Paintings with two images in one. Dual images

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Even the most hardened skeptics believe what their senses tell them, but the senses are easily deceived.

Optical illusion - impression of visible object or a phenomenon that does not correspond to reality, i.e. optical illusion. Translated from Latin, the word “illusion” means “error, delusion.” This suggests that illusions have long been interpreted as some kind of malfunction in the visual system. Many researchers have been studying the causes of their occurrence.

Some visual illusions have long been scientific explanation, others still remain a mystery.

website continues to collect the coolest optical illusions. Be careful! Some illusions can cause tearing, headaches and disorientation in space.

Endless chocolate

If you cut a chocolate bar 5 by 5 and rearrange all the pieces in the order shown, then out of nowhere an extra piece of chocolate will appear. You can do the same with a regular chocolate bar and make sure that it doesn’t computer graphics, but a real-life mystery.

Illusion of bars

Take a look at these bars. Depending on which end you are looking at, the two pieces of wood will either be next to each other, or one of them will be lying on top of the other.

Cube and two identical cups

Optical illusion created by Chris Westall. There is a cup on the table, next to which there is a cube with a small cup. However, upon closer examination, we can see that in fact the cube is drawn, and the cups are exactly the same size. A similar effect is noticeable only at a certain angle.

Illusion "Cafe Wall"

Take a close look at the image. At first glance, all the lines seem to be curved, but in fact they are parallel. The illusion was discovered by R. Gregory at the Wall Cafe in Bristol. This is where its name came from.

Illusion of the Leaning Tower of Pisa

Above you see two pictures of the Leaning Tower of Pisa. At first glance, the tower on the right appears to lean more than the tower on the left, but in fact both of these pictures are the same. The reason is that the visual system views the two images as part of a single scene. Therefore, it seems to us that both photographs are not symmetrical.

Disappearing circles

This illusion is called "Vanishing Circles". It consists of 12 lilac pink spots arranged in a circle with a black cross in the middle. Each spot disappears in a circle for about 0.1 seconds, and if you focus on the central cross, you can get the following effect:
1) at first it will seem that there is a green spot running around
2) then the purple spots will start to disappear

Information about the outside world comes to a person primarily through the visual senses, which include the eyes, optic nerves and the visual center in the brain. For brevity, in the following chapters we will refer to all these organs with one word EYE (In cases where the word eye is written in lower case, the eye is meant as an optical instrument.)

As noted in the previous chapter, the visual process begins with a projected image of the surrounding world, passed through the lens, onto the retina. The information obtained from the retina is extremely complex. For our purposes, we will distinguish two categories of information: image information, based on pictographic elements that reproduce represented objects, and spatial information, composed of stereographic elements, which reproduces spatial relationships between objects.

Basically, these two types of information appear together, as a simple example illustrates. In the picture with two fishermen on the bank of the canal (Fig. 1), pictographic elements show us two human figures and a canal (or ditch). Stereographic elements tell us the following: one figure is larger than the other and partially obscures it, the figures are partly light and partly dark, two shadows fall behind the dark parts of the figures, the banks of the canal converge towards each other.

The EYE transforms both types of information, pictographic and stereographic, into a meaningful interpretation. In our normal environment, this does not cause any difficulties, and the entire process takes a split second. But sometimes deviations occur and this process reaches a dead end, which allows us to find out the peculiarities of the functioning of the EYE.

Perhaps you have also experienced a phenomenon similar to what happened to me. One day, lying on the bed and looking at the objects on the bedside table, I noticed something completely foreign: a small frame with a metallic glare only on its left side. I knew for sure that I did not have such an object, and there was no way it could be there. I did not move and continued to carefully examine the unusual object, hoping to understand the mystery. Suddenly I recognized my lighter on the left, standing upright, and on the right, a glass partially obscured by a postcard. There was much to this more meaning, and subsequently it was difficult for me to reproduce the original impression and frame in my brain.

