M.C. Escher – Biography He is most famous for his so-called impossible constructions , such as Ascending and Descending , Relativity , his Transformation Prints , such as Metamorphosis I , Metamorphosis II and Metamorphosis III , Sky & Water I or Reptiles . But he also made some wonderful, more realistic work during the time he lived and traveled in Italy. Castrovalva for example, where one already can see Escher's fascination for high and low, close by and far away. The lithograph Atrani , a small town on the Amalfi Coast was made in 1931, but comes back for example, in his masterpiece Metamorphosis I and II . M.C. Escher, during his lifetime, made 448 lithographs, woodcuts and wood engravings and over 2000 drawings and sketches. Like some of his famous predecessors, - Michelangelo, Leonardo da Vinci, Dürer and Holbein-, M.C. Escher was left-handed. Apart from being a graphic artist, M.C. Escher illustrated books, designed tapestries, postage stamps and murals.

He was born in Leeuwarden, the Netherlands, as the fourth and youngest son of a civil engineer. After 5 years the family moved to Arnhem where Escher spent most of his youth. After failing his high school exams, Maurits ultimately was enrolled in the School for Architecture and Decorative Arts in Haarlem. Escher in Rome, Italy - 1930. Escher with wife, Jetta on beach in Italy - 1924. Escher in Ravello, Italy - 1925. After only one week, he informed his father that he would rather study graphic art instead of architecture, as he had shown his drawings and linoleum cuts to his graphic teacher Samuel Jessurun de Mesquita, who encouraged him to continue with graphic arts. After finishing school, he traveled extensively through Italy, where he met his wife Jetta Umiker, whom he married in 1924. They settled in Rome, where they stayed until 1935. During these 11 years, Escher would travel each year throughout Italy, drawing and sketching for the various prints he would make when he returned home.

Many of these sketches he would later use for various other lithographs and/or woodcuts and wood engravings, for example the background in the lithograph Waterfall stems from his Italian period , or the trees reflecting in the woodcut Puddle , which are the same trees Escher used in his woodcut " Pineta of Calvi ", which he made in 1932. M.C. Escher became fascinated by the regular Division of the Plane, when he first visited the Alhambra, a fourteen century Moorish castle in Granada, Spain in 1922. During the years in Switzerland and throughout the Second World War, he vigorously pursued his hobby, by drawing 62 of the total of 137 Regular Division Drawings he would make in his lifetime. He would extend his passion for the Regular Division of the Plane, by using some of his drawings as the basis for yet another hobby, carving beech wood spheres. He played with architecture, perspective and impossible spaces. His art continues to amaze and wonder millions of people all over the world. In his work we recognize his keen observation of the world around us and the expressions of his own fantasies. M.C.

Escher shows us that reality is wondrous, comprehensible and fascinating. Painting after M.C. Escher - M.C.Escher's Legacy. A Centennial Celebration - Impossible world M.C.Escher's Legacy. A Centennial Celebration Painting after M.C. Escher Jos de Mey My title has dual significance : painting "after", or "from" Escher, and painting "as" Escher. At the outset, it should clearly be pointed out that M.C.Escher did not make any paintings during his professional career as an artist. His complete works are limited to drawings and prints - lithos, woodcuts and wood engravings, some rare etchings, and a few that use other printing techniques. Although there were some commissioned designs for public buildings that involved painting panels or walls, paintings, by which I mean artworks designed and painted on canvas, panel, or paper, simply do not exist. That does not mean, however, that M.C. Escher hasn't influenced artists in general or any painter in particular. In light of these observations, "painting as Escher" isn't really an appropriate theme for my essay. So how about painting "after" or "from" Escher?

