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An impossible object (also known as an impossible figure or an undecidable figure) is a type of
optical illusion Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual perception, percept that arguably appears to differ from reality. Illusions come in a wide v ...
that consists of a two-
dimensional In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordi ...
figure which is instantly and naturally understood as representing a projection of a three-dimensional object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipline.


Notable examples

Notable impossible objects include: *
Borromean rings In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from each other, but that break apart into two unknotted and unlinked loops when any one of the ...
— although conventionally drawn as three linked circles in three-dimensional space, any realization must be non-circular * Impossible cube — invented by
M.C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in th ...
for ''
Belvedere Belvedere (from Italian, meaning "beautiful sight") may refer to: Places Australia *Belvedere, Queensland, a locality in the Cassowary Coast Region Africa * Belvedere (Casablanca), a neighborhood in Casablanca, Morocco * Belvedere, Harare, Z ...
'', a lithograph in which a boy seated at the foot of the building holds an impossible cube. * Penrose stairs – created by
Oscar Reutersvärd Oscar Reutersvärd (29 November 1915 – 2 February 2002) 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 fathe ...
and later independently devised and popularised by Lionel Penrose and his mathematician son Roger Penrose. A variation on the
Penrose triangle 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 ...
, 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. *
Penrose triangle 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 ...
(Tribar) – first created by the Swedish artist
Oscar Reutersvärd Oscar Reutersvärd (29 November 1915 – 2 February 2002) 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 fathe ...
in 1934. Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form". *
Impossible trident An impossible trident, also known as an impossible fork, blivet, poiuyt, or devil's tuning fork,Brooks Masterton, John M. Kennedy"Building the Devil's Tuning Fork" ''Perception'', 1975, vol. 4, pp. 107-109 is a drawing of an impossible object (un ...
(or devil's tuning fork) – The Blivet, has three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end. * '' L'egsistential Quandary'' – Created by
Roger Shepard Roger Newland Shepard (January 30, 1929 – May 30, 2022) 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, a ...
in 1990, is a drawing of an elephant whose four feet are drawn at the bottom of the white space between legs, instead of on the legs themselves.


Explanations

Impossible objects can be unsettling because of our natural desire to interpret 2D drawings as three-dimensional objects. This is why a drawing of a
Necker cube The Necker cube is an optical illusion that was first published as a Rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it ...
would most likely be seen as a cube, rather than "two squares connected with diagonal lines, a square surrounded by irregular planar figures, or any other planar figure". Looking at different parts of an impossible object makes one reassess the 3D nature of the object, which confuses the mind. 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. Roger Penrose wrote about describing and defining impossible objects mathematically using the
algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...
concept of
cohomology In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewe ...
.


History

An early example of an impossible object comes from ''
Apolinère Enameled ''Apolinère Enameled'' was painted in 1916–17 by Marcel Duchamp, as a heavily altered version of an advertisement for paint ("Sapolin Enamel"). The picture depicts a girl painting a bed-frame with white enamelled paint. The depiction of the fr ...
'', a 1916 advertisement painted by Marcel Duchamp. It depicts a girl painting a bed-frame with white enamelled paint, and deliberately includes conflicting perspective lines, to produce an impossible object. To emphasise the deliberate impossibility of the shape, a piece of the frame is missing. Swedish artist
Oscar Reutersvärd Oscar Reutersvärd (29 November 1915 – 2 February 2002) 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 fathe ...
was one of 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 The ''British Journal of Psychology'' is a quarterly peer-reviewed psychology journal. It was established in 1904 and is published by Wiley-Blackwell on behalf of the British Psychological Society. The editor-in-chief is Stefan R. Schweinberger ( ...
'' 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, of whom they were unaware. The article was published in 1958. From the 1930s onwards, Dutch artist
M.C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in th ...
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 impossible object. '' Waterfall'' and ''
Belvedere Belvedere (from Italian, meaning "beautiful sight") may refer to: Places Australia *Belvedere, Queensland, a locality in the Cassowary Coast Region Africa * Belvedere (Casablanca), a neighborhood in Casablanca, Morocco * Belvedere, Harare, Z ...
'' are good examples of impossible constructions. 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 was a sculptor, medallist, 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 ...
,
Sandro del Prete Sandro Del-Prete (born 1937) is a Swiss artist who creates illusionary and surrealistic paintings. His style has been compared to M. C. Escher, though it lacks the latter's mathematical precision. Biography Del-Prete was born in Bern, Switzerlan ...
,
István Orosz István Orosz (born 24 October 1951) 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 ...
(
Utisz Outis (a transliteration of the Ancient Greek pronoun = " nobody" or "no one") is an often used pseudonym that appeared famously in Classical Greek legends. Modern artists, writers, and others in public life have adopted the use of this pseudonym ...
),
Guido Moretti Guido is a given name Latinised from the Old High German name Wido. It originated in Medieval Italy. Guido later became a male first name in Austria, Germany, the Low Countries, Scandinavia, Spain, Portugal, Latin America and Switzerland. The m ...
, Tamás F. Farkas, Mathieu Hamaekers, and Kokichi Sugihara.


Constructed impossible objects

Although possible to represent in two dimensions, it is not geometrically possible for such an object to exist in the physical world. However some models of impossible objects have been constructed, such that when they are viewed from a very specific point, the illusion is maintained. Rotating the object or changing the viewpoint breaks the illusion, and therefore many of these models rely on forced perspective or having parts of the model appearing to be further or closer than they actually are. The notion of an "interactive impossible object" is an impossible object that can be viewed from any angle without breaking the illusion.


See also

* * * * * * * * * * * * *


References


Further reading

* Bower, Gordon H. (editor), (1990).
''Psychology of Learning & Motivation''
Academic Press. Volume 26. p. 107. * ''Mathematical Circus'', Martin Gardner 1979 (Chapter 1 – Optical Illusions) * ''Optical Illusions'', Bruno Ernst 2006


External links


Impossible World

The M.C. Escher Project



"Escher for Real"
(3D objects)
Inconsistent Images

Echochrome
a video game that incorporates impossible objects into its gameplay {{DEFAULTSORT:Impossible Object Optical illusions