In 1967, on seven consecutive Monday evenings, 200 people took part in an experiment testing the possibility of mental telepathy. As a result of certain apparent random coincidences during those experiments, another test was devised. The results of those experiments produced some striking results, opening up whole new areas of research into the concept of chance.
The telepathy experiments are not convincing. In fact, the authors appear to show that they get the same results randomly. Arthur Koestler's discussion of the new physics is interesting.