At the start of the lesson we were put into groups of five and given a word to base our research on. The word we received was 'Deception.' As a group we discussed and made a list of words that we could research.
- Small print
- Claire Voyant
- Visual Deception
We each had to pick a word to research and I chose 'Visual Deception'.
I am going to ask people a set of ten questions that tests peoples ability to solve visual illusions and to see how different peoples brains work.Some of the questions have no right or wrong answer, they are designed to see how people perceive things differently. The questions are as follows:
Others can see that `something is wrong' with the picture, but are not fascinated enough to inquire how the deception was accomplished. These are people who go through life never quite understanding, or caring, how the world works, because they can't be bothered with the details, and lack the appropriate intellectual curiosity.
It may be that the appreciation of such visual paradoxes is one sign of that kind of creativity possessed by the best mathematicians, scientists and artists. M. C. Escher's artistic output included many illusion pictures and highly geometric pictures, which some might dismiss as `intellectual mathematical games' rather than art. But they hold a special fascination for mathematicians and scientists.
It is said that people in isolated parts of the world, who have never seen photographs, cannot at first understand what a photograph depicts when it is shown to them. The interpretation of this particular kind of visual representation is a learned skill. Some learn it more fully than others.
Historically, artists learned geometric perspective and used it long before the photographic process was invented. But they did not learn it without help from science. Lenses became generally available in the 16th century, and one early use of lenses was in the camera obscura. A large lens was put in a hole in the wall of a darkened room so that an upside down image was cast on the opposite wall. The addition of a mirror allowed the image to be cast onto a flat floor or table top, and the image could even be traced. This was used by artists who experimented with the new `European' perspective style in art. It was aided by the fact that mathematics had developed enough sophistication to put the principles of perspective on a sound theoretical basis, and these principles found their way into books for artists.
It is only by actually trying to make illusion pictures that one begins to appreciate the subtlety required for such deceptions. Very often the nature of the illusion seems to constrain the whole picture, forcing its `logic' on the artist. It becomes a battle of wits, the wit of the artist against the strange illogic of the illusion.
ISOMETRIC DRAWINGSTwo-dimensional drawings (on a flat surface) can be made to convey an illusion of three dimensional reality. Usually this deception is employed to depict real, solid objects in spatial relationships achievable in our world of sensory experience.
The conventions of classical perspective are very effective at simulating such reality, permitting `photographic' representation of nature. This representation is incomplete in several ways. It does not allow us to see the scene from different vantage points, to walk into it, or two view objects from all sides. It does not even give us the stereoscopic depth sensation that a real object would have due to the lateral separation of our two eyes. A flat painting or drawing represents a scene from only one fixed viewpoint, as does an ordinary monocular photograph.
One class of illusions appears at first look to be ordinary `perspective' renderings of solid, three dimensional objects or scenes. But on closer examination, they reveal internal contradictions such that the three dimensional scene they depict could not exist in reality. These pictures have a special fascination for those of us used to the convention of depicting nature on a flat surface of paper, canvas, or in a photograph.
Isometric illusory art was created as early as 1934 by Swedish Artist Oscar Reutersvärd with the impossible arrangement of blocks shown here. The colors in this version are not to be blamed on Oscar. This design has been widely used, and even appears on a Swedish postage stamp.
THE PENROSE ILLUSIONOne particular example of the Reutersvard illusion is sometimes called the `Penrose' or `tribar' illusion. Its simplest form is illustrated here.
The picture appears to depict three bars of square cross section joined to form a triangle. If you cover up any one corner of this figure, the three bars appear to be fastened together properly at right angles to each other at the other two corners–a perfectly normal situation. But now if you slowly uncover a corner it becomes apparent that deception is involved. These two bars that connect at this corner wouldn't even be near each other if they were joined properly at the other two corners.
The Penrose illusion depends on `false perspective,' the same kind used in engineering `isometric' drawings. This sort of illusion picture displays an inherent ambiguity of depth, which we will call `isometric depth ambiguity.'
Isometric drawings represent all parallel lines as parallel on the flat page, even if they are tilted with respect to the observer in the actual scene. An object tilted away from the observer by some angle looks the same as if were tilted toward the observer by the same angle. A tilted rectangle has a two-fold ambiguity, as demonstrated by Mach's figure (right), which may be seen as an open book with pages facing you, or as the covers of a book, with the spine facing you. It may also be seen as two symmetric parallelograms side by side and lying in a plane, but few people describe it that way.
The Thiery figure (above) illustrates the same artistic deception.
Schroeder's reversible staircase illusion is a very `pure' example of isometric depth ambiguity. It may be perceived as a stairway that one could ascend from right to left, or as the underside of a stairway, seen from below. Any attempt to draw this with vanishing points would destroy the illusion.
The illusion can be enhanced by adding recognizable figures, as in the version at the right is © 2001 by John C. Holden. It should carry an OSHA warning: Caution: Illusory stairways can be hazardous.
The simple design below looks like three faces of a string of cubes, seen either from the outside, or the inside. If you put your mind to it, you can see them as alternating: inside, outside, inside. But it's very hard, even if you try, to see at as simply a pattern of parallelograms in a plane. This is the same as the `tumbling blocks' design sometimes used in quilts.
