending on their movement, the eye sees successively almost the entire surface of the torso, and we directly see it incomparably more voluminously than we would see if it were motionless: we see these torsos moving. On the contrary, motionless legs stop the physical movement of the figures and transfer our perception to evaluate this movement as spiritual. Physical movement would introduce an inappropriate restlessness into the Deesis rite, something unpeaceful and therefore worldly. Complete immobility would split the rank into separate independent figures. Only this motionless movement unites the entire rank with the spiritual life flowing through it, an etheric current that permeates everything, but does not raise any dust. This is an imperturbable world that is from above, but despite its equanimity it is full of life and tireless movement. The Deesis rite, if left alone in contemplation, gives the impression of music, an endless melody, and never stopping, but never boring. Ancient churches are filled with this and sounds - although they do not vibrate the eardrum, they are clearly audible. External movement and mechanical movement in general are not given to the aesthetically contemplating eye as such, i.e. not as external ones, but as symbols and projections of internal movements, processes and states of our spirit. Regarding music, this statement is self-evident: after all, no art is so full of movement as music; and yet what kind of external movement can we be talking about here? It’s not about sliding the bow or running your hands across the keys. Music deals with the inner essence of movement, with movement as the pure quality of everything moving, but does not take into account the manifestation of this quality in the external world. In relation to the visual arts, the same symbolism of movements is not as self-evident; but nevertheless, even here, if you look deeper, the external movement of objects concerns the artist no more than listening to music - the sliding of the bow or the running of the hands and the striking of the fingers. The perception of moving objects can become artistic only when the law of external movement is understood and assimilated as a special rhythm of our inner life, and the moving object dissolves in the spirit, transmitting its movement to it as a certain vibration. In an artistic sense, the movement of external objects means only the trembling of the motionless spirit. And the artist’s task is to consolidate these internal rhythms in the vibrating soul. Therefore, it is natural that the artist can receive the most powerful vibrations not where the living force of external movement is great, in the mechanical sense, but where reality itself has already processed external movement into internal processes and where, therefore, the artist is already provided with sufficient material for his own perception. After all, what does it matter if a huge mass of a steam hammer falls in front of the artist or a projectile thrown by a gun flashes at high speed? These movements, significant mechanically, are too meager in internal rhythm to give much artistic depiction. On the contrary, even a slight movement of the commander’s hand or, to take an even more extreme example, the slight play of the facial muscles provides the artist with very rich material, because they themselves are extremely condensed internal movements and rhythms of these powerful energies, leaving far behind them the fall of the hammer and the years of the projectile. That is why it should not seem surprising that the types of depicted movement discussed above in the previous paragraphs are predominantly internal in nature, and the richness of the movement appeared all the more clearly the deeper it was hidden in the inner life. The limit of this deepening known to us on earth, that focus of internal rhythms to which they strive and in which all movements are united according to their inner meaning, is the human personality in its own self-consciousness. And the visible symbol of all these internal movements is the face. Therefore, an artistic portrait, before all other types of fine art, must primarily solve the problem of movement. And the more motionless the face, the head itself, as an object among other objects, the more acute the artist faces the task of conveying the internal movement that furrows the inner space of the personality. A portrait that does not convey these movements of inner life, i.e., in other words, that does not unite in a single image various expressions, each of which corresponds to its own state of mental life, has nothing to do with art at all: it is an image not of a person, but of a microtomic slice of it. In this sense, individual parts of the face image should contradict each other in an artistic portrait, if we think anatomically. Otherwise, instead of a portrait there will be a plaster cast. This inconsistency of various features and organs of expressiveness is a condition of artistry, necessary, but not sufficient, even with the proviso that the contradictory features are brought as lines and color spots to compositional unity. A portrait, like any other image, must have constructive unity in mind, i.e. the real connection between the individual organs and parts of the depicted object in its own reality, independent of the artist’s compositional intentions. It was just said here: “like any other image”; but this must be said stronger and more insistently. After all, the portrait painter does not take the personality as a part of the world, which he can put in real or imaginary relationships with other objects and thereby legally, albeit arbitrarily, according to his own intentions, one way or another change the structure of the space in which the objects he depicts interact. On the contrary, in a portrait, at least in its purest implementation, the personality is depicted in itself or emerging from itself only to the extent that this is characteristic of its structure. Therefore, the space depicted here is already predetermined by the structure of the personality, like its internal space or the space of its face. Here the design powerfully subjugates the artist, more than in works of a different kind. Thus, the unity of the image is predetermined by the unity of the facial structure, i.e. some actual relationship between its functions and organs. The contradiction in the image mentioned earlier must be subordinated to the functional unity of the facial structure, in which each organ of expressiveness performs its own service, although anatomically the activities of the various organs are not joint, but each act at their own time. The artist takes in the portrait these characteristic, but sequential states of individual organs. The purpose of composition is to present to the consciousness in sequential order the images of the organs appearing in appropriate order when some movement takes place in the inner life. This is what gives the portrait life. A movement can, generally speaking, take place in different ways, and, no matter how it goes in reality, it will not surprise us, being considered as an isolated case. But fixed with a pencil or brush, such a movement would give an unbearable grimace, would be anecdotal and random. There are, among many possibilities, some specific orders and rhythms of movements, one might say, eternal movements that characterize the life of the individual, conveying its very structure. There is an internally logical order of the sequential appearance of different organs, and only if this is observed can the internal movement of the personality, as its form in time, be expressed in the portrait. Perhaps this form is ambiguous, i.e. it corresponds to several different orders of succession - several tonalities characteristic of a given personality, probably at different depths. The artist is then free to choose one or another order, one or another tonality, one or another aspect of understanding a given personality. But nevertheless, he must take into account some of these rhythms, i.e. construction of personality over time. For the sake of certainty, we will indicate one of the most important orders of sequential performance of organs - one of the most important, although not the only one: “The main melodic motive of the face is given by the relationship of the mouth and eye to each other. The mouth speaks, the eye answers. Excitement and tension of will are concentrated in the folds of the mouth, and the permissive dominance of the intellect dominates in the eyes. ... An arc of less tension is thrown by portrait painters from one eye to the other. They give both eyes different emotional expression; at the same time, one thing is further emphasized and becomes the finale, so that the teleological relationship is definite and irreversible. ... In the same way, other factors of facial expression can become a counterweight to the emotional content of the dominant eye, and in the same way everything that expresses the own language of individual forms. Then our eye glides again and again, starting from its resting point, and finds more and more new stimulations and questions, which, upon its return, are resolved in the basic tone of the eye. And in its calm, wide movement - back and forth - it collects a rhythm of consistency and tension and resolutions, promises and fulfillments, which we feel as the calm breath of healthy life" 29. This is one of the rhythmic schemes of a portrait, not the most sublime, but perhaps the most characteristic of a person of Renaissance culture. A portrait, as it is considered here, necessarily has a certain temporary depth of personality, a temporary amplitude of internal movements. It embraces the personality in its dynamics, which, due to the comparative slowness of its own change, is taken here statically. But nevertheless, the very dynamics of the personality are subject to some natural process, and should not be taken stationary in relation to the entire life of the individual. In short, the personality has the dynamics of its dynamics, and, therefore, along with itself the correct arc of its repeating movements - the general trajectory along which this arc itself shifts and reforms. There is a general path of internal growth of the entire personality, considered as a whole connected in time, just as there is a general flow of a river, with the presence of separate waves on it. The portrait, such as it is presented here, is intended to capture and express the typical form of a single wave, which changes little over a relatively narrow period of biography. But nevertheless, there is a whole biography, so that the portrait painter’s immeasurably more significant task would be to depict the personality in this general flow. Can a portrait, in the above sense, capture this great movement? – It is difficult to give an abstract answer to such a question, but judging by the absence of such portraits, such an extensive synthesis is beyond the power of a portrait painter. In those cases when attempts of this kind were made and, to one degree or another, succeeded, they brought the portrait onto the path of icon painting and powerfully pushed the painter to use icon painting techniques and to master the icon painting way of seeing things. Since the set task of biographical synthesis has been achieved, the image must deviate especially far from anatomical identity, for it conveys not this or that separately captured section of the life of a given person, but the connected course of its entire development. Such an image relates at once to infancy, and to youth, and to adulthood, and to old age of the person depicted: relating to all ages in their totality, it obviously cannot and should not give a separate image of any separate strip of biography. By depicting the personality in its temporal whole, it is thereby incomparable with each individual moment of this whole. It sparkles with individual moments that flicker in it, like cells in a cut watermelon. And every moment finds a place for itself in this whole and gives its trace there, but cannot exhaust the whole: it is similar to the whole, but the whole is not like it. In such an image one can feel and recognize every deep manifestation of a given personality, at all its ages and at all stages of growth; but it would be a complete misunderstanding