There are other cases when the EYE offers us two (and in some cases even more) equally correct interpretations for the same configuration of objects. Note that such interpretations do not come from our mental conclusions about what we see, but directly from the EYE. We are aware of ambiguity as we first see one interpretation, then another, and a few seconds later the first again, and so on. Here we are dealing with a process that we can neither control nor stop, since it occurs automatically. In these cases we are talking about dual retinal images, and about dual figures, if the switching occurs due to some graphic figure. By its nature, duality can be pictographic or stereographic. Because the this book associated mainly with stereographic (spatial) duality, I would not like to deprive the reader of some of the particularly interesting ambiguities that arise in the pictographic field. Therefore, to clarify the difference between these two areas, I have added a few examples below.

Pictographic duality

Almost all of us have encountered the phenomenon of pictographic duality, especially in the form of “Freudian” paintings. A good example is the image "My wife and my mother-in-law" (Fig. 2), published in 1915 by cartoonist W.E. Hill, which presents a well-balanced selection of interpretations to the exclusion of extraneous details. See who you see first - this can be a difficult task even for psychologists. A few years later, Jack Botwinick created a companion image to the previous one - “My husband and my father-in-law” (Fig. 3). A bunch of similar paintings was created in subsequent years, among which the “Eskimo-Indian” (Fig. 4) and “Duck-Rabbit” (Fig. 5) are also widely known.

There are also dual figures, whose interpretation depends on the angle from which we look at them. A remarkable example is the series of cartoons by Gustave Verbeek, which were published in the New York Herald from 1903 to 1905.

Each picture must first be viewed in its normal position, and then turned upside down. Figure 6 shows the little girl Lady Lovekins caught by the giant Rock bird. The upside-down painting shows a large fish capsizing an old man's canoe, Muffaroo, with its tail. Also very famous are "double images", in which the purpose and function of objects and backgrounds change with each other. At first glance, in Sandro del Prete's painting "The Window Opposite" (Fig. 7), you will probably see something more than just a vase of flowers, a glass and a pair of stockings hanging to dry.

Stereographic duality

The images formed on our retina are two-dimensional. An important task EYE is the reconstruction of three-dimensional reality from these two-dimensional images. When we look with both eyes, the two images on the retinas of our eyes contain slight differences. An independent EYE program uses these differences to calculate (with high degree accuracy for objects located at a distance of no more than 50 meters) spatial relationships between objects and our body, giving us a direct understanding of the surrounding space. But even an image from the retina of one eye is enough to create a believable three-dimensional picture of the world around us. The transformation of three-dimensionality into two-dimensionality forms the basis of duality, as illustrated simple example. Segment AB in Fig. 8a can be interpreted by the EYE in several ways. For example, it can be considered simply as a segment drawn with ink on paper, or as a straight line segment in space, but we cannot say which of points A and B is closer to us. As soon as we provide the EYE with a little more information, for example, by placing the segment AB inside the drawing of the cube, the positions of points A and B will be determined in space. In Fig. In Figure 8b, point A looks closer to point B, and also point B looks lower than point A. In Figure 8c, these relationships are reversed. In Fig. 8d the same segment AB is located horizontally in the direction from the trees to foreground to the horizon.

A cube in which all twelve edges are depicted by identical straight lines (Fig. 9) is called a Necker cube in honor of the professor of mineralogy L.A. Necker from Germany, who was the first to study stereographic duality from a scientific point of view.

Necker cube

On May 24, 1832, Professor Necker wrote a letter to Sir David Brewster, with whom he had recently visited in London. He devoted the second half of the letter to what has since become known as the Necker cube. This letter is important not only because it is the first time a scientist described the phenomenon of optical inversion, but also because this phenomenon surprised the author himself. It also sheds light on typical scientific practice at a time when it was not yet common to use test samples of participants or to create special scientific instruments. Instead, the researcher recorded his own observations and tried, often in very general terms, to guess what was hidden behind the appearance in the hope of reaching a conclusion within the limits of his knowledge.

