This paper uses bio-economic modeling and simulation to investigate the de-mise of the sperm whale industry in the mid-19th century. Petroleum is widely credited both contemporaneously and today with 'saving the whales.' We investigate the transition in illumination technologies from whale oil to petroleum as a stochastic dynamic process in which there is uncertainty over the parameters of the fishery and the timing of available substitutes for sperm oil in order to determine the effect on the whale population. Using new biological analysis of the sperm whale fishery (Whitehead, 2002) and insights from natural resource economics we show that under most economic conditions the dynamics, even without a substitute, would have prevented extinction; this result is notably different, for economic and biological reasons, than that usually determined for the better studied baleen whales. This research builds on a long history of understanding the whale fisheries, particularly Davis et al. (1988) and related work, integrating new scientific and economic evidence.