Myths

Myths about impossible objects

Ten common ideas, checked against the sources.

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.

1. MythRoger Penrose invented the impossible triangle.

   FactOscar Reutersvärd had drawn the shape earlier, though the Penroses didn’t know. Escher in The Palace In 1934, aged only 18, he drew an impossible triangle while sketching cubes in perspective. Escher in The Palace The Illusions Index says Reutersvärd created it first and the Penroses discovered it independently and made it popular. Illusions Index

2. MythEscher invented the never-ending staircase.

   FactHe designed an impossible staircase in 1937. Escher in The Palace The Penroses’ 1958 article included a drawing and a 3D model of a continuous flight of stairs that seems to lead up, or down, for ever. Escher in The Palace The Penrose article sparked the idea, and he started work in late 1959. Escher in The Palace

3. MythImpossible objects are a 20th-century invention.

   FactThe oldest impossible scene Bach knows is the Madonna and Child in the Pericope of Henry II, from around 1025, though he thinks that one was probably not on purpose. Michael Bach Bach lists Josef Albers’s “Rolled Wrongly” from 1931 and Hogarth’s Satire on False Perspective from 1754. Michael Bach

4. MythAn impossible triangle can’t be built.

   FactIn 1968 Richard Gregory made a wooden object that looks like a real impossible triangle from one position only; from anywhere else it is clearly three joined struts. Illusions Index The minister said it can only be fully appreciated by moving around it to watch the shape change and the illusion appear. WA Government, 1999

5. MythOnce you know the trick, you stop seeing it.

   FactCognitive 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

6. MythThe Necker cube is an impossible object.

   FactA Necker cube is a cube drawn with all its edges showing, so you can’t tell which face is at the front. It can exist on paper; the man’s cube can’t. Escher in The Palace 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

7. MythEscher was a mathematician.

   FactHe did not excel at mathematics at school. Britannica Britannica: his mature style, after 1937, combined meticulous realism with puzzling optical illusions. Britannica

8. MythReutersvärd drew only a handful of figures.

   FactHe drew thousands of them, plain, with no settings or decoration, unlike Escher, who hid his impossibilities in realistic scenes. Escher in The Palace

9. MythThe devil’s fork has one proper name.

   FactThe devil’s fork is also called the blivet; in his 1964 paper D. H. Schuster called it a “three-stick clevis”. Michael Bach Other names include the impossible fork, the devil’s pitchfork and the poiuyt. MathWorld

10. MythWaterfall shows a working perpetual-motion machine.

    FactWater always flows to the lowest point, but in Waterfall the lowest, furthest point is also the highest and nearest. The water falls and the cycle starts again: perpetual motion. Escher in The Palace Waterfall’s water channel is built from three Penrose triple bars combined. Escher in The Palace