II. Пути и средоточия

The writer is not a reliable interpreter of his work, and he can often say what exactly he wrote with less confidence than any of his attentive readers. He, like the reader, has to approach his book from the outside, having first forgotten as completely as possible both his joyful emotions and the thoughts united by them. It is pointless to ask about the work of someone who has already done everything that depends on him so that the plan is implemented accordingly. And it is difficult to explain in a nutshell what, in the extreme conviction of the writer, required hundreds of pages to be revealed: let them be interpreted by those who will judge them - the reader. But if it is pointless to ask the writer about the meaning of his book, then perhaps it is not useless to ask him about his well-being during the formation of the book. How he feels, from within, the creative forces that formed the fabric of the verbal whole - yes, forces that sought to express themselves outwardly, but, perhaps, the words that penetrated the element so indistinctly that an outsider’s eye will not even be able to discern their dull flicker. It is not the person who wrote it who will tell us the content of the book, but will outline the semantic stresses and thereby reveal more clearly the rhythm of its formative scheme. It is this question about his sense of self as a writer that those who wrote about watershed areas of thought consider useful to answer. This is what his composition asked for in word 19: ...this is not one, tightly welded and finally united presentation by a single plan, but rather an inflorescence, even an inflorescence, of questions, often only outlined and not yet fully answered, connected to each other not by logical schemes, but by musical echoes, consonances and repetitions. These are mental, thinking And a noisy exodus from the earth 20, - thought in its birth - which has the greatest ebullience here, but has not yet broken through a definite channel for itself. The connections between individual thoughts are organic and essential; but they are outlined lightly, sometimes interrogatively, with many, but thin lines. These connections, half-found, half-sought, are not represented as steel rods and beams of abstract structures, but as bundles of countless fibers, countless hairs and cobwebs, going from thought not only to the nearest ones, but to many, to the majority, to all others. The structure of such a mental fabric is not linear, not a chain, but a mesh, with countless nodes of individual thoughts in pairs, so that from any starting point of this network, having made one or another round trip and capturing along the way any combination of other thoughts, moreover, in any or almost any sequence, we return to it. Just as in Riemannian space every path closes into itself, so here, in a circular presentation of thoughts, moving forward along various roads, you again and again come to the starting contemplations. It is this multiplicity and diversity of mental connections that makes the fabric itself both strong and flexible, as inseparable as it is adaptable to every particular requirement, to every individual structure of the mind. Moreover, in this mesh fabric and the one who provided it, all the relationships of its individual nodes and all the mutual connections of mental centers contained in the possibility are not immediately visible: and to him, unexpectedly, new approaches from center to center are revealed, already fixed by the network, but without the clear intention of the author. This is circular thinking 21, a way of thinking and a method of expressing contemplatively, called Eastern, for some reason. English thinking comes closer to it than many others, much less so does German thinking, although Goethe, Hoffmann, Novalis, Baader, Schelling, Boehme, Paracelsus and others could be cited as evidence to the contrary; but in any case, the mindset of the French, generally Romanesque, is deeply alien to him. It would be in vain to look for esprit de système 22 in this book. The reader will not find any system here and should not ask for one; to whom this spirit is dearer than thought itself, it is better to immediately put the book aside. Truly, we repeat with Wackenroder, “whoever believes in any system has driven love out of his heart! Much more tolerable is the intolerance of feelings than of reason: Superstition is always better than System belief - “Aberglaube ist besser, als Systemglaube” 23. Yes, no system is given here... But there are many questions about the very roots of thought. In the primary intuitions of philosophical thinking about the world, first boilings, rotations, vortices, whirlpools arise - they are not characterized by rational planning, and it would be false to disguise them as a system - unless, in fact, such a system is always a vaticinium post eventum 24, a broadcast after the very event of thought; but, not being orderly-distributed, countably-added, these effervescences of thought, this urgently needed, for they are the very origins of life. It is from them that solid theses are subsequently frozen out - it is necessary to study the emerging whirlpools of thought as they really are, in their immediate echoes, in their frank pre-scientific, pre-systematic nature. Without them, without the source keys of thought flowing from pre-conceived depths, we still cannot understand large systems, just as we would not understand ourselves. Perhaps sketches similar to those proposed will subsequently grow together into a denser, more solid, more linear unification, although at the cost of the withering away of some of the currently living connections; however, the initial fermentation of thought forever has its value, and the comparisons that arise do not lose their ability to serve as ferments of knowledge in the future. But, no matter what happens in the future, for now, in any case, we should not draw on the connecting channels of thought where they have not emerged by themselves - although it would, undoubtedly, be more tempting and easier to draw them than to leave, to have the courage to leave the overall picture undeveloped, in its initial multi-centredness, in its non-perspective, spatial inconsistency not brought to a single point of view. But this does not mean that it essentially excludes any order. The order of thoughts is organically absorbed; However, it seems to the author that it is violence against the life of the mind and philosophical insincerity to force a scheme where it did not appear by itself in his understanding, just as it did not appear in the understanding of his contemporaries. Don’t come up with some kind of order... So, here a unified construction is not given, but only some bonds of concrete philosophical understanding, concrete metaphysics, which is philosophical anthropology in the spirit of Goethe, are fixed. When it arises, secretly ripening under the husk of positivism, then, perhaps, some of the proposed notes will not remain superfluous. Even approximately, completeness is still very far away - if you fall into weakness - to believe in the possibility of completeness of knowledge, further insurmountable. At the present time, it is impossible to take into account exactly what kind of associations individual perspectives will subsequently come to, while they remain logically inconsistent and seem to be alien to each other. Our job is to carefully collect a specific thought, driving into one backwater the whirlpools of primary intuitions that we have noticed: fidelity to fact. This accumulation is the path to the philosophical anthropology of our grandchildren, when the chain of knowledge is tightly closed with the tradition of hoary antiquity and the universal human experience is fully justified. But 25 where there is no logical unity of the scheme, another unity can be heard, incomparably more coherent, vitally deeper than a smooth plan, superimposed superficially and with its gloss covering up the wretchedness of internal discrepancies and crumbling ideas. Its rhythmic unity sounds to the author like the sound of distant surf. Themes go away and come back, and go away again, and come back again, and so on and on, each time intensifying and enriching, each time filling with new content and the juice of life. Themes run into each other, catch up with each other, push each other aside, so that, having sounded out, they then give way to new themes. But in the new ones, the old, already former ones sound. Arising in as yet unheard of developments, intertwining with each other in various ways, they are like the tissues of the body, heterogeneous, but forming a single body: so the themes dialectically reveal the unity of primary contemplation with their connections and echoes. When added up as a whole, each theme turns out to be somehow connected with each other: this is a mutual responsibility, a rhythmic interruption of interpenetrating themes. Here none dominates, and one should not look for the ancestor in any one. The topics are not presented here in a sequential series, where each link more geometrico 26 is derived from the previous one. This is a friendly society in which everyone talks to everyone, maintaining, all together, a mutually educational conversation. The connecting relations here are multiple, vitally organic, as opposed to the formal, calculable and accountable connections of rational systems, and the systems themselves beg to be likened to an office mechanism, with external and meager, but precisely defined relationships in advance. On the contrary, the rhythm of thought that the author strives for is diverse and complex due to the multiplicity of its approaches; but one breath breathes in all: this is synarchy. Another similarity is requested: Russian song 27. In music, two polyphonic styles have so far been revealed: homophony of the New Age, or harmonic style, with the dominance of the main melodic voice over all the others, and polyphony of the Middle Ages, or contrapuntal style, with the mutual subordination of all voices to each other. But symphonists are making their way to a third style, which in its essence precedes polyphony and is uniquely revealed in the polyphony of Russian folk song. This, in Adler’s terminology, is heterophony, complete freedom of all voices, “composing” them with each other, as opposed to subordination. There are no fixed, unchangeable choral “parts” here. With each repetition of the chant, new variants appear for new words, both for the lead singer and for the choir singers. Moreover, often the choir, during repetitions, enters in a different place than before, and does not enter immediately, as there, - at random; or even does not stop speaking at all during one or several chants. Unity is achieved by the internal mutual understanding of the performers, and not by external frameworks. Each, more or less, improvises, but does not disintegrate the whole - on the contrary, it binds more firmly, because the common cause is joined by each performer - many times and in a variety of ways. The choir retains complete freedom to move from unison, partial or general, to accomplished polyphony. Thus, folk music embraces an inexhaustible ocean of emerging feelings, in contrast to the frozen and crystallized gothic style of contrapuntal style. Otherwise, Russian song is the realization of that “choral principle” on which the Slavophiles thought to base the Russian public. This is a feocratic synarchy, as opposed to the legalism of the 28 Western Middle Ages (contrapuntal style) and the enlightened absolutism of the New Age - be it imperialism or democracy - which corresponds to the harmonious style. In philosophy, here the author wants to say the very thing that the soul of the Russian people sings in the song 29. Not the system of subordinate philosophical concepts recorded in Summa 30, and not the official, conditionally pragmatic use of many, subordinate to one, as a practically set goal, but the free “composition” of themes determines the composition of the entire mental fabric. And if the writer cannot always explain abstractly, or cannot immediately find an answer that satisfies him, why exactly a given circle of observations and certain particulars appear in a given place, this does not mean that he agreed to set aside these questions or transfer them to another place. It is not the relationship to the immediate preceding and immediately subsequent statements that motivates this, but the relationship of this latter to the whole, as is generally the case in all living things, while the property of a mechanism is to have parts that depend only on the closest adjacent ones directly attached to it. “Oh, grammarian! In my poems, do not look for paths, look for their focus.” 31 This key to understanding Paul Claudel, given by the poet himself, should be held firmly in the hand of anyone who wants to enter into thinking not of a system, but of an organic one, be it the works of Faraday and Maxwell, the odes of Pindar or the Kabbalistic Book of Splendor 32 . And about each work of organic thought, if only it was successful, one can rightfully repeat what was said about one of the odes of the above-mentioned poet: “He goes to the final goal along various roads, from all sides at once: not reaching the end along one, he abandons it and leads another from afar and from the other side, in the same direction, so that the middle thought turns out to be enclosed within a vast circle of radii, striving towards it, but not reaching it, which gives the reader’s thoughts the aspiration with which he himself is transported through the unsaid, and a single sun suddenly flares up at the end of all paths, which seem to the blinded consciousness no longer roads, but rays of the middle flame.” 33 The whole point is in the objectivity of this thinking: the object of knowledge is not constructed by paths and evidence, and therefore it is not comprehended from them, as happens in subjective thinking, but, on the contrary, it itself, although not analyzed, from the very beginning serves as the focus of thought, and the paths are outlined from the center. There can be countless numbers of them, this is a game of knowable reality; and it is not this sparkle that the thinker values, although some kind of play is necessary for the conscious assimilation of reality, for understanding the form of reality. Calling up a game is a method of cognition. “Every method is a rhythm,” says Novalis 34, and the comprehension of reality is a co-rhythmic beating of the spirit, responding to the rhythm of the cognizable. In other words, the method of cognition is determined by the knowable, and the organic form of its subject speaks in the organic composition of the book. Therefore, the composition is difficult to contrast with the subject: this is partly - as in music, where it is difficult to explain in words what the subject of a given work is - not at all from the “formality” of the music, in the sense of the opposition of form and content, but precisely because of their close connection, so that the presentation begins directly from its subject, and no intermediate word can be inserted between one and the other. So here, in this attempt to trace the origins of thought, the subject or focus of the focus is this very organic unity or form, in the sense of Plato-Aristotelian idealism, aka the realism of the Middle Ages 35 and Goethe, aka, in another aspect, the concrete idealism of Schelling or the magical idealism of Novalis, aka, in another aspect, the vitalism of our time, etc. etc. Of course, these currents of thought are far from the same thing; but to those accustomed to penetrating the thought-driving forces of the writer, even without deliberate explanation, it is clear that the thoughts mentioned above feed on the same pastures and reach for the same sun. Throughout history, this sun has raised a never-ending race of thinkers, although the corresponding mindset either flared up in a high candlestick, or hid, driven away, like a secret teaching. The names mentioned above are only the more famous and glorious representatives of this philosophical blood, but a great many similar ones could be cited. In Russia, this trend was nourished primarily by Schelling, and here modern defenders of the form are not at all rootless, but have a strong ideological tradition of Russian Schellingism 36 . Finally, all modern thought, both general and special - in psychology, biology, physics and mathematics, not to mention the verbal and historical sciences, is clearly set in the direction of form, as the creative principle of reality, and for the historian of thought - the crisis of the analytical worldview and the new flowering of the Platonic-Aristotelian-Goethe-Schelling family tree are obvious. It is around this category of form, as the focus, that the presentation of this book turns; but this category is considered here not in its ready-made and completely distinct sedimentation, but as an evaporation rising from areas that are very different, but, however, considered by attention seeking food of a certain composition. Creativity - in language, technology or organ construction of living beings; the whole as a type of creatively embodied; personality and name as its formative face, etc. etc. - all these focuses of this book are different, but they are all about one thing, and this alone is that solid ground, without which the thought of the immediate future behind us will not take a single step. This book does not propose any particular worldview; but the common ground of the various currents of thought that are percolating and which are yet to percolate to the surface of historical consciousness will inevitably be mental moves close to those outlined here. From these watersheds, the idea of ​​the whole, form, creativity, life, thought will flow into a new eon of history. 1918. X 9. Evening. Serg Pos. at the funeral of Fr. Joseph Iv. Fudelya, on the day of the Saints of Moscow 37. The individuality of various perceptions must be in accordance with the metaphysical lines of the world. Metaphysical planes of cleavage of being are expressed in the peculiarities of the psychological structure of our experience. In ontological order it would be said: metaphysics produces psychology; in psychological order, on the contrary: psychology determines our metaphysical constructions. In the symbolic order, let us say, as we have already said: the metaphysical is expressed in the psychological, the psychological expresses metaphysics. That is why we will not hesitate to admit that the five, or six, or seven senses - the seven gates of knowledge, according to W. Thomson 38 - the seven ways of sensual attitude to the world are the seven metaphysical axes of the world itself. And if we find a deep difference in feelings, then this is, of course, because the very reality of the world already contains these seven parameters. Anthropology is not the self-sufficiency of a solitary consciousness, but is a condensed, representative being, reflecting an expanded holistic being: a microcosm is a small image of the macrocosm, and not just something in itself. But among the senses, the gates farthest from each other are sight and hearing. What is given by sight is primarily objective. Visible images stand before the spirit with the greatest self-sufficient clarity. What is contemplated by the eye is assessed as given to it, as revelation, as revealed. This is truly a phenomenon, for fainTmenon is precisely what appears to the eye - the visible. On the contrary, what is perceived by hearing is predominantly subjective. The sounds that are most audible are embedded in the fabric of our soul and therefore are the least clear, but they most deeply capture our inner world. In sounds we perceive the given, melted into our subjectivity. An internal response to what is given from the outside flows into the ear with sound; the inner being of existence responds to the phenomena of the world with sound, and coming to us, flowing into us, this sound, this response flows precisely as internal. When we hear a sound, we do not think about it, we do not think about it, but we think about it: this internal echo of being is internal in our interior. Sound directly (diffuses) seeps into our intimacy, is directly absorbed by it, and, without the need for elaboration, is itself always perceived and realized as the soul of things. Things and beings speak to us from soul directly to soul, On the contrary, the visible is always perceived as external, as something that is ahead of us, as given to us, and therefore in need of processing into the internal: through this processing it is transformed, melted into sound, into our visible echo. Therefore, the perception of light is always passive at its core, even if we ourselves give a visible signal, a sign, shme‹on. But the perception of sound is always active at the core, at least not by us, but we were told. In the perception of sound, we are active through participation in the activity of the sound, which we directly share. And therefore, by listening, we thereby speak, with our inner activity not responding to the speech, but first of all reproducing it within ourselves, responding with our whole being, together with the speaker, to the visible impressions given to him, revealed to him. Truly, cum tacent – ​​clamant 39! For it is always cum tacemus - clamamus 40, and it cannot be otherwise - as long as we listen to it. We listen not with the ear, but with the mouth. The problem of a portrait is a problem of antinomy: passivity - activity, objectivity - subjectivity, given - given, eye - mouth. It is known that the most difficult parts of a portrait are the eyes and mouth. The most difficult - because they are the most responsible, the most responsible - because it is in them, precisely in them, that the artist gives the idea of ​​​​the person depicted. Between the eye and the mouth lies the entire range of his life, his greatest receptivity to the world and his greatest responsiveness to the world. The eye asks, the mouth answers. The eye drinks into reality, the mouth transforms it into an internal echo. And since it is not what enters into him that defiles a person, but what comes out of him 41 , then the visible is always pure, since it is precisely visible, since it is a pure given, since our selfhood does not participate in it - and therefore the eye itself is pure, as a receiver of pure, objective light, by which everything that appears to us appears 42 , but the mouth, which drains our selfhood, easily risks being unclean, can easily turn out to be defiler of the world. The sound we send, like sound in general - the discovery of selfhood, the selfhood of being, is passionate - can easily turn out to be passionate. That is why it is easy to have clean eyes, but almost impossible to have clean lips. Hence the shyness of the mouth, characteristic of eastern peoples. An Armenian woman considers it indecent to show her mouth, especially when speaking. The maiden - she covers him with her hand and turns away when she speaks with a face that is somewhat respectable; married - she ties it. There is no shyness of the eyes, but there is shyness of the mouth. I was told that in some areas this modesty is so great that a woman would prefer to lift her hem and be naked, just to close her mouth. It is clear that the objectivity of visual impressions and the subjectivity of auditory impressions are respectively taken into account by religious dispositions and attitudes of the soul. Where the external is considered the most sublime, where the givenness of the world, spread out before our spirit, is recognized as the subject of religious experiences, vision is proclaimed to be the main thing in religious life. Where, on the contrary, the emotions of the human spirit are most valued, and they are considered the most intelligible witnesses to the Unconditional, there the supremacy is established for hearing, hearing and speech, for hearing and speech are one, and not two, according to what has been said. That is why, if you see - however unfoundedly or not very thoroughly - in the religion of the given, in the religion of objectivity - paganism, as a pan-human religion of nature, a deviation towards naturalism and naturalism itself, and in Christianity, on the contrary, a religion of subjective “intimate-personal” unrest, which in fact is all Protestantism, then the struggle against visible images and for audible sounds is natural. Then "revelation" stands against "appearance". On the contrary, when sounds are humiliated before contemplation, i.e. with the striving for objectivity, only phenomena are valued, while revelation seems to be “words alone,” “empty words,” “literature alone.” Mourant Brock in his book – La Croix païenne et Chrétienne. Notice sur son existence primitive chez les païens et son adoption postérieure par les chrétiens. Traduction faite sur la deuxième édition augmentee et enrichie d'illustrations nouvelles. Paris, 1881 43 - in the name of religion, in the name of the purity of Christianity, he does not weaken in striking the cross, trying to prove that it belongs to paganism both in meaning and in origin. Mourant Brock is tireless in his crucifixion and iconoclasm, but he does this not as a positivist, but as a Protestant of some extreme kind - a Puritan, or something. And so, regarding one of the crucifixes, where the body of the Lord is covered with drops of blood, he notes, with amazing clarity he expresses the very basis of Protestantism: “Combien touchante en vérité doit être une religion qui, à l`éxemple du paganisme, a recours à de pareils stimulants de dévotion. La foi vient par les oreilles et non par les yeux.” (Chp. XX. p. 130) 44 1920.I.9. My birthday Mb the main difference in the aspirations for Catholicism and Protestantism comes down to the difference in psychological types - visual and auditory. "Catholics", i.e. Catholics are people of the visual type, and “Protestants”, i.e. Protestants - auditory. Orthodoxy is harmony, a harmonious balance of both, visual and auditory types. And therefore, in Orthodoxy, singing is as completely ontological as the visual arts - icon painting. 