"The object to which I would like to draw your attention relates to the phenomenon of perception in the field of optics, a phenomenon that I have observed many times while studying images crystal lattices. I'm talking about a sudden, unintentional change in the apparent position of a crystal or other three-dimensional body depicted on a two-dimensional surface. What I mean is easier to explain with the help of the illustrations attached to the letter. The segment AX is depicted in such a way that point A is closer to the viewer, and point X is further away. Thus ABCD represents the frontal plane and triangle XDC is on the posterior plane. If you look at the figure a little longer, you will see that the apparent orientation of the figure sometimes changes so that point X appears to be the closest point, and point A appears to be the farthest point, and the ABCD plane moves back behind the XDC plane, giving the entire figure a completely different orientation.

For a long time it was unclear to me how to explain this random and unintentional change that I regularly encounter in various forms in books on crystallography. The only thing I could detect was an unusual sensation in the eyes at the moment of change. It determined for me that there was an optical effect, and not just a mental one (as it seemed to me at first). Having analyzed the phenomenon, it seems to me that it is associated with focusing the eye. For example, when the focal point on the retina (i.e., the macula) points to an angle with its vertex at point A, that angle has a sharper focus than the other angles. This naturally suggests that the corner is closer, that is, in the foreground, while the other corners being less clearly visible create the feeling that they are further away.

The "switch" occurs when the focal point moves to point X. After discovering this solution, I was able to find three different proofs of its correctness. First, I can see the object in the desired orientation of my choice by moving the focus between points A and X.

Secondly, by concentrating on point A and seeing the figure in the correct position with point A in the foreground, without moving either the eyes or the figure, slowly moving the concave lens between the eyes and the figure from bottom to top, the switch occurs the moment the figure becomes visible through the lens. Thus, an orientation is assumed in which point X is visible even further away. This only happened because point X replaced point A at the focus point without any spatial adjustment to the latter.

In conclusion, when I look at a figure through a hole made in a piece of cardboard with a needle, so that either point A or point X is not visible, the orientation of the figure is determined by the angle that is visible in currently, since this angle is always the closest. IN in this case the figure cannot be seen in any other way and no switching occurs.

What I said about angles is also true for individual sides. Planes located on the line of sight (or opposite macular spot retina) always appear to lie in the foreground. It became clear to me that this small, and at first glance mysterious phenomenon, is based on the law of eye focusing.

No doubt you can draw your own conclusions from the observations I have described here, which I, in my ignorance, cannot predict. You can use these observations as you wish."

Many people who have conducted the same experiment as Necker have come to the conclusion that switching occurs spontaneously and independently of the point of focus. However, Necker's original assumption that this phenomenon occurs when retinal images are processed in the brain is correct. In the Necker cube, the EYE cannot determine which of the points (or planes) is closer or further. Figure 10 shows the Necker cube as solid lines ABCD-A"B"C"D" between two other illustrations of two possible interpretations. When we look at a Necker cube, we first see the figure in the center, then the figure on the right, and a little later the figure on the left, etc. Switching from "A is closer than A" to "A is further than A"" is called perceptual inversion: the central cube inverts the representation of the cube on the right to the cube on the left and vice versa.

However, alternating relative distances ABCD and A"B"C"D" is not the most strong impression. Most noticeable is the fact that both cubes have completely different orientations, as Necker pointed out in his letter. Thus, the segments AD and AD" look intersecting, although in the figure they are depicted in parallel. The phenomenon of perceptual inversion can be described more precisely: all lines have the same orientation on the retinal image, but as soon as the interpretation of the figure changes to inverse, all lines (in space) look as if they have changed orientation. As we can see, such changes in orientation can be very unexpected. The perceptual inversion in the top pair of dice in Figure 11 is caused by the choice of the angle at which the dice are drawn. These figures are based on two photographs of one and the same configuration of dice made at different angles. The left dice is located next to the wall. The wall and floor are marked with squares that match the size of the face of the dice. The bottom drawing forms the different orientations of the dice more clearly.

