Based on a calculation of neural decoherence rates, we argue that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence time scales ( approximately 10(-13)-10(-20) s) are typically much shorter than the relevant dynamical time scales ( approximately 10(-3)-10(-1) s), both for regular neuron firing and for kinklike polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.