View source for Physics:Impossible object

{{short description|Type of optical illusion}}
{{for multi|John Frankenheimer's film|Impossible Object|the independent rock band|The Impossible Shapes}}

[[File:Impossible cube illusion angle.svg|thumb|An [[Impossible cube|impossible cube]]]]
An '''impossible object''' (also known as an '''impossible figure''' or an '''undecidable figure''') is a type of [[Physics:Optical illusion|optical illusion]] that consists of a two-dimensional figure which is instantly and naturally understood as representing a [[Graphical projection|projection]] of a three-dimensional object but cannot exist as a solid object. Impossible objects are of interest to [[Social:Psychologist|psychologist]]s, mathematicians and artists without falling entirely into any one discipline.

==Notable examples==
Notable impossible objects include:
* [[Borromean rings]] — although conventionally drawn as three linked circles in three-dimensional space, any realization must be non-circular<ref>{{cite book |contribution=Chapter 15: The Borromean Rings Don't Exist |title=Proofs from THE BOOK |title-link=Proofs from THE BOOK |pages=99–106 |first1=Martin |last1=Aigner |first2=Günter M. |last2=Ziegler |edition=6th |publisher=Springer |doi=10.1007/978-3-662-57265-8_15 |isbn=978-3-662-57265-8 |year=2018}}</ref>
* [[Impossible cube]] — invented by M.C. Escher for ''[[Unsolved: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 |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 |publisher=Oxford University Press |year=1999 |isbn=9780195130829 |page=14 |url=https://books.google.com/books?id=0jRa1a4pD5IC&pg=PA14 }}</ref>
* [[Physics:Penrose stairs|Penrose stairs]] – created by Oscar Reutersvärd and later independently devised and popularised by Lionel Penrose and his mathematician son [[Biography:Roger Penrose|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) – first created by the Swedish artist Oscar Reutersvärd in 1934. Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form".
* [[Physics:Impossible trident|Impossible trident]] (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.<ref name=IFMW>{{cite web |title=Impossible Fork |url=http://mathworld.wolfram.com/ImpossibleFork.html |publisher=[[Company:Wolfram Research|Wolfram Research]] |access-date=10 February 2014}}</ref>
* ''[[Physics:Shepard elephant|L'egsistential Quandary]]''  – Created by [[Biography:Roger Shepard|Roger Shepard]] 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.<ref name="AnOpt">{{cite web |url=http://www.anopticalillusion.com/2012/03/impossible-elephant/ |title=Impossible Elephant |last= Honeycutt |first= Brad |work=anopticalillusion.com |quote=..one of the most famous and classic optical illusions of all time.  While most people know it simply as the "impossible elephant", the actual title of the work is "''L’egs-istential Quandary''".|date=March 9, 2012 |access-date=March 11, 2019}}</ref>

{{Gallery
|title=Examples of impossible objects
|width=160 |height=160
|align=center
|File:Borromean Rings Illusion.png |[[Borromean rings]]
|File:Reutersvärd’s triangle.svg |Oscar Reutersvärd's optical illusion (1934)
|File:Impossible staircase.svg |[[Physics:Penrose stairs|Penrose stairs]]
|File:Penrose-dreieck.svg|[[Penrose triangle]]
|File:Poiuyt.svg|[[Physics:Impossible trident|Impossible trident]]
|File:Waterfall.svg|[[Unsolved:Waterfall (M. C. Escher)|Impossible waterfall]]
|File:Elephant legs illusion, variant of Roger Shepard's L'egsistential paradox.png|A variant of ''[[Physics:Shepard elephant|L'egsistential Quandary]]''
}}

==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]] would most likely be seen as a [[Cube|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.<ref>{{cite web |url=http://www.fink.com/papers/impossible.html |title=Impossible Figures in Perceptual Psychology |publisher=Fink.com |access-date=11 February 2014}}</ref>

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]] 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]] concept of [[Cohomology|cohomology]].<ref>{{cite web|last=Phillips|first=Tony|title=The Topology of Impossible Spaces|publisher=American Mathematical Society|url=http://www.ams.org/publicoutreach/feature-column/fc-2014-10}}</ref><ref>{{cite journal|last=Penrose|first=Roger|title=On the Cohomology of Impossible Figures|journal=Leonardo|year=1992 |volume=25|number=3,4|pages=245–247|publisher=The MIT Press|doi=10.2307/1575844|jstor=1575844 |s2cid=125905129 }}</ref>

