Likelihood of the Unlikely

According to Deirdre Bair, biographer of C. J. Jung, (“Jung”, Little Brown, N.Y. 2003) the term ‘synchronicity’ was introduced by the well known psychologist that was her subject.

Synchronicity refers to a confluence of events that is so startling and improbable as to constitute a miracle – usually received as a blessing conferred by unknown and unfathomable forces in nature.  It is currently popular among devotees of the mystical and supernatural. For them it validates their belief that nature has aspects that are beyond access to the methods of science.

Synchronicity is a highly improbable conjunction of events that may be received as a message or insight delivered to enter ones consciousness from the universe itself. You are in distress and have abandonned hope when, lo, someone arrives unexpectedly whose presence precisely meets your needs. This is the classic generic synchronicity. You gave your precious and only shawl to your aunt who was suffering from the cold. The next day you receive, quite unexpectedly, a gift from someone. It is a shawl of just the same weave and fabric. Synchronicity, is what your friends call this improbable event.

But, we may ask ourselves, what, in fact, is the probability of the improbable? With what frequency may we expect events that we might deem improbable? Are they, in fact, more probable than we think! Does our intuition compute probabilities differently than does mathematics? According to psychologist Daniel Kahneman, “Thinking Fast and Slow”, (2011) that is exactly the case.

Do we mistake for magical synchronicity, events that are merely less-than-probable? I propose we can answer this question via a conceptual model.

I and some of my friends each have three dice. We all roll our three. The probability of ‘synchronicity’ – that I find all three faces to be the same; all fives, all threes – is 1/36. The chance is small. That I roll three of a kind will happen less than 3% of the time.

But one of my friends may find synchronicity. For her the probability was as low as for me; 3%. She will enthusiastically report her three-of-a-kind as magical good fortune. And we will rejoice with her.

But let us ask this question: What is the probability that one or more among our band of twenty-five comrades will report synchronicity? Answer: this probability is about 50%. Far greater than the mere 3% for a single individual. The mathematical formula for this probability is 1-(1-1/36)25. That one or more of us will find synchronicity is quite probable! Half the time someone among us will find all three die faces the same.  Among 100 friends three-of-a-kind synchronicity is just about certain; 94% certain. Even though the event is rare, one or more among many will experience it.

What is the likliehood of an unlikely event? The answer depends upon the level of thought that goes into the computation. Imprecise thinking can rank an event as miraculous when, in fact, it isn’t at all miraculous. One can deceive oneself into perceiving an event as being far less likely than it actually is. In the limited constellation of events to which a single person is privy what appears to be miraculous – low probability – is, in fact, much more probable on the grand scale of things. On the basis of pure chance, the probability that someone will experience a ‘synchronicity’ is quite respectably large.

So I’m happy to report that miracles are commonplace. Expect one soon.

Here’s the idea in verse.