Impossible object
Encyclopedia
Optical illusion
An optical 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...
consisting of a two-dimensional figure which is instantly and subconscious
Subconscious
The term subconscious is used in many different contexts and has no single or precise definition. This greatly limits its significance as a definition-bearing concept, and in consequence the word tends to be avoided in academic and scientific settings....
ly interpreted by the visual system
Visual system
The visual system is the part of the central nervous system which enables organisms to process visual detail, as well as enabling several non-image forming photoresponse functions. It interprets information from visible light to build a representation of the surrounding world...
as representing a projection
Graphical projection
Graphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing.- Overview :...
of a three-dimensional object although it is not actually possible for such an object to exist (at least not in the form interpreted by the visual system).
In most cases the impossibility becomes apparent after viewing the figure for a few seconds. However, the initial impression of a 3D object remains even after it has been contradicted. There are also more subtle examples of impossible objects where the impossibility does not become apparent spontaneously and it is necessary to consciously examine the geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
of the implied object to determine that it is impossible.
Impossible objects are of interest to psychologist
Psychologist
Psychologist is a professional or academic title used by individuals who are either:* Clinical professionals who work with patients in a variety of therapeutic contexts .* Scientists conducting psychological research or teaching psychology in a college...
s, mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
s and artist
Artist
An artist is a person engaged in one or more of any of a broad spectrum of activities related to creating art, practicing the arts and/or demonstrating an art. The common usage in both everyday speech and academic discourse is a practitioner in the visual arts only...
s without falling entirely into any one discipline.
Notable examples
- Necker CubeNecker cubeThe Necker Cube is an optical illusion first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker.-Ambiguity:The Necker Cube is an ambiguous line drawing....
- Penrose stairsPenrose stairsThe Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Lionel Penrose and his son Roger Penrose...
- Penrose trianglePenrose triangleThe Penrose triangle, also known as the Penrose tribar, is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form". It is...
- BlivetBlivetA blivet, also known as a poiuyt, devil's fork or widget, is an undecipherable figure, an optical illusion and an impossible object...
(or Devil's tuning fork)
History
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
artist Oscar Reutersvärd
Oscar Reutersvärd
Oscar Reutersvärd , "the father of the impossible figure", was an artist who pioneered the art of impossible objects. These are images such as what was later renamed the Penrose triangle that appear to depict solid objects, which, however, are impossible to construct in reality...
was the first to deliberately design many impossible objects. He has been called "the father of impossible figures". In 1934 he drew the Penrose triangle, some years before the Penroses. In Reutersvärd's version the sides of the triangle are broken up into cubes.
In 1956, British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
psychiatrist Lionel Penrose
Lionel Penrose
Lionel Sharples Penrose, FRS was a British psychiatrist, medical geneticist, mathematician and chess theorist, who carried out pioneering work on the genetics of mental retardation. He was educated at the Quaker Leighton Park School and St...
and his son, mathematician Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College...
, submitted a short article to the British Journal of Psychology titled Impossible Objects: A Special Type of Visual Illusion. This was illustrated with the Penrose Triangle and Penrose stairs. The article referred to Escher, whose work had sparked their interest in the subject, but not Reutersvärd, whom they were unaware of. The article was only published in 1958.
From the 1930s onwards Dutch
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
artist M. C. Escher
M. C. Escher
Maurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
produced many drawings featuring paradoxes of perspective gradually working towards impossible objects. In 1957 he produced his first drawing containing a true impossible object: Cube with Magic Ribbons
Cube with Magic Ribbons
Cube with Magic Ribbons is a lithograph print by the Dutch artist M. C. Escher which was first printed in 1957. It depicts two interlocking bands wrapped around the frame of a cube. The cube framework by itself is perfectly possible but the interlocking of the "magical" bands within it is impossible...