of the very task of the image to try to identify it with one or another particular aspect. This face is neither young nor old, nor in either individual experience, but, of course, not something in between. This is not an abstract common to all states, but a concrete and visual unity of them, that is, the spiritual appearance of a given personality, its idea in the Platonic sense, or entelechy. In this image, a person is more similar to himself than how he appears each time in nature at separate times - more like him than himself, as he appears from the outside. A butterfly that has flown out of a cocoon and lives, perhaps, only for a few days, is the entelechy of that creature that lived for months in the form of a caterpillar. There is no resemblance between the butterfly and the caterpillar, and a more attentive glance of the comparative anatomist and histologist dispels even the superficial similarity that apparently is established between the caterpillar and the elongated body of the butterfly. Everything in a butterfly is new, every organ, every tissue. And yet, the butterfly is the real appearance, the innermost soul, the entelechy of the caterpillar, and in the butterfly the caterpillar resembles itself incomparably more than in its own worm-like appearance. Thus, a biographical portrait has the task of representing the transtemporal unity of the personality. If we talk about it in the cognitive plane, then it should be called an image in which the coordinate of time is viewed across, whereas usually it is taken along (an allusion to the famous expression of Martin Luther: “We look at time along, but God sees it across”). On the ontological plane, this image is the appearance of a resurrected body, combining in itself everything deep and strong of all individual ages, but not separately, but in an integral unity. This is the whole person, throughout his entire life, valuable in every moment of it. So, the stage of synthesis under discussion could be called a portrait after the resurrection. Such a portrait could achieve its full expression only then: “Now I understand in part, but then I will know as I know myself.” Now, in the present state of the world, such a portrait is possible as an anticipation, and, moreover, an anticipation in two ways. Firstly, in the artist’s thoughts, with a special premonition or insight approaching that future state. Secondly, by the vital self-transfer of the depicted person to his future state. In the first case, the artist sees the future as the present; in the second, the person he portrays lives in the present as in the future. The artist exposes invisible things; depicted by him, according to the words of some ascetics, “having achieved perfect dispassion, he has already risen in this life, before the general resurrection.” Thus, a naturalistic person can still be depicted from the angle of eternity, by the power of artistic insight; and vice versa, a naturalistic artist can, to a certain extent, by the strength of the depicted face, show a reflection of eternity on it. This aspect of eternity is fully expressed in art without the slightest hindrance, when both paths of eternity, the path of knowledge and the path of life, intersect - in other words, when a holy person is painted by a holy artist. This is in the proper and precise sense an icon. But along with this there can also be icon portraits of two kinds. Firstly, a naturalistic depiction of the holy face. Such an image has value - a historical document; but it does not relate to art and the equivalent photographic photograph will always be more appreciated in front of it. An image of this kind, like a photograph, provides less than direct external vision, and turns out to be necessary only in the absence of the latter. On the contrary, the artistic insight of the resurrected appearance in natural man gives much more external vision; in the very essence of the matter, such an image is an overcoming of the naturalistic shell of a given person and therefore itself in no way should and cannot be naturalistic. It expresses the synthetic spiritual image of a given person, that internal image that is formed by those who know him throughout life, and even something even deeper, because here the secret, unexpressed and, perhaps, will never break through, is woven into the obvious and revealed by a person. The saint to a large extent makes himself through the “art of arts,” asceticism, coinciding [with] his spiritual appearance or, in any case, transparent to it. Its appearance can be likened to a portrait icon from it. On the contrary, a non-spiritual person is a dark, undeveloped thickness, a damp shell, impenetrable to the rays of glory of the inner appearance. And therefore, a portrait from such a face (we mean a naturalistic portrait) is not capable of being an icon, even a portrait one. If you want to show the spiritual essence of this person, despite its non-manifestation in external features, then it is necessary to make your starting point not these external features, not the periphery of the face, but to penetrate beyond it. In other words, an iconic portrait is needed here. There is a special kind of portrait, belonging to a synthesis of a high order, in which the combined fullness is given twice, once by a sequence of the most important life moments, and another time - directly, by an enlightened face. These are the so-called icons with a life. The center of such an icon is occupied by a face, whether it be a face or a full figure, but in both cases without external action, therefore, without expression and in addition to the relationship to other objects. The face here is the center of all relationships and contains all space. This is the world as it is contained in the face. On the contrary, the fields of such an icon with a life are occupied by individual moments from the life of a given person, and based on this alone, the fields are divided into a multiplicity of these moments: here the entire life of a given person passes sequentially, outlined by its nodal or corner points that determine the main turns of its movement. If the middle does not represent a person, then the fields are dedicated to the main events where the activity of this non-human person was reflected (such, for example, is the icon with the life of the Archangel Michael in the Trinity Cathedral of the Trinity-Sergius Lavra). Individual compositions of these hagiographic fields of the icon show actions, feats, trials, etc. from the life of a given person, i.e., his relationship with the outside world, his active connection with it. And therefore, in complete contrast to the contemplative, detached face of the middle, they must be saturated with drama and unfold the action of life in its most movement-filled turns. In this sense, the icon-life contrasts the serene and supermundane calm of the middle, this peace of the heavenly center, with the movement and excitement of the fields, like the periphery. However, this periphery is not some kind of secondary importance, compared with the essentiality of that center: both the fields and the middle show the same thing, but once - when viewed from bottom up, and the other time - from top to bottom. They relate to each other as noumenon and phenomena of the same essence, and the face of the middle is the beginning and end, the cause and goal of the movement unfolding in a series of everyday events in the fields. From the cradle to the grave, human life passes before us in the greatest effort of life’s struggles, and each composition itself excites with the drama of what is depicted on it, because it excites thought to before and after it. But all together, the entire circle of the field closing in on itself is perceived as a whole as a single phenomenon of eternity, as motionless movement and is affirmed as such by its motionless center, where there is peace, balance and self-sufficiency. Then the entire circle of fields turns out to be just a disclosure and explanation of this middle, notes to the face. From the diversity of fields and the constant sliding along them, we ascend to the unity of the middle and contemplative peace in it. And vice versa, we comprehend the simple completeness of this latter with greater consciousness and dissected in the complex construction of the field. We are now moving no longer along the periphery, but centripetally and centrifugally, seeing with the help of each of the individual field compositions the corresponding side of the personality depicted in the middle, and now we relate the individual compositions of the fields to each other through the unity of the center, which makes them possible and coherent, just as vice versa, we see the fullness of the face as vitally expressed in a number of life manifestations. The icon-life was considered in ancient times to be a high, if not the highest, form of fine art. And in fact, it combines frescoes and icons in a closer sense, a facial life with a spiritual portrait. This poses enormous difficulties for her to give compositional unity to each other of individual field compositions, without making them, however, ornamentally repetitive and therefore monotonous. In a book that is leafed through, the impression of each individual illustration is somewhat erased, and therefore some exaggeration of the compositional unity of individual illustrations may even be necessary for the sake of greater coherence of the book as a whole. Here, in the icon-life, all the individual compositions are presented to the viewer together and are constantly compared with each other in all sorts of combinations. Their compositional inconsistency with each other would be immediately noted as something glaring. But at the same time, the mechanical repetition of the composition would nevertheless hurt the eye, like a stop in the dramatic development of life, like a useless delay in action. The artist needs enormous wisdom here in order not to err in either direction. But not only that: all the field compositions together belong to one whole and, in addition to their compositional affinity as individual compositions, they must also have a common compositional whole, together with the image of the middle, although this latter must, in turn, be significantly different from the fields. This task of constructing an icon, from drawings and paints, from constructions, makes the type under consideration really difficult, but at the same time it most powerfully covers space along the fourth coordinate, time. The time coordinate in all the cases considered here was introduced as characterizing movement, change, growth, in general, the life of the depicted reality; but at the same time the artist himself is not thought of as a reality among other realities of the world and is not considered as a living being. This is only the contemplating eye, only the thinking mind, something abstract. For the sake of clarity of analysis, it was advantageous to limit ourselves to such a conditional premise, although it does not comprehensively cover reality. But now, having performed a narrowed analysis, we can and must remove the restriction made and take into account the coordinate of time not only in the structure of what is depicted, but also in the internal form of the image itself. In fact, a work of art is a fixed act of aesthetic cognition, and, as such, a work of art should be recognized as manifesting a knowable reality with the same right as a cognizing artist. It is reality itself, but it is also the personality of the artist. More precisely, it is the fruit of the marriage of a cognizing artist and a cognizable reality, in which two heterogeneous energies form an inextricable unity. This word “marriage” should not be considered to have slipped through here by chance: there is, in fact, a deep analogy of knowledge, especially aesthetic knowledge, with marriage, recognized from ancient times by all peoples and enshrined in all languages; however, this is not the place to discuss these epistemological questions. The essence of the matter is the need, when discussing a work of art, to take into account the artist as something completely different from a mirror, as a being that itself has a form in time and is determined by time in all its manifestations, large and small. Everything that has been said about time in