Two types of brain model are currently the center of a fundamental controversy in cognitive science. Traditional artificial intelligence models are based on the discrete, programmable symbol systems normally associated with Turing/von Neumann computation, and for which language and logic are the essential tools. This type of model is now being challenged by the rebirth of concurrent, distributed networks that are based on analog models of physical systems, and that also claim some similarity to neural architecture. In the former, discrete symbols are local, sequential, and rewritten under total program control. In the latter, symbols are only the end result of coherent network dynamics that need little explicit program control. The behavior of these networks is determined by the constraints within the network and the initial conditions. In this respect, network behavior is functionally similar to a complex measurement process, since measurement in physics discriminates and classifies implicate dynamical patterns by mapping them to explicit symbols. But what determines when a measurement is completed is an unresolved problem in physics, especially in quantum theory. It involves complementary modes of description, one based on the rate-dependent, continuous, time-symmetric dynamics of inexorable physical laws, and the other based on the rate-independent, discrete, irreversible constraints of programmable symbol systems. In physics, these modes are both distinguished and related only by measurement, but when a measurement occurs appears to be a matter of arbitrary choice. The brain uses many complementary modes of description, and must constantly choose among them, but the ultimate nature of this choice remains a problem.