Common diseases tend to appear sporadically, i.e., they appear in an individual who has no first or second degree relatives with the disease. Yet diseases are often associated with a slight but definite increase in risk to the children of an affected individual. This weak pattern of inheritability cannot be explained by conventional interpretations of Mendelian genetics, and it is therefore commonly held that there is "incomplete penetrance" of a gene, or that there are polygenic, or multifactorial modes of inheritance. However, such arguments are heuristic and lack predictive power. Here, we explore the possibility that "incomplete penetrance" means the existence of a second, disease-related, gene. By examining in detail a specific common condition, Parkinson's disease (PD), we show that the sporadic form of the disease can be fully explained by a compact fully penetrant genotype involving an interaction between two, and only two, genes. In this model, therefore PD is fundamentally genetic. Our digenic model is complementary to Mendelian recessive genetics, but taken together with the latter forms a complete description for recessive genetics on one chromosome. It explains the slight increase in risk to the children if one parent has sporadic PD, and makes strict predictions where both parents coincidentally have sporadic PD. These predictions were verified in two large and carefully selected kindred, where the data also argue against other genetic models, including oligogenic and polygenic schemes. Since the inheritance patterns of sporadic PD are reminiscent of what is seen in many common diseases, it is plausible that similar genetic forms could apply to other diseases. Seen in this light, diseases wash in and out of every family, so that in a sense, over time every human family is equally at risk for most diseases.