Let us remind ourselves of what reverse perspective is. Unlike normal or optical perspective, where the vanishing point is in the imaginary depth of the painting, in reverse perspective this vanishing point is in front of the painting, on the viewer's side, in such a way that the space appears to expand with the growing distance from the viewer. In normal perspective, parallel lines converge to a single point and objects become smaller with distance. In reverse perspective, it is the opposite that happens.
We are offered very scholarly and highly spiritual explanations of the use of reverse perspective. Leonid Uspensky said that it helped maintain the two-dimensionality of the icon. It also brought the viewer into a special world, which opens out in the depths of the icon.
Right from the start, two questions arise: does not the use of perspective, per se, deny a priori the concept of two-dimensionality? And does not optical perspective, too, "open out” a special world in the depth of a picture?
We should underscore that what Father Pavel Florensky appreciates in the icon the fact that the viewer forgets he is in front of a certain surface that acts as a "wall", in order to enter into a spiritual space. Uspensky instead emphasizes the two-dimensionality of the icon, setting store by the fact that the viewer never forgets that what he sees are not the events themselves, but only their images, flat, and of another kind. And he attributes, with the very greatest of naivety, the possibility of such naive forgetfulness to the viewers of realistic paintings (with their "optical" perspective). The flagrant contradiction between these two explanations on the perception of space in the icon, coming from two classical writers in the area, is very significant.
Before attaching any spiritual values to a system of "reverse" perspective, let us first consider whether the laws of reverse perspective really govern the world of the icon. For this reason we prefer to avoid from now on phrases such as “bringing the viewer into”, “englobing the viewer”, “getting people to forget”, “opening up another world”, and other equally subjective and relative notions, for example, when reverse perspective is described as "evangelical perspective" or “foolishness for Christ” that overturn the laws of this world.
We refuse to follow those writers who see a parallel in this purported “overturning of the laws of nature” with the phenomenon of foolishness-for-Christ. Foolishness-for-Christ is a form of "spiritual prowess" (one of the hardest and rarest) and not a form of theological knowledge. The tiny number (about twenty) of fools for Christ canonized by the Church over a period of two millennia indicates that the Church has always been very cautious towards this form of "prowess" and has not canonized everyone who took the liberty to reverse the laws of this world. In any event, authentic fools for Christ carried on their shoulders all the risks and all the burden of this reversal. They endured incredible physical privations, endured the ridicule and blows of those around them, and yet their assistance to their neighbors remained "reasonable" and in line with the ideas of "normal" people on what is good and useful. By contrast, the image of the artist who by his creativity overturns the laws of this world, while retaining a pleasantly comfortable status, is far removed not only from the painting of icons, but from Christian culture itself. We refuse to make an amalgam of icon painting and foolishness for Christ. Rather our task and duty are to apply the artistic language of the icon with logic and simplicity.
Let us return to perspective. It is not for nothing that we have placed the word "reverse" in quotation marks. First, the concept of reverse perspective assumes, indeed asserts, that artists have always been acquainted with normal perspective, which one day they consciously rejected in favor of reverse perspective. But this is very far from the truth. Uspensky was visibly irritated by the very historic fact that the laws of normal perspective were only discovered and systematized in the fifteenth century, by Brunelleschi. He found it necessary defend himself here with a long footnote in the re-edition of his book, in which he states that that iconographers — a catch-all term that encompasses fifteen centuries and three continents — knew normal perspective, proposing as "proof" the fact that in Rublev's Trinity the house, and the notch in the table, are, according to him, presented in "normal" perspective. In fact, the famous notch that ought to make all iconographers across the world independent of Brunelleschi is presented to us in axonometric perspective, while the house is clearly in reverse perspective: it is enough to measure the front and rear walls. But even if, in these two cases, the objects reduced in size with distance, it would be quite incorrect to argue on that basis that iconographers knew normal perspective and consciously rejected it.
To be able to make such statements, we would need to have data on artists who used normal perspective, systematically and consciously, with a view to presenting space in a realistic, or illusionist manner, from the sixth, eighth, tenth or twelfth centuries, as they did in Europe from the fifteenth century onwards.
In other words we would need information on a "school of the normal perspective" working for centuries in parallel with that of reverse perspective. Without this, to attribute a knowledge of optical perspective to medieval artists based on the notches in a small table is, to say the least, highly risky. Thus, "reverse" perspective is not reversed from a known and consciously rejected optical perspective. In fact, it was not reversed at all: it was the only perspective which was in use until Brunelleschi's discoveries. Nor was it ever a system of perspective specific to icon painting, because applied in painting of any subject for any purpose.
