Impossible object: Difference between revisions

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[[File:Cube with Magic Ribbons.jpg|right|thumb|''[[Cube with Magic Ribbons]]'' (1957) is a [[Lithography|lithograph]] by [[M. C. Escher]]. This print is significant for being the first Escher drawing to use a true impossible object.]]

An '''impossible object''' (also known as an '''impossible figure''' or an '''undecidable figure''') is a type of [[optical illusion]]. They consist of a two-[[dimensional]] figure which is instantly and [[subconscious]]ly interpreted by the [[visual system]] as representing a [[graphical projection|projection]] of a three-dimensional object.

The unsettling nature of impossible objects occurs because of our natural desire to interpret 2D drawings as 3 dimensional objects. This is why a drawing of a [[Necker cube]] would be most likely seen as a [[cube]], rather than "two squares connected with diagonal lines, a square surrounded by irregular planar figures, or any other planar figure." With an impossible object, looking at different parts of the object makes one reassess the 3D nature of the object, which confuses the mind.<ref>{{cite web |url=http://www.fink.com/papers/impossible.html |title=Impossible Figures in Perceptual Psychology |publisher=Fink.com |accessdate=11 February 2014}}</ref>

Impossible objects are of interest to [[psychologist]]s, [[mathematician]]s and [[artist]]s without falling entirely into any one discipline.

Notable impossible objects include:

* '''[[Impossible cube]]''' — The impossible cube was invented by [[M.C. Escher]] for ''[[Belvedere (M. C. Escher)|Belvedere]]'', a [[lithograph]] in which a boy seated at the foot of the building holds an impossible cube.<ref>{{cite book |author=Bruno Ernst (Hans de Rijk) |editor1-last=Schattschneider |editor1-first=D. |editor1-link=Doris Schattschneider |editor2-last=Emmer |editor2-first=M. |contribution=Selection is Distortion |pages=5–16 |publisher=Springer |title=M. C. Escher's Legacy: A Centennial Celebration |year=2003 |ref=harv |isbn=978-3-540-28849-7}}</ref><ref>{{Cite book |title=Impossibility: The Limits of Science and the Science of Limits |first=John D |last=Barrow |authorlink=John D. Barrow |publisher=Oxford University Press |year=1999 |isbn=9780195130829 |page=14 |url=http://books.google.com/books?id=0jRa1a4pD5IC&pg=PA14 |ref=harv}}</ref>

* '''[[Penrose stairs]]''' — The Penrose stairs was created by [[Lionel Penrose]] and his son [[Roger Penrose]].<ref name=p1958/> 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.

* '''[[Penrose triangle]]''' (Tribar) — The Penrose triangle 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".

* '''[[Blivet]]''' (or devil's tuning fork) — Blivet appears to have three cylindrical prongs at one end which then mysteriously transform into two rectangular prongs at the other end.<ref name=IFMW>{{Cite web |title=Impossible Fork |url=http://mathworld.wolfram.com/ImpossibleFork.html |publisher=[[Wolfram Research]] |accessdate=10 February 2014}}</ref>

{{Gallery

|title=Examples of impossible objects

|width=160 | height=160

|align=center

|File:Impossible cube illusion angle.svg

|An [[impossible cube]]

|File:Impossible staircase.svg

|[[Penrose stairs]]

|File:Penrose-dreieck.svg

|[[Penrose triangle]]

|File:Poiuyt--opaque.svg

|[[Blivet]]

}}

{{Gallery

|title=[[M. C. Escher]] drawings featuring impossible elements

|width=140 | height=140

|align=center

|File:Ascending_and_Descending.jpg

|''[[Ascending and Descending]]''

|File:belvedere.jpg

|''[[Belvedere (M. C. Escher)|Belvedere]]''

|File:Escher_Waterfall.jpg

|''[[Waterfall (M. C. Escher)|Waterfall]]''

}}

[[File:Penrosetrianglemodel.jpg|thumb|A 3D-printed version of the Reutersvaard Triangle illusion, its appearance created by a [[forced perspective]].]]

An early example of an impossible object comes from ''[[Apolinère Enameled]]'', 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.

[[Sweden|Swedish]] artist [[Oscar Reutersvärd]] was one of the first to deliberately design many impossible objects. He has been called "the father of impossible figures".<ref name=Seckel>{{cite book |url=http://books.google.co.uk/books?id=t5IgWas4rJwC&pg=PA261#v=onepage&q&f=false |title=Masters of Deception: Escher, Dalí & the Artists of Optical Illusion |last=Seckel |first=Al |isbn=1402705778 |year=2004 |pages=261 |publisher=Sterling Publishing Company}}</ref> 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, [[United Kingdom|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, of whom they were unaware. The article was published in 1958.<ref name=p1958>{{cite journal |first1=LS |last1=Penrose |first1=R. |last1=Penrose |title=Impossible objects: A special type of optical illusion |journal=British Journal of Psychology |volume=49 |issue=1 |year=1958 |pages=31–33}}</ref>

From the 1930s onwards [[Netherlands|Dutch]] artist [[M.C. Escher]] produced many drawings featuring paradoxes of perspective gradually working towards impossible objects".<ref name="Seckel"/> 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. 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]].

==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.<ref>{{cite journal |first1=Chih W. |last1=Khoh |first1=Peter |last1=Kovesi |url=http://www.csse.uwa.edu.au/~pk/Impossible/impossible.html |title=Animating Impossible Objects |date=February 1999 |accessdate=10 February 2014}}</ref>

{{Wide image|Perth Impossible Triangle.jpg|800px|alt=|Views of a sculpture from different angles. As the view rotates, a Penrose triangle appears to form.|Impossible triangle sculpture as an [[optical illusion]], East Perth, Western Australia|dir=rtl}}

{{div col|colwidth=30em}}

* [[Four-dimensional space]]

* [[Multistable perception]]

* [[Necker cube]]

* [[Non-Euclidean geometry]]

* [[Paradox]]

* [[Puzzle]]

* [[Strange loop]]

* [[Surrealism]]

* [[Tesseract]]

* [[Mobius strip]]

{{div col end}}

{{portal bar|Mathematics|Geometry|Psychology|Visual arts}}

{{reflist}}

==Further reading==

* Bower, Gordon H. (editor), (1990). [http://books.google.com/books?id=UiRvY5MqKfwC&pg=PA107 ''Psychology of Learning & Motivation'']. Academic Press. Volume 26. p. 107. ISBN 0080863779

* ''Mathematical Circus'', Martin Gardner 1979 ISBN 0-14-022355-X (Chapter 1 – Optical Illusions)

* ''Optical Illusions'', Bruno Ernst 2006 ISBN 3-8228-5410-7

{{Commons category multi|Impossible objects|Optical illusions}}

* [http://www.im-possible.info/ Impossible World]

* [http://www.cs.technion.ac.il/~gotsman/Escher/ The M.C. Escher Project]

* [http://psylux.psych.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/art_of_reutersvard.html Art of Reutersvard]

* [http://www.cs.technion.ac.il/~gershon/EscherForReal/ Real Escher Objects]

* [http://www.hss.adelaide.edu.au/philosophy/inconsistent-images/ Inconsistent Images]