Abstract

In 1934, Oscar Reutersvärd drew what is generally acknowledged to be the first impossible triangle. Over the course of his lifetime, Reutersvärd created thousands of impossible figures, three of which would later adorn a series of Swedish postage stamps. But despite his enormous, inventive output, Reutersvärd is not widely known. Instead, impossible figures are popularly associated with M. C. Escher—three of whose more famous works include impossible figures—and the mathematical physicist Roger Penrose, who published the first academic article about impossible figures in 1958 after independently discovering the impossible triangle. For Escher and Penrose, however, impossible figures were merely a passing interest. And while Penrose was concerned primarily with the mathematics of impossible figures and Escher integrated them into familiar human scenes, Reutersvärd’s abstract, minimalistic renderings express a fascination with the figures themselves. Free of adornment, they attract and command the eye, and exhibit a strange and peculiar beauty. In this chapter, I investigate why we find impossible figures so visually compelling. In other words, my concern here is the specifically aesthetic appeal of impossible figures. Mathematicians and logicians have studied them for their mathematical and logical properties (Mortensen 2010), psychologists for what they reveal about the visual system (Gregory 1997, chap. 10), and philosophers in part for what they tell us about the limits of the imagination (Elpidorou 2016, 11), but we value them mainly as things to look at. This is what I want to understand. I will work in three stages, using three methods. First, I will define the domain of investigation. What exactly is an impossible figure? Answering this question requires a form of conceptual analysis and raises a variety of interesting philosophical issues. Second, I will ask about the experience of looking at impossible figures. Here I will proceed by introspection—a first-person study of my own experience. Finally, I will appeal to results from experimental psychology to develop an empirically-grounded hypothesis about the visual appeal of impossible figures. If things go well, we will learn something not only about impossible figures, but about ourselves, and how and why we look at visual art in general.