But maybe it can be called "reverse" not in a relative sense, but in an absolute sense? Maybe this characterizes the opposition of these two systems, until the fifteenth century artists — really all artists! — used the first system, and then, all of a sudden, began to use another. Then, a few centuries on, this new system was referred to as "normal" and the old system as "reverse". This presentation of the facts seems particularly bizarre. Even more bizarre given the fact that in the languages of many Christian people the notion of "normal" is connoted to "correct", "true", "honest", and what is called "reverse" has a connotation of "lying" "apostasy", "perversion" and the like. This linguistic opposition is already very significant. Could it be that the world of the icon was based on laws contrary to what is normal and proper, so that everything that is "normal" becomes profane, superficial, lacking in spirituality?
So let us check by looking more closely: in iconography does the construction of separate objects, their positioning in space and the treatment of space itself follow laws contrary to those of normal perspective? The example discussed above, of the table of the Trinity, already shows us that even the drawing of separate objects did not submit to this need for placing the vanishing point in front of the icon. This combination of reverse perspective with axonometric perspective, with frontal projection and even normal perspective, within a single building or a single throne, is visible at every step when we look at icons. Doors, windows, niches and arcades are almost never presented in reverse perspective, because such a system would remove any impression of thickness from the walls and of depth from the notches. We would find ourselves as if in front of walls of cardboard. Indeed the only objects completely built according to the system of a frontal vanishing point are simple parallelepipeds, like small footstools. But if we then take a ruler and try to determine this vanishing point, we discover that each pair of lines has its own vanishing point, even for a single parallelepiped, and that these vanishing points are not aligned either horizontally or vertically: there is no common horizon. If we extend with a ruler all the sagittal lines on any icon, we will not get logical system that can carry the viewer somewhere, but a chaotic dispersion. Thus, even for free-standing objects, reverse perspective is essentially unstable and unpredictable. In addition, it is always combined with frontal and axonometric projections, and even optical perspective.
In addition to these four forms of projection of space on a flat surface, there is also a fifth, called the bird's eye view (or isometric perspective). It is used, for example, to draw round tables loaded with dishes (dishes being normally drawn in front projection). Cities or monasteries as a whole are presented in bird's eye perspective and individual buildings in frontal projection. We also find seas and rivers with all their shores in isometric perspective as on a map, while their shores are presented as a rule in axonometric projection.
It is a known fact that the treatment of separated objects is only one aspect of spatial projection. Let us check now: is the perspective of the icons really reversed in relation to optical perspective as regards the placing of objects in space? In optical perspective, as we know, objects become smaller the further they are distant from the viewer. This obliging particularity allows us to make holiday snaps containing both happy tourists and the pyramid of Cheops or the Eiffel Tower. But how many times do we not observe the irritating fact that in wanting to fit in the whole pyramid, our boyfriend or girlfriend has been reduced to the size of an ant? Or, on the contrary, that the section of metal next to our friend is hardly recognizable as the Eiffel Tower? It becomes an effort to find the point of view that enables us to frame both friends and monument in the desired ratio. But if our camera were to record the world in reverse perspective, the result would be hopeless. At any distance we would see at most a block of stone or a metal beam behind our friends. And the further they distance themselves from the monument, the larger the block of stone or metal beam becomes!
In which icon do we see such a perspective? None, and never. Even in the works of diehards who view reverse perspective as a fundamental to iconography. It is quite the opposite we see: all the architectural constructions are shown at normal height, from the foundations to the cross on the roof, even if there are people next to them, and even inside them. In fact these buildings are represented even smaller than in optical perspective: what we have in fact resembles more an enhanced optical perspective. We could use for this the term "sliding perspective": space is divided into a series of planes, in each of which the objects and characters are spatial agreement between themselves, and in turn these planes are join together like theatre scenery.
