Type of optical illusion
An
impossible object
(also known as an
impossible figure
or an
undecidable figure
) is a type of
optical illusion
that consists of a two-
dimensional
figure which is instantly and naturally understood as representing a
projection
of a
three-dimensional object
but cannot exist as a solid object. Impossible objects are of interest to
psychologists
, mathematicians and artists without falling entirely into any one discipline.
Notable examples
[
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]
Notable impossible objects include:
-
Borromean rings
? although conventionally drawn as three linked circles in three-dimensional space, any realization must be non-circular.
[3]
-
Penrose stairs
? created by
Oscar Reutersvard
and later independently devised and popularised by
Lionel Penrose
and his mathematician son
Roger Penrose
.
[4]
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 Reutersvard
in 1934. Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form".
-
Impossible trident
(or devil's tuning fork) ? also known as a "blivet", this has three cylindrical prongs at one end, which then mysteriously transform into two rectangular prongs at the other end.
[5]
-
-
Oscar Reutersvard
's optical illusion (1934)
Explanations
[
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]
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
, 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.
[6]
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
of the implied object to determine that it is impossible.
Roger Penrose wrote about describing and defining impossible objects mathematically using the
algebraic topology
concept of
cohomology
.
[7]
[8]
History
[
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]
An early example of an impossible object comes from
Apolinere 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.
Swedish
artist
Oscar Reutersvard
was one of the first to deliberately design many impossible objects. He has been called "the father of impossible figures".
[9]
In 1934, he drew the Penrose triangle, some years before the Penroses. In Reutersvard's version, the sides of the triangle are broken up into cubes.
In 1956, 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 Reutersvard, of whom they were unaware. The article was published in 1958.
[4]
From the 1930s onwards, Dutch artist
M.C. Escher
produced many drawings featuring paradoxes of perspective gradually working towards impossible objects.
[9]
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.
Waterfall
and
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
,
Istvan Orosz
(
Utisz
),
Guido Moretti
,
Tamas F. Farkas
,
Mathieu Hamaekers
, and
Kokichi Sugihara
.
Constructed impossible objects
[
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]
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.
[10]
See also
[
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]
- Four-dimensional space
? Geometric space with four dimensions
- Mathematics and art
? Relationship between mathematics and art
- Mobius strip
? Non-orientable surface with one edge
- Multistable perception
? Perceptual phenomenon
- Necker cube
? Form of perceptual phenomena
- Non-Euclidean geometry
? Two geometries based on axioms closely related to those specifying Euclidean geometry
- Paradox
? Statement that apparently contradicts itself
- Pareidolia
? Perception of meaningful patterns or images in random or vague stimuli
- Puzzle
? Problem or enigma that tests
- Strange loop
? Cyclic structure that goes through several levels in a hierarchical system
- Surrealism
? International cultural movement active from the 1920s to the 1950s
- Tesseract
? Four-dimensional analogue of the cube
- Tritone paradox
? An auditory illusion perceived by some people to be rising in pich and by others to be falling
References
[
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]
- ^
Bruno Ernst (Hans de Rijk) (2003). "Selection is Distortion". In
Schattschneider, D.
; Emmer, M. (eds.).
M. C. Escher's Legacy: A Centennial Celebration
. Springer. pp. 5?16.
ISBN
978-3-540-28849-7
.
- ^
Barrow, John D
(1999).
Impossibility: The Limits of Science and the Science of Limits
. Oxford University Press. p. 14.
ISBN
9780195130829
.
- ^
Aigner, Martin
;
Ziegler, Gunter M.
(2018). "Chapter 15: The Borromean Rings Don't Exist".
Proofs from THE BOOK
(6th ed.). Springer. pp. 99?106.
doi
:
10.1007/978-3-662-57265-8_15
.
ISBN
978-3-662-57265-8
.
- ^
a
b
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
.
- ^
"Impossible Fork"
.
Wolfram Research
. Retrieved
10 February
2014
.
- ^
"Impossible Figures in Perceptual Psychology"
. Fink.com
. Retrieved
11 February
2014
.
- ^
Phillips, Tony.
"The Topology of Impossible Spaces"
. American Mathematical Society.
- ^
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
b
Seckel, Al (2004).
Masters of Deception: Escher, Dali & the Artists of Optical Illusion
. Sterling Publishing Company. p.
261
.
ISBN
1402705778
.
- ^
Khoh, Chih W.; Kovesi, Peter (February 1999).
"Animating Impossible Objects"
. Archived from
the original
on 28 May 2015
. Retrieved
10 February
2014
.
Further reading
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External links
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