1916.XI.18. Sergiev Pos. While reading Aristotle's Metaphysics. 1. The task of philosophical anthropology is to reveal human consciousness as a whole, i.e. show the coherence of its organs, manifestations and definitions. In this sense, we can say that its task is from the basic definitions of his being, from his idea. 2. Many senses are usually considered something like 45 It is necessary to find the place of each of the organs, i.e. show the internal necessity of the specificity of different sensations, and, moreover, not generally different, but precisely each of the different ones. What is the place of each sensation in human life? What is the meaning of each of them? Why is each of them necessary? That is, what does each sensation give, what is new, compared to others. (example: Aristotle in “Metaphysics”, 1, 1, 2... considers auditory sensations to be a condition of memory, and visual sensations as the most discriminating...) 46 3. “The most basic of knowledge and the predominant. above the official there is that which contains an understanding of the purpose for the sake of which everything separately should be done” (Arist. Metaph, 1, 1, 6; according to the translation of Rozanov, p. 16) 47. Understanding the purpose for which everything in man exists will be anthropology, for the purpose of everything in man is man. This is the same task that Goethe sets himself. 4. "Die Natur nicht gesendert und vereinzelt vorzunehmen, sonder, sie wierkend und lebendig aus dem Ganzen in die Teile strebend darstellen" (First acquaintance with Schiller, 1794). 48 “Concrete metaphysics” (Medtner, 151) 49. The results of the whole to the parts, as Goethe wrote. Introduction to the collection of introductory courses met: This is not a system of philosophy, but a historical introduction to specific philosophical thought, specific metaphysics, its contours. Philosophy and anthropology in the spirit of Goethe. III. Reverse perspective 50 1. Historical observations The attention of those approaching for the first time Russian icons of the 14th and 15th centuries, and partly of the 16th, is usually struck by unexpected perspective relationships, especially when it comes to the depiction of objects with flat edges and straight edges, such as, for example, buildings, tables and seats, especially books, the gospels themselves, with which the Savior and Saints are usually depicted. These special relationships stand in blatant contradiction with the rules of linear perspective, and from the point of view of this latter they cannot but be considered as gross illiteracy in drawing. When looking more closely at the icons, it is not difficult to notice that bodies bounded by curved surfaces are also depicted from angles that are excluded by the rules of perspective depiction. Both in curved and faceted bodies, the icon often shows parts and surfaces that cannot be seen immediately, which is easy to learn from any elementary perspective textbook. Thus, if the line of sight is normal to the façade of the buildings depicted, both side walls are shown together; in the gospel three or even all four edges are visible at once; the face is depicted with the crown, churches and ears turned forward and, as it were, spread out on the plane of the icon, with the planes of the nose and other parts of the face turned towards the viewer, which should not have been shown, and even with the planes rotated, which, on the contrary, would naturally be facing forward; Also characteristic are the humps of the bent figures of the Deesis row, the back and chest, which are simultaneously represented in St. Prochorus, writing under the guidance of the Apostle John the theologian, and other similar connections of profile and front surfaces, dorsal and frontal planes, etc. In connection with these additional planes, lines that are parallel and do not lie in the plane of the icon or parallel to it, which in perspective should have been depicted converging to the horizon line, are depicted on the icon, on the contrary, diverging. In a word, these and similar violations of the perspective unity of what is depicted in the icon are so obvious and definite that the first thing they will be pointed out by the most mediocre student, even if only in passing and third-hand, has tasted perspective. But, a strange thing: these “illiteracy” of the drawing, which, apparently, should have enraged any viewer who understood the “visual inconsistency” of such an image, on the contrary, do not cause any annoying feeling and are taken for granted, even liked. Moreover: when two or three icons, approximately of the same translation and more or less the same mastery of writing, can be placed next to each other, then the viewer with complete certainty sees enormous artistic superiority in the one of the icons in which the violation of the rules of perspective is greatest, while the icons of a more “correct” design seem cold, lifeless and devoid of any immediate connection with the reality depicted on them. Icons, the most creative for direct artistic perception, always turn out to have a promising “flaw”. And the icons that more satisfy the textbook perspective are soulless and boring. If you allow yourself to temporarily simply forget about the formal requirements of perspective, then immediate artistic instinct leads everyone to recognize the superiority of icons that violate perspective. Here the assumption may arise that what one likes is not the method of depiction as such, but the naivety and primitiveness of art, which is still childishly carefree in terms of artistic literacy: there are also amateurs who are inclined to declare icons to be cute baby babble. But no: the fact that icons with a strong violation of the rules of perspective belong specifically to high masters, while a lesser violation of these same rules is characteristic primarily of second- and third-class masters, prompts us to consider whether the very judgment about the naivety of icons is not naive. On the other hand, these violations of the rules of perspective are so persistent and frequent, so, I would say, systematic, and, moreover, stubbornly systematic, that the thought involuntarily arises that these violations are not accidental, about a special system of depiction and perception of reality depicted in icons. As soon as this thought appeared, observers of icons were born and gradually strengthened the firm conviction that these violations of the rules of perspective constitute the use of a conscious technique of icon painting and that they, whether good or bad, are very deliberate and conscious. This impression of the consciousness of the said violations of perspective is extremely strengthened by the emphasis on the special angles being discussed - by the use of special colors or, as icon painters say, openings: the features of the drawing here not only do not slip past consciousness through the use of some neutral colors in the appropriate places or softened by the general color effect, but, on the contrary, appear as if with a challenge, almost shouting against the general colorful background. So, for example, the additional planes of the building-chambers not only do not hide in the shadows, but, on the contrary, are often painted in bright colors and, moreover, completely different from the planes of the facades. In such cases, the object that most persistently declares itself in such cases is the one that, through various techniques, is already most brought forward and strives to be the pictorial center of the icon - the gospel; its edge, usually painted with cinnabar, is the brightest part of the icon and thereby extremely sharply emphasizes its additional planes. These are the techniques of underlining. These techniques are all the more conscious because they are, moreover, in contradiction with the usual coloring of objects and, therefore, cannot be explained by a naturalistic imitation of what usually happens. The Gospel did not usually have a cinnabar edge, and the side walls of the building were not painted in colors other than the facade, so in the originality of their colors on the icons one cannot help but see a desire to emphasize the complementarity of these planes and their non-subordination to linear perspective as such. These techniques are generally called reverse or inverted perspective, and sometimes - perverted or false perspective. But the reverse perspective does not exhaust the diverse features of the drawing, as well as the chiaroscuro of the icons. As the closest extension of reverse perspective techniques, it is worth noting the multi-centeredness in the images: the drawing is constructed as if his eyes were looking at different parts, changing their place. Here, some parts of the chambers, for example, are drawn more or less in accordance with the requirements of ordinary linear perspective, but each from its own special point of view, i.e. with its own special center of perspective; and sometimes with its own special horizon, and other parts, in addition, are depicted using reverse perspective. This complex development of perspective angles occurs not only in ward writing, but also in faces, although it is usually carried out not with very great persistence, moderately and quietly, and therefore can pass here as “mistakes” in the drawing; but in other cases, all school rules are overturned with such boldness, and their violation is so imperiously emphasized, and the corresponding icon says so much about itself, about its artistic achievements, and immediate artistic taste, that no doubt remains: the “incorrect” and mutually contradictory details of the drawing represent a complex artistic calculation, which, if you like, can be called daring, but in no way naive. What can we say, for example, about the icon of the Savior Pantocrator in the Lavra sacristy 51, on which the head is turned to the right, but on the right side it has an additional plane, and the angle of the left side of the nose is less than the right, etc.? The plane of the nose is so clearly turned to the side, and the surfaces of the crown and churches are turned out that there would be no difficulty in rejecting such an icon if it were not for - despite its “irregularity” - its amazing expressiveness and completeness. This impression is realized with complete certainty if we look right there, in the Lavra sacristy, at another 52 icon, similar in design, translation, size and colors of the same name, but painted almost without the above-mentioned deviations from the rules of perspective and school-wise - much more correct: this last icon, in comparison with the first, seems meaningless, inexpressive, flat and devoid of life, so that there remains no doubt, given their overall striking similarity, that promising rule-violations are not the tolerable weakness of the icon painter, but his positive strength - precisely as a result of which the first of the considered icons is immeasurably higher than the second, the incorrect one is higher than the correct one. Further, if we turn to chiaroscuro, then here too we find in the icons a peculiar distribution of shadows, emphasizing and highlighting the discrepancy between the icon and the image required by naturalistic painting. The absence of a specific focus of light, the inconsistency of lighting in different places of the icon, the desire to highlight masses that should have been shaded - these are again not accidents or mistakes of a primitivist master, but artistic calculations that give maximum artistic representation. Among similar means of icon-painting, one should also include the lines of the so-called cutting, made in a different color than the color of the opening of the corresponding place of the icon, and most often metallic-shiny - gold or very rarely silver assist or created gold. By this emphasis on the color of the cutting lines, we want to say that the icon painter consciously draws attention to it, although it does not correspond to anything physically visible, i.e. some similar system of lines on clothing or the seat, for example, but there is only a system of potential lines, lines of the structure of a given object, similar, for example, to lines of electric or magnetic field strength, or systems of equipotential or isothermal and similar curves. The cutting lines express the metaphysical scheme of a given object, its dynamics, with greater force than its visible lines, but in themselves they are completely invisible and, being inscribed on the icon, constitute; according to the icon painter’s plan, a set of tasks for the contemplating eye, lines of movements given to the eye when contemplating the icon. These lines are a scheme for reconstructing the contemplated object in the consciousness, and if we look for the physical foundations of these lines, then these are lines of force, lines of tension, i.e. in other words, not folds formed from tension, not yet folds, but folds only in possibility, in potency - those lines along which the folds would lie if they began to fold at all. The cutting lines drawn on an additional plane reveal to the consciousness the structural nature of these planes and, therefore, help, not limiting themselves to the passive contemplation of these planes, to understand the functional relationship of them to the whole and, therefore, provide material with particular acuteness to notice the non-subordination of such angles to the requirements of linear perspective. We will not talk about other, secondary, techniques of icon painting, with which it emphasizes its immunity from the laws of linear perspective and the awareness of its perspective violations. We will only mention the inventory that outlines the drawing and therefore extremely emphasizes its features - the animations, movements and marks, as well as spaces that reveal convexities and therefore accentuate all the irregularities that should not be visible, etc. One might think that what has been said is enough to remind everyone who looked closely at the icons of the already existing stock of impressions about the non-randomness of deviations from the rules of perspective and, moreover, about the aesthetic fruitfulness of such violations. And now, after such a reminder, we are faced with the question of the meaning and legality of these violations. That is, in other words, we are faced with a related question about the boundaries of application and the meaning of perspective. Does perspective, as its supporters claim, really express the nature of things and therefore should always and everywhere be considered as an unconditional prerequisite for artistic truthfulness? or is this only a scheme, and, moreover, one of the possible schemes of figurativeness, corresponding not to the worldview as a whole, but only to one of the possible interpretations of the world, associated with a very definite sense of life and understanding of life? Or again: is there a perspective, a perspective image of the world, a perspective interpretation of the world - a natural image flowing from its essence, the true word of the world, or is it just a special spelling, one of many constructions, characteristic of those who created it, characteristic of the age and life understanding of those who invented it and expressing their own style - but not at all excluding other orthographies, other transcription systems, corresponding to the life understanding and style of other centuries? and, moreover, perhaps, transcriptions that are more related to the essence of the matter - in any case, in such a way that a violation of this perspective interferes at least as little with the artistic truth of the images as grammatical errors in the letter of a holy man - with the vital truth of the experience he recounts? To answer our question, let us first of all give historical information, namely: let us understand historically how, in fact, representation and perspective are inseparable from each other. Babylonian and Egyptian flat reliefs do not show signs of perspective, just as they do not show, however, what in the proper sense should be called reverse perspective; the multi-centeredness of Egyptian images, as is known, is extremely great and canonical in Egyptian art: everyone remembers the profile of the face and legs when turning the shoulders and chest of Egyptian reliefs and paintings. But in any case there is no direct perspective in them 53 . Meanwhile, the amazing truthfulness of portrait and genre Egyptian sculptures shows the enormous powers of observation of Egyptian artists, and if the rules of perspective are indeed so fundamentally included in the truth of the world, as their supporters insist, then it would be completely incomprehensible why the perspective was not noticed and how the sophisticated eye of the Egyptian master could not have noticed it. On the other hand, the famous historian of mathematics Moritz Cantor notes that the Egyptians already possessed geometric preconditions for perspective images. They knew, in particular, geometric proportionality and, moreover, had advanced so far in this regard that they knew how, where required, to use an increased or decreased scale. “It is hardly surprising, therefore, that the Egyptians did not take a further step and did not open up prospects. As is known, there is no trace of it in Egyptian painting, and although one can recognize religious or other reasons for this, the geometric fact remains assured that the Egyptians did not use the technique of thinking of a painted wall as inserted between the looking eye and the depicted object and connecting through a line the points of intersection of this plane with the rays directed to that object" 54. Moritz Cantor's passing remark about the religious grounds for the futility of Egyptian images is very worthy of attention. In fact, Egyptian art, dating back thousands of years in its past, acquired a strictly canonical character and was cast in immutable hieratic formulas, perhaps, in their internal meaning, not too far from hieroglyphic inscriptions, just as the inscriptions, in turn, have not yet departed too much from metaphysical figurativeness. Of course, Egyptian art did not need any innovations and gradually became more and more self-contained. Perspective relationships, even if they were noticed, could not be admitted into the self-closed circle of the canons of Egyptian art. The lack of direct perspective among the Egyptians, as, although in a different sense, among the Chinese, proves rather the maturity and even senile overripeness of their art, rather than its infantile inexperience - liberation from perspective or the initial non-recognition of its power, as we will see, characteristic of subjectivism and illusionism - for the sake of religious objectivity and super-personal metaphysics. On the contrary, when the religious stability of a worldview is disintegrating, and the sacred metaphysics of the general national consciousness is corroded by the individual discretion of an individual with his separate point of view, and, moreover, with a separate point of view at this particular moment, then the perspective characteristic of an isolated consciousness appears; but at the same time - still, first, not in pure art, which by its very essence is always more or less metaphysical, but in applied art, as a moment of decorativeness, which has as its task not the truth of being, but the plausibility of showing. It is remarkable that it was to Anaxagoras, that Anaxagoras who tried to turn the self-living deities the Sun and the Moon into red-hot stones, and to replace divine peacemaking with a central vortex in which the luminaries arose, it was to this Anaxagoras that Vitruvius attributes the invention of perspective and, moreover, in what the ancients called stenography, i.e. in painting theatrical scenery. According to Vitruvius 55, when, approximately around 470 BC, Aeschylus staged his tragedies in Athens, and the famous Agatharchus arranged the scenery for him and wrote a treatise on them, “Commentarius”, it was on this occasion that Anaxagoras and Democritus were encouraged to investigate this very subject - the writing of scenery - scientifically. The question posed by them was how lines should be drawn on a plane so that, assuming a certain center, the rays drawn to them from the eye correspond to the rays drawn from the eye located in the same place to the corresponding points of the building itself - so that the image on the retina from the original object, in modern terms, completely coincides with that of the decoration representing this object. So, perspective does not arise in pure art and, according to its very original task, does not express a living artistic perception of reality, but is invented in the field of applied art, more precisely, in the field of theatrical technology, which attracts painting to its service and subordinates it to its tasks. Whether these tasks correspond to the tasks of pure painting is a question that does not need an answer. After all, painting has the task not to duplicate reality, but to provide the most profound understanding of its architectonics, its material, its meaning; and the comprehension of this meaning, this material of reality, its architectonics is given to the contemplating eye of the artist in living contact with reality, experiencing and feeling reality. Meanwhile, theatrical scenery wants, as far as possible, to replace reality with its appearance: the aesthetics of this appearance is the internal coherence of its elements, but not at all a symbolic signification of the prototype through an image