relation to the reality depicted should be repeated, with slight appropriate changes, also in relation to the depicting artist himself. And in it, as well as in the depicted reality, duration and time enter not as an accident, something that, although not eliminated in each particular case, is fundamentally eliminated, but as an absolutely necessary aspect of existence. And this side with an immutable necessity is imprinted in a work of art and builds it. Considering the coordinate of time in art with this vital understanding of the artist as a being among other beings does not seem particularly difficult: to a large extent, it would require paraphrasing everything that was said about time earlier, when it was considered more narrowly. Indeed, in relation to time, the principle of relative flow can be stated. In a particular case, it is reduced to the principle of relative motion. It makes no difference which of the two systems changing their mutual position moves relative to the other - the perceived image of the observed system, as a certain form in time, will remain the same in both cases. In short, movement is something mutual, not self-sufficient, a way of relating two or more numbers to reality in time. And in relation to art, i.e. in relation to the artistic collection of time, in this simplest case, the principle of relative movement means indifference in the construction of an artistic image whether something is moving past or near the artist, or vice versa - whether the artist himself is moving past or near something. Both will give the same fruit, and, starting from the latter, we will no longer have the data to decide to whom exactly the movement should be attributed here. But what has been said also has a broader meaning: relativity, or, more precisely, correlativity, extends not only to mechanical movement, but also to all kinds of changes, to growth, to all life. After all, life is always thought of as a way of mutual relationship between at least two realities, generally speaking - many, and we live, grow, change - just as we move, that is, in relation to something else. Whether to attribute these processes to ourselves or to the environment is a conditional matter and depends on the arbitrariness of our understanding: the emerging image here and there will remain the same. Thus, the coordinate of time in the cognizing artist should not have introduced any significant changes into all previous discussions about time, if the conceivable motionless artist did not interfere, in everyday understanding, with the corresponding enrichment of the environment with time. But the habit of thought usually limits the diversity of environmental processes, because part of the movements, changes, processes and life in general is attributed to man, in particular the artist. That is why it turns out to be necessary to note at least something from the time coordinate of the artist himself. The very first thing that should be noted in this sense is the basic fact of the binocularity of our vision - a fact as indisputable as it is stubbornly ignored by those who need to defend linear perspective at all costs. Kunrath has an allegorical drawing: an owl wearing huge round glasses, and behind her two large torches and telescopes, and under it the inscription: “ah, glasses, pipes and torches will not help someone who does not want to see” 30. And yet we see with two eyes, and not with one, that is, from two points of view at once, and not from one, as required by perspective projection. Consequently, the image that takes shape in us through real vision, and not abstractly asserted in perspective textbooks, this image necessarily represents a combination of at least two separate, and non-coinciding aspects, according to perspective assessment. He plays and gives the themes fullness and volume. Each eye provides, in relation to the other, an additional surface, visible to it, but inaccessible to the other eye. Even if we make the completely lifeless and incredible assumption of the complete immobility of the depicted and the depicting, then additional surfaces still remain, and, when examining close objects, they can be very significant. So, to take an extremely convincing example, let’s pay attention to vision when the object is placed very close to the face. The hand at the bridge of the nose is seen by one eye from the palm, and by the other from the back surface. If you place an apple close to your face, then when you alternately close your eyes, it seems to jump from place to place and differ in appearance. This is a case of complete separation of both visual images, right and left, from the same object. It’s clear that even if each of them separately were consistent with the requirements of perspective, then both of them together cannot in any way be combined into a single perspective image of one object; and if in our imagination they are nevertheless combined into a single image, then, obviously, this image contradicts the perspective projection. If the object is now moved further, then an area of ​​its surface is formed that is visible to both eyes at the same time, although each eye sees it in its own way. In addition, each eye has a portion of the surface of an object that is visible only to that eye and makes up for the surface available to the other eye. When conveying the visible in an image, it is necessary, if we want to remain faithful to actual experience, to give an additional surface of the object, which clearly contradicts the perspective image. At the same time, one cannot think that this additional surface, even with the above assumed complete immobility of the eyes and the object, is something negligibly small. As an example, we will calculate for a ball with a radius of 10 cm and at a distance of 50 cm from the eyes. Let the distance between two points of view be equal to 6 cm. Then, in a horizontal equatorial section, approximately one third of the same value is added to the sector visible by one eye from one point of view. This calculation corresponds to the case when we observe an interlocutor close to us, almost motionless. To a certain extent, the same conditions of vision were used when painting portraits, when they tried to convey motionless vision. The indicated one third already goes to direct and obvious refutation of the perspective, even in this, deliberately and contrary to life, adjusted ratio, the most favorable perspective. But life, life relationships, generally speaking, are not like that at all. The point of view, or more precisely, the double point of view of a pair of eyes, changes all the time, and the image that we perceive necessarily in time must be single, that is, in other words, it must combine many different aspects, combining each two aspects, from a double point of view. Our head rises and falls: as a result of this, the horizon rises and falls, and this circumstance gives us the consciousness of vertical space, as an opportunity to rise and fall. The assessment of the height of a building is most convincing during such ascents and descents, i.e., when the horizon shifts. And therefore, when an artist wants to convey to us an architectural image along with the assessment of its height that it evokes, he must inevitably abandon the perspective requirement of a single horizon. If it is necessary to increase this assessment and instill the idea of ​​the grandeur and greatness of a certain building, then it is necessary to resort to the mental experience of very large rises and falls, which leads to a significant shift in the horizon. This condensation of the impression of height is achieved very simply: by raising the horizon of the lower part of the image and lowering the horizon of its upper part. This is the favorite technique of a number of even those artists who, as a general rule, tried to maintain perspective. Rembrandt, Paul Veronese (“Christ at the Publican’s Feast” and “Marriage in Cana of Galilee”), Raphael (“The School of Athens”, compare also “The Vision of Ezekiel”, etc.) achieved with its help the impression of splendor and grandeur, depicting spaces that are not at all high, if you measure with an arshin, and not with the contemplating eye. On the contrary, if it were necessary to have a lot of canvas available to convey low and oppressive architectural spaces, then it would not be difficult to achieve the impression of this oppression, these low ceilings and constricted breathing, also by shifting the horizon. But only here it would be necessary to lower the horizon of the lower parts of the image, and raise the horizon of the upper parts. Of course, everything that has been said about architectural motifs can and should be repeated about all other vertical distributions of visual masses. The pictorial surface can also be saturated horizontally, and this compaction expresses the movement of the observer in the horizontal plane. A sign of such a horizontal shift is the non-unique center of perspective. Two motionless, but overlapping observations from two different places on a horizontal plane are expressed by two coexisting centers of perspective. A larger number of observations from different places gives a corresponding number of perspective centers. It may be, and even most often happens, the continuous movement of the contemplator; then the corresponding centers of perspective are located as a continuous set of points on a segment of the horizon. It is possible, further, to combine horizontal movements. Then the centers of perspective are located on different horizons, or even form in their totality some continuous curve, not identical, of course, with the observer’s trajectory or even with its projection onto the image plane, but in any case connected with the path of the observer himself and thus being a symbolic record of this path. In order to cover a certain internal volume, for example the volume of a room, we always try to move around a little, to walk around the room a little. How exactly to move in the most natural way for any observer - this, perhaps, given the lack of knowledge of such issues, cannot be said; but nevertheless, it is certain that there must be some specific methods of such observation, arising from the basic conditions of perception. In particular, it should be noted here: even in perspective textbooks it is indicated that it is useful when depicting space not to maintain a single horizon and a single center of perspective, but to locate the latter, or, more precisely, the centers of perspective along some closed curve. The development of an ellipse is especially recommended for this purpose. It, being made the geometric place of the center of perspective on the pictorial plane, corresponds to the movement of the observer inside the architectural volume of the room, with which movement this volume is covered most fully and most evenly, and this gives the impression of a calm and, so to speak, residential possession of this space, i.e. conveys the characteristic spiritual tonality of the interior. But, of course, the proposed technique is only one of the techniques and corresponds to a certain, in its own way legal, but very particular relationship to space. A different rhythm of mental life results in a different relationship to space and, accordingly, a different geometric location of the center of perspective. These are all general outlines and general considerations. They can be briefly expressed in words: the artist’s path is also recorded in the image. First of all, the path in the literal and most humble sense. Let's go, for example, through the forest. We move, and images of tree trunks appear before us. Let us stop: instantly the picture, while remaining formally identical, at the same time becomes significantly different. The trunky depth of the forest space instantly disappears, and the trunks themselves lose their volume. The impression is as if the tree-trunked distance suddenly lost one dimension. The relationship between the image of the forest, perceived from a moving point of view, and the new one, perceived when stopping, is the same as between a flower and its dried preparation in a herbarium. In short, by stopping the observer, the image of the forest is flattened, and by its movement it unfolds. [The forest] is perceived with amazing, almost painfully acuteness in