Integral World: Exploring Theories of Everything
An independent forum for a critical discussion of the integral philosophy of Ken Wilber


Desultory Decussation

Where Littlewood’s Law of Miracles
meets Jung’s Synchronicity

David Lane & Andrea Diem Lane

The high improbability of an event oftentimes blinds us from the probability, even if rare, that such events are probabilistic.

I enjoyed reading Eliot Benjamin’s intriguing essay, License Plate Synchronicity, because he graphically demonstrates how apparently random outer events can coincide with our own subjective wants and needs and produce tremendously powerful intersections.

Eliot Benjamin in his conclusion suggests that such synchronicities “may serve as a reminder that there is indeed inherent spirituality in the universe that cannot be explained by our rational scientific technological minds or brains.”

While I understand that unusual occurrences can indeed be interpreted in super-mundane ways, it doesn’t mean that such events are the result of something trans-rational. Indeed, even the most apparently miraculous of synchronicities may have a mathematical basis.

The probability of any two events intersecting in meaningful ways is higher than we usually suspect. The linchpin in all of this is our ability to remain aware of how probabilities arise in our life, moment to moment, hour to hour, day to day.

John Edensor Littlewood, one of the great mathematicians of the last century and a senior wrangler at Cambridge University, worked intensively on the theory of large numbers. In his extensive research, oftentimes partnering with his more famous cohort G.H. Hardy, Littlewood unearthed some remarkable properties in large numbers that at first glance seem extraordinarily odd. One peculiar oddity is what is now known as Littlewood’s Law of Miracles.[1] Freeman Dyson writing in the New York Review of Books explains it this way:

“Littlewood's Law of Miracles states that in the course of any normal person's life, miracles happen at a rate of roughly one per month. The proof of the law is simple. During the time that we are awake and actively engaged in living our lives, roughly for eight hours each day, we see and hearthings happening at a rate of about one per second. So the total number of events that happen to us is about thirty thousand per day, or about a million per month. With few exceptions, these events are not miracles because they are insignificant. The chance of a miracle is about one per million events. Therefore we should expect about one miracle to happen, on the average, every month. Broch tells stories of some amazing coincidences that happened to him and his friends, all of them easily explained as consequences of Littlewood's Law.”[2]

Or, as framed in an internet posting, one commentator wrote,

“Succinctly put, the law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen. The point is that truly rare events, say events that occur only once in a million [as the mathematician Littlewoood (1953) required for an event to be surprising] are bound to be plentiful in a population of 250 million people. If a coincidence occurs to one person in a million each day, then we expect 250 occurences a day and close to 100000 such occurences a year. Going from year to a lifetime and from the population of the United States to that of the world (5 billion at this writing), we can be absolutely sure that we will see incredibly remarkable events. When such events occur, they are often noted and recorded. If they happen to us or someone we know, it is hard to escape that spooky feeling.”

There is another branch off of Littlewood’s theory of large numbers that underpins Eliot Benjamin’s experiences, which I call Desultory Decussation (where two apparently random events intersect to form an X).

If there are thousands, nay millions, of events in our lives (measured in transparently fractal ways), then it should be expected that for every 10,000 plus events, there may be two or more events which intersect. Notice that intersection and you will be aware of a meaningful coincidence--the meaning being that two disparate parts have something in common (whatever that intersection may entail).

We can even splinter off from this and make a broad sweeping generalization. There are those who look or seek out these desultory decussations and those who do not. I would imagine that some of us are more attuned or keenly aware of the intersections (which happen randomly) and they will end up seeing more meaning in their lives, even if the meaning quota is the same relatively speaking for all.

In other words, there are those who seek the Littlewood stream and plunge right in and those who do not. Blind typing may in fact produce a legible word just by chance, but the key in all this is to actually become aware of that probability and notice it when such does occur. Otherwise, so many amazing happenings of chance go by completely undetected.

If we could remain conscious of this mathematical matrix, we could be experiencing stunning hierophanies not only monthly, but perhaps daily. We already know that the theory of large numbers bears this possibility out. The only real glitch resides within our selves. To experience Littlewood miracles or desultory decussations (random events interwining in meaningful X patterns), it takes a Herculean effort on our part to remain open to what strange coincidences nature may throw out at us. Littlewood’s Law, interestingly enough, first requires us to be attentive, exceptionally so. I think Eliot Benjamin’s experiment with license plates illustrates this quite nicely.

I would suggest that a modified version of Littlewood’s Law, similar to what we define as desultory decussation, can explain anomalous synchronicities and therefore we do not need to invoke spiritual or paranormal theories for them.

The high improbability of an event oftentimes blinds us from the probability, even if rare, that such events are probabilistic.


[1] The law was framed by Cambridge University Professor J. E. Littlewood, and published in a collection of his work, A Mathematician's Miscellany; it seeks (among other things) to debunk one element of supposed supernatural phenomenology and is related to the more general Law of Truly Large Numbers, which states that with a sample size large enough, any outrageous thing is likely to happen. Littlewood defines a miracle as an exceptional event of special significance occurring at a frequency of one in a million. He assumes that during the hours in which a human is awake and alert, a human will experience one event per second, which may either be exceptional or unexceptional (for instance, seeing the computer screen, the keyboard, the mouse, the article, etc.). Additionally, Littlewood supposes that a human is alert for about eight hours per day. As a result, a human will, in 35 days, have experienced, under these suppositions, 1,008,000 events. Accepting this definition of a miracle, one can be expected to observe one miraculous occurrence within the passing of every 35 consecutive days � and therefore, according to this reasoning, seemingly miraculous events are actually commonplace. --Wikipedia entry on Littlewood’s Law

[2] Dyson, Freeman. "One in a Million." In The Scientist as Rebel. New York Review of Books: New York, 2006; paperback ed., pub. 2008: p. 327

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