embodied by means of artistic technique. Decoration is a deception, even if it is beautiful, but pure painting is, or at least wants to be, first of all, the truth of life, not replacing life, but only symbolically signifying in its deepest reality. Decoration is a screen that obscures the light of being, and pure painting is a wide-open window into reality. For the rationalistic mind of Anaxagoras and Democritus, fine art as a symbol of reality could not exist, and was not required: as for any “peredvizhniki” of thought - if we allow ourselves to make a historical category out of this small phenomenon of Russian life - they needed not the truth of life, which gives comprehension, but an external similarity, pragmatically useful for immediate life actions - not the creative foundations of life, but an imitation of the surface of life. Until then, the Greek scene had only been marked by “paintings and textiles” 56 ; now the need for illusion began to be felt. And so, assuming that the viewer or decorator-artist is chained, truly, like a prisoner of Platonov’s cave, to a theater bench and cannot, and equally should not, have a direct, vital relationship with reality - as if separated from the stage by a glass partition and there is only one motionless looking eye, without penetration into the very essence of life and, most importantly, with a paralyzed will, for the very essence of the secularized theater requires a weak-willed looking at the stage as some kind of “not true”, “not really”, as some empty deception - these first theorists of perspective, I say, give the rules for the naive deception of the theater spectator. Anaxagoras and Democritus replace a living person with a spectator poisoned by curare, and clarify the rules for deceiving such a spectator. There is no need for us to argue now; Let us temporarily agree: for the visual illusion of such a patient, deprived of most of the common human life, these techniques of perspective depiction really have their meaning. Consequently, we must recognize it as established that, at least in Greece, in the 5th century BC, perspective was known, and if, in one case or another, it was still not applied, then, obviously, this did not happen at all from the unknown of its beginnings, but for some other, deeper motives, and precisely impulses emanating from the highest requirements of pure art. And it would be extremely incredible and inconsistent with the state of the mathematical sciences and the high geometric observation of the sophisticated eye of the ancients - to assume that they did not notice the perspective of the image of the world, supposedly inherent in normal vision, or were unable to derive the corresponding simple applications from the elementary theorems of geometry; it would be very difficult to doubt that when they did not apply the rules of perspective, it was because they simply did not want to apply them, considered them unnecessary and anti-artistic. In fact, Ptolemy in his “Geography” 57, dating back to the 2nd century BC, considers the cartographic theory of the projection of a sphere onto a plane, and in his “Planisphery” he discusses different methods of projections, mainly the projection from the pole onto the equatorial plane, i.e. that projection, which in 1613 Eguillion called stereographic, and also solves other difficult projective problems 58. Is it possible to imagine that, given this state of knowledge, simple techniques of linear perspective were unknown? And, in fact, where we are dealing not with pure art, but with decorative illusions used to deceptively expand the space of a theater stage or to destroy the plane of a home wall, we invariably come across the use of linear perspective, which corresponds to the intended purpose. This is especially observed in those cases when life, moving away from its deep sources, flows in the shallow waters of light Epicureanism, in the atmosphere of the lightweight bourgeoisness of Greek little men - graeculorum, as the Romans of their time called them, little men who have lost the noumenal depth of the Greek genius and did not have time to acquire the majestic scope, universal in scope, of the moral and political thought of the Roman people. Here we mean the elegantly empty paintings of houses in Pompeii, the architectural wall decorations of Pompeian villas 59. Brought to Rome mainly from Alexandria and other centers of Hellenistic culture in the 1st and 2nd centuries, this baroque of the ancient world was posed with purely illusionistic goals and sought precisely to deceive the viewer, who was therefore supposed to be more or less motionless. Architectural and landscape paintings of this kind are perhaps absurd, in the sense of the impossibility of their implementation in reality, 60 but nevertheless they want to deceive, as if they are playing and teasing the viewer. Other details are conveyed with such naturalism that the viewer only by touch is convinced of the optical illusion: this impression is facilitated by the masterful chiaroscuro, located depending on the light source - a window, a hole in the ceiling, a door - that illuminated the room 61 . The remarkable fact that from this illusionistic landscape again stretches connecting threads to the architecture of the Greco-Roman stage 62 is worthy of the greatest attention. The root of perspective is theater, not only for the historical and technical reason that theater first needed perspective, but also due to a deeper impulse: the theatricality of a perspective image of the world. This is, after all, the essence of an unworking worldview, devoid of a sense of reality and consciousness of responsibility, that for him life is only a spectacle, and not at all a feat. And therefore - returning to Pompeii - it is difficult to look for genuine works of pure art in these paintings. Indeed, the technical smartness of these home decorations still does not make art historians forget that in them we have before us “only the works of virtuoso artisans, and not real inspired artists.” The same applies to landscape backgrounds in narrative paintings, painted “always very approximately,” quickly and skillfully sketched. “Whether the backgrounds in the famous paintings of the classics were painted this way is still a question” 64 . These monuments suffer from approximate solutions to promising problems, which the artists seemed to approach exclusively through experience, says Benoit. – Still, the big question is: do these features mean that the laws of perspective were really not known to the ancients? Don’t we see, Benoit asks, “at the present time the same oblivion of perspective as science? The time is not far off when we too will reach “Byzantine” absurdities in this area and leave behind us the inability and approximate nature of late classical painting. Will it be possible on this basis to deny knowledge of the laws of perspective in the generation of artists that preceded us?..” 65 Indeed, one can partly see in this semi-accuracy of promising implementations the beginnings of the collapse of perspective, which soon begins in the Eastern and Western Middle Ages. But, I think, these inaccuracies in perspective are a compromise between the strictly decorative tasks - illusionistic painting - and the synthetic tasks - pure painting: after all, we must not forget that a residential building, even if it is very unlaborable, is still not a theater and that the inhabitant of the house is not at all as chained to his place and not as disadvantaged in his life as a theater viewer. If the wall painting of some Vittiev house strictly obeyed the rules of perspective, then it, claiming to be a deception or a playful joke, would achieve this only when the viewer is motionless and, moreover, located in a strictly defined place in the room; on the contrary, any movement of him or, especially, a change of place would produce a disgusting feeling of a failed deception or an exposed trick. It is precisely in order to avoid gross violations of illusions that the decorator abandons its unconditional obsession for each individual point of view and therefore gives some synthetic perspective, some approximate solution to the problem for each individual point of view, but at least extending to the space of the entire room: figuratively speaking, he resorts to the tempered tuning of a keyboard instrument, within the limits of the required accuracy - sufficient. And also, to put it differently, he partly abandons the art of similarities and embarks on a certain, albeit to a very small extent, path of a synthetic image of the world, i.e. a decorator becomes somewhat of an artist. But, I repeat, one can see the artist in him not because he partly, and for a very large part, adheres to the rules of perspective, but because he deviates from them. Starting from the 4th century A.D. – illusionism is decomposing, and perspective spatiality in painting disappears: there is a clear non-recognition of the rules of perspective, failure to pay attention to the proportional relationships of individual objects and even, sometimes, their individual parts. This destruction of late classical, essentially perspective, painting proceeds with extreme speed, and then deepens with each century, including until the time of the Early Renaissance. The masters of the Middle Ages “have no idea of ​​​​the reduction of lines to a single point or of the meaning of the horizon. Late Roman and Byzantine artists seemed to have never seen buildings in real life, but dealt only with flat toy cutouts. They care just as little about proportions and, as time goes on, less and less. There is no relationship between the height of the figures and the building assigned to these figures. To this we must also add that over the centuries, even in details, an ever-increasing distance from reality is noticeable. Some more parallels between actual architecture and architectural painting can be established in the works of the 6th, 7th and even the 10th and 11th centuries, but then that strange type of “chamber painting” in which everything is arbitrary and conventional is established in Byzantine art” 66 . We took this characteristic of medieval painting from the “History of Painting” by A. Benois, but from here only because the book was at hand; in Benoit’s lamentations it is not difficult to hear the long, long-tired slander of medieval art, especially for the “ignorance” of perspective, which can be read in any book on the history of art, with the usual reference to the depiction of houses “on three fronts”, as children draw, to the “conventionality” of coloring, to the divergence of parallels towards the horizon, to disproportionality and, in general, any kind of perspective and other spatial ignorance. To complete this description of the Middle Ages, it must be added that in the West, from the same point of view, the situation was no better, but even much worse: “If we compare what was happening in Western Europe approximately in the 10th century with what was happening at the same time in Byzantium, then the latter will seem the height of artistic sophistication and technical splendor” 67. With a secret understanding of Byzantium, it goes without saying that the summary, whether Benoit’s or most others’, does not matter, it has become so boring with countless repetitions, hand in hand with the even more boring cries of cultural historians about the “darkness” of the Middle Ages, a summary that reads: “The history of Byzantine painting with all its fluctuations and temporary rises there is a history of decline, savagery and deadness. Byzantine samples increasingly removed from life, their technology becomes more and more slavish traditional and craft" 68. The scheme of the history of art and the history of education in general, as is known, from the Renaissance to almost the present day, is invariably the same, and, moreover, extremely simple. It is based on an unshakable belief in unconditional value, in final completion and, so to speak, canonization, elevation almost into the metaphysical realm of the bourgeois civilization of the second half of the 19th century, i.e. Kantian, although not directly taken from Kant, orientation. Truly, if anywhere we can talk about ideological superstructures over economic forms of life, it is here, among the cultural historians of the 19th century, who blindly believed in the absoluteness of the petty bourgeoisie and assessed world history by the degree of proximity of its phenomena to the phenomena of the second half of the 19th century. So it is in the history of art: everything that is similar to the art of this time or moves towards it is recognized as positive, while the rest is considered a fall, ignorance, savagery. With such an assessment, the enthusiastic praise that often comes from the lips of venerable historians becomes understandable: “in a completely modern way,” “they couldn’t have done better even then,” and some year close to the time of the historian himself is indicated. Indeed, for them, who believe in modernity, complete trust in their contemporaries is inevitable, just as the provincials of science are deeply convinced that this or that book is “recognized” (as if there is some kind of ecumenical council for the formulation of dogmas in science) as the final truth in science. And then it is clear that ancient art, passing from the holy archaics through the medium of beauty to the sensual and, finally, to the illusionistic, seems to such historians to be developing. The Middle Ages, which decisively broke with the tasks of illusionism and set as its goal not the creation of similarities, but symbols of reality, seems to be falling. And finally, the art of the New Time, beginning with the Renaissance and then, through a silent wink, through some current of mutual agreement, decided to replace the creation of symbols with the construction of likenesses, this art, which led along a broad road to the 19th century, seems to historians to be undeniably improving. “How can this be bad if, by an immutable internal logic, it led to you, to me?” - this is the true thought of our historians, if expressed without affectation. And they are deeply right in their awareness of a direct connection, and moreover, not only an external historical connection, but an internal logical, transcendental connection between the premises of the Renaissance and the life understanding of the most recent past, just as they are deeply right in their feeling of the complete incompatibility of medieval premises and the worldview just indicated. If we sum up everything that is said in a formal sense against the art of the Middle Ages, then it comes down to the reproach: “There is no understanding of space,” and this reproach, in its expanded form, means that there is no spatial unity, there is no scheme of Euclidean-Kantian space, which, within painting, is reduced to linear perspective and proportionality, or more precisely, to one perspective, for proportionality is only its particularity. At the same time (and - what is most dangerous - unconsciously) it is assumed to be self-evident or absolutely proven somewhere and by someone that no forms exist in nature - they do not exist, each living in its own little world - for in general there are no realities that have a center in themselves and are therefore subject to their own laws; that, therefore, everything visible and perceived is only simple material for filling some general ordering scheme imposed on it from the outside, which is the Kantian-Euclidean space, and that, consequently, all forms of nature are only apparent forms, superimposed on impersonal and indifferent material by the scheme of scientific thinking, i.e. They are, as it were, cells of the delineation of life - and nothing more. And finally, the logically first premise is about qualitative homogeneity, infinity and limitlessness of space, about its, so to speak, formlessness and non-individuality. It is not difficult to see that these premises deny both nature and man at once, although they are rooted, according to the mockery of history, in slogans called “naturalism” and “humanism”, and culminated in the formal proclamation of the rights of man and nature. This is not the place to establish or even explain the connection between Renaissance sweet roots and Kantian bitter fruits. It is sufficiently known that Kantianism, in its pathos, is precisely the in-depth humanitarian-naturalistic understanding of life of the Renaissance, and in its scope and depth, it is the self-awareness of that historical epoch that calls itself the “new European enlightenment” and not without right recently boasted of its actual dominance. But in modern times we are already learning to understand the imaginary finality of this enlightenment and have learned, both scientifically and philosophically, and historically, and especially artistically, that all those scarecrows with which they scared us away from the Middle Ages were invented by the historians themselves, that in the Middle Ages flows a deep and meaningful river of true culture, with its science, with its art, with its statehood, in general with everything that belongs to culture, but precisely with its own, and, moreover, adjacent to true antiquity. And the prerequisites that are considered immutable in the life understanding of the New Time, here, as in antiquity (-yes, as in antiquity!-), are not only considered immutable, but are rejected, not due to a lack of consciousness, but essentially due to the aspirations of the will. The pathos of the new man is to get rid of all reality, so that “I want” is legislated by a newly constructed reality, phantasmagorical, although enclosed in graphed cells. On the contrary, the pathos of ancient man, like that of medieval man, is acceptance, grateful recognition and affirmation of all reality as good, for being is good, and good is being; the pathos of medieval man is the affirmation of reality in oneself and outside oneself, and therefore objectivity. The subjectivism of the new man is characterized by illusionism; on the contrary, there is nothing so far from the intentions and thoughts of medieval man (and his roots are in antiquity) as the creativity of likenesses and life among likenesses. For the new man, let’s take his frank admission through the mouth of the Marburg school, reality exists only if and to the extent that science deigns to allow it to exist, issuing its permission in the form of a constructed scheme; this scheme must be the solution to a legal incident, why a given phenomenon can be considered entirely included in the prepared outline of life and therefore permissible. The patent is approved for validity - only in the office of G. Cohen, and without his signature on the seal it is invalid. What the Marburgers express openly constitutes the spirit of Renaissance thought, and the entire history of enlightenment is largely occupied with a war on life in order to completely strangle it with a system of schemes. But it is worthy of attention and the deepest inner laughter that this distortion, this corruption of the natural human way of thinking and feeling, this re-education in the spirit of nihilism, is strenuously presented by the new man as a return to naturalness and as the removal of some kind of shackles supposedly imposed on him by someone, and, truly, trying to scrape the writings of history from the human soul, he makes a hole in the very soul. Ancient and medieval man, on the contrary, first of all knows that in order to want, one must be, be a reality and, moreover, among the realities on which one must rely: he is deeply realistic and stands firmly on the ground, unlike a new person, who considers only his desires and, of necessity, the immediate means of their implementation and satisfaction. It is clear from this that the prerequisites for a realistic understanding of life have been and will always be: there are realities, i.e. there are centers of being, certain clots of being, subject to their own laws, and therefore each having their own form; therefore, nothing that exists can be considered as indifferent and passive material for filling any schemes, much less taken into account with the scheme of Euclidean-Kantian space; and therefore forms must be comprehended through their life, depicted through themselves, according to comprehension, and not from the angles of a predetermined perspective. And, finally, space itself is not just a uniform, structureless place, not a simple graph, but itself a unique reality, thoroughly organized, nowhere indifferent, having internal order and structure. So: the promise or lack of promise of painting of an entire historical period cannot at all be considered as something equivalent to skill or ineptitude, but lies much deeper in the definitions of the fundamental will, which has a creative impulse in one direction or another. Our thesis - and we will return to it more than once - is that in those historical periods of artistic creativity when the use of perspective is not observed, the creators of the visual arts do not “cannot”, but do not want to use it, or, more precisely, they want to use a different principle of pictoriality than perspective, and they want to do so because the genius of the time understands and feels the world in a way that immanently includes this method of figurativeness. On the contrary, in other periods they forget the meaning and significance of non-perspective figurativeness, they decisively lose their instinct for it, because the life understanding of time, having become completely different, leads to a perspective picture of the world. Both have their own internal consistency, their own forced logic, which is very elementary in the essence of the matter, and if it does not come into full force extremely quickly, then this is not due to the complexity of this logic, but from the ambiguous fluctuation of the spirit of the time between two mutually exclusive self-determinations. After all, there are, ultimately, only two experiences of the world - universal human experience and “scientific” experience, i.e. Kantian, how there are only two attitudes to life - internal and external, how there are two types of culture - contemplative-creative and predatory-mechanical. The whole matter comes down to the choice of one path or another - a medieval night or an enlightening day of culture; and then everything is determined, as if written, with complete consistency. But, alternating in history, these stripes of culture are not at all immediately separated from each other, due to the uncertainty of the state at the corresponding times of the spirit itself, already bored with one and not yet daring to try another. Without going into the meaning of violations of perspective now - in order to return to the discussion of this issue later with greater psychological persuasiveness - let us recall the fact of medieval painting that violations of perspective do not appear here at times, this way or that, but are subordinated to a certain system: receding parallels always diverge towards the horizon, and moreover, the more noticeable, the more it is necessary to highlight the object limited by them. If in the features of Egyptian reliefs we see not an accident of ignorance, but an artistic method, for these features occur not once or twice, but thousands, tens of thousands of times, and therefore are deliberate, then for precisely the same reason one cannot help but recognize in the originality of the violation of perspective by medieval art - also precisely the method. And it is psychologically impossible to imagine that, over the course of many centuries, strong and profound people, the builders of a unique culture, would not be able to notice such an elementary, such an immutable and, one might say, glaring fact about themselves as the convergence of parallels to the horizon. But if