Residence time and choice in concurrent foraging schedules

Five pigeons were trained on a concurrent-schedule analogue of the “some patches are empty” procedure. Two concurrently available alternatives were arranged on a single response key and were signaled by red and green keylights. A subject could travel between these alternatives by responding on a second yellow “switching” key. Following a changeover to a patch, there was a probability (p) that a single reinforcer would be available on that alternative for a response after a time determined by the value of λ, a probability of reinforcement per second. The overall scheduling of reinforcers on the two alternatives was arranged nonindependently, and the available alternative was switched after each reinforcer. In Part 1 of the experiment, the probabilities of reinforcement, ρ_red and ρ_green, were equal on the two alternatives, and the arranged arrival rates of reinforcers, λ_red and λ_green, were varied across conditions. In Part 2, the reinforcer arrival times were arranged to be equal, and the reinforcer probabilities were varied across conditions. In Part 3, both parameters were varied. The results replicated those seen in studies that have investigated time allocation in a single patch: Both response and time allocation to an alternative increased with decreasing values of λ and with increasing values of ρ, and residence times were consistently greater than those that would maximize obtained reinforcer rates. Furthermore, both response- and time-allocation ratios undermatched mean reinforcer-arrival time and reinforcer-frequency ratios.     

Changeover behavior and preference in concurrent schedules

Pigeons were trained on a multiple schedule of reinforcement in which separate concurrent schedules occurred in each of two components. Key pecking was reinforced with milo. During one component, a variable-interval 40-s schedule was concurrent with a variable-interval 20-s schedule; during the other component, a variable-interval 40-s schedule was concurrent with a variable-interval 80-s schedule. During probe tests, the stimuli correlated with the two variable-interval 40-s schedules were presented simultaneously to assess preference, measured by the relative response rates to the two stimuli. In Experiment 1, the concurrently available variable-interval 20-s schedule operated normally; that is, reinforcer availability was not signaled. Following this baseline training, relative response rate during the probes favored the variable-interval 40-s alternative that had been paired with the lower valued schedule (i.e., with the variable-interval 80-s schedule). In Experiment 2, a signal for reinforcer availability was added to the high-value alternative (i.e., to the variable-interval 20-s schedule), thus reducing the rate of key pecking maintained by that schedule but leaving the reinforcement rate unchanged. Following that baseline training, relative response rates during probes favored the variable-interval 40-s alternative that had been paired with the higher valued schedule. The reversal in the pattern of preference implies that the pattern of changeover behavior established during training, and not reinforcement rate, determined the preference patterns obtained on the probe tests.     

Semilattice-based dualities

The paper discusses regularisation of dualities. A given duality between (concrete) categories, e.g. a variety of algebras and a category of representation spaces, is lifted to a duality between the respective categories of semilattice representations in the category of algebras and the category of spaces. In particular, this gives duality for the regularisation of an irregular variety that has a duality. If the type of the variety includes constants, then the regularisation depends critically on the location or absence of constants within the defining identities. The role of schizophrenic objects is discussed, and a number of applications are given. Among these applications are different forms of regularisation of Priestley, Stone and Pontryagin dualities.     

Is community necessary? Quasi-philosophical ruminations

In responding to and examining Mary Anne Raywid's (1989) adoption of community building as an aim for schools, I survey a number of types of communities, including recreational, intentional and language communities. In considering all these communities, I try to show both the power of communities in our personal lives and some idea of why we might be of two minds about promoting community as an ideal in the modern world and in schools in particular.     

Commonalities and differences in similarity comparisons

Similarity is a central component of many cognitive processes. Current research suggests that similarity is well characterized as a comparison of structured representations. This process yields commonalities, differences related to the commonalities (alignable differences), and differences not related to the commonalities (nonalignable differences). In the first study, further evidence for this tripartite distinction is provided in a commonality and difference listing study involving pairs of pictures. This study indicates that alignable differences rather than nonalignable differences are central to the comparison process by virtue of their connection to the commonalities. The second study further demonstrates that alignable differences count more against the similarity of a pair than do nonalignable differences. We end by discussing implications of the distinction between alignable and nonalignable differences for other cognitive processes involving comparisons.     

Pascalian wagers

A person who does not have good intellectual reasons for believing in God can, depending on his probabilities and values for consequences of believing, have good practical reasons. Pascalian wagers founded on a variety of possible probability/value profiles are examined from a Bayesian perspective central to which is the idea that states and options are pragmatically reasonable only if they maximize subjective expected value. Attention is paid to problems posed by representations of values by Cantorian infinities. An appendix attends to Robinsonian hyperreals. Another appendix presents for comparison Newcomb's Problem and a problem in some ways like it suggested, I think, by ideas of John Calvin.     

On Alan Turing's anticipation of connectionism

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks unorganised machines. By the application of what he described as appropriate interference, mimicking education an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of neurons is sufficient. Turing proposed simulating both the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948.In Memory of Robin Gandy     

You'll Never Believe This: Irony and Hyperbole in Expressing Surprise

Three experiments compared how people comprehend irony and hyperbole as expressing surprise. Experiment 1 demonstrated that, when irony and hyperbole are used together, they express more surprise than if either is used alone. There was no difference between the degree of surprise expressed by hyperbole and irony, although both expressed more surprise than literal commentary. Experiment 2 revealed that, when a speaker has exaggerated about some unexpected event, as much surprise is expressed by very slight, realistically possible hyperbole as by outlandish, impossible hyperbole. In a third experiment the range of possible levels of hyperbole tested in Experiment 2 was shown to cause differences in how easy it was to determine that a speaker was surprised at some turn of events. The results are discussed in terms of theories of irony and hyperbole comprehension.     

Lifelong Mild Bad Feelings: A Review and Solution to a Psychotherapeutic Enigma

A review indicates that (a) comparatively little is known about the common phenomenon of lifelong mild bad feelings, and (b) psychotherapy has generally overlooked an effective focus on this enigmatic feeling state. As an invitation for clinicians to provide more attention to this feeling state, a proposal is suggested toward one way of freeing a patient of lifelong mild bad feelings in the course of a session.