Blackening some facets enhances the illusion, as is shown below. The black parallelograms at the top are seen either as from below, or from above. Try as hard as you can to see them as alternating, one from below, one from above, and so on, left to right. Most people can't. Why should we be unable to do this?
The design at the right uses the tribar illusion relentlessly in strict isometric drawing style. This is one of the `hatching' patterns of the AutoCAD (TM) computer graphics program. It is called the `Escher' hatching pattern.
The isometric wire-frame drawing of a cube (below left) shows isometric ambiguity. This is sometimes called the Necker cube. If the black dot is on the center of a face of the cube, is that face the front, or the rear face? You can also imagine the dot is near the lower right corner of a face, but still you can't be sure if it is the front or rear face. You have no reason to assume that the dot is in or even on the cube, but might be behind or in front of the cube, since you have no clue to determine the relative size of the dot.
If the edges of the cube are given a suggestion of solidity, as if the cube were made of wooden 2x4s nailed together, a contradictory figure results. But here we have used ambiguous connectivity of the horizontal members, which will be discussed in the next section. This version is called the `crazy crate'. Perhaps it would serve as as the frame to build a shipping crate for illusions. Nailing the plywood faces onto the frame to complete the crate would be a real challenge, but necessary to keep the illusions from falling out!
AMBIGUOUS CONNECTIVITYSome illusions depend on the ambiguous connectivity possible in line drawings. This three (?) tined fork above is sometimes called Schuster's conundrum. It can be drawn in perspective, but natural shading or shadowing would destroy the illusion.
What's the basis of this illusion? Is this a variation on Mach's `open book' illusion? Certainly the drawing is isometric.
Actually this is a combination of Mach's illusion and ambiguous connectivity. The two books share a common front cover. This makes the tilt of the book cover even more ambiguous.
Some use the general term undecidable figure to describe these pictures. That term is so broad that it could be applied to nearly all illusions.
Here's an illusory musical tuning-fork, with only two tines. The figure on the right shows its perspective, with vanishing points.
ILLUSIONS OF SHAPEClosely related to alignment illusions are those where a dominating pattern alters our judgment of a geometric shape. The example below is similar to the Zoelner, Wundt, and Herring illusions in which the pattern of short diagonal lines distorts the long parallel lines. [Yes, the horizontal lines are perfectly straight and parallel.
These illusions take advantage of the way our brains process information containing repeating patterns. One regular pattern can dominate so strongly that other patterns appear distorted.
A classic example is the pattern of concentric circles with a superimposed square. Though the sides of the square are absolutely straight, they appear curved. The straightness of the square's sides may be checked by laying a ruler along them. This effect is found in many illusions of shape.
The same principle is at work in this example. Though the two circles are exactly the same size, one looks smaller. This is one of many illusions of size. It is a close relative of the "Ponzo Illusion".
Some have explained this illusion as a result of our experience with perspective in photographs and works of art. We interpret the two lines as `parallel' lines receding to a vanishing point, and therefore the circle not touching the lines must be nearer, and hence larger.
The same picture is shown (above right) with darker circles, and the parallel lines have become part of dark triangles. If the `receding parallel line' theory were correct, this illusion should be weaker.
The width of the brim of this hat is the same as its height, though it doesn't seem so at first look. This is an illusion of relative dimensions within a picture, which is a distortion of shape.
ILLUSIONS OF ALIGNMENTThe Poggendorf illusion, or `crossed bar' illusion invites us to judge which line, A or B, is aligned exactly with C.
AMBIGUOUS ELLIPSESTilted circles appear as ellipses. Circles drawn in perspective appear on the page as ellipses, and ellipses have an inherent ambiguity of depth. If this figure represents a circle seen tilted, there's no way to tell whether the top arc is nearer or farther than the bottom arc.
Improper connectivity is also an essential element of this ambiguous ring illusion:
And here's a more elaborate version of it.
Cover about one third of the picture at either end, and the rest of the picture looks like part of a very normal ring or washer. Only two colors have been used, for this figure, like a Möbius strip, has only two faces. Or you may wish to think of this as a Möbius strip made from very thick, flexible material, with the face one color and its edge another colour.
|Impossibly linked ambiguous rings. © 2004 by Donald Simanek.|
THE ENDLESS STAIRCASE
The other classic Penrose illusion is the impossible staircase. This illusion is often rendered as an isometric drawing, even in the Penrose paper. The color version to the right allows you to follow a particular color on a step through the layers below. You discover that there aren't enough layers for all the steps.
This could be drawn with vanishing points in full perspective. M. C. Escher, in his 1960 lithograph Ascending and Descending, (above) chose to construct the deception in a different manner. He placed the staircase on the roof of a building and structured the building below to convey an impression of conformity to strong (but inconsistent!) vanishing points. He has the right vanishing point higher than the left one.
An optical illusion (also called a visual illusion) is characterized by visually perceived images that differ from objective reality. The information gathered by the eye is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. There are three main types: literal optical illusions that create images that are different from the objects that make them, physiological ones that are the effects on the eyes and brain of excessive stimulation of a specific type (brightness, colour, size, position, tilt, movement), and cognitive illusions, the result of unconscious inferences.
As the square rotates, we only see the part of it not covered by the grid. It appears to grow and shrink in its roatation, as if it were breathing!