this doesn’t seem enough, here’s more proof: children’s drawings, in terms of non-perspective, and specifically reverse perspective, vividly resemble medieval drawings, despite the efforts of teachers to instill in children the rules of linear perspective; and only with the loss of a direct relationship to the world do children lose their backward perspective and obey the pattern they have chanted. All children do this, independently of each other. And, therefore, this is not a simple accident and not an arbitrary invention of some Byzantine of them, but a method of representation arising from the nature of the perceptual synthesis of the world. Since children's thinking is not weak thinking, but a special type of thinking 69, and moreover, it can have any degree of perfection, including genius, and even predominantly akin to genius, then it should be recognized that the reverse perspective in the depiction of the world is not at all just a failed, misunderstood, understudied linear perspective, but is precisely a unique embrace of the world, which should be taken into account as a mature and independent method of depiction, perhaps - to hate it as a hostile reception, but, in any case, about which one does not have to speak with condolences or with patronizing condescension. Indeed, a new worldview was marked in the 14th century in the West and a new attitude to perspective. As you know, the first subtle vapors of naturalism, humanism and reformation rise from the innocent “lamb of God” - Francis of Assisi, canonized for the sake of immunization, for the simple reason that they did not remember to burn him in time. And the first manifestation of Franciscanism in the field of art was Giottism. The idea of ​​the Middle Ages is usually united in thought with the work of Giotto, but this is erroneous. Giotto looks the other way. His “cheerful and happy, in the Italian manner, genius,” prolific and easy-going, was prone to a Renaissance-style shallow view of life. “He was very inventive,” says Vasari, “very pleasant to deal with and a great master of speaking sharp words, the memory of which is still alive in this city” 70. However, those that are repeated to this day are obscene and rude, and many are also ungodly. Under the cover of church subjects, one can notice in it a secular spirit, satirical, sensual and even positivistic, hostile to asceticism. Eating from the mature past that preceded his era, he breathes, however, a different air. “Although born in a mystical age, he was not himself a mystic, and although he was a friend of Dante, he was not like him,” Yip writes about Giotto. Ten 71. Where Dante reeks of sacred anger, Giotto chuckles and condemns - not the violation of the ideal, but the ideal itself. He, who wrote “The Betrothal of St. Francis with Poverty,” in his poem ridicules the very ideal of poverty. “As for poverty, supposedly desired and sought, then, as can be clearly seen from experience, it is observed or not observed, but not for the sake of glorifying it, for neither subtlety of reason, nor knowledge, nor courtesy, nor virtue are combined with it. And, it seems to me, it is very shameful to call something virtue that suppresses good qualities, and it is very bad to prefer something animal to real virtues that bring virtue to every intelligent person and which are such that the more you enjoy them, the more you value them.” It is difficult to believe that this open preference for worldly glory over the feat of self-restraint belonged to Dante's friend. But that’s true; and, besides Dante, he also had friends of the Epicureans, the deniers of God. Giotto created for himself the ideal of a universal and humanitarian culture, and he imagines life in the spirit of the Liberal Panzers of the Renaissance, as earthly happiness and human progress, with subordination to the main goal - the complete and perfect development of all natural forces - everything else; inventors of the useful and beautiful belong here to the first place. And he himself strives to be the same, the prototype of the most typical genius of the era - Leonardo. “He was very inquisitive,” says Vasari about Giotto, “he walked around forever immersed in thinking about new things and tried to get closer to nature, which is why he deserves to be called a student of nature and not anyone else. He painted a variety of landscapes, full of rocks and trees, which was a novelty in his time." 72 Still full of the noble juices of the Middle Ages and not a naturalist himself, he had already experienced the very first, pre-dawn breeze of naturalism and became its herald. The father of modern landscape, Giotto comes out with the technique of written architecture that “deceives the eye,” and by eye, with luck surprising for his time, solves bold, long-term problems. Art historians doubt Giotto’s knowledge of the rules of perspective: if this is correct, then here is proof that when the eye began to be guided by an internal search for perspective, it almost immediately found it, although not in a minted form. Giotto not only does not make gross violations of perspective, but, on the contrary, seems to play with it, posing complex perspective problems for himself and solving them insightfully and completely; in particular, the receding parallels converge towards the horizon at one point. Moreover, in the frescoes of the upper church of St. Francis in Assisi, Giotto begins with the fact that mural painting has for him “the meaning of something independent and, as it were, even competing with architecture.” A fresco is “not a wall pattern with a plot,” but “a view through the wall of certain actions” 73 . It is worthy of note that later Giotto rarely resorted to this method, which was too bold for that time, and all his closest followers rarely resorted to it, whereas in the 15th century such architecture became the general rule, and in the 16th and 17th centuries it led to the focal enrichment of architectural painting in completely flat and simple rooms, devoid of any real architectural decoration 74 . Consequently, if subsequently the father of modern painting does not resort to a similar technique, it is not because he did not know it, but because the strengthened artistic genius, i.e. realizing himself in the sphere of pure art, he alienated himself from the deceptive perspective, at least from its obsession, just as his rationalistic humanism apparently softened later. But then, what did Giotto set off from? Or, in other words, where did he get the ability to use perspective? – Historical analogies and the inner meaning of perspective in painting suggest the answer we already know. When the unconditionality of theocentrism is suspected, and along with the music of the spheres the music of the earth sounds (I mean “earth” in the sense of self-affirmation of the human “I”), then an attempt begins to substitute likenesses and ghosts in place of dim and clouded realities, illusionistic art in place of theurgy, and theater in place of divine action. It is natural to think that Giotto developed the habit and taste for promising visual illusions on theatrical stage sets: we have already seen a precedent of this kind in Vitruvius’ report on the staging of Aeschylus’ tragedies and on Anaxagoras’s participation in it. That transition from theurgy to secular vision, which was the tragedy in ancient Greece that successively led away from the mystical and, more precisely, the mysterious reality - of Aeschylus, then of Sophocles and, finally, of Euripides, in the development of the theater of the New Time, mysteries appeared, which eventually gave rise to a new drama. It seems likely to art historians that Giotto’s landscape actually arose from the scenery of what was then called “mysteries”, and therefore could not, let’s say from ourselves, not obey the beginning of illusionistic decorativeness, i.e. perspective. In order not to seem unfounded, let us confirm our considerations with the opinion of an art historian who is alien in his way of thinking: “What was the dependence of Giotto’s landscape on the scenery of the mysteries? - A. Benois asks himself to give an answer: - In some places this dependence is felt to such a strong degree (in the form of tiny “fake” houses and pavilions, in the form of rocks that look like slides, flat, as if cut out of cardboard) that it is simply impossible to doubt the impact of the performances of spiritual performances on his painting: we probably see directly recorded scenes of these spectacles in some frescoes. However, it must be said that precisely in the paintings that undoubtedly belong to Giotto, this dependence is less pronounced and each time in a highly revised form, according to the conditions of monumental painting” 75. In other words, Giotto, maturing as a pure artist, gradually moves away from scenery, which, moreover, as a work of the artel, was hardly completely individual. Giotto's innovation was, therefore, not in perspective as such, but in the pictorial use of this technique, borrowed from the applied and popular branches of art, just as Petrarch and Dante transferred the common language to poetry. As a result, the conclusion arises that knowledge, or at least the ability to use the techniques of perspective, as a “secret science of perspective” 76, as A. Durer put it, already existed, and, perhaps, always existed among the masters who painted the scenery for the mysteries, although strict painting of these techniques was alienated. Could she not know them? – It is difficult to imagine the opposite, since Euclid’s “Elements of Geometry” were known. Already Dürer, in his “Instructions on Methods of Measurement” 77, published in 1525 and containing the doctrine of perspective, begins the first book of the treatise with words that clearly show the small novelty of the theory of perspective in comparison with elementary geometry - small novelty, according to the consciousness of the people of that time: “The most profound Euclid set out the foundations of geometry,” writes Dürer, “and to those who are good I’m already familiar with them, what is written here will be superfluous” 78. So: elementary perspective was known for a long time - it was known, although it did not have access to high art beyond the hallway. But, as the religious worldview of the Middle Ages became secularized, pure religious action degenerated into semi-theatrical mysteries, and the icon into so-called religious painting, in which the religious plot more and more became only a pretext for depicting the body and landscape. A wave of peace is spreading from Florence; in Florence, the Giottists discovered and then disseminated, like artistic copybooks, the beginnings of naturalistic painting. Giotto himself, and from him Giovani da Milano, and especially Altichieri and Avanso, make bold, promising constructions. Naturally, these artistic experiences, as well as traditions, partly drawn from the works of Vitruvius and Euclid, form the basis of a theoretical system in which the doctrine of perspective was to be presented fully and substantiated. Those scientific foundations that, after a century of development, gave “the art of Leonardo and Michel Angelo” were found and developed in Florence. The works of two theorists of that time have not reached us: Paolo del Abbaco (1366) and the later Biagio de Parma. But it is possible that they mainly prepared the ground on which, from the beginning of the 15th century, the main theoreticians of the doctrine of perspective 79 worked, Filippo Brunelleschi (1377 - 1449) and Paolo Ucello (1397 - 1475), then Leon Alberti, Piero dei Franceschi (about 1420 - 1492) and, finally, a number of sculptors, of whom it follows in particular note Donatello (1386 – 1466). The strength of the influence of these researchers was determined by the fact that they not only theoretically developed the rules of perspective, but also realized their achievements in illusionistic painting. Such are the murals in the form of monuments, depicted with great knowledge of perspective on the walls of the Florentine Duomo, painted in 1436 by Uccello and in 1435 by Castagna; the same is the fresco decoration by Andrea del Castagno (1390 - 1457) in Sant'Apollonio in Florence. “All its strict decoration: checkers on the floor, coffers in the ceiling, rosettes and panels on the walls - are depicted with obsessive clarity in order to achieve a complete impression of depth (we would say: “stereoscopic”). And this impression has been achieved to such an extent that the whole scene in its frozen state has the appearance of some kind of group from a panopticon - of course from the “brilliant panopticon” 80, - due to a misunderstanding, a supporter of perspective and the Renaissance caustically remarks. Piero also leaves a manual on perspective, under the title “De perspectiva pingendi.” 81 Leon Battista Alberti (1404 – 1472), in his three-volume work “On Painting,” written before 1446 and published in Nuremberg in 1511, develops the foundations of the new science and illustrates their application in architectural painting. Masaccio (1401 - 1429) and his students Benozzo Gozzoli (1420 - 1498) and Fra Filippo Lippi (1406 - 1469) strive to use the same science of perspective in painting, until, finally, Leonardo da Vinci (1452 - 1519) takes on the same problems theoretically and practically and completes the development of perspective by Raphael Santi (1483 – 1520) and Michel Angelo Buonarotti (1475 – 1564). We will not further note the stages of the theoretical and pictorial development of perspective in the eon of history that was immediately before ours, especially since the study of it passed mainly into the hands of mathematicians and has already become far from the immediate interests of art: the little lightly outlined here had the task not of communicating generally known historical information as such, but of something completely different - namely, to recall the complexity and duration of this development, completed only in the 18th century, by Lambert, and further, as one of the departments descriptive geometry, the works of Loria, Aschieri, Enriques in Italy, Chals and Poncelay in France, Staudt, Fiedler, Wiener, Kupfer, Burmester in Germany, Wilson in America and others, which merged into the general mainstream of an extremely important and extensive mathematical discipline - projective geometry 82. It follows from this that no matter how we evaluate perspective on its merits, we have no right to understand in it some simple, natural way of seeing the world, directly characteristic of the human eye as such. The need to forge the doctrine of perspective by a number of great minds and most experienced painters over the course of several centuries, with the participation of first-class mathematicians, and, moreover, obviously after the main signs of a perspective projection of the world were noticed, makes us think that the historical work of developing perspective was not at all about a simple systematization of what was already inherent in human psychophysiology, but about the forced re-education of this psychophysiology in the sense of the abstract demands of a new worldview, essentially anti-artistic, essentially excluding art, especially fine art. But the soul of the Renaissance, the soul of the New Time in general, is an incomplete, split soul, doubling in its thoughts. In this regard, art has benefited. Fortunately, living creativity still did not obey the demands of reason, and art in fact went far from the paths that were proclaimed in abstract declarations. A circumstance worthy of attention and laughter: even the artists themselves, the theorists of perspective, as soon as they did not tell the rules of perspective they prescribed and surrendered, although already knowing its secrets, to direct artistic instinct when depicting the world, they made gross “blunders” and “mistakes” against its requirements - everything, everything! But the study of the corresponding paintings reveals that their strength lies precisely in these “mistakes,” in these “misses.” Now when really Und predigen öffentlich Wasser 83 Now there is no time to enter into a detailed analysis of works of art, and we will have to be satisfied with only a few typical examples of them, proving the idea expressed, and, moreover, taking them superficially, without explaining what exactly their inconsistency with the perspective scheme means aesthetically. But, for the sake of complete clarity, let us recall, and in someone else’s words, that there is a task for perspectivists - the notorious “perspective unity.” In the heyday of perspective-belief and perspective-reverence, in the seventies of the 19th century, a textbook of perspective was compiled by Guido Schreiber, in the second edition reviewed by the architect and teacher of perspective at the Leipzig Academy of Art I.F. Vieweger and provided with a foreword by the professor and director of the same Academy - Ludwig Nieper 84. It seems respectable and highly authoritative! So, in this textbook, in the chapter on “perspective unity” there is the following: “Any drawing that claims to have a perspective action must be based on a certain place of the drawer or viewer. The drawing must therefore have only one point of view, only one horizon, only one scale. According to this one point of view, the retreat of all perpendicularly receding lines that run deep into the images should be directed. On this one horizon must equally lie the vanishing points of all other perpendicular lines; the correct ratio of quantities should dominate the entire image. This is what should be understood by perspective unity. If a picture is drawn from life, then only a little attentiveness to these provisions is required, and everything will be given to a certain extent by itself” 85. Violation of the uniqueness of point of view, the uniqueness of the horizon and the uniqueness of scale is a violation of the perspective unity of the image. If anyone is a prospect, it is, of course, Leonardo. His “Last Supper,” the artistic ferment of the later theological “Lives of Jesus,” has the task of removing the spatial distinction between that world, the gospel, and this, the everyday, to show Christ as having only a special value, but not a special reality. What is on the fresco is a stage production, but not a special space incomparable to ours. And this scene is nothing more than an extension of the space of the room; our gaze, and behind it our entire being, is drawn in by this receding perspective, leading to the right eye of the main face. We do not see reality, but we have a visual phenomenon; and we peep, as if through a crack, coldly and curiously, having neither reverence, nor pity, nor, even more so, the pathos of distance. The laws of Kantian space and Newtonian mechanics reign on this stage. Yes. But if only this were the case, then there would ultimately be no supper. And Leonardo marks the special value of what is happening - by violating the uniqueness of scale. A simple measurement will easily show that the upper room is barely twice the height of a person, with a width of three times, so that the room does not at all correspond to the number of people in it, nor to the grandeur of the event. However, the ceiling does not seem oppressive, and the smallness of the upper room gives the picture dramatic richness and fullness. Imperceptibly but surely, the master resorted to a violation of perspective 86, well known since Egyptian times: he applied different units of measurement to the characters and to the setting and, by diminishing the measure of the latter, moreover, differently in different directions, thereby exalted the people and gave the modest farewell dinner the significance of a world-historical event and, moreover, the center of history. The unity of perspective was broken, the duality of the Renaissance soul appeared, but the picture acquired aesthetic persuasiveness. It is known what a majestic impression the architecture of Raphael’s “School of Athens” 87 makes. If you characterize the impression of these vaults from memory, then you would like to compare them, for example, with the Moscow Cathedral of Christ the Savior: the vaults seem to be equal in height to the church ones. But the measurements show the height of the pillars to be only slightly more than twice the height of the figures, so that the whole building, apparently so magnificent, would be very insignificant - insignificant if it were actually built. The artist’s technique in this case is also very simple. “He accepted two points of view, located on two horizons. The floor and the entire group of faces are drawn from the upper point of view, and the vaults and generally the entire upper part of the picture are drawn from the lower point of view. If the figures of people had a common vanishing point with the lines of the ceiling, then the heads of the people located in the depths of the picture would sink lower and would be covered by the people standing in front, which would damage the picture. – The vanishing point of the ceiling lines is in the right hand of the central figure (Aristotle), who holds a book in his left hand and points as if to the ground with his right. If we draw a line to this point from the head of Alexander, the first figure located on the right side of Plato (with his arm raised), then it is not difficult to see how much the last figure of this group would have to decrease. The same applies to groups located on the right side of the viewer. To hide this perspective error, Raphael placed the characters in the background and thereby disguised the floor lines going to the horizon” 88. Of Raphael’s other paintings, let us at least mention “The Vision of Ezekiel.” Here there are several points of view and several horizons: the space of vision is not coordinated with the space of the lower world, and it was absolutely necessary to do this, because otherwise the one sitting on the cherubs would seem only like a person, contrary to mechanics, not falling from a height. (In this picture, as in many others by Raphael, there is a balance of two principles, promising and non-promising, corresponding to the calm coexistence of two worlds, two spaces. This is not shocking, but touching, just as if the curtain of another world was silently pulled apart in front of us, and our eyes were presented - not a scene, not an illusion in this world, but a genuine, although not intruding here, another reality Raphael gives a hint of this property of his spatiality in Sistine - with parted curtains.) As a direct contrast to the “Vision of Ezekiel,” one can point out, for example, Tintoretto’s painting “The Apostle Mark frees a slave from martyrdom” located in the Venice Academy. Appearance of St. Mark is presented in the same space as all the characters, and the heavenly vision seems to be a bodily mass about to fall on the heads of the witnesses of the miracle. Here one cannot escape the memory of the naturalistic techniques of Tintoretto’s work, who suspended wax figurines from the ceiling in order to accurately convey their angles in a naturalistic manner. And - the heavenly vision turned out to be, indeed, nothing more than a wax casting on a suspension, like Christmas tree cherubs. Such is the artistic failure of merging heterogeneous spaces. But the use of two spaces at once, promising and non-perspective, also occurs - and quite often, especially when depicting visions and miraculous phenomena; These are some of Rembrandt's works, although one can speak about the prospects of their parts only with many reservations. This technique is a characteristic feature of Domenico Theotokopoulo, nicknamed El Greco. “The Dream of Philip II”, “The Burial of Count Orgaze”, “The Descent of the Holy Spirit”, “View of Toledo” and his other works clearly fall apart - each into several, at least two, spaces, and the space of spiritual