Hmm. And the usual conclusion of the Turing test is "if you can't tell the difference then it doesn't matter anyway". If applied in this situation, that disturbs me!

If a figment of your imagination is none the less capable of answering prayers and suchlike, then it might as well be treated as a god; if a god declines to interact with the world outside your head, then it might as well be treated as a figment of your imagination. Doesn't seem altogether bonkers to me, though one can and probably should quibble with both halves.

Hmmm, a god who solves NP-complete problems quickly? Such a god could interact only with your head, and yet be far more powerful, and have much further reaching implications, than any figment.

And would therefore be distinguishable by means of prayer from a figment of your imagination. No problem. (Unless you believe that *you* can solve NP-complete problems quickly, I suppose.)