A layer or two of 3He atoms adsorbed on a flat surface at very low temperatures constitutes an almost ideal two-dimensional system in which a whole range of thermal and magnetic quantum phenomena may conveniently be investigated. Recent experiments, in several laboratories, have revealed some strange and unexpected behaviour that can arise in an apparently incomplete second atomic layer. Veit Elser has risen to the challenge provided by these data and, writing in Physical Review Letters (62, 2405-2408; 1989), suggests that the observed effects are associated with nuclear antiferromagnetism in what is actually a peculiarly loosely knit kind of two-dimensional solid.