Optical illusion - unreliable visual perception any picture: an incorrect estimate of the length of the segments, the color of the visible object, the magnitude of the angles, etc.
The reasons for such errors lie in the peculiarities of the physiology of our vision, as well as in the psychology of perception. Sometimes illusions can lead to absolutely incorrect quantitative estimates of specific geometric quantities.
Even carefully looking at the "optical illusion" picture, in 25 percent or more of cases you can make a mistake if you do not check the eye estimates with a ruler.
Illusion pictures: size
For example, consider the following figure.
Optical Illusion Pictures: Circle Size
Which of the circles located in the middle is larger?
Correct Answer: The circles are the same.
Illusion Pictures: Proportions
Which of the two people is taller: the dwarf in the foreground or the person walking behind everyone? 
Correct Answer: They are the same height.
Illusion pictures: length
The figure shows two segments. Which one is longer?
Correct Answer: They are the same.
Illusion Pictures: Pareidolia
One type of visual illusion is pareidolia. Pareidolia is an illusory perception of a particular object.
Unlike illusions of length perception, depth perception, dual images, pictures with images that are specially designed to provoke the appearance of illusions, pareidolia can occur on their own when viewing the most ordinary objects. So, for example, sometimes when looking at a pattern on a wallpaper or a carpet, clouds, spots and cracks on the ceiling, one can see fantastic changing landscapes, unusual animals, people's faces, etc.
The basis of various illusory images can be real details existing pattern. The first to describe such a phenomenon were Jaspers and Kalbaumi (Jaspers K., 1913, Kahlbaum K., 1866;). Many pareidolic illusions can arise from the perception of well-known images. In this case, such illusions can take place simultaneously in several people.
So, for example, in the following picture, which shows the building of the Center international trade on fire. Many people can see the terrible face of the devil on it. 
The image of the devil can be seen in the next picture - the devil in the smoke 
In the following picture, one can easily make out the face on Mars (NASA, 1976). The play of shadow and light has given rise to many theories about ancient Martian civilizations. Interestingly, in the later images of this region of Mars, the face is not detected.
And here you can see the dog.
Illusion Pictures: Color Perception
Looking at the picture, you can observe the illusion of color perception. 
In fact, the circles on different squares are the same shade of gray.
Looking at the following picture, answer the question: are the chess cells on which points A and B are located the same or different colors?
It's hard to believe, but yes! Don't believe? Photoshop will prove it to you.
How many colors do you enter in the following picture?
There are only 3 colors - white, green and pink. You may think that there are 2 shades of pink, but in fact it is not.
What do these waves look like to you?
Are the brown waves-stripes painted? But no! This is just an illusion.
Look at the following picture and say the color of each word.
Why is it so difficult? The fact is that one part of the brain is trying to read the word, while the other perceives the color.
Illusion Pictures: Elusive Objects
Looking at the following image, look at the black dot. After a while, the colored spots should go away. 
Do you see the gray diagonal stripes?
If you look at the center dot for a while, the stripes will disappear.
Illusion Pictures: Changeling
Another view visual illusion- flip. The fact is that the very image of the object depends on the direction of your gaze. Yes, one of these optical illusions- “duck hare” This image can be interpreted both as an image of a hare and as an image of a duck. 
Take a closer look, what do you see in the next picture? 
What do you see in this picture: a musician or a girl's face?
Oddly enough, it's actually a book.
A few more pictures: an optical illusion
If you look at the black color of this lamp for a long time, and then look at White list paper, then this lamp will be visible there.
Look at the dot, and then back away a little and get closer to the monitor. Circles will spin at the same time in different sides.
That. features of optical perception are complex. Sometimes you can't believe your eyes...
The snakes crawl in different directions.
Aftereffect illusion
After looking at an image continuously for a long period, there will be some effect on vision for a while. For example, prolonged contemplation of a spiral leads to the fact that all objects around will rotate for 5-10 seconds.
shadow shape illusion
This is a common type of erroneous perception, when a person guesses a figure in the shadow with peripheral vision.
Irradiation
This is a visual illusion that leads to a distortion of the size of an object placed on a background with a contrasting color.
Phosphene phenomenon
This is the appearance of unclear dots of different shades in front of closed eyes.