winter, when you walk along the road along naked alder and willow thickets. The interlacing of branches, projected against a light background, the sky or snow, appears as a flat lattice, in relation to which the question of depth does not even arise. But against a dark background, a spruce forest, the same branches give a depth so strongly perceived that the entire volume of this thicket appears to be a crystal mass with thin crystal needles in it. When you move, you see this depth quite clearly, like a crystal firmament. But stopping instantly dispels such a perception, as if the solid had melted and poured out, leaving only branches, already deprived of connection in the third dimension. But, of course, neither the trunky distance nor the branchy one can often be approached in its depths with the correct perspective: the whole essence of these perceptions of depth is precisely in the bright negation of perspective. They are even more clearly and clearly subverted when we look at the clumps of nearby trees from the window of a passing train. These kupas seem to rotate about their axes and show successively different aspects of themselves, so that the surface of the kupa unfolds before our eyes almost entirely, if not entirely. However, by this unfolding the volume of the grove is not only not erased from consciousness, but on the contrary - this is where the tree appears truly corporeal. There is no doubt that we have here a single and holistic image of a tree. But this image essentially excludes a perspective interpretation of itself and, in a perspective manner, must be recognized as nonsense. On the contrary, as soon as the train stops, the expansion of the tree surface also stops, with the successive extension of various aspects of the crown. The image of a tree approaches the perspective projection (although it does not completely merge with it), but at the same time it loses its volume and becomes flatter. It is interesting to observe how the physicality of the image fizzles out as the train slows down and how, on the contrary, the image is filled with volume and spatially comes to life as soon as the train speeds up. Here, in this observation from the train, as in the previously described observations on a walk, one very important circumstance should be noted: with the movement of the observer, the images not only acquire volume, but at the same time - reality. With motionless contemplation, they are likened to ghosts and shadows of things; when the observer moves, they become fuller, more real, stronger and denser - they become real things. By walking around the depicted objects, these objects are vitally connected with us and thus provide images in which we perceive the own life of things and their independence as realities. The artist’s path, however, can run not only past one or a few trees, but extend across an entire area, over many areas, and finally last for days, weeks and months. From such a journey, he may not have a complete image left in his consciousness, and all impressions will then scatter separately, internally unconnected with each other. However, this would only prove the looseness of his apperception and the lack of a sufficiently strong ability for synthesis. On the contrary, with greater apperceptive elasticity, the journey will give the artist, as a result of cohesion, compaction, generalization of what he saw, a certain holistic image, and this image can be fixed and embodied in art. Once this journey was perceived as a certain integrity, there could be an image of it, consolidated and embodied with internal movement. The thoughtful geographer has an idea of ​​large geographical regions, and he immediately distinguishes the landscape of one region from the landscape of another. And these ideas, perhaps in most cases, are somewhat vague, but nevertheless they are clear and concrete; It would be a mistake to think that the geographer analyzed them analytically, and in any case, he is not guided by analytical signs when recognizing them. If the geographer had a stronger apperception, then perhaps he could consolidate his ideas about geographical areas as artistic images with internal movement. The same thing should be repeated about travel in general. But there is a path of even greater scope than travel: this is the inner path of the artist. Changes in the artist's mood in the process of a famous work; its deepening into the depicted object; his spiritual growth; transition to a new style; finally, the entire biography as a whole - these are the artist’s increasingly significant changes, shifts in point of view. All this is summarized and fixed in the work as a certain path of the artist. It is not “can be part of the work,” but inevitably enters there, and the artist’s attempt to hide his path and pretend to be instantaneous leads to falsehood, to artistic untruth. In relation to verbal works, these traces of successive rearrangements of the concept and the internal growth of the work itself have been partly studied; in visual works much less attention was paid to such study. But here and there, these traces of growth, a kind of annual rings of the work, are usually established to expose the author, whom the researcher catches in some inconsistency, in self-contradictions and inconsistencies. Traces of the artistic path are considered as annoying shortcomings, a consequence of some negligence of the author. It is a deep mistake when a researcher imagines himself to be more attentive than the author and does not understand that the latter did not want to erase the traces of his creative path. After all, they are part of the structure itself, and to destroy or hide them would mean depriving the work of its structure along the time line. The reader or viewer must grow in the work along with the author and undergo the kinks and turns, the layers of which formed the very fabric of the work. After all, it is they, the fixed surf of Time, who give the work its internal rhythm, without which it is dead and mechanical. If you look in a work not for the bare plot, but for itself, then in this growth of the work, its development in the life of the artist, in these unexpected contradictions, caused, however, by the internal necessity of growth, one cannot help but see the main beauty of the work, its sharpness, its soul. “Faust,” invented in its plan at once and written according to this plan, would be unbearable, just as American buildings or similarly constructed works of Valery Bryusov, made by will, and not formed by life, are unbearable. “In 1921,” wrote P. A. Florensky in his “Autobiography” of 1927, “I was elected professor at the Higher Art Workshops (VKHUTEMAS) in the department of “Analysis of spatiality in works of art.” This discipline had to be created using the data of mathematics, physics, psychology and aesthetics. ...over the course of 3 academic years I developed this discipline and wrote the corresponding course.” Based on the material of these lectures in 1924–1925. a published book was created. In the afterword to the article “Reverse Perspective” (1922), Florensky, recalling the protracted debate on a report on the same topic, read at the Moscow Institute of Historical and Artistic Research and Museum Studies on October 29, 1920, noted: “The liveliness of the discussions once again confirmed to me that the question of space is one of the fundamental ones in art and, moreover, in the worldview in general.” (Florensky P.A. Works: In 2 vols. T. 2. At the watersheds of thought. M., 1990. P. 102). These words, in our opinion, best express the general ideological concept of the series of works by Fr. Pavel: from the analysis of direct and reverse perspective as concrete historical systems of artistic representation - to the concept of spatiality, spatial forms, and further - to iconology, philosophical and art history theory of imagery in art and culture. At the same time, the range of problems thought through by the author was constantly expanding, including, in particular, in addition to spatial forms, also artistically significant phenomena of time. In 1937, deprived of the opportunity to engage in science, shortly before his death, P. A. Florensky compiled a list of his most significant, in his opinion, scientific achievements. He included the following significant entry in it: “In art history: 1. Methodology for describing and dating objects of ancient Russian art (carving, jewelry, painting). 2. Spatiality in works of art, especially fine art” (Letter dated May 11–13, 1937). The range of Florensky’s artistic research is far from being exhausted by these two topics—it is truly incomprehensible—but perhaps it is these poles that most clearly indicate the creative tension of his artistic and spiritual experience. P. A. Florensky is least of all an armchair loner, fenced off from the excitement of artistic life. Even in his student and university years, he, together with Andrei Bely, was in the thick of the quest of the Moscow Symbolists (see about this: Hierodeacon Andronik (Trubachev). The main features of the personality, life and work of Priest Pavel Florensky // Journal of the Moscow Patriarchate. 1982. No. 4. pp. 12-19). L. F. Zhegin recalls that in 1912–1914 Florensky “was in the house of the cubist artist L. S. Popova,” where “artists and theorists of the left artistic sense – A. A. Vesnin, V. E. Tatlin, A. V. Grishchenko and others” gathered; He also conducted “something like a seminar with a small group of art historians and art lovers - in one of the premises of the Museum of Fine Arts” (Zhegin L.F. Memoirs of P.A. Florensky // Bulletin of the Russian Christian Academy. 1981. No. 135). A long friendship connected P. A. Florensky with V. A. Favorsky. The agreement of the masters on the main issues of understanding the nature of art is evidenced by Florensky’s bookplate by Favorsky, as well as his covers for the book by P. A. Florensky “Imaginaries in Geometry” (Moscow: Pomorie, 1922) and to the magazine “Makovets”. Both covers o. Pavel devoted art criticism essays. The history of collaboration between P. A. Florensky and artists Efimov and Simanovich-Efimova is interesting (Efimov I. About art and the artist. M., 1977; Simanovich-Efimova N. Ya. Notes of a parsley plant. M., 1978), etc. In the 20s, the work of Fr. Paul is associated with the literary and artistic association “Makovets”, the task of which he saw as being “the central elevation of Russian culture, from which the waters of creativity flow in different directions” in order to cultivate “awareness of the need for a righteous attitude towards life, the desire and decision to break through to reality” (In the praiseworthy “Makovets // St. Pavel Florensky. Collected works. T. 1. Paris: YMCA-Press, 1985, pp. 380–383). In his artistic and philosophical views, P. A. Florensky was not just a realist, but, one might say, he was a radical realist. In the chapter “Results” of the monumental work “At the Watersheds of Thought,” on which the philosopher worked in the early 20s, he wrote: “The prerequisite for activity, no matter whether it is visual art or verbal art, is reality. We must feel the authentic existence of what we come into contact with in order for cultural activity to become possible, which is closely recognized as necessary and valuable; without this premise of realism, our activity seems either externally useful, in achieving some immediate self-interest, or externally entertaining, fun, artificial filling of time” (Florensky P.A. Soch.: In 2 vols. M., 1990. Vol. 2. P. 341). In the atmosphere of that time, filled with the most violent attacks on the traditions of Russian realistic art, Florensky’s consistent defense of the principles of artistic and philosophical realism was extremely important. Preparatory materials for the lectures, student notes available to us, official documents and manuscript versions allow us to partially trace how the content of the lectures and the book was formed. In an official letter signed by the dean of the graphic faculty of VKHUTEMAS P. Pavlinov on 02/02/1924, P. A. Florensky was asked to “present the program ... of the course “Analysis of spatial forms” with a breakdown of all the material into two-hour lectures. When calculating, you must proceed from the annual lecture period of 20 weeks, i.e. for the course you are teaching, there are 10 two-hour lectures.” This course structure, judging by the available materials, was maintained throughout all three years of teaching. An interesting document has been preserved in the family archive: “Certificate No. 20. Given by gr. Florensky P.A. is that he is a professional. Anal.