. He produced many further drawings featuring impossible objects, sometimes with the entire drawing being an undecidable figure. His work did much to draw the attention of the public to impossible objects. Some contemporary artists are also experimenting with impossible figures, for example, Jos de Mey
Jos de Mey
Jos de Mey was a Flemish-Belgian painter. He is primarily known for depictions of impossible objects in a photo-realistic style, with oil paintings constituting the majority of his work. He frequently depicted characters of other artists - notably Magritte, M. C...
, Shigeo Fukuda
Shigeo Fukuda
was a sculptor, graphic artist and poster designer who created optical illusions. His art pieces usually portray deception, such as Lunch With a Helmet On, a sculpture created entirely from forks, knives, and spoons, that casts a detailed shadow of a motorcycle....
, Sandro del Prete
Sandro del Prete
Sandro Del-Prete is a Swiss artist who paints figures, situations and processes that cannot exist in the real world. Del-Prete ‘materializes the well-known psychological effect, of the difference between ‘looking’ and ‘seeing’ ’ – Abraham Tamir...
, István Orosz
István Orosz
István Orosz Hungarian painter, printmaker, graphic designer and animated film director, 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...
(Utisz
Utisz
Outis is an often used pseudonym. Artists, writers and others in public life use this pseudonym in order to hide their identity.- Origin of the name :...
), Guido Moretti, Tamás F. Farkas and Mathieu Hamaekers.
In fiction
- In H. P. LovecraftH. P. LovecraftHoward Phillips Lovecraft --often credited as H.P. Lovecraft — was an American author of horror, fantasy and science fiction, especially the subgenre known as weird fiction....
's celebrated short story, The Call of CthulhuThe Call of CthulhuThe Call of Cthulhu is a short story by American writer H. P. Lovecraft. Written in the summer of 1926, it was first published in the pulp magazine Weird Tales, in February 1928.-Inspiration:...
(1928), the titular entityCthulhuCthulhu is a fictional character that first appeared in the short story "The Call of Cthulhu", published in the pulp magazine Weird Tales in 1928. The character was created by writer H. P...
emerges from the vast and ancient alien city of R'lyehR'lyehR'lyeh is a fictional lost city that first appeared in the H. P. Lovecraft short story "The Call of Cthulhu", first published in Weird Tales in 1928. According to Lovecraft's short story, R'lyeh is a sunken city in the South Pacific and the prison of the malevolent entity called Cthulhu.R'lyeh is...
, which is described in terms of "non-Euclidean geometryNon-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
" and contains angles which are "all wrong" (appearing acute but behaving as if obtuse, for example) and planes which could be horizontal or slanted depending on how the observer looks at them. The overall description of 'impossible geometry' seems to strongly prefigure Escher's work. - In the 1982 Doctor WhoDoctor WhoDoctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...
story Castrovalva, the titular town is subject to apparently impossible architecture. The storyline also relied heavily on recursionRecursionRecursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from...
, a favorite theme in Escher's most famous works, and used ideas taken from BelvedereBelvedere (M. C. Escher)Belvedere is a lithograph print by the Dutch artist M. C. Escher, first printed in May 1958. It shows a plausible-looking building which turns out to be impossible....
, Ascending and DescendingAscending and DescendingAscending and Descending is a lithograph print by the Dutch artist M. C. Escher which was first printed in March 1960.The original print measures 14" x 11 1/4”. The lithograph depicts a large building roofed by a never-ending staircase. Two lines of identically dressed men appear on the staircase,...
, and RelativityRelativity (M. C. Escher)Relativity is a lithograph print by the Dutch artist M. C. Escher, first printed in December 1953.It depicts a world in which the normal laws of gravity do not apply. The architectural structure seems to be the centre of an idyllic community, with most of its inhabitants casually going about their...
. Despite the use of its name, the Escher lithograph of the same nameCastrovalva (M. C. Escher)Castrovalva is a lithograph print by the Dutch artist M. C. Escher, first printed in February 1930. Like many of Escher's early works, it depicts a place that he visited on a tour of Italy....
does not feature impossible architecture. - In the Star Trek: The Next GenerationStar Trek: The Next GenerationStar Trek: The Next Generation is an American science fiction television series created by Gene Roddenberry as part of the Star Trek franchise. Roddenberry, Rick Berman, and Michael Piller served as executive producers at different times throughout the production...
episode "I, Borg", a plan was made to destroy the entire race of BorgBorg (Star Trek)The Borg are a fictional pseudo-race of cybernetic organisms depicted in the Star Trek universe associated with Star Trek.Whereas cybernetics are used by other races in the science fiction world to repair bodily damage and birth defects, the Borg use enforced cybernetic enhancement as a means of...