reality definitely does not mix with the space of sensory reality. This is what gives El Greco’s paintings special credibility. However, it would be a mistake to think that only mystical plots require perspective violations. Let’s take for example Rubens’ “Flemish Landscape” from the Uffizi Gallery: its middle part is approximately perspective, and space draws it in, while the side parts are inversely perspective, and their spaces throw out apperceptive vision. The result is two powerful visual whirlpools, amazingly filling the prosaic plot. The same is the balance of the two principles of spatiality in the “Conversion of the Apostle Paul” by Michele Angelo. But there is a completely different spatiality in the Last Judgment of this latter. The fresco represents a certain slope: the higher a certain point in the picture, the further away the point it depicts is from the viewer. Consequently, as the gaze rises, the eye would have to encounter smaller and smaller figures, due to perspective contraction. This, by the way, is clear from the fact that the lower figures block the upper ones. But, as for their size, the size of the figures increases as they rise in the fresco, that is, as they move away from the viewer. This is the property of that spiritual space: the further away something is in it, the more, and the closer, the less. This is the opposite perspective. Having seen it, and moreover, carried out so consistently, we begin to feel our complete incommensurability with the space of the fresco. We are not drawn into this space; Moreover, it pushes us towards itself, just as the mercury sea would push our body. Although visible, it is transcendental to us, who think according to Kant and Euclid. Living in the Baroque, Michele Angelo was, however, either in the past or in the future of the Middle Ages - a contemporary and not at all a contemporary of Leonardo. When deviations from the rules of perspective are encountered for the first time, the absence of perspective unity is seen as an accidental mistake of the artist, a certain disease of his work. But the slightest attention quickly reveals such an error in almost every work, and lack of perspective begins to be assessed no longer as a pathology, but as the physiology of fine art. The inevitable question here is: can it do without a transformation of perspective? After all, its task is to provide some spatial integrity, a special, self-contained world, not mechanical, but contained within the frame by internal forces. Meanwhile, clippings from natural space, photography - as a piece of space - by the very essence of the matter cannot help but lead beyond its boundaries, beyond its frame, because there is a part mechanically separated from the larger one. Consequently, the artist’s first requirement is to reorganize the space he allocates as material into a self-closed whole, i.e. to abolish perspective relationships, the main function of which is the Kantian unity of total experience, expressed in the need to move from each experience to others and in the impossibility of encountering a self-sufficient area. Whether experience actually has perspective is another question, and not to be decided here. But whether it exists or not, its purpose is definite, and this purpose essentially contradicts the work of painting, since this latter has not sold itself to other activities that need the “art of likenesses,” the illusions of the imaginary continuation of sensory experience, when it really does not exist. With this in mind, we will no longer be surprised to see two points of view and two horizons in Paolo Veronese’s “Feast of Simon”, at least two horizons in his “Victory of Lepante”, several points of view located along one horizon in Horatio Vernet’s painting “The Taking of Smala Abd-El-Kader”, numerous perspective discrepancies in the landscape of Schwanefeldt, as well as Rubens, etc. etc., and in many other pictures, and we will understand why smart perspective manuals even give advice on how to violate perspective unity so that it is not too noticeable (obviously, to the zealots of this? –), and in what cases it is necessary to resort to such “lawlessness” 89. In particular, it is recommended to place the vanishing points of the perpendiculars to the picture plane - along some curve, for example, along the wrapping of the normals to some ellipse 90. And artists, even those who are very far from the tasks set for themselves by the art of the truly existent, have long used such deviations from perspective unity. Such, for example, in the Louvre is the famous painting by Paolo Veronese (1528 - 1588) “Marriage at Cana”: according to experts, this painting has seven points of view and five horizons 91. Fr. Bossuet tried to give a “corrected” sketch of the architecture of this painting, i.e. strictly perspective image, and found that it preserves “essentially the same order and the same beauty” 92. Good idea of ​​first-class works of art that can be “fixed” so easily! And wouldn’t it be more correct to check and correct your aesthetic views using existing historical objects of art? If, in fact, strict subordination to the perspective of a non-perspective picture does not in itself violate its beauty, then does this not mean that both perspective and the absence of it, aesthetically at least, are not at all as important as the supporters of perspective think? I remember how Albrecht Dürer rushed from Florence to Bologna at the end of 1506 to explore the “secret art of perspective” there. But the secrets of perspective were jealously guarded, and, complaining about the lack of communication of the Bolognese people, Dürer was forced to leave, having learned very little, so that then at home he could independently discover the same techniques and write a treatise about them (which, however, did not prevent him from falling into perspective “errors”). Without entering into a discussion of his work in general, let us recall his most perfect work, about which F. Kugler 93, in his review (recognized by an expert on Dürer as the “most complete and successful description” 94 of this work), says that “an artist who completed such a work could part with the world, because his goal in art was achieved: this work undoubtedly puts him on a par with the greatest masters of whom history is justly proud art." Here, of course, we are referring to the diptych known as “The Four Apostles,” painted in 1526, i.e. already after the publication of the “Instructions for Measurements” and two years before his death (Dürer died in 1528). So: in this diptych, the heads of the two figures standing behind are larger than those of those standing in front, as a result of which the main plane of the Greek relief is preserved, although the figures are not arranged in this plane. As the art critic rightly notes, “obviously, we are dealing here with the so-called “reverse perspective”, according to which the rear objects are depicted larger than the front ones” 95. Of course, this reverse perspective of the “Apostles” is not a mistake, but the courage of a genius who, with his instinct, overturns the most rational theories, even his own, since they required completely conscious illusionism. Indeed, what could be more definite than his instructions in chiaroscuro, which begin: “If you want to paint pictures in such relief that vision itself could be deceived¼” 96. This is his illusionistic theory; but his work is not illusionistic. The contradiction (-a characteristic contradiction of people of a transitional time!-) between theory and creativity in Dürer was indicated by his general inclination towards the medieval style and the medieval structure of the foundations of his spirit, with a new system of thought. Be that as it may, even perspective theorists did not observe and did not consider it necessary to observe the “perspective unity of the image.” How, after this, can we talk about the naturalness of the perspective image of the world? What kind of naturalness is this that needs to be overheard, so that then, with the greatest efforts and with constantly tense consciousness, not to make mistakes against the learned rules? Don’t these rules rather resemble a conventional one, undertaken in the name of theoretical ideas, a conspiracy against the natural perception of the world, a fictitious picture of the world, which, according to the humanistic worldview, is required to be seen, but which, despite all the training, the human eye does not see at all, and the artist lets slip about his non-seeing, only as soon as he moves from geometric constructions to what he actually perceives. The extent to which a perspective drawing is not something immediately understandable, but, on the contrary, is a product of many complex artificial conditions, can be seen with particular conviction from the instruments of the same A. Dürer, beautifully depicted by him in woodcuts in his “Instructions for Measurements.” But, as good as the engravings themselves are, with their closed, self-compressed space, the meaning of the instructions they give is just as anti-artistic. The purpose of the devices is to enable the most inexperienced draftsman to reproduce any object, purely mechanically, i.e. without an act of visual synthesis, and in one case – without an eye at all. The sincere Dürer bluntly explains with his instruments that perspective is a matter of anything, but not vision. One of these devices is as follows: at the end of a table that looks like an elongated rectangle, a rectangular frame with glass is fixed perpendicular to its plane. On the opposite, narrow side of the table, parallel to the frame, a wooden block is fixed on the table, the middle of which is hollowed out and contains a long screw. With the help of this screw, a block perpendicular to the plane of the table is moved, and in this latter there moves, capable of being secured at different heights with the help of teeth, a wooden rod, which has a plate with a small hole at the upper end. It is clear that such a device provides, to a certain extent, a model of a perspective projection from a hole in the board onto the plane of a glass sheet, and, looking at an object through the indicated hole, you can draw its projection on the glass. In another device, the point of view is established motionlessly, also with the help of a special stand, and the projection plane is created by a grid of threads intersecting at right angles, and the design is applied to paper marked with squares, lying between the stand and the vertical grid, right there on the table. By measuring the coordinates of the projection points by cells, you can find the corresponding points on the graphed paper. Dürer's third device has nothing to do with vision at all: the center of projection here is carried out not by the eye, even if artificially brought to immobility, but by a certain point on the wall, at which point a ring with a long thread tied to it is fixed. This latter almost reaches the frame with glass, standing vertically on the table. The thread is stretched, and a sighting tube is applied to it, directing the “ray of sight” at a point on the object projected from the place where the thread is secured. Then it is not difficult to mark on the glass the corresponding projected projection point with a pen or brush. Consistently visualizing various points of the object, the draftsman will project it onto the glass, but not “from the point of view”, but from the “point of the wall”; vision has an auxiliary function. Finally, with the fourth drawing device, there is no need for vision at all, because touch is sufficient. It works like this: a large needle with a wide eye is driven into the wall of the room in which a photograph is being taken. A long, strong thread is threaded through the eye and a weight is hung from the thread there, near the wall. A table with a rectangular frame standing vertically on it is placed against the wall. A door is attached to one of the sides of this frame, which can open and close; a thread cross is stretched in the frame hole. The depicted object is placed on the table in front of the frame. The above thread is passed through the frame and a nail is tied to the end of it. This is the device. This device is used in the following way. The assistant is given a nail in his hand, pulling a long thread, with instructions to touch its head sequentially to all the most important points of the depicted object. Then the “artist” moves the intersecting threads of the frame until they coincide with the long thread and marks the point of their intersection with wax. After this, the assistant loosens the long thread, and the “artist”, closing the door of the frame, marks on the door the place where the threads intersect. By doing this repeatedly, you can mark the main points of the required projection on the designated door. Is there a need, after these devices, for even greater proof that the perspective image of the world is not at all a natural way of contemplation? It took more than five hundred years of social education to accustom the eye and hand to perspective; but neither the eye nor the hand of a child, or even an adult, without deliberate training, obeys this training and does not take into account the rules of perspective unity. People, even with special training, fall into gross mistakes as soon as they are left without an auxiliary geometric drawing and trust their vision, the conscience of their eyes. And finally, entire groups of artists consciously express their protest against submission to perspective. After this unsuccessful experience of half a thousand years of history, all that remains is to admit that the perspective picture of the world is not a fact of perception, but is only a requirement, in the name of some, perhaps very strong, but decidedly abstract considerations. And if we turn to psychophysiological data, then we must necessarily admit that artists not only have no basis, but also do not dare to depict the world in a perspective diagram, as long as their task is recognized as being faithful to perception. In what has just been stated, a number of historical explanations are compared. It’s time to sum up the results and speak more to the point, although the author postpones the development of relevant issues in connection with the analysis of space in images until another book. So, historians of painting, like theorists of fine arts, strive, or at least until recently, sought to assure those who listen to them that the perspective image of the world is the only correct one, as the only one corresponding to genuine perception, for natural perception is supposedly perspective. In accordance with this premise, deviation from perspective unity is then regarded as a betrayal of the truth of perception, i.e. a distortion of reality itself, either due to the artist’s graphic illiteracy, or for the sake of subordinating the drawing to conscious tasks - ornamental, decorative or, at best, compositional. One way or another, deviation from the norms of long-term unity turns out, according to the above assessment, to be irrealism. However, both the word and the concept of reality are too weighty for the adherents of one or another worldview to be indifferent whether it remains with them or goes to the enemy. A lot of thought must be given before making such a concession if it were unavoidable. And the same applies to the word natural. Who wouldn’t be flattered by considering their own to be real and natural, i.e. arising without deliberate intervention - from reality itself. Supporters of the Renaissance understanding of life seized and captured these cherished words, stealing them from Platonism and its medieval heirs. But this is no reason for us to leave the values ​​of language in the mouths of those who abuse them: reality and naturalness must be demonstrated in practice, and not made bare claims to them. Our task is to return these words to the grandchildren of their rightful owners. As explained earlier, in order to draw and write “naturally”, i.e. promising - it is necessary to learn this, both for entire peoples and cultures, and again, every time - for individual people. The child does not draw perspectively; An adult who takes up a pencil for the first time does not draw perspectively until he has been trained on certain templates. But even a student, even one who has studied a lot, easily falls into errors, or, more precisely, with the sincerity of spontaneity, he sometimes overcomes the prim decency of a promising unity. In particular, few people will depict a ball with an elliptical outline or a colonnade extending parallel to the plane of the picture - successively expanding pillars, although this is precisely what is required by a perspective projection 97 . Is it rare to hear great artists accused of promising mistakes? Such errors are always possible, especially in complex drawings of composition, and are actually avoided only when drawing is replaced by drawing, with auxiliary lines drawn. Then the draftsman depicts not what he sees outside of himself or in himself - imaginary, but, however, visual, and not abstractly conceived, images - but what is required by the calculation of geometric structures, in the opinion of such a draftsman, based on the too limited meaning of geometry - natural, and therefore the only permissible calculation. Can those techniques of representation be called natural, even those who for many years have rigorously trained their eye and their understanding of the world cannot master them without the help of geometric drawing crutches? And don’t perspective errors sometimes indicate not the artist’s weakness, but, on the contrary, his strength, the strength of his genuine perception, breaking the shackles of social suggestion. Teaching perspective is precisely training. Even when a beginner draws voluntarily tries to subordinate his drawing to its rules, this does not always mean that he understood the meaning, i.e. artistic and visual meaning of perspective requirements: turning to the times of their childhood, won’t many remember how the perspective of a drawing was recognized by them as an incomprehensible, although for some reason generally forced convention, as a usus tyrannus 98, to which they obey not at all because of its truth, but because everyone does the same. An incomprehensible, often absurd convention is what perspective is in a child’s understanding. “It seems like a trifle to you to look at a painting and grasp its perspective,” says Ernst Mach 99 . – And yet, thousands of years passed before humanity learned this trifle, and many of us only got to this point under the influence of education. “I remember well,” continues Mach, “that at the age of about three years, drawings in which perspective was observed seemed to me to be distorted images of objects. I couldn’t understand why the painter depicted the table so wide on one side and so narrow on the other. The actual table seemed to me at the far end as wide as at the nearest, since my eye carried out its calculations without my assistance. That the image of a table on a plane cannot be looked at as a plane covered with paints, that it means a table and must be represented as continuing into the depths - this was a trifle that I did not understand. I console myself with the fact that entire nations did not understand him.” This is the testimony of a positivist among positivists, who, it seems, cannot in any way be suspected of being partial to “mysticism.” Thus, the whole point is that the image of an object is by no means an object as an image, is not a copy of a thing, does not double a corner of the world, but points to the original as its symbol. Naturalism in the sense of external truthfulness, as an imitation of reality, as making doubles of things, as a ghost of the world, is not only unnecessary, according to Goethe’s words about the beloved dog and the image of the dog, but is simply impossible. Perspective truthfulness, if it exists, if it is truthfulness at all, is such not by external similarity, but by deviation from it, i.e. in its internal meaning, because it is symbolic. And what kind of “similarity,” for example, of a table and its perspective image can we talk about, since obviously parallel outlines are depicted as converging lines, right angles as acute and obtuse, segments and angles equal to each other as unequal values, and unequal values ​​as equal. An image is always a symbol, every image, both perspective and non-perspective, whatever it may be, and the images of the fine arts differ from each other not in that some are symbolic, while others are supposedly naturalistic, but in that, being equally not naturalistic, they are symbols of different aspects of a thing, different worldviews, different degrees of syntheticity. Different methods of representation differ from each other not in the same way as a thing differs from its image, but on a symbolic plane. Some are more, others less rude; some are more, others are less perfect; some are more, others less, universal. But the nature of everyone is symbolic. And the perspective of images is by no means a property of things, as is thought in vulgar naturalism, but only a device of symbolic expressiveness, one of the possible symbolic styles, the artistic value of which is subject to special discussion, but precisely as such, outside of terrible words about its truthfulness and claims to patented “realism”. Consequently, when discussing the question of perspective, direct or inverse, single-centered or multi-centered, it is imperative to start from the very beginning from the symbolic tasks of painting and other fine arts in order to understand what place perspective takes among other symbolic techniques, what exactly it means and what spiritual achievements it leads to. The task of perspective, along with other means of art, can only be a certain spiritual excitement, a push that awakens attention to reality itself. In other words, perspective, if it is worth anything, must be a language, a witness to reality. What is the relationship between the symbolic tasks of painting and the geometric prerequisites for its possibility? Painting and other fine arts are necessarily subject to geometry, since they deal with extended images and extended symbols. This means that the question here is not about an acceptable direct perspective ahead of time, through an easy conclusion: If the geometry is correct, then the perspective is undeniable. Therefore, the prospect is undeniable, - in which both premises excite a million thoughts, and in some delimitation of applicability and some explanation of its action, it is necessary to precisely establish the geometric premises of painting if we want the legality, internal meaning and limits of application of this or that technique and means of representation to be able to gain ground for installation. Postponing a deeper consideration until a special book, for now we will only note the following about the geometric premises of painting: the painter has at his disposal a certain cut-out plane - canvas, board, wall, paper, etc. – and paints, i.e. the ability to give different points of the designated surface different colors. This latter, in order of importance, may have no sensory meaning and must be understood abstractly; for example, in an engraving, the blackness of printing ink is not understood as a black color, but is only a sign of the carver’s energy, or, conversely, the lack thereof. But psychophysiologically, i.e. at the basis of aesthetic perception, it is color. For the sake of simplicity of reasoning, we can imagine that there is only one paint, black, or pencil. The task of the painter is to depict on the specified plane with the specified colors the reality perceived by him, or imagined as perceived. What, geometrically speaking, does it mean to depict some reality? This means bringing