The Shepard elephant, also known as L'egs-istential Quandary or the impossible elephant is an optical illusion, of the type impossible object, based on figure-ground confusion. As its creator Roger Shepard explains: [1]
The elephant…belongs to a class of objects that are truly impossible in that the object itself cannot be globally segregated from the nonobject or background. Parts of the object (in this case the elephant’s legs) become the background, and vice versa.
Shepard first published this optical paradox in his 1990 book Mind Sights (page 79) giving it the name "L'egs-istential Quandary". [2] It is the first entry in his chapter on "Figure-ground impossibilities". The pen-and-ink drawing is based on a dream Shepard had in 1974, and on the pencil sketch he made when he woke up. [2]
The image is widely reproduced and discussed. Brad Honeycutt, author of Exceptional Eye Tricks, calls the Shepard elephant "one of the most famous and classic optical illusions." [3]
The MIT Encyclopedia of the Cognitive Sciences classifies it under "Illusions of Interpretation" as an example of "Impossible Pictures", saying, "Impossible figures embody conflicting 3D clues...Shepard's elephant (figure 2) confuses its legs with the spaces in between. Local votes about depth are not properly integrated." [4]
The Oxford Companion to Consciousness suggests as a way to understand "Shepard’s many-legged elephant": "try slowly uncovering the elephant from the top, or from the bottom." (If you cover the bottom of the drawing, you see the top of an elephant with four legs. If you cover the drawing's top, you see four elephant feet, plus trunk and tail.) [5]
Al Seckel, who devotes Chapter 18 of his book Masters of Deception to Roger Shepard, draws a contrast between Shepard's elephant and the impossible trident (aka the "blivet" or "Devil's tuning fork"). Although an impossible trident has a closed edge, Seckel says the "conspicuous line discontinuity" of the elephant's tail is necessary to avoid a "counting paradox": a blivet is an imaginary object, but everyone knows an elephant has exactly four legs and exactly four feet. [6]
The Shepard elephant has attracted interest outside scholarly sources. Author Clive Gifford included it in his 2013 book for children Eye Benders, and told The Guardian it is one of his favorites. [7]
Sometime before 2012, someone created a modified version of the Shepard elephant. The modified elephant has an extra hind leg, with foot attached, made by extending the curved line that Shepard left ambiguous (to look like either the top of a leg or the end of a tail.) This modified image, which now has four legs but five feet, was circulated as "How many legs does this elephant have?" [8] [9] [10]
The Shepard elephant has also inspired some other derivative works. Dutch psychologist Hugo Schouppe made a video, showing how GIMP can be used to reverse-engineer the elephant illusion, moving its feet so that each one connects to a leg. [11] The OpticalSpy website also cited the Shepard elephant as inspiration for manipulating a photograph of an Indian elephant to give it six legs. [12]
Maurits Cornelis Escher was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics. Despite wide popular interest, for most of his life Escher was neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the late twentieth century, he became more widely appreciated, and in the twenty-first century he has been celebrated in exhibitions around the world.
A strange loop is a cyclic structure that goes through several levels in a hierarchical system. It arises when, by moving only upwards or downwards through the system, one finds oneself back where one started. Strange loops may involve self-reference and paradox. The concept of a strange loop was proposed and extensively discussed by Douglas Hofstadter in Gödel, Escher, Bach, and is further elaborated in Hofstadter's book I Am a Strange Loop, published in 2007.
An illusion is a distortion of the senses, which can reveal how the mind normally organizes and interprets sensory stimulation. Although illusions distort the human perception of reality, they are generally shared by most people.
In visual perception, an optical illusion is an illusion caused by the visual system and characterized by a visual percept that arguably appears to differ from reality. Illusions come in a wide variety; their categorization is difficult because the underlying cause is often not clear but a classification proposed by Richard Gregory is useful as an orientation. According to that, there are three main classes: physical, physiological, and cognitive illusions, and in each class there are four kinds: Ambiguities, distortions, paradoxes, and fictions. A classical example for a physical distortion would be the apparent bending of a stick half immerged in water; an example for a physiological paradox is the motion aftereffect. An example for a physiological fiction is an afterimage. Three typical cognitive distortions are the Ponzo, Poggendorff, and Müller-Lyer illusion. Physical illusions are caused by the physical environment, e.g. by the optical properties of water. Physiological illusions arise in the eye or the visual pathway, e.g. from the effects of excessive stimulation of a specific receptor type. Cognitive visual illusions are the result of unconscious inferences and are perhaps those most widely known.
A Shepard tone, named after Roger Shepard, is a sound consisting of a superposition of sine waves separated by octaves. When played with the bass pitch of the tone moving upward or downward, it is referred to as the Shepard scale. This creates the auditory illusion of a tone that seems to continually ascend or descend in pitch, yet which ultimately gets no higher or lower.
The Penrose triangle, also known as the Penrose tribar, the impossible tribar, or the impossible triangle, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot exist as a solid object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, prominent Nobel Prize-winning mathematician Sir Roger Penrose, who described it as "impossibility in its purest form". It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.
An impossible object is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object but cannot exist as a solid object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline.
An impossible trident, also known as an impossible fork, blivet, poiuyt, or devil's tuning fork, is a drawing of an impossible object, a kind of an optical illusion. It appears to have three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end.
The impossible cube or irrational cube is an impossible object invented by M.C. Escher for his print Belvedere. It is a two-dimensional figure that superficially resembles a perspective drawing of a three-dimensional cube, with its features drawn inconsistently from the way they would appear in an actual cube.
