Roger and Lionel Penrose

Two careers, one famous paper

Lionel Penrose (1898–1972) was a British psychiatrist and geneticist, one of the founders of modern medical genetics, who spent much of his career at University College London studying the genetics of learning disability. His son Roger Penrose (born 1931) became a mathematical physicist, whose work on general relativity and black holes earned him a share of the 2020 Nobel Prize in Physics, together with Reinhard Genzel and Andrea Ghez (Nobel Foundation, 2020).

Father and son shared a love of geometric puzzles. In 1958 they published a short paper in the British Journal of Psychology called "Impossible objects: A special type of visual illusion" (Penrose & Penrose, 1958). It introduced two figures that have become the best-known impossible objects in the world: the Penrose triangle and the endless staircase now called the Penrose stairs.

The triangle and the stairs

The triangle is made of three beams, each meeting the next at a believable right angle, arranged so the whole thing seems to form a closed loop. Every joint makes sense; the loop doesn't, because following the beams round always leaves you at a different depth from where you started. The stairs apply the same idea to a staircase that climbs, or descends, forever in a closed square.

The Penroses didn't know that the Swedish artist Oscar Reutersvärd had drawn an impossible triangle in 1934. What made their paper influential was the analysis: they treated the figures as evidence about how the visual system builds three-dimensional structure from flat cues, and as tools for probing the assumptions it makes.

Escher, both ways

The story connects with M. C. Escher in both directions. Roger Penrose saw Escher's work at an exhibition held during the International Congress of Mathematicians in Amsterdam in 1954, and it set him thinking about impossible structures. The Penroses later sent their paper to Escher, who corresponded with them and used its figures in two of his best-known lithographs, Ascending and Descending (1960) and Waterfall (1961) (Ernst, 1976). Escher's prints took the Penroses' figures to an audience far beyond any psychology journal.

Why the paper matters

The Penroses didn't invent a new trick so much as give a name, a careful description and a scientific framing to a whole category of illusion. Impossible objects have since become a standard way of studying depth perception and how the visual system combines local and global information. The demo on the Penrose triangle page shows the idea in reverse: a real object that looks impossible from exactly one direction.