The angle at which the cube is depicted also determines the angle at which its sides will be visible after perceptual inversion. The left pair of cubes in Figure 12 has a very small angle, and the right pair has a maximum angle (which corresponds to the top image of Figure 11)

Convexity and concavity

Although the Necker cube offers two different geometric shapes, the terms “convexity” and “concavity” cannot be applied to them. We can always see both the inside and outside of the cube. The situation changes when we remove from the figure three planes that meet near the center of the cube, as shown above in the figure with dice. Now we have a figure which again suggests two opposite spatial bodies, but now these bodies are of a different nature: one is convex, as we see the cube from the outside, and the other is concave, in which we perceive three planes inside the cube. Most people recognize a convex shape immediately, but have some difficulty perceiving a concave shape until secondary supporting lines are added to the drawing.

In the lithograph “Concave and Convex” (Fig. 14) M.K. Escher demonstrates how, through specific geometric techniques, the viewer is forced to interpret the left side of the drawing as convex, and right side like a concave In particular, the transition between the two parts of the picture is interesting. At first glance, the building looks symmetrical. The left side is more or less mirror image on the right side, and the transition in the center of the picture is not rough, but smooth and natural. But when we look past the center, we find ourselves plunging into something worse than a bottomless abyss: everything is literally inside out. The top side becomes the bottom, the front becomes the back. Only figures of people, lizards and flower pots resist this inversion. We continue to perceive them as real, since we do not know their “inside out” form. Yet they, too, must pay to reach the other side: they are forced to inhabit a world in which upside-down relationships leave the viewer dizzy. Take the man climbing the stairs in the lower left corner: he has almost reached the platform in front of the small temple. He may wonder why the jagged pool in the center is empty. He could then try to place a ladder on the right. And now he has a dilemma: what he thought was a flight of stairs is actually the lower part of the arch. He will suddenly realize that the ground is much lower than his feet and has become a ceiling to which he is strangely stuck, defying the laws of gravity. The woman with the basket will find something similar happening to her if she goes down the stairs and crosses the center. However, if she remains on the left side of the picture, they will be safe.

The greatest discomfort is caused by two trumpeters located on opposite sides of the vertical line passing through the center of the picture. The top trumpeter, on the left, looks out the window over the vaulted roof of the small temple. From his position, he could easily climb out (or in?) through the window, climb down to the roof and then jump to the ground. On the other hand, the music played by the bottom trumpeter on the right will flow upward to the vault above his head. This trumpeter better give up all thoughts of climbing out of his window, because there is nothing under his window. In his part of the painting, the earth is inverted and lies below him, out of his field of vision. The emblem on the flag in the upper right corner of the painting cleverly sums up the content of this composition.

By allowing our eyes to move slowly from the left side of the painting to the right, it is possible to see that the arch on the right side is like a flight of stairs, in which case the flag looks completely implausible... But let me leave you to explore for yourself the many other mixed dimensions of this intriguing painting.

We often experience geometric ambiguity in our retinal images, even where this was not intended. For example, when studying a photograph of the moon, after some time we may discover that the craters have spontaneously transformed into hills, despite the fact that we know that they are craters. In nature, the interpretation of an image as "concave" or "convex" is highly dependent on the angle of incidence of the light. When light comes from the left, the crater on the left will have a bright outer surface and a dark inner surface.

When we study a photograph of the moon, we assume some kind of certain angle light incidence to enable crater recognition. If next to the first photograph of the moon we place the same photograph, but turned upside down, the lighting conditions that we assumed for the first photograph will be used to perceive the second, and it will be very difficult to resist the “inverted” interpretation. Almost all of the crater depressions in the first photo will appear bulging in the second.

The same phenomenon can sometimes be observed by simply turning over an ordinary photograph upside down. This effect is illustrated here by a Belgian village postcard (Fig. 16) and a fragment of an Escher painting (Fig. 17), which are printed upside down.

