Important Variables in Reasoning about Social Rules

In everyday life people produce and accept behaviours that deviate to some extent from a rule, but are nevertheless recognised as examples of the rule. This study analyses the effects of three variables, i.e. type of substitution, centrality of the element involved in the transgression, and linguistic formulation of rules, on judgements of acceptability and seriousness of such deviations. Three groups of 60 subjects each (4-year-olds, 9-year-olds, and adults) were randomly assigned to receive one of three linguistic formulations of a prudential rule. In the first, the rule was stated without justification; in the second, the goal of the rule was stated; in the third, a description of the actions and the items necessary to obey the rule was given. All subjects had to judge a variety of rule transgressions based on elimination, unsuitable substitution or suitable substitution of a central or a peripheral element of the rule. Linguistic formulation had, at best, a modest effect on judgements. However, there were strong effects of type of substitution and centrality. Moreover, the effects of these variables differed with age and the subjects showed an increasing capacity to take into account all the elements involved.

Roots of unity and the character variety of a knot complement

Using elementary methods we give a new proof of a result concerning the special form of the character of the bounded peripheral element which arises at an end of a curve component of the character variety of a knot complement.