Impossible object

<h2 id="notable-examples">Notable examples</h2>
<p>Notable impossible objects include:
</p>

<h2 id="explanations">Explanations</h2>
<p>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 <a href="/facts/Necker_cube/0V4vU52d">Necker cube</a> would most likely be seen as a <a href="/facts/Cube/65lUaAqN">cube</a>, 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.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a>
</p><p>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 <a href="/facts/Geometry/wTQf5ffQ">geometry</a> of the implied object to determine that it is impossible.
</p><p>Roger Penrose wrote about describing and defining impossible objects mathematically using the <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a> concept of <a href="/facts/Cohomology/J7FJzTNh">cohomology</a>.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p>
<h2 id="history">History</h2>
<p>An early example of an impossible object comes from <i><a href="/facts/Apolin%25C3%25A8re_Enameled/8KYKq9Fv">Apolinère Enameled</a></i>, a 1916 advertisement painted by <a href="/facts/Marcel_Duchamp/Ud7neb1R">Marcel Duchamp</a>. 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.
</p>

<p><a href="/facts/Sweden/u3qC7lyj">Swedish</a> artist <a href="/facts/Oscar_Reutersv%25C3%25A4rd/47HsGVN4">Oscar Reutersvärd</a> was one of the first to deliberately design many impossible objects. He has been called "the father of impossible figures".<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> 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.
</p><p>In 1956, British psychiatrist <a href="/facts/Lionel_Penrose/Nxm02xvI">Lionel Penrose</a> and his son, mathematician <a href="/facts/Roger_Penrose/r4mlrFUH">Roger Penrose</a>, submitted a short article to the <i><a href="/facts/British_Journal_of_Psychology/9LKA1jVY">British Journal of Psychology</a></i> 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.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p><p>From the 1930s onwards, Dutch artist <a href="/facts/M._C._Escher/6uuAGlDx">M. C. Escher</a> produced many drawings featuring paradoxes of perspective gradually working towards impossible objects.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> In 1957, he produced his first drawing containing a true impossible object: <i><a href="/facts/Cube_with_Magic_Ribbons/ua4MtWbQ">Cube with Magic Ribbons</a></i>. He produced many further drawings featuring impossible objects, sometimes with the entire drawing being an impossible object. <i><a href="/facts/Waterfall_(M._C._Escher)/I7by2x4q">Waterfall</a></i> and <i><a href="/facts/Belvedere_(M._C._Escher)/WMKb56f7">Belvedere</a></i> are good examples of impossible constructions. His work did much to draw the attention of the public to impossible objects.
</p><p>Some contemporary artists are also experimenting with impossible figures, for example, <a href="/facts/Jos_de_Mey/2rhymAf4">Jos de Mey</a>, <a href="/facts/Shigeo_Fukuda/wSIaGADk">Shigeo Fukuda</a>, <a href="/facts/Sandro_del_Prete/Yx6EBxxM">Sandro del Prete</a>, <a href="/facts/Istv%25C3%25A1n_Orosz/jGe4hC8u">István Orosz</a> (<a href="/facts/Utisz/w9jvMlUv">Utisz</a>), Guido Moretti, Tamás F. Farkas, Mathieu Hamaekers, and <a href="/facts/Kokichi_Sugihara/HJlpxxEX">Kokichi Sugihara</a>.
</p>
<h2 id="constructed-impossible-objects">Constructed impossible objects</h2>
<p>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 <a href="/facts/Forced_perspective/VDjfWf7w">forced perspective</a> or having parts of the model appearing to be further or closer than they actually are.
</p><p>The notion of an "interactive impossible object" is an impossible object that can be viewed from any angle without breaking the illusion.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a>
</p>
As the  viewing angle changes of this sculpture in <a href="/facts/East_Perth/Cj620SDq">East Perth</a>, Australia,  a <a href="/facts/Penrose_triangle/A3UK4ov2">Penrose triangle</a> appears to form.
<h2 id="see-also">See also</h2>