Even perfectly normal everyday objects can suddenly suggest ambivalence, particularly if we view them in silhouette or almost in silhouette.

Mach illusion

The Mach illusion is a phenomenon observed when viewing three-dimensional objects, and cannot be reproduced in the form of two-dimensional reproductions. Can be demonstrated with a simple and fun experiment. Take a rectangular sheet of paper measuring approximately 7x4 cm and fold it in half lengthwise. Open the sheet to form a V-shape (Fig. 18) and hold it vertically with the corner pointing into the distance. Now look at it with only one eye. After a few seconds, the vertical sheet inverts into a shape similar to a horizontal roof. Now if you turn your head left, right, up and down, you will be looking at a "roof" - a rotating roof in a still background. Two things are striking: first, this rotational movement occurs contrary to our expectations; secondly, the inverse form remains stable as long as the movement continues. (Naturally, the experiment can also be carried out with the paper placed horizontally with the fold pointing upward. In this case, the inverse shape will be vertical.)

We can come up with many models to demonstrate this illusory movement. Paolo Barreto came up with a simple but very effective inversion model in his Holocube (Fig. 19), a composition of three concave cubes. However, the inverse shape of the figure (convex) is more stable than its actual concave shape. Thus, when viewed from some distance, the figure appears as three convex cubes that float strangely in space when we turn our heads. This phenomenon, first described by Ernst Mach, also appears spontaneously in images of concave figures. We see such images as convex, since the concave shape seems implausible to us (Fig. 20 and 21). When we move, the inverse image follows us. This is especially surprising when the image in question is someone's face!

Pseudoscopy

In connection with the painting Convexity and Concavity, Escher told me that although he could see many objects inverted with one eye, he could not do this with a cat. Around the same time, I introduced him to the phenomenon of pseudoscopy, in which this kind of "inside-out" vision is formed in the EYE. We can cause our 3D vision program to go the wrong way by presenting the left eye with an image intended for the right eye, and vice versa. The same effect could be achieved a little more easily by using two prisms, showing mirror images to both eyes.

Escher was delighted with these prisms and for a long time carried them with me everywhere to look at various three-dimensional objects in their pseudoscopic form. He wrote to me: “Your prisms are the simplest means of experiencing the same type of inversion that I tried to achieve in the painting “Convexity and Concavity.” The small white staircase made of sheet steel, given to me by mathematics professor Schouten, inverts as soon as you look at it through prisms, as in the painting "Convexity and Concavity". I attached the prisms between two pieces of cardboard and secured them with an elastic band. It turned out something similar to "binoculars". On a walk, this device entertained me. So, some leaves that fell into the pond suddenly rose, the water level became lower than the air level, but there was no “fall” of water! Also interesting is the change in where is left and where is right. If you look at your legs in motion, moving right leg the left leg will appear to be moving."

You can use Figures 23 and 24 to create your own pseudoscope to experience illusory movement for yourself.

Thiéry's figure

In 1895, Armand Thiéry published a detailed article about his research in a specific area optical illusions. It is the first mention of the figure that today bears his name, and which was used in countless variations by artists of the Op Art movement. Most known variant The figure consists of five rhombuses with angles of 60 and 120 degrees (Fig. 26). To many people, this figure appears to be very dual, in which two cubes are successively represented either in a convex or in a concave form. Thierry carefully carried out all experiments under the same conditions. He recruited several participants for tests "to make the observations more reliable." However, he was far from the methods of modern statistics, since he did not calculate the arithmetic mean for his results, and, moreover, he selected test participants from specialists in related fields, such as experimental psychology, applied graphics, aesthetics, etc. which, in particular, the modern researcher should avoid.

Thierry writes: “All drawings with perspective reflect a certain position taken by the eye of the artist and the observer. Depending on the distance at which we perceive this position, the drawings can be interpreted differently. Figure (27) is an illustration of a prism viewed from below, drawing ( 28) is a prism seen from above. But these drawings become dual when the two figures are combined so that both prisms share one common side (Fig. 29). When viewing the drawing from right to left, the drawing appears as a wrapped screen viewed from above."