==History==
An early example of an impossible object comes from ''[[Unsolved:Apolinère Enameled|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.
[[File:Penrosetrianglemodel.jpg|thumb|A 3D-printed version of the Reutersvärd Triangle illusion, its appearance created by a [[Forced perspective|forced perspective]].|left]]
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=https://archive.org/details/mastersofdecepti00alse |url-access=registration |title=Masters of Deception: Escher, Dalí & the Artists of Optical Illusion |last=Seckel |first=Al |isbn=1402705778 |year=2004 |page=[https://archive.org/details/mastersofdecepti00alse/page/261 261] |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, British psychiatrist Lionel Penrose and his son, mathematician [[Biography:Roger Penrose|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 |first2=R. |last2=Penrose |title=Impossible objects: A special type of optical illusion |journal=British Journal of Psychology |volume=49 |issue=1 |year=1958 |pages=31–33 |doi=10.1111/j.2044-8295.1958.tb00634.x |pmid=13536303}}</ref>

From the 1930s onwards, 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: ''[[Unsolved:Cube with Magic Ribbons|Cube with Magic Ribbons]]''. He produced many further drawings featuring impossible objects, sometimes with the entire drawing being an impossible object. ''[[Unsolved:Waterfall (M. C. Escher)|Waterfall]]'' and ''[[Unsolved:Belvedere (M. C. Escher)|Belvedere]]'' 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, Sandro del Prete, István Orosz (Utisz), Guido Moretti, Tamás F. Farkas, Mathieu Hamaekers, and [[Biography:Kokichi Sugihara|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|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 |first2=Peter |last2=Kovesi |url=http://www.csse.uwa.edu.au/~pk/Impossible/impossible.html |title=Animating Impossible Objects |date=February 1999 |access-date=10 February 2014 |archive-url=https://web.archive.org/web/20150528135957/http://www.csse.uwa.edu.au/~pk/Impossible/impossible.html |archive-date=28 May 2015 |url-status=dead }}</ref>

{{Wide image
|Perth Impossible Triangle.jpg
|800px
|alt=
|As the  viewing angle changes of this sculpture in East Perth, Australia,  a [[Penrose triangle]] appears to form.|Impossible triangle sculpture as an [[Physics:Optical illusion|optical illusion]], East Perth, Western Australia|dir=rtl}}

==See also==
{{div col}}
* {{annotated link|Four-dimensional space}}
* {{annotated link|Mathematics and art}}
* {{annotated link|Möbius strip}}
* {{annotated link|Physics:Multistable perception}}
* {{annotated link|Necker cube}}
* {{annotated link|Non-Euclidean geometry}}
* {{annotated link|Philosophy:Paradox}}
* {{annotated link|Physics:Pareidolia}} 
* {{annotated link|Puzzle}}
* {{annotated link|Strange loop}}
* {{annotated link|Tesseract}}
* {{annotated link|Tritone paradox}}
{{div col end}}

==References==
{{reflist}}

==Further reading==
* Bower, Gordon H. (editor), (1990).  [https://books.google.com/books?id=UiRvY5MqKfwC&pg=PA107 ''Psychology of Learning & Motivation'']. Academic Press. Volume 26. p.&nbsp;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}}

==External links==
* [https://im-possible.info/ Impossible World]
* [https://www.cs.technion.ac.il/~gotsman/Escher/ The M.C. Escher Project]
* [https://web.archive.org/web/20110719100440/http://psylux.psych.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/art_of_reutersvard.html Art of Reutersvard]
* [http://gershonelber.org/EscherForReal/ "Escher for Real"] (3D objects)
* [http://www.hss.adelaide.edu.au/philosophy/inconsistent-images/ Inconsistent Images]
* [https://www.youtube.com/watch?v=GybxIwfU4rI Echochrome], a video game that incorporates impossible objects into its gameplay

{{Optical illusions}}

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[[Category:Optical illusions]]

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