Intrigued by the Low Probability of Synchronicities?

Coincidence theorists and statisticians dispute the meaning of rare events.

Posted Apr 15, 2018

M. W. Toews Creative Commons
 Normal distribution curve that illustrates standard deviations. Each band has 1 standard deviation, and the labels indicate the approximate proportion of area .
Source: M. W. Toews Creative Commons

The low probability of meaningful coincidences grabs our attention. What are the odds? Statisticians find them interesting for this reason, as do synchronicity theorists. Their perspectives appear to be in direct conflict. 

For statisticians the meaning is to be found in, well,  statistics. Their opinions are often couched in the language of the Law of Truly Large Numbers. This "law" proposes that any weird thing can happen given a large number of possibilities. This idea is not a law in the usual mathematical sense--it does not have a mathematical proof like other mathematical laws. The similarly named Law of Large Numbers does have a mathematical proof. This law states that the more trials one does (like flipping a coin) the closer the result comes to the theoretical average of 50/50 heads/tails. The basis for the support of the Law of Truly Large Numbers is plausibility, not mathematical proof. 

Statistician extraordinaire' David Hand, author of the Improbability Principle, proposes that coincidences and many other low probability events can be explained by the 5 strands of the Improbability Principle. One of these strands is the Law of Truly Large Numbers. To convey this idea in simple language, he quotes Persi Diaconis: “The really unusual day would be where nothing unusual happens.”

The other 4 strands include:

The Law of Selection:

Out of the myriad of information entering your mind, you can pick the events that match your preconceived desire to find coincidences.

The Law of the Probability Lever:

A slight change in circumstances can have a huge impact on probability. If two events appear to be independent but turn out not to be, that can strongly impact the probability.

The Law of Near Enough:

Approximately similar become equivalent. The person takes two events and claims they are near enough to be similar. To substantiate his support for a coincidence involving multiple elements, a person claimed that December 24 and January 4th were both Christmas Eve. Close, but not the same. 

The Law of Inevitability:

Something must happen. If you roll the dice, some number must come up. 

Professor Hand believes that meaning is "out there" and that this meaning is statistical. I think meaning is out there but far more nuanced, including statistics.

To hear him discuss the Improbability Principle and meaningful coincidences, please click here.