Improbabilities: Amazing ?

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Improbabilities: Amazing?

No sooner than I had started the car for my trip to North Bay the car radio announced a happy tidbit. Coming up next was a phone-in-show that would surely keep my interest for most of the drive. CBC had a program focusing on amazing improbabilities, or coincidences. Host Amanda Pheffer would be joined by a statistics prof and authour, David Hand of the Imperial College, London, to discuss crazy coincidences. Listeners would be calling in from across the province to tell their tales of unusual experiences and the prof would comment on them from a statistical vantage point. His theme: remarkable coincidences that ordinary folk experience are invariably compatible with mathematical laws however incompatible they may seem at first.

As someone with an abiding interest in numbers and probabilities, the timing of the show was itself a felicitous coincidence.

I was not disappointed. A score of callers recounted their own memorable stories. One fellow told of meeting his future wife. They had grown up in communities separated by a few thousand miles, apparently with no friends or acquaintances in common. Turns out though, the grandfather of the wife had been a neighbour of the caller, and a good acquaintance during his youth. This auspicious connection was to bode well for the couple’s relationship.

These stories got me thinking about my own improbable encounters. I fancied that if I were inclined to call in with a story I would tell one that happened when I was on a high school trip to Europe. It was the summer of 1969; the year certain in my memory because Neil Armstrong had set foot on the moon while we were overseas.

The trip drew to a close as our large student group waited in the airport in Florence Italy. Then and there, to my utter amazement I think I see my neighbour from home, 2 doors over. And dang, it was indeed my neighbour from Sudbury, travelling on her own in Italy. Of course I approached her immediately, and we hugged, and both of us could hardly stop yakking about this amazing connection.

Over the years I have reflected on this encounter many times. Surely it had been mere coincidence. In trying to make sense of it I had wondered about quantifying the probabilities of the two of us meeting in an airport an ocean away from our family homes. Needless to say, quantifying the odds of such a meeting was well beyond my capabilities, and I imagined well beyond any human capabilities. But the probability had to be a ridiculously low figure – amazingly improbable.

At one point in my reflections of this event, I conjured up an explanation that while silly, had superficial appeal. The probability of our meeting in a foreign airport might be related to the number of people in the world (3.5 billion then), and the subset of those people who would have been in an international airport. And with so many people to factor into the calculations, whatever the probability of our encounter it would be a very long shot indeed. But, I surmised, what if the estimate of the number of people on the planet had been grossly overstated. What if instead of 3.5 billion people in the world, there were only 3.5 million. And while I had no evidence that the demographers were off by a factor of a thousand, it would serve to make the chances of our airport encounter much more probable. And that provided a certain satisfaction all by itself. Alas, I digress….

As the radio show came to an end, (coincidentally?) I pulled into the parking lot of my destination, the North Bay Hospital. My work would take up the remainder of the day, and I would head back home about the supper hour.

But rather than head home directly, I decided to stop at the hospital cafeteria, nearly deserted late on this Friday afternoon in the summer. I say nearly deserted, but there was one other customer, grabbing a snack at the counter.

Perhaps you know where this is headed. On a day when bizarre coincidences was the topic du jour, there was one more coincidence in store for me. That lone customer at the counter was an old childhood friend of mine. Someone who I had not seen often since we both left our family homes to make our own way many years earlier. She was working at the hospital part time as a chaplain, and when she spotted me, called out. Surprised, but pleased, I went over to her with greetings, and we spend a few pleasant minutes chatting about old times and catching up on the new.

I’m sure there are some readers who might say this cafeteria encounter was not such an amazing coincidence. Happens all the time some would offer. I would have thought the same things myself but for one additional element of the story.

The chaplain at the cafeteria counter, my old childhood friend, was one and the same person as the student in the Florence airport I coincidentally met up with in 1969. The same person I had been thinking about in the car on the trip to North Bay all the while listening to a radio show on amazing coincidences. Put that into your probability calculation device, and stand back to be amazed.

All this stuff hurts my head. I want to turn to something simpler and easier to relate to. And so I close with my favourite, and most silly aphorism about coincidences from the late American journalist H.L. Mencken.

24 hours in a day. 24 bottles of beer in a case.

Coincidence?

I think not.

Michael Hennessy
2015.Aug 15