The categorization of sentential contexts

A new experimental method, involving the sorting of linguistic contexts, is shown to be effective in discriminating the contexts of polysemous words as well as the contexts of synonyms of those words. These results are interpreted as support for the claim that the method of sorting linguistic contexts is a valid technique for studying the contextual information available to support inferences about word meanings.The research reported in this article was part of the author's work submitted as a doctoral thesis to Princeton University. It was supported in part by Contract MDA 903-86-K-0242 between the Army Research Institute and Princeton University. The views and conclusions in this article are those of the author and should not be interpreted as representing official policies, either expressed or implied, of the Army Research Institute or Princeton University.     

Some statistical considerations in multidimensional scaling

Some shortcomings of current methods of estimating the magnitude of perceived difference are considered. A statistical model for perceived difference is derived which avoids these difficulties and employs judgments of ratios of differences as data. Three estimators of squared difference are developed.This study was conducted while the author was a Psychometric Fellow at Princeton University and Educational Testing Service and is part of a dissertation presented in candidacy for the degree of doctor of philosophy. This research was supported by Office of Naval Research Contract Nonr 1858 and by National Science Foundation Grant GB3402. Extensive use was made of the computing facilities of Princeton University supported in part by National Science Foundation Grant NSF-GP579. The author wishes to express his appreciation to Prof. H. Gulliksen, Prof. F. Geldard, Dr. C. Helm, and Dr. F. Lord for their comments and encouragement.     

Children's Perception of Munsell Colors

This study examined perception of Munsell notation color by seven third-graders and three college adults (both with normal color vision) and three children (from the same family) who were red-green color blind. The stimuli varied in terms of Munsell Hue (red, green, and purple), Munsell Value (brightness), and Munsell Chroma (saturation). Each S judged the dissimilarity of 325 color pairs (from 26 stimuli). The data were analyzed via individual difference multidimensional scaling that defined a common perceptual space for the group. The results indicated that the third-graders’ color perception was like that of the adults. The color circle was reproduced, as were dimensions based on Munsell Value and Chroma. The color deficient children's data did not fit into that common space. Their perception was guided primarily by the brightness of the stimulus. In sum, the data indicated that, for the domain of Munsell colors, results obtained from adults concerning the dimensionality of the color space could be applied to young children (as long as they have normal color vision).     

Numerical methods for polynomial models in nonlinear factor analysis

The basic concepts of nonlinear factor analysis are introduced and some extensions of the general theory are developed. An elementary account of the class of multiple-factor polynomial models is presented, using more elementary algebraic methods than have been employed in earlier accounts of this theory. Working formulas are developed for the multiple-factor polynomial model without product terms.Some empirical results are presented.This work was carried out while the author was a Visiting Research Fellow at the Educational Testing Service, Princeton, N. J. It made use of computer facilities at Princeton University that are supported in part by National Science Foundation Grant NSF-Gp579.     

Big Gods,historical explanation,and the value of integrating the history of religion into the broader academy

This article discusses critiques raised by historians of religion concerning Ara Norenzayan's Big Gods: How Religion Transformed Cooperation and Conflict (Princeton: Princeton University Press, 2013), offering some defense of Norenzayan's position, but also discussing in detail the more substantive challenges. It concludes with some reflections on the current position of the history of religion within the Academy, and an argument for why large-scale explanatory projects and interdisciplinary collaboration should be part of the future of our field.     

A factor analytic method for investigating differences between groups of individual learning curves

In this method of analyzing learning data, entire learning curves are described quantitatively by single numbers which are used in a statistical test to determine whether two or more groups of learning curves are significantly different. The method has some logical advantages over prevailing methods in that it avoids the use of average learning curves and of arbitrary measures of slope and asymptote. Its disadvantage is computational. Since it involves the use of factor analytic procedures, it may be tedious to apply unless computation is carried out on a high-speed computer.This investigation was begun and carried out for the most part while the author was a Psychometric Fellow of Educational Testing Service at Princeton University. It was completed at University College, London, during successive tenures of post-doctoral fellowships from The National Institute of Mental Health, U.S.P.H.S., and The National Science Foundation. Data for the numerical example were processed by the high-speed computer facilities of the Western Data Processing Center, Los Angeles.     

