Here is a selection of prints by M.C. Escher, a Dutch graphic artist from the twentieth century. His work mystifies our eyes with his prints, forming a three dimensional illusion on a two dimensional print. Pertaining to perceptual theories, I was taken in by the illusions he incorporated in his prints and how he manipulated our eyes to follow his artistic perspective.
This print includes the idea of the impossible triangle or tri-bar, which was created by Robert Penrose and his father. Each right angle is completely normal, but they have been joined in an impossible wway to create a triangle who's angle's add up to 270 degrees.The triangle appears three times in the picture. As one examines the building, it seems realistic, however, when it is examined as a whole, one can see the paradox of water travelling up a flat plane, yet the water is falling and spinning a miller's wheel, generating power from nothing.
The "Strange Loop" phenomenon occurs whenever, by moving upwards or (downwards) through the levels of some hierarchical system, we surprisingly find ourselves right back where we started. This theme occurs in Waterfall.
Beginning at the upper left part of the print, we see the water falling in a zig zag fashion down a gutter making the wheel turn. It then flows down a brick outlet-channel. If we look at the water, there is no doubting that it is moving down as it does according to the laws of gravity, and at the same time it recedes from our point of view, violating the laws of physics. Suddenly, the furthest and lowest points turn out to be identical with the highest and nearest point; therefore, the water is able to fall over and over again keeping the wheel turning- perpetual motion.
It seems as though the two towers are of equal height, but in reality the left is made up of three stories and the left has two. Why does Escher choose to have under water plant life greatly magnified to an above water garden?
The objects outside of the waterfall (overgrown water plants, and polyhedrons-aesthetic value- on the roof) strengthen the uncanniness of the print, and at the same time the viewer is drawn away from the pecularities by the images of the Southern italian terrace lanscape and the little house.
"Here is a perspective drawing, each part of which is accepted as representing a three dimenional, rectangular structure. The lines of the drawing are, however, connected in such a manner as to reproduce an impossibility. As the eye peruses the lines of the figure, sudden changes in the interpretation of the distance of the object from the observer are necessary."(Escher on Escher, p79,Penrose, The British Journal of Psychology, 1958)
A rectangular inner court of a cloister of some sort . It has a never ending circuit of 45 steps that allows the inhabitants, a secret sect of monks, to walk around the four levels to the top of the complex. It seems to be part of their daily ritual to ascend the stairway in a clockwise direction and when they are tired of that, they descend in the opposite direction. This ritual is useless because there is no progression. Each pace takes a monk a step higher, but after finishing the lap, the monk is back where he started from. Two stubborn members refuse to participate and instead sit outside of the court, for they see no use in the exercise, however, soner or later, they will realize there is nothing else to do but go with the crowd and conform.
Staircases that go in every which way with people walking in different directions on a single staircase. The staircases are "islands of certainty"(Hofstadter, p97) We shouldn't question them. We can't backtrack and check to see if they really are stairs. We have to not interpret, not symbolize and just accept. "In such worlds, the laws of biology, physic, mathematics, or even logic will be violated on one level, while simultaneously being obeyed on another, which makes them extremely wired worlds." (Hofstadter, p99)
Inhabitants of different worlds unaware of each other's existences because they have different perceptions of what is horizontal and what is vertical. Three gravitational forces operate perpendicularly to one another. Men are walking crossing on the floor and on the stairs-unaware of others.
There are sixteen tiny figures in this print divided among three groups what is a ceiling for one group is a wall for another and a door for one is a trap door for another. Divivding up ther three groups, we have the Uprighters, the figures at the bottom of the picturewalking up the stairs with their heads pointing upwards. The left-leaners have their heads pointing leftward and the third group is the Right-leaners. The structure of the print is in favor of the Uprighters because the viewer can follow their path more clearly.
There are three gardens. The Upright at the bottom of the picture can reach his by turning left up the stairs, and it is right through the archway shown with a big tree with a hot sun coming down on it. The banister in front of that garden does't connect, it seems almost if it is connected to the tree itself. If he wants to join either of his companions who flank on the left and right staircases, he can do so. Escher doesn't show us the ground on which the Uprighters stand only the ceiling in the top right corner. Quite frankly, the floor could descend for infinity.
In the center of the print, we see a Left-leaner sittng on a bench reading; and if he were to look up, he would see an uprighter climbing stairs infront of him and to his left, and to his immediate left, he would see a Right-leaner coming out of a cellar, hovering over the floor with a bag of coal.