After having observed all the adapters of Escher I know, I find that there are few painters among them. Artists working with paint on canvas or panel seem to practise almost exclusively the pure non-figurative genre. I believe (if I'm not mistaken) this kind of art would not have been appreciated by Escher. I'm even convinced of the fact that if the meticulous Escher had ever painted, his technique would certainly have had similarities with mine. Carelessness in brush technique, neglecting details, negligent composition of materials, erroneous usage of colors - these would never have ocurred in the hypothetical works of Escher. (Although I've heard or read somewhere that Escher was partly color-blind!) Lacking directly comparable paintings, I decided to search for basic figures that Escher and his followers used when composing 'impossible pictures'. I purposely use the term "composing" here. Neither the works of Escher nor his followers are thrown impulsively on canvas. Thinking through the composition thoroughly and trying it out in several preliminary studies are indispensable ingredients in the birth of an Escherian work. The potential for making 'impossible' pictures is limited: they depend on fairly rare geometric configurations.

Escher (and others) borrowed most of the basic figures from others, reworking them into concrete, figurative forms. This is where we touch on the thorny problem of the boundary between exact (theoretical) science and art. Or to put it as a question: when does a scientific model become art? The solution to this problem I leave to specialized art critics but I would certainly like to point out that few (or perhaps no) scientific theorists have ever produced art of quality. By now I think it has become clear to you, respected reader, that my essay is restricted to impossible figures or impossible constructions. However, my introduction to the works of Escher had nothing to do with impossible figures. The Path to Painting Impossible Figures In 1956, in the Museum of Applied Art in Ghent (Belgium), I saw a series of Escher's prints. Among them were Dewdrop, Rippled Surface, and Puddle, which made a deep impression on me (Fig. 1; [1, cat. no. 367]). Reflecting the attitude of official art authorities towards Escher's work, this first and only exhibition of M.C.

Escher in Ghent was not shown in the Museum for Fine Art, but in the Museum for Ornamental or Applied Art. Fig. 1. M.C. Escher, Dewdrop, 1948. Mezzotint At that time, design (of furniture) was still my main occupation. I also held a strong, rather theoretical, interest in painting and sculpture. Three years later, in 1959, I read the famous Penrose's article in the British Journal of Psychology, in which they exhibited the impossible tribar and other impossible constructions. This first contribution about impossible figures would later become an important influence in my decision to exchange interior architecture and design for the risky profession of a painter. As a lecturer at the Royal Academy of Fine Arts and later at the Higher Institute for Architecture, I was, apart from being a teacher of interior architecture and furniture design, also responsible for classes on the theory of color and on design technique. The mathematical basis of harmony of forms in art was always in the forefront of these subjects. The possible applications of Fibonacci series, the Golden Ratio, and other mathematical-aesthetical systems were discussed in this course, organised as a discussion-forum.

We focused especially on the Swiss group of "Concrete Kunst:" Max Bill, Karl Gestner, and Richard P. Lohse (see [4]). It was also there that I began to take an interest in the boundary between art and science. Several antipodal ideas arise in the search for this difficult limit: picturesque versus pictural (or the colorful scene versus the art of painting) the means versus the objective the basic scheme versus the result the technique versus the art mathematical art or artistic mathematics. (See [8] and [9].) When I decided in 1968 to leave interior architecture and design for the free art of painting, I wanted to depict things that can only exist as "picture". What I was going to depict in my drawings and paintings had to be infeasible or unrealizable. So I inevitably arrived at Impossible Figures. This was probably a reaction to my previous compelling duty to always draw things that techniquely and spatially had to be 'correct', 'measurable', and 'realisable'. A first basic scheme was the famous dual stairs (Fig. 2) of which I drew and painted a series of variations for a whole year (Fig. 4).

The next step was the Thiéry figure of 1895, some variations of which are reproduced in Fig. 5. A typical application of the Thiéry figure is at the right of Fig. 6: my 1972 Ode to architect J. Hoffmann number 10/38. Fig. 2. The dual stairs or "Schröder's Steps". This drawing was the inspiration behind Escher's lithograph Convex and Concave The Escher lithograph Convex and Concave (Fig. 3) plays with the dual stairs and the kind of Thiéry figure that is reproduced on the flag at top right in the print. Escher explained this convex/concave dichotomy in a letter to his son Arthur in 1954: Convex and Concave ... is concerned with the widely known phenomenon of spatial suggestion which can be imagined as convex or concave, as desired. In the middle of the picture I draw the shapes in such a way that the observer may just as well see them convex as concave; to the right I force him to see things in a convex way (e.g.