(iza) Perspective(actives) Graff. (iki?) Moscow Higher State Artistic and Technical Workshops, receives maintenance for the 17th category in the amount of 22 rubles. 40 k. per month. 10/15/1924. Moscow, Rozhdestvenka, 11.” Neither the lectures nor the book written on their basis received a final author's title. In the margins of one of the notes from 1924, which lists the topics of speeches at Shekhtel’s apartment, we find the question: “What is the title of a course on perspective?” In the introductory speech to the first series of lectures, delivered on October 13, 1921, the course was designated “Perspective Analysis.” The same name appears in the course record made in 1923/24. In the magazine “Makovets” (1922. No. 2), “Lectures on the Analysis of Perspective” were announced as being prepared for publication. The title of the book, adopted in this publication, and earlier in a partial publication of the magazine “Decorative Art of the USSR” (1982. No. 1), goes back to the article by P. A. Florensky: The physical significance of the curvature of space. From lectures 1923/24 at VKHUTEMAS on the analysis of spatiality in works of art/ /Mathematical education. 1928. No. 8. pp. 331–336. The change in title of the lectures and book reflected the change in their content. Based on the texts of the programs of 1921/22 and 1922/23, on student notes from 1922/23 and 1923/24, as well as on the notes and notes of the author, one can judge the nature of the changes that took place. Here are some of these texts: (Lectures in the second year of the Higher State Art Workshops, in Moscow, autumn semester 1921, given on Wednesdays, from 3 hours 50 minutes to 6 pm) (I am writing retroactively 10/05/1921 Moscow). (read 09/30/1921, Old Style, Wednesday) 1. I speak with the greatest embarrassment before you, existing or wishing to be artists, and this embarrassment is intensified by my own theoretical views on the artist and art. After all, the artist is a pure, simple eye looking at the world, the pure eye of humanity with which it contemplates reality. And, seeing the pure lines of reality, the artist shows them to us, and only then do we begin to see them. After all, our vision (nrzb.) depends on whether our attention is drawn to this something or not. Until it was addressed, we do not see, but when it was pointed out to us, we began to see. So it is in natural science - we are surrounded by a known phenomenon, we encounter it thousands of times, but we do not see it. And when someone was able to show it to us, isolating it in the laboratory or presenting it in the pure form of an experiment, or we ourselves pay attention to it, then we begin to see it at every step, and the hitherto rare becomes almost intrusive. An artist is such an experimenter. How can one teach him to look - for this, looking, is the essence of art - and not learn from him? Thus, the idea to teach appears as audacity. But this insolence will weaken in your eyes if we continue our likening of the artist to the eye. No nanny can make a child sighted, nor a doctor. But it is up to her to look after the eyes of her pet, so that there is no dust or dirt in them, so that nothing foreign obscures the vision and does not spoil the eyes. She should wash her eyes. In relation to our comparison, we can say that neither I nor anyone else can make you sighted. But it is possible and should take care that artistic perception is not clogged with tendencies, false views, theories that are acquired both consciously and unconsciously or semi-consciously from the environment, because theories are floating in the air and we are imbued with their poison, often without noticing or knowing it. It may be my duty to warn against lurking dangers, and this desire not to teach, but to protect, to philosophically protect the artist is no longer so daring. And besides, I admit, I willingly agreed to the offer to give me a course on “Perspective Analysis”, meaning not to teach, but to learn to look closely at the processes of your creativity, test your views and draw new conclusions from your observations. (read on 10/05/1921, Wednesday) Art is a symbol of reality. 1. The meaning of the word “symbol” (essence and energy). A symbol is something that is greater than itself: example: a painting as reality is a canvas, paints, frame, stretcher, but it is greater than it is in the real order - physical - as an essence. She is a window. Metaphysically, a symbol is an essence whose energy carries within itself the energy of another, higher essence, is dissolved in it, united with it, and through it manifestly reveals the higher essence. A symbol is a window to another entity not given directly. The first essence is the artist himself, his hands, his fingers, his brushes, his paints, etc. - connected by the movement of all this (?) - his energy, the energy of the lower. In this energy lives the energy of another reality, one that is not given to us directly: a flower, a garden, the whole earth, a face... And thus a different essence of the phenomenon. 2. Therefore, in the problem of art we have three points: a) reality itself, cognizable by perception; b) the perceiver with all his apparatus; c) the work as such, as a ready-made symbol of perception; Or in other words, in relation to fine art: a) the subject of the image, transformation; b) the act of artistic vision: perception-image (for one is inseparable from the other), one cannot say: sees and, therefore, depicts, physically the imprint with paint can move away in time; c) contemplation of a work of art as already finished. We are currently not dealing with the entire content of these three moments, but take them only in a certain context - the main spatial synthesis. We don’t take paint, but only form, and only one-sidedly... In this case, we will talk about time-space very abstractly, from our point of view: a) time, space, reality, b) the act of artistic visual perception, c) the act of artistic consideration, In order to get acquainted with the nature of the preparatory materials for the “Lectures”, we bring to the attention of readers one of the most detailed fragments (most of the others are cursory notes): 05/17/1922. On the train on the way to Moscow. 1. In all art there is the creation of a special space of its own (I will use the term “space” in the general sense, as space-time, three-dimensional space); and all art strives to create in spaces of space, new other spaces. But poetry (and music), by directly organizing time, allows the reader’s imagination, based on the instructions they give, to imagine for himself how these instructions are implemented in practice. Here the artist shifts the construction of space from himself to the reader or listener. Theater and sculpture (as well as architecture) provide space in space, but illusory, therefore the power of material space, the substrate of this art - that is, the space in which these actors and scenery, these sculptures, these buildings are contained - appears too powerful here, and it is not for the director to fight this space, but for the theurgist. Of course, the playwright can give all sorts of tasks to the director and demand a lot; but these demands will not be satisfied by the nature of the material with which the director is dealing, and the drama will remain pure poetry, not transferring to the stage, or, what is worse, being significantly distorted on the stage. Thus, a scene on stage is always staged falsely, because according to the playwright’s plan, it is viewed from the point of view of the characters on the stage, and not from the point of view of the audience. The things of the physical world - props and actors - are spatially too weighty to be placed in any space. The poet is too flexible, and the stage performer is too inflexible, they are not adapted to each other, and therefore, for example, the appearance of ghosts on stage is deeply false and fundamentally false, like the mask and the stage itself - this is the penetration of the viewer into a closed volume, that is, it assumes that the viewer is looking from four-dimensional space - along the fourth coordinate (not counting time). The stage has its own measure of time and its own measure of space. Painting (and graphics) alone not only gives the artist the means to actually organize the image of the space that he has conceived; and it is not connected by the properties of physical space, or, if connected, then very little, exactly as much as is necessary for the connectedness of the transition of physical space, the space of the canvas, to the space on the canvas. The pictorial plane provides a scale for estimating space on the plane. To understand the space of the image, we need to have a fulcrum in the space of its canvas, in order to distinguish there the symbolic from the total mass of the simply given, to separate the ideal from the actual. This point of departure should be as easily visible and recognizable as possible: this is the image plane, a rectangular frame of vertical and horizontal. Other surfaces are, of course, possible, just as other frames are possible, but both of them should be as simple as possible and immediately understandable: a sphere, an ellipse of rotation, a cylinder for pictorial surfaces, a circle, an oval, a square placed on an angle for others, although all this complicates understanding. In some special cases, all this may correspond to the internal requirements of the plan, but in general it is rarely advisable. On the contrary, if the surface is uneven, if the frame is arbitrary, if it is not rational (?), cannot be properly clear (?) of the space itself, the image then becomes incomprehensible. So, painting is busy organizing space. 2. The organization of space, as the creation of special spaces, is, as has been said, the task of all art. But to make this idea clearer, it is useful to consider several different activities in parallel. Let's take examples - those examples that come to mind. "Aida". In the last act, the stage is two-story (?): the inside of the church and the inside of the dungeon are visible. As stated, the scene as a whole is a somewhat naive attempt to organize vision along the fourth dimension. The stage is a world, closed in on itself by scenes and scenery. (The two floors of the stage are, however, not two spaces, but one. Both floors are thought of as coordinated with each other.) There are certain spatial relationships between the actors on the upper and lower stages - not only physically (the actors), but also the symbolically depicted persons. On the contrary, in the ballet scene with black children, the black children, as if dancing in front of the viewer on stage, form a special, their own space. A new space is formed in the space of the stage, that is, according to the author’s intention, but is not formed in reality, because this ballet is subject to the same spatiality as the actions of the threads of the mise-en-scène (?) (for example, they are visible from the same point of view, although they should be visible from the point of view of those spectators). There are (ideally) no ties between the stage audience and the stage actors. distances, as there are none (ideally) between the audience of the hall and the actors. The content of the lectures was shaped not only by their program, but also by the author’s lecturing style. In a special note “Lecture and Lectio” Florensky wrote: “... the essence of the lecture is direct scientific life, joint reflection with the listeners on the subjects of science... this is the initiation of listeners into the process of scientific work, introducing them to scientific work, introducing them to scientific creativity, a kind of visual and even experimental teaching of work methods, and not just the transfer of the “truths” of science in its “present”, in its “modern” position" (Florensky P. A. First steps in philosophy. Sergiev Posad, 1917. P. 2–5). Behind this attitude to lecturing work was not only the didactic style once chosen, but also a sublime, spiritual understanding of the tasks of higher education as such. The value of it about. Paul saw “not in the technical benefits of learning, but in the opportunity to establish a special spiritual and cultural environment that would have such a powerful effect on those in it, both professors and students, that their spiritual and cultural forces, receiving thousands of invisible currents, would unfold on their own, grow and bear fruit” (see the cited article by Abbot Andronikos, p. 239). As for P. A. Florensky himself, having ten years of professorial experience behind him, he retained his characteristic style of communication with students, his understanding of the tasks of higher education in VKHUTEMAS, although the general ideological atmosphere here was undoubtedly different, much more ideologized by representatives of the Left Front of the Arts and much less spiritual. In one of the surviving notes addressed to the professor, an unknown listener asked: “After the lecture, be kind enough to highlight your view of scientific communism.” Apparently, reflecting on questions of this kind, in a note dated January 24, 1924, P. A. Florensky wrote: “An explanation regarding LEF - about the mystical interpretation of artistic laws.” The author worked on the manuscript of the book from 02/05/1924 to 01/09/1925, dictating it paragraph by paragraph to S.I. Ogneva 31. The dates of work on individual parts are given in the margins of this publication. In the typewritten form that has come down to us, the manuscript contains the following sequentially printed parts: 1. Main text of the book §§ 1–33. 