I read a book on synchronicity last summer (
C.G. Jung's Psychology of Religion and Synchronicity by
Robert Aziz). Rather heavy reading, at least for me. Anyway, Jung's explanation for synchronicity has something to do with "archetypes," or specifically the idea that two coincidental events are noticed by us primarily because of the fact that we are able to perceive a common pattern between them, an "archetype" as he calls it. I know when most people see the word "archetype" they think of "literary archetypes," ie common roles for characters, but I believe the definition here is meant to be a much larger one encompassing any basic "pattern" our minds can perceive.
The book goes into all kinds of ridiculous detail about how the human race knows many archetypes collected over the years into what he calls the "collective unconscious," and then there's some metaphysical speculation as to the nature of the collective unconscious and so forth.
What does it all mean?
After reading through 200-some-odd pages of deep stuff, it's still anyone's guess.
(addendum: ) Actually now that I recall, the book's point is to consider such "meaningful coincidences" in terms of, well, what "meaning" you find from them. The point is that one's own perception of such coincidences is a highly personalized interpretation and that interpretation tells us a lot about ourselves, our character and what is important to us at that point in time. The more important such patterns are to us, the more emotion we will feel when we notice these coincidences (the "numinous charge" as they call it).
Robert Aziz has another book,
"The Syndetic Paradigm" - The Untrodden Path beyond Freud and Jung, which I've purchased but haven't cracked quite yet. I gave the first chapter a read and decided to move on to something else. I think, as the title suggests, he's trying to create a superset theory to Freud and Jung's ideas, something about reality being a "self-organizing system" or whatever.
(warning: my crackpot theory below, please use iodized salt to flavor)
My personal guess? By definition, anyone who's highly "intuitive"--definable as someone who can perceive reality in terms of "patterns" (and this doesn't only mean an N-type preference, it could mean an S-type who has very well developed intuition)--has a natural ability to be highly sensitive to viewing archetypes, or "seeing meaning in coincidences" around them.
I consider the act of perceiving events and reducing them to an "archetype" to be potentially the "essence" of Ni, or an essential description of what it does. A pattern may have sequence to it--you might know that if A happens, B will happen next, followed by C or D, and E after all of that. I believe that one can take a subset of events and consider a number of possible known "patterns" (or "archetypes") that may apply to them, and an Ni-adept type may in fact do just that. As a result, if an Ni-type sees a small subset of events, their mind determines the root archetype at play there, and based on what they know of that archetype's sequence, they may be able to "predict" what will happen next, and this "prediction" is the root source of an Ni-type's so-called "prophetic" ability.