<ul><li><a href="/facts/Four-dimensional_space/vFQd0M7T">Four-dimensional space</a> – Geometric space with four dimensions</li>
<li><a href="/facts/Mathematics_and_art/kT01G7la">Mathematics and art</a> – Relationship between mathematics and art</li>
<li><a href="/facts/M%25C3%25B6bius_strip/35kzqqFL">Möbius strip</a> – Non-orientable surface with one edge</li>
<li><a href="/facts/Multistable_perception/SG2q6GxR">Multistable perception</a> – Perceptual phenomenon</li>
<li><a href="/facts/Necker_cube/0V4vU52d">Necker cube</a> – Form of perceptual phenomena</li>
<li><a href="/facts/Non-Euclidean_geometry/efKa7De2">Non-Euclidean geometry</a> – Two geometries based on axioms closely related to those specifying Euclidean geometry</li>
<li><a href="/facts/Paradox/3VLGjuWf">Paradox</a> – Logically self-contradictory statement</li>
<li><a href="/facts/Pareidolia/JWvWUvkK">Pareidolia</a> – Perception of meaningful patterns or images in random or vague stimuli</li>
<li><a href="/facts/Puzzle/jHj94E7b">Puzzle</a> – Problem or enigma that tests</li>
<li><a href="/facts/Strange_loop/RhbBHH3X">Strange loop</a> – Cyclic structure that goes through several levels in a hierarchical system</li>
<li><a href="/facts/Surrealism/VUJpoo6c">Surrealism</a> – International cultural movement (1920s–1950s)</li>
<li><a href="/facts/Tesseract/tlqouBoU">Tesseract</a> – Four-dimensional analogue of the cube</li>
<li><a href="/facts/Tritone_paradox/VLbolJrv">Tritone paradox</a> – Auditory illusion</li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Bower, Gordon H. (editor), (1990).  <a href="https://books.google.com/books?id=UiRvY5MqKfwC&pg=PA107"><i>Psychology of Learning & Motivation</i></a>. Academic Press. Volume 26. p. 107. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0080863779</li>
<li><i>Mathematical Circus</i>, Martin Gardner 1979 <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-14-022355-X (Chapter 1 – Optical Illusions)</li>
<li><i>Optical Illusions</i>, Bruno Ernst 2006 <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 3-8228-5410-7</li></ul>
<h2 id="external-links">External links</h2>

Wikimedia Commons has media related to <i>Impossible objects</i> and <i>Optical illusions</i>.

<ul><li><a href="https://im-possible.info/">Impossible World</a></li>
<li><a href="https://www.cs.technion.ac.il/~gotsman/Escher/">The M.C. Escher Project</a> <a href="https://web.archive.org/web/20220123183803/http://www.cs.technion.ac.il/~gotsman/Escher/">Archived</a> 23 January 2022 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li>
<li><a href="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</a></li>
<li><a href="http://gershonelber.org/EscherForReal/">"Escher for Real"</a> (3D objects)</li>
<li><a href="http://www.hss.adelaide.edu.au/philosophy/inconsistent-images/">Inconsistent Images</a></li>
<li><a href="https://www.youtube.com/watch?v=GybxIwfU4rI">Echochrome</a>, a video game that incorporates impossible objects into its gameplay</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Impossible Figures in Perceptual Psychology". Fink.com. Retrieved 11 February 2014. <a href="http://www.fink.com/papers/impossible.html" target="_blank">http://www.fink.com/papers/impossible.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Phillips, Tony. "The Topology of Impossible Spaces". American Mathematical Society. <a href="http://www.ams.org/publicoutreach/feature-column/fc-2014-10" target="_blank">http://www.ams.org/publicoutreach/feature-column/fc-2014-10</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Penrose, Roger (1992). "On the Cohomology of Impossible Figures". Leonardo. 25 (3, 4). The MIT Press: 245–247. doi:10.2307/1575844. JSTOR 1575844. S2CID 125905129. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Seckel, Al (2004). Masters of Deception: Escher, Dalí & the Artists of Optical Illusion. Sterling Publishing Company. p. 261. ISBN 1402705778. <a href="1402705778" target="_blank">1402705778</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Penrose, LS; Penrose, R. (1958). "Impossible objects: A special type of optical illusion". British Journal of Psychology. 49 (1): 31–33. doi:10.1111/j.2044-8295.1958.tb00634.x. PMID 13536303. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Seckel, Al (2004). Masters of Deception: Escher, Dalí & the Artists of Optical Illusion. Sterling Publishing Company. p. 261. ISBN 1402705778. <a href="1402705778" target="_blank">1402705778</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Khoh, Chih W.; Kovesi, Peter (February 1999). "Animating Impossible Objects". Archived from the original on 28 May 2015. Retrieved 10 February 2014. <a href="https://web.archive.org/web/20150528135957/http://www.csse.uwa.edu.au/~pk/Impossible/impossible.html" target="_blank">https://web.archive.org/web/20150528135957/http://www.csse.uwa.edu.au/~pk/Impossible/impossible.html</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
</ol>

Impossible object open-in-new

Impossible object