Perceptual limits on low-dimensional models of Munsell reflectance spectra

Some experimental and theoretical approaches to surface-colour perception depend on approximating surface reflectance spectra by low-dimensional models. In the psychophysical experiment reported here, observers had to discriminate between patterns of Munsell surfaces and their spectral approximations under either the same or different illuminants. The approximations were produced by principal component analysis, by independent component analysis, and by artificial neural networks trained with a supervised-learning rule. In all experimental conditions, observers required, on average, at least 5 basis functions for discrimination performance to be at chance, thus placing a lower limit on the dimensionality of models of Munsell reflectance spectra.     

Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the scale of stimuli obtained in the traditional paired comparisons methods. In this scale, however, instead of locating each stimulus-object on a given continuum, the distances between each pair of stimuli are located on a distance continuum. As in paired comparisons, the procedures for obtaining a scale of comparative distances leave the true zero point undetermined. Hence, a comparative distance is not a distance in the usual sense of the term, but is a distance minus an unknown constant. The second step involves estimating this unknown constant. When the unknown constant is obtained, the comparative distances can be converted into absolute distances. In the third step, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of stimuli on axes of this space are obtained. A set of analytical procedures was developed for each of the three steps given above, including a least-squares solution for obtaining comparative distances by the complete method of triads, two practical methods for estimating the additive constant, and an extension of Young and Householder's Euclidean model to include procedures for obtaining the projections of stimuli on axes from fallible absolute distances.This study was carried out while the author was an Educational Testing Service Psychometric Fellow at Princeton University. The author expresses his appreciation to his thesis adviser, Dr. H. Gulliksen, for his guidance throughout the study and to Dr. B. F. Green, Jr., for valuable assistance on several of the derivations.     

Greek Buddha: Pyrrho’s Encounter with Early Buddhism in Central Asia

In his book Greek Buddha: Pyrrho’s Encounter with Early Buddhism in Central Asia (Princeton and Oxford: Princeton University Press, 2015), Christopher Beckwith argues that not only was the Buddha a Scythian from Central Asia, but that the earliest reliable record of Buddhist teaching is to be found in a text attributed to Pyrrho, the Greek founder of philosophical scepticism, cited by the third-century Christian bishop Eusebius. This review considers these claims in the light of epigraphical, textual and archaeological evidence. It then offers an alternative account of Pyrrho’s possible encounter with Buddhist ideas during his stay in India as part of the entourage of Alexander the Great in the fourth century bce, and considers the formative role that the teaching of Democritus and his followers may have had in the evolution of Pyrrho’s sceptical attitude to life.     

On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

Nonmetric multidimensional scaling: A monte carlo study of the basic parameters

Metric determinacy of nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the amount of error in the data being scaled, and the accuracy of estimation of the Minkowski distance function parameters, dimensionality and the r-constant. It was found that nonmetric scaling may provide better models if (1) the true structure is of low dimensionality, (2) the dimensionality of recovered structure is not less than the dimensionality of the true structure, (3) degree of error is low, and (4) the degrees of freedom ratio is greater than about 2.5. It was also found that (5) accurate estimation of the Minkowski constant leads to a better model only if the dimensionality has been properly estimated.This report is based on a thesis submitted in partial fulfillment of the degree of Master of Arts at the University of North Carolina, April, 1970. The thesis is an outgrowth of earlier work done with Forrest W. Young. The author is indebted to Forrest W. Young, Norman Cliff, and Lyle V. Jones for their assistance in the preparation of this report. This report was supported in part by PHS research grant No. M-10006 from the National Institute of Mental Health, Public Health Service.     

