> How could Turing have thought this? I don’t know much about Turing but it does seem, when reading old-time literature, that belief in the supernatural was pretty common back then, lots of mention of ghosts etc.

I think that today we overestimate how much we know, and discount the existence of “supernatural” phenomena that we don’t fit into our model of the universe.

Karma (or something like it) is a thing that probably exists; but we do not have the necessary concepts or tools to qualitatively or quantitatively describe how it works.