—malevolent cybernetic aliens whose minds were interconnected—by showing one of the Borg a picture of a highly complex impossible object. This image would be transmitted back to the Borg hiveCollective consciousnessCollective consciousness was a term coined by the French sociologist Émile Durkheim to refer to the shared beliefs and moral attitudes which operate as a unifying force within society...
, overloading its consciousness in larger and larger attempts to understand the image. This plan was dismissed as being genocideGenocideGenocide is defined as "the deliberate and systematic destruction, in whole or in part, of an ethnic, racial, religious, or national group", though what constitutes enough of a "part" to qualify as genocide has been subject to much debate by legal scholars...
, so its potential results were never seen. - In the computer game Diablo IIDiablo IIDiablo II is a dark fantasy/horror-themed hack and slash, with elements of the role playing game and dungeon crawl genres. It was released for Windows and Mac OS in 2000 by Blizzard Entertainment, and was developed by Blizzard North. It is a direct sequel to the 1996 hit PC game, Diablo.Diablo II...
, parts of the "Arcane Sanctuary" region were based on impossible drawings. - Alan MooreAlan MooreAlan Oswald Moore is an English writer primarily known for his work in comic books, a medium where he has produced a number of critically acclaimed and popular series, including Watchmen, V for Vendetta, and From Hell...
's miniseries 1963 features a character called the Hypernaut that lives in a space station shaped like an impossible object. - In the video game Eternal Darkness: Sanity's RequiemEternal Darkness: Sanity's RequiemEternal Darkness: Sanity's Requiem is a psychological horror action-adventure video game released for the Nintendo GameCube. Developed by Canadian developer Silicon Knights and originally planned for the Nintendo 64, it was first released and published by Nintendo on June 24, 2002 in North America...
the Essence of Xel'lotath, the Sigil of Xel'lotath, is an impossible artifact resembling a warped angel. - In The SimpsonsThe SimpsonsThe Simpsons is an American animated sitcom created by Matt Groening for the Fox Broadcasting Company. The series is a satirical parody of a middle class American lifestyle epitomized by its family of the same name, which consists of Homer, Marge, Bart, Lisa and Maggie...
episode "Treehouse of Horror IVTreehouse of Horror IV"Treehouse of Horror IV" is the fifth episode of The Simpsons fifth season and the fourth episode in the Treehouse of Horror series of Halloween specials. It originally aired on the Fox network in the United States on October 28, 1993, and features three short stories called "The Devil and Homer...
", homer is seen chasing bart in a painting parodying the famous M.C. Escer painting "Ascending and descendingAscending and DescendingAscending and Descending is a lithograph print by the Dutch artist M. C. Escher which was first printed in March 1960.The original print measures 14" x 11 1/4”. The lithograph depicts a large building roofed by a never-ending staircase. Two lines of identically dressed men appear on the staircase,...
" "Treehouse of Horror VIIITreehouse of Horror VIII"Treehouse of Horror VIII" is the fourth episode of The Simpsons ninth season and first aired on the Fox network on October 26, 1997. In the eighth annual "Treehouse of Horror" episode, Homer Simpson is the last man left alive when a neutron bomb destroys Springfield until a gang of mutants come...
", a blivet (or devil's tuning fork) can be seen on Professor Frink's yard sale. In The Simpsons MovieThe Simpsons MovieThe Simpsons Movie is a 2007 American animated comedy film based on the animated television series The Simpsons. The film was directed by David Silverman, and stars the regular television cast of Dan Castellaneta, Julie Kavner, Nancy Cartwright, Yeardley Smith, Hank Azaria, Harry Shearer, Tress...
