Mental Telepathy
In 1885, a group of distinguished scholars and scientists founded the American Society for Psychical Research (ASPR). The group's goal was to use serious scientific research methods to study psychic phenomenon. To that end, the ASPR performed various experiments in mental telepathy and continues to research psychic phenomenon. Various experiments are outlined in past ASPR journals. For example, the January 1997 edition of "The Journal of the American Society for Psychical Research" details an experiment with the "alleged human aura," which involved an experimental group and a control group tasked with trying to guess who was on the other side of the door by concentrating on the aura emitted by the person.
William Crookes
In the late 19th century, respected chemist and physicist Sir William Crookes was initially skeptical about mental telepathy until an experience with a psychic medium opened his mind. As a man of science, he tried to come up with a rational explanation behind mental telepathy and theorized that telepathy traveled in the same manner as electromagnetic waves. Crookes conducted numerous experiments with Scottish medium Daniel Dunglas Home, including one that he claimed proved Home could affect the weight of a board as it sat on a scale simply by placing his fingers in a glass of water that sat on one end of the board.
Stanford Experiments
Psychologist John E. Coover was Stanford University's first Fellow in Psychical Research. By 1917, he had performed four major experiments in mental telepathy. The most important of these involved 100 test subjects in 100 different trials. About half of these subjects would look at an image on a card and attempt to telepathically communicate that image to another person. With the other half of the subjects, serving as the control group, the sender wouldn't look at the card until after the receiver made a guess. After his research, Coover reported the results did not serve as evidence of the existence of mental telepathy.
Apollo 14
Astronaut Edgar D. Mitchell was the sixth man to walk on the moon and claims to have conducted a telepathy experiment during the Apollo 14 mission. The experiment was entirely Mitchell's own and was not sanctioned by NASA. In his experiment, Mitchell assigned the numbers one through five to corresponding symbols. He then looked at the symbol and concentrated on it for a period of time. Back on Earth, 150,000 miles away, four different people were instructed to concentrate on guessing what symbol he was thinking of at that moment. Mitchell published his results in 1971 in the "Journal of Parapsychology," indicating that two of the subjects performed above the statistical average and two subjects performed below it.