A new solution to the additive constant problem in metric multidimensional scaling

A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates.This research is based in part on the author's Ph.D. dissertation at the University of Illinois at Urbana-Champaign. Computer time was provided by the Campus Computing Network of the University of California, Los Angeles.     

Book Reviews

Book Reviewed
The Politics of Cultural Differences. By David C. Leege, Kenneth D. Wald, Brian S. Krueger, and Paul D. Mueller. Princeton, NJ: Princeton University Press. 2002. 304 pp. $21.95 paper, $60 cloth.
The Psychological Assessment of Political Leaders. Edited by Jerrold M. Post, M.D. Ann Arbor, MI: University of Michigan Press. 2003. 412 pp.
FDR's Body Politics: The Rhetoric of Disability. By Davis W. Houck and Amos Kiewe. College Station, TX: Texas A&M University Press. 2003. 141 + xii pp.
The Power of Legitimacy: Assessing the Role of Norms in Crisis Bargaining. By Christopher Gelpi. Princeton, NJ: Princeton University Press. 2003. 232 pp. $39.50.     

Bound by Recognition

Books reviewed:
Bound by Recognition. By Patchen Markell. Princeton, N.J: Princeton University Press. 2003. 320 pp. Reviewed by Sophia Jane Mihic Northeastern Illinois University     

Retreat from Non-Being

Book Information Welfare and Rational Care. Welfare and Rational Care Stephen Darwall, Princeton: Princeton University Press, 2003, pp. xi + 135, US$24.95 (cloth). By Stephen Darwall. Princeton: Princeton University Press. Pp. xi + 135. US$24.95 (cloth:),     

Determining the dimensionality in spatial representations of semantic concepts

When multidimensional scaling solutions are used to study semantic concepts, the dimensionality of the optimal configuration has to be determined. Several strategies have been proposed to choose the appropriate dimensionality. In the present paper, the traditional dimensionality choice criteria were evaluated and compared to a method based on the prediction of an external criterion. Two studies were conducted in which typicality of an exemplar within a semantic concept was predicted from its distance to the concept centroid. In contrast to the low-dimensional solutions selected by the traditional methods, predictions of an external criterion improved with additional dimensions up till dimensionalities that were much higher than what is common in the literature. This suggests that traditional methods underestimate the richness of semantic concepts as revealed in spatial representations derived from similarity measures.     

The additive constant problem in multidimensional scaling

The problem of choosing the correct additive constant to convert relative interstimulus distances to absolute interstimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed, and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Dr. Ledyard R Tucker, is presented; each of the computational steps in this solution is set down for easy reference.This study was supported in part by Office of Naval Research Contract N6onr-270-20 and by National Science Foundation Grant G-642 to Princeton University.     

The self in Kierkegaard's pseudonyms

Conclusion This is essentially what I take to be Kierkegaard's ontological foundation of human existence. It is the structure which both makes possible and unifies the different modes of existing which he so fully describes in his pseudonyms. The further task is one of demonstrating concretely the relation of these modes (stages) of existing to his ontology.This essay will appear in my book, Being and Existence in Kierkegaard's Pseudonyms, to be published by Princeton University Press in 1975. I would like to thank the Princeton University Pres for permission to publish a portion of the book in this journal. I would also like to acknowledge my colleagues' helpful criticisms of the original draft of this paper which I read in a departmental seminar at Iowa State University last fall. Some of their suggestions were incorporated in the final draft.     

A general least squares solution for successive intervals

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service.     

Determination of parameters of a functional relation by factor analysis

Consideration is given to determination of parameters of a functional relation between two variables by the means of factor analysis techniques. If the function can be separated into a sum of products of functions of the individual parameters and corresponding functions of the independent variable, particular values of the functions of the parameters and of the functions of the independent variables might be found by factor analysis. Otherwise approximate solutions may be determined. These solutions may represent important results from experimental investigations.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642.