Two famous undecidable figures, the Penrose triangle and devil's pitchfork
An impossible object is an object that cannot exist according to the known laws of nature, but has a description or representation suggesting, at first sight, that it can.
Drawings of objects that cannot exist are called "undecidable figures". The undecidability of these figures invariably rests on them being interpreted as two-dimensional projections of what would be an impossible higher-dimensional object. Artist M. C. Escher is notable for many drawings that feature undecidable figures, sometimes with the entire drawing being an undecidable figure.
In the Star Trek: The Next Generation episode "I, Borg", a plan was made to destroy the entire race of Borg – malevolent cybernetic aliens whose minds were interconnected – by showing one of the borg a picture of a highly-complex impossible object. This image would be transmitted back to the Borg hive, overloading its consciousness in larger and larger attempts to understand the image. This plan was dismissed as being genocide, so its potential results were never seen.
References
Mathematical Circus, Martin Gardner 1979 ISBN 0-14-02-2355-X (Chapter 1 – Optical Illusions)
External links
Things Impossible (http://www.cut-the-knot.org/impossible/index.shtml)
This blivet is reminiscent of an M.C. Escher print—it portrays two impossible perspectives at once, creating a 'lost' layer between the top two rods, and an impossible extra, vanishing rod in between the bottom two.
The blivet is an undecipherable figure, an optical illusion and an impossibleobject.
It is an object that appears to have three cylindrical prongs at the bottom, which then somehow mysteriously transform into two rectangular prongs at the top.
Furthermore, the property ``to be an impossible figure'' is not the property of the drawing alone, but the property of its spatial interpretation by a human observer [9].
Impossible figures convey the impression of a 3D object and this strongly implies that one might be able to rotate such an object and view it from different angles.
The constant adjustment of the 3D model that is required to maintain the impossible figure as the viewpoint changes, is reduced to a simple rescaling of the dimensions of the object being used to model one of the complementary halves.
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