With the expanding role of computers in society, some assumptions underlying well known theorems in the theory of parallel computation no longer hold universally. In particular, the speedup theorem and Brent's theorem do not apply to dynamic computers that interact with their environment. The phenomenon of a disproportionate decrease in execution time of P₂ over p₁ processors for p₂ > p₁ is referred to as superunitary speedup. An analogous phenomenon that we call superunilary 'success ratio' occurs in dealing with tasks that can either succeed or fail, when there is a disproportionate increase in the success of p2 over p1 processors executing a task. We identify a range of conditions that may lead to superunitary speedup or success ratio, and propose several new paradigms for problems that admit such superunitary behaviour. Our results suggest that a new theory of parallel computation may be required to accommodate these new paradigms.