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.

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    I think there is terminological confusion. These are not computable tasks because they are not tasks at all in the sense of the theory of computation. Neither is ordinary perception or doing back flips, Turing machines can not do those either, computation is a procedure for transforming specified inputs into specified outputs. Not everything is a computation, and not everything that violates the laws of physics (as we know them) is uncomputable. – Conifold Jan 2 '18 at 22:54
  • @Conifold I couldn't find anything in the article you cited that would claim that doing a backflip is not computable. There is input: a command to move in some way. There is a state change: configure to perform the backflip. There is output: perform the backflip. It seems like something a finite state machine could perform let alone a Turing machine. However, I will look for better definitions of this. It is precisely the kind of objections you are raising that interests me. Thanks! – Frank Hubeny Jan 3 '18 at 0:58
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    Computation consists of transcribing symbols into symbols, any physical action or sensory perception are already beyond the word's usefulness. What you describe concerns simulating a backflip, not the action itself, and there is of course no problem with simulating ESP either, as movies do. – Conifold Jan 3 '18 at 1:39
  • @Conifold The problem with the traditional and alternative Turing tests is that they are like magic shows. If the magician convinces you that he pulled a rabbit out of a hat then the claim is that he really pulled the rabbit out of the hat. Such results are hard to take seriously. I've edited my question to focus on a particular experiment using a double-slit experiment. – Frank Hubeny Jan 3 '18 at 3:37

Although it seems intuitively obvious that they are not computable tasks, how would one argue that telepathy, or other ESP tasks, are not computable?

One would have to argue that there exists no test that can measure the phenomenon of telepathy and, further, no such test could possibly exist. In other words, not only has such a measurement never been made (it just might not have been found yet), but it is logically impossible that it could ever be made. This response assumes the laws of physics as currently known. However, if ever it were ever discovered that telepathy follows a discrete set of laws, then once the process became clear, a telepathic Turing machine would become theoretically possible.

  • Measuring psi phenomena in humans has been documented. See Dean Radin's "Selected Psi Research Publications": deanradin.com/evidence/evidence.htm So Turing's concern is justified. As you mention there could be a "discrete set of laws" explaining it that we currently are unaware of. I will edit my question to include a specific psi phenomenon I am particularly interested in examining. – Frank Hubeny Jan 3 '18 at 2:52

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