Responding to this issue's invitation to bring new disciplinary insights to the field of improvement science, this article takes as its starting point one of the field's guiding metaphors: the imperative to "mind the gap". Drawing on insights from anthropology, history, and philosophy, the article reflects on the origins and implications of this metaphoric imperative, and suggests some ways in which it might be in tension with the means and ends of improvement. If the industrial origins of improvement science in the twentieth century inform a metaphor of gaps, chasms, and spaces of misalignment as invariably imperfect and potentially dangerous, and therefore requiring bridging or closure, other currents that feed the discipline of improvement science suggest the potential value and uses of spaces of openness and ambiguity. These currents include the science of complex adaptive systems, and certain precepts of philosophical pragmatism acknowledged to inform improvement science. Going a step further, I reflect on whether or not these two contrasting approaches within improvement science should be treated as incommensurable paradigms, and what each approach tells us about the very possibility of accommodating seemingly irreconcilable or incommensurable approaches within improvement science.