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You read about a chemistry experiment in which a clear liquid becomes red, defying the predictions of your scientific theory. Does this demand explanation? You read about an event in which Jesus turns water into wine, challenging your assumptions about the natural world. Does this demand explanation? The “Need for Explanation” (NFE) can be compelling, but it is also highly selective: we do not feel compelled to explain most observations most of the time. And in some cases, it seems acceptable to respond to an explanation request by declaring the answer a mystery. (Perhaps it is appropriate to declare the transformation of water into wine a mystery, but not the outcome of the scientific experiment.) What is it about some observations that demands explanation? Does seeking explanations under precisely these circumstances satisfy a particular epistemic (or non-epistemic) aim? And do the observations that trigger NFE, or the aims served in doing so, differ across scientific and religious domains? Through a series of empirical studies and theoretical analyses, we will explore these questions with the aim of developing both descriptive and normative accounts of NFE and of the acceptability of mysteries. This work will build on past work on curiosity and explanation within psychology, as well as formal and theoretical work on explanation and religious belief within philosophy of science and formal epistemology. Our ultimate goal is to achieve a better understanding of human curiosity and the drive to explain as impulses that help us flourish in a complex world. In addition, by understanding whether and how NFE and mystery acceptability (MA) differ across scientific and religious domains, we can paint a more accurate picture of how our epistemic aims and attitudes differ across these domains, with implications for how to negotiate the relationship between science and religion.