2. The text of “The Law of Illusions” published as an article (03/22–05/24/25). 3. “The meaning of spatiality” (04/18/1925) is a fragment containing the fundamental ontological interpretation of spatiality, which precedes in meaning its epistemological and cultural interpretation given in §§ 1, 8 and 22. 4. Absoluteness of spatiality" (04/26–07/07/25) is an independent, apparently not completely finished work, which in its meaning develops the content of §§ 3–7 and 9–21 of the main text of the book. It is quite possible that this text was supposed to be the beginning of a new edition of the book, which the author, however, did not prepare for publication. The text of the published book is very diverse in material: there are philosophical justifications, mathematical calculations, physical concepts, data on psychophysical perception, and much more that can not often be found on the pages of one book. And this is not a whim of genius, not a concession to a compressed curriculum. Behind the diversity of the material and the flexibility of the movement of thought, an established methodology and the intuition of the once chosen creative method are obvious. Along with the joy of spiritual gains, it brought a lot of inconvenience to the author. Even at the beginning of his career, Florensky wrote to A. Bely: “There is absolutely no place to publish: for one magazine it is too scholarly, for another it is too “in the new style”; for one it is too mathematical, etc., for another the mystical and theological elements are disgusting. In a word, I cannot please anyone, and in good conscience I cannot change the method that seems to me to be my real path (the study of concepts and the synthesis of heterogeneous materials). As a result, you prefer to think more than to write” (Letter to A.N. Bely dated January 31, 1906). The “Analysis of Spatiality” is also imbued with the desire to “explore concepts and synthesize heterogeneous materials.” “Our task,” said VKHUTEMAS, “is to more accurately clarify for ourselves the concepts that we constantly use, but which need to be deepened, to find out in what sense we want and have the right to apply these concepts to aesthetic problems. These concepts are the following: integrity, spatiality, thing, as well as function and power” (Lectures 1923–1924 at VKHUTEMAS: December 5, 1923). But even twenty years after Bely’s letter, it turned out that “there was absolutely nowhere to publish it”: individual mathematical and physical fragments had to be printed “in retail,” but the main part of the manuscript remained unpublished to this day. The text of “Analysis of spatiality and time...” is printed from a manuscript handwritten by S. I. Ogneva and P. A. Florenskaya) (several fragments). Whenever possible, the features of the author's spelling and punctuation are preserved; editorial conjectures are placed in square and angle brackets; All corrections are indicated in footnotes from the publishers, marked with an asterisk. Digital footnotes belong to the author. §1. Clifford William Kingdon (1845–1879), English mathematician and philosopher who proposed in 1870 that matter is a type of curvature in space; Poincaré Jules Henri (1854–1912), French. mathematician, physicist; Weil Hermann (1885–1955), mathematician; Eddington Arthur Stanley (1882–1944), English, astronomer; they all developed the theory of relativity regardless of §9 M. Mordecai-Bolnyuvakiy. – Apparently, this means Dmitry Dmitrievich Mordukhai-Boltovskoy (1876–1952), famous mathematician, prof. Warsaw and Moscow Universities. Reference to English, mathematician J. Wallis (1616–1703) has not survived. §10. “fiat justitia, id est geometria Euclidiana...” - “Let justice be done, that is, Euclid’s geometry, and let the world perish, let experience perish” (Latin). §14. ...the concept of Gaussian curvature... - See: Gauss K.F. General studies on curved surfaces // On the foundations of geometry. M., 1956. §18. Link on it. mathematics and physics G.F.B. Riemann (1826 – 1866) has not survived. §19. Link to prof. The University of Vienna Joseph Clemens Kroebig (Kroebig) has not survived, but the preparatory materials indicate the book: Kroebig. Human sense organs. St. Petersburg, 1906. §21. Kantor Georg (1845 – 1918), German. mathematician, one of the founders of set theory. His works in this area have been republished: G. Kantor. Works on set theory. M., 1985. §22. It’s in vain, artist, you imagine... – A not entirely accurate quote from A. K. Tolstoy’s poem “It’s in vain, artist, you imagine...” (1857). §24. “area of Mothers” - Goethe I. F. “Faust”, part 2, act 1: “Goddesses rise in isolation from the world, and space, and times... Their world is unknown, untrodden, virgin, inaccessible, inaccessible to desires” (translated by B. Pasternak). §26. “...industrial classification”... - Calling the classification of works of art on the basis of the material used in their creation industrial and contrasting it - as more consistent with the essence of art - classification by purpose, Florensky develops a range of ideas that in VKHUTEMAS were usually associated with “industrial art” (Sidorina E. V. Towards the aesthetics of expediency: Some aspects of the theory of “industrial art” of the 20s as an aesthetic concept // Problems of formation and composition of industrial products. – Proceedings of VNIITE. Series “Technical Aesthetics”. M., 1975; Sidorina E. V. Once again about the aesthetics of expediency // Design, function, artistic image. However, unlike production workers, for whom expediency merged with functionality and was limited to the area of ​​social and everyday functions, P. A. Florensky defines the goals of art much more broadly - in relation to all reality, including spirituality. LEF's position in VKHUTEMAS was clearly opposed to the positions of other creative directions. In the editorial article “VKHUTEMAS” (LEF. 1923. No. 2. P. 174) three such directions are named: “finishers” (Shevchenko, Lentulov, Fedorov, Mashkov, Falk, Kardovsky, Arkhipov, Korolev, etc.), “applied workers” (Filippov, Favorsky, Pavlinov, Novinsky, Sheverdyaev, Egorov, Norvert, Rukhlyadev, etc.) and “constructivists and productionists” (Rodchenko, Popova, Laviisky, Vesnin, etc.). “Among applied workers,” reports LEF, “a curious subgroup has formed - “industrial mystics” (Pavlinov, Favorsky and priest Florensky). This small company has declared war on all groups and considers only themselves to be the true artists of production art. They are found in the graphics department and fill students’ heads with problems like: “The spiritual meaning of the letter form” or “The struggle between white and black verse in graphics.” Constructivists and production workers saw their task as “on the one hand, to beat the “finish workers”, defending the production line, and on the other, to press on the applied arts, trying to revolutionize their artistic consciousness.” §26. P. A. Florensky addressed the work of Pablo Picasso (1881–1973) in his art historical reflections earlier: “Among the various stages in the artistic path of this ... experimenter on himself and on the world, we are now occupied by the last one (cubist - O. G.), where the poisoned soul of a sick artist is presented with images of four-dimensional perception and in which, however, true life is not felt. I mean a series of his musical instruments, beautifully presented in the Moscow Shchukin Exhibition Gallery" (Florensky P. A. The meaning of idealism // In memory of the centenary (1814–1914) of the Emperor of the Moscow Theological Academy. Collection of articles belonging to former and present members of the academic corporation. Part 2. Sergiev Posad, 1915. pp. 41–134). This assessment stemmed from Florensky’s general negative attitude towards various methods of external “opening of feelings”, to “forcing out new abilities”, which, in his opinion, related cubism to the then popular science-based occultism and in which he saw something “artificial, premature and therefore violent in relation to the spiritual organism” (Ibid.). In particular, the following note is devoted to the analysis of the compositions of Henri Rousseau (1844–1910) in the preparatory materials: 10.10.1924 Art. Art. Moscow Formation by Henri Rousseau Apparently, Rousseau has two types of constructions (if not more). But both of them are vertical structures, with numerous strictly defined and very rigid (?) vertical axes. One construction relates to objects. Where a separate object is given as such and everything else serves as its background, relatively indifferent, or in any case disproportionately significant in front of the object itself, there is one vertical that dominates, passing right in the middle of the picture and serving as the axis of the object itself. These are portraits (child, (nrzb.) wife (?) Rousseau), still life (vase with flowers). On the contrary, where it is not an object that is given, but space, there is no longer just one axis, but the entire space is penetrated by these verticals. But they are not evenly distributed across the plane, but accumulate towards the left edge of the picture. There are relatively few of them on the right, but as you move to the left, their number increases and is greatest at the left edge. The left edge represents the line of condensation, the completeness, the striking place of the picture - its construction and content. There is one more technique characteristic of Rousseau. This is the installation of the bodies of this dominant part of the picture on the right at the right edge in order to expand it to the left. There is a connecting link between the introduction on the right and the disclosure of the topic on the left. Rousseau sometimes likes to give this function of connection in the image of a bridge. So, the diagram: on the right is the introductory announcement of the topic, then the growth and then the disclosure of it on the left in a complete or even multiple way. Tree – trees, big trees; house - a large building, etc. §26. Overbeck Friedrich Johann (1789–1869) – German. painter who worked in Rome. Member of the Academy of St. Luke and the head of the group of artists, the so-called. "Nazarene". The reference may be to his painting “The Seven Sacraments” (1861). Chekrygin Vasily Nikolaevich (1897–1922) – Russian. graphic artist. See the catalog of his works: M., “Soviet Artist”, 1969. §32. ...vision is a widespread and refined sense of touch. - Aristotle. "On the Soul", II. 7, 418v – 4196. §32. Wolfgang Ostwald. – In the preparatory materials for the lectures there is an extract by P. A. Florensky from the article by V. Oswald “New teaching about colors and its application to technology” // Chemical industry and trade. 