Necker Cube

The Necker Cube: a wire frame cube with no depth cues.

The Necker Cube is an optical illusion first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker.^[1]

Ambiguity

See also: Ambiguity#Visual art

The Necker Cube is an ambiguous line drawing.

Necker Cube on the left, impossible cube on the right.

One possible interpretation of the Necker Cube, often claimed to be the most common interpretation^{[citation needed]}

Another possible interpretation

The effect is interesting because each part of the picture is ambiguous by itself, yet the human visual system picks an interpretation of each part that makes the whole consistent. The Necker Cube is sometimes used to test computer models of the human visual system to see whether they can arrive at consistent interpretations of the image the same way humans do.

Humans do not usually see an inconsistent interpretation of the cube. A cube whose edges cross in an inconsistent way is an example of an impossible object, specifically an impossible cube (compare Penrose triangle).

With the cube on the left, most people see the lower-left face as being in front most of the time. This is possibly because people view objects from above, with the top side visible, far more often than from below, with the bottom visible, so the brain "prefers" the interpretation that the cube is viewed from above. Another reason behind this may be due to the brain's natural preference of viewing things from left to right, therefore seeing the leftmost square as being in front.

There is evidence that by focusing on different parts of the figure one can force a more stable perception of the cube. The intersection of the two faces that are parallel to the observer forms a rectangle, and the lines that converge on the square form a "y-junction" at the two diagonally opposite sides. If an observer focuses on the upper "y-junction" the lower left face will appear to be in front. The upper right face will appear to be in front if the eyes focus on the lower junction (Einhauser, et al., 2004).

This is an example of two identical necker cubes, the one on the left showing an intermediate object going in "down from the top" while the one on the right shows the object going in "up from the bottom" which shows how the image can change its perspective simply by changing which face (front or back) appears behind the intervening object.

It is possible to cause the switch to occur by focusing on different parts of the cube. If one sees the first interpretation on the right it is possible to cause a switch to the second by focusing on the base of the cube until the switch occurs to the second interpretation. Similarly, if one is viewing the second interpretation, focusing on the left side of the cube may cause a switch to the first.

The Necker Cube has shed light on the human visual system. The phenomenon has served as evidence of the human brain being a neural network with two distinct equally possible interchangeable stable states.^[2] Sidney Bradford, blind from the age of ten months but regaining his sight following an operation at age 52, did not perceive the ambiguity that normal-sighted observers do.^[3]

Epistemology

The Necker Cube is used in epistemology (the study of knowledge) and provides a counter-attack against naïve realism. Naïve realism (also known as direct or common-sense realism) states that the way we perceive the world is the way the world actually is. The Necker Cube seems to disprove this claim because we see one or the other of two cubes, but really, there is no cube there at all: only a two-dimensional drawing of twelve lines. We see something which is not really there, thus (allegedly) disproving naïve realism. This criticism of naïve realism supports representative realism.

A rotating Necker Cube was used to demonstrate that the human visual system can recruit new visual cues that affect the way things look.

Impossible cube

Viewed from a certain angle, this cube appears to defy the laws of geometry.

The impossible cube or irrational cube is an impossible object that draws upon the ambiguity present in a Necker Cube illustration^{[citation needed]}. An impossible cube is usually rendered as a Necker Cube in which the edges are apparently solid beams. This apparent solidity gives the impossible cube greater visual ambiguity than the Necker Cube, which is less likely to be perceived as an impossible object. The illusion plays on the human eye's interpretation of two-dimensional pictures as three-dimensional objects.

Viewed from another angle, however, the non-impossibility of the shape is apparent—its cubic nature itself is an illusion.

In M. C. Escher's lithograph Belvedere, the figure of a boy seated at the foot of the building is holding a type of impossible cube; the rest of the scene is based on the same principle that makes the impossible cube. In the scene, a ladder from the inside of the first story leads to the outside of the second. However, this is not appreciated by the prisoner in the basement cell because the basement is a possible cuboid and he is unambiguously on the inside.

A doctored photograph purporting to be of an impossible cube was published in the June 1966 issue of Scientific American, where it was called a "Freemish Crate".

See also

• Penrose triangle
• The Spinning Dancer
• Blivet

References

1. ^ Necker, L. A., 1832, “Observations on some remarkable optical phaenomena seen in Switzerland; and on an optical phaenomenon which occurs on viewing a figure of a crystal or geometrical solid,” London and Edinburgh Philosophical Magazine and Journal of Science, Vol. 1, No. 5, pp. 329–337
2. ^ David Marr: Vision. 1982.
3. ^ Gregory, Richard. The Blind Leading the Sighted: An Eye-Opening Experience of the Wonders of Perception.. Nature, Vol 430, August 2004.

• Einhäuser, Wolfgang; Martin, Kevan A. C. & König, Peter (2004). "Are switches in perception of the Necker cube related to eye position?". European Journal of Neuroscience 20 (10): 2811–2818. doi:10.1111/j.1460-9568.2004.03722.x. PMID 15548224. 

External links

• History of the cube and a Java applet
• Modelling human perception of the cube
• Video demonstration of the Necker Cube