We have shown the use, or rather the non-use of reverse perspective in the drawing of separate objects, and in the relative dimensions of more or less distant from the viewer. But the world of the icon is not limited to landscapes or buildings. The essential part of the icon is the image of man. In realistic painting, human beings are also drawn subject to the law of optical perspective, but, in the icon, should they be subject to the law of reverse perspective? It is in vain that in the faces that we find on icons we go looking for the conscious rejection of normal optics. To convey facial expressions, the direction of the gaze, and the beating life behind them is a very complicated task, calling for extreme precision, where all recipes are useless if the artist has no sense of form. The masters of the classical period of iconography but also the weakest contemporary amateur iconographer, when painting the face of a saint, the Mother of God or the Lord Himself make an effort, sometimes unconsciously and despite all the theories, to show this face like a real face, and not a frozen mask. It would be madness, indeed blasphemy to say that in a face painted in three-quarter profile, we need to enlarge and to turn towards the spectator the two ears, and to render the more distant eye, cheek, wing of the nose and corner of the mouth larger than the nearer eye, cheek, etc., or in Florensky’s words, “to turn forward and flatten against the surface of the icon the crown, the temples and the ears” so as not to betray the fundamental principle of reverse perspective which forms, we are told, the basis for the iconographic vision of the world.
But the example of human faces depicted in three-quarter profile tells us that it never entered the mind of a medieval painter to treat a human head according to the rules of reverse perspective! There is no one medieval image in three-quarter profile in which the more distant half of the face is larger than the closer one. All Florensky’s charming reverse perspective constructions are based on front-facing images. In other words, what we have here is the obvious manipulation and adjustment of facts to fit a preconceived idea.
Even if elements of reverse perspective may be present in the icon - just like those of normal perspective (bird's eye, sliding perspective and axonometric or frontal projection) - not one of these systems can claim to dominate the vision of the divine world in iconography and as a basis for the theological flights of fancy we have too often known.
Better yet, not one of these systems is specific to iconography. We already find elements of each of these systems — elements, but never complete systems — in the wall paintings and reliefs of ancient Egypt, in the drawings of Eskimos and the primitive peoples of Africa, in the decoration of Greek vases, in Romanesque frescoes, in the Italian art of the Early Renaissance, in the Flemish Primitives, in the naïve painters and in several modernist movements of the twentieth century. This list could be extended indefinitely (on this question there also exists the fundamental work of Russian Academician B.V. Rauchenbach  devoted to the psychology of visual perception and different space systems in the fine arts. This work, despite long being considered a classic, remains totally ignored by "theologians of the icon").
In fact, only Academic painting followed a coherent and scientifically-based treatment of space, that is to say optical perspective, which was consciously applied for the drawing of objects, for their spatial relationships and for space itself, and for drawing human faces and human. But if we start, with a ruler and a compass, carefully to check the regularity of the spatial constructions in the paintings of Academic painters, we shall see right away that they continually violate the laws of optical perspective. A notable exception is the group of works of the High Renaissance when artists, intoxicated with Brunelleschi's discoveries, multiplied arches and columns at will. With the exception therefore of the works of these pioneers, realistic painting does not blindly follow geometric patterns, but freely adapts them to its own purposes. The presence in the same painting of various vanishing points, multiple skylines, more or less discrete spatial planes, changes in the proportion of objects, all this is everyday in realistic painting. An uninformed viewer does not even realize how little the characters and objects that seem so alive fit into the network of geometric perspective. To give but one example: if one checks with a ruler the perspective of Karl Bryullov's Last Day of Pompeii, one will realize that the Pompeian woman who has fallen to the ground in the foreground of the picture is at least five meters tall. However the fact is that she is painted in a highly realistic manner, and the spatial relationship with the other figures hide the “inaccuracy” of the spatial construction.
This tells us that, in realistic art too, artists for one reason or another have avoided geometric precision. We do not know why they did not structure space and objects with a ruler, even though the secrets of the horizon line and vanishing point have been known for five hundred years. "The eye is more accurate than a compass" is an aphorism that drawing masters have always repeated to their students, putting them on guard against the temptation to measure too mechanically the world around them. The eye of the artist is always more accurate than a compass, not just after Brunelleschi's discovery, but also before! For artists of the Academic school, the important thing is not to have a single vanishing point, but to succeed in giving the painting the general impression of the reality of space. The same applies to the iconographers of the classical period: what was important to them was not to turn space inside out, according to theories invented a thousand years later, but, for them also, to express in icons the reality of space. What can be more important for an artist whose object is Truth itself?