1923. Nos. 7 and 8, written by order of this magazine. Leibniz G. W. (1646–1716) – famous German philosopher and scientist. Leibniz's doctrine of small perceptions is one of the first concepts of the unconscious in the history of European science. In his main epistemological treatise, he wrote: “We have small perceptions, which we are not aware of in our present state. True, we could be perfectly aware of them and reflect on them, if we were not distracted from this by their multitude, scattering our attention, or if they were not pushed aside, or, rather, were not obscured by stronger perceptions” (New experiments on human understanding of the author of the system of pre-established harmony // Leibniz G.V. Soch.: In 4 vols. T. 2. M., 1983. P. 133). §32. With fingers as light as a dream... – And from the poem “The Prophet” (1826) by A. S. Pushkin. §32. ... “concepts without sensation are empty...” - Quote from the “Critique of Pure Reason” by Immanuel Kant (1724–1804), apparently given by Florensky in his own translation. Wed. another translation: “Thoughts without contemplations are empty, contemplations without concepts are blind” // Cant. Works: In 6 vols. M., 1963–1966. T.III. P. 154. §32. Florensky mentions economic philosophy, as well as the philosophy of creation, as types of philosophical thought and principles of poetics realized in artistic creativity. The first type of thought is usually associated with the name of Plotinus (c. 203 - c. 270), for whom emanation meant the process of sequential unfolding, the embodiment of the one - in the mind, the mind - in the soul, the soul - in space, in matter. A.F. Losev gives the following final characteristic of Plotinian emanation: it is “the outpouring of one area of being into another, one category into another category, when the area or category we are considering appeared before us in its entirety and thereby (due to its overflow) the need for it to pour out onto everything else, thereby transitioning to the creation of this other” (History of ancient aesthetics. Late Hellenism. M., 1980. P. 378). The second type of thought and creativity - in its purest form - is represented in Christian creationism, the primary source of which is considered to be the Book of Genesis, which begins with the words: “In the beginning God created the heavens into the earth” (1:1). But since, according to Augustine (354–430), before the creation of the world there could be nothing but God (De civ. Dei, XII, 2), God created the world “out of nothing” (De nat. bon., 27), into this “nothing” from which everything was created, itself enters into the “nature of the created” (De Gen. op. imp., 51) // Mayorov G. G. Formation of medieval philosophy. Latin patristics. M., 1979. P. 301. Referring pure painting to the philosophy of emanation, and pure graphics to the philosophy of creation, Florensky relies on his idea of painting as the art of vision-touch, “close vision”, emanating from the tactile reality of the material flesh of the world, and about graphics as the art of vision-gesture, vision-movement, “far-sighting”, which involves viewing large spaces emptied of things (the moment of “nothing”), but still filled with light. §35. Pascal Blaise (1623–1662), French. religious philosopher, mathematician, physicist. Formulated one of the theorems of projective geometry. Brianiun Charles Julien (1785–?), French. mathematician, prof. Royal Guard Artillery School; in 1806, independently of Pascal, he proved a similar theorem, known as “Brianchon’s theorem.” §38. Poisson S. D. (1781–1840) – French. mathematician and physicist. §38. “Descartes’ space is one of the central philosophical ideas of Descartes’ program for the development of natural science: “Space or internal place... differs from the bodily substance contained in this space only in our thinking. The only difference between them is that we attribute a certain extension to the body, understanding that it changes place along with it every time it moves; to space we attribute an extension so general and indefinite that, having removed from a certain space the body that fills it, we do not believe that we have moved the extension of this space, which, in our opinion, remains unchanged as long as it has the same size and figure and does not change position in relation to the external bodies by which we define this space” (Principles of Philosophy // R. Descartes. Selected Works. M., 1950. P. 469). The Cartesian term “extension” was for a long time synonymous with “spatiality” and was opposed to “thinking” as external - internal, as material - ideal and spiritual. The concept of spatiality by P. A. Florensky, on the contrary, is aimed at returning to space its symbolic functions and spiritual meaning, which it had in medieval art and worldview. §39. Laplace P. S. (1749–1827 - French astronomer, mathematician and physicist. §40. Plato talks about dialectics... - See: “Phaedrus”, 265e // Plato. Works: In 3 volumes. T. 2. M., 1970. P. 205. §42. The relationship between “composition” and “construction” or, in today’s language, the plane of expression and the plane of content of artistic images is a key theme of creative searches and theoretical discussions in the art of the early 20s. With the slogan “from image to construction,” production workers and constructivists expressed their rejection of such traditional artistic values ​​as representation, objectivity, emotional expressiveness, and spiritual meaningfulness. The possibility of the withering away of art based on them was allowed and the importance of other values was affirmed - expediency, functionality, constructiveness, organization, productivity, workmanship, etc. (Khan-Magomedov S. O. Discussion at INKHUK about the relationship between design and composition. (January-April 1921) // Artistic and combinatorial problems of shape formation. - Proceedings of VNIITE. Series "Technical aesthetics". Issue 20. M., 1979; Khan-Magomedov S. O. Young and older generations of production artists at the stage “from image to design” // Traditions and origins of domestic design. - Right there. Vol. 21. M., 1979). Florensky's theoretical views, reflected in these paragraphs, were to some extent formed as the author's intellectual reaction to the problematic situation that took place in the artistic circles of Moscow and could not help but attract the attention of his listeners. However, Florensky’s understanding of the structure of the artistic image, the place of construction and composition in it was based on the recognition of the intrinsic value of beauty and the fundamental connection between spatiality and imagery in art and nature. §45. ...on canvas by P. Potter... - In the painting of the famous Dutchman. The painter Paul Potter (1625–1654) “Bull” (1647, Mauritshuis, The Hague) depicts a life-size cow and bull. §45. ..unmerged and indivisible”... - One of the constant epithets related to the Holy Trinity. §46. Florensky quotes the famous words of Aristotle (384–322 BC) about the philosophical nature of poetry in abbreviated form: “Poetry is more philosophical and more serious than history, for poetry speaks more about the general, while history speaks more about the individual. The general thing is that, by necessity or probability, it is fitting for such and such [a character] to say or do such and such; This is what poetry strives to [show] by giving [heroes fictitious] names. And the individual is, for example, what Alcibiades did or suffered” (Poetics, 1451 c). §46. sacred protection of things from the attack of evil forces. – Encouragement is a term of Orthodox asceticism, “smart doing”, related to the traditional psychological culture of hesychasm. He describes the first stage of the influence of various spiritual forces on the human soul, which in hesychasm were recognized as having a real existence and which were experienced in the form of “thoughts” coming from outside. The Russian-language terminology of “smart doing” was systematized in the 16th century. Rev. Neil Sorsky, who established the following names for the stages of hesychast psychodrama: 1) “preposition” - the event of the first touch of a thought (as an image or thought) to the human soul; 2) “combination” – paying attention to the content of the adjective, “interviewing” with it; 3) “composition” – the tendency of the will to accept a thought as the theme and energy of experience; 4) “captivity” – immersion in a thought as a state of the soul, “dwelling copulation” with it; 5) and, finally, “passion”, when a thought completely takes possession of the soul, subjugating a person and forcing him to implement it in word or deed (Borovkova-Maikova M. S. Nil Sorsky “Tradition” and “Charter”. St. Petersburg, 1912). The spiritual and practical goal of “smart doing” was understood as mastering the skill of “discerning spirits,” separating evil, “evil” thoughts that seduce into deeds contrary to the commandments of the Savior Jesus Christ - from good, saving thoughts that correspond to these commandments. P. A. Florensky, using the word “attack” in relation to things and images, metaphorically characterizes the purpose of art as “the sacred protection of things from the attack of evil forces,” further transferring the functions of ornament in traditional cultures to imagery as such. §48. Full text of the quote from ancient Greek. philosopher Protagoras of Abdera (c. 480 - c. 410 BC): “Man is the measure of all things, those that exist, that they exist, and those that do not exist, that they do not exist (Diog. Laert., IX, 51). §48. Segner wheel is a device that clearly illustrates the pressure of a liquid on the walls of a vessel, invented by him. mathematician and naturalist Segner (1704–1777). §55. ...either “yes, yes” or “no, no”... – See below, approx. to s. 221. §62. Gulak N.A. - Apparently, a typo, since we mean Nikolai Ivanovich Gulak, member of the Tiflis circle, author of the book “An Experience in Geometry in Four Dimensions. Synthetic geometry" (Tiflis, 1877). §62. ...Venetian beads... - For details about the deep impression they made on little Florenskaya), see the book: Florensky P. A. To my children. Memories of past days. M., 1992. pp. 59–61. §65. Morozov Georgy Fedorovich (1867–1920) – Russian. botanist and geographer, founder of Russian forestry, one of the authors of the theory of biogeocenosis. §66. eadem sed aliter – exactly the same, but differently (lat.). §66. Auguste Comte called the collective humanity... the Great Being... in his cult of Clotilde de Vaux... – The image of the Great Being appears in the first chapter of the four-volume work of O. Comte (1798–1857) “The System of Positive Politics” (1851–1854) – “The General Theory of Religion”. Biographers associate the turn to religious issues in the works of the famous positivist with the tragic story of his love for the wife of the deprived criminal C. de Vaux, who died a year after meeting Comte, in 1846. See, for example, the article “Auguste Comte” in the Encyclopedic Dictionary of Brockhaus and Efron (Vol. 31), owned by Vl. S. Solovyov (Collected works. Ed. 2nd. T. 11); biographical sketch by V. D. Yakovenko “O. Comte, his life and philosophical activity" (Series "Life of Remarkable People" by F. Pavlenkov.) St. Petersburg, 1894. pp. 39–57. Unlike P. A. Florensky, these authors do not share the opinion of the philosopher’s “mental disorder.” §68. ...gospel: to her, to her - neither, nor... - Words of Jesus from the Sermon on the Mount: “But let your word be: “yes, yes,” “no, no”; and anything beyond this is from the evil one” (Matthew 5:37, from the teaching on the oath). Wed. With. 172. §68. “When I am alone with myself, there is no other listening.” - “Mozart’s description of his own work” - a quote from the book by K. Du Prel “Philosophy of Mysticism” (St. Petersburg, 1895. P. 96). Florensky addressed this book earlier, in particular in “Iconostasis”. In the preparatory materials for the lectures, this passage is entitled “Music as the Supertemporal.” §69. This leaf that withered and fell... – Inaccurate quote from A. A. Fet’s poem “To the Poets” (June 5, 1890). §72. ...atom of time required for the perception of a single element. – In the archive of P. A. Florensky there is a selection of materials dated July 5, 1919 and entitled “Atoms of Time.” It contains extracts on the history of religious and mathematical thought - about the elementary