Occurrence and nonoccurrence of random sequences: comment on Hahn and Warren (2009).

On the basis of the statistical concept of waiting time and on computer simulations of the "probabilities of nonoccurrence" (p. 457) for random sequences, Hahn and Warren (2009) proposed that given people's experience of a finite data stream from the environment, the gambler's fallacy is not as gross an error as it might seem. We deal with two critical issues in Hahn and Warren's argument, a possible ambiguity in distinguishing the events of occurrence and nonoccurrence, and an incomplete consideration of the context in which the statistics of waiting time are defined. Our analyses show that the statistics of waiting time and the probabilities of nonoccurrence, once correctly interpreted, do not vindicate the error in the gambler's fallacy.

Mathematical representations in science: a cognitive-historical case history.

The important role of mathematical representations in scientific thinking has received little attention from cognitive scientists. This study argues that neglect of this issue is unwarranted, given existing cognitive theories and laws, together with promising results from the cognitive historical analysis of several important scientists. In particular, while the mathematical wizardry of James Clerk Maxwell differed dramatically from the experimental approaches favored by Michael Faraday, Maxwell himself recognized Faraday as "in reality a mathematician of a very high order," and his own work as in some respects a re-representation of Faraday's field theory in analytic terms. The implications of the similarities and differences between the two figures open new perspectives on the cognitive role of mathematics as a learned mode of representation in science.

Contextualizing counterintuitiveness: how context affects comprehension and memorability of counterintuitive concepts.

A number of anthropologists have argued that religious concepts are minimally counterintuitive and that this gives them mnemic advantages. This paper addresses the question of why people have the memory architecture that results in such concepts being more memorable than other types of concepts by pointing out the benefits of a memory structure that leads to better recall for minimally counterintuitive concepts and by showing how such benefits emerge in the real-time processing of comprehending narratives such as folk tales. This model suggests that memorability is not an inherent property of a concept; rather it is a property of the concept, the context in which the concept is presented, and the background knowledge that the comprehendor possesses about the concept. The model predicts how memorability of a concept should change if the context containing the concept were changed. The paper also presents the results of experiments carried out to test these predictions.