"cube from the outside"; to the left, he has to view things in a concave way ("cube from the inside"). [1, p. 79] Fig. 3. M.C. Escher, Convex and Concave, 1955. Lithograph On further consideration, one could suggest that the Thiéry figure in perspective was used as a starting point for the 1947 Escher lithograph Up and Down. The small floor a little above the middle of the picture is the double-use surface in the Thiéry figure; here it is simultaneously a floor or ceiling. Fig. 4. Jos De Mey, variations on the "Schröder's Steps", 1969 All the works from the early years of my painting career are abstract and very often reversible, both horizontally and vertically. Later I made more realistic reproductions, still with the abstract "things" but now resting on firmer ground. The base component from that period is the impossible cube, which also appears frequently later on. In Escher's vignette Man with Cuboid , this cube is not completely impossible. It still shows two normal faces - the bottom and the top (Fig. 6a). Fig. 5.

Jos De Mey, different variations on the Thiéry figure from 1895 and (right) drawing Ode to Architect J. Hoffman, 1972-1973 Around 1975 I drew several new versions of the cube in which all the surfaces were impossible. And even better: there are no longer any real clear-cut surfaces. All the aspects of the cube flow into one another. It could be described as a Möbius strip in the form of a cube (Figs. 6b and 7). I'm probably not the inventor of this fully impossible version, but in 1975 I was aware only of Escher's drawing and interpretation. Fig. 7. Jos De Mey, Die Unterweisung der Messung und seine Folge (The result of the theory of measuring) (after A. Dürer), 1988. Acrylic on canvas Eschers Influence There are only a few prints by Escher that can be related directly to my works. The most important is Belvedere for which the impossible cube served as a starting point (Fig. 8).

The small man on the bench contemplating the absurd cube in his hands, as well as the sketch in the foreground on which the ribs of a cube are drawn with their hazardous crossings, are the keys to understanding this enigmatic construction. Fig. 8. M.C. Escher, Belvedere, 1958. Lithograph Closely related to the impossible cube is the normal cube with impossible connections (Fig. 9a). I'm not acquainted with any works of Escher based on this impossible figure. That's why two of my works reproduced here give reference to other artists (Figs. 9b and 9c). Fig. 9. Jos De Mey. (a) A normal cube with impossible connections, 1976. (b) Souvenir of Margriet, 1977. Acrylic on canvas. (c) Rather Illogical Architecture - Surrounds for a Very Logical Figure of Max Bill, 1998. Drawing Apart from the impossible cube we can also make the impossible square and the impossible rectangle (Figs. 10a, 10b). As far as I know Escher used neither of these figures in his works.

Some of my works utilize this motif, appearing in several variations, frontally as well as in perspective (Fig. 11). Fig. 10. (a) Two variations of the impossible square. (b) An impossible four-beam figure with a perspective effect. (c) An impossible four-beam figure with impossible connections We have seen that apart from the completely impossible cube there can exist also a possible cube with impossible connections. That is also true for the impossible rectangle where a possible rectangle with impossible connections can be devised (Fig. 10c). Fig. 11. Jos De Mey, Curious Wagtail in a Strange Small Window, 1977. Acrylic on canvas. Finally there is the impossible triangle of the Penroses, already mentioned above, and also a little bit from Oscar Reutersvärd. Escher used this feigned triangle as a starting point for his 1961 lithograph Waterfall . The great number of preliminary studies [3, p. 89] show the long and difficult process Escher went through before he finally obtained a clear image of his idea. My own drawings based on the impossible triangle (Fig. 12) are much more simple than Escher's intricate picture. Fig. 12.

