Rudolf Arnheim was a distinguished psychologist, philosopher and critic whose work explored the cognitive basis of art — how we interpret it and, by extension, the world. His father owned a small piano factory and he was expected to take over one day, but he eschewed this path. Studying at the University of Berlin, he took psychology, philosophy, music and art, earning a doctorate in philosophy (of which psychology was then a discipline) in 1928. He then became an editor at Die Weltbühne, a leftist magazine of politics and culture, where he published articles on film, art and architecture. In 1933, with the rise of Nazism, Arnheim, who was Jewish, fled to Rome. In the late 1930s, after Mussolini allied himself with Hitler, Mr. Arnheim fled to England, where he became a translator for the BBC. In 1940, he arrived in New York. There he taught at the New School for Social Research and also worked as a researcher for Columbia University, where he studied the habits of radio listeners. His work from this period includes collaborating on a survey of daytime-serial audiences. In 1943 Professor Arnheim joined the faculty of Sarah Lawrence. From the mid-’70s on, after retiring from Harvard, he was associated with the University of Michigan and at his death, he was emeritus professor of the psychology of art at Harvard University. His work was focused on the ways in which humans experience the sensory world and was grounded in his training on Gestalt psychology. His best-known books include “Art and Visual Perception” (1954), “Film as Art” (1957) and “Visual Thinking” (1969).