Ion channels are irresistible objects for biological study because they are the [nano] valves of life controlling an enormous range of biological function, much as transistors control computers. Ion channels are appealing objects for physical investigation because conformation changes are not involved in channel function, once the channel is open. Open channels are interesting objects for chemical study because they effectively select among chemically similar ions, under unfavorable circumstances. Channels are interesting objects for physical study because they contain an enormous density of charge, fixed, mobile, and induced. Direct simulation of channel behavior in atomic detail is difficult if not impossible, because ion transit takes ~ 10-8 sec compared to a simulation calculation time step of 10-16 sec and a biological time scale beginning at 10-4 sec. Direct simulation must deal with concentrations of 10-7 to 55 M in a single calculation, and macroscopic electric fields and concentration gradients produce substantial flows which are the function of the channel, making equilibrium analysis unhelpful.