Ultimate choice between two attractive goals: Predictions from a model

A mathematical model for two-choice behavior in situations where both choices are desirable is discussed. According to the model, one or the other choice is ultimately preferred, and a functional equation is given for the fraction of the population ultimately preferring a given choice. The solution depends upon the learning rates and upon the initial probabilities of the choices. Several techniques for approximating the solution of this functional equation are described. One of these leads to an explicit formula that gives good accuracy. This solution can be generalized to the two-armed bandit problem with partial reinforcement in each arm, or the equivalent T-maze problem. Another suggests good ways to program the calculations for a high-speed computer.Support for this research has been received from the National Science Foundation (Grant NSF-G2258), the National Institute of Mental Health (Grant M-2293), and the Laboratory of Social Relations, Harvard University.We wish to acknowledge and express our appreciation for the cooperation and assistance given by Phillip J. Rulon, Albert Beaton, Wai-Ching Ho, and Donald Spearritt, who set up, programmed, and executed numerous calculations connected with the linear equations method of solution, and by Cleo Youtz for extensive calculations at every stage of the work. We also wish to thank Ray Twery and Robert R. Bush for permission to use in Table 3 some of the unpublished results of their calculations. Those calculations were made on the Illiac through the cooperation of the Digital Computer Laboratory of the University of Illinois, Dr. John P. Nash, Director.     

Some comments in connection with Rozeboom's linear correlation theory

It is shown that certain correlation measures suggested by information theory are simple functions of the determinants of the correlation matrices involved, if multivariate normality is assumed. This illuminates and in a sense strengthens Rozeboom's point in [3], that information theoretical statistics have classical correlational counterparts.     

Une hypothèse sur l'extension des relations finies et sa vérification dans certaines classes particulières

Sans résumé     

Some reflections on the notion of hypotyposis in Kant

In the Critique of Judgement, Kant, despite his strong condemnation of rhetoric, introduces the figure of hypotyposis at the very moment he sets out to tackle the philosophical problem of presentation as such. This study holds that this choice of the rhetorical term is not fortuitous. Its connotations of vivid illustration, synopsis, and moral grandeur serve Kant in arguing that, on a transcendental level, presentation secures the mind's life, unity, and self-affection. Although of rhetorical origin, hypotyposis is thus shown to link up with a specifically philosophical meaning of the term in the writings of Aristotle.     

Stereo-motion cooperation and the use ofmotion disparity in the visual perception of 3-D structure

When an observer views a moving scene binocularly, both motion parallax and binocular disparity provide depth information. In Experiments lA-1C, we measured sensitivity to surface curvature when these depth cues were available either individually or simultaneously. When the depth cues yielded comparable sensitivity to surface curvature, we found that curvature detection was easier with the cues present simultaneously, rather than individually. For 2 of the 6 subjects, this effect was stronger when the component of frontal translation of the surface was vertical, rather than horizontal. No such anisotropy was found for the 4 other subjects. If a moving object is observed binocularly, the patterns of optic flow are different on the left and right retinae. We have suggested elsewhere (Cornilleau-Pérès & Droulez, in press) that this motion disparity might be used as avisual cue for the perception of a 3-D structure. Our model consisted in deriving binocular disparity from the left and right distributions of vertical velocities, rather than from luminous intensities, as has been done in classical studies on stereoscopic vision. The model led to some predictions concerning the detection of surface curvature from motion disparity in the presence or absence of intensity-based disparity (classically termedbinocular disparity). In a second set of experiments, we attempted to test these predictions, and we failed to validate our theoretical scheme from a physiological point of view.