Evaluating the decay gradient for collinearity bias with lateral displacement from the axis of induction

The misperception of alignment which is found in many geometric illusions can be quantified using relatively simple stimulus configurations. Perceived collinearity of one segment (designated as the test segment) is biased by a second segment (designated as the induction segment), with the size of effect being a function of the relative angle between the two segments. The process can be described as angular induction. The strength of bias is greatest when the induction segment is centered at the tip of the test segment. Tong and Weintraub have reported that lateral displacement from the tip, i.e., at right angles to the axis of the induction segment, produces a sharp drop in the strength of effect. This decline is described as a decay gradient for the angular induction. One experiment replicates and provides better quantification of this decay gradient. Two other experiments examine the decay gradient using a pair of induction segments, one on each side of the tip of the test segment. Displacement of the segments (either in the same direction or in opposite directions) produces substantially the same gradient of effect. Therefore, previous evidence of tandem boosting of effect for segment pairs does not depend on collinearity among the stimulus components. Finally, a fourth experiment finds that an induction segment which is at a fixed position and orientation differentially affects the influence of a variable induction segment. At some angles the influence of the variable segment is augmented, and at others it is suppressed. These findings are discussed in a neuroreductionist context, and a simple model for angular induction is presented.