the points of perceived space into correspondence with the points of some other space, in this case a plane. But reality is at least three-dimensional - even if we forget about the fourth dimension, time, without which there is no art - the plane is only two-dimensional. Is such a correspondence possible? Is it possible to display a four-dimensional or, let’s say for simplicity, a three-dimensional image on a two-dimensional extent, is there enough points in the latter corresponding to the points of the first, or, mathematically speaking, can the power of a three-dimensional image and the same power of a two-dimensional one be comparable? – The answer that naturally comes to mind is “Of course not,” “Of course not, because in a three-dimensional image there is an infinite number of two-dimensional cuts, and, therefore, its power is infinitely greater than the power of each individual cut.” But a careful examination of the question posed in the theory of point sets shows that it is not as simple as it seems at first glance, and moreover, that the answer given above, apparently natural, cannot be considered correct. More specifically: the power of any three- and even multi-dimensional image is exactly the same as the power of any two- and even one-dimensional image. It is possible to depict four- or three-dimensional reality on a plane, and it is even possible not only on a plane, but also on any segment of a straight or curved line. Moreover, such a mapping can be established by countless sets, both arithmetic or analytical, and geometric correspondences. The type of the first can be Georg Cantor's technique, and the second - the Paano curve or the Hilbert curve 100. To explain the essence of these studies with their unexpected results as simply as possible, we will limit ourselves to the case of depicting a square with a side of one unit of length on a straight segment equal to the side of the above-mentioned square - i.e. the case of depicting the entire square on its own side; all other cases can be considered quite easily on the model of this one. So, Georg Cantor indicated an analytical technique with the help of which a correspondence is established between each point of the square and each point of its side: this means that if we are determined, by two coordinates x and y, to be located at any point of the square, then by some uniform technique we will find the coordinate z, which defines a certain point of the side of the square, the image of the above-mentioned point of the square itself; and vice versa, if an arbitrary point is indicated on a segment representing a square, then the point of the square itself represented by this point will also be found. Thus, not a single point of the square remains undisplayed, and not a single point of the image will be empty, not corresponding to anything: the square will be displayed on its side. Similarly, a cube, a hypercube and, in general, a square-shaped geometric formation (polyhedroid, multi-cell) of any and even an infinitely large number of dimensions can be depicted on the side of a square or on the square itself. And speaking generally: any continuous formation of any number of dimensions and with any limitation can be reflected on any other formation, also with any number of dimensions and also with any limitation; anything in geometry can be mapped onto anything. On the other hand, various geometric curves can be constructed in such a way that the curve passes through any point of the square given at random - if we return to our initial case - and thus a geometric correspondence between the points of the square and the points of the curve is established; It is not at all difficult to bring the points of this latter into correspondence with the points of the side of the square, as one-dimensional spaces, this way the points of the square will be displayed on its side. The Paeno curve and the Hilbert curve are compared with countless other curves of the same property ( - for example, before the trajectory of a billiard ball launched at an angle to the board incommensurate with a straight line; - non-closed epicycloids, when the radii of both circles are incommensurable; - Lissajous curves; - Rodoneans, etc., etc. – ) have one significant advantage: the correspondence between the points of a two-dimensional image and a one-dimensional one is carried out practically, so that the corresponding points are easily found, while with other curves the correspondence is established only in principle, but in fact it would be difficult to find which point corresponds to which. Without going into the technical details of the curves of Paeno, Hilbert and others, we only note that with its twists in the spirit of meanders, such a curve fills the entire surface of the square, and every point of the square, with one or another finite number of meanderings of this curve, systematically accumulated, i.e. according to a certain uniform technique - will certainly be affected by the twists of the curve. Similar processes apply to displaying, as explained above, anything on anything. So, continuous sets are all equally powerful. But, having the same power, they do not have the same “intelligible” or “ideal” numbers in the sense of G. Cantor, i.e. are not “similar” to each other. In other words, you cannot display them within each other without affecting their structure. When establishing correspondence, either the continuity of the depicted image is violated ( - this is when they want to maintain the mutual unambiguity of the depicted and the image - ), or - the mutual unambiguity of both ( - when the continuity of the depicted is preserved - ). Using Cantor's technique, the image is transferred point to point, so that any point of the image corresponds to only one point of the image, and vice versa, each point of the latter reflects only one point of the image. In this sense, Cantor's correspondence satisfies the usual idea of ​​an image. But in another property it is extremely far from the latter: it, like all other one-to-one correspondences, does not preserve the neighborhood relations between points, does not spare their order and connections, i.e. cannot be continuous. If we move very little inside the square, then the image of the path we travel can no longer be continuous itself, and the representing point jumps throughout the entire image area. The impossibility of giving a correspondence between the points of a square and its side; one-to-one and at the same time continuous, was proven by Thome, Netto, G. Cantor 101, but due to some objections from Luroth in 1878, E. Jurgens 102 was proven anew. This latter relies on the “intermediate meaning proposition.” “Let points P of a square and P' of a straight segment correspond to each other; then some line AB of the square containing point P must correspond to a whole connected segment on a straight line segment containing point P '; therefore, due to the assumed uniqueness of the correspondence of the remaining points of the square, in the neighborhood of the point P, they can no longer correspond to any point on the line in the vicinity of the point P', from which it clearly and obviously follows that the impossibility of a unique and continuous mapping between the points of the line and the square." This is Jurgens's proof. On the other hand, the correspondence of Paano, Hilbert, etc. cannot be, as proven by Lurot, Jurgens 103 and others, one-to-one, so that a point on a line is not always represented by a single point on a square, and in addition, this correspondence is not completely continuous. In other words, the image of a square on a line, or a volume on a surface, conveys all the points, but is not able to convey the shape of the image depicted as a whole, as an object internally defined in its structure: the content of space is conveyed, but not its organization. In order to depict a certain space with all its point content, it is necessary, figuratively speaking, either to crush it into an infinitely fine powder and, having thoroughly mixed it, scatter it over the pictorial plane, so that not a trace remains of its original organization, or to cut it into many layers, so that something of the form remains, but to arrange these layers with repetitions of the same elements of form, and on the other hand, with the mutual penetration of these elements through each other, the consequence of which is the embodiment of several form elements at the same points in the image. Behind the above mathematical considerations, it is not difficult to hear the “principles” of divisionism, complementarism, etc., found, independently of mathematics, by leftist movements of art, with the help of which leftist art destroyed the form and organization of space, sacrificing them to volume and materiality. As a result: it is possible to depict space on a plane, but not otherwise than by destroying the shape of what is depicted. Meanwhile, it is form, and only form, that is occupied by fine art. And, therefore, with this, the final verdict is pronounced on painting, on fine art in general, insofar as it claims to give a semblance of reality: naturalism is once and for all an impossibility. Then we immediately enter the path of symbolism and renounce all threefold extended point content, so to speak, from the filling of images of reality. We renounce, in one blow, the very spatial essence of things and focus, since we are talking about the point-by-point transfer of space, on their skin alone: ​​now by things we do not mean the things themselves, but only the surfaces delimiting areas of space. In the naturalistic order, this, of course, is a decisive betrayal of the slogan of truthfulness: we have replaced reality with its husk, which has only symbolic significance, only hinting at space, but in no way giving it directly, point to point. Is it now possible to depict such “things” or, more precisely, the skins of things on a plane? – The answer, affirmative or negative, will depend on what is meant by the word depict. It is possible to establish a one-to-one correspondence between the points of the image and the points of the image, so that the continuity of both will, generally speaking, be observed; but – only generally speaking, i.e. for “most points” - it would hardly be appropriate to go into detail about the exact meaning of which expression here. But with this correspondence, no matter how it is invented, some breaks and some violations of the one-to-one relationship are inevitable, at separate points or at points forming some continuous formations. In other words, the sequence and relationships of most points of the image in the image will be observed, but this still does not mean the invariance of all properties, even geometric ones, of the image when it is transferred, through correspondence, to the plane. True, both spaces, the one depicted and the one depicting, are two-dimensional, and in this respect are akin to each other; but their curvature is different, and besides, in the one depicted it is not constant, changing from point to point; it is impossible to superimpose one on top of the other, even by unbending one of them, and an attempt to do so will certainly lead to tears and folds of one of the surfaces. There is no way to apply an eggshell, or at least a fragment of it, to the plane of a marble table - for this it would be necessary to deshape it, crushing it to the smallest powder; for the same reason it is impossible to depict, in the exact sense of the word, an egg on paper or canvas. The correspondence of points on spaces of different curvature certainly implies the sacrifice of some properties of the image. Of course, here we are talking only about geometric properties, for the sake of conveying some in the image: the entire set of geometric characteristics of what is depicted cannot be present in the image, and, being similar in some ways to its original, its image inevitably diverges from it in many other respects. An image is always more unlike the original than similar. Even the simplest case, the image of a sphere on a plane, representing the geometric scheme of cartography, turns out to be extremely complex and has given rise to the invention of many dozens of various techniques, both projection, using rectilinear rays emanating from a certain point, and non-projection, carried out by more complex constructions or based on numerical calculations. And yet, each of these methods, intending to convey on the map some property of the territory being photographed, with its outlines of geographical objects, misses and distorts many others, no less important. Each technique is good in relation to a strictly defined goal and unsuitable as long as other tasks are set. In other words, a geographical map is an image and is not one - it does not replace the true image of the earth, at least in geometric abstraction, but only serves to indicate some of its characteristics. It depicts, because through it and by means of it we turn spiritually to the very thing depicted, and does not depict if it does not take us beyond itself, but lingers on itself, as on some false reality, as on the semblance of reality, and claims self-sufficient significance. Here we were talking about the simplest case. But the forms of reality are infinitely more diverse and complex than the sphere, and accordingly, the methods of depicting each of these forms can be infinitely more diverse. If we take into account the complexity and diversity of the organization of one or another spatial area in the real world, then the mind is decisively lost in the countless possibilities when conveying this area by image - it is lost in the abyss of its own freedom. Mathematically normalizing the methods of depicting the world is a task of insane arrogance. And when such a normalization, which also claims supposedly mathematical proof, moreover, uniqueness, exclusivity, is confined without further consideration to one, particular of the particular, cases of correspondence, then it seems that this is not done as a mockery. A perspective image of the world is nothing more than one of the methods of drawing. If someone wants to defend it in the interests of composition or any other purely aesthetic sense, then the conversation will be separate; although, by the way, it is precisely in this direction that we have not heard anything about attempts to defend the perspective. But there is nothing to refer to either geometry or psychophysiology in this defense; There is nothing to be found here other than a refutation of the perspective. So, the image, no matter what principle is used to establish the correspondence of the points of the depicted and the points of the image, inevitably only means, indicates, hints, suggests the representation of the original, but does not in any way give this image in some kind of copy or model. From reality to the picture, in the sense of similarity, there is no bridge: here is a gap, jumped over first by the creative mind of the artist, and then by the mind, co-creatively reproducing the picture within itself. This latter, we repeat, not only is not a doubling of reality in its entirety, but is not even capable of giving a geometric similarity to the skin of things: it is necessarily a symbol of a symbol, since the skin itself is only a symbol of a thing. From the picture the contemplator goes to the skin of the thing, and from the skin to the thing itself. But at the same time, painting, taken in principle, opens up a limitless field of possibilities. This breadth of scope depends on the freedom to establish the correspondence of points on the surface of things with points on the canvas on very different bases. Not a single principle of correspondence produces an image that is at least geometrically adequate to what is depicted; and consequently, the various principles, without any one having the sole possible advantage of being a principle of adequacy, are each applicable in their own way, with their own advantages and their own disadvantages. Depending on the inner needs of the soul, however, and not at all under forced pressure from the outside, a certain principle of correspondence is chosen by the era, or even by individual creativity, in accordance with the tasks of a given work - and then all its features, both positive and negative, automatically follow from it. The combination of these features layers the first formation of what we call style and manner in art. The choice of principles of correspondence reflects the primary character that determines the attitude of the creative artist to the world, and therefore the very depth of his worldview and sense of life. A perspective image of the world is one of the countless possible ways of establishing the indicated correspondence, and, moreover, the method is extremely narrow, extremely limited, constrained by many additional conditions that determine its possibility and the limits of its applicability. In order to understand that life orientation, from which the perspective of the fine arts necessarily follows, it is necessary to clearly express the premises of the perspectivist artist, silently implied with every movement of his pencil. This is the gist: Firstly: the belief that the space of the real world is Euclidean space, i.e. isotropic, homogeneous, infinite and boundless (in the sense of Riemannian distinction 104), zero curvature, three-dimensional, providing the opportunity through any point to draw a parallel to any straight line, and, moreover, only one single one. The perspectival artist is convinced that all the constructions of geometry, studied by him in childhood (and since then safely forgotten), are not only abstract schemes, and, moreover, one of many possible, but vitally realized constructions of the physical world, and, moreover, not only existing, but also observable. The artist of the type under discussion believes in the straightness of the rays coming in a beam from the eye to the contour of the object - an idea, by the way, derived from the most ancient view, according to which light does not come from the object to the eye, but from the eye to the object; he also believes in the immutability of the measuring rod when moving it in space from place to place and when turning it from direction to direction, etc. etc. In short, he believes in the structure of the world according to Euclid and in the perception of this world according to Kant. This is the first thing. Secondly: he, already contrary to logic and Euclid, but in the spirit of the Kantian worldview, with a transcendental subject reigning over the illusory world of subjectivity - even worse, it is forced - among all the points of infinite space, absolutely equal in Euclid, one exceptional, unique, special in value, so to speak, monarchical point, but the only definition of this point is that it is the residence of the artist himself, or, more precisely, his right eye, the optical center of his right eye. All places in space, with this understanding, are places of no quality and equally colorless, except for this one, absolutely dominant one - the artist’s right eye, blessed as the residence of the optical center. This place is declared to be the center of the world: it claims to reflect spatially the Kantian absolute epistemological significance of the artist. Truly, he looks at life “from a point of view,” but without further definition, because this point, elevated to an absolute, is absolutely no different from all other points in space, and its exaltation over others is not only not motivated, but in essence the entire worldview under consideration is not motivated. Thirdly: this king and legislator, “from his point of view,” of nature is thought of by the one-eyed man as a Cyclops, for the second eye, competing with the first, violates the uniqueness, and therefore the absoluteness of the point of view, and thereby exposes the deception of the perspective picture. In essence, the whole world does not even relate to the contemplating artist, but only to his right eye, and moreover, represented by its only point - the optical center. This center legislates the universe. Fourthly: the above-mentioned legislator is conceived of as forever and inextricably chained to his throne: if he leaves this absolutized place or even moves on it, then all the unity of perspective constructions is immediately destroyed and all prospects crumble. In other words, the looking eye is, in this understanding, not the organ of a living being living in the world and working, but the glass lentil of a camera obscura. Fifthly: the whole world is thought of as completely motionless and completely unchanging. There cannot and should not be any history, no growth, no measurements, no movements, no biography, no development of dramatic action, no play of emotion in the world to be depicted in perspective. Otherwise, the perspective unity of the picture again falls apart. This is a world dead, or engulfed in eternal sleep - invariably the same numb picture in its frozen real estate. Sixth: all psychophysiological processes of the act of vision are excluded. The eye looks motionless and dispassionate, like an optical lens. He himself does not move - he cannot, has no right to move, contrary to the basic condition of vision - activity, active reconstruction of reality in vision, as the activity of a living being. Moreover, this looking is not accompanied by memories, spiritual efforts, or recognition. This is an external-mechanical process, at least a physical-chemical one, but by no means what is called vision. The entire mental aspect of vision, and even the physiological one, is completely absent. And so, if the above six conditions are met, then and only then is the correspondence between the skin points of the world and the points of the image that the perspective picture wants to give possible. If at least one of the above six conditions is not fully met, then this type of correspondence becomes impossible, and the prospect will then inevitably be destroyed to a greater or lesser extent. The picture approaches prospects insofar and to the extent that the above conditions are met. And if they are not observed at least partially, if the legality of even local violation of them is allowed, then perspectivity ceases to be an unconditional requirement hanging on the artist, and becomes only an approximate method of conveying reality, one along with many others, and the degree of its application and the place of application in a given work is determined by the special tasks of a given work and its given place, but by no means for any work, as such, and in all respects. But let us assume temporarily: the conditions of perspectivity are fully satisfied, and therefore, exactly perspectival unity is realized in the work. The image of the world given under such conditions would be like a photograph, instantly capturing a given relationship between the light-sensitive plate of the lens and reality. Abstracting from the question of the properties of space itself and the psychophysical processes of vision, we can say that in relation to the actual contemplation of real life, this instantaneous snapshot is a differential, and, moreover, a differential of the highest, at least second order. In order to obtain a true picture of the world from it, it is necessary to integrate it several times, according to variable time, on which both changes in reality itself and the processes of contemplation depend, and according to other variables - variable apperceptive mass, etc. However, if all this were done, then, nevertheless, the resulting integral image would not coincide with the truly artistic one due to the discrepancy between the understanding of space implied in it and the space of the work of art, organized as a self-closed, integral unity. It is not difficult to recognize in such a perspectival artist the