Two famous undecidable figures, the Penrose triangle and devil's tuning fork.

An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion consisting of a two-dimensional figure which is instantly and subconsciously interpreted by the visual system as representing a projection 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). Image File history File links Impossible_objects. ... Image File history File links Impossible_objects. ... The Penrose triangle Impossible Triangle sculpture, East Perth, Australia The Penrose triangle, also known as the tribar, is an impossible object. ... This blivet is reminiscent of an M.C. Escher print—it portrays two impossible perspectives at once, creating a lost layer between the top two rods, and an impossible extra, vanishing rod in between the bottom two. ... Two famous undecidable figures, the Penrose triangle and devils tuning fork. ... An optical illusion. ... Dimension (from Latin measured out) is, in essence, the number of degrees of freedom available for movement in a space. ... See also: Unconscious mind. ... The visual system is the part of the nervous system which allows organisms to see. ... Graphical projection in the visual sciences is an imaging procedure the protocols of which preclude the necessity of mathematical calculation. ...

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 of the implied object to determine that it is impossible. For other uses, see Geometry (disambiguation). ...

Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline. A psychologist is an expert in psychology, the systematic investigation of the human body, including behavior, cognition, and affect. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... The definition of an artist is wide-ranging and covers a broad spectrum of activities to do with creating art, practicing the arts and/or demonstrating an art. ...

Notable examples

Viewed from a certain angle, this cube appears to defy the laws of geometry.

Notable undecidable figures include: Image File history File links Impossible_cube_illusion_angle. ... Image File history File links Impossible_cube_illusion_angle. ...

• Impossible cube
• Penrose stairs
• Penrose triangle
• Blivet (or Devil's tuning fork)

Viewed from a certain angle, this cube appears to defy the laws of physics. ... The Penrose stairs is an impossible object devised by Lionel Penrose and his son Roger Penrose and can be seen as a variation on his Penrose triangle. ... The Penrose triangle Impossible Triangle sculpture, East Perth, Australia The Penrose triangle, also known as the tribar, is an impossible object. ... This blivet is reminiscent of an M.C. Escher print—it portrays two impossible perspectives at once, creating a lost layer between the top two rods, and an impossible extra, vanishing rod in between the bottom two. ...

History

Swedish artist Oscar Reutersvärd 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. The Stockholm-born artist Oscar Reutersvärd (1915–2002), the father of the impossible figure, pioneered the art of impossible objects. ... Year 1934 (MCMXXXIV) was a common year starting on Monday (link will display full 1934 calendar) of the Gregorian calendar. ...

In 1956, British psychiatrist Lionel Penrose and his son, mathematician Roger Penrose, 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 referenced 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. Lionel Sharples Penrose (1898-1972) was a British geneticist, psychiatrist, mathematician and chess theorist, who carried out pioneering work on inherited mental illnesses. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) 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. ... Jan. ...

From the 1930s onwards Dutch artist M. C. Escher 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. 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, Shigeo Fukuda, Sandro del Prete, István Orosz (Utisz), Guido Moretti, Tamás F. Farkas and Mathieu Hamaekers. The 1930s were described as an abrupt shift to more radical and conservative lifestyles, as countries were struggling to find a solution to the Great Depression, also known as the [[. In East Asia, the rise of militarism occurred. ... Maurits Cornelis Escher (June 17, 1898 – March 27, 1972), usually referred to as M. C. Escher, was a Dutch graphic artist. ... Year 1957 (MCMLVII) was a common year starting on Tuesday (link displays the 1957 Gregorian calendar). ... Cube with Magic Ribbons is a lithograph print by the Dutch artist M. C. Escher which was first printed in 1957. ... Shigeo Fukuda (福田 繁雄, born 1932) is a sculptor who creates optical illusions. ... István Orosz (b. ... Utisz: Self portrait Utisz (the Hungarian spelling of the Greek name ουτις, or OYTIΣ, pronounced: outis) often used pseudonym of István Orosz Hungarian visual artist. ...

In fiction

• In the Star Trek: The Next Generation episode "I, Borg", a plan was made to destroy the entire race of Borg—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 hive, overloading its consciousness in larger and larger attempts to understand the image. This plan was dismissed as being genocide, so its potential results were never seen.
• In the computer game Diablo II, the "Arcane Sanctuary" region was based on impossible drawings.
• Alan Moore'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 Requiem the Essence of Xel'lotath, the Sigil of Xel'lotath, is an impossible artifact resembling a warped angel.
• In The Simpsons episode "Treehouse of Horror VIII", a blivet (or devil's tuning fork) can be seen on Professor Frink's yard sale. In The Simpsons Movie, Homer falls down miles of the impossible infinite House of Stairs while having an epiphany.
• The video game Echochrome for the PSP features a mannequin who must travel a series of impossible objects. The game is entirely based on perspective, as in, if you can't see it, it's not there.

The title as it appeared in most episodes opening credits. ... I, Borg was the twenty third episode of the fifth season of the television show Star Trek: The Next Generation // Overview: A member of the dangerous cybernetic race known as the Borg is captured by the Enterprise crew and examined. ... The Borg are a fictional pseudo-race of cyborgs depicted in Star Trek. ... Cybernetics is a theory of the communication and control of regulatory feedback. ... A hive mind (sometimes spelled hivemind) is a form of collective consciousness strongly exhibiting traits of conformity and groupthink. ... For other uses, see Genocide (disambiguation). ... Diablo II, sequel to the popular game Diablo, is a dark fantasy-themed action role-playing game in a hack and slash or Dungeon Roaming style. ... For other persons named Alan Moore, see Alan Moore (disambiguation). ... 1963 is a comic book by esteemed author Alan Moore. ... Xel’lotath is the Ancient Goddess of Madness in Eternal Darkness: Sanitys Requiem. ... Simpsons redirects here. ... Treehouse of Horror VIII is the fourth episode of The Simpsons ninth season and first aired on the Fox network on October 26, 1997. ... The Simpsons Movie is a 2007 animated comedy film based on the animated television series The Simpsons, directed by David Silverman, and scheduled to be released worldwide by July 27, 2007. ... House of Stairs is a lithograph print by the Dutch artist M. C. Escher which was first printed in November, 1951. ... Echochrome will be a downloadable game on the PlayStation Store and available for the PSP. Announced at E3 2007 [1] and created by Sonys Japan Studios, it is a graphically simple puzzle game, with gameplay involving rotating a world occupied by impossible constructions to be traversed by a mannequin... PSP most often refers to: PlayStation Portable, a handheld game console produced by Sony Computer Entertainment PlayStation Portable Slim & Lite, a new model of the original PlayStation Portable console Corel Paint Shop Pro, a graphics editor distributed by Corel Corporation, formerly a product of Jasc Software PSP may also refer...

References

• Mathematical Circus, Martin Gardner 1979 ISBN 0-14-022355-X (Chapter 1 — Optical Illusions)
• Optical Illusions, Bruno Ernst 2006 ISBN 3-8228-5410-7

See also

• Optical illusion
• Multistable perception
• Necker cube
• Paradox
• Surrealism
• Puzzle

An optical illusion. ... Examples of visually ambiguous patterns. ... It has been suggested that this article or section be merged with Impossible cube. ... Look up paradox in Wiktionary, the free dictionary. ... Max Ernst. ... A puzzle undone, which forms a cube Puzzle cube; a type of puzzle For other uses, see Puzzle (disambiguation). ...

External links

• Art of Reutersvard
• Real Escher Objects
• Impossible World, a repository of impossible object images