The Poggendorff figure was simplified by removing the right transversal segment. When Ss judged the distance between a dot located on the right parallel and the imagined point where the left transversal, if extended, would intersect the right parallel, the error was independent of dot location. This result is consistent with the idea that the Poggendorff figure is processed asymmetrically by (mis)projecting one of the transversals across to the opposite parallel. Systematically omitting line segments reduced (and sometimes reversed) illusory effects. The most critical Poggendorff feature was the obtuse angle formed between transversal and parallel. Ss vertically adjusted one of two dots to apparent collinearity with an implied transversal, the tip of an intervening vertical line and the other (stationary) dot. Which dot was stationary proved critical. This primitive Poggendorff display generated no illusion unless the implied transversal, defined by the stationary dot, was the one that formed an obtuse angle with the vertical line. This result also strongly supports asymmetric active processing ideas. Perceived orientation is a property of directed line segments.

A theory of extensive measurement is a set of assumptions. Among the physical quantities that are considered extensive, several are basically periodic. The two most familiar examples are clock time, which has a period of either 12 or 24 hours, and angle, which has a period of 2π radians. In both cases, the periodic measure relates simply to an ordinary extensive measure. For example, the time duration of 76:35 hours is the same as 3 days and 4:35 hours, and so in terms of clock time, it is simply equivalent to 4:35 hours, because the complete cycles drop out. This chapter presents several classical empirical examples of extensive measurement in physics. In all these examples, the primitives have a natural physical interpretation, and the axioms reduce to well-known physical principles.

Studies of the Poggendorff illusion (a transversal interrupted by parallel lines) showed that illusory effects increased linearly with increasing separation between the parallels, increased in inverse proportion to the tangent of the angle of intersection between transversal and parallels, decreased whenever line segments (other than a transversal segment) were omitted, decreasing to zero when the segment of a parallel forming the obtuse angle with the transversal was omitted, and varied systematically with the tilt of the whole display, approaching zero when the transversal was oriented in a horizontal or vertical position. Hypothesis: The Poggendorff illusion involves at least three kinds of effects on the perceived orientation of a segment: distortion by other segments (especially a segment intersecting at an obtuse angle), stability of vertical and Horizontal orientations, and assimilation towards vertical or horizontal.

Fechner deduced his logarithmic law from Weber's Law by integrating the equation du = dxkx. Since the work of Luce and Edwards, this method has been regarded as incorrect. Reexamination shows that the method can be reformulated and justified in a rigorous manner.

In this study we obtained direct and comparative judgments of the dissimilarity between schematic faces varying on three binary attributes. These data were used to test the hypothesis that the overall dissimilarity between faces can be decomposed (in an ordinal sense) into three additive components, one for each attribute. The hypothesis was strongly confirmed by both the direct and the comparative judgments. The study illustrates the possible usefulness of the measurement-theoretic analysis of simple combination mies for psychological dimensions.

Worthington (1964) reported detectability differences favoring neutral over taboo four-letter words. He measured the dark-adaptation time necessary, not to recognize, but merely to detect a stimulus. Our aim: to duplicate all the essential features of Worthington’s experiment; the outcome: no significant differences involving word class. Therefore it seems premature to conclude that perceptual defense plays a role in visual detection.