Whereas most sensory information is coded on a logarithmic scale, linear expansion of a limited range may provide a more efficient coding for the angular variables important to precise motor control. In four experiments, we show that the perceived declination of gaze, like the perceived orientation of surfaces, is coded on a distorted scale. The distortion seems to arise from a nearly linear expansion of the angular range close to horizontal/straight ahead and is evident in explicit verbal and nonverbal measures (Experiments 1 and 2), as well as in implicit measures of perceived gaze direction (Experiment 4). The theory is advanced that this scale expansion (by a factor of about 1.5) may serve a functional goal of coding efficiency for angular perceptual variables. The scale expansion of perceived gaze declination is accompanied by a corresponding expansion of perceived optical slants in the same range (Experiments 3 and 4). These dual distortions can account for the explicit misperception of distance typically obtained by direct report and exocentric matching, while allowing for accurate spatial action to be understood as the result of calibration
