Computational experiments are reported involving the concept of foreknowledge, an agent’s direct, unmediated and accurate, but possibly incomplete, awareness of its future including states and events involving the agent itself. Foreknowledge is used here as a conceptual tool with which to explore certain issues around time and rationality. We first explain how foreknowledge in this sense may be given to the agents in an agent society on a computer. The generation of a world history is viewed as a process of solving a constraint satisfaction problem. Then we seek to understand the circumstances in which foreknowledge may be either beneficial or detrimental to a society of rational agents. A special case is when agents have foreknowledge of their own “deaths”. An experimental interpretation of this special case has been implemented, and results are presented and discussed. Finally, the work reported is briefly discussed in the context of current theories of time.