But was Truth changed with the discovery of optical perspective? Not at all! What did change was the vision of the artist and the viewer. Specifically, it is their ideas on the possibilities of representing three-dimensional space in two dimensions that have changed (and become richer). The fact is that any two-dimensional representation is a fiction. The whole question is to know which features of the objects this fiction conserves, and which it leaves to one side.
Ask a child aged three or four to draw a table. He will certainly start by drawing in the upper part, from a bird's eye view. Because this projection ideally expresses the fact that the table has four square corners and two pairs of parallel edges. But once it comes to drawing the legs of the table, our young artist is faced with the classic problem of bringing together different projections in the same drawing. He knows that there are two feet on each side. If he draws them all, they will be eight. If he leaves only four, two sides of the table will have no feet. If he turns the feet to make them belong simultaneously to both sides of the table, he will lose the right angle. The child may choose any one of these three variants, while being aware of the imperfection of each. But he tolerates this imperfection in order to make correct all other characteristics of the table. And if an adult condescendingly shows him how properly to draw a table by presenting him with a front projection of one of these sides, the child will probably find this variant even more bizarre. Why does is there only a line instead of the rectangular table-top? Why are the four legs on the same side? The adult will be obliged to prove the benefits of this projection, for example by explaining that in this way all the feet touch the floor. Maybe he will draw a line to represent the floor, with a chair and a little man in the same frontal projection. And the child will accept, but not without sadness at abandoning its 'primitive' vision and the possibilities it offered, for example, for putting a lot of dishes on the table-top.
But if the adult offers him, instead of front projection, do draw the table in optical perspective, the child will refuse outright. There we will find no resemblance at all with Nature. And not without reason. The table-top will have no angles. The feet will be of different lengths, with only two touching the floor. One of these shorter feet, if not both, will not start from a corner of the table. In other words, your drawing, deprived of all basic characteristics of the object, will be deemed worthless. Neither the drawing nor your explanations will be understood. And you will have to wait a few years for your secret of perspective to be finally appreciated. A 10 year-old artist will certainly love your picture drawn in perspective, imitating you and leave aside its miserable front projection.
What has happened? Has he already forgotten that a table has four right-angled corners, that its feet are all the same length and have to touch the floor? Not at all. His idea of the shape of the table has not changed. What has changed is his vision. Now he is able to appreciate the possibility of showing the table at once from above, from the front and from the side. Now he has learned to "see" the fourth leg by analogy, even if it is hidden, and to "read" it as starting from a corner of the table and not from its side. He learned to see the surface of the floor by analogy with the surface of the table and place on it in its thought the four feet. And with no regrets he will leave behind the projection he previously saw as the correct one.
This brings us to the end of this long digression, which has served to show in detail the relative nature of any two-dimensional image. We see that, while keeping the same idea of the shape of the object, one can have very different priorities in selecting the one or the other projection, that is to say, ideas about what is more significant and what is not.
What was, and remains important in iconography is to define correctly and unambiguously every object making up the composition, making sure it is identifiable by the most general, traditional items characterizing it, even if this means moving away from a realistic, "photographic" representation. A bed should be "read" as a bed. A footstool as a footstool. A throne with two cushions, the color of which symbolizes the sky and the earth, must be presented as the throne with its two attributes. If the event takes place in a church or in another building, we need to show this building, seen from outside, from the foundations to the roof. If the church has five domes, we must show them all. If it is a city or monastery, we must close the enclosure around the group of buildings. A river must have two edges. A sea must be lined with coasts all round and, in the same composition, you have to find room for an island with a town or a monastery, for a boat and for the figures themselves. And that is not yet all. In several icon subjects, these natural objects exist side-by-side with the symbolic images of the invisible world: for example, the glory (mandorla) surrounding Christ and populated with angels and cherubim. Or these imaginary heavens with the figures of Christ, the Mother of God, a blessing hand, or hell with Satan, devils and the damned. Or other spheres outside and beyond any earthly space.
From the beginning, iconographers have set to the task with a miraculous and blessed audacity, with surefootedness and with the conviction that one can perfectly describe and blend such different objects in the same composition. In selecting the projection for any one object they chose precisely the one that which best puts across the required characteristics of the object. This principle applies to the human face and figure. The "flattening against the surface of the icon of the crown, the temples and the ears” that so struck Florensky, that is, the combination of different projections in a the drawing of a single head, derive from the special features of medieval thought described by us elsewhere: the artist tries to show all the important parts of an object, even if they are not visible or barely visible from the chosen "base point of view." It is clear that such an approach is in constant conflict with the directly visible picture of the world, and artists are constantly forced to make a choice in favor of the known or in favor of the visible. Reconciling themselves to the distortion or loss of some features of the subject, artists nevertheless did not place them out of sight. It is for this reason that mankind as a whole has evolved from flat projections to axonometric construction, and to optical perspective or reverse perspective.
