Impossible Objects




What to observe


The neighbouring contraption consists of the so-called “devil’s fork” (top right, also known as “blivet”), the “Penrose Frame” (centre) and the “hexnut” (3 of them bottom left, an enlarged specimen bottom right). Boggle your mind when trying to envisage to build such an object.




Our brain reconstructs an internal 3-dimensional world model from the flat retinal image.


The oldest –known to me– example of an impossible scene: “Madonna and Child ~ Adoration of the Magi” from the Pericope of Henry II around 1025. The impossible architecture in that painting, however, seems not done purposefully to me, in contrast to Hogarth’s ‘Frontispiece’. Often the first impossible object is attributed to Reutersvard (a design for a Swedish stamp), however Albers and Hogarth were clearly earlier. After the Penroses formally described the phenomenon, examples abound, beautifully drawn for instance by Escher.




Oscar Reutersvard (1934) “Opus 1”
William Hogarth (1754) ‘Frontispiece’: Satire on False Perspective
Josef Albers (1931) “Falsch gewickelt”
Magritte (1965) “Carte blanche”
Penrose & Penrose. Impossible objects: A special type of illusion. Brit J Psychol 1958;49–31
M. C. Escher (1960) “Belvedere” or “Ascending and descending” (Andrew Lipson’s LEGO version for the latter)
Artsy's Escher page
More on perspective: Chris Tyler
Wu, Fu, Yeung, Yia & Tang (2010) Modeling and rendering of impossible figures. ACM Transactions on Graphics 29 13:2–13:15



A draw-it-yourself impossible object




On the above you see an animation where you can draw along.


Start with 6 vertical equidistant lines, give them hats. You get a rendition of “3 towers” or a “three-pronged fork”. Obviously, a sensible 3-dimensional interpretation.


Cover the top, and draw connecting circle segments at the bottom. You see the bottom of a square bar, bent into an U-shape. Again, a sensible 3-dimensional interpretation.


However, uncovering the top also reveals the fact that the two interpretations are not compatible with each other.



Created: 2013-04-21

Last update: 2013-11-09