personification of a passive thought doomed to all sorts of passivity, instantly, as if furtively, stealthily peeping at the world through the hole of subjective facets, lifeless and motionless, unable to embrace movement and claiming the divine unconditionality of precisely its place and its moment of peeping. This is an observer who does not bring anything into the world from himself, cannot even synthesize his scattered impressions, who, without coming into living contact with the world and not living in it, is not aware of his own reality, although he imagines himself, in his proud solitude from the world, as the final authority and, based on this thieving experience, constructs all of reality, all of it, under the pretext of objectivity, squeezing it into the observed differential This is exactly how the worldview of Leonardo - Descartes - Kant arose on the basis of the Renaissance; the visual artistic equivalent of this worldview also arises - perspective. Artistic symbols should be promising here because this is such a way to unite all ideas about the world, in which the world is understood as a single, indissoluble and impenetrable network of Kant-Euclidean relations, having a focus in the I of the contemplator of the world, but in such a way that this I is itself inactive and mirror-like, a kind of imaginary focus of the world. In other words, perspective is a technique that necessarily follows from a worldview in which a certain subjectivity, itself devoid of reality, is recognized as the true basis of semi-real things-ideas. Perspectivalism is an expression of meonism and impersonalism. It is this school of thought that is usually called naturalism and humanism - what arose with the end of medieval realism and theocentrism. But, the question arises, to what extent is it possible to doubt the validity of the six prerequisites for prospects listed above, i.e. Is it really true that a perspective image, although one of many abstractly possible ways to depict the world, is in fact the only one based on the vital presence of the exposed conditions of its possibility? In other words, is the Renaissance, Kantian worldview viable? If it turned out that the conditions of perspective in actual experience are violated, then the vital significance of this understanding would be refuted. So, let's look at the conditions we set step by step. Firstly: on the question of the space of the world, it must be said that in the very concept of space there are three, far from identical, layers. This is precisely: abstract or geometric space, physical space and physiological space, and in this latter, in turn, visual space, tactile space, auditory space, olfactory space, gustatory space, space of general organic feeling, etc., are distinguished, with their further more subtle divisions. For each of the intended divisions of space, large and fractional, one can, abstractly speaking, think very differently. To imagine that a whole series of extremely complex questions can be answered by a simple reference to the geometric doctrine of the similarity of figures in three-dimensional Euclidean space would mean not even to touch upon the difficulties of the problem posed. First of all, it should be noted that on different points of the question raised about space, the answers, quite naturally, come out very different. Abstractly geometrically, Euclidean space is only a special case of various, very diverse spaces, with properties that are the most unexpected in the elementary teaching of geometry, but which explain a lot in direct relation to the world. Euclidian geometry is one of countless geometries, and we have no basis to say that physical space, the space of physical processes, is precisely Euclidean space. This is just a postulate, a requirement to think about the world in this way and to conform all other ideas to this requirement. The same requirement follows from their predetermined belief in physical and mathematical natural science of a certain type, i.e. with the principle of continuity, with absolute time, with absolutely rigid bodies, etc. But let us assume temporarily that in fact physical space satisfies Euclidean geometry. From here nothing follows, as if the direct observer of the world perceives him as such. No matter how much someone living in it wants to think about physical space, no matter how much he considers it necessary to build all his other ideas according to the main one - about the Euclidean composition of external space, subsuming physiological space under the Euclidean scheme, nevertheless physiological space is not included in it. Not to mention the olfactory, gustatory, thermal, auditory and tactile spaces, which have nothing in common with Euclidean space, so that they are not even subject to discussion in this sense, one cannot ignore the fact that even visual space, the least distant from Euclidean space, turns out to be deeply different from it when paying attention to it; and it is this that underlies painting and graphics, although in various cases it may be subordinate to other types of physiological space - and then the picture will be a visual transposition of non-visual perceptions. “If we now ask what, in fact, physiological space has in common with geometric space, we will find only very few common features,” says Mach. – Both spaces are a variety of three dimensions. Each point of geometric space A, B, C, D¼ corresponds to Á, B', C', D' ¼ of physiological space. If C lies between B and D then C' lies between B' and D'. One can also say this: the continuous movement of a point in geometric space corresponds to the continuous movement of a corresponding point in physiological space. That this continuity, accepted for convenience, does not necessarily have to be a real continuity for either one or the other, we have already proven elsewhere. Even if we accept that physiological space is innate to us, it reveals too little resemblance to geometric space for it to be possible to discern in it a sufficient basis for a developed a priori geometry (in the sense of Kant). Based on it, one can, at most, construct a topology” 105. – “If this dissimilarity between physiological space and geometric space does not strike the eye of people who are not specifically engaged in such research, if geometric space does not seem to them something monstrous, some kind of falsification of innate space, then this can be explained by a closer consideration of the conditions of human life and development” 106. – But “even with its greatest approach to Euclidean space, physiological space is still quite different from it. A naive person easily overcomes the difference between right and left, front and back, but he does not so easily overcome the differences between top and bottom, due to the resistance that geotropism has in this regard” 107 . In another work the same thinker sketches some of the features of this difference. “It has already been pointed out more than once how very different the system of our spatial sensations, physiological space, so to speak, is from geometric space, from Euclidean space. [¼] Geometric space is the same everywhere and in all directions; it is limitless and infinite (in the sense of Riemann). Visual space is limiting and finite, and even, as the contemplation of the flattened “vault of heaven” shows, has an unequal extension in all directions. The decrease in the size of bodies when moving away, as well as their increase when approaching, brings visual space closer to some ideas of metageometers than to Euclidean space. The difference between “up” and “down,” “front” and “back,” and—to be precise—“right” and “left” exists for both tangible and visual space. For geometric space there is no such difference” 108. – Physiological space is not homogeneous, not isotropic - this is reflected in different estimates of angular distances, different distances from the horizon, different estimates of subdivided and undivided lengths, different subtleties of perception in different places of the retina, etc. etc. 109 So, one can and should doubt that our world is in Euclidean space. But even if this doubt were eliminated, then nevertheless we probably do not see and do not perceive the Euclidean-Kantian world at all - we only talk about it according to the requirements of the theory as about the visible. Meanwhile, the artist’s job is to write not abstract treatises, but paintings - i.e. depict what he really sees. He sees, by the very structure of the visual organ, not the Kantian world at all and, therefore, he must depict something that is by no means subject to the laws of Euclidean geometry. Secondly: not a single person in his right mind considers his point of view to be the only one and recognizes every place, every point of view as a value that gives a special aspect of the world that does not exclude, but affirms other aspects. Some points of view are more meaningful and characteristic, others less so, each in its own respect, but there is no absolute point of view. Consequently, the artist tries to look at the object he depicts from different points of view, enriching his contemplation with new aspects of reality and recognizing them as more or less equally significant. Thirdly: having a second eye, i.e. having at least two different points of view at once, the artist has a constant correction of illusionism, for the second eye always shows that perspective is a deception, and, moreover, a failed deception. And besides, the artist sees more with two eyes than he could see with one, and, moreover, with each eye in a special way, so that in his mind the visual image is composed synthetically, like a binocular one, and in any case there is a mental synthesis, but cannot in any way be likened to a monocular, single-objective photograph on a retina. And it is not for the defenders of perspective and supporters of the Helmholtzian theory of vision to refer to the insignificance of the difference between the two pictures given by one and the other eye: this difference, according to their own theory, is just enough for the sensation of depth, and without it this latter would not be recognized; therefore, by noticing the difference between the images in the right and left eye, they destroy the reason why space is perceived as three-dimensional. However, this difference is not at all as small as it might seem at first glance. As an example, I made a calculation for the case when a ball 20 cm in diameter is viewed at a distance of half a meter, and the distance between the pupils is taken to be 6 cm. Then the addition of the equatorial arc of the ball, assuming the center of the ball at eye level, which is invisible to the right eye, but visible to the left, is equal to approximately one third of the arc of the same equator, visible to the right eye. Upon closer examination of the ball, the ratio of what the left eye sees in addition to what is seen by the right eye will be even more than one third. These are quantities that have to be dealt with under ordinary conditions of vision, for example, when examining a human face, and even with the smallest degrees of accuracy they cannot be assessed as quantities that could be neglected. In general, if the eye distance is denoted by s, the radius of the ball in question by r, and the distance of the center of that ball to the middle of the interocular distance by l, then the ratio x of the additional equatorial arc added to the same arc of the right eye by the left eye to the arc visible by the right eye is expressed quite accurately by the equality: Fourth: the artist, even sitting still, is constantly moving, moving his eyes, head, body, and his point of view is constantly changing. What should be called a visual artistic image is a mental synthesis of infinitely many visual perceptions from different points of view, and, moreover, each time double; this is the integral of such dual images. To think of it as a purely physical phenomenon means to understand nothing about the processes of vision and to confuse the quadrata rotunds 110 - the mechanical with the spiritual. The one who has not yet grasped the spiritual-synthetic nature of visual images as an axiom has not yet begun the theory of vision, much less artistic vision. On the other hand, fifthly, things change, move, turn to the viewer in different directions, grow and shrink, the world is life, and not icy stillness. And, therefore, here again the creative spirit of the artist must synthesize, forming integrals of particular aspects of reality, its instantaneous sections along the time coordinate. The artist depicts not a thing, but the life of a thing according to his impression of it. And therefore, generally speaking, it is a great prejudice to think that one must contemplate in the stillness and with the stillness of the thing being contemplated. After all, the point is what kind of perception of a thing needs to be depicted in this or that given case - from a crack in a prison wall or from a car. In itself, not a single way of relating to reality can be rejected in advance. Perception is determined by life’s relationship to reality, and if the artist wants to depict the perception that is obtained when he and things move mutually, then he must summarize the impressions during movement. Meanwhile, this is precisely the most common and most vital perception of reality - casually, and it is precisely this that gives the most profound knowledge of reality. The pictorial expression of such knowledge is the natural task of the artist. Is it possible? We know that movement is conveyed, even of a galloping horse, the play of feelings on the face, the developing action of events. Consequently, there is no reason to recognize that life perception of reality as inconceivable. The difference from the more usual case is that moving objects are often depicted with relatively little mobility of the artist, whereas here the artist’s movement is assumed to be significant, while reality itself can be almost motionless or even completely motionless. Then, in the images of houses with three and four facades, additional surfaces of the head and similar phenomena are obtained, known to us from ancient art. Such an image of reality will correspond to the motionless monumentality and ontological massiveness of the world, with the activity of the knowing spirit living and working in these strongholds of ontology. Children do not synthesize an instant image of a person, placing the eyes, nose, mouth, etc. separately, uncoordinated on a sheet of paper; The perspectival artist does not know how to synthesize a series of instant impressions and places them uncoordinated on different pages of his album. But both of these only testify to the inactivity of thought, which spreads into elementary impressions and is unable to embrace in a single act of contemplation, and therefore, in a single form corresponding to it, any complex perception, and cinematically decomposes it into moments and moments. However, there are cases when such a synthesis cannot be avoided, and then the most zealous perspectivist abandons his positions here. A spinning top, a wheel of a passing train or a sliding bicycle, a waterfall or a fountain, no naturalist-artist will stop at his image, but will convey the overall perception of the play of impressions merging and transforming into each other. However, instant photography or vision when illuminating these processes with an electric spark will show something completely different from what the artist depicted, and then it will be discovered that a single impression stops the process, gives its differential, while general perception integrates these differentials. But if everyone agrees with the legality of such integration, then what is the obstacle to applying something equivalent in other cases, when the speed of the process is somewhat slower? And finally, sixthly: defenders of perspective forget that artistic vision is a very complex mental process of fusion of mental elements, accompanied by mental overtones: on the image reconstructed in the spirit, memories and emotional responses to internal movements grow, and around the specks of dust the present mental content of the artist’s personality sensually crystallizes. This clot grows and has its own rhythm - the last thing that expresses the artist’s response to the reality he depicts. In order to see and examine an object, and not just look at it, it is necessary to successively transfer its image on the retina in separate sections to its sensitive spot. This means that the visual image is not at all given to consciousness as something simple, without labor and effort, but is built, composed of parts successively stitched together, each of them being perceived, more or less, from its own point of view. Further, an edge is synthetically added to an edge, by a special act of the psyche, and in general a visual image is consistently formed, but is not given ready-made. In perception, a visual image is not contemplated from one point of view, but in essence, vision is an image of a multi-centered perspective. By adding here additional surfaces attached to the image of the right eye - the left one, we must recognize the similarity of any visual image with the primordial chambers, and from now on the dispute can be about the measure and desired degree of this heterocentricity, but no longer about its fundamental assumption. Next begins either the demand for even greater mobility of the eye, for the sake of intensely condensed syntheticity, or the demand, if possible, to fix the eye - when decomposing vision is sought, and perspective stands in the way of this visual analysis. But a person, while alive, cannot completely fit into a perspective scheme, and the very act of vision with a motionless, fixed eye (- forget about the left eye -) is psychologically impossible. They will say: “But you can’t, after all, see three walls of a house at once!” – Even if this objection were correct, then we must continue it and be consistent. You cannot immediately see not only three, but also two walls of the house, or even one. Immediately - we see only an insignificant piece of the wall, and we don’t even see it right away, but immediately, literally, we don’t see anything. But not right away - we definitely get the image of a house with three or four walls, this is how we imagine a house. In a live performance there is a continuous flow, flow, change, struggle; it continuously plays, sparkles, pulsates, but never stops in internal contemplation as a dead scheme of a thing. And it is precisely this way, with internal beating, radiance, play, that the house lives in our imagination. The artist must and can depict his idea of ​​the house, and not at all transfer the house itself to the canvas. He captures this life of his idea, whether of a house or a human face, by taking from different parts of the idea the brightest, most expressive, and instead of a mental firework that lasts over time, he gives a motionless mosaic of its individual, most striking moments. When contemplating a picture, the viewer's eye, sequentially passing through these characteristic features, reproduces in the spirit a temporary-long-lasting image of a playing and pulsating representation, but now more intense and more cohesive than the image from the thing itself, because here the bright moments observed at different times are given in a pure form, already condensed, and do not require the expenditure of mental effort to melt slag out of them. As if on the hummed roller of a phonograph, the tip of the clearest vision slides along the lines and surfaces of the picture with their notches, and in every place of it the viewer is excited by corresponding vibrations. These vibrations are the purpose of a work of art. Here is an approximate mental path from the premises of naturalism to the promising features of icon painting. There may be a completely different understanding of art than in naturalism, emanating from the fundamental commandment of spiritual self-activity; For the author personally, the latter is closer. But on the basis of such an understanding, the question of perspective does not arise at all, and it remains as far from creative consciousness as other types and techniques of drawing. In the present consideration, it was necessary to overcome the limitations of naturalism from within and show how fata volentem ducunt, nolentem trahunt 111 - to liberation and spirituality. This passage was probably written in 1922, perhaps after the entire work was completed. It is followed by a text compiled on December 8–9, 1918. From the last stanza of F.I. Tyutchev’s poem “Madness”: “And he thinks he hears boiling jets, What does the current of underground water hear, And a noisy exodus from the earth!..” In Florensky's draft materials there are excerpts entitled “Dismemberment in Pushkin,” which explores “circular thinking.” We provide only footnotes: “A.A.Tomashevsky. Experience in analyzing autumn motifs in Pushkin’s works. - “Pushkiniana”. T. 2, Ptg., 1916, p. 196 – 198. "Pushkiniana". T. 2. Petrograd. 1916, from the preface by S.A. Vengerov, pp. XI, XII – XIII.” The term “circular thinking” goes back to Parmenides: being is spherical, thought and being are one; therefore, thought is spherical, round. “Truth has a solid heart in its perfect circle” (translated by S.N. Trubetskoy). “The truth is round my undaunted heart” (translated by M.A. Dynnik). “Wackenroder V.G. About art and artists. 1914, p. 65, German text, S. 58". – Note P.F. Prediction after the fact (lat.). The following texts are based on drafts dated March 7, April 15 (O.S.), 1918. Geometrically (lat.). In Florensky's draft materials there is a clipping of an article: Y. Engel. Great Russian folk song. - “Russian Gazette”, 1910, March 12, No. 58, which is a review of the collection by E.E. Lineva “Great Russian Song in Folk Harmonization.” Vol. 2. From this article, Florensky borrows discussions about the homophony of the New Age, the polyphony of the Middle Ages and the heterophony of an earlier era, which, according to the Viennese professor Adler, corresponds to Russian folk polyphony. In the original versions, this passage had the following wording: “This is theocratic anarchism, or Russian Orthodox autocracy, as opposed to theocratic jurisprudence...” In the original versions, this passage had the following wording: “But in philosophy we are talking about exactly what the soul of Holy Rus' is talking about in its song and in its faith in the Tsar as the God-given father “place in Christ.” This and the previous passage were edited by Florensky, clearly due to censorship requirements. A little earlier, he wrote: “The fact of the matter is that in the consciousness of the Russian people, autocracy is not a legal right, but is a fact revealed by God himself - the mercy of God, and not human convention, so that the autocracy of the Tsar is not a legal concept, but a doctrinal one, enters the realm of faith, and is not derived from extra-religious premises that have in mind public or state benefit” (Okolo Khomyakov. Sergiev Posad. 1916, p. 26). See also about this: Averintsev S.S. Poetics of early Byzantine literature. M., 1977, p. 117. That is a kind of systematizing treatises (such as, for example, the Summa Theologiae of Thomas Aquinas). In Florensky's draft materials there is an extract about the composition of odes by Pindar and Paul Claudel with the following link: “Maximilian Voloshin. Faces of creativity. Book one. St. Petersburg, 1914 (article “Paul Claudel”).” This quote - p. 118. See also: M. Voloshin. Faces of creativity. L., 1988, p. 72. M. Voloshin. Faces of creativity (St. Petersburg, 1914, p. 118. – L., 1988, p. 72). Novalis. Fragments. M., 1914, p. 16. According to P.F.’s draft notes: “Every method is a rhythm: if someone has mastered the rhythm of the world, this means that he has mastered the world. Every person has his own individual rhythm. Algebra is poetry. Rhythmic feeling is genius." See also the section “Results”, p. 341. In Florensky's drafts there is the following note: 1. D.M. Vellansky (1774 – 1847) 3. M.A. Maksimovich (1804 – 1873) 5. N.D. Kurlyandtsev (1802 – 1835) 6. V.A.Androsov (1803 – 1841) 7. A.I.Galich (1783 – 1848) 8. I.I. Davydov (1794 – 1866) (Probably a typo. It should be 1863.) 