Of all of these spatial systems, optical perspective is without any doubt the more correct from the optical point of view. And for this reason it is the only one suitable for the coherent and realistic organization of any space presented by the artist. Despite all this, optical perspective is far from ideal for images where it is important to define and "name" each object precisely and unambiguously, and where one needs to present in the same composition the whole man from head to foot, and the whole church, the whole mountain, the whole sea, and on top of that heaven or hell. For achieving this, optical perspective is far from suitable, for all its technical accuracy.
It is on account of its "accuracy" that the discovery of optical perspective created a remarkable revolution in painting, and that all artists of the Christian church so keenly appropriated it. Let us note well an important fact: that there is no document criticizing this new perspective at the time of its dissemination, whether in the Catholic countries or in Russia. Even the famous controversy surrounding the iconographic tradition, towards the end of the seventeenth century, does not mention the issue of optical perspective. One can find in the documents of that time the fiercest anathemas against the new way of painting icons, but these concern themselves exclusively with the appearance of the Lord and the saints. The polemicists are silent about the spatial constructions, as if they did not even realize that under their very eyes, the "evangelical" perspective was turning into "profane" perspective. This change, viewed much later by some as fundamentally destructive to iconography, aroused no criticism, no opposition at the time. Even the terms "optical perspective" and "reverse perspective", or their equivalents, are nowhere to be found in the treatises of the opponents of the "Italian novelties". Nor do we find them in the conventional treatises on iconographic art. The Greek and Russian books of descriptions (podlinniki) abound in data on the appearance and clothing of the saints, the colors of their clothes, and descriptions of the compositions and their meanings. In the technical treatises, we find the recipes of the trade, the different working stages, the peculiarities of pigments and varnishes, even at times the teachings of the Church about icons and tips for beginners. But we find no teaching concerning the construction of objects in space and organization of space itself, and certainly no rules opposed to the "normal" rules, what we would call today optical perspective. Knowing the spirit of sobriety these treaties, it is impossible to imagine finding in them a teaching that prescribes us to draw things, not as they appear in nature, but "in reverse".
In the Erminia of Dionysius of Fourna, a monument of the Athonite iconographic tradition, copied and widely distributed in Russia, it is recommended to all those who wish to become iconographers simply to practice first of all drawing "without relying on canonical diagrams". It is only "once accustomed", that is to say, only after acquiring a certain experience, that a monk could ask a blessing to paint icons and start drawing from the canonical models. Translated into modern language, this means that the painter must first have a classical training in the Fine Arts, and only then begin to practice iconography. Can we imagine, seriously and honestly, that this prior experience would have been required, only to reject or "reverse" it immediately thereafter?
But perhaps the authors of classic treatises did not see the need to pass on a theory of perspective, because the vision of nature as expressed in their icons for them was quite normal? And is it because now our vision has changed, that a particular theory - specifically "reverse" - has become necessary in order to paint "correctly"?
Since we are talking about the present day, I may be permitted an empirical argument. Throughout our apprenticeship in a reputed iconography workshop of northern Russia, in all these years of daily contact with Mother N., we never heard the comment "Here your perspective is not reverse enough" or "Why didn't you use reverse perspective here? ". Nor did we ever hear such remarks from her husband Father N., a specialist with a degree in History of Art, even though prior to beginning in their workshop we had already accumulated experience fifteen years of study and work in the Academic tradition. Logically we should have been constantly making mistakes, breaking the rules of reverse perspective before coming to use it properly. Observing the progress of the other apprentices who had, or had not, had a classical training in the Fine Arts, we always saw the same thing: no one ever explained to anyone the rules of "reverse" perspective and no one was ever scolded for transgressing its rules.
The apprentice artist drawing from life his first volumes (cubes, pyramids, spheres) constantly hears "your perspective is not correct", "you've poorly chosen the horizon", "the vanishing point is not there", or "the top of the book is not shortened more than the bottom", and he corrects, always erasing until his paper tears with thinness in order to put in their right place all the lines and all the angles. And all this despite the fact that he draws as he "sees", according to the laws of optics and normal perspective, laws known for centuries.
