A macroscopic system involving permanent magnets is used as an analogue to nucleons in a nucleus to illustrate the significance of the pairing interaction. This illustrates that the view of the total nuclear energy based only on the nucleon occupancy of the energy levels can yield erroneous results and it is only when the pairing interaction is considered that a correct picture emerges. The macroscopic analogue of combined gravitational and magnetic interactions shows that a consideration of only the gravitational interaction can lead to an incorrect picture and that the inclusion of magnetic coupling is needed to properly describe the ordering of the energy levels.