In Alan Turing’s “Computing Machinery and Intelligence” he writes in 6(9) The Argument from Extrasensory Perception that
I assume that the reader is familiar with the idea of extrasensory perception, and the meaning of the four items of it, viz., telepathy, clairvoyance, precognition and psychokinesis. These disturbing phenomena seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming. It is very difficult to rearrange one's ideas so as to fit these new facts in. Once one has accepted them it does not seem a very big step to believe in ghosts and bogies. The idea that our bodies move simply according to the known laws of physics, together with some others not yet discovered but somewhat similar, would be one of the first to go.
Based on Turing’s remarks, I suspect the task of telepathy is not a computable process, that is, a task one could expect a Turing machine to perform.
Although it seems intuitively obvious that they are not computable tasks, how would one argue that telepathy, or other ESP tasks, are not computable?
Edit: There is a psi phenomenon I am particularly interested in. In Dean Radin's "Selected Psi Research Publications" there is one he co-authored called "Consciousness and the double-slit interference pattern: Six experiments". Human subjects, but not computers, were able through their intentionality to affect a double slit experiment.
How would one formulate that task as an algorithm to run on an AI machine? If that can be formulated it looks like it would serve as a modified Turing test without involving human judges to determine if the simulation convinced them. If that can't be formulated, then strong AI does not explain human mental behavior.
A video of a talk by Radin, "New Experiments Show Consciousness Affects Matter", summaries the above and similar results.