  If our actions are determined by the laws of nature, can we meaningfully
claim to possess free will? Compatibilists argue that the answer is yes, and
that free will is compatible with complete determinism. Previously, it has been
suggested that the notion of computational irreducibility can shed light on
this relation: it implies that there cannot in general be "shortcuts" to the
decisions of agents, explaining why deterministic agents often appear to have
free will. In this paper, we introduce a variant of computational
irreducibility that intends to capture more accurately aspects of actual (as
opposed to apparent) free will: computational sourcehood, i.e. the phenomenon
that the successful prediction of a process' outputs must typically involve an
almost-exact representation of the relevant features of that process,
regardless of the time it takes to arrive at the prediction. We conjecture that
many processes have this property, and we study different possibilities for how
to formalize this conjecture in terms of universal Turing machines. While we
are not able to settle the conjecture, we give several results and
constructions that shed light on the quest for its correct formulation.
