If we categorize religions according to whether they give greater prominence to time or to space, the role of “promise” marks a religion of covenant as clearly a religion of time. Yet the future is unknowable and can only be present to us as a field of possibilities. How far do these possibilities extend? The question directs us back to the nature of time, a question that became concealed in th...

The polynomial hierarchy is a grading of problems by difficulty, including P, NP and coNP as the best known classes. The promise polynomial hierarchy is similar, but extended to include promise problems. It turns out that the promise polynomial hierarchy is considerably simpler to work with, and many open questions about the polynomial hierarchy can be resolved in the promise polynomial hierarc...