Here, we reconcile millennia of scholarship to show that realist thought is not incompatible with the concept of soft power. In fact, the ideological ancestors of modern realists showed remarkable alignment with the neoliberal concept. We support theory presented by ancient realists and modern neoliberals with findings from social psychology and develop a framework for psychological significance. Using this framework, we demonstrate that psychologically significant visits by heads of government or state yield an increase in approval rate among the citizens of the host country over five times larger than routine visits. We take advantage of a natural experiment which allows us to isolate the effect of psychological mechanisms from military and economic forces. These findings should change how leaders interact with foreign publics, and also suggest changes in realist approaches to the study of power and a reconceptualization of soft power as social and cultural cognition.