Since Descartes' and Leibniz's time the question of mind-body interaction has involved a more scientific question: how are physical conservation laws relevant? According to Dennett, "...the conservation of energy...is apparently violated by dualism. This confrontation...is widely regarded as the inescapable and fatal flaw of dualism." What do theoretical physics and neuroscience have to say? This project is needed because the recent debate on both sides has been inadequately informed by physics. The locality and (in part) the conditionality of conservation laws have been neglected. _Local_ conservation laws are stricter, but they can fail more gently, holding outside brains even if not inside. Conditionality arises due to the Lagrange-Noether link between symmetries and conservation laws, so that an a priori objection begs the question. Physicist Sean Carroll has sharpened the debate by doubting whether soul-brain interaction is compatible with particle physics. Crucially, the debate ought be empirically informed by neuroscience, a principle often flouted in practice on both sides because either earlier a posterior considerations or a priori arguments are thought to decide the issue. The tension between a priori and a posteriori considerations makes fruitful a Bayesian formulation, to make explicit on what inputs the posteriors depend and how. How does the larger 500-year trend constricting spirit-matter interactions affect this issue? The project bears upon parts of four Big Questions, most obviously, what is mind? It also bears upon the fundamental structures of the natural world, how science, philosophy, and theology inform our understanding of Ultimate Reality, and the role of religion in human experience. The project will produce five journal submissions. The results will help various audiences to see the value of seeking the new spiritual information available empirically from places such as neuroscience.