Strangely, Thierry does not mention the second interpretation, but emphasizes that the figure has similarities in the Schröder staircase (a drawing of the same staircase that the processor Prof. Schouten gave to Escher) and notes: “Here, too, there are two possible interpretations.” He comes to the conclusion that we can see the figure in two versions - as a prism from Figure 27 and as a prism from Figure 28, each of which has a unique extension.

Less well known is the fact that the symmetrical figure of Thierry (Fig. 26) can be represented as a completely non-dual figure. One day Professor J.B. Deregowski brought me wooden block, having exactly the same shape. For those who saw this object, the figure of Thierry ceases to be ambiguous. If you transfer the “drawing” of the figure’s development (Fig. 30) to another sheet of paper, cut along the lines and glue, you will immediately see how this illusion works. Looking at the paper model from above, you will see the figure of Thierry, and then it will be difficult to ever see it again as dual. EYE prefers simple solutions!

When geometrically dual figures are presented to the EYE, it spontaneously alternately offers us two spatial solutions. Something is either concave or convex, depending on whether we are looking up at the bottom side or looking down at the top side. The obvious question is whether it is possible to confront the EYE with a situation where the alternatives "either/or" become simultaneous "both/and". Such a situation can produce an impossible object, since two interpretations cannot be true at the same time. In Chapter 4 we will meet figures in which such an extraordinary situation arises.

The author of the picture opposite (Fig. 2) presented new type flywheel, combining mathematical imagination with a fair amount of technical ideas. Its individual components are shown in the drawing attached to the wall on the left, while frontal view The wheel axle in the drawing on the right reveals the whole concept of the square wheel. However, the viewer remains unconvinced - such a wheel cannot be built. It is not impossible to connect six beams to form a wheel rim, even if they lie in the same plane, but four spokes simply cannot be connected as shown. The inventor of this wheel forces us to look for at least one connection that would be clearly incorrect. But, as we will soon discover, they are all correct. And yet the object represented in this particular case cannot exist in the real world. This is an impossible object! Only by disconnecting the connections at several points will we arrive at an object that can be built. Rice. 3 shows one of the possible options. The result, however, is significantly different from what the inventor originally envisioned - it is now a bizarre three-dimensional design rendered possible and useless...

Sadro del Pret combined two impossible triangles into this "impossible wheel". The impossible triangle (or tribar) is the simplest and at the same time the most captivating object of all known impossible objects (Fig. 4). It looks very "real" but still cannot exist.

However, its impossibility is not as absolute as that of, for example, a square circle, which can neither be imagined nor drawn. The impossible objects that interest us can, oddly enough, be easily visualized, which underlies their appeal. They show us new world and thus reveal to us the incredibly complex process we call vision. Is tri-bar really impossible? Rice. Figure 5 shows how, by dividing the two arms of a triangle at certain points, we arrive at an object that can be created in the real world. Obviously we've transformed it into something completely different.

Sandro del Prete's "Three Candles" (Fig. 6) represents a completely different category of impossible objects. How many candles are shown: two or three? If we look down from the middle flame, we will see that the candle on which it burns mysteriously disappears. At the same time, if we look up from the square base of the right candle, we will see that the left side of the candle disappears into the background, leaving only the right side. A characteristic feature of such impossible objects is that they can only be depicted in black and white and cannot be colored. The following three images (Figure 7-9) were created by Oscar Reutersvärd. There is something irritating in such paintings, when a figure that initially seems monolithic suddenly eludes our gaze. Matter disappears into emptiness.

Figure 6. Sandro del Prete, "Three Candles", pencil drawing

Figure 7.	Figure 8.	Figure 9.