Jos De Mey. LEFT: An Awkward Drilling Platform, 1987-1990. RIGHT: A Latent Threat for an Unstable Construction, 1995. Ink drawings To make the series of basic figures complete I would like tomention so-called "multiple surfaces". That term was invented by Bruno Ernst (Hans de Rijk) to be able to interpret my works better [2]. He states "a multiple surface looks in a certain place in a drawing or painting like only one flat surface; put in another place in that same picture it is like two or more flat surfaces. This is the oldest type of impossible figure (i.f.) that was , often unintentionally and unconsciously, put into the pictures". [2, p. 62] Fig. 13. Bruno Ernst, the history of a multiple surface, 1986 In Fig. 13, you can see Ernst's depiction of how this can originate. In my ink drawing of 1983 (Fig. 14) there is only one surface on the upper part of the wall.

This surface multiplies itself on the ground to four walls that stand at different distances from the viewer and that enclose a rather large space like a summerhouse. Fig. 14. Jos De Mey, Carefully Restored Roman Ruin in a Forgotten Flemish Locality with Oriental Influences, 1983. Ink drawing My last two illustrations (Fig. 15) give a glimpse of my design technique. These drawings show how, beginning with a scheme of Reutersvärd, I finally reach an apparently possible pictural figure by reversing, broadening, and narrowing, then finally by using perspective with the viewing angle that of a standing person's eye. That final figure could be used as a basis for a painting or an elaborated drawing. Fig. 15. Jos De Mey, starting from a scheme of Reutersvärd, developing into painting projects, 1991 Some Final Thoughts It is probably useful at this point to quote Escher himself, "Always try to do that which seems too difficult for you; try to exceed your supposed limits". (from a letter to his son George on June 29, 1969) [10].

Escher always wanted to do just that: what was, in fact, too difficult. Was it ambition? Yes, but not primarily that. It was a typical inner passion that is so characteristic of the real artist. His willpower, his stubborn perseverance and his enormous skill made it possible for him to convert visionary images into clear images. It was often at the expense of sleepless nights and eternal experimenting in order to finally achieve the fragile balance between inner rest and creative expression. He was looking for balance but always preserving emotions. Escher also always tried to bridge the opposition between abstract and figurative. His works (and also mine) are figurative in form but abstract in meaning. In other words: a figurative representation of abstract ideas. In a lecture in Amsterdam in 1963 he explained that subtlety is also necessary. "In my opinion an impossible situation only really stands out when the impossibility is not immediately obvious... There should be a certain mysteriousness that does not immediately hit the eye". [1, p. 147] The link between Escher and the scientific world was his insatiable urge to know everything. In this he resembled what a scientific investigator should be.

Escher and his adapters belong to the category of "thinking artists" such as many great artists before them were and many still are. These are artists who investigate systematically the surounding world in an artistic-methodical way. The strong need for studying the phenomenon of human perception is another characteristic that Escher and his followers have in common. In this, they put the liability of that perception in perspective. Without M.C. Escher, my works as well as those of many other artists would certainly have been completely different. Nevertheless I think I can say that I have been using enough different pictural elements and techniques to distinguish my paintings clearly from the works of Escher. My intention is to elaborate his ideas, using new approaches and a more painted elaboration. The architecture, the scene, the figuration, and the application of colors in my works are strongly related to my own Flemish present and past. It is striking that Escher rarely made use of Dutch scenery. Apart from Day and Night with its bird's-eye view of a typical Dutch landscape, his architecture, scenery, and figuration are almost exclusively southern, and in particular, more Italianesque. I especially try to respect Escher's attitude towards art.

His searching for exactitude and the best possible technical quality when conceiving and realising his works have always been an example for me. I also want to express my gratitude to Bruno Ernst who has often helped me with his analytical understanding and comments on the things that I instinctively put on paper or canvas. I also want to emphasize strongly that I am not, even less than Escher was, a practitioner of exact science. If I was, I would never make any art, even less paint... Fortunately there are scientists who are interested in art. Science can, to a certain extent, be considered as art. I see myself as an artist with a certain interest in science. I'm probably a scientific artist but I'm certainly not an artistic scientist. References F.H. Bool, J.R. Kist, J.L. Locher, F. Wierda, M.C. Escher, His Life and Complete Graphic Work, Harry Abrams, 1982.

