Color charts, esthetics, and subjective randomness

Color charts, or grids of evenly spaced multicolored dots or squares, appear in the work of modern artists and designers. Often the artist/designer distributes the many colors in a way that could be described as "random," that is, without an obvious pattern. We conduct a statistical analysis of 125 "random-looking" art and design color charts and show that they differ significantly from truly random color charts in the average distance between adjacent colors. We argue that this attribute generalizes results in subjective randomness in a black/white setting and gives further evidence supporting a connection between subjective randomness and what is esthetically pleasing.     

Canada 2001: Alternative futures for the Canadian communities

The global “problématique humaine” is described in terms of the “grand issues” of population, resources, development in the rich and poor countries, and the environment. Three competing paradigms about the future and their implications for the Canadian communities are examined, and a model is offered showing interrelationships between the different Canadian communities, organizational levels, and various societal/environmental activities. A comprehensive programme of future‐oriented studies is proposed.

This article is a shortened version of a monograph to appear as one of a series entitled Queen's Studies of the Future of the Canadian Communities, published by the Institute of Intergovernmental Relations, Queen's University, Kingston, Ontario. The research was funded by the Donner Canadian Foundation.     

The test taker's fallacy: How students guess answers on multiple‐choice tests

Many students and applicants take multiple‐choice tests to demonstrate their competence and achievement. When they are unsure, they guess the most likely answer to maximize their score. Despite the impact of guessing on test reliability and individual performance, studies have not examined how patterns of answer sequences in multiple‐choice tests affect guessing. This research presents the test taker's fallacy, which refers to an individual's tendency to expect a different answer to appear for the next question given a run of the same answer choices. The test taker's fallacy exhibits negative recency, similar to the gambler's fallacy. However, extending the sequential judgment literature, the test taker's fallacy shows that negative recency arises even when sequences may or may not be randomly generated. In three studies, including a survey and experiments, the test taker's fallacy is robustly observed. The test taker's fallacy is consistent with the operation of the representativeness heuristic. This research explains what and how test takers guess given a streak of answers and extends judgment under uncertainty to the test‐taking context.     

A monte carlo study of kruskal's variance based measure on stress

Researchers in the past ten years have studied various parameters involved in nonmetric multidimensional scaling by utilizing Monte Carlo procedures. This paper develops stress distributions using Kruskal's second stress formula based upon a null hypothesis of equal likelihood in the ranking of a set of proximities. These distributions can serve to determine whether a set of data has other than random structure.This research was supported in part by a grant from the Baruch College Scholar Assistance program.     

The Equiprobability Bias from a Mathematical and Psychological Perspective

The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase with probability education. Because it results in probability errors resistant to pedagogical interventions, it has been described as a deep misconception about randomness: the erroneous belief that randomness implies uniformity. In the present paper, we show that the EB is actually not the result of a conceptual error about the definition of randomness. On the contrary, the mathematical theory of randomness does imply uniformity. However, the EB is still a bias, because people tend to assume uniformity even in the case of events that are not random. The pervasiveness of the EB reveals a paradox: The combination of random processes is not necessarily random. The link between the EB and this paradox is discussed, and suggestions are made regarding educational design to overcome difficulties encountered by students as a consequence of the EB.     

A RANDOMNESS‐BASED THEODICY FOR EVOLUTIONARY EVILS

We develop and knit together several theodicies in order to find a more complete picture of why certain forms of (nonhuman) animal suffering might be permitted by a perfect being. We focus on an especially potent form of the problem of evil, which arises from considering why a perfectly good, wise, and powerful God might use evolutionary mechanisms that predictably result in so much animal suffering and loss of life. There are many existing theodicies on the market, and although they offer helpful resources, we combine and further develop several proposals to produce a composite theodicy that avoids certain shortcomings of the individual theodicies. An important element of our project is locating a role for randomness in cosmic and biological evolution. In particular, we show how randomness might enhance or enable certain goods, including everlasting goods, at the risk of temporary evils.     

Epicurus and B. F. Skinner: In search of the good life

This paper examines similarities in the works of Epicurus, an ancient Greek philosopher, and B. F. Skinner, a behavioral psychologist. They both were empiricists who argued in favor of the lawfulness of behavior while maintaining that random events were included within those laws. They both devoted much effort to describing how individuals could live effective, rewarding and pleasurable lives. They both emphasized simple and natural pleasures (or reinforcers) and the importance of combining personal pleasures with actions that benefit friends and community. They both opposed punishment and all aversive measures used by governments and religions to control behaviors. And both created utopias: a real community, The Garden, where Epicurus lived with his followers, and a fictional one, Walden Two, by Skinner. We consider how a combination of the ideas of Epicurus and Skinner can contribute to their common goal of helping people to live better lives.     

DOES GOD PLAY DICE? INSIGHTS FROM THE FRACTAL GEOMETRY OF NATURE

Abstract Albert Einstein and Huston Smith reflect the old metaphor that chaos and randomness are bad. Scientists recently have discovered that many phenomena, from the fluctuations of the stock market to variations in our weather, have the same underlying order. Natural beauty from plants to snowflakes is described by fractal geometry; tree branching from trunks to twigs has the same fractal scaling as our lungs, from trachea to bronchi. Algorithms for drawing fractals have both randomness and global determinism. Fractal statistics is like picking a card from a stacked deck rather than from one that is shuffled to be truly random. The polarity of randomness (or freedom) and law characterizes the self‐creating natural world. Polarity is in consonance with Taoism and contemporary theologians such as Paul Tillich, Alfred North Whitehead, Gordon Kaufman, Philip Hefner, and Pierre Teilhard de Chardin. Joseph Ford's new metaphor is replacing the old: “God plays dice with the universe, but they're loaded dice.”     

The God of Chance and Purpose

The author argues that ontological randomness is genuine, and that God does not determine the outcome of every scientifically random event, but instead controls randomness by setting broad boundaries. Through paleontological examination, this paper looks at how randomness shapes the world from the bottom up. However, the phenomena known as convergence indicate that evolution through natural selection may proceed along various paths, but the destinations are few. Thus there is a dichotomy: randomness is constrained within pattern.     

THE SECULARIZATION OF CHANCE: TOWARD UNDERSTANDING THE IMPACT OF THE PROBABILITY REVOLUTION ON CHRISTIAN BELIEF IN DIVINE PROVIDENCE

This article gives a brief history of chance in the Christian tradition, from casting lots in the Hebrew Bible to the discovery of laws of chance in the modern period. I first discuss the deep‐seated skepticism towards chance in Christian thought, as shown in the work of Augustine, Aquinas, and Calvin. The article then describes the revolution in our understanding of chance—when contemporary concepts such as probability and risk emerged—that occurred a century after Calvin. The modern ability to quantify chance has transformed ideas about the universe and human nature, separating Christians today from their predecessors, but has received little attention by Christian historians and theologians.