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We consider the properties of “Potts” neural networks where each neuron can be in Q different states. For a “Potts-perceptron” with N Q-states input neurons and one Q' states output neutron, we compute the maximal storage capacity for unbiased patterns. In the large N limit the maximal number of patterns that can be stored is found to be proportional to N(Q-1)f(Q'), where f(Q') is of order 1

Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the whole framework is built. This requires looking past obscuring noises present ubiquitously in the real world. The beginnings of physics, classical mechanics with Galileo and Newton, required seeing past friction to get at the basic laws of inertia and motion. Later, in Einstein's Special Theory of Relativity, ideas of location in space and time, and relative velocities in motion, were modified. The recognition that all inertial observers, those moving with constant relative velocity with respect to one another, are on par with respect to a common physics necessitated a re--examination of the concepts of space and time.Quantum physics, first in non--relativistic mechanics and later in quantum field theories, went further in regarding even familiar concepts of position, momentum, wave or particle, as derived constructs from the classical limit in which we live but not intrinsic to the underlying physics. They are not elements of the underlying reality of the Universe, only the near--universal presence of decoherence making them appear so. It is this noise of decoherence that so shapes our intuition and the very definition of terms with which we experience our world that makes it difficult to understand the quantum nature of that world at its base. Most crucially, the very idea of the individual, whether an object or an event, distinguished only in a mere label of identity from others identical to it in all the physics, exists only as an approximation in what is called the classical limit. It is not an element of underlying quantum reality. Failure to recognize this and seeking alternative