Working out the place of probability in coincidence studies.
The study of coincidences requires a basic education in probability. Why? Because the lower the probability (or the higher the improbability), the more likely that there is a hidden cause or explanation.
How do we determine the probability of a coincidence? When is it possible to explain a coincidence by probability alone?
In most coincidences, multiple influences produce the outcome. I call these influences vexing vectors. They are vexing to human minds because it is difficult to keep several of them in mind at the same time. One cause for one effect is easier. Vectors are lines of varying force that influence an outcome. The various forces creating coincidences include probability, personal responsibility, and the parapsychological including telepathy and clairvoyance as well as the mysterious. The mysterious includes God, spirits, quantum holograms, entanglement, complexity theory and many others. In discussing coincidences conventional statisticians use probability in the following way: it happened so it has a probability, therefore it could happen, so probability explains it because there is a probability of it happening. This is circular reasoning.
Gary Schwartz is working on a Probability for Coincidences or, as he calls, it Synchronicity Statistics. He estimates how many lifetimes it would take for an ultra-low probability coincidence to come into existence. Some probabilities are so low that Gary calls them "astronomically improbable" in his new book Super Synchronicity.