Necker cube

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

The Necker cube is an optical illusion first published in 1832 by Swiss crystallographer Louis Albert Necker.

1 Ambiguity
2 Epistemology
3 Impossible cube
4 See also
5 External links
6 References

[edit] Ambiguity

The Necker cube is an ambiguous line drawing. It is a wire-frame drawing of a cube in isometric perspective, which means that parallel edges of the cube are drawn as parallel lines in the picture. When two lines cross, the picture does not show which is in front and which is behind. This makes the picture ambiguous; it can be interpreted two different ways. When a person stares at the picture, it will often seem to flip back and forth between the two valid interpretations (so-called multistable perception).

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

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.

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).

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.^[1] 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.

[edit] 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.

Richard Dawkins in his 1982 book The Extended Phenotype, and later new preface to a later edition of The Selfish Gene, uses a Necker cube as an analogy of two ways to view the same object to introduce the gene-centric view of evolution.

[edit] 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. 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 an 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".