Ambiguous figures are another category. Unlike impossible objects, which cannot exist in the real world, ambiguous figures represent three-dimensional realities of more than one. Thus, we can interpret the figure in the center of Monica Bush's drawing (Fig. 10) as both a projection of the outer surface of the cube and as a concave cubic space. It is quite possible to create two different three-dimensional models of this painting, each of which will illustrate one of the interpretations of the painting. As we will see in Chapter 3, every image projected onto the retina is essentially ambiguous, whether we are looking at a painting or at objects. real world. Fortunately, this rarely creates problems in everyday life, since our consciousness accepts only the information received from the picture on the retina that corresponds to reality. We talk about figure ambiguity when two (or sometimes more) interpretations of the same figure are equally plausible.

The first scientists who began to study impossible objects and ambiguous figures defined both of these categories under the same name “optical illusions,” which is not entirely accurate, since this name does not reveal the unique characteristics of these objects. Optical illusions are objects that we see, but which either cannot exist in reality or whose true nature is different from what we see. We constantly encounter optical illusions in our lives without noticing them, simply because we constantly make allowances for them. For example, although it seems to us that the moon is moving after us when we move down the street at night, we know for sure that it is standing still. Likewise, the moon appears larger when it is just above the horizon than when it is high in the sky, but we do not think of the moon as expanding and contracting every night. When I look out the window at the buildings below, they don't seem more pot with a flower on my windowsill, but still I do not allow such a thought. Optical illusions are for the most part a component of our perception.

Some forms of optical illusions have very unusual characteristics, some of them even bear the name of their “inventor” or researcher. In the picture Prof. A.J.W.M. Thomassen (Fig. 11) we see among the figures the parallelogram of Sander (1926, Fig. 12). If you are seeing this optical illusion for the first time, then take a ruler and measure the difference in length between the long segment AB and the short segment BC. Fraser's illusion (1908, fig. 13) shows us the extent to which additional factors influence our conscious determination of the direction of lines: although the letters of the word LIFE appear to be curved, they are all vertical and parallel to each other. Estimation of the size of a circle depends on the objects surrounding it (Lipps, 1897, Fig. 14): the central circles in both cases have the same size.

Figure 14.

These kinds of illusions have been the subject of study for more than 150 years, and they can teach us about how our vision functions. The ambiguity of figures was explored by Necker as early as 1832, while impossible objects only attracted attention in 1958 with the publication of a paper by the Penroses, whose impossible triangle is also depicted in Thomassen's painting.

In this book we will show, among other things, that ambiguous figures and impossible objects are important not only because they shed light on the features of our vision, but also because their discovery by artists opened up previously unexplored areas in the history of art.

(eng. ambiguous figures, reversible figures)- images that allow different relationships between “figure” and “background” depending on the subject’s ideas. The selected object (figure) becomes the object of perception, and everything that surrounds it recedes into the background of perception. So, fig. 2a can be perceived either as an image of a black vase on a white background, or as two profiles of a person’s face on a black background. More multi-valued images are also possible. For example, when continuously viewing the figure (“Schröder figure”) in Fig. 2b its appearance changes, and one can observe: 1) a staircase; 2) a paper strip folded like an accordion; 3) overhanging cornice.

Dual or ambiguous images are explained by the fact that when perceiving such pictures, a person experiences different views, identically corresponding to the picture. Therefore, it is enough to single out the k.-l. a characteristic detail corresponding to a certain idea, in order to then immediately see a certain object.

Rice. 2. Examples of dual images.

Addition : Classic figure with reversible perspective is the Necker cube; this is D. and. named after the Swiss mathematician and physicist Louis Albert Necker (1730-1804), who reported that crystals and their designs during scientific observations they seem to spontaneously rotate in depth (which, of course, makes their visual examination very difficult). The above reversible vase was published in 1915 by the Danish philosopher Edgar Rubin (1886-1951); this vase very popularly illustrates the reversibility of figure and ground. Dual images often found in paintings famous artists, an example of which is Salvador Dali’s painting “The Slave Market with the Appearance of an Inconspicuous Bust of Voltaire” (when viewed from a close distance, the figures of people dominate; as the viewing distance increases, Voltaire’s bust becomes noticeable).

