How a flat picture becomes 3D
Why you see a solid object in a few lines on a page, and why you keep seeing it when it can’t exist.
How this site works. Every fact is in our own words and linked to its source, beside it. Where good sources disagree, we show each version in a “Sources differ” box. Every drawing is our own.
A flat image, a 3D world
Your brain builds a 3D model of the world from the flat image on the back of your eye. Michael Bach
At the start of the 18th century the philosopher George Berkeley argued that we can’t see depth directly, because the image of anything on the retina is flat, like a painting. Britannica Britannica notes that modern research does not back Berkeley’s idea that reasoning is the key to seeing depth; today’s theories mix inborn abilities with things we learn. Britannica
Psychologists also study how we know a cube has six sides when only three can be seen at once. Britannica
The Necker cube
Even seeing a wire cube in a flat line drawing is an interpretation: many shapes could cast those same lines, but the brain picks a cube as the most likely answer. Michael Bach
Stare at a Necker cube and it suddenly flips between two orientations, typically every 3 to 5 seconds. Michael Bach You can’t hold one version for long: after 10 seconds or so it flips again. Blinking can make it flip. Michael Bach
L. A. Necker was a Swiss mineralogist who came across the flip by chance while looking at a drawing of a cube-like crystal. He described it in 1832. Michael Bach
Flip timer
Look at the cube above. Press start, then tap the big button every time the cube flips. After 30 seconds we work out your flip rate.
Needs JavaScript. Without it, count the flips yourself for 30 seconds.
The missing corner
The “missing corner” cube can be seen three ways: a cube with a corner cut out, a small cube stuck on the front, or a cube sitting in the corner of a room. Michael Bach Without stereo depth or clear lighting, all three readings are geometrically possible. Michael Bach
Why impossible objects fool you
With an impossible object, every corner makes sense on its own. The trouble is that the corners combine viewpoints that can’t all be true at once. Michael Bach
Trace it from the top corner: one side seems to run away from you, the other towards you, yet they meet on the same level at the bottom. Illusions Index
Researchers describe impossible structures as having odd geometry that isn’t obvious “pre-attentively”: within a single fixation of the eye, about 120 milliseconds. J. Imaging, 2020
A 2020 study modelling the human retina argued that Escher’s secret was to place the clashing parts just outside the area the eye can check for 3D sense in one fixation. J. Imaging, 2020
Knowing doesn’t help
Cognitive scientists ask why we keep seeing an impossible figure as a real object even after we know it can’t exist. Illusions Index One standard answer is that parts of the visual system are “cognitively impenetrable”: knowing better doesn’t change what they output. Illusions Index
Philosophers are interested because impossible figures seem to give us experiences with contradictory content. Illusions Index
Mathematicians have studied impossible figures to model them for uses such as computer vision. Illusions Index
Michael Bach points out that an impossible figure is a different thing from the Necker cube’s flipping, though he finds his impossible version even less stable. Michael Bach
Our view: impossible objects are the best proof that seeing is guessing. Your eye isn’t lying to you; your brain is making its best bet, one corner at a time.
Size illusions work on the same brain, but on lengths rather than shapes: see the Ponzo illusion and size constancy on size.illusions.im.