Depth perception
This is an optical illusion, implying two options for perceiving the depth and volume of an object. Looking at the image, a person does not understand a concave object or a convex one.
Optical illusions: video
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Even the most hardened skeptics believe what their senses tell them, but the senses are easily deceived.
An optical illusion is an impression of a visible object or phenomenon that does not correspond to reality, i.e. optical illusion vision. Translated from Latin, the word "illusion" means "mistake, delusion." This suggests that illusions have long been interpreted as some kind of malfunction in the visual system. Many researchers have studied the causes of their occurrence.
Some visual illusions have long been scientific explanation others are still a mystery.
website continues to collect the coolest optical illusions. Be careful! Some illusions can make you teary headache 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 chocolate piece will appear. You can do the same with regular chocolate and make sure it's not computer graphics but a real 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 lie on top of the other.
Cube and two identical cups
An 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 inspection, we can see that in fact the cube is drawn, and the cups are exactly the same size. A similar effect is noticed only at a certain angle.
Cafe wall illusion
Take a close look at the image. At first glance, it seems that all the lines are curved, but in fact they are parallel. The illusion was discovered by R. Gregory at the Wall Cafe in Bristol. That's where its name came from.
Illusion of the Leaning Tower of Pisa
Above you see two pictures leaning tower of pisa. At first glance it looks like the tower on the right is leaning more than the tower on the left, but the two pictures are actually the same. The reason lies in the fact that the visual system considers 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 "Disappearing 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 a green spot is running around
2) then the purple spots will start to disappear
Information about the external world comes to a person mainly through the visual sense organs, 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 the same 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, which has passed through the lens, onto the retina. The information received from the retina is extremely complex. For our purposes, we distinguish two categories of information: image information based on pictographic elements that reproduce the represented objects, and spatial information composed of stereographic elements that reproduces the spatial relationships between objects.
Basically, these two types of information appear together, which is illustrated by a simple example. In the drawing with two fishermen on the bank of a canal (Fig. 1), the 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 partially light and partially dark, two shadows fall behind dark parts figures, the banks of the channel converge to each other.
Picture 1.
The EYE transforms both types of information, pictographic and stereographic, into a meaningful interpretation. In our usual environment, this does not cause any difficulties, and the whole process takes a fraction of a second. But sometimes there are deviations and this process comes to a standstill, which allows us to find out the features of the functioning of the EYE.
Perhaps you have also experienced a phenomenon similar to what happened to me. Lying one day on the bed and examining the objects standing on the bedside table, I noticed something completely extraneous: 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 it could not possibly be there. I did not move and continued to carefully examine the unusual object, hoping to comprehend the riddle. Suddenly, I recognized my lighter on the left, standing upright, and on the right, a glass partially blocked by a postcard. This made much more sense, and subsequently it was difficult for me to reproduce the initial 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 become aware of the ambiguity because 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 proceeds automatically. In these cases we are talking about dual images of the retina, and dual figures if the switch is due to some graphic figure. By its nature, duality can be pictographic and stereographic. Because the this book connected 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, a few examples are added below.
Pictographic duality
Figure 2. W.E. Hill, "My wife and stepmother"
Almost every one of us has experienced the phenomenon of pictographic duality, especially in the form of "Freudian" paintings. good example is the image "My wife and stepmother" (My wife and my mother-in-law) (Fig. 2), published in 1915 by the 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 daunting task, even for psychologists. A few years later, Jack Botwinick created an image to match the previous one - "My father and stepfather" (My husband and my father-in-law) (Fig. 3). Many similar paintings were created in subsequent years, among which the Eskimo-Indian (Fig. 4) and Duck-Rabbit (Fig. 5) are also widely known.
Figure 3. Jack Botwinick, "My father and stepfather"
Figure 4. Eskimo Indian
Figure 5. Duck-rabbit
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 that appeared in the New York Herald from 1903 to 1905.
Figure 6. Gustave Verbeek, Upside Down cartoon
Each picture must first be considered in its normal position, and then turned upside down. Figure 6 shows a little girl, Lady Lovekins, caught by a giant rock bird. The painting, turned upside down, shows a large fish tipping over old man Muffaroo's canoe with its tail. Also very famous are "double images" in which the purpose and function of the objects and the background change with each other. At first glance, Sandro del Prete's painting "The Window Opposite" (Fig. 7) will probably see more than just a vase of flowers, a glass and a pair of stockings hanging to dry.
