  The principle of energy conservation is widely taken to be a serious
difficulty for interactionist dualism (whether property or substance).
Interactionists often have therefore tried to make it satisfy energy
conservation. This paper examines several such attempts, especially including
E. J. Lowe's varying constants proposal, showing how they all miss their goal
due to lack of engagement with the physico-mathematical roots of energy
conservation physics: the first Noether theorem (that symmetries imply
conservation laws), its converse (that conservation laws imply symmetries), and
the locality of continuum/field physics. Thus the "conditionality response",
which sees conservation as (bi)conditional upon symmetries and simply accepts
energy non-conservation as an aspect of interactionist dualism, is seen to be,
perhaps surprisingly, the one most in accord with contemporary physics (apart
from quantum mechanics) by not conflicting with mathematical theorems basic to
physics. A decent objection to interactionism should be a posteriori, based on
empirically studying the brain.