The Right-leaner goes up the stairs, turns to the right, and climbs a second staircase, where he encounters one of his companions. However, there is someone on this stairway, a Left-leaner who is actually moving in the same direction up, yet he is going up downstairs, rather than up. The two stair climbers are at right in relation to each other.
It is implied how the all the Right-leaners can reach their gardens, but in the case of two Left-leaners, the one with a sack of coals on his back and the other with a basket. It seems that they are trapped without access to a garden, but usinfg their imaginations they could enter another world and take a short cut, or make their existence in another world.
Out of two of the three large staircases, the one on the far left and far right can be climbed on both sides. Bruno Ernst writes that this particular print would be useful to astronauts in that every plane in space has the ablity to become a ground at will, and that one needs to be prepared to encounter one's collegues in any arbitrary position without becoming overly confused.
The little happy man leaves his house, pouncing with glee down the stiars, unaware that he is to loose his 3 dimensionality and dissolve into a gray and flat geometric design amongst his white and black fellow creatures. The metamorphosis of this human figure to a geometric figure progresses to a tumbling and rotation, where the pattern used has "three axes of symmetry, and these are of three different types: that in which the three heads meet, that with three feet coming together, and one where three knees touch. At each one of these points the whole pattern can be mapped onto itself by rotation hrough an angle of 120 degrees." (The Magic Mirror of M.C. Escher, Ernst, p.39) The geometric figure evolves to a more basic design of diamond changing to a shape of a cube, which constitute the make up of hte house; and the patternis the same as the mosaics squares in the little courtyard. It appears that somehow, the image of the little man makes his way back the the house, and the whole cycle is continues.
This drawing inspired by the story of the invisible man, where the hero created this chemical potion which after he drank it, caused him to become invisible, and unsatisfied with the inconvenience, strives to become visble again, so he swahes his face with a bandage. Escher in this print, has two spirals, portraying a man and wioman's head, united in one endless strip. With their foreheads attached, they form together an indissoluble bond of union. Spheres floating mystically in front, in between and behind the interlocked strips of Eve and Adam, ideas of infinite tme and space arise.
In the background, on a gray wall, these human figures develop into contrasting and opposing and ultimately agreeable beings as they arrive at the center. Detaching theselves from the wall, a representative from each group, black and white, walk into space, paying heed to the deadly drop in the floor, which a few figures fall into.
Seemingly racial differences bring out the harsh, pessimistic, apelike characteristics of the dark figure who warns his counterpart, the joyful optimist who is more upright and boisterous. Both figures curving around the pit and encounter each other, finally shaking hands like real men, letting the evil tensions dissipate.
Interestingly enough, when this print was first reproduced, Escher's art dealer was reluctant to display it because the little white man looked like Colijn, a well known Dutch prime minister. Escher was oblivious to the resemblance.
Here the impossible building has been constructed. In the foreground, on the floor, lays a piece of paper with the edges of a cube drawn on it. Small circles indicate which of the two lines lies infront of the other, but it all depends on how one views the cube. The boy on the bench, holds a cuboid puzzle in his hands, which has contradicting top and bottom. Trying to figure out the cube, the boy is continually confused, and only if he were to examine the piece of paper, lying infront of his foot, would he understand how to view the puzzle. Moreover, the boy is sitting infront of a building that shows the same impossibility.
The eight pillars that hold the two stories together are peculiar because only the top far left and top far rightwork realistically. The other six continually connect the front side to the rear side, and in some way, they diagonally pass through the middle, and if the entranced merchant man placed his left hand on the next pillar, he would realize the perplea mystery. The woman leaning on the balustrade on the top floor, stares out in the direction of the longitudinal plane, while in relation to her,the wealthy man beneath her, faces at a right angle, inhaling the fresh mountain air.
The ladder in the center, is correctly drawn, according to the laws of perspective, and there is no doubt that as an object it is unrealistic. However, it stands with its base inside the building, and its top outside, therefore, the two persons on it are not harmonious with each other. The man in the middle of the ladder can't tell whether he is inside or outside the building. And the poor prisoner has been neglected by everyone,trapped in the dungeon below the impossible building has blown his mind. To divide the drawing in half, one would notice the normality of the picture, and see that it is truly this piecing together that creates the impossibility.