Figure 7. Sandro del Prete, "Opposite the Window", pencil drawing
Stereographic duality
The images formed on our retina are two-dimensional. An important task of the EYE is to reconstruct three-dimensional reality from these two-dimensional images. When we look with two eyes, the two images on the retinas of our eyes contain slight differences. The independent EYE program uses these differences to calculate (with a high degree accuracy for objects within 50 meters) of the spatial relationships between objects and our body, giving us a direct view 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. The transformation of three-dimensionality into two-dimensionality forms the basis of duality, which is illustrated simple example. Segment AB in fig. 8a can be interpreted by the EYE in several ways. For example, it can be viewed simply as a line drawn in ink on paper, or as a straight line in space, but we cannot tell which of the 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 cube drawing, the positions of points A and B will be determined in space. On fig. 8b point A looks closer than point B, and also point B looks lower than point A. In figure 8c, these relationships are reversed. On fig. 8d, the same segment AB is horizontal in the direction from the trees in the foreground to the horizon.
Figure 8
A cube in which all twelve edges are depicted by the same straight lines (Fig. 9) is called a Necker cube in honor of professor of mineralogy L.A. Necker from Germany, who was the first to study the stereographic duality c scientific point vision.
Necker cube
Figure 9. Necker box
On May 24, 1832, Professor Necker wrote a letter to Sir David Brewster, 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 case when a scientist described the phenomenon of optical inversion, but also because this phenomenon surprised the author himself. It also sheds light on the typical scientific practice of the time, when neither the use of a test sample of participants nor the creation of special scientific instruments was still common. Instead, the researcher recorded his own observations and tried, often in a very general way, to guess what was behind outward manifestation hoping to come to a conclusion within the limits of their knowledge.
"The object to which I would like to draw your attention is related to the phenomenon of perception in the field of optics, a phenomenon that I have observed many times when studying images crystal lattices. I'm talking about a sudden, inadvertent 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 farther away. Thus ABCD represents the frontal plane and triangle XDC is on the plane behind. If you look at the shape longer, you will see that the apparent orientation of the shape sometimes changes so that point X looks like the closest point and point A looks the farthest, and the ABCD plane moves back behind the XDC plane, giving the whole shape a completely different orientation.
For a long time it was not clear 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 fix was an unusual sensation in the eyes at the moment of the 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 connected with the focusing of the eye. For example, when the focal point on the retina (i.e., the macula) points to an angle with its apex 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 are less clearly visible, giving the impression that they are farther away.
The "switch" occurs when the focus point shifts to point X. When I opened this solution, I could 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.
Second, 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 at the moment when the figure becomes visible through the lens. Thus, an orientation is assumed in which point X is seen even farther away. This only happened because the X point replaced the A point in the focus point without any spatial adjustment of 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 this case, the figure cannot be seen in any other way, and the switch does not occur.
What I said about corners is also true for individual sides. Planes that are in the line of sight (or opposite the macula lutea) 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 focusing the eyes.
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 see fit."
Many people who have done the same experiment as Necker have come to the conclusion that switching occurs spontaneously and independently of the focus point. However, Necker's original assumption that this phenomenon occurs in the processing of retinal images in the brain is correct. In the Necker cube, the EYE cannot determine which of the points (or planes) is closer or further away. Figure 10 shows the Necker cube in the form solid lines ABCD-A"B"C"D" between two other illustrations of two possible interpretations. When we look at the Necker Cube, we see first the figure in the center, then the figure on the right, and a little later the figure on the left, and so on. The switch from "A is closer than A" to "A is farther 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.
Figure 10.
However, the alternation of relative distances ABCD and A"B"C"D" is not the most strong impression. Most notable is the fact that both cubes have a completely different orientation, as Necker pointed out in his letter. Thus, segments AD and AD" look intersecting, although they are shown in the figure in parallel. It is possible to describe the phenomenon of perceptual inversion more precisely: all lines have the same orientation on the image of the retina, but as soon as the interpretation of the figure changes to inverse, all lines (in space) look like they have changed orientation. As we can see, such orientation changes can be very unexpected. The perceptual inversion in the top pair of dice in Figure 11 is caused by choosing the angle at which the dice is drawn. These figures are based on two photographs of one and the same configuration of dice made under different angles. The left dice is located next to the wall. The wall and floor are marked with squares that match in size with the edge of the dice. The bottom drawing forms the different orientations of the dice more clearly.
