Alan Turing (1912-1954) was a mathematician and computer scientist who formulated a test of a machine's ability to demonstrate intelligence. (The full text can be read here). The test is based on the idea of the 'imitation game', with an intelligent machine, unseen, trying to convince a human interrogator that it is in fact human, on the basis of its answers to questions put to it.
Turing reckoned that by around the beginning of the 21st century computing would be so advanced that, in such a test, an interrogator would not have more than a 70 per cent chance of making the right identification after five minutes of questioning.
Turing anticipated various objections to the idea that machines could ever match humans in the capability to reason. Among them was the statistical evidence for telepathy, which he considered 'overwhelming'. This is the relevant extract:
The Argument from Extrasensory Perception
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.
This argument is to my mind quite a strong one. One can say in reply that many scientific theories seem to remain workable in practice, in spite of clashing with ESP; that in fact one can get along very nicely if one forgets about it. This is rather cold comfort, and one fears that thinking is just the kind of phenomenon where ESP may be especially relevant.
A more specific argument based on ESP might run as follows: "Let us play the imitation game, using as witnesses a man who is good as a telepathic receiver, and a digital computer. The interrogator can ask such questions as 'What suit does the card in my right hand belong to?' The man by telepathy or clairvoyance gives the right answer 130 times out of 400 cards. The machine can only guess at random, and perhaps gets 104 right, so the interrogator makes the right identification." There is an interesting possibility which opens here. Suppose the digital computer contains a random number generator. Then it will be natural to use this to decide what answer to give. But then the random number generator will be subject to the psychokinetic powers of the interrogator. Perhaps this psychokinesis might cause the machine to guess right more often than would be expected on a probability calculation, so that the interrogator might still be unable to make the right identification. On the other hand, he might be able to guess right without any questioning, by clairvoyance. With ESP anything may happen.
If telepathy is admitted it will be necessary to tighten our test up. The situation could be regarded as analogous to that which would occur if the interrogator were talking to himself and one of the competitors was listening with his ear to the wall. To put the competitors into a "telepathy-proof room" would satisfy all requirements.
(A. M. Turing, ‘Computing Machinery and Intelligence’, Computing machinery and intelligence’, Mind, 59, 1950, 433-460.)