particles of space and time. Apparently, the impetus for thinking on this topic was the thinker’s acquaintance with the just published book of the famous Russian Indologist O.O. Rosenberg, Problems of Buddhist Philosophy. Introduction to the study of Buddhism from Japanese and Chinese sources." Part 2. Pg., 1918. Florensky draws attention to the analysis of the various meanings of the fundamental concept of Buddhism “dharma” and the related theory of instantaneity. One of the key extracts read: “According to the theory of instantaneity, a change in the composition of the content of consciousness occurs so quickly that the very process of transition to a new content cannot be observed. The moment (“kshana”), not being zero, is such a small particle of time that it is inaccessible to direct impression... The theory of instantaneity consists, therefore, in the conditional reduction of the stream of consciousness and its content to the level of identical, infinitely small particles of time” (p. 103). Florensky in this manuscript compares the Buddhist theory of instantaneity, on the one hand, with the mathematical analysis of infinitesimals, and on the other, finds parallels to it in the history of the Christian worldview, citing the “Prayer of the Holy Seven Youths” (from an unidentified handwritten “Trebnik”): “resurrected in a single instant of time, to the glory of Thy grace”; and “Canon of Prayer to the Guardian Angel” (canto 5, glory): “lower by one hour, but below the line, or so soon I left you my benefactor and guardian” (emphasized by P. A. Florensky). §73. ...Walter Scott's account of Quentin Dorward's journey through the Parana Gorge. – Difficult to explain typo or error: Paraná – a river in Brazil and Argentina; The novel Quentin Dorward (1823) describes the heroes’ journey along the banks of the Loire and Meuse. ...a picture of Consuelo's journey with Joseph Haydn by Georges Sand. – This refers to chapters 64–81 of George Sand’s novel “Consuelo” (1842–1843). §73. Life of Rev. Sergius of Radonezh was written by Epiphanius the Wise in 1417–1418. and revised by Pachomius Logothetes after the discovery of the relics of St. Sergius in 1422. Publication and translation see: Monuments of literature of Ancient Rus'. 14th–mid 15th century. M., 1981. pp. 256–429. The front manuscript of the life that P. A. Florensky speaks of is now kept in the manuscript department of the State Russian Library (formerly GBL). In the 19th century the manuscript was published with engraved color illustrations by the Trinity-Sergius Lavra. §74. Giotto di Bondone (1266 or 1267–1337). Stamps depicting the life of St. Francis of Assisi - 1296–1300 St. Vladimir's Cathedral in Kyiv was built in 1862–1896. Architects A. Beretti and A. Sparro. §74. Kotarbinsky Wilhelm Aleksandrovich (1851–?), academic artist who graduated from the Academy of St. Luke in Rome, was invited to paint the Vladimir Cathedral (together with P. Svedomsky). “Numerical identity”, that is, identity in number, equality, is contrasted, on the one hand, with “generic identity” in gender, which is established through the identity of concepts about the things being compared, and on the other, with “specific identity” in type, also called “similarity”, “similarity”. P. A. Florensky resorts to this distinction in “Letter Four: The Light of Truth” in the book “The Pillar and Statement of Truth.” (M.: Put, 1914, pp. 79–80) and comments on it in Appendix 18 “The Concept of Identity in Scholastic Philosophy” (pp. 515–518). §75. Nesterov M.V. (1862–1942) was friendly with Florensky, painted his portrait (“Philosophers”, 1918). “Soul of the People” – 1915–1916 (Moscow, Tretyakov Gallery). §75. Watteau A. (1684–1721). “Pilgrimage to the Island of Cythera” (1717, Paris, Louvre) is one of his most famous paintings, “the apotheosis of gallant painting”, written on the theme of the 3rd act of F. Doncourt’s play “Three Cousins”. In his original interpretation of the plot of the painting, apparently not knowing the history of its creation, Florensky absolutely accurately indicated the “time coordinate”. Wed. in modern times study: Nemilova I. S. Watteau and his works in the Hermitage. L., 1964. S. 24–25. §77. ...in Leon Battista Alberti... in his treatise “On Painting”... – 06 of this work (1435–1436) ital. scientist, architect, theorist L.B. Alberti (1404–1472) is said in “Reverse Perspective” (Index. ed. p. 67). The translation of the following passage apparently belongs to Florensky. §81. Entelechy is one of the central, literally untranslatable concepts of Aristotle’s philosophy. In “Metaphysics” he characterizes entelechy in connection with other concepts important to him: “For action is a goal, and activity is action, which is why “activity” is derived from “action” and is aimed at “realization” (1050a). Interpreting this synthetic concept, A.F. Losev wrote: “We... understand Aristotelian entelechy as expanded and analyzed energy... we fix in energy its material cause (since entelechy speaks of existence and being), its eidetic cause (since it is already thought of as a certain way organized energy), and, finally, the active and target cause present in energy” // History ancient aesthetics. Aristotle and the late classics. M., 1975. P. 701. Cf. present ed., p. 201. Quote from Luther - not established. §82. The words “now I understand in part” belong to St. Paul: “Now we see as if through a glass darkly, but then face to face; Now I know in part, but then I will know, even as I am known” (1 Cor. 13:12). “Having achieved perfect dispassion, I have already risen in this life...” – There are no indications of the source of the quotation. In 1917, with the participation of P. A. Florensky, “Divine Hymns of St. Simeon the New Theologian" (Sergiev Posad). In this publication, according to Abbot Andronik (Trubachev), Florensky, in addition to translations, contains a commented subject index to the two-volume “Words of St. Simeon the New Theologian" (T. 1 – M., 1882; T. 2 – M., 1890) and to the “Hymns” themselves. The theme of lifetime resurrection is one of the hidden ones in the spiritual experience of Simeon the New Theologian, the great ascetic and spiritual writer of the 11th century. Rev. Simeon wrote: “there is death, or mortification, before the death of the body, and before the resurrection of bodies there is a resurrection of souls - real, experientially conscious, true. For when mortal wisdom is destroyed by the immortal mind (and a state of perfect dispassion is achieved. - O.G.) ... then the soul clearly sees itself resurrected, just as those awakened from sleep see themselves awake - with the consciousness that God has resurrected it” (Slovo 79. T. 2. P. 316). He who has achieved perfect dispassion and risen in soul also knows “what kind of crowns and what rewards the saints receive in another life, making sure that they surpass every mind and every word of man; he also knows what kind of person he (himself) and all the saints are expected to become after the general resurrection. However, the saints do not receive everything they want in this life, although some slander that I say that the saints receive everything here” (Ibid. pp. 118–119). Thus, we are talking about spiritual experience, a higher vision, experienced in the form of states of consciousness/will, the memory of which is then preserved in ordinary life and creates the basis of confidence in the beyond-mortal future. In relation to art, this means that an artist, who has reached a state in his contemplative experience comparable to the state of perfect dispassion of an ascetic, is able to acquire new prototypes that correspond to the spirit of place and time and embody them in artistic images, which can then acquire the status of iconographic types and enrich the iconographic canon. The iconology of P. A. Florensky, fully consistent with the data of spiritual tradition, became a step towards its theoretical reconstruction and served to deepen our contemporaries’ understanding of the essence of medieval fine art. §82. “Art of the arts” or “art of the arts” is one of the traditional names of Orthodox psychological culture and psychotechnics. In the preface “To the Reader” from “The Pillar and Statement of Truth,” Florensky wrote: “Yes, there is a special spiritual beauty, and it, elusive to logical formulas, is at the same time the only true path to determining what is Orthodox and what is not. The connoisseurs of this spiritual beauty are the spiritual elders, masters of “the art of art,” as the holy fathers call asceticism” (p. 8). P. A. Florensky understood asceticism as “the knowledge of the saints, the structure of their personality, the laws of their life, the originality of their experience and thinking, the relationship of these laws, this experience, this thinking to the ordinary, characteristic of sinful humanity” (quoted from: Hegumen Andronik (Trubachev). Priest. Pavel Florensky - Professor of the Moscow Theological Academy // Moscow Theological Academy. 300 years (1685–1985). - Theological works. Anniversary issue. M., 1986. P. 235. §85. Khunrath has an allegorical drawing... - This means the edition: Amphitheatrum sapientiae aetegnae solius verae, christiano-kabalisticum, divino-magicum, nec non physicochymicum, tertiunum, catholicon: instructore Henrico Khunrath Lips., Theosophiae amatore fideli, et Medicinae utriusque doc.; etc.; Magdeburgi, anno 1608. L. vegtand. Développement nouveau la partie élémentaire des mathématiques, prize dans toute son étendue. Geneve, , 1778. Against these lines in the margin is a note in pencil by P.A. Florensky: “Prof. M. Morduchai-Boltovsky. The similarity theory of Christian Wolf and Levesque’s postulate (“Bulletin of Experimental Physics and Elementary Mathematics”, No. 623–624. 2nd ser. VII pp. 1–2, pp. 1–13).” – Approx. ed. Delboeuf. Sur les fondements de Géométrie; L'ancienne et les nouvelles Géométries. – Revue philosophique, T. 36, 37. 1893–1894. Roussel. Essai sur les fondements de Géométrie. §§ 11–13 are missing from the manuscript. – Approx. ed. Paragraph not finished = Approx. ed. In the handwritten version, §§ 18–29 are missing. The text is typewritten. – Approx. ed. The text follows according to the manuscript. – Approx. ed. In the original – “response” – probably a typo – Editor’s note. Further in the manuscript it is crossed out: “which requires too much effort.” – Approx. ed. § 37 is missing from the manuscript. In the margin there is a note from the author: “37. Graphics and painting as projections of a dual understanding of three-dimensional space.” – Approx. ed. Below is a note in pencil in Florensky's hand; [The following is a mathematical explanation of the Poisson equation]. – Approx. ed. In the margins of the manuscript there is a pencil note by P.A. Florensky: “Ornament. Hypertrophy comp and construct. Car". – Approx. ed. In the manuscript - “by”. – Approx. ed. "St. Art." – abbreviation of the phrase “old style”. – Approx. ed. Against this line in the margin is a note in Florensky’s hand: “The magical meaning of an ornament is to represent a pictorial image with a diagram of feeling.” – Approx. ed. After this phrase, the paragraph number is repeated once again in the manuscript - 52, and in the margins, under the date, there is a pencil note in Florensky’s hand: “Coins, medals.” – Approx. ed. There is an omission in the manuscript - Approx. ed. The manuscript further crossed out: “some life goal.” – Approx. ed. At the end of § 67 a blank page is left in the manuscript. – Approx. ed. In the manuscript - “with each other” - apparently a typo. – Approx. ed. In the manuscript - “unites” - apparently a typo. – Approx. ed. Further, about seven lines are missing in the manuscript - Approx. ed. Further in the manuscript there is a gap left unfilled - Note. ed. There is an omission in the manuscript. – Approx. ed. B. Christiansen. Philosophy of art. St. Petersburg, 1911, p. 167. Further in the manuscript three lines are left blank - Approx. ed. Ogneva Sofia Ivanovna (1857–1940), born. Kireevskaya and her husband, Honored Professor of Moscow University Ivan Florovich Ognev (1855–1928), lived in Sergiev Posad from 1919 and were friends at home with the Florenskys. S. I. Ogneva helped P. A. Florensky in preparing his works for publication, taking dictation of his thoughts aloud and rewriting intermediate manuscripts.