Figure 11.
The angle at which the cube is drawn also determines the angle at which its sides will be seen after perceptual inversion. The left pair of cubes in figure 12 has a very small angle, while the right pair has a maximum angle (which corresponds to the top image of figure 11)
Figure 12.
Figure 13. Monika Buch, "Intersecting Bars", acrylic on cardboard, 60x60 cm, 1983. The feeling of intersecting bars is enhanced here by the fact that the bars appear to be grouped at a slight angle relative to each other. This impression is emphasized by the regular arrangement of twenty-four small diamonds that form the ends of the bars.
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 inner and outer side Cuba. The situation changes when we remove from the picture three planes that meet near the center of the cube, as shown in the figure above with dice. Now we have a figure that again assumes two opposite spatial body, but now these bodies have 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 the convexity immediately, but have some difficulty in perceiving the concave shape until minor auxiliary lines are added to the drawing.
On the lithograph "Concavity and Convexity" (Fig. 14) by M.K. Escher demonstrates how, through specific geometric techniques, the viewer is forced to interpret the left side of the picture as convex, and the right side as 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 right side, and the transition in the center of the picture is not rough, but smooth and natural. But when we look over the center, we find ourselves sinking into something worse than a bottomless abyss: everything is literally turned inside out. The top 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 because we do not know their "inside-out" form. Yet they, too, have to pay to cross over: they are forced to inhabit a world in which upside-down interconnections make the viewer dizzy. Take the man who is 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. Then he could try to put the ladder on the right. And now he faces a dilemma: what he took for 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 glued against 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 stays on the left side of the picture, they will be safe.
Figure 14. M.K. Escher, "Convex and Concave", lithograph, 27.5x33.5 cm, 1955. "Can you imagine, I spent More than a month thinking about this picture, as my initial sketches were too difficult to understand." (M.C. Escher)
The greatest discomfort is caused by two trumpeters located on opposite sides of the vertical line passing through the center of the picture. The upper trumpeter, on the left, looks out the window over the vaulted roof. small temple. From his position, he could well have climbed out (or in?) through the window, climbed down to the roof, and then jumped 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 had better put aside all thoughts of climbing out of his window, because there is nothing under his window. In his part of the picture, the ground is inverted and lies below him out of his field of vision. The emblem on the flag in the upper right corner of the picture deftly sums up the content of this composition.
By allowing our eyes to move slowly from the left side of the picture to the right, it is possible to see that the vault 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 jumbled dimensions of this intriguing picture.
We often experience geometric duality in our retinal images, even where it was not intended. For example, when studying a photograph of the moon, after a while we may find that the craters have transformed into hills of their own accord, despite the fact that we know 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 hits 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 a certain angle of incidence of light in order to be able to recognize craters. If next to the first photograph of the moon we put 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.
Figure 15. A photograph of the moon (left) and the same photograph upside down (right).
The same phenomenon can sometimes be observed simply by flipping a normal 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.
Figure 16. Photograph of a Belgian village, printed upside down.
Figure 17. Fragment of a painting by M.K. Escher "City in southern Italy", 1929, printed upside down.
Even perfectly normal everyday objects can suddenly assume ambivalent perception, particularly if we view them in silhouette or near-silhouette.
Mach illusion
The Mach illusion is a phenomenon observed when viewing three-dimensional objects, and is not reproducible in the form of two-dimensional reproductions. Can be demonstrated by a simple and entertaining experiment. Take rectangular sheet paper about 7x4 cm in size and fold it in half lengthwise. Open the sheet so that it forms a V-shape (Figure 18) and hold it upright with the corner pointing away. Now look at it with only one eye. After a few seconds, the vertical sheet is inverted into a shape similar to a horizontal roof. Now, if you turn your head left, right, up and down, you will see the "roof" of the rotating roof in the 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. (Of course, the experiment can also be done with paper laid out horizontally with the fold pointing up. In this case, the inverted shape will be vertical.)
