The Staircase That Goes Nowhere
September 5, 2026 · by White Nights
In 1958, mathematician Lionel Penrose and his son Roger — who would later win the Nobel Prize in Physics for his work on black holes and singularities — published a paper in the British Journal of Psychology titled "Impossible Objects: A Special Type of Visual Illusion." In it, they described several figures that appeared three-dimensional but could not exist in three-dimensional space.
One of them was a triangle made of three square beams, each perpendicular to the others, each appearing to connect seamlessly at the corners despite the geometry being physically impossible. Another was a staircase that, if you followed it continuously in one direction, would always be ascending — but would bring you back to where you started. They called it the Penrose stairs.
M.C. Escher had encountered Penrose's earlier impossible triangle in 1954, and it had immediately captured his imagination. After seeing the Penrose stairs paper, he produced Ascending and Descending in 1960 — a painting of monks walking perpetually up or down staircases that loop back on themselves, going nowhere forever. It became one of his most famous works.
What makes impossible objects interesting isn't that they're tricks. They reveal something about how perception works: the brain constructs a coherent three-dimensional model from two-dimensional information, and it can be made to commit to an interpretation that the geometry doesn't support. The impossibility only becomes apparent when you try to reconcile the parts into a whole.
Roger Penrose went on to describe Penrose tilings — patterns that tile a plane without repeating — and made fundamental contributions to our understanding of space, time, and cosmology alongside Stephen Hawking. The staircase was a side project.