Another example of the striking competition of figure and ground is the engraving by M. Escher “Concentric Limit IV (Heaven and Hell)”: here the spontaneous alternation of devils and angels, which has no end, is symbolic and has a deep philosophical Meaning.

Theoretical value Dual images in the psychology of perception is that they convincingly prove famous thesis Gestalt psychology is about the relative independence of the perceptual whole from sensory elements. The method of proof is simple: on the same sensory basis, with the same stimulation, completely different perceptions can arise. T. o., D. and. prove the same thesis as the transposition effect (which consists in demonstrating the constancy, stability of the perceptual whole with a complete change of the sensory basis), but directly opposite. way. (B.M.)

Psychological Dictionary. A.V. Petrovsky M.G. Yaroshevsky

Dictionary of psychiatric terms. V.M. Bleikher, I.V. Crook

no meaning or interpretation of the word

Neurology. Full Dictionary. Nikiforov A.S.

no meaning or interpretation of the word

Oxford Dictionary of Psychology

no meaning or interpretation of the word

subject area of ​​the term

Dual or polysemantic images, as the Big Psychological Dictionary tells us, are explained by the fact that when perceiving such drawings, a person has different ideas that are equally consistent with what is depicted.

How many women do you see?

At first glance, 90% of people see attractive girl 20-25 years old, the remaining 10% see an old woman over 70 with a huge nose. For those who see the picture for the first time, it is difficult to see the second image.

Clue: A girl's ear is an eye elderly woman, and the oval of a young face is the nose of an old woman.

The first impression, according to psychologists, usually depends on what part of the picture your gaze fell on at the first moment.

After a little training, you can learn to order yourself who you want to see.
Psychiatrist E. Boringou used the portrait in the 1930s as an illustration for his work. The author of such an image is sometimes called the American cartoonist W. Hill, who published the work in 1915 in the magazine “Pak” (translated into Russian as “elf”, “fairy-tale spirit”).

But back in the first years of the 20th century, a postcard was issued in Russia with the same picture and the inscription: “My wife and my mother-in-law.”

The picture with two ladies can be found in many psychology textbooks.

Hare or duck?

Which character did you see first on modern version"Ehrenstein illusions"? The very first "duck-hare" drawing was published in Jastrow's book in 1899. It is believed that if children are shown the picture on Easter Day, they will be more likely to see it as a rabbit, but if shown to them in October, they will tend to see a duck or similar bird

Clue: In the picture you can see a duck, which is directed to the left, or a hare, which is directed to the right.

Singing Mexicans or old men?

Mexican artist Octavio Ocampo is the author of quite unusual paintings with hidden meaning. If you look closely, you will see another, hidden image in each of his drawings. He made the scenery of more than 120 Mexican and American films. Created several portraits famous people the Western world in a surreal style (“Portrait of the singer Cher”, “Portrait of the actress Jane Fonda”, “Portrait of Jimmy Carter”, etc.).

Clue: The old man and the old blonde woman look at each other. Their eyebrows are the hats of Mexican musicians, and their eyes are the faces of musicians.

Just Rose?

At first glance, yes. An ordinary flower and nothing more. But it was not there. The author of this image, Sandro del Pre, formed a new direction in art, which he called “illusorism,” focusing on creating optical illusions when painting.

Clue: In the center of the rose you can see a couple kissing.

Old man or cowboy?

This painting by Ya. Botvinnik, first half of the twentieth century, USA, is called “My husband and my father-in-law.”
Who did you see first? Young man in a cowboy hat or an old man with a big nose?
Psychologists say that a person’s attitude towards himself influences the choice of image: with a positive attitude, people are more likely to perceive a young image in the first seconds.

Clue: The cowboy's neck is the old man's mouth, the ear is the eye, the chin is the nose.

What do you see in the sixth picture?

Leave your options in the comments to this article. The answer will appear at 13:00 on October 8, 2013.

Answer: Skull or young couple