Escherian Stairwell : snopes.com Escherian Stairwell Claim: Video documents the existence of a never-ending "Escherian Stairwell." FALSE Example: [Collected via e-mail, May 2013] I would like to know if the Escherian stairwell located in the RIT is actually a never-ending stairwell or just a camera trick. Origins: In April 2013, Internet users were puzzled and amazed by a video from the Rochester Institute of Technology (RIT) purportedly documenting the existence of a so-called 'Escherian Stairwell' (named for the Dutch graphic artist M. C. Escher , famous for his "impossible reality" artworks, such as the never-ending Penrose Stairway ) which "violates the laws of physics and basic logic by looping back into itself." As described in a 30 April 2013 article published on RIT's web site, the video showing off the unusual stairway was supposedly the third installment of a "Can You Imagine" series about "interesting facts, stories and myths of RIT": Is it possible for a staircase to violate the laws of physics and basic logic by looping back into itself?

This is one of the questions Michael Lacanilao, a film and animation graduate student at RIT, examines in his video series and Imagine RIT exhibit The Escherian Stairwell. Lacanilao created the video series, "Can You Imagine," to highlight the many interesting facts, stories and myths of RIT. The exhibit, located in Artistic Alley in Gannett Hall room A171, will help festivalgoers search for the stairwell and give them a behind the scenes look at "Can You Imagine." "Four years can go by quickly and a lot of us don't have the time to learn about all the things that RIT does and offers," says Lacanilao. "When we take the time to venture outside our daily routines, we find that it really is the place where the left brain and right brain collide. I'm proud to be a part of that." Quite obviously no physics-defying "Escherian Stairwell" exists in the real world.

The video was a bit of trickery created through the use of deceptive camera angles, careful editing, and digital effects, produced in conjunction with a (failed) Kickstarter campaign ("The Stairwell Project: Building a Modern Myth") intended to help fund the creation of videos, articles, web pages, and other material establishing a backstory for the mythical stairway in time for Imagine RIT, the school's annual Innovation & Creativity Festival: The most powerful aspects of myths are their ability to incite wonder and excitement. We're creating a myth that does these things while also challenging audiences to think. The myth is that located in Rochester, NY, is the Escherian Stairwell, an architectural marvel that seems to violate the laws of physics and basic logic by looping back into itself. In order to lend credence to this myth, we're creating an episode for a family-friendly science show that demonstrates the staircase in action, various clips from a 1997 documentary with prominent thinkers grappling with the existence of this apparent contradiction and pontificating on its implications, and a whole slew of supplemental online materials for today's internet savvy audience to stumble across while trying to see if this thing is real (websites, scholarly articles, fan-pages, blogs, etc.).

Help us build the myth! We are passionate about immersing audiences with a sense of wonder and surrounding them with a wealth of detail executed with such rigorous realism that they can choose to step into it, get lost in it, and believe in it. Films like Close Encounters and 2001 inspired us with awe, and even a hint of fear, when we first saw them. How do we capture that feeling again? The internet and the age of social media seem to be opening up doors to reinvent the medium and reignite those in-theater experiences that have gotten stale over the decades. The following video features an explanation of the intent behind the Kickstarter campaign: Last updated: 2 October 2015 Snopes Delivered to Your Inbox: Sign Up The Principles of Artistic Illusions THE PRINCIPLES OF ARTISTIC ILLUSIONS Copyright � Donald E. Simanek, December 1996 Illusory works of art have a curious fascination. They represent a triumph of art over reality. They are illogic masquerading as logic. Why do illusions capture our interest? Why have so many artists gone to the trouble to produce them?

