Apparent Shape of the Mach Book

The Mach book is a two-dimensional figure which looks three-dimensional. Despite the impression of depth in the figure, the apparent shape has not been determined. It has been suggested that the book appears as part of a ‘cubic corner’, ‘as flat as possible’, or with each half rotated about its long diagonal. Alternative hypotheses as to the three-dimensional orientation of the book were tested by means of a probe-line technique. It was found that, although no hypothesis matched the results of all of the subjects, the probe-line settings of individual subjects were approximately linear or piecewise linear functions of the angles in the picture. The technique was also applied to asymmetric versions of the figure and it was found that the subjects modified their settings in accord with the constraint that the two halves of the figure must join in depth along their common edge. The findings are in agreement with models of the interpretation of line drawings in which local estimates of edge orientation in depth are formed, and subsequently checked for consistency.