Distinguishing Two Classes of Impossible Objects

Abstract

Psychologists disagree about what is wrong with the fork. R L Gregory says that its spatial orientation is impossible. J M Kennedy claims that it lacks the intact boundaries characteristic of solid objects. In fact, the fork possesses both these flaws. It cannot be made out of wires because the rectangular/trapezoidal shapes representing its conjoined middle plate and prong create a self-contradictory angle between planes. Further, the fork cannot be cut from a flat sheet of paper because figural contours delineating its boundaries show us self-contradictory transformations of surfaces into air space. The fork is important because its two flaws form the bases of distinct classes into which all the recognized impossibles fall. Different arrangements of the fork's critical rectangle/trapezoid shapes are the sole source of paradox in ‘depth impossibles’—for instance, the triangle and staircase drawings by R and L S Penrose, the window design published anonymously in Aviation Week & Space Technology in 1964, and Belvedere by M C Escher. And variations on the fork's self-contradictory boundary constitute the only source of paradox in ‘impossible solids’—for instance, Escher's Day and Night, Victor Vasarely's Study in Axonometric Perspective, and Escher's Convex and Concave.