Mountain climbers say they scale mountains "because they are there." Perhaps we seek illusions because they aren't there. Waterfall by M. C. Escher. We have all admired the lithograph Waterfall by Maurits C. Escher (1961). His waterfall recycles its water after driving the water wheel. If it could work, this would be the ultimate perpetual motion machine that also delivers power! If we look closely, we see that Mr. Escher has deceived us, and any attempt to build this structure using solid masonry bricks would fail. All M. C. Escher works � - Cordon Art B. V. - P.O. Box 101-3740 Ac - Baarn - The Netherlands. All rights reserved. M.C. Escher (TM) is a Trademark of Cordon Art. Used by permission. ISOMETRIC DRAWINGS Two-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. But the method can also be used to create pictures of spatial relationships impossible in the real three dimensional world.

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 to 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 ILLUSION One 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 proper perspective 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. Mach's figure, or the open book illusion, can be the basis of even more deception. This construction shows the intimate symbiotic relation between mathematics and physics.

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. 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. They call it the 'Escher' 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! PHOTOGRAPHING ILLUSIONS The crazy crate cannot be made of lumber. Yet the photograph shown here is of something made of lumber, something that certainly looks like the crazy crate. It is a cheat. One piece, that seem to pass behind another, is actually two pieces with a break, one nearer, one farther than the crossing piece.

This only seems to be a crate from one particular viewing point. If you looked at the real thing from near this point, your stereoscopic vision would give the trick away. If you moved your head away from the viewing point for which it was designed, you'd see the trick. In museum displays of this you are forced to look through a small hole in a wall, using only one eye. To make such a photograph, one has to engage in deception. If an ordinary camera is used, the more distant lumber pieces subtend a smaller angle than the nearer ones. So the more distant ones must be made physically larger, and those that have one end nearer than the other end must be tapered in size from one end to the other. There's another way to accomplish this for smaller objects. The small model below left is made of plastic Quobo ® bricks, 1 cm high. The entire model is over 7 cm high. Notice that there's a size disparity where the nearer yellow horizontal tier touches the more distant red brick. But in the picture to the right, there is no size difference there.

Note also in the picture to the right, that all bricks subtend the same angle, opposite edges of the green base are parallel and all other parallel lines of the model are parallel on the picture. This is an isometric photograph. The normal photo on the left shows the chair and lamp behind, as well as other clutter of a small workroom. It was taken with a digital camera with the subject only about 30 cm from the lens. The photo on the right was taken with the same camera, and approximately the same subject distance. But a telecentric optical system was used, consisting of a large 13 cm diameter lens placed with its focal point very near the camera's own lens. This particular large lens didn't have high quality (it was molded, not polished), so the resolution of the picture is poorer. Such systems suffer from the problem that any dust or scratches or other defects on the lens can show in the final picture. Use of a single lens also produces "pincushion" distortion that renders straight lines as slightly curved. Telecentric lens systems of high quality are used in industry for product inspection, and in microscopy, for increased depth of focus (DOF).

They are limited to photographing small objects smaller than the diameter of the front surface of the lens. See: Telecentric systems . For some subjects one can "get away" with this kind of deception by using a telephoto lens of high magnification and placing the subject very far away from the camera. AMBIGUOUS CONNECTIVITY Some 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. 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 SHAPE Our judgment of shapes can be fooled when a dominating background pattern is present. The example below is similar to the Zöllner, 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.

Check them on the printed copy with a ruler.] 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. You can also superimpose a circle on a pattern of squares. Perfectly straight and parallel lines superimposed on a pattern of radial lines seem to be curved, and the strength of the curvature depends on how near the straight line is to the center of the radiating lines. This is one of the Herring illusions. ILLUSIONS OF SIZE. Though the two circles in the figure below 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. You be the judge. The width of the brim of this hat is the same as the hat's height, though it doesn't seem so at first. This is the classic "plug hat" illusion. Try turning the picture on its side. Is the illusion the same? This is an illusion of relative dimensions within a picture, which is a distortion of shape. A related illusion is observed in 3d. Find a drinking glass, pill bottle or other cylindrical container. The "zombie" glasses are perfect for this demonstration as a "bar bet". Try to judge by eye whether the cylinder's circumference is larger or smaller than its length. With a tape measure or just a piece of ribbon, string or tape, measure the circumference. Then lay off the ribbon along the length. You may be surprised, for we usually judge the length to be greater then the circumference—until we measure them. The picture shows several cylindrical containers that can be used to demonstrate this illusion. The 26 oz peanut can on the left shows the illusion very well.

