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Meaningful factor analysis and algebraic operations during stimulation, learning, and discrimination experiments have been performed on averaged evoked potential responses, suggesting that, at least under some circumstances, the signal space of average evoked potentials is linear. Alternatively, the "behavior" of simulated neural nets is defined as the observation of an average over an ensemble of the trajectories of solutions of interconnected nonlinear dynamical systems. This behavior is a mathematical counterpart of the physiological macropotential observations. In this paper, a mathematical model corresponding to the ensemble average over an unconnected set of statistically distributed linear elements suggests duplication of both the simulated neural net and the neurophysiological findings. In contrast with the simulated neural network, the statistical properties of this model are amenable to analysis. The model suggests experiments of the prediction and control of multidiscrimination experiments in cats and provokes questions on the significance of the specification of detail in different levels on the structural hierarchy of the brain.