The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Oscar Reutersvärd in 1937 and later independently discovered and made popular by Lionel Penrose and his son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three-dimensional Euclidean geometry but possible in some non-Euclidean geometry like in nil geometry.
Oscar Reutersvärd was a Swedish graphic artist, who in 1934 pioneered the art of 3D drawings that may initially appear feasible, yet cannot be physically constructed. He is sometimes described as "the father of the impossible figure", although there are much older examples, e.g. Hogarth's Satire on False Perspective.
The Ponzo illusion is a geometrical-optical illusion that was first demonstrated by the Italian psychologist Mario Ponzo (1882–1960) in 1913. He suggested that the human mind judges an object's size based on its background. He showed this by drawing two identical lines across a pair of converging lines, similar to railway tracks. The upper line looks longer because we interpret the converging sides according to linear perspective as parallel lines receding into the distance. In this context, we interpret the upper line as though it were farther away, so we see it as longer – a farther object would have to be longer than a nearer one for both to produce retinal images of the same size.
The Ehrenstein illusion is an optical illusion of brightness or colour perception. The visual phenomena was studied by the German psychologist Walter H. Ehrenstein (1899–1961) who originally wanted to modify the theory behind the Hermann grid illusion. In the discovery of the optical illusion, Ehrenstein found that grating patterns of straight lines that stop at a certain point appear to have a brighter centre, compared to the background.
Roger Newland Shepard was an American cognitive scientist and author of the "universal law of generalization" (1987). He was considered a father of research on spatial relations. He studied mental rotation, and was an inventor of non-metric multidimensional scaling, a method for representing certain kinds of statistical data in a graphical form that can be comprehended by humans. The optical illusion called Shepard tables and the auditory illusion called Shepard tones are named for him.
Alfred Paul "Al" Seckel was an American collector and popularizer of visual and other types of sensory illusions, who wrote books about them. Active in the Freethought movement as a skeptic in the 1980s, he was the co-founder and executive director of the Southern California Skeptics. News coverage arising from his connection to Jeffrey Epstein has stressed Seckel's misrepresentation of his education and credentials.
István Orosz is a Hungarian painter, printmaker, graphic designer and animated film director. He is known for his mathematically inspired works, impossible objects, optical illusions, double-meaning images and anamorphoses. The geometric art of István Orosz, with forced perspectives and optical illusions, has been compared to works by M. C. Escher.
Cube with Magic Ribbons is a lithograph print by the Dutch artist M. C. Escher first printed in 1957. It depicts two interlocking bands wrapped around the frame of a Necker cube. The bands have what Escher called small "nodules" or "buttonlike protuberances" that make use of the dome/crater illusion, an optical illusion characterized by shifting perception of depth from concave to convex depending on direction of light and shadow. Escher's interest in reversible perspectives, as seen in Cube with Magic Ribbons, can also be noted in an earlier work, Convex and Concave, first printed in 1955.
Apparition of Face and Fruit Dish on a Beach (1938) is a painting by the Spanish surrealist Salvador Dalí. This work belongs to a group of paintings by Dalí that instantiate an optical illusion called the double, multiple, or ambiguous image.
Schroeder stairs is an optical illusion which is a two-dimensional drawing which may be perceived either as a drawing of a staircase leading from left to right downwards or the same staircase only turned upside down, a classical example of perspective reversal in psychology of perception. It is named after the German natural scientist Heinrich G. F. Schröder, who published it in 1858.
Shepard tables are an optical illusion first published in 1990 as "Turning the Tables," by Stanford psychologist Roger N. Shepard in his book Mind Sights, a collection of illusions that he had created. It is one of the most powerful optical illusions, typically creating length miscalculations of 20–25%.
The elephant…belongs to a class of objects that are truly impossible in that the object itself cannot be globally segregated from the nonobject or background. Parts of the object (in this case the elephant's legs) become the background, and vice versa.
This drawing, entitled L'egs-istential Quandary, sprang from a visual image that came to scientist Roger M. Shepard just before he awakened one morning in 1974. The quick pencil sketch he made when he awoke became the basis for this ink drawing, for which Shepard holds the copyright.
..one of the most famous and classic optical illusions of all time. While most people know it simply as the "impossible elephant," the actual title of the work is "L'egs-istential Quandary."
Shepard's elephant (figure 2) confuses its legs with the spaces in between. Local votes about depth are not properly integrated. Impossible objects cannot be consistently painted with colors.
To avoid the counting paradox with the number of legs, Shepard introduced the more conspicuous line discontinuity at the far right.
Famous impossible images include the Penrose staircase and this little beauty, courtesy of renowned cognitive scientist and author of Mind Sights, Roger Newland Shepard. With his usual love of a quick joke, Shepard entitled the illusion L'egs-istential Quandary.
On several websites, a slightly modified version of the [Shepard elephant] illusion is presented with the question "How many legs do you count?". After a few moments of thought, you certainly can figure out what is wrong and how the artist has done it. In fact, it's rather easy and Shepard gives us a clue by omitting the left back foot. Each foot is displaced to the left.
There's something not quite right about the elephant below. Can you see it? How many legs does it really have? The elephant illusion is an adaptation of the original which was created by Roger Shepard and published in his book Mind Sights (1990, WH Freeman & Co).
Can you tell how many legs this elephant has? If looking at the legs is giving you a headache, you're not alone.
Famous cognitive illusion by Roger Shepard. Added interactivity by Hugo Schouppe.
How many legs has this elephant got? Well six of course, it is a special six legged Indian elephant designed by us. We wondered what a real elephant would look like if it was similar to the old favourite optical illusion shown on the left here. So just for a bit of fun we made one.