"The 'law of causality' is obsolete and misleading. The principle 'same cause, same effect' is utterly otiose. As soon as the antecedents have been given sufficiently fully to enable the consequent to be calculated with some exactitude, the antecedents have become so complicated that it is very unlikely they will ever recur." - Bertrand Russell "On the Notion of Cause", 1913

Thanks - makes sense. My fault, I don't know how I missed that post... I love this blog!

Reason for downvotes please?

I'd say that is a fair answer. Without more context it’s hard to say exactly what Turing meant; he might have been referring to the different ways science and religion each handle causality. In science, causes are local in space and time -- perfectly modeled by a differential equation. In religion, causality is placed by fiat: a First Cause (boundary condition at the beginning of time) or final causes (teleology).

Another way of looking at the quote is to notice that physics especially concerns itself with continuous changes in space and time. Each infinitesimal chunk of spacetime is governed by its immediate neighbor. But this leads to a difficult question as you expand the system under consideration: who or what determines the ultimate boundary conditions of the differential equation?

"Science is a differential equation. Religion is a boundary condition."

Alan Turing, Alan Turing: the Enigma (Vintage edition 1992), p. 513