Necker cube

A drawing of a wire cube (drawn without perspective) which spontaneously reverses in depth (Fig. 1). It was first described by the Swiss naturalist and crystallographer L. A. Necker in a letter to Sir David Brewster in 1832. Necker discovered it while looking at rhomboid crystals with a microscope and drawing them: the drawings switched in depth and no longer seemed to compare with the crystals as seen with the microscope. There are many other depth-ambiguous figures.

A true wire cube will also reverse in depth, when it will stand up bizarrely on a corner, and rotate as the observer moves — following every movement, though at twice the speed. It also changes in shape.

Necker's drawing was not quite the familiar cube (Fig. 1). As Boring (1942) points out, his original figure is reversed more easily than the cube: 'for the rhomboid stands upon an edge and is prejudiced by neither perspective, whereas that cube is seen more easily flat upon the ground ("M near") than in the alternative peculiar uplifted position ("N near")'. John Harris (1979) found this for the Schröder staircase — tending to remain stable when drawn in perspective — though perspective Necker cubes will still sometimes reverse. Evidently the perceptual system dynamically seeks alternatives against considerable evidence for one 'hypothesis'.

Try holding a skeleton cube (made of wire, or matches glued together) in the hand, and wait for it to reverse (viewed with one eye if necessary) and slowly rotate it. As it rotates, the cube swings round visually in the opposite direction. It moves counter to touch and proprioception. This feels as though one's wrist has broken, though with no pain (Shopland and Gregory 1964). The counter-rotation shows that vision is not essentially tied to touch, though it can be affected by touch. Why does the flip-reversed cube appear to rotate backwards to its real motion, and backwards also to the observer moving around it? Depth-reversed vision effectively reverses motion-parallax, as near and far are perceptually switched.

The reason for the shape-change of a flipped cube is significant. We may ask first: why normally does a skeleton cube look like a true cube — its near and far faces appearing practically the same size, though they are very different on the retina? (One can see this by viewing the cube as a shadow, from a small source of light such as a candle. The shadow is a perfect perspective projection, and is precisely the form of the retinal image (whether reversed or not) given by the cube, yet it looks very different.) It is surprising that the unreversed wire cube appears with its near and further faces the same size, as there are no 'bottom up' cues for setting size constancy. The perspective drawing of the cube does not have these effects. What is the crucial difference between the wire cube object and the drawing? The difference is: the cube object is seen in realistic depth — the drawing is seen as flat, or in the curious pseudo-depth of pictures. We can show that this is a crucial difference by making the drawing appear in true depth, by removing the paper background. This can be done by drawing it in luminous paint, and viewing in the dark with one eye. Then it appears as strikingly three-dimensional, like a true cube, and will change shape when it flips in depth.

Such ambiguous objects are wonderfully useful as demonstrations for separating 'bottom-up' from 'top-down' visual processing. When the perception changes though there is no change of the sensory input, the change of appearance cannot be due to bottom-up processing. It must be set downwards by the prevailing perceptual hypothesis of what is near and what is far. This shows that size constancy can operate 'downwards' from the prevailing perception of depth, which is important for explaining many distortions, such as the moon illusion.


Fig. 1. Necker cube. This can be seen as switching spontaneously in depth, the front face reversing with the back face.


(Published 1987)

See also illusions.

— Richard L. Gregory

Bibliography
• Boring, E. G. (1942). Sensation and Perception in the History of Experimental Psychology.
• Gregory, R. L. (1963). 'Distortion of visual space as inappropriate constancy scaling'. Nature, 119.
• — —  (1968). 'Perceptual illusions and brain models'. Proceedings of the Royal Society of London, 171.
• — —  (1997). Eye and Brain (5th edn.).
• Harris, J. P. (1979). 'The Schröder Staircase: a new perspective'. Perception and Psychophysics, 26.
• Necker, L. A. (1832). 'Observations on some remarkable phaenomena seen in Switzerland; and an optical phaenomenon which occurs on viewing of a crystal or geometrical solid'. Philsophical Magazine, series 3 1.
• Shopland, C., and Gregory, R. L. (1964). 'The effects of touch on a visually ambiguous three-dimensional figure'. Quarterly Journal of Experimental Psychology, 16.

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