Our different kinds of minds and types of thinking affect the ways we decide, take action, and cooperate (or not). Derived from these types of minds, innate biases, beliefs, heuristics, and values (BBHV) influence behaviors, often beneficially, when individuals or small groups face immediate, local, acute situations that they and their ancestors faced repeatedly in the past. BBHV, though, need to be recognized and possibly countered or used when facing new, complex issues or situations especially if they need to be managed for the benefit of a wider community, for the longer‐term and the larger‐scale. Taking BBHV into account, we explain and provide a cyclic science‐infused adaptive framework for (1) gaining knowledge of complex systems and (2) improving their management. We explore how this process and framework could improve the governance of science and policy for different types of systems and issues, providing examples in the area of natural resources, hazards, and the environment. Lastly, we suggest that an “Open Traceable Accountable Policy” initiative that followed our suggested adaptive framework could beneficially complement recent Open Data/Model science initiatives.