Figure 18.
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, viewed from a distance, the figure appears as three convex cubes that strangely float in space when we turn our heads. This phenomenon, first described by Ernst Mach, also spontaneously appears in the images of concave figures. We see such images as convex, since the concave shape seems implausible to us (Fig. 20 and 21). As we move, the inverted image follows us. This is especially surprising when the image in question is someone's face!
Figure 19. Paolo Barreto, Holocube
Figure 20. Photograph of a small sheet metal staircase donated by Prof. Schouten to M.K. Escher. This model was the inspiration for Escher's lithograph Convex and Concave. In the form of a drawing, this figure is known as "Schroeder's steps".
Figure 21. Two photographs of a concave painting by Sandro del Prete. The EYE, however, prefers a convex interpretation.
Figure 22. Monika Buch, "Thieri Figure 2", acrylic on board, 60x60 cm, 1983. The vertical stripes that make up the painting are elongated to fill the entire surface.
Pseudoscopy
In connection with the "Convexity and Concavity" painting, Escher told me that although he could see many objects inverted with one eye, he could not do so 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 get our 3D vision program to go the wrong way by giving the left eye an image intended for the right eye, and vice versa. The same effect could be achieved a little more simply by using two prisms showing mirror images to both eyes.
Escher was delighted with these prisms and for a long time I carried them with me everywhere to look at various three-dimensional objects in their pseudoscopic form. He wrote to me: "Your prisms are the easiest means of experiencing the same type of inversion that I was trying to achieve in the painting Convexity and Concavity. The little white sheet steel staircase given to me by mathematics professor Schouten is inverted as soon as you look at it through the prisms, as in the picture "Convexity and Concavity". I fixed the prisms between two pieces of cardboard and secured 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 "falling" of the water! It is also interesting to change where to the left and where to the 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 the illusory movement yourself.
Figure 23 and 23. Views of the pseudoscope from the side and top.
Thiéry's figure (Thiery's figure)
Figure 25. An illustration of Mitsumasa Anno that can be flipped upside down. Several houses have a common roof and are a variant of Thierry's figure.
In 1895, Armand Thiéry published a detailed article about his research in the specific field of optical illusions. It mentions for the first time the figure that bears his name today, and which has been used in countless variations by op art artists. Most famous variant the figure consists of five rhombuses with angles of 60 and 120 degrees (Fig. 26). To many people, this figure seems to be very dual, in which two cubes are sequentially presented in either a convex or a concave form. Thierry carefully carried out all the experiments under the same conditions. He recruited several test subjects "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 participants for tests from specialists in related fields, such as experimental psychology, applied graphics, aesthetics, etc., which, in particular, the modern researcher should avoid.
Figure 26. Thierry's figure.
Thierry writes: "All perspective drawings 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 in different ways. Figure (27) is an illustration of a prism observed from below, figure ( 28) is a prism viewed from above. But these drawings become dual when the two figures are combined so that both prisms share one common side (Fig. 29). Viewed from right to left, the drawing appears as a wrapped screen viewed from above."
Figure 27, 28, 29
Oddly, Thierry does not mention the second interpretation, but emphasizes that the figure bears a resemblance to the Schroeder ladder (a drawing of the same ladder 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 peculiar 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 a block of wood that had exactly the same shape. For those who saw this object, Thierry's figure ceases to be dual. If you transfer the "drawing" of the unfolded figure (Fig. 30) to another sheet of paper, cut along the lines and glue, you will immediately see how this illusion works. Viewing the paper model from above, you will see Thierry's figure, and then it will be difficult to ever see it again as a dual one. EYE prefers simple solutions!
Figure 30. "Sweep" of Thierry's figure.
When geometrically dual figures are presented to the EYE, it spontaneously offers us two spatial solutions in turn. 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 arises whether it is possible to confront the EYE with a situation where the alternatives "either-or" become simultaneous "both/and". Such a situation may produce an impossible object, since two interpretations cannot be true at the same time. In Chapter 4 we will meet figures in whom this extraordinary situation arises.
