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A Response to
"Desultory Decussation"

M.A. Rose

In "Desultory Decussation: Where Littlewood's Law of Miracles meets Jung's Synchronicity", David Lane and Andrea Diem Lane responded to Elliot Benjamin's essay on synchronicity ["License Plate Synchronicity"] with an amused and dismissive air, opining that "even the most apparently miraculous of synchronicities may have a mathematical basis." To support their position, they invoke Littlewood's Law of Miracles. Quoting Freeman Dyson's description of Littlewood's law, they illustrate that a seemingly miraculous event can be mathematically expected in the life of an individual in approximately one out of a million chances, that being translated into a time frame of about once a month (a citation at the end of the Lane essay gives an estimate of 1,008,000 total events experienced in 35 days). The authors argue the case that Benjamin's recounted experiences of synchronicity on license plates bears this out, but an examination of Benjamin's report hardly supports their conclusion.

Benjamin highlights four instances of meaningful coincidences involving license plate numbers. The first is recorded on 9-1-10 and is dated a few days earlier. The second is dated the day before the 9-1 recording (8-31-10), the third is recorded on 9-21-10 and dated the previous week and the fourth is recorded on and dated to 10-8-10. The total span of these experiences is probably under 50 days. Thus in less time than Littlewood's calculation allows for two synchronicities, about 60-70 days, Benjamin experienced four.

The Lanes refer to a "branch off" of Littlewood's theory in which the one-million figure is conveniently and ambiguously lowered to "10,000 plus". It is ambiguous in that "10,000 plus" could mean 10,000 plus anything; even Littlewood's one-million figure is 10,000 plus 990,000. I am not sufficiently familiar with Littlewood's work to know if he himself originated this "branch off", but if he did it seems strange that he would, since it's such a radical stretching of the core statement of his law which the Lanes initially cited.

The authors include the offering of an internet commentator who invokes the popular "law of truly large numbers" to argue that even with one person in a million experiencing a coincidence each day, a population of 250 million can mathematically expect to experience nearly 100,000 miraculous events every year, which is supposed to relegate such experiences to the commonplace. It sounds intellectually impressive until we remember that it's irrelevant. The number of people each of whom experiences a miracle in a day has no bearing on the number of miracles each person is supposed to experience in a month. Conveniently overlooked here is Littlewood's conclusion that each individual in the human population is still supposed to experience a miracle only about once a month, a rate which Benjamin's experience trounces. Indeed, with the claim that such a "mathematical matrix" can have observers "experiencing stunning hierophanies not only monthly, but perhaps daily", the Lanes seem to want to have their cake and eat it too. How can they extol the mathematics of Littlewood, who figured that it takes about a month for an individual to experience the million waking moments which he required for one surprising event to come about and, at the same time, claim that the individual can experience those one-chance-in-a-million miracles every day when Littlewood's numbers don't allow for there to be a million experiential moments in a day?

The authors assert, "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." Actually, there's more to it than this. If blind typing produces words, it's reasonable to assume that there will be a mathematically predictable rate at which those words can be expected to appear. If they appear at a higher rate than is mathematically predictable, it's not unreasonable to suspect that something other than mathematics is responsible, especially if the words are connected by a common theme. The "key in all this" is not just being aware of probability, but also noticing when coincidence goes beyond it. The authors' suggested "Herculean effort" does not detract from the significance of this; if odds-defying coincidences are noticeable, it's because they are there.

If Littlewood's Law of Miracles is to be taken at face value, any shortcomings in its predictions must be accepted. Those with experiences like Benjamin's have seen that, although Littlewood's mathematics may be sound and solid, the law based on it does not govern the universe. A "modified version of Littlewood's law" is proposed, but this seems to be essentially a crutch for a principle which, against observations like Benjamin's, fails to stand on its own.

The best description of synchronicities, especially those which beat the mathematical odds, which I have ever seen is the brief address on flowers delivered by one of the greatest logicians in Western literature, Arthur Conan Doyle's great detective Sherlock Holmes in "The Naval Treaty":

"Our highest assurance of the goodness of Providence seems to me to rest in the flowers. All other things, our powers, our desires, our food, are all really necessary for our existence in the first instance. But this rose is an extra. Its smell and its colour are an embellishment of life, not a condition of it. It is only goodness which gives extras, and so I say again that we have much to hope from the flowers."

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