Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules

Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.     

Civic religion in England: Traditions and transformations

As the religious diversity of English towns and cities has grown over the past thirty years due to the establishment in some places of sizeable communities of Hindus, Muslims and Sikhs, as well as other faiths, there have been important changes to local public religion. Traditional civic ceremonies, such as Remembrance Sunday, as well as new forms of civic celebration and commemoration, are now increasingly taking account of the diversity of faiths represented in Britain. This paper examines the consequences of religious diversity for English civic religion by looking at some of the traditions of civic ceremonies in England and at the way in which they have been transformed by the changing religious landscape of towns and cities. The paper also explores some of the dilemmas and questions that have emerged both for the Church of England as well as for the other faith communities when it comes to the design and delivery of civic ceremonies.     

The Microanalysis of Memory Span and Its Development in Childhood

It is not clear from the literature why, as children develop, there are important increases in memory span, the number of just-presented items that the participant can repeat in the correct serial order. To understand this, some recent results on capacity limits and processing rates were re-analyzed. We first describe results using a conventional measure of performance in immediate memory tasks that is affected by the list length (proportion correct). Next we describe results using a less conventional measure (number correct) that is unaffected by list length under circumstances in which attention to the list during its presentation is curtailed. This measure can estimate an individual's limited-capacity storage ability. Last, we examine measures of spoken response timing that do and do not change with list length. We show that unconventional measures that do not change with list length, but do change with development, are especially useful in assessing basic changes in information processing parameters, including increases in memory capacity and processing speed.     

Mathematical engineering and mathematical change 1

In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception of mathematical knowledge, in particular mathematical growth.