Go deeper · Exercise 1
There may be times when what is most needed is, not so much a new discovery or a new idea as a different 'slant'; I mean a comparatively slight readjustment in our way of looking at the things and ideas on which attention is already fixed.
— Owen Barfield, Saving the Appearances (1957), Introduction
Why a simple line drawing keeps flipping between two 3D shapes, what that reveals about how the brain builds what we see, and why it makes a gentle object for meditation.
The figure is just twelve straight lines on a flat screen: two overlapping squares joined at the corners. Yet almost nobody sees it as flat. Your visual system reads it as a wire-frame cube, and then runs into a problem: the drawing contains no clue about which square is at the front. Both answers fit the lines equally well.
So the cube flips. For a while one face seems to sit in front; then, without anything on the screen changing, the other face jumps forward and the cube seems to point a different way. Some people can also let it fall back into a flat pattern of lines. Psychologists call figures like this ambiguous, and the experience of switching between interpretations is known as bistable, or more generally multistable, perception.
The figure is named after Louis Albert Necker (1786–1861), a Swiss crystallographer and geographer from Geneva. In 1832 he published a letter in the London and Edinburgh Philosophical Magazine describing, among other things, “an optical phænomenon which occurs on viewing a figure of a crystal or geometrical solid”: the apparent orientation of a drawn crystal would reverse on its own while he looked at it. The cube that now carries his name went on to become one of the most studied images in perception research.
In 1957 Owen Barfield opened Saving the Appearances with this drawing. He calls it a rectangular glass box in perspective and tells the reader to slide a hand across it and look again. The box turns inside out and lies at a different angle; the drawing has not changed. Then he says the whole book is an attempt to slide that same hand across three hundred years of Western assumptions about what perceiving is.
His word for what the brain does when it builds a cube out of twelve lines is figuration. His word for forgetting that we do it is idolatry. The cube is the one object that will not let you forget, because it flips.
Late in the book he describes what he calls final participation: taking part in the figuring on purpose, knowing that you do it. Three minutes with this cube is a small, repeatable version of that.
Because the image stays exactly the same while the experience changes, ambiguous figures let researchers separate what reaches the eyes from what the brain makes of it. Reviews of this work describe a consistent picture: perception alternates spontaneously between the possible interpretations, typically every few seconds, and the switches involve an interplay between visual areas and frontal and parietal regions of the brain (Sterzer, Kleinschmidt & Rees, 2009).
The timing is not fixed. How often the cube flips varies from moment to moment, and it also differs between people, enough that researchers study reversal rate as something like an individual trait (Kleinschmidt, Sterzer & Rees, 2012). Brain-recording (EEG) studies suggest the visual system settles on one interpretation within roughly 50 milliseconds of a new image appearing, and that a reversal is already under way well before you notice it and report it (Kornmeier & Bach, 2012).
Can you choose which cube you see? Partly. In one study, observers asked to hold one view of the Necker cube made it last noticeably longer, a much stronger effect of attention than in a related phenomenon called binocular rivalry (Meng & Tong, 2004). But the reversals did not stop. Attention leans on the process; it does not fully run it.
One influential way of thinking about this comes from predictive processing, which treats perception as the brain's best guess about the causes of its sensory input. When two guesses explain the input equally well, neither can win for good, and experience swings between them. Hohwy, Roepstorff and Friston (2008) set out this account for binocular rivalry. Applying it to the Necker cube is a natural extension, but it is a theoretical framework rather than a settled fact.
This section is our interpretation, offered as a way of practicing, not a research finding.
Watching the cube flip is a small, safe demonstration of something contemplative traditions point to: the content of experience keeps changing, often without your permission, while the awareness that notices the change stays the same. You did not decide to see the cube the other way round. It simply happened, and you were there to notice it.
So the exercise asks for a light touch. Rest your gaze on the cube without forcing a flip or clinging to a view. Notice each change as it arrives, and notice the knowing of it. If you catch yourself straining to control the image, that is worth noticing too, and then you can soften. Over a few minutes the shifting cube becomes a simple reminder: the content changes, the witnessing doesn't.
The same kind of flip also works in motion: a diamond of glowing points that can be seen turning either way.
The Illusions Index: Necker Cube.
Barfield, O. (1957). Saving the Appearances: A Study in Idolatry. Faber & Faber.