Paul C. Anagnostopoulos said:
It's time for some theories!
I have some underlying reservations about asking people for theories before they've shown that any effect occurs, but in this case, I think we definitely need something to help the design of the experiment.
The more I think about the observation by Hans about precognition vs telepathy, the more problematic it becomes.
It seems to me that even removing feedback wouldn't be enough. You can sometimes have the results of experiments you've participated in sent to you, can't you? I'm expecting a brain scan to be sent to me, for this very reason. What if this was done in this case and the results are quite detailed? It might tell the recipient who was the caller for each trial. If this is the case, then it could also be used for precognition, so it would have to be arranged that the recipients never get to see the results (unless precognition still works when you're a ghost, in which case it seems pretty hopeless).
Even if that didn't happen, at some point, Sheldrake and Smart totted up the results, didn't they? So they would have known who was calling and when. So it's possible that the recipient used precognitive telepathy to read the mind of either Sheldrake or Smart at some point in the future.
In method 3 of the videotaped experiment, the results were evaluated blind by Dr Amanda Jacks, who didn't know who the callers were or when they were calling, which I suppose would help rule out this explanation, although only if the results were pre-compiled before Sheldrake and Smart were allowed to see them or the recipient and callers were recoded, so they weren't aware of the identities, which seems unlikely. Also Jacks could have got a clue as to whether the guess was right or not by the response of the recipient on being given the feedback, so she could have been a target for precognitive telepathy.
Furthermore, what if at some point in the future, one of us asks to see the original data of callers and guesses and either Sheldrake or Smart send them to us? Then we know all the results, and it could be that the recipient was using precognitive telepathy to read our minds!
I realise this is getting progressively more convoluted and ludicrous, but perhaps not a lot more than the idea of either telepathy or precognition.