Spiralling (as opposed to circulating) connubia abound in the Highlands of Papua New Guinea but, overlain by cermonial exchange ad warfare, they have remained largely unidentified for want of a suitable statistical method. By analogy with the natural sciences, we may expect fields to be structured such that flows within thein take the shortest possible pathways. The theory of chaos shows that these paths never repeat themselves, but trace out cascading, vortical patterns. Flows of women given in marriage by men, constituting potential connubia, assume similar patterns. Connubia are not states of being, but come into being out of the flux of Highlands social life. Drawing on material from the Etoro and the Polopa, a statistical method is outlined which would assess not the existence of connubia, but the realisation of a potential for them to exist. The null hypothesis, that marriage depends on availibility alone, is rejected. What requires explanation is the absence of spiralling connubia, not their presence.