, Homer falls down miles of the impossible infinite House of StairsHouse of StairsHouse of Stairs is a lithograph print by the Dutch artist M. C. Escher which was first printed in November 1951. This print measures 18⅝" × 9⅜". It depicts the interior of a tall structure crisscrossed with stairs and doorways at paradoxical angles...
while having an epiphany. The couch gag in the episode "The PTA Disbands", the family is running through an Escher-like living room. - On the cover of July 1985 MadMad (magazine)Mad is an American humor magazine founded by editor Harvey Kurtzman and publisher William Gaines in 1952. Launched as a comic book before it became a magazine, it was widely imitated and influential, impacting not only satirical media but the entire cultural landscape of the 20th century.The last...
magazine, a picture describing devil's tuning fork can be seen upon the wall along with a stuffed St. Bernard's head on the wall of Alfred E. NeumanAlfred E. NeumanAlfred E. Neuman is the fictional mascot and cover boy of Mad magazine. The face had drifted through American pictography for decades before being claimed and named by Mad editor Harvey Kurtzman...
's living room - The video game EchochromeEchochromeis a puzzle game created by Sony's JAPAN Studio and Game Yarouze, which is available for PlayStation 3 from the PlayStation Store and for PlayStation Portable on either UMD or from the PlayStation Store. Gameplay involves a mannequin figure traversing a rotatable world where physics and reality...
for the PlayStation PortablePlayStation PortableThe is a handheld game console manufactured and marketed by Sony Corporation Development of the console was announced during E3 2003, and it was unveiled on , 2004, at a Sony press conference before E3 2004...
and PlayStation 3PlayStation 3The is the third home video game console produced by Sony Computer Entertainment and the successor to the PlayStation 2 as part of the PlayStation series. The PlayStation 3 competes with Microsoft's Xbox 360 and Nintendo's Wii as part of the seventh generation of video game consoles...
features a mannequin who must traverse a series of impossible objects. - The set of the climactic scene in the Goblin King's castle in the 1986 fantasy film, LabyrinthLabyrinth (film)Labyrinth is a 1986 British/American fantasy film directed by Jim Henson, produced by George Lucas, and designed by Brian Froud. Henson collaborated on the screenwriting with children's author Dennis Lee, Terry Jones from Monty Python, and Elaine May .The film stars David Bowie as Jareth the Goblin...
, directed by Jim HensonJim HensonJames Maury "Jim" Henson was an American puppeteer best known as the creator of The Muppets. As a puppeteer, Henson performed in various television programs, such as Sesame Street and The Muppet Show, films such as The Muppet Movie and The Great Muppet Caper, and created advanced puppets for...
, is based on M. C. EscherM. C. EscherMaurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
's "RelativityRelativity (M. C. Escher)Relativity is a lithograph print by the Dutch artist M. C. Escher, first printed in December 1953.It depicts a world in which the normal laws of gravity do not apply. The architectural structure seems to be the centre of an idyllic community, with most of its inhabitants casually going about their...
", and features impossible staircases and perspectives. - In the big-screen film version of "The AvengersThe AvengersAvengers or The Avengers may refer to:*The Avengers , a 1960s British television show**The Avengers , a film based on the characters of the television series...
", Mrs Peel (Uma Thurman) is trapped in a labyrinthine mansion which features a direct downward view of a Penrose Stair. - In Pokémon PlatinumPokémon Platinumis a title in the Pokémon series of video games. It was developed by Game Freak and published by Nintendo for the Nintendo DS handheld game console. It is an enhanced remake of Pokémon Diamond and Pearl in the same vein as Pokémon Yellow, Crystal, and Emerald were for their respective games...
there is an area called "Distortion World" full of impossibilities such as these. - In the Family GuyFamily GuyFamily Guy is an American animated television series created by Seth MacFarlane for the Fox Broadcasting Company. The series centers on the Griffins, a dysfunctional family consisting of parents Peter and Lois; their children Meg, Chris, and Stewie; and their anthropomorphic pet dog Brian...
episode "No Meals on WheelsNo Meals on Wheels"No Meals on Wheels" is the fourteenth episode of the fifth season of the animated comedy series Family Guy. It originally aired on Fox in the United States on March 25, 2007. The episode features the Griffin family opening a restaurant, and eventually become overwhelmed by Joe Swanson and his...