9. N.I. Nadezhdin (1804 – 1856) 10. V.F.Odoevsky (1803 – 1869) 11. D.V. Venevitinov (1805 – 1827) 12. I.V.Kireevsky (1806 – 1856) 14. M.P. Pogodin (1800 – 1875) 15. S.P.Shevyrev (1806 – 1864) 16. N.A. Polevoy (1796 – 1846) 17. K.A. Polevoy (1801 – 1867) 18. A.A.Grigoriev (1822 – 1864) 19. M.N. Kareev (1818 – 1887) 20. P.Ya.Chaadaev (1793 – 1836) (Probably a typo. It should be 1794 – 1856.) 21. F.I. Tyutchev (1803 – 1873) 22. V.G. Belinsky (1801 – 1848) 23. A.S. Khomyakov (1804 – 1360) 24. I.G. Mikhnevich (1809 – 1885) 25. prot. I.M.Skvortsov (1795 – 1863) 26. prot. F.F. Sidonsky († 1873) 27. prot. F.A. Golubinsky (1797 – 1854) 28. V.D. Kudryavtsev (1828 – 1891) (Probably a typo. It should be 1892.) 29. Vl. S. Soloviev (1853 – 1900) 30. book. S.N. Trubetskoy (1862 – 1905) About the Schellingian tradition in Russia, see: Kamensky Z.A. Russian philosophy of the early 19th century. and Schelling. M., 1980; Moscow circle of wise men. M., 1980. Sakharov V.I. On the existence of Schellingian ideas in Russian literature. – Context-77. M., 1978. Sokulin P.N. From the history of Russian idealism. Prince V.F. Odoevsky. Thinker. - Writer. M., 1913, vol. 1, parts I – II. Literary evenings and salons. First half of the 19th century M. - Leningrad, Academia, 1930. Kolyupanov N. Biography of A. I. Koshelev. St. Petersburg, 1889, vol. I – II. Akhutin A.V. Sophia and the Devil (Kant in the face of Russian religious metaphysics). – (“Questions of Philosophy”, No. 1, 1990, pp. 51 – 69. Fudel Joseph Ivanovich, archpriest (1864 - 1918) - was born into the family of a clerk in the economic department of the Vladimir Dragoon Regiment. After graduating from the Faculty of Law of Moscow University in 1899, he accepted the priesthood. Served in Bialystok from 1892 to 1907. - priest of the Moscow Butyrka prison, in 1907 he served in the church on Arbat. In 1908 – 1914 published the “Parish Bulletin”, published about 250 brochures and articles. He was close to the Optina and Zosimova hermitages, was friends with K.N. Leontyev and a circle of people who were members of the Society of Seekers of Christian Enlightenment (M.A. Novoselov, F.D. Samarin, P.B. Mansurov, V.A. Kozhevnikov, S.N. Bulgakov, priest Pavel Florensky). He died on October 2 (15), 1918. The son of Archpriest Joseph, Sergei Fudel, owned a number of works of a memoir nature: Father Pavel Florensky. Paris, 1972 (under the pseudonym F. Udelov); Memoirs (manuscript). See: Thomson (Lord Kelvin) William. The structure of matter. Popular lectures and speeches. St. Petersburg, 1895. When they are silent, they shout loudly (lat.). - Cicero. First speech against Catiline 8, 21; building meaning "eloquent silence". When we are silent, we shout (latin). Mk. 7, 15. Wed. Matt. 15, 11. “Pagan and Christian cross. Notes on its original existence in paganism and subsequent adaptation by Christianity. Translation based on the second edition, supplemented and expanded with new illustrations" (French). “Truly, how touching must be a religion that, following the example of paganism, resorts to such excitement of piety. Faith enters through the ears, not through the eyes” (French). Compare: “So faith comes by hearing, and hearing by the word of God” (Rom. 10:17). See: Aristotle. Metaphysics, 980a – 980c (Aristotle. Works in four volumes. T. 1. M., “Thought”, 1976, p. 65). Aristotle Metaphysics. Per. from Greek original and explanations by P. Pervov and V. Rozanov. Vol. 1. Books I – V. St. Petersburg, 1895. – Extracted from ZhMNP for 1891 – 1895, p. 16. “Nature does not strive to isolate and seclude, but, acting and living, it represents a striving from the whole to the parts” (German). Taken from the book. Emilius Medtner. Analysis of R. Steiner's views in connection with issues of criticism, symbolism and occultism. M., “Musaget”, 1914, p. 150. “Nature does not strive to isolate and seclude, but, acting and living, it represents a striving from the whole to the parts” (German). Taken from the book. Emilius Medtner. Analysis of R. Steiner's views in connection with issues of criticism, symbolism and occultism. M., “Musaget”, 1914, p. 150. This article was written in October 1919 as a report of the Commission for the Protection of Monuments of Art and Antiquity of the Trinity-Sergius Lavra, but due to various external circumstances it was heard not in the Commission, but in a meeting of the Byzantine section of M.I.H.I.M (Moscow Institute of Historical and Artistic Research and Museum Studies at the Russian Academy of the History of Material Culture of the People's Commissariat for Education) October 29, 1920. The debate on the report was very long; As far as I remember, the following took part in them: P.P.Muratov, B.A.Kuftin, P.I.Romanov, A.A.Sidorov, N.A.Afrikanov, N.M.Shkotov, M.I.Fabrikant and N.D.Lange. The liveliness of the discussions once again confirmed to me that the question of space is one of the fundamental ones in art and, I will say more, in the worldview in general. But this issue - space in the fine arts - is not considered in this article and is the subject of my forthcoming lectures on the analysis of perspective, given in 1921 and 1922 at the Moscow Higher Art Workshops, the so-called Khudemast, at the printing and graphic department; and this article provides only some concrete historical approach to the concept of organic thought about the world. The author has no intention of constructing a theory of reverse perspective, but only wants to note with sufficient energy the fact of organic thought - in one field. – In conclusion of this afterword, I would like to gratefully remember Alexandra Mikhailovna Butyagina, now deceased, who once wrote down the first part of this article under my dictation. Icon No. 23/328, XV – XVI centuries; its size is 32 cm ´ 25.5 cm, cleared in 1919. Contribution of Nikita Dmitrievich Velyaminov to the princess nun Olga Borisovna in 1625. (See “Inventory of the icons of the Trinity-Sergius Lavra”, Sergiev Posad, 1920, publication of the Commission for the Protection of the Lavra, pp. 89 – 90). Icon No. 58/160, 16th century, size 31.5 cm ´ 25.5 cm, contribution of Ivan Grigorievich Nagov in 1601 (See “Inventory of icons of the Trinity-Sergius Lavra”, Sergiev Posad, 1920, publication of the Commission for the Protection of the Lavra, pp. 102 – 103). There is, however, a view according to which the image of warriors or horses protruding from behind each other, when they move in one line perpendicular to the direction of movement, should be interpreted as the beginning of perspective. Of course, this is some kind of projection, such as military, axonometric or the like, a projection from an infinitely distant center, and it has meaning in itself, as such. To see in it the germ of something else, i.e. misunderstood perspective, this means losing sight of the fact that every image is a correspondence, and many images are projections, but not perspectives, and just as little are the rudiments of perspective as they are of reverse perspective and much more, and perspective, in turn, is the rudiment of reverse perspective, etc. It seems that researchers in such cases simply do not have the proper attention to the mathematical side of the matter, therefore all the techniques - countless techniques - of representation are divided into correct, perspective, and incorrect, unpromising. Meanwhile, lack of perspective does not mean incorrectness at all, but in relation to Egyptian images, special attention is required, because there tactile sensations prevailed over visual ones. What correspondence between the points of the depicted and the image do the Egyptians use is a difficult question and has not yet received a satisfactory solution. Moritz Cantor, Vorlesungen über Geschichte der Mathematik, Bd. 1, 3-te Auflage, Lpz., 1907, S. 108. Vitruvius Pollio, De architectura libri decem, VII, pret. 11. And the same is reported in the Life of Aeschylus (See: Aeschyli Tragoediae ed. H. Weil, Lipsiae Teubneri, 1884, p. 310. - Ed.). But, according to the instructions of Aristotle in Poetics, 4, the first to give rise to stenography was Sophocles (“Manual for measuring with compasses and rulers in lines, planes and whole bodies, compiled by Albrecht Dürer and printed for the benefit of all who love knowledge with appropriate drawings in 1525” (German). The treatise is partially published in the book: A. Dürer. Diaries. Tracts. T. II. – M., “Iskusstvo”, 1957, p. However, this news does not differ, for one must think that the more naturalistic Sophocles than Aeschylus began to strive for more illusory scenery. G. Emichen. Greek and Roman theater. Per. I.I. Semenova. Ed. E. Gerbel. M., 1894, pp. 160 – 161. Claudius Ptolomaeus, GeografikΎ Ψ f"ghsij. See M.Cantor, – id. – (Moritz Cantor, Vorlesungen über Geschichte der Mathematik, Bd. 1, 3-te Auflage, Lpz., 1907, S. 108.), Bd. 1, S. 423. N.A. Rynin. Descriptive geometry. Image methods. Petrograd, 1916. Numerous reproductions, from photographs and sketches, of a Greco-Roman architectural landscape, and an archaeological survey of this landscape, can be found in a detailed study: M. Rostovtsev. Hellenistic-Roman architectural landscape, St. Petersburg, 1908 (From volume VI of the “Notes of the Classical Department of the Imperial Russian Archaeological Society”, pp. 1 – 143). XII 143 pages and XX playlists. – But, unfortunately, M. Rostovtsev’s work does not at all concern the historical, artistic and art criticism side of the matter and, in particular, does not at all discuss the spatiality of the Hellenistic-Roman landscape. – Let us note by the way that in the landscapes reproduced by Rostovtsev, some of them use direct perspective, although not quite strictly, and some of them use other methods of projection, akin to perspective like axonometry - projection from an infinitely distant point. In any case, the general nature of the images is quite close to perspective. “However, the question of the Greco-Roman architectural landscape, its origin and history, its reality or fantastic nature has never been seriously raised in science. I personally have been interested in it for a long time, from the first days of my acquaintance with Pompeii. It was immediately clear to me that the limits of real fantasy in the Pompeian landscape are extremely limited and are entirely within the framework of an illusionistic rendering, partly of the motifs of the surrounding nature, partly of landscape and architectural originals that came from outside. Fantastic architecture in general is a term that is poorly understood by me: details of an ornamental nature can be inspired by fantasy, the combination of motifs can be arbitrary and unusual, but the motifs themselves and the general character will certainly be real, if not portrait-relief (we are not looking at the designs of an architect or photographs), then they are typically real. From this point of view, the study of the seemingly completely fantastic architectural motifs in the so-called architectural style of wall decoration has already yielded a number of unexpected and extremely important results - the connection between this “fantastic” architecture and the architecture of the Greco-Roman stage has been revealed or is being revealed - and further research, of course, will yield even more, especially now that one after another monuments of real Hellenistic architecture are being discovered in Asia. My long-term study of the architecture of Pompeian landscapes led me to the same results. Everything here, to an even greater extent than in the architectural decoration, turns out to be real, conveying the types of real Hellenistic architecture. There is even less room for pure imagination here than in the architecture of the Pompeian walls.” (Rostovtsev, id. (Numerous reproductions, from photographs and sketches, of a Greco-Roman architectural landscape, and an archaeological survey of this landscape, can be found in a detailed study: M. Rostovtsev. Hellenistic-Roman architectural landscape, St. Petersburg, 1908 (From volume VI of the “Notes of the Classical Department of the Imperial Russian Archaeological Society”, pp. 1 – 143). XII 143 pages and XX playlists. – But, unfortunately, M. Rostovtsev’s work does not at all concern the historical, artistic and art criticism side of the matter and, in particular, does not at all discuss the spatiality of the Hellenistic-Roman landscape. – Let us note by the way that in the landscapes reproduced by Rostovtsev, some of them use direct perspective, although not quite strictly, and some of them use other methods of projection, akin to perspective like axonometry - projection from an infinitely distant point. In any case, the general nature of the images is quite close to perspective. – Ed. ), pp. IX – X. Preface). The author connects this landscape with views of Roman villas, Egyptian landscapes, etc. Alexander Benois. History of painting, St. Petersburg, 1912, ed. "Rose hip". Part I, issue I, p. 41, etc. See (“However, the question of the Greco-Roman architectural landscape, its origin and history, its reality or fantasy has never been seriously posed in science until now. Personally, it has occupied me for a long time, from the first days of my acquaintance with Pompeii. It was immediately clear to me that the limits of real fantasy in the Pompeian landscape are extremely limited and are entirely kept within the framework of the illusionistic rendering, partly of the motives of the surrounding nature, partly of those that came from the outside of landscape and architectural originals. Fantastic architecture in general is a term that is poorly understood by me: details of an ornamental nature can be inspired by fantasy, the combination of motives can be arbitrary and unusual, but the motives themselves and the general character will certainly be real, if not portrait-relief (we are not looking at the designs of an architect or photographs), then they are typically real. From this point of view, the study of the seemingly completely fantastic architectural motifs in the so-called architectural style of wall decoration has already yielded a number of unexpected and extremely important results - the connection between this “fantastic” architecture and the architecture of the Greco-Roman stage has been revealed or is being revealed - and further research, of course, will yield even more, especially now that one after another monuments of real Hellenistic architecture are being discovered in Asia. My long-term study of the architecture of Pompeian landscapes led me to the same results. Everything here, to an even greater extent than in the architectural decoration, turns out to be real, conveying the types of real Hellenistic architecture. There is even less room for pure imagination here than in the architecture of the Pompeian walls.” (Rostovtsev, id. (Numerous reproductions, from photographs and sketches, of a Greco-Roman architectural landscape, and an archaeological survey of this landscape, can be found in a detailed study: M. Rostovtsev. Hellenistic-Roman architectural landscape, St. Petersburg, 1908 (From volume VI of the “Notes of the Classical Department of the Imperial Russian Archaeological Society”, pp. 1 – 143). XII 143 pages and XX playlists. – But, unfortunately, M. Rostovtsev’s work does not at all concern the historical, artistic and art criticism side of the matter and, in particular, does not at all discuss the spatiality of the Hellenistic-Roman landscape. – Let us note by the way that in the landscapes reproduced by Rostovtsev, some of them use direct perspective, although not quite strictly, and some of them use other methods of projection, akin to perspective like axonometry - projection from an infinitely distant point. In any case, the general character of the images is quite close to perspective.), pp. IX – X. Preface). The author connects this landscape with views of Roman villas, Egyptian landscapes, etc.). Benoit, id. (Alexander Benois. History of painting, St. Petersburg, 1912, “Rosehip” edition. Part I, issue I, p. 41, etc.), p. 45. D. M. Baldwin. Spiritual development of the child individual and the human race. Translation from the 3rd American edition. "Moscow Book Publishing House", M., 1911. For a new translation, see: Vasari Giorgio. Lives of the most famous painters, sculptors and architects T. I. M., 1956, p. 254. I. Ten. Travel to Italy. Translation by P.P. Pertsov. T. 2, M., 1916, pp. 87 – 88. For a new translation, see: Vasari Giorgio. Lives of the most famous painters, sculptors and architects T. I. M., 1956, p. 237. Benois, id (Alexander Benois. History of painting, St. Petersburg, 1912, ed. “Rosehip.” Part I, issue I, p. 41, etc.), I, p. 100. Wed. Alexey Mironov, Albrecht Durer, his life and artistic activity, M., 1901, p. 375 (Scientific Notes of the Imperial Moscow University. Department of Historical and Philological. Issue 31). Underweisung der Messung mit dem Zirkel und Richtscheit in Linien, Ebnen und gantzen Corporen durch Albrecht Dürer zusam-mengezogen und zu Nutz aller Kunstliebhabenden mit zugehörigen Figuren in Druck gebracht im Jahr MDXXV. Gedruckt zu Nürnberg im 1525 Jahr (“Manual for measuring with compass and ruler in lines, planes and whole bodies, compiled by Albrecht Dürer and printed for the benefit of all who love knowledge with appropriate drawings in 1525” (German). The treatise is partially printed in the book: A. Dürer. Diaries. Letters. Treatises. T. II. – M., “Iskusstvo”, 1957, pp. 43 – 93. – Ed. – In addition, there are no less than five later editions. Mironov, id (Cf. Alexey Mironov, Albrecht Durer, his life and artistic activity, M., 1901, p. 375 (Scientific Notes of the Imperial Moscow University. Department of Historical and Philological. Issue 31).), p. 380, note. 1. In Russian, some of these treatises are available in extracts in the book Allesch - Renaissance in Italy. Translation by E.Yu. Grigorovich. Ed. M. and S. Sabashnikov. M., 1916. Benoit, id. (Alexander Benois. History of painting, St. Petersburg, 1912, ed. “Rosehip.” Part I, issue I, p. 41, etc.), I, p. 381. Correct: “De prospectiva pingendi” – “On pictorial perspective” (Latin). See: Masters of Art about Art. T. 2. M., 1966, p. 73 – 80. Extensive literature on these issues can be found in N.A. Rynin’s book “Image Methods” (N.A. Rynin. Descriptive Geometry. Image Methods. Petrograd, 1916.), pp. 245 – 264. “And publicly preach water” (German). From Heine: “The Winter's Tale” (“They secretly drink wine and publicly preach water”). Guido Schreiber, Lechrbuch der Perspective mit einen Anfang über den Gebrauch geometrischer Grundrisse, 2-te Auflage, Lpz., 1874 (Guido Schreiber. A textbook of perspective with the beginnings of the use of geometric drawings (German). – Ed.). Edition reviewed by A.F.Viehweger and with a foreword by L.Nieper. N.A. Rynin, Descriptive geometry. Perspective, M., 1918, § 8, pp. 72 – 73. Rynin, id. (N.A. Rynin, Descriptive Geometry. Perspective, M., 1918, § 8, pp. 72 – 73.), § 8, pp. 70 – 82, 89. G. Schreiber, id. (Guido Schreiber, Lechrbuch der Perspective mit einen Anfang über den Gebrauch geometrischer Grundrisse, 2-te Auflage, Lpz., 1874 (Guido Schreiber. Textbook of perspective with the beginnings of the use of geometric drawings (German). Edition reviewed by A.F.Viehweger and with a preface by L.Nieper.). Rynin, id. (N.A. Rynin, Descriptive Geometry. Perspective, M., 1918, § 8, pp. 72 – 73.), § 8, p. 75, drawing 144. Friedrich Schilling. Über die Anwendungen der darstellenden Geometrie insbesondere über die Photogrammetrie, (Friedrich Schilling. On the application of the concepts of geometry, in particular about lightography (German). - Ed.) Lpz. und Berlin, 1904. S. 152 – 153. Rynin, id. (N.A. Rynin, Descriptive Geometry. Perspective, M., 1918, § 8, pp. 72 – 73.); Rynin, id. (N.A. Rynin. Descriptive geometry. Image methods. Petrograd, 1916.). Schilling, id. (Friedrich Schilling. Über die Anwendungen der darstellenden Geometrie insbesondere über die Photogrammetrie, (Friedrich Schilling. On the application of the concepts of geometry, in particular about lightography (German).) Lpz. und Berlin, 1904. S. 152 – 153.), S. 153, Anm. 1 Franz Kugler. Guide to the history of painting since the time of Constantine the Great, 3rd edition, M., 1874, p. 584. Mironov, – id. (Cf. Alexey Mironov, Albrecht Durer, his life and artistic activity, M., 1901, p. 375 (Scientific Notes of the Imperial Moscow University. Department of Historical and Philological. Issue 31).), p. 347. A.A. Sidorov, “The Four Apostles” by Albrecht Durer and related controversial issues. P., 1915 (separate reprint from “Notes of the Classical Department of the Imperial Russian Archaeological Society”), p. 15. One of Durer's manuscripts owned by the British Museum and representing the artist's rough sketches for his intended future printed works. Published by A. von Zahn in 1868, W.M. Conwey in 1889, republished by K. Lange und F. Fuchs. Dürers schriftliche Nachlass auf Grund der Original Handschriften und theilweise neu entdeckter alter Abschriften. (K. Lange and F. Fuchs. Dürer's handwritten heritage, based on original manuscripts and, in part, newly found ancient copies (German). - Ed.) Halle, 1893, S. 326. Rynin, Perspective (N.A. Rynin, Descriptive Geometry. Perspective, M., 1918, § 8, pp. 72 – 73), § 8, pp. 75 – 78. Rynin, Image methods (N.A. Rynin. Descriptive geometry. Image methods. Petrograd, 1916), § 15, pp. 113 – 117. Custom tyrant (lat.) Horatius. Ars poet. 71. (See: Quintus Horace Flaccus. Complete collected works. M.-L., Academia, 1936, p. 343: “Many who have fallen will be reborn again; others now Taking advantage of honor, they will fall, only the imperious custom demands, In whose will everything is - both the laws and the rules of speech! Compare: A.S. Pushkin. Evgeniy Onegin, 1, 25: “The custom of a despot among people.”) E.Mach. Why does a person need two eyes? "Popular-scientific essays." Translation by G.A. Kotlyar, “Education”, 1909, p. 64. An elementary explanation of the terms used here in the “doctrine of sets” – set, correspondence, power, equivalence, similarity or conformity, etc. – can be found in the article: P.A. Florensky. On the symbols of infinity, “New Path”, 1904, September, pp. 173 – 235. For establishing correspondences between the points of a square and its sides, see the proof of G. Cantor himself. Rynin (N.A. Rynin. Descriptive geometry. Image methods. Petrograd, 1916.). Riemann proposed to distinguish between the properties of boundlessness and infinity. The infinity of space does not imply its infinity. For example, spaces of constant positive curvature (Riemann spaces) are unlimited but finite. The sphere is an example of such a space (Bernhard Riemann. On the hypotheses underlying geometry (1866). See in the book: On the foundations of geometry. M., 1956, p. 322). Mach E. Cognition and delusion. Essays on the psychology of research, M., 1909, p. 346. (Mach E. Cognition and delusion. Essays on the psychology of research, M., 1909, p. 346), p. 349. (Mach E. Cognition and delusion. Essays on the psychology of research, M., 1909, p. 346.), p. 354. Mach E. Analysis of sensations, M., 1908, pp. 157 – 158. Square with round (lat.). Horatius. Ep. I, 1, 100. “Fate leads the obedient, attracts the obstinate” is the Latin translation of the famous saying of the Greek philosopher, Stoic Cleanthes, given by Seneca in his “Moral Letters to Lucilius,” letter CVII. See: Lucius Annaeus Seneca. Moral letters to Lucilius. M., “Science”, 1977, p. 270.