A central open question of computational neuroscience is to identify the data structures and algorithms that are used in mammalian cortex to support successive acts of the basic cognitive tasks of memorization and association. This paper addresses the simultaneous challenges of realizing these two distinct tasks with the same data structure, and doing so while respecting the following four basic quantitative parameters of cortex, the neuron number, the synapse number, the synapse strengths, and the switching times. Previous work had not succeeded in reconciling all these opposing constraints, the low values of synapse strengths that are typically observed experimentally having contributed a particular obstacle. In this paper we describe a computational scheme that supports both memory formation and association, and is feasible on networks of model neurons that respect the widely observed values of the above-mentioned four quantitative parameters. Our scheme allows for both disjoint and shared representations. The algorithms are simple, and in one version both memorization and association require just one step of vicinal or neighborly influence. The issues of interference among the different circuits that are established, of robustness to noise, and of the stability of the hierarchical memorization process are addressed. A calculus, therefore, is implied for analyzing the capabilities of particular neural systems and subsystems, in terms of their basic numerical parameters.