Multivariance of the image of the subject

The task of complete, protocol-accurate transmission of the geometry of subjective space on the plane of the picture, it turns out, has no solution. To illustrate this statement and discuss the difficulties that arise and how to overcome them by artists, let us consider an elementary, but very obvious example.

Let the artist set a goal (not artistic, but rather related to the technique of drawing) - to depict an ordinary stool or similar object so that all of its elements (the plane of the seat, legs and touch points of the floor) are depicted exactly as they are visible when living visual perception - in other words, in subjective space. In fig. 2 shows three options for such an image. Option A (scheme) seems to be the most natural for us, accustomed to such drawings. In it, all four legs have the same length and stand firmly on the floor: we can say that the stool is transferred in a parallel perspective. However, the seat plane is transmitted here with great distortion. When contemplating close and well-known objects from everyday experience, a person experiences the action of a mechanism known in the psychology of visual perception as a mechanism of constant form. Its essence boils down to the fact that the brain, as it were, brings the visible shape of an object closer to its true shape - in particular, the corners of the seat plane of a stool are straight in nature, they are visible to him more direct than in diagram A. As a result, a person sees this plane as shown in figures B and C - that is, significantly larger than in figure A. But if it is correct (in accordance with visual perception) to show the plane of the seat, that is, refer to schemes B and C, then there are difficulties in transmitting the image of the legs. Or, contrary to visual perception, you need to make the hind legs higher than the front ones (and then the legs will have different lengths, while they are visible the same), or, leaving the legs the same size, allow the rear legs to come off the floor and “fly up” (this is also a gross distortion of the natural visual perception). It is impossible to convey the stool on the flat image as it is visible (what is its geometry in subjective space): it would be necessary to show the plane of the seat, as in diagrams B and C, and the legs - of the same length and touching the floor. To do this, as is quite obvious, is impossible, although a person sees in his visual perception the stool just like that.

It should be noted that all three types of images were used in painting. The reasons that determined the choice are relatively clear. If we turn to the Novgorod icon, then the choice was most likely determined by the fact that, when using a high point of view, the surface of the throne turned out to be small relative to visual perception, but large enough to show the laying of shrines properly, and the icon painter chose not to distort the legs leaving their lengths equal. Dionysius and the author of the Indian miniature were in a completely different position: they strove for the most adequate transfer of the object (tables, sofa) with a rather low point of view.

If you raise the question of the best image of an isolated object, then another question immediately arises: what is more important - the legs or the horizontal plane they support? Of course, the planes are functionally important - the planes stand on them, people are on them, while the legs perform completely secondary functions. In an effort to best convey the main thing, both masters turned to those schemes, marked B and C, and which make it possible to accurately convey exactly the plane. In this case, the image errors passed to the legs.

The problem of the most reasonable (although inevitably distorted) transmission of the image of the legs made Dionysius and the masters of Indian miniature use various methods. Dionysius chose to show the hind legs elongated. And this is natural, because with him they were only 30% longer than the front ones, which can be called visually reasonable distortion. If the author of the Indian miniature embarked on the same path, he would have had to make the back legs (assuming their length from the horizontal plane of the sofa) to make more than two times longer than the front ones! This would be a visual absurdity, and, having lengthened them somewhat, he nevertheless preferred that they take off the floor and “fly up”.

Of course, the above considerations do not pretend to reconstruct the train of thought of the three artists in question. Each of them worked in a certain cultural environment where certain traditions already existed, including traditional methods of transmitting spatiality. The existence of such traditions leads to the uniformity of works of art for each individual culture (to the emergence of schools, styles). Consequently, the provisions formulated above in the form of hypothetical reflections of specific masters should actually be attributed to the totality of artists of a certain country and era. The existence of traditional methods of conveying spatiality is also important for viewers. Accustomed to a certain method, accustomed to it, the viewer better understands the artist, as if he does not notice geometric errors, perceiving them as the norm.

In fact, we have already begun the discussion of the second question formulated earlier: which of the three images above is more correct? Each of them is within the framework of its culture and taking into account compositional requirements. But objective criteria must exist that allow evaluating the different schemes applied by the three masters, based on the objective laws of visual perception (which did not change during the transition from era to era and were the same for people of different races and cultures). This issue will be discussed in more detail in the following chapters, but here we give only a number of preliminary considerations.

It turned out that with any image deviations from the geometry of natural visual perception are inevitable. If these deviations are called errors (without giving this word an evaluative character), then the three options considered differ from each other in what specific elements these inevitable errors shifted to. For the Novgorod master, they are shifted to the image of the plane, for Dionysius - for the ratio of the lengths of the front and rear legs, for the Indian artist - for the fact that the legs touched the floor. There are no objective criteria that would allow one of these options to be preferred over another. Therefore, not only from the position of correspondence of a certain type of image to a certain culture, but also from the point of view of absolutely objective laws of visual perception of the external world by a person, these images should be considered equivalent. By virtue of what has been said, it would be a mistake to speak of masters of the 16th and 17th centuries, whose works were taken as examples, in a condescending tone, as artists of something “not knowing how”.

Comparing the three considered works of art, it can now be argued that they are all equally correct and at the same time equally wrong, if the criterion of correctness is taken to be the ability to accurately transmit a person’s natural visual perception. Now it becomes clear that none of them can be accepted as a standard, a comparison with which would allow us to evaluate other images. However, the standard is necessary, because only it allows you to find and evaluate image errors, and this standard certainly exists: it is the human visual perception itself - what was called the “brain picture” above. When discussing the initial schemes (Fig. 2), which made it possible to evaluate the three works used to illustrate, the argument was used everywhere, saying something like this: “a person sees that all legs are of the same height” or “in fact, a person sees that this plane is significantly large sizes ”, etc. Therefore, the identification of image errors occurs by comparing it with live visual perception. But the description of natural, lively, direct visual perception was actually introduced declaratively. Nowhere has it been rigorously mathematically proven that it has just that, and not any other character, therefore, an effective appeal to such a standard requires the ability to objectively describe the visual perception of a person (of course, not verbally, but with the help of precise geometric concepts). It is necessary to find out how much one object compared to another is not in kind, but in the visual perception of a person, how much his apparent size changes as he moves away from the beholder, etc. Moreover, all estimates should not be qualitative, but accurate, quantitative. It is worth recalling that, as was shown in the previous chapter, it is impossible to answer such questions in the system of the Renaissance perspective.