(English ambiguous figures, reversible figures)- images that allow different ratios of "figure" and "background" depending on the subject's ideas. The selected object (figure) becomes the object of perception, and everything that surrounds it goes to the background of perception. Yes, 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 meaningful images are also possible. For example, when continuously examining the figure ("Schroeder's figure") in Fig. 2b, its appearance changes, while 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 drawings, a person has different ideas that equally correspond to the image. Therefore, it suffices to isolate the c.-l. a characteristic detail corresponding to a certain idea, in order to then immediately see a certain object.
Rice. 2. Examples of dual images.
Addendum : The 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 patterns during scientific observations seem to spontaneously revolve in depth (which, of course, makes them very difficult to visualize). The reversible vase mentioned above 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 seen in pictures 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, with an increase in the observation distance, the bust of Voltaire becomes noticeable).
Another example of a striking competition between figure and background is M. Escher's engraving "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.
The theoretical significance of dual images in the psychology of perception lies in the fact that they convincingly prove the well-known thesis of Gestalt psychology 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 percepts can arise. T. o., D. and. prove the same thesis as the effect of transposition (which consists in demonstrating the constancy, stability of the perceptual whole when full shift sensory basis), but directly against. way. (B. M.)
Psychological dictionary. A.V. Petrovsky M.G. Yaroshevsky
Dictionary of psychiatric terms. V.M. Bleikher, I.V. Crook
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Neurology. Full Dictionary. Nikiforov A.S.
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Oxford Dictionary of Psychology
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The author of the figure 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 the frontal view of the wheel axle in the drawing on the right reveals the whole concept of the square wheel. However, the viewer remains in his opinion - 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 wrong. But, as we shall 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 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 construction made possible and useless...
Sadro del Prete 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 it cannot exist.
However, its impossibility is not as absolute as, for example, a square circle, which can neither be represented in the mind nor drawn. The impossible objects that interest us can be, oddly enough, easily visualized, which is the basis of their attraction. They show us new world and thus reveal to us the incredibly complex process we call vision. Is tribar really impossible? Rice. Figure 5 shows how, by dividing the two arms of the triangle at certain points, we arrive at an object that can be created in the real world. Obviously, we have transformed it into something completely different.
Sandro del Pret's "Three Candles" (Fig. 6) represent 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 in a mystical way 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 background, and only the right side remains. A characteristic feature of such impossible objects is that they can only be depicted in black and white and cannot be colored. Three following images(Fig. 7-9) were created by Oskar Reutersvärd. There is something annoying in such paintings, when a figure that initially seems monolithic suddenly escapes our gaze. Matter disappears into the void.
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| Figure 6. Sandro del Prete, "Three Candles", pencil drawing |
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| 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 with more than one. Thus, we can interpret the figure in the center of Monica Bush's drawing (Fig. 10) both as a projection of the outer surface of the cube and as a concave cubic space. It is entirely possible to create two different 3D models of this painting, each illustrating one of the interpretations of the painting. As we will see in Chapter 3, every image projected onto the retina of the eye 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, which corresponds to reality. We are talking about the ambiguity of a figure, when two (and 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 we think the moon is following us when we walk down the street at night, we know for sure that it is standing still. Similarly, the moon appears larger when it is just above the horizon than when it is high in the sky, but we do not think that the moon expands and contracts every night. When I look out the window at the buildings below, they seem no bigger than a flowerpot on my windowsill, but still I don't allow such a thought. Optical illusions are for the most part an integral feature 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 Sander's (1926, fig. 12) parallelogram among the figures. If you are seeing this optical illusion for the first time, then take a ruler and measure the difference in length between long AB and short BC. Fraser's illusion (1908, fig. 13) shows us the extent to which additional factors influence our consciousness's determination of the direction of the lines: although the letters of the word LIFE appear to be curved, they are all vertical and parallel to each other. The 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.
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| Figure 14. |
These kinds of illusions have been the subject of study for over 150 years, and they can teach us how our vision functions. The ambiguity of figures was explored by Necker as early as 1832, while impossible objects did not come to attention until 1958 after the publication of an article by the Penroses, whose impossible triangle is also depicted in a painting by Thomassen.
In this book, we will show, among other things, that dual figures and impossible objects are important not only because they shed light on the peculiarities of our vision, but also because their discovery by artists opened up hitherto unexplored areas in the history of art.
