Fisheries management often relies heavily on precautionary reference points estimated from complex statistical models. An alternative approach uses management strategies defined by mathematical algorithms that calculate controls, like catch quotas, directly from the observed data. We combine these two distinct paradigms into a common framework using arguments from the historical development of quantum mechanics. In fisheries, as in physics, the core of the argument lies in the technical details. We illustrate the process of designing a management algorithm similar to one actually used by the International Whaling Commission. Reference points and surplus production models play a conceptual role in defining management strategies, even if marine populations do not obey such simplistic rules. Physicists have encountered similar problems in formulating quantum theory, where mathematical objects with seemingly unrealistic properties generate results of great practical importance.