“Impossible figures” and interpretations of polyhedral figures

The concept “impossible figure” is analyzed by formalizing the interpretations of a polyhedral figure by an observer, and defining several types of inconsistency in such interpretations. Tests for these inconsistencies are developed using simple graph theory, and a sufficient condition is established for the feasibility of an interpretation. Finally, techniques are derived for the automatic construction of usual or unusual multibar figures.     

A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Dilthey''s narrative model of human development: Necessary reconsiderations after the philosophical hermeneutics of Heidegger and Gadamer

Paper delivered at theEighth International Human Science Research Conference at Aarhus University (Denmark), 18–22 August 1989.     

Subliminal stimulation, choice behavior and some personality correlates of subliminal sensitivity

The aim of this study was to investigate the possible relations between specific personality variables and the effect of subliminal stimulation on choice behavior. It was hypothesized that subjects with low anxiety, less neuroticism, and external locus of control and the trait of extraversion would be more susceptible to subliminal stimulation. 38 undergraduate students were exposed to subliminal messages urging them to choose symbols instead of numbers or letters. Analysis showed that subliminal stimulation did not generate a preference for symbols over numbers or letters. No support was observed for the hypothesis of an association between susceptibility and personality variables. These results may be explained in terms of symbol choice being a neutral message that did not relate to the subjects' needs and motivation.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

Toward understanding sex differences in pay allocation: Agency,communion, and reward distribution behavior

This research examined the extent to which the personality characteristics of agency and communion are sex linked, and the extent to which differences in these orientations can account for sex differences in reward distribution behavior. In two studies, the agency and communion level of large samples of male and female undergraduates were assessed. As expected, males were more agentic and females were more communal. Moreover, when subjects who scored high or low on agency and high or low on communion were asked to allocate rewards between themselves and a co-worker, these personality differences were related to their allocation decisions. These results were used as the basis for discussing the role that sex-linked personality differences might play in distributive justice judgments.This article is an adaptation of a colloquium presentation at the meeting of the American Psychological Association, Los Angeles, August 1981. The research reported here was supported by NIMH grant MH29987-1, Goals, Motives, and Norms of Reward Distribution, and by NIMH Biomedical Research Support Grant from the College of Social Science, Michigan State University. The authors wish to thank Andrea Doughty for her valuable advice, and to gratefully acknowledge the help of Mark Teicher, Julie B. Klein, Sue Schnelbach, Pat Loepp, Barb Allen, Gavin Goodrich, Bob O'Hara, Kelly Bowen, Rod Hollenstein, Steve Schultz, and Mary Hurst.