Impossible object

For John Frankenheimer's film, see Impossible Object.

For the independent rock band, see The Impossible Shapes.

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).

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.

Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline.

Notable examples

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

Notable undecidable figures include:

• Necker Cube
• Penrose stairs
• Penrose triangle
• Blivet (or Devil's tuning fork)

History

The Penrose stairs

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.

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 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 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.

In fiction

• In H. P. Lovecraft's celebrated short story, The Call of Cthulhu (1928), the titular entity emerges from the vast and ancient alien city of R'lyeh, which is described in terms of "non-Euclidean geometry" 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 Who story Castrovalva, the titular town is subject to apparently impossible architecture. The storyline also relied heavily on recursion, a favorite theme in Escher's most famous works, and used ideas taken from Belvedere, Ascending and Descending, and Relativity. Despite the use of its name, the Escher lithograph of the same name does not feature impossible architecture.
• 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, parts of the "Arcane Sanctuary" region were 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 Simpsons episode "Treehouse of Horror IV", homer is seen chasing bart in a painting parodying the famous M.C. Escer painting "Ascending and descending" "Treehouse of Horror VIII", a blivet (or devil's tuning fork) can be seen on Professor Frink's yard sale.
• On the cover of July 1985 Mad 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. Neuman's living room
• The video game Echochrome for the PlayStation Portable and PlayStation 3 features a mannequin who must traverse a series of impossible objects.
• In the big-screen film version of "The Avengers", Mrs Peel (Uma Thurman) is trapped in a labyrinthine mansion which features a direct downward view of a Penrose Stair.
• In "Science Girls", made by Hanako Games, 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 Flame" the final battle features impossible geometry when you jump down the vertical part of an impossible triangle
• The 1984 game Realm of Impossibility features levels which largely involve impossible objects.
• In the 2010 movie Inception, 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 Showdown 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.
• In "Futurama" when Fry and Bender are searching for a new apartment, one of the options is an Escher-like design. Fry remarks 'I don't wanna pay for dimensions I won't use.'

See also

• Four-dimensional space
• Multistable perception
• Necker cube
• Non-Euclidean geometry
• Optical illusion
• Paradox
• Puzzle
• Strange loop
• Surrealism
• Tesseract
• Three hares
• M.C. Escher

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

External links

• Impossible World
• The M. C. Escher Project
• Art of Reutersvard
• Real Escher Objects
• Inconsistent Images