The length of the vertical red twist-tie (from supermarket lettuce) is exactly equal to the can's circumference. This can be verified by wrapping it around the can. The other containers include common prescription pill bottles. All of these illustrate the fact that our visual judgment of length is flawed. We just can't visually compare lengths of lines of different shape reliably. The clearest demonstration of this is shown here. Which is longer, the straight line AB, or the circumference of the circle B? Most will judge the straight line to be much longer. But we have drawn them to be nearly equal in length. This simple figure is seldom mentioned in the discussions about illusions. ILLUSIONS OF ALIGNMENT The Poggendorf illusion, or 'crossed bar' illusion invites us to judge which line, A or B, is aligned exactly with C. A good ruler can be used on the printed copy to check your answer. AMBIGUOUS ELLIPSES Tilted 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. Ambiguous Ring, � Donald E. Simanek, 1996. Cover about one third of the picture at either end, and the rest of the picture looks like part of a normal ring or washer. This may remind you of a Möbius strip model made by giving a paper strip a half twist and joining the ends. But this is different. Two colors have been used, for this figure, unlike a Möbius strip, has two faces. You may wish to think of this as a Möbius strip model made from thick, flexible material, its face one color and its edge another color. One reader says this isn't an illusion, for you can make one of flexible material, and he mailed me a model made from foam strip. However, while you can do this with a strip of square cross section, my illusion above seems to have a rectangular cross section. The wide face magically morphs into a narrower face.

That is the subtle aspect of this illusion that most people don't notice right away. He makes a valid point, however, he'll have to go to a lot more trouble to make each face change width as you go around 180°. When I devised this picture I thought that it might be an entirely original illusion. But then I noticed an advertisement with the corporate logo of the Canstar corporation [above left], a manufacturer of fiber optics. This is another case of two great minds independently inventing the non-existent wheel! If we dig deeply enough, we'd probably find even earlier examples. Now [October 2003] I find this ring illusion [above right] on the web, without any credit to me, even though the proportions and layout match mine perfectly. At the site where I found this version, there was no clue who drew it. Such is the Internet. If the person who borrowed this idea will come forward, I'll acknowledge that person here. At least it indicates that someone was taken by the idea. I have changed the color of the version I found, because I considered it ugly. Impossibly linked ambiguous rings. © 2004 by Donald Simanek.

Finally [Dec, 2004], this illusion evolves into something more interesting. Here two ambiguous rings are ambiguously linked. All of these illustrations are available in higher-resolution versions on request. Readers have suggested several names or captions for it: "the interconnectedness of everything," "a new atomic theory," "tying mental knots," "super-colliding synchronous orbitals," "illusory quantum entanglement," (I like that one.) and "virtual unreality." 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. Our version is identical to that of the Penrose paper, except for its lack of shading. 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. Ascending and Descending by M. C. Escher. 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. One task artists have not yet successfully addressed is to draw an illusion picture with its shadow. Just as shading could kill an illusion, its shadow could also give away the illusion. Possibly an artist could be clever enough to place the light source in such a location that the shadow would be consistent with the rest of the picture. Maybe the shadow could become an illusion itself! The possibilities boggle the mind. SEEING ILLUSIONS Some persons look at these illusion pictures and are not at all intrigued. "Just a mis-made picture", some will say. Some, perhaps less than 1 percent of the population, do not 'get' the point because their brains do not process flat pictures into three dimensional images. These same persons have trouble with ordinary engineering line drawings and textbook illustrations of three dimensional structures. They also can't perceive depth in 3D stereoscopic pictures and 3D movies. 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. Display Case For Illusions,

Question: Who famously painted endless staircases and other impossible constructions?
Answer: M. C. Escher