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Theories by D.O. Hebb and P.M. Milner on how the brain works were tested by simulating neuron nets on the IBM Type 704 Electronic Calculator. The formation of cell assemblies from an unorganized net of neurons was demonstrated, as well as a plausible mechanism for short-term memory and the phenomena of growth and fractionation of cell assemblies. The cell assemblies do not yet act just as the theory requires, but changes in the theory and the simulation offer promise for further experimentation.