" there is a scene parodying M. C. EscherM. C. EscherMaurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
's RelativityRelativity (M. C. Escher)Relativity is a lithograph print by the Dutch artist M. C. Escher, first printed in December 1953.It depicts a world in which the normal laws of gravity do not apply. The architectural structure seems to be the centre of an idyllic community, with most of its inhabitants casually going about their...
. - In "Science Girls", made by Hanako GamesHanako GamesHanako Games, is an independent video game development company founded by Georgina Bensley that develops PC games mostly involving female heroines centered around fantasy- and anime-inspired style. Games on the site include Fatal Hearts, Cute Knight, Summer Session, and Science Girls. The website...
, the wormhole that leads to the aliens' home planet has a double Penrose Triangle as its power source, possibly to create a spacial paradox to warp dimensions. - In the video game "Prince of Persia 2: The Shadow and the FlamePrince of Persia 2: The Shadow and the FlamePrince of Persia 2: The Shadow and the Flame is a platform game released by Brøderbund in 1993.-Gameplay:Similar to the first Prince of Persia, the character explores various deadly areas by running, jumping, crawling, avoiding traps, solving puzzles and drinking magic potions. Prince of Persia 2...
" the final battle features impossible geometry when you jump down the vertical part of an impossible triangle - The 1984 game Realm of ImpossibilityRealm of ImpossibilityRealm of Impossibility is a computer game created by Mike Edwards and published by Electronic Arts in 1984 for the Apple IIe, Atari 8-bit family and Commodore 64 computer systems. It was converted to the ZX Spectrum in 1985 and published by Ariolasoft UK Ltd.-Summary:The game was originally...
features levels which largely involve impossible objects. - In the 2010 movie InceptionInceptionInception: The Subconscious Jams 1994-1995 is a compilation of unreleased tracks by the band Download.-Track listing:# "Primitive Tekno Jam" – 3:23# "Bee Sting Sickness" – 8:04# "Weed Acid Techno" – 8:19...
, Arthur shows Ariadne how to install a Penrose staircase in dreams. He later uses the same configuration to flank a pursuing enemy. - The first episode of the second season of Xiaolin ShowdownXiaolin ShowdownXiaolin Showdown is an American animated television series that aired on Kids WB and was created by Christy Hui. Set in a world where martial arts battles and Eastern magic are commonplace, the series follows four young warriors in training that battle the forces of evil...
has a fight sequence in which the protagonist chases his opponent through a building constructed of various Escheresque rooms. - There is also signficant reference to an impossible object in Jonathan Lethem's most recent novel, "Chronic City." where it plays a major part in the storyline.
See also
- Four-dimensional space
- Multistable perceptionMultistable perceptionMultistable perceptual phenomena are a form of perceptual phenomena in which there are unpredictable sequences of spontaneous subjective changes...
- Necker cubeNecker cubeThe Necker Cube is an optical illusion first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker.-Ambiguity:The Necker Cube is an ambiguous line drawing....
- Non-Euclidean geometryNon-Euclidean geometryNon-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
- Optical illusionOptical illusionAn optical 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...
- ParadoxParadoxSimilar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
- PuzzlePuzzleA puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...
- Strange loopStrange loopA strange loop arises when, by moving up or down through a hierarchical system, one finds oneself back where one started.Strange loops may involve self-reference and paradox...
- SurrealismSurrealismSurrealism is a cultural movement that began in the early 1920s, and is best known for the visual artworks and writings of the group members....
- TesseractTesseractIn geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8...
- Three haresThree haresThe three hares is a circular motif appearing in sacred sites from the Middle and Far East to the churches of southwest England , and historical synagogues in Europe....