Why do we spend so much time learning these laws, while "reverse" perspective — which historically is dead, but is special, spiritual — is something we succeed at right away, without explanation, patterns, or education? We do not even mention it. We are not even warning that one cannot take two steps in iconography without it.
This "reverse" perspective is a really amazing phenomenon, with quite curious features.
- In iconography we find only episodically constructions with a really reversed perspective and never as a coherent system.
- Before Brunelleschi, "reverse" perspective was not understood as a system, we have no record of its theoretical foundation, nor any data on any special education in it.
- After Brunelleschi, nobody, not even a defender of the Byzantine tradition, rose up to condemn optical perspective in favor of "reverse" perspective, touting it as a system that confers a specific spiritual value. The theory of optical perspective spread quietly and naturally in the West and the East.
- The theory of "reverse" perspective, as something specific to the icon, and even as "evangelical", appeared only when iconography in the "Byzantine" style was on the point of disappearing, after several centuries of decadence.
- Today iconographers can receive an excellent training, which hardly makes any reference to this theory. No method of teaching reverse perspective exists, even in schools that recognize its existence and tout the benefits.
It is time to come to the conclusions of this chapter.
- What is commonly referred to as "reverse" perspective in fact englobes an informal ensemble of projections and volumetric systems that was, and remains, in use among icon painters, but also by other artists, Christian or not, professional or amateur, adult or children, consciously or unconsciously.
- The use of this set of projections has no other intention than to represent three-dimensional space — and in a certain sense, to create an illusion of three-dimensionality — on a two-dimensional surface.
- Optical perspective, systematized since the fifteenth century, has the same goal, and for that reason was naturally preferred to this informal ensemble of projections. Or more accurately, this "conglomerate" was not replaced suddenly and abruptly but gradually came closer, slowly and gropingly over the centuries, to normal optical perspective, correcting spatial constructions and making them more and most similar to reality.
- In art, whether sacred or profane, perspective is a means and not an end. What is more natural than for the artist to transgress the pure and simple geometric scheme? For five centuries already, professional artists have been learning optical perspective in order better to transgress it in a creative effort to achieve the best possible expression in their paintings.
- In voluntarily transgressing optical perspective, that is to say, using other projections instead of the latter, the artist of our time may apply these transgressions very discreetly. But he may also, on the contract, openly use frontal projection, bird's eye view or "sliding" perspective, and of course also reverse perspective. But this freedom in the treatment of space is not necessarily an "evangelical" freedom. The spatial experiments of the contemporary artist expressed in profane art can also be dictated by other reasons: vanity, passion, pride.
Reverse perspective cannot be considered as a coherent system of the treatment of space.
Reverse perspective is not the monopoly of iconography.
Reverse perspective has no particular mystical value, and certainly not for constructing theological castles in the air!
The basis for the iconographic vision (and transfiguration) of the world is to be found in the Orthodox idea of Goodness, Beauty and Truth, and not in any "reverse" geometry.
With these proposals, which we have supported with evidence, we have no intention to debase iconography or to deprive it its spirituality. But we oppose and resist any attempt to snatch iconography out of the history of art in Christian countries and isolate it by surrounding it with a "mystical cloud". Classical iconography is the iconography of the time when it was not yet separated from the art and culture of Christian countries, but was rather its spearhead. In those days the iconographic worldview, and its use of perspective, did not appear "reversed" to anyone. The people of God saw in icon painting not incomprehensible esotericism, but simple Beauty, something quite understandable to them, and a Beauty that attracted them.
The legends that have been spread about reverse perspective are the product of esoteric research in an area where artists enlightened by the Spirit are constantly in search of beauty. These legends are not only false and stupid, but they also risk diverting people's understanding from the true specificity of iconography, in theory and in practice.
 L. Uspensky, op. cit. p. 472.
 Pavel Florensky, op. cit. p. 41
 L. Uspensky, op. cit. pp. 469-472
 Deacon Andrej Kouraiev, op. cit. p. 292, also L. Uspensky, op. cit. p. 172 and 469
 L. Uspensky, V. Lossky, The meaning of icons, New York, 1989. p. 41
 Pavel Florensky, op. cit. p. 178
 B. V. Rauchenbach, Пространственные построения в живописи, Moscou, 1980
 Dionisi Phournoagraphiot, op. cit. p. 22