The three arrows of Zeno

We explore the better known paradoxes of Zeno including modern variants based on infinite processes, from the point of view of standard, classical analysis, from which there is still much to learn (especially concerning the paradox of division), and then from the viewpoints of non-standard and non-classical analysis (the logic of the latter being intuitionist).The standard, classical or Cantorian notion of the continuum, modeled on the real number line, is well known, as is the definition of motion as the time derivative of distance (we are not concerned with position and motion in more than one dimension, since Zeno wasn't). The real number line consists of its points, the distance between distinct points being positive and finite. The standard, classical derivative relies on the classical notion of limit, which does not use infinitesimals.In non-standard analysis, the real line is again the set of its points, but infinitesimal distances between points are allowed, while the derivative is defined in terms of the ratio of infinitesimals. This has the surprising consequence that there is a function of time giving positions, which is not constant, but whose derivative is everywhere zero, so that a particle whose position is given by this function can move a finite distance in a finite time, while being at rest all along. Such a function, of course is external — it can't be defined in the formal language. More suprising still, a model of the non-standard real line can be found which is internally finite — that is there is an injection from an initial segment of non-negative integers to the non-standard interval [0,1) whose range includes all the standard real numbers, and the ratio of the number of points in the range in any subset S of the interval to the number of those in the entire interval differs by an infinitesimal from the Lebesgue measure of the set of standard points in S. Of course, the formalism can't tell the difference between standard and non-standard integers or points — that is an external concept. Still, this allows a discrete model of the line with points an infinitesimal distance apart, without sacrificing any of the results of standard analysis, including measure theory.Non-classical analysis is based on topos theory in an intuitionist setting. All curves are piecewise linear, or straight over infinitesimal distances, and the non-classical derivative is defined as the slope in such intervals. So whereas the direction of a non-standard smooth curve changes infinitesimally over infinitesimal distances, the direction of a non-classical curve (all of them are smooth), doesn't change at all over infitesimal distances. And while a standard or non-standard line can be identified with the set of its points, the points on a non-classical line might be said not to occupy all positions, and the line is an object which is not the set of its points.We explore the implications of all this for the various paradoxes of Zeno, and some modern variants.     

Nurses' attitudes and behavioral intentions concerning AIDS care

The problem of the rapidly growing AIDS epidemic is compounded by negative attitudes and unwillingness to care for such patients by reportedly high percentages of nurses. On the basis of the literature, an exploratory interactive model predicting willingness to provide care is derived and tested. Results suggest that attitude is positively related to the behavioral intention to provide AIDS care. This relationship is more pronounced for nurses who score low on the variable of conservative views.     

The neuropsychology of depression and its implications for cognitive therapy

The past few years have witnessed a growing interest in the specialty of neuropsychology as well as continued support for cognitive therapy of depression. The purpose of this paper is the examination of the neuropsychology of depression and its implications for A. T. Beck's cognitive theory and therapy of depression ([1963] Thinking and Depression: Idiosyncratic Content and Cognitive Distortions,Archives of General Psychiatry, Vol. 9, pp. 324–333; [1964] Thinking and Depression,Archives of General Psychiatry, Vol. 10, pp. 561–571; [1967]Depression: Clinical, Experimental, and Theoretical Aspects, New York: Harper & Row). Specifically, the neuropsychological and cognitive theory and therapy literatures related to depression are reviewed followed by an antegration of these areas. Neuropsychological evidence is presented that both supports cognitive theory and therapy of depression and helps explain why such therapy may prove ineffective in treating depression. Implications for clinical practice, including neuropsychological assessment of depressives, and potential future research directions are also provided.     

An apparatus for use in 2 by 2 game research

This article describes a solid state apparatus for use in 2 by 2 game research. There are two individual player’s boards and a control panel for E. Following E’s signal, each player chooses one of two responses. Their choices are immediately registered on E’s panel, but appear on each individual game board only after both have responded. Provisions are made for E to transmit false feedback.     

Note on the selection of a panel of judges so as to maximize panel efficiency

Attempts to develop improved methods of selecting a panel of judges for psychometric work are presented. The applications reported are in the sensory field and are limited to the assumption of a unidimensional ability underlying the judgments in question. Some aspects of cost efficiency are also considered.The writers wish to acknowledge the value of a discussion with Dr. Harold Gulliksen of Princeton University and the Educational Testing Service, Princeton; Dr. Frederic Lord, also of the Educational Testing Service, contributed some valuable criticisms. The writers' thanks are also due Mr. George Bosy, at the Research Laboratories, Kraft Foods Company, where the senior author is currently employed.     

Later-life depression: Influences of irrational thinking and cognitive impairment

The relationship of personality styles to depression at later-lifeand the influence of irrational thinking and cognitive impairment on this relationshp are addressed. Sixty older (>55) male psychiatric patients at a large medical center were given a battery of psychological tests, including the MCMI, BDI, the Idea Inventory, and the Hooper VOT. A record review for background/treatment factors was also conducted. Results showed that personality styles at later-life are distinctly related to depression, with four styles having an inverse relationship. The personality styles also have the same relationship to irrational thinking. When the influence of irrational thinking and cognitive impairment were removed from the relationship of each personality style to depression, there were only minimal changes in correlation coefficients. These components, therefore, are largely independent of the personality style and depression relationship with later-life inpatients.Leon Hyer, a clinical psychologist at the Veterans Administration Medical Center, Augusta, Georgia and assistant professor at the Medical College of Georgia, is Co-Director of the Psychogeriatric Unit at the Augusta VA Medical Center.William R. Harrison is the coordinator of the Augusta VA Medical Center's Psychodiagnostic Laboratory.Rebecca H. Jacobsen is currently a staff psychologist at the Veterans Administration Medical Center in Augusta, Georgia, where she works with psychiatric inpatients on the Psychosocial Unit. Dr. Jacobsen also is an assistant professor at the Medical College of Georgia.     

Anger and denial as predictors of cardiovascular reactivity in women

The relationship between behavioral and physiological reactivity and cardiovascular disease has been extensively researched in men, indicating that the expression of anger may be a contributory factor in the development of coronary heart disease. Few studies, however, have focused on women. Among these, women generally have been found to be less reactive to laboratory tasks than men. In the present study, 45 women aged 19–21 years were selected to represent three groups—(1) low anger/low denial, (2) high anger/low denial, and (3) low anger/high denial—based on their scores on the State-Trait Anger Expression Inventory and the Marlowe-Crowne Social Desirability Scale. Subjects received three conditions: (1) no feedback, (2) error feedback without observer present, and (3) error feedback with observer present. As hypothesized, women who reported a high level of denial and low anger exhibited elevated stress-related reactivity. The results are suggestive of a subgroup of highly reactive women not previously identified within the literature. The hypothesis that all groups would display greater reactivity in a condition providing error feedback with observation was not supported.This study was supported by a research grant to Carol S. Emerson from the Women's Research Institute of Virginia.     

Statistical power analysis for one-way analysis of variance: A computer program

To facilitate the computation of statistical power for analysis of variance, Cohen developed the index of effect sizef, defined as theSD between groups divided by theSD within groups. A microcomputer program for statistical power allows the user to compute the value off in any of several ways: by specifying the mean andSD for every cell in the ANOVA; by specifying the mean value for the two extreme cells and the pattern of dispersion for the remaining cells; by estimating the proportion of variance in the dependent variable that will be explained by group membership; and/or with reference to conventions for small, medium, and large effects. The program will compute power for any single set of parameters; it will also allow the user to generate tables and graphs showing how power will vary as a function of effect size, sample size, andα.