There are not many researchers who have studied this issue: the major ones are the biologist Paul Kammerer and the psychologist Carl Jung, but unfortunately even they did it in a rather superficial and incomplete manner.
Arthur Kessler, in his work with the catchy title The Roots of Coincidence, just mentions the two previous theories and regards the coincidences as a part of the field of parapsychology. The most interesting way of analysis of coincidences was tried by the Greek scientist Christos Markopoulos.
Paul Kammerer from twenty to forty years old consistently has kept a diary of coincidences, which were then analyzed in his book The Law of the Series. In the first part of his book Kammerer suggests a typology of coincidences depending on their class (the number of successive iterations), their strength (number of parallel coincidences) and their parameters (the number of common characteristics), proving that all coincidences obey the law of repetitive sequences.
In the second and theoretical part of his book Kamerer develops the basic idea, that in parallel with the law of causality there is and a law of non-causality in the world, which tends to unite similar phenomena and events in groups.
At the end of his book Kammerer concludes that the Law of the Series is ever-present in Life, Nature and the World and connects Thoughts, Feelings, Art and Science with the matrix that gave birth to the universe.
Carl Jung worked on parapsychology and spiritualism from an early age and was open to exploring all kinds of “oddities”. Therefore, it was quite natural for him to deal with the issue of coincidences. In collaboration with Wolfgang Pauli he wrote the book called Synchronicity: An Acausal Connecting Principle.
Synchronicity, according to Jung, “is the simultaneous occurrence of two phenomena that are not deterministically but conceptually related, or a coincidence in time of two or more non-causally related events that have a same or similar concept, tied by causality.” Jung as psychologist tried to explain all the phenomena that can not rely on physical causality as manifestations of the concepts he introduced in psychology, i.e. of the “collective unconscious” and the “archetypes”.
Jung went so far as to claim that the archetypes are psycho-physical entities that can cause various unexplained phenomena.
Let’s move on to more interesting attempt to explain the coincidences by Christos Markopoulos. He begins his research with the various aspects of the Law of Probability and the results of experiments related to the random (or not) things, made by mathematicians. Then he extends the results in the areas of chemistry, biology, and human society with very interesting findings.
We’ll start with a simple everyday example – a lottery draw. Common sense says that a number that has not shown for a long time is more likely to be drawn than the one which has just been drawn. Yet, the relevant experiments proved exactly the opposite! For example, in the last four draws the following numbers appeared: 2, 5, 7, 1. In next draws these four numbers are 70% likely to show again, while the 3, 4, 6, 8, 9, 0 have a 30% chance to be drawn!
Thus Markopoulos comes to the following regularities:
- In any finite number of equally likely events there is an inequality of occurring frequencies. Some of them occur more frequently than others.
- Events that occur first are more likely to occur again than those that have not occurred at all.
- While the first events occur (at least theoretically) at random, the subsequent ones seem to be governed by a mysterious determinism of forced randomness, i.e. a combination of randomness and necessity.
All of the above have been found experimentally and empirically and are indeed incredible. If there are no random events, then we live in a purely deterministic world. Since this basic question is not answered, unfortunately it is not possible to say how “random” the coincidences are.